Unperturbed inverse kinematics nucleon knockout measurements with a 48 GeV/c carbon beam
M. Patsyuk, J. Kahlbow, G. Laskaris, M. Duer, V. Lenivenko, E.P. Segarra, T. Atovullaev, G. Johansson, T. Aumann, A. Corsi, O. Hen, M. Kapishin, V. Panin, E. Piasetzky, Kh. Abraamyan, S. Afanasiev, G. Agakishiev, P. Alekseev, E. Atkin, T. Aushev, V. Babkin, V. Balandin, D. Baranov, N. Barbashina, P. Batyuk, S. Bazylev, A. Beck, C.A. Bertulani, D. Blaschke, D. Blau, D. Bogoslovsky, A. Bolozdynya, K. Boretzky, V. Burtsev, M. Buryakov, S. Buzin, A. Chebotov, J. Chen, A. Ciszewski, R. Cruz-Torres, B. Dabrowska, D. Dabrowski A. Dmitriev, A. Dryablov, P. Dulov, D. Egorov, A. Fediunin, I. Filippov, K. Filippov, D. Finogeev, I. Gabdrakhmanov, A. Galavanov, I. Gasparic, O. Gavrischuk, K. Gertsenberger, A. Gillibert, V. Golovatyuk, M. Golubeva, F. Guber, Yu. Ivanova, A. Ivashkin, A. Izvestnyy, S. Kakurin, V. Karjavin, N. Karpushkin, R. Kattabekov, V. Kekelidze, S. Khabarov, Yu. Kiryushin, A. Kisiel, V. Kolesnikov, A. Kolozhvari, Yu. Kopylov, I. Korover, L. Kovachev, A. Kovalenko, Yu. Kovalev, A. Kugler, S. Kuklin, E. Kulish, A. Kuznetsov, E. Ladygin, N. Lashmanov, E. Litvinenko, S. Lobastov, B. Loher, Y.-G. Ma, A. Makankin, A. Maksymchyuk, A. Malakhov, I. Mardor, S. Merts, A. Morozov, S. Morozov, G. Musulmanbekov, R. Nagdasev, D. Nikitin, V. Palchik, D. Peresunko, M. Peryt, O. Petukhov, et al. (69 additional authors not shown)
UUnperturbed inverse kinematics nucleon knockout measurements with a 48 GeV/ccarbon beam
M. Patsyuk,
1, 2
J. Kahlbow,
1, 3
G. Laskaris,
1, 3
M. Duer, V. Lenivenko, E.P. Segarra, T. Atovullaev,
2, 5
G.Johansson, T. Aumann,
4, 6, 7
A. Corsi, O. Hen, ∗ M. Kapishin, V. Panin,
8, 6 and E. Piasetzky et al.(The BM@N Collaboration) Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA Joint Institute for Nuclear Research, Dubna 141980, Russia School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel Institut f¨ur Kernphysik, Technische Universit¨at Darmstadt, 64289 Darmstadt, Germany Dubna State University, Dubna 141980, Russia GSI Helmholtzzentrum f¨ur Schwerionenforschung GmbH, Planckstr. 1, 64291 Darmstadt, Germany Helmholtz Forschungsakademie Hessen f¨ur FAIR, Max-von-Laue-Str. 12, 60438 Frankfurt, Germany IRFU, CEA, Universit´e Paris-Saclay, F-91191 Gif-sur-Yvette, France
From superconductors to atomic nuclei,strongly-interacting many-body systems areubiquitous in nature. Measuring the microscopicstructure of such systems is a formidable chal-lenge, often met by particle knockout scatteringexperiments [1, 2]. While such measurementsare fundamental for mapping the structure ofatomic nuclei [2–6], their interpretation is oftenchallenged by quantum mechanical initial- andfinal-state interactions (ISI/FSI) of the incomingand scattered particles [1, 2, 7–9]. Here weovercome this fundamental limitation by mea-suring the quasi-free scattering of 48 GeV/c Cions from hydrogen. The distribution of singleprotons is studied by detecting two protons atlarge angles in coincidence with an intact Bnucleus. The B detection is shown to selectthe transparent part of the reaction and excludethe otherwise large ISI/FSI that would breakthe B apart. By further detecting residual Band Be nuclei, we also identified short-rangecorrelated (SRC) nucleon-nucleon pairs [9–13],and provide direct experimental evidence for theseparation of the pair wave-function from that ofthe residual many-body nuclear system [9, 14].All measured reactions are well described bytheoretical calculations that do not containISI/FSI distortions. Our results thus showcase anew ability to study the short-distance structureof short-lived radioactive atomic nuclei at theforthcoming FAIR [15] and FRIB [16] facilities.These studies will be pivotal for developing aground-breaking microscopic understanding ofthe structure and properties of nuclei far fromstability and the formation of visible matter inthe universe.
Strongly-interacting systems are difficult to study. Inthe special case of strongly-interacting quantum gasses,ground-state properties can be directly measured usingultra-cold atomic traps, where one can instantaneously turn off the interactions between the atoms and the trapitself [17]. This allows exploring a wide range of funda-mental quantum mechanical phenomena and to imitatestrongly correlated states in condensed matter systemswhere similar control over inter-particle interactions can-not be obtained [18].Due to their high-density and complex strong interac-tion, constructing such model systems for atomic nucleiis extremely challenging. Instead, the distribution of nu-cleons in nuclei is traditionally studied using high-energyelectron scattering experiments that detect the scatteredelectron and knockout nucleon with high-resolution spec-trometers [2]. ISI/FSI cause a reduction of the quasielas-tic cross-section (attenuation) as well as distortion ofthe reconstructed single nucleon ground state properties.Pre-selection of the reaction kinematics or post-selectionof the un-detected residual nucleus allows suppressingISI/FSI distortions and use energy and momentum con-servation to reconstruct the distribution of nucleons inthe nucleus [2, 9, 13, 19, 20].While largely limited to stable nuclei, such experimentshelped establish the nuclear shell model [2] and the exis-tence and dynamics of SRC nucleon pairs [6, 10, 12, 19]that constitute the next significant approximation to nu-clear structure after the shell model [2, 9, 13].Extending these studies to radioactive nuclei far fromnuclear stability is a growing frontier of nuclear sci-ence [7]. Such studies require performing scattering ex-periments in inverse kinematics, where low luminosityhigh-energy beams of radioactive nuclei are scatteredfrom protons in hydrogen targets [21]. The cross-sectionfor such reactions is significantly higher than that forelectron scattering, but comes at the price of large ISIthat prevents kinematical pre-selection. Additionally,since there is rarely sufficient energy resolution to de-termine the residual nuclear state from the measuredmomenta of the knocked-out nucleons, post-selection re-quires direct detection of the residual nuclear system [22].Here we use post-selection in high-energy inverse kine-matics ( p, p ) scattering to probe single-particle states a r X i v : . [ nu c l - e x ] F e b RPC DCHSiGEMTCTargetMWPC BC48 GeV/ c C IonsC Ions Proton Proton B (a) B B Be Be Li Li Li He He Be Z eff P / Z [ G e V / c ] (b) Nuclear Fragments BM@N
Fig. 1. | Experimental setup and fragment identification. (a) Carbon nuclei traveling at 48 GeV/c hit protons in a liquidhydrogen target, knocking out individual protons from the beam-ion. Position- and time-sensitive detectors (MWPC, GEM,RPC, Si, and DCH) are used to track the incoming ion beam, knockout protons, and residual nuclear fragments and determinetheir momenta. (b) The bend of the nuclear fragments in the large dipole magnet, combined with charge measurements withthe beam counters (BC) allows identifying the various fragments. In this work we refer to events with detected B, B, and Be heavy fragments, see text for details. and SRCs in the well understood C nucleus. By de-tecting a bound nuclear fragment we select the trans-parent part of the scattering reaction where single stepscattering dominates and distortions due to ISI/FSI ofthe incoming/outgoing nucleons are suppressed.By identifying B fragment we successfully study thedistribution of protons in the p -shell of C, where weobtain consistent distributions for both quasielastic (QE)and inelastic (IE) scattering reactions. Selecting B and Be fragments we further identify, for the first time ininverse kinematics, the hard breakup of SRC pairs. Wedirectly measure the pair motion in the nucleus and es-tablish the separation of the strong inter-pair interactionfrom the residual nuclear system. The latter is a key fea-ture of modern theoretical SRC models [9, 11, 13, 14, 23],that has not been experimentally confirmed.While significantly reducing the measured event rate,these post-selection requirements are shown to ensurethat the measured reaction has little to no sensitivity toISI/FSI induced distortions, thereby opening the door tostudying the single-particle and short-distance structureof nuclei far from stability.
Experimental setup
The experiment took place at the Joint Institute forNuclear Research (JINR), using a 4 GeV/c/nucleon ionbeam from the Nuclotron accelerator, a stationary liquid-hydrogen target, and a modified BM@N (Baryonic Mat-ter at Nuclotron) experimental setup, as shown in Fig. 1a.The beam was monitored upstream the target us-ing thin scintillator-based beam counters (BCs) used for charge identification, a veto counter (V-BC) for beam-halo rejection, and two multi-wire proportional cham-bers (MWPCs) for event-by-event beam tracking. TheBC closer to the target was also used to define the eventstart time t .A two-arm spectrometer (TAS) was placed down-stream of the target to detect the two protons from the( p, p ) reaction that emerge between 24 ◦ and 37 ◦ , corre-sponding to 90 ◦ QE scattering in the two-protons center-of-mass (c.m) frame. Each spectrometer arm consistedof two scintillator trigger counters (TC), a gas electronmultiplier (GEM) station and a multi-gap resistive platechamber (RPC) wall.Proton tracks were reconstructed using their hit loca-tion in the GEM and RPC walls. We only consider eventswhere the distance of closest approach between the pro-ton tracks is smaller than 4 cm and the interaction vertexof each proton is reconstructed within the central 26 cmof the target (Extended Data Fig. 1). The time differencebetween the RPC and t signals define the proton timeof flight (TOF), that is used to determine its momentumfrom the measured track length, assuming a proton mass.As the protons of interest for our analysis have mo-menta between 1 . . . < β < . β > .
96 or < . C( p, p ) reactiontrigger for the experiment. Additional triggers were setup for monitoring and calibration purposes, see OnlineSupplementary Materials for details. [ d e g ] p θ + p θ QE IE B ) p ,2 p C( (b) C oun t s ( x10 ³ ) BM@N [GeV] miss E QE IEISI / FSI ) p ,2 p C( (a) QE IEISI / FSI (d)(c)BM@N − − miss E × Fig. 2. | Quasi-Free Scattering (QFS) distributions. (a) and (b): The correlation between the measured missing-energy ( E miss , calculated in the C rest-frame) and the mea-sured lab-frame two-proton in-plane opening angle ( θ + θ ).Distributions are shown for inclusive C( p, p ) events (a)and exclusive C( p, p ) B events (b). (c) and (d): One-dimensional projections of the missing-energy distributionsfor inclusive (c) and exclusive (d) events (see Extended DataFig. 2a for opening angle projections). Data error bars showstatistical uncertainties of the data at the 1 σ confidence level.The lines show the results of a fit to the measured quasielas-tic (QE) and inelastic (IE) peaks, using the same functionalform for both distributions. The inclusive distribution re-quires an additional fit component, associated with ISI/FSIdistortions, to fully describe the data. QE events are seenas a peak around low missing energy and opening angles of ∼ ◦ . IE reactions populate higher missing-energy and loweropening angles while ISI/FSI populate both regions and theridge between them in the inclusive spectra. Nuclear fragments following the ( p, p ) reaction areemitted at small angles with respect to the incident beamwith momentum, that is similar to the per nucleon beammomentum. Three silicon (Si) planes and two MWPCswere placed in the beam-line downstream the target tomeasure the fragment scattering angle. Following theMWPCs the fragments enter a large acceptance 2 .
