Extending the Southern Shore of the Island of Inversion to 28 F
A. Revel, O. Sorlin, F.M. Marques, Y. Kondo, J. Kahlbow, T. Nakamura, N.A. Orr, F. Nowacki, J.A. Tostevin, C.X. Yuan, N.L. Achouri, H. Al Falou, L. Atar, T. Aumann, H. Baba, K. Boretzky, C. Caesar, D. Calvet, H. Chae, N. Chiga, A. Corsi, H. L. Crawford, F. Delaunay, A. Delbart, Q. Deshayes, Z. Dombradi, C. A. Douma, Z. Elekes, P. Fallon, I. Gasparic, J.-M. Gheller, J. Gibelin, A. Gillibert, M. N. Harakeh, W. He, A. Hirayama, C.R. Hoffman, M. Holl, A. Horvat, A. Horvath, J.W. Hwang, T. Isobe, N. Kalantar-Nayestanaki, S. Kawase, S. Kim, K. Kisamori, T. Kobayashi, D. Korper, S. Koyama, I. Kuti, V. Lapoux, S. Lindberg, S. Masuoka, J. Mayer, K. Miki, T. Murakami, M. Najafi, K. Nakano, N. Nakatsuka, T. Nilsson, A. Obertelli, F. de Oliveira Santos, H. Otsu, T. Ozaki, V. Panin, S. Paschalis, D. Rossi, A.T. Saito, T. Saito, M. Sasano, H. Sato, Y. Satou, H. Scheit, F. Schindler, P. Schrock, M. Shikata, Y. Shimizu, H. Simon, D. Sohler, L. Stuhl, S. Takeuchi, M. Tanaka, M. Thoennessen, H. Tornqvist, Y. Togano, T. Tomai, J. Tscheuschner, J. Tsubota, T. Uesaka, Z. Yang, M. Yasuda, K. Yoneda
aa r X i v : . [ nu c l - e x ] A p r Extending the Southern Shore of the Island of Inversion to F A. Revel, O. Sorlin, F.M. Marqués, Y. Kondo, J. Kahlbow,
4, 5
T. Nakamura, N.A. Orr, F. Nowacki,
6, 7
J.A. Tostevin, C.X. Yuan, N.L. Achouri, H. Al Falou, L. Atar, T. Aumann,
4, 11
H. Baba, K. Boretzky, C. Caesar,
4, 11
D. Calvet, H. Chae, N. Chiga, A. Corsi, H. L. Crawford, F. Delaunay, A. Delbart, Q. Deshayes, Z. Dombrádi, C. A. Douma, Z. Elekes, P. Fallon, I. Gašparić,
17, 5
J.-M. Gheller, J. Gibelin, A. Gillibert, M. N. Harakeh,
11, 16
W. He, A. Hirayama, C.R. Hoffman, M. Holl, A. Horvat, Á. Horváth, J.W. Hwang, T. Isobe, N. Kalantar-Nayestanaki, S. Kawase, S. Kim, K. Kisamori, T. Kobayashi, D. Körper, S. Koyama, I. Kuti, V. Lapoux, S. Lindberg, S. Masuoka, J. Mayer, K. Miki, T. Murakami, M. Najafi, K. Nakano, N. Nakatsuka, T. Nilsson, A. Obertelli, F. deOliveira Santos, H. Otsu, T. Ozaki, V. Panin, S. Paschalis, D. Rossi, A.T. Saito, T. Saito, M. Sasano, H. Sato, Y. Satou, H. Scheit, F. Schindler, P. Schrock, M. Shikata, Y. Shimizu, H. Simon, D. Sohler, L. Stuhl, S. Takeuchi, M. Tanaka, M. Thoennessen, H. Törnqvist, Y. Togano, T. Tomai, J. Tscheuschner, J. Tsubota, T. Uesaka, Z. Yang, M. Yasuda, and K. Yoneda (SAMURAI21 collaboration) Grand Accélérateur National d’Ions Lourds (GANIL),CEA/DRF-CNRS/IN2P3, Bvd Henri Becquerel, 14076 Caen, France LPC Caen, ENSICAEN, Université de Caen, CNRS/IN2P3, F-14050 CAEN Cedex, France Department of Physics, Tokyo Institute of Technology,2-12-1 O-Okayama, Meguro, Tokyo 152-8551, Japan Institut für Kernphysik, Technische Universität Darmstadt, 64289 Darmstadt, Germany RIKEN Nishina Center, Hirosawa 2-1, Wako, Saitama 