87 T · mdipole magnet. Two drift chambers (DCH) are used tomeasure the fragment trajectory after the magnet.The fragment momenta are determined from theirmeasured trajectories through the the dipole magnet.Fragments are identified from the combination of theirrigidity ( P/Z ) in the magnet and energy deposition inthe two scintillator BCs placed between the target andthe magnet entrance, see Fig. 1b. The latter is pro-portional to the sum of all fragment charges squared( Z eff = (cid:112)(cid:80) Z ).See Methods and Online Supplementary Materials foradditional details on the experimental setup and dataanalysis procedures. Single proton knockout
We identify exclusive C( p, p ) B events by requiringthe detection of a B fragment in coincidence with twocharged particle tracks in the TAS. Energy and momen-tum conservation for this reaction reads:¯ p C + ¯ p tg = ¯ p + ¯ p + ¯ p B , (1)where ¯ p C = ( (cid:113) ( p C + m C ) , , , p C ) and ¯ p tg =( m p , , ,
0) are respectively the incident beam-ion andtarget proton four-momentum vectors. ¯ p , ¯ p , and ¯ p B are the four-momentum vectors of the detected protonsand B fragment. Assuming QE scattering off a nu-cleon which is moving in a mean-field potential, we canapproximate ¯ p C = ¯ p i + ¯ p B , where ¯ p i is the initial pro-ton four-momentum inside the C ion. Substituting intoEq. 1 we obtain:¯ p i ≈ ¯ p miss ≡ ¯ p + ¯ p − ¯ p tg , (2)where ¯ p miss is the measured missing four-momentum ofthe reaction and is only equal to ¯ p i in the case of unper-turbed (no ISI/FSI) QE scattering. Through the text,the missing momentum vector is shown and discussed af-ter being boosted from the lab-frame to the incident Cion rest-frame.Figure 2 shows the measured missing energy E miss ≡ m p − e miss (where e miss is the energy component of ¯ p miss in the C rest-frame) distribution and its correlationwith the lab-frame two-proton in-plane opening angle, θ + θ , for inclusive C( p, p ) (left panels) and exclu-sive C( p, p ) B (right panels) events. Both distribu-tions show two distinct regions: (A) low missing-energyand large in-plane opening angles that correspond to QEscattering and (B) high missing energy and small in-planeopening angles that correspond to IE scattering.As seen in the E miss projections, the inclusive C( p, p ) events are contaminated by ISI/FSI back-grounds around and underlying both IE and QE regions.This background is not evident in the C( p, p ) B case,which is our first indication that requiring the coincidencedetection of B fragments selects a unique subset of one-step processes where a single nucleon was knocked-outwithout any further interaction with the residual frag-ment. We note that while bound excited states cannot beseparated from the ground state in C( p, p ) B events,their contribution is small [24] and should not impactthe measured momentum distribution. See Methods fordetails.Figure 3a shows further evidence for ISI/FSI suppres-sion by comparing the measured missing-momentum dis-tribution for C( p, p ) QE events with and without Btagging. The QE selection was done using the missing-energy and in-plane opening-angle cuts depicted in Fig. 2following a 2 σ selection (see Methods for details). The − − γ cos(050100 C oun t s (c) BM@N B p C oun t s B ) p ,2 p C( QuasielasticInelastic (b) BM@N miss p C oun t s Quasielastic) p ,2 p C( B ) p ,2 p C( Simulation (a) BM@N
Fig. 3. | Momentum distributions and angular correlation. (a) Missing-momentum distribution in C rest-frame forquasielastic C( p, p ) and C( p, p ) B events. (b) B fragment momentum distribution in C rest-frame for quasielasticand inelastic C( p, p ) B events. The light blue points in (a) and the open symbols in (b) have a small artificial offset forbetter visibility. (c) Distribution of the cosine of the opening-angle between the missing- and fragment-momentum in theplane transverse to the beam. Solid red line shows the result of our quasielastic reaction simulation. Data error bars showstatistical uncertainties at the 1 σ confidence level. The y-axis shows the counts for the quasielastic distribution. The inelasticdistributions are normalized to the peak region of the quasielastic distribution. All variables are shown in the C rest-frame. measured C( p, p ) QE events show a significant high-momentum tail that extends well beyond the nuclearFermi-momentum ( ≈
250 MeV/c) and is characteristicfor ISI/FSI [9]. This tail is completely suppressed by the B detection.Figure 3b compares the measured B momentum dis-tribution in the C rest-frame for both QE and IE C( p, p ) B events. The fragment momentum distri-bution is equal for both reactions. This shows that theobservation of a bound fragment selects quasi-free unper-turbed single-step reactions, even in the case of hard in-elastic
N N scattering and in a kinematical region whichis otherwise dominated by FSI events.In true unperturbed single-step C( p, p ) B QE scat-tering the measured missing- and fragment-momentashould balance each other. Fig. 3c shows the distributionof the cosine of the opening angle between the missing-and fragment-momenta in the plane transverse to the in-cident beam-ion (which is insensitive to boost effects andis measured with better resolution). While broadeneddue to detector resolutions, a clear back-to-back corre-lation is observed which is a distinct signature of QEreactions.The data shown in Fig. 3 are compared to theoreti-cal calculations of QE ( p, p ) scattering off a p -shell nu-cleon in C. The calculation is implemented via a sim-ulation that accounts for the experimental acceptanceand detector resolutions, uses measured H( p, p ) elas-tic scattering cross section, and does not include ISI/FSIeffects. The total simulated event yield was scaled tomatch the data. See Methods for details. The calcula-tion agrees well with all measured C( p, p ) B distri-butions, including the fragment momentum distributionfor IE events and the distribution of the angle betweenthe missing- and fragment-momenta (including its tail induced by detector-resolution).Additional data-theory comparisons are shown in Ex-tended Data Fig. 2 and 3 exhibiting good agreement.This is a clear indication that the B detection stronglysuppresses ISI/FSI, providing access to ground-stateproperties of C.Comparing the tagged and inclusive reaction yields wefind that in ∼
50% of the measured inclusive C( p, p )QE reactions the residual nucleus is fragmented to lighterfragments ( Z < C( p, p ) B QE event yield accounts for (43 . ± . +4 . − . (sys))% of the measured inclusive C( p, p )QE yield, and C( p, p ) B and C( p, p ) Be QEevents, due to QE scattering to an excited B state thatde-excites via nucleon emission, account for an additional(7 . ± . +1 . − . (sys))% and ≤ Hard breakup of SRC pairs
Next we study SRCs by measuring the C( p, p ) B and C( p, p ) Be reactions. SRC breakup reactions pro-duce B and Be fragments when interacting with aproton-neutron ( pn ) or proton-proton ( pp ) pair, respec-tively. The fragment selection guarantees exclusion ofsecondary scattering processes, as shown above, and re-stricts the excitation-energy of the residual A-2 systemto below its nucleon separation energy. Furthermore, thefragment detection offers a direct experimental probe forthe interaction between the SRC pair nucleons and theresidual A − B and Be fragments can be produced inSRC breakup reaction, they can also be produced fol-lowing ( p, p ) interactions involving mean-field nucle-ons. As discussed above, ∼
10% of the measured in-clusive mean-field C( p, p ) QE events produce excited [GeV/c] miss p − [ G e V ] m i ss E C oun t s B / ) p,2p C( Be (a) (b) (c) BM@N
Fig. 4. | SRC Selection in missing momentum andenergy. (a) Correlation between the missing-energy andmissing-momentum for the measured C( p, p ) B (upwardsfacing purple triangles) and C( p, p ) Be (Downwards fac-ing brown triangles) selected SRC events, on top of the GCFsimulation (color scale). (b) and (c): One-dimensional pro-jections for the measured (black points) and GCF simulated(orange line) missing-energy (b) and missing-momentum (c).The width of the bands and the data error bars show thesystematic uncertainties of the model and the statistical un-certainties of the data, respectively, each at the 1 σ confidencelevel. B fragment that decay to B and Be via nucleonemission. These processes can be suppressed by requir-ing | p miss | >
350 MeV/c, which selects protons with ini-tial momenta that is well above the nuclear Fermi levelwhere SRCs predominate over mean-field nucleons [13].See Methods for details.High p miss 12 C( p, p ) B and C( p, p ) Be events canalso result from IE interactions that produce additionalparticles. Such reactions can involve mean-field nucleonsand will not be suppressed by the high p miss requirement.However, as shown in Fig. 2, they can be suppressed byrestricting the missing-energy of the reaction and requir-ing a large in-plane opening angle between the measured( p, p ) protons.To guide this selection we used the Generalized Con-tact Formalism (GCF) [14] to simulate ( p, p ) scatteringevents off SRC pairs (see Methods for details). Followingthese calculations we select SRC breakup reactions by re-quiring an in-plane opening angle larger than ∼ ◦ and − ≤ E miss ≤
240 MeV (see Extended Data Fig. 4).We further use total-energy and momentum conservationto ensure exclusivity and suppress IE contributions byrequiring a missing nucleon mass in the entire reaction: M , excl . = (¯ p C + ¯ p tg − ¯ p − ¯ p − ¯ p B(Be) ) ≈ m N (seeExtended Data Fig. 5).Applying these selection cuts, we measured 23 − ) rel p , B p θ cos( (b) − − ) n p , miss p θ cos( C oun t s (a) B SRC ) p,2p C( BM@N
Fig. 5. | Angular correlations in SRC breakup events.