351-0198, Japan Université de Strasbourg, IPHC, 23 rue de Loess 67037 Strasbourg, France CNRS, UMR7178, 67037 Strasbourg, France Department of Physics, University of Surrey, Guildford, Surrey GU2 7XH, United Kingdom Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-Sen University, Zhuhai 519082, China Lebanese University, Beirut, Lebanon GSI Helmholtzzentrum für Schwerionenforschung, 64291 Darmstadt, Germany Irfu, CEA, Université Paris-Saclay, 91191 Gif-sur-Yvette, France IBS, 55, Expo-ro, Yuseong-gu, Daejeon, Korea, 34126 Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA Institute of Nuclear Research, Atomki, 4001 Debrecen, Hungary KVI-CART, University of Groningen, Zernikelaan 25, 9747 AA Groningen, The Netherlands Ruđer Bošković Institute, HR-10002 Zagreb, Croatia Physics Division, Argonne National Laboratory, Argonne, Illinois 60439, USA Eötvös Loránd University, Pázmány Péter Sétány 1/A, H-1117 Budapest, Hungary Department of Physics and Astronomy, Seoul National University,1 Gwanak-ro, Gwanak-gu, Seoul 08826, Republic of Korea Department of Advanced Energy Engineering Science,Kyushu University, Kasuga, Fukuoka, 816-8580 Japan Department of Physics, Tohoku University, Miyagi 980-8578, Japan Unversity of Tokyo, Tokyo 1130033, Japan Institutionen för Fysik, Chalmers Tekniska Högskola, 412 96 Göteborg, Sweden Center for Nuclear Study, University of Tokyo, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan Institut für Kernphysik, Universität zu Köln, 50937 Köln, Germany National Superconducting Cyclotron Laboratory,Michigan State University, East Lansing, Michigan 48824, USA Department of Physics, Kyoto University, Kyoto 606-8502, Japan Department of Physics, Osaka University, Osaka 560-0043, Japan (Dated: April 3, 2020)Detailed spectroscopy of the neutron-unbound nucleus F has been performed for the first timefollowing proton/neutron removal from Ne/ F beams at energies around 230 MeV/nucleon. Theinvariant-mass spectra were reconstructed for both the F ( ∗ ) + n and F ( ∗ ) + 2 n coincidences andrevealed a series of well-defined resonances. A near-threshold state was observed in both reactionsand is identified as the F ground state, with S n ( F ) = − keV, while analysis of the n decaychannel allowed a considerably improved S n ( F ) = 1620(60) keV to be deduced. Comparison withshell-model predictions and eikonal-model reaction calculations have allowed spin-parity assignmentsto be proposed for some of the lower-lying levels of F. Importantly, in the case of the ground state,the reconstructed F + n momentum distribution following neutron removal from F indicates that it arises mainly from the p / neutron intruder configuration. This demonstrates that the island ofinversion around N = 20 includes F, and most probably F, and suggests that O is not doublymagic.