Distributions of the cosine of the angle between (a) the recoilnucleon and missing momentum and (b) B fragment andpair relative-momentum. Data (black points) are comparedwith GCF predictions (orange lines). The width of the bandsand the data error bars show the systematic uncertainties ofthe model and the statistical uncertainties of the data, respec-tively, each at the 1 σ confidence level. C( p, p ) B and 2 C( p, p ) Be events. The large Bto Be event yield ratio is generally consistent with thepreviously observed predominance of pn - over pp -SRCpairs [10, 12, 13, 25, 26], and is in full agreement with theGCF calculated B / Be yield ratio of 12 . B dominance also contradicts an expec-tation of similar B and Be yields if the measuredreactions were dominated by mean field QE scatteringfollowed by FSI with a single nucleon in B.Figure 4 shows the missing-energy and missing-momentum distributions of the selected SRC C( p, p ) B events. The measured distributionsshow good agreement with the GCF predictions. Addi-tional kinematical distributions are shown and comparedwith the GCF in Extended Data Fig. 6 and 7. We specif-ically note that the distributions of the z -componentof the missing-momentum is not centered around zeroand is shifted towards the incident beam-direction(Extended Data Fig. 6c). This is expected given thestrong s -dependence of the large-angle elementaryproton-proton elastic scattering cross-section. Seediscussion in Methods.Next we examine the angular correlations between thenucleons in the pair and between the pair and the Bfragment. Figure 5a shows the distribution of the cosineof the angle between the missing momentum (Eq. 2) andthe reconstructed undetected recoil neutron momentum.A clear back-to-back correlation is observed, as expectedfor strongly-correlated nucleon pairs. The width of thedistribution is driven by the pair c.m. motion and de-tection resolutions. It shows good agreement with theGCF prediction that assumes a three-dimensional Gaus-sian c.m. momentum distribution [14, 27].An independent determination of the SRC pair c.m.momentum distribution can be obtained from the Bmomentum distribution that is measured here for thefirst time (Extended Data Fig. 6e-h). We extract fromthe data an SRC pair c.m. momentum distribution withGaussian width of σ c . m . = (156 ±
27) MeV/c (see Meth-ods for extraction details), in agreement with previouselectron scattering measurements [27].Last we examine the factorization of the measured SRCpairs from the the residual nuclear system. The strongtwo-body interaction between the nucleons in the pairwas predicted [9, 14, 23] to allow modeling its distribu-tion as independent functions of the pair relative and c.m.motion, with no correlation between them. Such fac-torization dramatically simplifies SRC calculations andshould be evident experimentally by a lack of correlationbetween the pair c.m. and relative momenta.Figure 5b shows the distribution of the cosine of theangle between the B fragment momentum (i. e. pairc.m. momentum) and the pair relative momentum givenby p rel = ( p miss − p n ) /
2, where p n is the reconstructedrecoil neutron momenta. The GCF assumes the abovementioned factorization and therefore predicts a flat dis-tribution, that is slightly shaped by the acceptance ofour detectors. The data is in full agreement with thisassumption.Therefore, by reporting here on the first measurementof SRC pairs with the detection of the residual bound A − Conclusions
The dominant contributions of ISI/FSI to nucleon-knockout scattering measurements has been a majordifficulty for experimentally extracting nucleon distri-butions in nuclei [9, 13, 28–30]. Even in high-energyelectron scattering at selected kinematics that minimizetheir contributions, the remaining FSI effect had to betaken into account using theoretical estimates that in-troduce significant model dependence to the obtained re-sults [9, 13, 30, 31].At lower beam energies, the method of quasi-freeproton-induced nucleon knockout in inverse kinematicshas been recently developed and applied to study thesingle-particle structure of exotic nuclei [4, 5, 22, 24]. Thedata analysis and interpretation of these results heavilyrelies on the assumption that the extracted particle dis-tributions are free from FSI contamination that has notbeen experimentally proven to date.Our findings however clearly demonstrate the fea-sibility of accessing properties of single-nucleons andSRC nucleon pairs in short-lived nuclei, in particu-lar neutron-rich nuclei, using high-energy radioactivebeams, produced at upcoming accelerator facilities such as FRIB and FAIR. With this method, we accomplisheda big step towards realizing the goal of such facilities,which is exploring the formation of visible matter in theuniverse in the laboratory. The presented experimentalmethod thus provides a basis to approximate, as closelyas possible, the dense cold neutron-rich matter inneutron stars in the laboratory. ∗ Contact Author ([email protected])[1] Jacob, G. & Maris, Th.A.J. Quasi-Free Scattering andNuclear Structure.
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We acknowledge the efforts of thestaff of the Accelerator and High-Energy Physics Divi-sions at JINR that made this experiment possible andI. Tserruya for fruitful discussions of the analysis andresults. The research was supported by the Israel Sci-ence Foundation, the Pazi Foundation, by the BMBF viaProject No. 05P15RDFN1, through the GSI-TU Darm-stadt co-operation agreement, by the U.S. DOE undergrant No. DE- FG02-08ER41533 and by the DeutscheForschungsgemeinschaft (DFG, German Research Foun-dation), Project-ID 279384907, SFB 1245, and the RFBRunder grant numbers 18-02-40046 and 18-02-40084 \ Author Contributions
The experimental set up atthe Nuclotron was designed and constructed by theBM@N Collaboration at JINR. Data reconstruction andcalibration, Monte Carlo simulations of the detectorand data analyses were performed by a large numberof BM@N Collaboration members, who also discussed and approved the scientific results. In particular, thedesign and construction of the TAS was lead by G.L.,who also led the data taking period. The developmentand operation of the Data acquisition and triggersystems were lead by S.B. and V.Y., respectively. Thedevelopment and operation of the GEM and Silicondetectors were lead bt A.M. and N.Z., respectively. Rawdata processing and online monitoring were performedby S.M. and I.G. M.R. contributed to the RPC analysis,V.P. contributed to the Si/MWPC analysis, D.B.contributed to the GEM analysis, and N.V. contributedto the DCH analysis. The main data analysis was doneby J.K., M.P., V.L., E.P.S., T.A., G.J., V.P., and M.D.,with input from O.H., E.P., T.A., M.K. and A.C., andreviewed by the BM@N collaboration.
Competing interests
The authors declare no compet-ing interests.
Data Availability
Source data are available for thispaper. All other data that support the plots within thispaper and other findings of this study are available fromthe corresponding author upon reasonable request.
Author Information
Full Author List
M. Patsyuk, , J. Kahlbow, , G. Laskaris, , M. Duer, V. Lenivenko, E.P. Segarra, T. Atovullaev, , G.Johansson, T. Aumann, , , A. Corsi, O. Hen, M.Kapishin, V. Panin, , E. Piasetzky, Kh. Abraamyan, S. Afanasiev, G. Agakishiev, P. Alekseev, E. Atkin, T. Aushev, V. Babkin, V. Balandin, D. Baranov, N.Barbashina, P. Batyuk, S. Bazylev, A. Beck, C.A.Bertulani, D. Blaschke, D. Blau, D. Bogoslovsky, A. Bolozdynya, K. Boretzky, V. Burtsev, M.Buryakov, S. Buzin, A. Chebotov, J. Chen, A. Ciszewski, R. Cruz-Torres, B. Dabrowska, D.Dabrowski, , A. Dmitriev, A. Dryablov, P. Dulov, D. Egorov, A. Fediunin, I. Filippov, K. Filippov, D. Finogeev, , I. Gabdrakhmanov, A. Galavanov, , I. Gasparic, O. Gavrischuk, K. Gertsenberger, A. Gillibert, V. Golovatyuk, M. Golubeva, F.Guber, , Yu. Ivanova, A. Ivashkin, , A.Izvestnyy, S. Kakurin, V. Karjavin, N. Karpushkin, R. Kattabekov, V. Kekelidze, S. Khabarov, Yu.Kiryushin , A. Kisiel, V. Kolesnikov, A. Kolozhvari, Yu. Kopylov , I. Korover, L. Kovachev, , A.Kovalenko, Yu. Kovalev, A. Kugler, S. Kuklin, E.Kulish, A. Kuznetsov, E. Ladygin, N. Lashmanov, E. Litvinenko, S. Lobastov, B. L¨oher, Y.-G. Ma, A. Makankin, A. Maksymchyuk, A. Malakhov, I.Mardor, S. Merts, A. Morozov, S. Morozov, , G. Musulmanbekov, R. Nagdasev, D. Nikitin, V.Palchik, D. Peresunko, M. Peryt, O. Petukhov, Yu.Petukhov, S. Piyadin, V. Plotnikov, G. Pokatashkin, Yu. Potrebenikov, O. Rogachevsky, V. Rogov, K. Ros(cid:32)lon, , D. Rossi, I. Rufanov, P. Rukoyatkin, M.Rumyantsev, D. Sakulin, V. Samsonov, H. Scheit, A. Schmidt, S. Sedykh, I. Selyuzhenkov, P. Senger, S. Sergeev, A. Shchipunov, A. Sheremeteva, M.Shitenkov, V. Shumikhin, A. Shutov, V. Shutov, H.Simon, I. Slepnev, V. Slepnev, I. Slepov, A. Sorin, V.Sosnovtsev, V. Spaskov, T. Starecki, A. Stavinskiy, E. Streletskaya, O. Streltsova, M. Strikhanov, N.Sukhov, D. Suvarieva, J. Tanaka, A. Taranenko, N. Tarasov, O. Tarasov, V. Tarasov, A. Terletsky, O. Teryaev, V. Tcholakov, V. Tikhomirov, A.Timoshenko, N. Topilin, B. Topko, H. T¨ornqvist, I.Tyapkin, V. Vasendina, A. Vishnevsky, N. Voytishin, V. Wagner, O. Warmusz, I. Yaron, V. Yurevich, N.Zamiatin, Song Zhang, E. Zherebtsova, V. Zhezher, N. Zhigareva, A. Zinchenko, E. Zubarev, M. Zuev, Massachusetts Institute of Technology, Cambridge,Massachusetts 02139, USA. Joint Institute for NuclearResearch, Dubna 141980, Russia. School of Physics andAstronomy, Tel Aviv University, Tel Aviv 69978, Israel. Institut f¨ur Kernphysik, Technische Universit¨at Darm-stadt, 64289 Darmstadt, Germany. Dubna State Uni-versity, Dubna 141980, Russia. GSI Helmholtzzentrumf¨ur Schwerionenforschung GmbH, Planckstr. 1, 64291Darmstadt, Germany. Helmholtz ForschungsakademieHessen f¨ur FAIR, Max-von-Laue-Str. 12, 60438 Frank-furt, Germany. IRFU, CEA, Universit´e Paris-Saclay,F-91191 Gif-sur-Yvette, France. Institute for Theo-retical and Experimental Physics (ITEP), Moscow, Rus-sia. National Research Nuclear University MEPhI,Moscow, Russia. Moscow Institute of Physics andTechnology (MIPT), Moscow, Russia. Texas A&MUniversity-Commerce, Commerce, Texas 75429, USA. University of Wroclaw, Wroclaw, Poland. KurchatovInstitute, Moscow. Key Laboratory of Nuclear Physicsand Ion-Beam Application (MOE), Institute of ModernPhysics, Fudan University, Shanghai, China. Institutefor Nuclear Research of the RAS (INR RAS), Moscow,Russia. Rudjer Boskovic Institute, Zagreb, Croatia. Warsaw University of Technology, Warsaw, Poland. Nuclear Physics Institute, CAS, ˇReˇz, Czech Repub-lic. Plovdiv University “Paisii Hilendarski”, Plovdiv,Bulgaria.
Methods
Ion beam.
The primary beam ions were produced in aKRION source and accelerated in the Nuclotron [32], de-livered quasi-continuously in pulses for 2 seconds followedby 8 second pauses between spills. Each pulse delivered2 . × ions on average.The beam contained a mixture of Carbon-12, Nitrogen-14, and Oxygen-16 ions with fractions on average of 68%,18%, and 14% respectively. The C ions have a beammomentum of 3 .
98 GeV/c/u at the center of the LH target. They are focused on the target with a beam di-ameter of about 4 cm, See Extended Data Fig. 1c.The beam ions are identified on an event-by-event ba-sis using their energy loss in the BC detectors (BC1, BC2upstream the target), which is proportional to their nu-clear charge squared Z . The selection of the incomingnuclear species is shown in Extended Data Fig. 8. Pile-up events are rejected by checking the multiplicity of theBC2 time signal. The detectors upstream the target.
Prior to hit-ting the target the beam was monitored by the two thinscintillator-based beam counters (BC1, BC2) and twomulti-wire proportional chambers (MWPCs) mentionedabove. The MWPCs determined the incident beam iontrajectory for each event. Besides using the energy de-position in the BCs for beam ion identification, the BCcloser to the target was readout by a fast MCP-PMT usedto define the event start time t . Beam halo interactionswere suppressed using a dedicated BC veto counter (V-BC), consisting of a scintillator with a 5 cm diameterhole in its center. Liquid-hydrogen target.
The target [33] was cryogeni-cally cooled and the hydrogen was recondensated usingliquid helium. The liquid hydrogen was held at 20 Kelvinand 1.1 atmospheres in a 30 cm long, 6 cm diameter,aluminized Mylar cylindrical container. The containerentrance and exit windows were made out of 110 micronthick Mylar. The target constitutes a 14% interactionlength for C. A sketch of the target cell is shown inExtended Data Fig. 1.
Two-arm spectrometer (TAS).
A two-arm spectrom-eter was placed downstream of the target and was usedto detect the two protons from the ( p, p ) reaction thatemerge between 24 ◦ and 37 ◦ . The vertical acceptanceof each arm is ± ◦ . These laboratory scattering anglescorrespond to ∼ ◦ (75 ◦ to 101 ◦ ) QE scattering in thetwo-proton center-of-mass (c.m.) frame. Each spectrom-eter arm consisted of scintillator trigger counters (TC),gas electron multiplier (GEM) stations, and multi-gapresistive plate chamber (RPC) walls.Proton tracks are formed using their hit locations inthe GEM and RPC walls. The vertex resolution along the beam-line direction is 1 . σ ) and was measuredusing a triple lead-foil target as detailed in the OnlineSupplementary Material.The time difference between the RPC and t signalsdefine the proton time of flight (TOF). The TOF, com-bined with the measured track length (accounting for theexact interaction vertex in the target), is used to deter-mine its momentum. Measurements of gamma rays frominteractions with a single lead-foil target were used forabsolute TOF calibration. An absolute TOF resolutionof 175 ps was extracted, which dominates the momen-tum resolution, see Online Supplementary Materials fordetails. Data taking and quality.
Signals from the TAS-TCswere combined with the BC and V-BC scintillator sig-nals to form the main C( p, p ) reaction trigger for theexperiment. Additional triggers were set up for monitor-ing and calibration purposes, see Online SupplementaryMaterials for details.The stability of the trigger was monitored online dur-ing the experiment as part of our data quality control.We collected and recorded about 20 million triggers. Aspart of the beam monitoring and quality, the ratio be-tween BC2/BC1 and BC4/BC3 was not smaller than65%, and the rate on the V-BC is on average 24% rel-ative to BC2. The main C( p, p ) reaction trigger hada rate of about 180 Hz, as measured during live beam.Variations of BC pulse height over the measurement timewas monitored and accounted for in the analysis. No sig-nificant run-to-run variations were observed in any of thefinal observables. Reaction vertex and proton identification.
The z -position (along the beamline) of the reaction vertex is re-constructed from two tracks in the TAS, while the ( x, y )position is obtained from the extrapolated MWPC trackin front of the target (the latter provides a better trans-verse position resolution). Details about the algorithmand performance can be found in the Online Supplemen-tary Materials.The reconstructed vertex position along the beam-lineand transverse to it with the liquid-hydrogen target in-serted is shown in Extended Data Fig. 1. The structureof the target – the LH volume and other in-beam materi-als, such as the target walls, styrofoam cover, and variousisolation foils – is well reconstructed The vertex quality isensured by requiring that the minimum distance betweenthe two tracks, which define the vertex, is smaller than4 cm. In addition, we place a selection on the absolute z -vertex requiring it to be reconstructed within ±
13 cmfrom the center of the target.Scattering from the target vessel that was not rejectedby the veto counter is removed by a cut on the ( x, y )-vertex direction. This removes a strong peak due to astyrofoam cover over the target (Extended Data Fig. 1c).0Having determined the tracks and the vertex, the mo-mentum of each proton is calculated with respect to theincoming beam direction, using the TOF information be-tween the target and the RPC.In order to select ( p, p ) events from Quasi-Free Scat-tering (QFS), other particles which also create a trackbut originate from inelastic reactions, mostly pions, needto be rejected. We apply several criteria (outlined inthe next section), but the basic selection is a cut to thevelocity of the two measured particles, shown in OnlineSupplementary Material Fig. 4b. In the analysis, bothparticles detected in the TAS must pass a velocity con-dition 0 . < β < .
96, removing fast and slow pions.
Fragment detection.
Nuclear fragments following the( p, p ) reaction are emitted at small angles with respectto the incident beam with momentum that is similar tothe beam momentum. To measure the fragment scatter-ing angle, three silicon (Si) planes and two MWPCs areplaced in the beam-line downstream the target. Follow-ing the MWPCs the fragments enter a large acceptance2 .
87 T · m dipole magnet, and are bent according to theirmomentum-to-charge ratio ( P/Z ), i. e. magnetic rigidity.Two large-acceptance drift chambers (DCH) with 8 wire-planes each are used to measure the fragment trajectoryafter the magnet.The fragment momenta are determined from the mea-surement of their bending angle in the magnet. Fragmentidentification (nuclear mass and charge) is done usingtheir bend in the magnetic field and energy depositionin two scintillator BCs (3,4) placed between the targetand the magnet entrance, see Fig. 1b. The latter is pro-portional to the sum over all fragment charges squared, Z eff ≡ (cid:112)(cid:80) Z . Fragment momentum and identification.
We fol-low a simulation-based approach to derive
P/Z from amulti-dimensional fit (MDF) to the measured fragmenttrajectories before and after the magnet. The particletrajectory is determined using the MWPC-Si track be-fore the magnet and the DCH track after the magnet.Both tracks serve as input for the
P/Z determination.The momentum resolution was determined using unre-acted C beam ions (from empty-target runs) and foundto equal 0.78 GeV/c (1.6%) (Online Supplementary Ma-terial Fig. 2). This resolution is consistent with the res-olution expected from events obtained with simulationthat accounts for the incoming beam energy spread. Us-ing beam-trigger events (see Online Supplementary Ma-terial) we verified that the momentum reconstruction res-olution is the same when the C ions go through a fullliquid-hydrogen target. The achieved momentum accu-racy is evaluated from simulation to equal 0.2%.The fragment tracking efficiency, including the detec-tion efficiency of the upstream MWPC-Si, downstreamDCH detectors, and track reconstruction and selection algorithm equals ∼ P/Z obtainedby the MDF vs. total charge measured in the scintilla-tors.This work focuses only on fragments with nuclearcharge of 4 or larger with a single track matched be-tween the upstream and downstream tracks. Althoughthe charge of the fragments is only measured as an inte-grated signal in BC3 and BC4 counters, the Boron iso-topes can be selected unambiguously since no possiblecombination of fragments could otherwise mimic a sig-nal amplitude proportional to (cid:80) Z = 25. In the caseof Be, the only other fragment of interest here with Z eff = 4, contamination from within the resolution is ex-cluded by using the additional P/Z information. Be isthe only possible fragment with
P/Z ∼
10 GeV/c in thatregion and is well separated.Besides requiring a good vertex and single global-trackevents, we employ Z eff and P/Z selection criteria to iden-tify B, B, or Be. A two-dimensional charge selec-tion, as for the incoming charge, was applied here forBC3 and BC4. For the selection in
P/Z vs. Z eff also atwo-dimensional cut was applied as indicated in Fig. 1bwith a ∼ σ selection in P/Z . Single heavy fragment detection efficiencies.
Asdiscussed above, this work is limited to reactions with asingle heavy ( Z ≥
4) fragment in the final state. The de-tection of such a fragment depends on the ability of thefragment to emerge from the liquid hydrogen target with-out re-interacting, and our ability to identify its charge inthe two BCs downstream of the target, and reconstructits tracks before and after the magnet.We extract the efficiencies for the charge and track re-construction using beam-only data (i.e. no target vesselin the beam-line). We assume that, within the quoteduncertainties below, there is no difference between theefficiencies for detecting Z = 6 and Z = 5 and 4 frag-ments.In order to determine the efficiency for determining thefragment’s charge in the BCs downstream the target, wefirst select incident C ions based on their energy loss inthe BC1 and BC2 counters (see Extended Data Fig 8).We then examine the fraction of those C ions also iden-tified by their energy loss in BC3 and BC4 downstreamthe target. This fraction defines a charge identificationefficiency of (cid:15) Z = (83 ± − σ on the Gaussian distribution in BC3 andBC4. The standard deviation in efficiency from this cutvariation relative to the mean value defines the uncer-tainty. The fraction of such Z in = Z out = 6 events with asingle reconstructed track and P/Z = 8 GeV/c is equal to1(39 . +1 . − . )%, determined in a ± . σ range with ± . σ range to account for the uncertainty. In case of Befragments the tracking efficiency is (39 . +5 . − . )% due tolarger systematic effects. The larger asymmetry towardssmaller efficiency arises from a possible background con-tribution in the reconstructed P/Z that is taken intoaccount. More details are given below in “ExtractingQE ratios” and in the Online Supplementary Material,in particular about a single-track identification and itsefficiency.
Single-proton knockout data-analysis.
The basicselection for any analysis requires an incoming C, agood reaction vertex, and particles in the arms passingthe velocity condition. These selections criteria define theinclusive ( p, p ) reaction channel, which is dominated byFSI and IE scattering. The exclusive reaction channelrequires the additional detection of a B fragment, witha single global-track condition and defines the one-protonQFS, that includes both QE and IE scattering.We select a bound B where the 3 / − ground-stateis populated with the largest cross section. However, wecannot distinguish bound excited states that de-excitevia γ -ray emission that are also populated in our experi-ment. Previous works [24] found the contribution fromsuch states to be small, coming primarily from the 1 / − and 3 / − states that contribute ∼
10% each to the totalcross section. This contribution also correspond to p -shellknockout and does not impact the resulting momentumdistribution significantly.In order to identify ( p, p ) QE events and reject IEevents, we look at the missing energy and the in-planeopening angle of the two particles measured in the arms.An elliptical cut denoted by 2 σ is applied in each direc-tion (Fig. 2). The standard deviation was obtained froma Gaussian fit to E miss ( σ = 0 .
108 GeV) and θ p + θ p ( σ = 1 . ◦ ).The missing energy is defined as E miss = m p − e miss ,where e miss is the energy component of ¯ p miss in the restframe of the C nucleus. The boost from the laboratorysystem into the rest frame is applied along the incoming-beam direction taking into account the reduced beamenergy at the reaction vertex. The selection region for QEevents is defined in the exclusive channel with fragmentselection, in a 2 σ ellipse as indicated in Fig. 2. The IEpart is defined from the remaining events within the otherellipse. The same criteria are applied in the inclusivechannel. Correlations with other kinematical variablesare shown in Extended Data Fig. 9.The M spectrum in Extended Data Fig. 2a showsthe squared missing mass for the exclusive channel be-fore and after applying the QE cut, clearly showing thatwe select background-free QE events with a missing massthat equals the proton mass. A lower boundary in thesquared missing mass of M > .
47 GeV /c is ap-plied. Since the chosen selection criteria might influence other kinematical variables of ¯ p miss (Eq. 2), we show themomentum distributions and angular correlations withless strict selection in the Extended Data (Figs. 2, 3)which do not show a different behavior and are also de-scribed well by the simulation. Single-proton knockout simulation.