PACS numbers:
Introduction.—
The study of nuclei located at the neu-tron dripline, beyond which they are no longer boundwith respect to neutron emission, has become possibledue to significant technological developments in high-intensity neutron-rich beams and high-efficiency detec-tion arrays [1]. Despite these advances, the neutrondripline is only accessible experimentally for light nuclei( Z . ) [2], and even in this region it remains a theoret-ical challenge to predict it [3]. Models incorporating theeffect of three-nucleon forces [4–6] have led to a betterreproduction of the dripline. However, the effect of thecontinuum, which can drastically change the shell struc-ture [7, 8], is not taken into account except for lighternuclei [9]. The comparison between the isotopic chainsof carbon, nitrogen and oxygen on the one hand, andof fluorine on the other, is particularly interesting: thedripline is located at N = 16 for the former, while thefluorine chain extends to N = 22 ( F [2]). The reasonfor this, however, is not fully understood.In the fluorine chain, the odd neutron-number , Fisotopes are unbound, as they lack the extra binding en-ergy provided by pairing. Christian et al. [10] found that F is unbound by 220(50) keV, and based on the agree-ment with the predictions of USDA/USDB shell-modelcalculations F was placed outside the “Island of Inver-sion” (IoI) [11]. This means that the ground state of F could be described by a particle-hole configuration( π d / × ν d − / ) with respect to an unbound core of O, forming a multiplet of J π = 1 + – + states as in F[12, 13]. On the other hand, the relatively low energies ofthe first excited states in , F suggest the presence ofintruder neutron pf -shell contributions [14]. If F con-tains such contributions, negative-parity states, like the J π = 1 − – − multiplet resulting from the π d / ⊗ ν p / coupling, should appear at low energy.The location of the dripline in fluorine at N = 22 sug-gests a profound change in shell structure around doubly-magic O [15–17]. A direct experimental signature ofthese structural changes can be found in the evolution ofthe energies of the / + , / − and / − states, arisingfrom the neutron d / , f / and p / orbits, in the N = 17 isotones from Z = 14 to 10 (Fig. 3 of [18]). In Si, the spacing between the ground / + and the / − states, which is linked to the size of the N = 20 gap, is3.2 MeV, and the / − state lies 0.5 MeV above the / − .In Ne, the / + – / − gap is reduced to 2 MeV, and the / − level moves below the / − state, at only 0.8 MeVabove the / + g.s. [19–21]. In Ne, the / − intruderstate becomes the ground state [22]. This migration oflevels has been suggested to be due to the hierarchy of the p - n forces present above O [18], and in particularto the central and tensor components [23–25].This Letter reports on the first detailed spectroscopicstudy of F, which has been carried out using proton andneutron removal from high-energy Ne and F beams,respectively. In the former reaction, the Ne neutronconfiguration will remain unchanged and negative-paritystates are expected to be populated at low energy in Fthrough the removal of a d / proton. Neutron removal,however, can lead to both positive- and negative-paritylevels in F depending on the degree to which intruder( p h and beyond) configurations are present in F. Thisstudy was possible owing to the high luminosity providedby a thick liquid H target and the relatively intense sec-ondary beams, coupled with state-of-the-art arrays forthe detection of the high-energy neutrons and chargedfragments and of the de-excitation γ -rays. The resultsindicate that F, and most probably F, lie within theIoI, and also suggest that O is not doubly magic.
Experimental setup.—
The experiment was performedat the Radioactive Isotope Beam Factory (RIBF) ofthe RIKEN Nishina Center. Secondary beams of Ne( ∼ . kHz, 228 MeV/nucleon) and F ( ∼ Hz,235 MeV/nucleon) were produced by fragmentation ofa 345 MeV/nucleon Ca beam ( ∼ pnA) on a 15mm-thick Be target, and prepared using the BigRIPS frag-ment separator [26, 27]. Secondary beam particles wereidentified via their energy loss and time of flight as mea-sured using thin plastic scintillators, and tracked on tothe object point of the SAMURAI spectrometer [28] us-ing two sets of multi-wire drift chambers, where theMINOS target [29] was located. The latter consisted ofa 15cm-thick liquid-hydrogen cell surrounded by a time-projection chamber, that allowed the reconstruction ofthe reaction vertex with a precision of 3 mm (sigma) inthe beam