We comparethe quasielastic C( p, p ) B data to a MonteCarlo sim-ulation for the proton quasielastic scattering off a moving C. In the calculation, the C system is treated as spec-tator plus initial proton, p C = p B + p i . The proton’sinitial momentum distribution in C is sampled from atheoretical distribution. Note that all kinematical quan-tities discussed here correspond to the carbon rest-frame.The momentum distributions are calculated in theeikonal formalism for quasi-free scattering as describedin Ref. [34]. In this work we compare the data tothe momentum-distribution calculated without absorp-tion effects, i. e. without multiple-scattering. Here wealso compare to the same calculation that includes ab-sorption effects from the imaginary part of the potentialexplicitly, calculated in the optical limit of Glauber the-ory. See in Extended Data Fig. 10.The distorted waves are calculated from the real andimaginary part of the optical potential for the inter-action between proton and nucleus. The single parti-cle wave function of the removed proton is generatedfrom a Woods-Saxon potential with radius given by R =1 . · A / fm and diffuseness a = 0 .
65 fm, while the depthof the potential was adjusted to reproduce the removalenergy, S p = 15 .
96 MeV, of a proton from the p / -shell.For the C nucleus a density distribution from electronscattering was used as input, assuming that is has thesame profile for the proton and neutron densities. Thedensity is of the form ρ C = (1+ α · ( r/b ) ) · exp (cid:8) − r /b (cid:9) ,with α = 1 . b chosen so as to reproduce the RMSradius of the C, b = 2 .
47 fm.Although the fragment selection removes events fromFSI and we do not need to account for their scatteringinto measured phase space, we look at the calculationwith absorption since the survival probability is larger ifthe knockout happens at the nuclear surface. This effectmight create a difference from no distortions. However,the momentum distributions with and without absorp-tion look very similar, see Ext. Data Fig. 10, and do notseem to have a large impact on the reconstructed initialmomentum distribution in a light system such as C.In terms of the kinematics, we raffle | p i | from the total-momentum distribution and randomize its direction. Theproton’s off-shell mass is m = m C + m B − m C · (cid:113) m B + p i . (3)The two-body scattering between the proton in C andthe target proton is examined in their c.m. frame. Theelastic-scattering cross section is parameterized from free2 pp differential cross section data. Following the scatter-ing process, the two protons and B four-momenta areboosted back into the laboratory frame.The two-arm spectrometer was placed such that it cov-ers the symmetric, large-momentum transfer, 90 ◦ c.m.scattering region. Given the large forward momentum,the detectors cover an angular acceptance of ∼ ◦ <θ < ◦ in the laboratory system which corresponds to ∼ ◦ < θ c . m . < ◦ in the c.m. frame.In order to compare the simulated data to the exper-imental distributions, the simulation is treated and an-alyzed in the same way as the experimental data. Ex-perimental acceptances are included. Resolution effectsare convoluted to proton and fragment momenta. Theproton time-of-flight resolution ∆ToF / ToF is 0 .
95% at2 GeV/c and the angular resolution 5 mrad, while thefragment momentum resolution is 1.5% and the angu-lar resolution 1.1 mrad in the x and y directions. Theangular resolution of the incoming beam is 1.1 mrad.The beam-momentum uncertainty, examined as Gaus-sian profile, does not significantly impact rest-frame mo-mentum distribution as long as the same nominal beammomentum is used for extracting physical quantities (orobservables) from the experimental data and the simu-lated events. However, the momentum distributions aredominated by the width of the input p-shell momentumdistribution. When comparing, the simulation is nor-malized to the integral of the experimental distributions.We find overall good agreement between experiment andMonte Carlo simulation showing that the reaction mech-anism and QE events sample the proton’s initial momen-tum distribution in C. Additional data-simulation com-parison is shown in Extended Data Fig. 3.
Extracting QE C( p, p X) / C( p, p ) ratios for B , B , and Be . To extract the fraction of ( p, p ) eventswith a detected heavy fragment we need to apply severalcorrections to the number of measured events which donot cancel in the ratio. The ratio of the exclusive crosssection with a detected fragment to the inclusive crosssection is given by: C( p, p )X C( p, p ) = R(cid:15) Z × (cid:15) track × att , (4)where • R is the measured ratio based on the number ofQE events for each sample. We added a cut onlow missing momentum, p miss <
250 MeV / c, in ad-dition to the missing energy and in-plane openingangle cuts to clean up the inclusive ( p, p ) sample,and focusing at the region of small missing momen-tum. • (cid:15) Z is the outgoing fragment charge efficiency. Weconsider a value of (cid:15) Z = (83 ± • (cid:15) track is the outgoing fragment tracking efficiencywith all the selection cuts applied in a ± . σ P/Z range. We consider a value of (cid:15) track = (39 . +1 . − . )%for , B , and (cid:15) track = (39 . +5 . − . )% for Be, seediscussion above. • att is the attenuation of the outgoing fragment dueto secondary fragmentation in the target. After thereaction, the flux of the fragment depends on theremaining distance the fragment needs to travel inthe target. The attenuation is given by the reduc-tion of this flux att = exp( − ρσ tot z ) , (5)where ρ is the target density and σ tot the total re-action cross section. We evaluate the attenuationfactor by taking an average over the 30 cm targetlength, using σ tot = 220 ±
10 mb (assumed to bethe same for B , Be within uncertainty), suchthat att = 0 . ± .
01. Additional break-up reac-tions due to material in the beam-line downstreamthe target were estimated (and scaled) based on thetotal cross section on carbon. The contribution tothe secondary reaction probability is comparablysmall, in particular reactions from B to B or Be are negligible.The total reaction cross section σ tot is calculated ineikonal reaction theory [35] using the B harmonic-oscillator like density distribution and the
N N cross sec-tion at 4 GeV/c/u as the input. In a benchmark testit reproduces the measured cross section for B+ C atkinetic energy of 950 MeV/u [36] while the beam energyhas only a very small impact. We consider the ∼
5% sys-tematic overestimate of eikonal cross sections comparedto measurements as uncertainty.From Eq. 4 we see that there are four individ-ual contributions to the uncertainty in the ratio of C( p, p X) / C( p, p ): statistics ∆ R , efficiencies (∆ (cid:15) Z and ∆ (cid:15) track ) and attenuation (∆ att ). In addition wehave a systematic uncertainty due to the event selectioncuts. Each event cut was modified over a given σ rangeand the resulting change in the relative yield was takenas the systematic uncertainty. The 2D E miss -angle cutswere varied as (2 ± / σ , where both these quantities aredescribed by a Gaussian. The cut in missing momentumwas varied according to the missing momentum resolu-tion like p miss < ±
50 MeV / c. These uncertainties arequoted as symmetric uncertainties since in the simulationwe did not observe a significant asymmetry in the mea-sured quantities. Besides that, we also consider a pos-sible background contribution in the P/Z determinationas additional asymmetric systematic uncertainty. It isdetermined for each charge selection separately with a fitin shape of a second order polynomial to the
P/Z distri-bution under quasielastic conditions. Since the fits with3and without background contribution result in very sim-ilar goodness we chose to adapt the possible backgroundas 2 σ uncertainty. Combining these contributions we ob-tain the following fractions given with statistical (stat)and systematic (sys) uncertainties: C( p, p ) B C( p, p ) = (43 . ± . +4 . − . (sys))% , C( p, p ) B C( p, p ) = (7 . ± . +1 . − . (sys))% , C( p, p ) Be C( p, p ) = (0 . ± . +0 . − . (sys))% . Selecting high-momentum SRC events.
Westudy SRC events by focusing on C( p, p ) B and C( p, p ) Be events. We start with the two-proton de-tection imposing the vertex and β cuts mentioned above.The first cut applied to select SRC breakup events is tolook at high-missing momentum, p miss >
350 MeV / c.The remaining event selection cuts are chosen follow-ing a GCF simulation of the C( p, p ) scattering reactionoff high missing-momentum SRC pairs. After applyingthe high-missing momentum cut, we look at the in-planeopening angle between the protons for different cases:(a) inclusive C( p, p ) events, (b) GCF simulated SRCevents, (c) exclusive C( p, p ) B events, and (d) exclu-sive C( p, p ) Be events. The GCF predicts relativelylarge opening angles that guides our selection of in-planelab-frame opening angle larger than 63 ◦ (that also sup-presses contributions from inelastic reactions that con-tribute mainly at low in-plane angles).Next we apply a missing-energy cut to further excludeinelastic and FSI contributions that appear at very largemissing-energies. To this end we examine the correla-tion between the missing energy and missing momentum,after applying the in-plane opening angle cut, for thefull range of the missing momentum (i. e., without the p miss >
350 GeV / c cut), see Extended Data Fig. 4. Wechose to cut on − < E miss <
240 MeV.To improve the selection cuts we use the total energyand momentum conservation in reactions at which weidentified a fragment ( B or Be). We can write theexclusive missing-momentum in these reactions as¯ p miss , excl . = ¯ p C + ¯ p tg − ¯ p − ¯ p − ¯ p B(Be) . (6)Neglecting the center-of-mass motion of the SRC pair,the missing-mass of this 4-vector should be equal to thenucleon mass m , excl . (cid:119) m N . The distributions for C( p, p ) B and C( p, p ) Be events that pass themissing-momentum, in-plane opening angle, and missing-energy cuts are shown in Extended Data Fig. 5 togetherwith the GCF simulation. To avoid background eventswith very small values of the missing-mass we choose tocut on M , excl . > .
42 GeV / c . After applying this cut we are left with 23 C( p, p ) B and 2 C( p, p ) Beevents that pass all the SRC cuts.We note that if the measured SRC events were causedby FSI with a neutron in B, we would expect to alsodetect a similar number of Be fragments due to FSIwith a proton in B. At the high energies of our mea-surement these two FSI processes have almost the samerescattering cross sections [37]. Our measurement of only2 Be events is consistent with the SRC np -dominanceexpectation and not with FSI.In addition, while our selection cuts suppress QEscattering events off the tail of the mean-field momen-tum distribution they do not completely eliminate them.Therefore, some events could result from de-excitationof high- p miss 11 B fragments. Using the de-excitationcross-sections of Ref. [24] and the measured number of C( p, p ) B events that pass our SRC selection cuts(except for the exclusive missing-mass cut), we estimatea maximal background of 4 B and 2 Be events dueto knockout of mean-field protons and subsequent de-excitation.
Characterizing the selected C( p, p ) B events. The majority of SRC events with a detected fragmentcomes with B. In the Extended Data we presentsome kinematical distributions of these selected eventstogether with the GCF simulation. Extended Data Fig. 6shows the total B fragment and missing moments aswell as their different components. Overall good agree-ment between the data and simulation is observed.The pair c.m. momentum width of σ c . m . = (156 ±
27) MeV/c was obtained from the distribution in thetransverse direction to the beam by χ comparison forseveral different c.m. width in the GCF simulation.The result is consistent with electron scattering measure-ments [27].Due to the high momenta of the nucleons in SRC pairs,it is beneficial to also analyze the missing-momentum dis-tribution in the relativistic light-cone frame where thelongitudinal missing-momentum component is given by α = ( E miss − p z miss ) /m p . Similar to p miss , α is calculatedin the C rest frame where ˆ z is boosted target-proton di-rection. α = 1 for scattering off standing nucleons. α < >
1) corresponds to interaction with nucleons that movealong (against) the beam direction and therefore decrease(increase) the c.m. energy of the reaction √ s . ExtendedData Fig. 7a shows the α distribution for the measuredSRC events. We observe that α <
1, as predicted by theGCF and expected given the strong s -dependence of thelarge-angle elementary proton-proton elastic scatteringcross-section. For completeness, Extended Data Fig. 7also shows additional angular correlations between thenucleons in the pair and the B fragment, all well repro-duced by the GCF.
Estimating the number of SRC C( p, p ) B and C( p, p ) Be events. As a consistency check we per-formed a simple estimate of the expected number of ex-clusive SRC events based on the measured mean-field C( p, p ) B event yield. We assume SRCs account for20% of the wave function [38–40], and that their contri-bution to the exclusive measurements is suppressed by afactor of 2 as compared to the mean-field C( p, p ) Bdue to the transparency of the recoil nucleon [41–43].Therefore, we expect a contribution of 11% SRC and 89%mean-field.The mean-field has contributions leading to boundstates (i. e. p -shell knockout leading to B) and con-tinuum states ( s -shell knockout, non-SRC correlations,etc.) with relative fractions of 53% and 36% respectively(53% + 36% = 89%) [24]. Therefore, given that we mea-sured 453 C( p, p ) B MF ( p -shell knockout) events,we expect a total of 453 · (11% / · ·
50% = 24 SRC events.If the SRC pair removal results in A − np -dominance (20times more np than pp pairs) we expect a population of90% B and 10% Be. We also considered that for a pp pair the knockout probability is twice larger than for pn . Using the estimation of 24 total SRC events willlead to 22 events for B (we measure 23) and 2 eventsfor Be (we measure 2). These simple estimates showoverall self-consistency in our data.Last, as our selection cuts suppress, but do not elim-inate events originating from the tail of the mean-fielddistribution, some events could result from de-excitationof high- p miss 11 B fragments. To evaluate that fraction, weconsider B events that pass the SRC selection cuts (ex-cept for the exclusive missing mass cut). 28 such eventsare observed of the total 453 MF B events (i. e. a frac-tion of 9%). Reference [24] measured a neutron (pro-ton) evaporation cross-section relative to the total con-tinuum cross-section of 17% (7%). Using these fractionswe expect a B ( Be) contribution from neutron (pro-ton) evaporation based on the measured B events of(28 / · ·
17% = 3 events ((28 / · ·
7% = 1).This is the maximum number that can be expected fromthis background, since for B and Be we apply an ad-ditional cut on the exclusive missing mass as explainedabove.
GCF simulations.
The GCF was derived and validatedagainst many-body Quantum Monte Carlo calculationsin Refs. [14, 40, 44]. Its implementation into an eventgenerator that can be used for analysis of experimentaldata is detailed in Ref. [45], and was successfully appliedto the analysis of electron scattering SRC measurementsin Refs. [19, 26, 45, 46]. The adaptation of the GCF event generator from( e, e (cid:48) p ) reactions to ( p, p ) reactions is simple and mainlyrequired replacing the electron mass with a proton masswhen calculating the reaction kinematics and phase-space factors and replacing the elementary electron-nucleon cross-section by the elastic proton-proton cross-section used in the mean-field simulation discussed above.We accounted for the experimental acceptance and de-tector resolution in the same way as described for themean-field simulation discussed above.The input parameters of the GCF calculation include:an N N interaction model, for which we used the AV σ GCFc . m . =150 MeV/c [27]; and an A − σ GCFc . m . = ±
20 MeV/c, and the A − ∗ Contact Author ([email protected])[32] Kekelidze, V. et al. Project NICA at JINR.
Nucl. Phys.A , 904-905:945c–948c (2013).[33] Agapov, N. N. et al. Cryogenic targets of the lightestgases (hydrogen, deuterium and helium-4) with GM cry-ocooler for experiments of high energy physics. In
Cryo-genics 2019. Proceedings of the 15th IIR InternationalConference: Prague, Czech Republic (2019).[34] Aumann, T., Bertulani, C.A. & Ryckebusch, J. Quasifree( p, p ) and ( p, pn ) reactions with unstable nuclei. Phys.Rev. C , 064610 (2013).[35] Hussein, M.S., Rego, R.A. & Bertulani, C.A. Microscopictheory of the total reaction cross-section and applicationto stable and exotic nuclei. Phys. Rept. , 279–334(1991).[36] Ozawa, A., Suzuki, T. & Tanihata, I. Nuclear size andrelated topics.
Nucl. Phys. A , 32–62 (2001).[37] Alkhazov, G.D., Belostotsky, S.L. & Vorobev, A.A. Scat-tering of 1-GeV Protons on Nuclei.
Phys. Rept. , 89–144 (1978).[38] Egiyan, K. et al. Measurement of 2- and 3-nucleon shortrange correlation probabilities in nuclei. Phys. Rev. Lett. , 082501 (2006).[39] Wiringa, R. B., Schiavilla, R., Pieper, S.C. & Carlson,J. Nucleon and nucleon-pair momentum distributions in a ≤ Phys. Rev. C , 024305 (2014).[40] Weiss, R., Cruz-Torres, R., Barnea, N., Piasetzky, E. &Hen, O. The nuclear contacts and short range correla-tions in nuclei. Phys. Lett. B , 211 (2018).[41] Hen, O. et al. Measurement of transparency ratios forprotons from short-range correlated pairs.
Phys. Lett. B , 63–68 (2013).[42] Duer, M. et al. Measurement of Nuclear TransparencyRatios for Protons and Neutrons.
Phys. Lett. B , Prog. Part. Nucl.Phys. , 1–27 (2013).[44] Weiss, R., Bazak, B. & Barnea, N. Generalized nuclearcontacts and momentum distributions. Phys. Rev. C ,054311 (2015).[45] Pybus, J. R. et al. Generalized Contact Formalism Anal-ysis of the He( e, e (cid:48) pN ) Reaction. Phys. Lett. B ,135429 (2020).[46] Weiss, R., Korover, I., Piasetzky, E., Hen, O. & Barnea,N. Energy and momentum dependence of nuclear short-range correlations - Spectral function, exclusive scatter-ing experiments and the contact formalism.
Phys. Lett.B , 242–248 (2019).[47] Kapishin, M. Studies of baryonic matter at the BM@Nexperiment (JINR).
Nucl. Phys. A , 967–970 (2019).[48] Conceptual design report BM@N – Baryonic Matter atNuclotron (2013).[49] Khabarov, S. et al. First glance at the tracking detectorsdata collected in the first BM@N SRC run.
EPJ WebConf. , 04002 (2019).[50] Kovalev, Y. et al. Central tracker for BM@n experimentbased on double side si-microstrip detectors.
Journal ofInstrumentation , C07031 (2017).[51] Babkin, V. et al. Triple-stack multigap resistive platechamber with strip readout. Nucl. Instrum. Meth. A ,490–492 (2016).[52] BM@N DAQ system (2020). https://afi.jinr.ru [53] ROOT Cern: Multi-dimensional fit. https://root.cern.ch/doc/master/classTMultiDimFit.html . Extended Data − − − − z C oun t s entrancewindowBC2 liquidHydrogen styrofoamcover (a) (a)(b) Beam Cryostat
BM@N (b) − − x − − ( c m ) y (c)BM@N Extended Data Fig. 1. | Reaction vertex.
Reconstructed reaction vertex in the LH target. The position along the beamline is shown in (a), scattering off in-beam material is also visible. For comparison, a sketch of the target device is shown in(b), scattering reactions are matched at the entrance window, the target vessel, styrofoam cover. A selection in z < |
13 cm | isapplied to reject such reactions. The xy position at the reaction vertex is shown in (c), measured with the MWPCs in front ofthe target. The dashed line indicates the target cross section. Scattering at the target vessel at around ( x = 2 cm, y = 2 cm)can be seen which is removed by the selection as indicated by the red circle.
50 55 60 65[deg] p θ + p θ C oun t s ) p ,2 p C( B ) p ,2 p C( (a) BM@N − /c [GeV miss2 M C oun t s (b) B ) p ,2 p C( Quasielastic
BM@N
25 30 35[deg] p θ [ d e g ] p θ (c) QE BM@N IE
160 170 180[deg] pp φ C oun t s (d) B ) p ,2 p C( QuasielasticSimulation
BM@N
Extended Data Fig. 2. | Single-proton knockout signatures. (a) Projection for in-plane opening angle of Fig. 2,comparing the inclusive reaction C( p, p ) and tagged events with B coincidence. The inclusive distribution is area normalizedto the tagged one. The fragment selection clearly suppresses FSI, and the QE signal separates from IE. (b) Proton missingmass for tagged C( p, p ) B events. After the QE selection in E miss and in-plane opening angle, the distribution is shownin dark blue dots with artificial offset for better visibility. We apply an additional missing mass cut M > .
47 GeV /c ,indicated by the dashed line. (c) Angular correlation between the two ( p, p ) protons for quasielastic ( M > .
55 GeV /c )and inelastic ( M < .
55 GeV /c ) reactions only selected by missing mass. The QE events show a strong correlation witha polar opening angle of ∼ ◦ . (d) The off-plane opening angle peaks at 180 ◦ as expected, shown for M > .
55 GeV /c . The width of this distribution is narrower than that dictated by the TAS acceptance. Data error bars show the statisticaluncertainties of the data at the 1 σ confidence level. − miss,z p C oun t s (d) − miss,y p C oun t s (c) − miss,x p (b) miss p C oun t s (a) QuasielasticB ) p ,2 p C( Simulation
BM@N − miss,z p C oun t s (h) − miss,y p C oun t s (g) − miss,x p C oun t s (f) miss p C oun t s (e) − B,z p C oun t s (l) − B,y p C oun t s (k) − B,x p (j) B p C oun t s (i) BM@N − B,z p C oun t s (p) − B,y p C oun t s (o) − B,x p C oun t s (n) B p C oun t s (m) Extended Data Fig. 3. | Missing and fragment momentum.
Momentum components for quasielastic C( p, p ) Breactions compared to simulation. The proton missing momentum is shown for (a)-(d), while (e)-(h) show the same distributionsbut with missing mass cut only (0.55 GeV /c < M < /c ). Agreement with the simulation is found in bothcases. The shift in p miss ,z is associated with a strong pp cross-section scaling with c.m. energy. For the same conditions the B fragment momentum components are shown in (i)-(l), and (m)-(p). The dashed lines in p B ,z indicate the momentumacceptance due to the fragment selection in P/Z . Data error bars show the statistical uncertainties of the data at the 1 σ confidence level.
25 30 3525303540 [ d e g ] p2 θ (d) B / ) p,2p C( Be
25 30 35 [deg] p1 θ [ d e g ] p2 θ (c) B / ) p,2p C( Be
25 30 3525303540 [ d e g ] p2 θ (b) ) p,2p C(
25 30 3525303540 [ d e g ] p2 θ (a) GCF simulation
BM@N − [ G e V ] m i ss E (h) Be ) p,2p C( [GeV/c] miss p − [ G e V ] m i ss E (g) B ) p,2p C( − [ G e V ] m i ss E (f) ) p,2p C( − [ G e V ] m i ss E (e) GCF simulation
BM@N
Extended Data Fig. 4. | SRC selection.
The proton-proton polar angular correlations are shown in (a)-(d) with p miss >
350 MeV/c, the in-plane opening angle cut to be applied is indicated by the dashed line: (a) GCF simulation, (b) C( p, p )data, (c) C( p, p ) B / Be data on top of simulation, and (d) the same as (c) but with additional E miss cut. The missing energyvs. missing momentum is shown in (e)-(h): for (e) GCF simulation, (f) C( p, p ), (g) C( p, p ) B, and (h) C( p, p ) Beevents that pass the in-plane opening angle cut. The selection cuts in −
110 MeV < E miss <
240 MeV and p miss >
350 MeV/care indicated by the dashed lines. (d) ] |u| [GeV C oun t s ] |t| [GeV ] /c [GeV miss,excl.2 M C oun t s B ) p,2p C( Be ) p,2p C( GCF simulation (a)BM@N (b) (c) BM@N ] |t| [GeV ] | u | [ G e V Extended Data Fig. 5. | SRC missing mass and momentum transfer. (a) The exclusive missing mass distributionsfor C( p, p ) B events and C( p, p ) Be events that pass the missing momentum, in-plane opening angle, and missingenergy cuts together with the GCF simulation (orange). The blue line represents the applied cut on the exclusive missing-mass M , excl . > .
42 GeV / c . (b) and (c) represent the Mandelstam variables for the same cases, B and Be, (d) showsthe two-dimensional momentum-transfer plot for B. The width of the bands and the data error bars show the systematicuncertainties of the model and the statistical uncertainties of the data, respectively, each at the 1 σ confidence level. [GeV/c] miss p (d) − [GeV/c] miss,z p (c) − [GeV/c] miss,y p (b) − [GeV/c] miss,x p C oun t s (a) B SRC ) p,2p C( GCF simulation
BM@N [GeV/c] B p C oun t s (h) − [GeV/c] B,z p C oun t s (g) − [GeV/c] B,y p C oun t s (f) − [GeV/c] B,x p C oun t s (e) BM@N Extended Data Fig. 6. | SRC missing and fragment momentum.
The missing momentum distributions (a)–(d) forthe selected C( p, p ) B SRC events (black) together with the GCF simulation (orange). Acceptance effects, especially in thetransverse direction are well captured by the simulation. The lower figures (e)–(h) show the fragment momentum distributionsin the rest frame of the nucleus for the same selected C( p, p ) B SRC events (black) together with the GCF simulation(orange). The width of the bands and the data error bars show the systematic uncertainties of the model and the statisticaluncertainties of the data, respectively, each at the 1 σ confidence level. − ) n p , miss p θ cos( (b) − − − ) miss p , B p θ cos( (c) α C oun t s (a) B SRC ) p,2p C( GCF simulation
BM@N
Extended Data Fig. 7. | SRC quantities.
Selected C( p, p ) B SRC events (black) together with the GCF simulation(orange). (a) Light-cone momentum distribution α = ( E miss − p z miss ) /m p . (b) Cosine of the opening angle between the missingmomentum and the neutron reconstructed momentum in the transverse direction. (c) Cosine of the angle between the Bfragment and missing-momentum. The width of the bands and the data error bars show the systematic uncertainties of themodel and the statistical uncertainties of the data, respectively, each at the 1 σ confidence level. BM@N
Extended Data Fig. 8. | Incoming beam ions.
Charge identification of incoming beam ions measured event-wise usingthe two BC counters in front of the target (BC1, BC2). Besides C, the
A/Z = 2 nuclei N and O are mixed in the beamwith less intensity. miss p − ] / c [ G e V m i ss M (b)
50 60 70[deg] p2 θ + p1 θ− ] / c [ G e V m i ss M (a) BM@N miss p − ] / c [ G e V m i ss M (e) [GeV/c] [GeV/c]50 60 70 p2 θ + p1 θ − ] / c [ G e V m i ss M [deg] (d) miss p [ G e V ] m i ss E (c) BM@N miss p − [ G e V ] m i ss E (f) Extended Data Fig. 9. | Kinematical correlations in single-proton knockout.
Figures (a)-(c) show the inclusive C( p, p ) channel, and (d)-(f) the exclusive channel, i. e. with tagging B. In both cases, the quasielastic peak (QE) andinelastic (IE) events are visible, while ISI/FSI are reduced by the fragment tagging. Eventually, a selection in E miss and in-plane opening angle was chosen to select QE events, see Fig. 2. The distributions are not corrected for fragment-identificationefficiency. miss p C oun t s QuasielasticB ) p ,2 p C( Sim. w/o abs.BM@NSim. w/ abs.
Extended Data Fig. 10. | Mean-field missing momentum calculations.
Missing-momentum distribution for quasielastic C( p, p ) B events, as in Fig. 3 of the main text. The data are compared with single-proton knockout simulation based onmomentum distributions from an eikonal calculation with and without including absorption effects in the calculation andnormalized to the same integral as the data. Both curves agree with the measured data and show only a small difference. Dataerror bars show the statistical uncertainties of the data at the 1 σ confidence level. Supplementary Materials for: Unperturbed inverse kinematics nucleon knockoutmeasurements with a 48 GeV/c Carbon beam
1. BM@N detector configuration.
The BM@N experimental setup at JINR allows to perform fixed-targetexperiments with high-energy nuclear beams that are provided by the Nuclotron accelerator [47]. Our experiment wasdesigned such that in particular protons under large laboratory angles can be measured. That dictated a dedicatedupstream target position and modified setup as used for studies of baryonic matter, but using the same detectors [48].The setup comprises a variety of detection systems to measure positions, times, and energy losses to eventually obtainparticle identification and determine their momenta. We are using scintillator detectors, multi-wire proportionalchambers, Silicon strip detectors, drift chambers, gas-electron multipliers, and resistive plate chambers as shown inFig. 1 and described in the following.
Beam Counters (BC):
A set of scintillator counters, each based on a scintillator plate with an air light guideviewed by a PMT, was installed in the beam line. Two counters (BC1 and BC2) were located before the target: BC1was located at the beam entrance to the experimental area. It is a 15 cm in diameter and 3 mm thick scintillatorread out by a XP2020 Hamamatsu PMT. BC2 was located right in front of the target and provided the start time t .This scintillator is of 4 cm x 6 cm x 0.091 cm size, and was tilted by 45 ◦ so that its effective area was around 4 cm x4 cm. It was read out by a Photonis MCP-PMT PP03656. Two counters (BC3 and BC4), each read out by a XP2020PMT, were located downstream the target to measure the total charge of the fragment particles in each event. BC3was based on 10 cm x 10 cm x 0.29 cm scintillator, and the BC4 was 7 cm x 7 cm x 0.3 cm. A veto-counter with thedimensions of 15 cm x 15 cm x 0.3 cm and a hole of 5 cm in diameter was located between BC2 and the target. Itwas read out by an XP2020 PMT and was included in the reaction trigger to suppress the beam halo. Multi-wire proportional chambers (MWPC):
We used two pairs of MWPC chambers, one before and oneafter the target for in-beam tracking [49]. Each chamber has six planes { X , U , V , X , U , V } . The X wires are alignedin y direction, U and V planes are oriented ± ◦ to X. The distance between wires within one plane is 2.5 mm, thedistance between neighboring planes is 1 cm. In total 2304 wires are read out. The active area of each chamber is500 cm (22 cm x 22 cm). About 1 m separated the chambers in the first pair upstream the target and 1.5 m betweenthe chambers in the second pair downstream the target. The polar angle acceptance of the chambers downstreamthe target is 1.46 ◦ . The efficiency of the MWPC pair in front of the target for particles with the charge of 6 is(92.2 ± ± Z = 6, and (89.3 ± Z = 5. Silicon trackers (Si):
As additional tracking system, three Silicon planes [50] were located after the target. Incombination with the MWPCs after the target, an increased tracking efficiency is reached. The first and second Siplanes share the same housing. The first plane consists of four modules, the second plane has two modules, the thirdplane has eight modules. Each module has 640 X -strips (vertical in y -direction) and 640 X (cid:48) -strips (tilted 2.5 ◦ relativeto X strips). The first plane has smaller modules with 614 X (cid:48) strips and 640 X strips. The first two planes and thethird plane are separated by 109 cm. The angular acceptance of the Si detector system is 1.58 ◦ . The design resolutionof 1 mm for the y -coordinate and 50 µ m for the x -coordinate was achieved in the experiment. The efficiency andacceptance of the Si tracking system, determined for reconstructed MWPC tracks before the target, is (81 . ± . Z = 6 ions, and (82 . ± . Z = 5 isotopes.Combined tracks were reconstructed using information from the MWPC pair after the target and the Si detectors.The efficiency to find a Si track, and/or a track in the second pair of the MWPC, or a combined track is (97 . ± . Z = 6 ions, and (97 . ± . Z = 5 isotopes evaluated for events with reconstructed tracks upstream thetarget. For the fragment tracking additional matching conditions are required with downstream DCH tracks, asexplained below, which ensures additional good track selection. Drift Chambers (DCH):
Two large-area drift chambers, separated by 2 m, are located downstream the bendingmagnet. These detectors are used for tracking the charged fragments in the forward direction. Together with theupstream-tracking information of MWPC and Si in front of the magnet, the bending angle and thus the magneticrigidity of the ions is determined. Each chamber consists of eight coordinate planes, twice { X , Y , U , V } , where X wiresare perpendicular to the x -axis, Y wires are at 90 ◦ relative to X, and U and V are tilted by + / − ◦ , respectively.The distance between wires within one plane is 1 cm, in total 12,300 wires are read out. The spatial resolution, givenas residual resolution, for one plane (X, Y, U, or V) is around 200 µ m (1 σ ). It is obtained by the difference betweenthe measured hit and the position from the reconstructed track at that plane. The efficiency of around 98% (97%) foreach plane was estimated for the first (second) DCH based on the reconstructed matched track in the second (first)DCH. A reconstructed track within one DCH chamber has at least 6 points. Two-Arm Spectrometer (TAS):
In order to detect light charged particles from the target, scattered to largelaboratory angles, the symmetric two-arm detection system around the beamline was constructed for this experiment.4Each arm, placed horizontally at + / − . ◦ (center) with respect to the beamline, was configured by the followingdetectors along a 5 m flight length: scintillator – scintillator – GEM – RPC. Each arm holds one GEM (Gas-ElectronMultiplier) station at a distance of 2.3 m from the target. Each GEM station contained two GEM planes with thedimensions of 66 cm ( x ) x 40 cm ( y ) each, placed on top of each other (centered at y = 0) to increase the overallsensitive area to 66 cm x 80 cm. The spatial resolution of the GEM hit is 300 µ m. Each RPC detector station,located at the end of the two arms at a distance of 5 m from the target, has a sensitive area of 1.1 m x 1.2 m. Eachstation consists of two gas boxes next to each other, each holds 5 multi-gap Resistive-Plate Chambers (RPCs) planesinside [51]. Two neighboring planes within one box overlap by 5 cm in y direction. Each plane has 30 cm long 1.2 cmwide horizontally aligned readout strips with a pitch of 1.25 cm. The measured x position is obtained by the timedifference measured between the ends of one strip. The resolution is 0.6 cm. Together with the position informationfrom the GEM, tracks are reconstructed along the arms and the time-of-flight information is taken from the RPCsystem. The clustering algorithm was applied to the neighboring strips fired in the same event. In addition, each armwas equipped with two trigger counters (TC), scintillator planes close to the target. The X planes consisted of twoscintillators with dimensions of 30 cm x 15 cm x 0.5 cm located vertically side by side and read out by a Hamamatsu7724 PMT each. The distance between the target center and the X-counters was 42 cm. Each Y plane was a singlescintillator piece of 50 cm x 50 cm x 2 cm, read out by two ET9954KB PMTs. The distance between the target centerand the Y planes was 170 cm. Each arm covers a solid angle of 0.06 sr, limited by the RPC acceptance. Data Acquisition System (DAQ) and Triggers:
The DAQ performs readout of the front-end electronics ofthe BM@N detectors event-by-event based on the information of the trigger system [52]. Timing information wereread out from DCH and RPC (two-edge time stamp) and processed by Time to Digital Converters (TDC) based onHPTDC chip with typical accuracy of 20 ps for RPC and 60 ps for DCH. The amplitude information were read outfrom coordinate detector systems of Si and GEMs and processed by Amplitude to Digital Converters (ADC). The last30 µ s of waveforms were read back. The clock and time synchronization was performed using White Rabbit protocol.As mentioned in the main text, the reaction trigger was set up requesting an incoming ion in coincidence with signalsin the left and right arm trigger scintillator-counters (TC). Additional triggers are built from coincident signals inthe various scintillator detectors, suited for either calibration purposes or data taking. The trigger matrix is shownin Table I, creating the so-called Beam trigger, and the physics triggers AndSRC and OrSRC. The input signals areBC1, BC2, and no veto signal (!V-BC). The coincidence condition AndXY requires signals in all TCs in the left andright arm, while OrXY takes the OR between the left and right arm of the spectrometer. The physics data weretaken requesting the AndSRC trigger at a rate of about 180 Hz as measured during a beam pulse duration, allowinga livetime close to 100%. Supplementary Table I. | Trigger matrix.
Different coincidence triggers for collecting the data.Trigger BC1 BC2 !V-BC AndXY OrXYBeam x x xAndSRC x x x xOrSRC x x x x
2. Fragment momentum calculation
Trajectories of charged particles are bent in the large analyzer magnetaccording to their magnetic rigidity Bρ , i. e. momentum-over-charge ratio Bρ = P/Q with charge Q . This allows todetermine the fragment total momenta.For this purpose, simulations of the fragments, propagating in the magnetic field, were carried out using thefield map of the magnet. The corresponding materials of the beam-line detectors were also implemented in thesimulation. The simulated fragments were chosen to have the maximum possible position, angular and momentumspread to cover the entire geometrical acceptance of the magnet and detectors. The output of the simulation is usedafterwards as a training sample for the multidimensional fit (MDF) algorithm [53] in the form of n-tuples whichhold positions and angles of the fragment trajectory upstream and downstream of the magnet: ( x , y , z , α x , α y ) and( x , y , z , β x , β y ) respectively. Performing MDF over the training sample yields an analytical fit function P/Z mdf = f ( x , y , z , α x , α y , x , y , z , β x , β y ), which can be applied to the positions and angles measured in the experiment.In a similar way, a second MDF function for α x angle was derived as α mdfx = g ( x , y , z , α y , x , y , z , β x , β y ). Thisfunction is used for the track-matching condition ( α mdfx − α x )=min, which allows to determine whether the tracks inupstream and downstream detection systems belong to the same global track through the magnet.Having determined the two functions, α mdfx and P/Z mdf , experimental data for the reference trajectory of unreacted C is used to adjust the input variables’ offsets, which reflect the alignment of the real detectors in the experimentalsetup with respect to the magnetic field. This is achieved by variation of the offsets in the experimental input5 α x mdf α x − − (a) BM@N − − C oun t s α x mdf - α x SignalBGSignal+BG (b) BM@N
Supplementary Fig. 1. | Track matching. (a) Correlation between α x angle measured upstream of the magnet and the α mdfx reconstructed by the MDF for unreacted C beam . (b) Residual distribution α mdfx − α x fit with a Gaussian peak andwider underlying contribution (“BG” as second order polynomial). variables simultaneously for α mdfx and P/Z mdf until the residual between
P/Z mdf and its reference value is minimal.The reference value is chosen to be the
P/Z of unreacted C at the exit of the liquid-hydrogen target. Usingthis approach a total-momentum resolution of 0.78 GeV/c for C is achieved, as estimated with the empty targetdata, consistent with the resolution limits of the detection systems, see Fig. 2. The same momentum resolution wasobtained for unreacted C events, analyzed under the same conditions but with LH target inserted. A width of σ = 0 .
78 GeV/c was measured with a reduced beam momentum of 47.6 GeV/c due to energy loss in the target andadditional straggling. The achieved momentum accuracy is evaluated from simulation to be 0.2%.Figure 1 shows the performance of the second MDF function for α x . A global track is constructed when thereconstructed α mdfx falls within the 5 σ gate indicated. In the analysis, only events with one heavy global track, whichcombines the up- and downstream detectors, are considered (if not stated differently). To ensure that real detectedsingle-track events are selected, a matching between the upstream and DCH angle in y direction is applied togetherwith the above explained x-angle matching, also in a 5 σ selection from their residual. Additionally, a single track inthe DCH, the one reconstructed track from DCH1 and DCH2, is required.The fragment tracking efficiency is (39 . +1 . − . )%, obtained for an empty target run and given with respect to theincoming and outgoing Z = 6 ion. This tracking efficiency includes the involved detector efficiencies, as well as thereconstruction and matching efficiency of good single tracks. We define the tracking efficiency for C as ratio ofevents, incoming carbon C in vs. carbon downstream the target C out , with (cid:15) track = C out C in = Z in = 6)&( Z eff = 6) Z in = 6)&( Z eff = 6) , (1)where a ”good track” is defined by • Tracks in one of the upstream detector systems and in DCH. • Exactly one reconstructed matched global track based on the combined information from upstream detectorsand DCH as explained above. • A “good”
P/Z value: for C out the P/Z value is expected to be centered around 7.98 GeV/c (for beammomentum of 47.9 GeV/c), cf. Fig. 2. The number of C events corresponds to the integral in a ± . σ range of P/Z , as applied on average for the fragment selection. The uncertainty to the tracking efficiency isdetermined from a (2 . ± . σ range which reflects the range in P/Z selection for the different fragments ofinterest. In addition, we consider a systematic uncertainty coming from possible remaining wide tails in the
P/Z distribution described by a second order polynomial. The signal-to-noise ratio is 10.0. That contributioncreates an asymmetric uncertainty in the efficiency, considered on the 2 σ level (cf. Fig. 2). This systematic6
42 44 46 48 50 52 540100200300400500600 h_mom C oun t s p [GeV/c] -2.2 σ +2.2 σ S/N = 10.02Signal BM@NBGSignal+BG
Supplementary Fig. 2. | Fragment-momentum resolution.
Total momentum for C measured with empty target,fitted with a Gaussian and possible underlying contribution (“BG”). The signal-to-noise ratio
S/N is 10.0. uncertainty is considered in the same way for the quasielastic event yield, fitting the
P/Z for the different chargeselections.Table II lists the different contributions to the extracted efficiency.
Supplementary Table II. The different contributions to the tracking efficiency.
Good track (cid:15) track (%) Z in = 6 , Z eff = 6 100Upstream track 98DCH track 93Upstream and DCH tracks 91Global track 70Good P/Z The tracking efficiency is reduced from 91% to 70% due to the MDF algorithm with the applied matching criteriain x angle and a reconstructed single global track. That event sample is further cleaned up requiring a single track inthe DCH itself, and additional angular matching condition in the y direction (non-bending direction). See discussionabove. Together with our analysis selection cuts of a good
P/Z , the efficiency equals 40%. The reaction probabilityfrom in-beam material downstream the target was estimated to be smaller 5% and thus contributes only a smallfraction in fragment misidentification. We estimated the uncertainty for B isotopes and Be identification using theexperimental data. We looked at the fraction of , B ( Be) from events with Z eff = 5 ( Z eff = 4). Z eff = 5 aredominated by B or B. We varied the fragment identification cuts to check the sensitivity of this fraction. Thisresulted in a very similar uncertainty as for C, and therefore we adapt the same uncertainty. Z eff = 4 events areassociated with several Be isotopes, or a combination of lighter fragments. In this case, to evaluate the uncertainty,we looked at the fraction of Be from events with Z eff = 4, and changed the identification cuts to evaluate thesensitivity. This resulted in ∼
15% difference (as opposed to 5% for C and B). Therefore, for Be, we consider (cid:15) track = (39 . +5 . − . )%. For the overall fragment identification efficiency an additional (83 ±
3. Reaction-vertex reconstruction
The reaction vertex is reconstructed whenever one track is reconstructed ineach arm of the TAS. This requires at least one hit in the GEM and RPC systems to form a linear track in eacharm. We consider only single-track options from the hit combinations. The coincident two tracks that come closest,formed from all possible hit combinations, determine the vertex position along the beam line in the z direction.Alignment procedures within the GEM-RPC system, the left and right arm, as well as relative to the incoming beamare applied. The initial detector positioning relied on a laser-based measurement, the alignment relative to the other7 − z C oun t s BM@N
Supplementary Fig. 3. | TAS vertex.
Vertex in z direction for 3 Pb foils at the target position to determine the positionresolution of the vertex reconstruction. The position resolution is 1.8 cm (1 σ ), the fit is shown by the red line (plus background).The dashed black lines indicate the absolute position alignment at z = ±
15 cm and zero. − − − C oun t s t meas − t γ [ns] p1 β p2 β (b) (a) BM@N Supplementary Fig. 4. | TAS timing. (a) Result of RPC ToF calibration, γ peak arising in subtracted spectrum for Pbtarget runs with and without Pb sheets directly in front of RPC. The extracted ToF resolution is 175 ps (1ß , σ ). (b) Basicvelocity condition to select protons, the velocity cut in the left and right arm are indicated by the red lines. detector systems and the beam using experimental data was done as mentioned before. The quality of the tracksis selected according to their minimum distance, a selection criteria of better than 4 cm is applied in this analysis.Given the smaller angular coverage of the RPC system compared to the GEMs and detector inefficiencies, the trackreconstruction efficiency is 40%, with an RPC detection efficiency of about 85%.The position resolution in z was determined by placing three Pb foils separated by 15 cm at the target position.The reconstructed vertex position is shown in Fig. 3, clearly three distinct peaks at a distance of 15 cm representingthe Pb foils are reproduced. Given the width of each peak, the z -position resolution from the two-arm spectrometeris on average 1.8 cm (1 σ ). Knowing the vertex and the track position in the RPC, the flight length is determined.
4. ToF calibration and proton momentum reconstruction resolution.
The time-of-flight (ToF) calibrationfor the RPC is done by measuring gamma rays emitted from interactions with a single-foil Pb target. A 9 mm thicksingle Pb target was installed at the center position of the LH target. In addition, a thin lead sheet was placeddirectly in front of the RPCs to convert gammas to charged particles. Measurements were done with and withoutthe RPC lead sheet and the difference in the measured ToF spectrum for the two measurements was used to isolate8gamma rays events. The subtracted ToF spectrum is shown in Fig. 4a, presenting a total ToF resolution (includingthe t resolution) of 175 ps. Together with the time-of-flight that is measured between the start counter BC2 and theRPC, the total proton momentum can be determined. For a 2 GeV/c proton this corresponds to ∆ToF / ToF ∼ . ∼
60 MeV/c for the missingmomentum from the two protons in the C rest frame.Fig. 4b shows the β distribution of measured charged particles in the TAS with the initial velocity selection cut of0 . < β < ..