direction using the intersection between the tra-jectory of the incoming beam and the measured track(s)of the outgoing proton(s) for the ( p, pn ) and ( p, p ) reac-tions. The DALI2 NaI array [30] surrounded the targetfor the detection of the in-flight de-excitation of frag-ments (with an efficiency of ε γ ∼ at 1 MeV).The beam-velocity reaction products were detected inthe forward direction using the SAMURAI setup, includ-ing the NEBULA [31] and NeuLAND demonstrator [32]neutron arrays, placed respectively some 14 and 11 mdownstream of the target. The SAMURAI superconduct-ing dipole magnet [33], with a central field of 2.9 T and avacuum chamber equipped with thin exit windows [34],provided for the momentum analysis of the charged frag-ments. Their trajectories and magnetic rigidity were de- ) (MeV) n F+ ( rel E C oun t s × ( ) ( ) ( ) ( ) ( ) ( ) (b) x100 1 2 3 4 5 C oun t s × ( ) ( ) ( ) ( ) ( ) (a) ( ) x10 ) (MeV) n F+ ( rel E × (d) ( ) ( ) F) (MeV) ( γ E × × × (c) -gated γ ( ) F) (MeV) ( γ E × × ) (MeV) n F+2 ( rel E × (f) ( ) ( ) ( ) ( ) ) n − F ( × (e) ( ) ( ) ( ) ( ) ( ) ( ) E(MeV) ) p − N e ( FIG. 1: Left: relative-energy spectra of the F + n system populated from the reactions (a) Ne( − p ) and (b) F( − n ).Right: same for the F +2 n system populated from (e) Ne( − p ) and (f) F( − n ). The fit in red corresponds to a sum ofresonances (blue, with the resonance energy in keV) plus a non-resonant distribution (dashed black). Center: same as left,obtained in coincidence with the 915 keV excited state of F (after background subtraction) populated from (c) Ne( − p )and (d) F( − n ). The energy axis E on the top right is given with respect to S n ( F), and orange dots mark resonances incoincidence with the corresponding fragment γ -rays (see Fig. 2). termined using drift chambers at the entrance and exit ofthe magnet [28]. This information, combined with the en-ergy loss and time of flight measured using a 24-elementplastic scintillator hodoscope, provided the identificationof the projectile-like fragments. The neutron momentawere derived from the time of flight, with respect to athin plastic start detector positioned just upstream ofthe target, and the hit position as measured using theNEBULA and NeuLAND arrays [35], with efficiencies of ε n ∼ and ε nn ∼ for decay energies of 0–3 MeV. Energy spectra.—
The relative energy ( E rel ) of the un-bound F system was reconstructed from the momentaof the , F fragments and neutron(s) [35]. The F+ n spectra for both reactions are shown on the left of Fig. 1.The resolution is considerably improved compared to pre-vious studies of neutron-unbound systems [10, 36], owingto the high-granularity NeuLAND array as well as theMINOS target. The resolution of E rel ( F+ n ) varied as fwhm ∼ . E . rel MeV. In order to deduce the charac-ter of resonances in F, the spectra were described usingsingle-level R-matrix line-shapes [37], which were used asthe input for a complete simulation of the setup (includ-ing the beam characteristics, the reaction, and the detec-tor resolutions and acceptances), combined with a non-resonant component obtained from event-mixing [38, 39]and from the simulation of independent fragments andneutrons, respectively for the two- and three-body spec-tra. The results of the fit are listed on the figure andsummarized in Ref. [40].The energy spectra of Fig. 1(a,b), from the Ne ( − p ) and F ( − n ) reactions, exhibit a lowest-lying resonancewith a width of Γ = 180(40) keV at respectively 204(16)and 198(6) keV above threshold, without any coincident γ -ray. The weighted mean, keV, provides there-fore a determination of the g.s. energy of F ( − S n ). Thisis compatible with the less precise value of 220(50) keVfrom Ref. [10] using the Ne ( − p ) reaction. As shownin Fig. 1(a), we observe a second peak in the ( − p ) channel at 363(17) keV, which is in coincidence with the915(12) keV transition (inset of Fig. 1c) from the decayof the excited state of F [14]. As such, the resonancelies at the sum energy of 1278(21) keV above threshold.As this value matches the energy of the fourth peak at1280(30) keV, we propose that the 1280 keV state, popu-lated in Ne ( − p ) , decays both to the ground and first-excited states of F, with corresponding branching ratiosof 60% and 40%. The 2810 keV resonance is also observedin coincidence with the 915 keV γ -ray. It is thus placed atan energy of 3725 keV (Fig. 2). Three other resonancesidentified in Fig. 1(a) at 940, 1840 and 3660 keV are alsoplaced in Fig. 2.The spectrum of Fig. 1(b), obtained from F ( − n ) ,displays three clear resonances, including the g.s. (seeabove). The resonance at 996(13) keV does not fullymatch the 940(20) keV observed in the ( − p ) reaction.We thus propose that they correspond to two differ-ent states, as shown in Fig. 2. Given the uncertain-ties, the 1880(80) and 1840(30) keV resonances observedin both reactions can correspond to the same state.If we require a coincidence with the 915 keV γ -ray of F, one can see in Fig. 1(d) the two resonances at406(28) and 3180(260) keV plus an additional structureat 1200(80) keV, corresponding therefore respectively tolevels at 1321, 4095 and 2115 keV (Fig. 2). Note that the406(28) keV resonance overlaps with that at 363(17) keV,which was proposed to decay in competition with the1280(30) keV transition in the ( − p ) channel with simi-lar intensities. However, as the fit of the ( − n ) data doesnot allow the placement of a 1280(30) keV resonance withthe required intensity, we propose that the 363(17) and406(28) keV transitions come from the decay of differentstates located respectively at 1280 and 1321 keV. Finallya resonance is placed at 3980 keV.Resonances in F decaying by n emission have beenidentified after applying cross-talk rejection conditions tothe F +2 n events [41]. As can be seen in Fig. 1(e,f), thelowest-lying peak produced in both the ( − p ) and ( − n ) reactions has compatible energies of respectively E rel =245(32) and 227(88) keV. The states observed in the n decay correspond to excitation energies of E rel + S n ( F),when referenced to the F g.s., or to an excitation energyof E rel + S n ( F). According to AME2016 [42], the un-certainty on S n ( F ) = 1270(410) keV is large, which alsoinfluences the present determination of S n ( F), makingthe placement of the resonances very uncertain.However, we first note that the two low-energy res-onances are, as for the 1840 and 1880 keV resonancesin the F + n decay, produced in both reactions. Sec-ond, they have compatible intrinsic widths [40], indepen-dent of the decay mode. Third, the ratios between the245 and 1840 keV resonances in ( − p ) , and the 227 and1880 keV resonances in ( − n ) , are the same ( ∼ ).This suggests that they all originate from a single stateat ∼ keV, that decays both by n and n emis-sion. Excellent agreement between the n and n decayspectra is obtained using S n ( F ) = 1620(60) keV and S n ( F ) = 1420(60) keV, the latter being deduced fromthe present determination of S n ( F). A summary of allthe levels identified is reported in Fig. 2.
Momentum distributions.—
In the ( − n ) reaction, thereconstructed momentum distribution of the F + n sys-tem allows the orbital angular momentum of the removedneutron to be deduced [44]. The transverse-momentumdistribution corresponding to the feeding of the F g.s. isfitted in Fig. 3(a) with eikonal-model calculations [45, 46]using a combination of ℓ = 1 , components. This choiceof negative-parity ℓ values is guided by the fact that theg.s. is also produced in the Ne ( − p ) reaction, which, asdiscussed earlier, is expected to lead to negative-paritystates at low E rel . The fit, which gives a spectroscopicfactor of C S = 0 . , is dominated by the ℓ = 1 com-ponent ( ), meaning that the g.s. of F is mainlycomposed of an intruder p -wave component.The momentum distribution of the resonance at406 keV, Fig. 3(b), is obtained after gating on the 915 keV γ -ray transition. It is well reproduced by a pure ℓ = 2 E ( M e V ) S n ( F ) (4 − ) 0.204(2 − ) 0.940(1 − ) 1.280(3 − ) 1.840 1.8692.754 .
608 3 .
648 3 .
761 4 . . . (4 − ) 0.198(3 + ) 0.996(1 + ) 1.321 1.8512.1151.880 3.0463.727 . . − + − + + − + − + + + − − + − − − − − − + − − + − − + − + − + − − + − + + + − − − + + +29 Ne(–1 p ) F(–1 n ) sdpf-u-mix sdpf-mu FIG. 2: Energies of the resonances observed in F in the n (black) and n (blue) decay channels compared to shell-modelcalculations (the g.s. energies are normalized to experiment).The resonances observed in the n channel are placed in thelevel scheme according to S n ( F ) = 1 . MeV (see text).The grey and blue bands represent the uncertainty in theresonance energies. Levels with an orange dot decay to excitedstates of F ( n decay) or F ( n decay). component, meaning that the parity of the 1321 keV stateis positive, with C S = 0 . . In order to account forits highly favored n decay through the (1 / + ) excitedstate of F, rather than to the (5 / + ) g.s. despite thehigher energy available, we propose that it has J π = 1 + .Indeed, this would result in an ℓ = 0 neutron decay to theexcited state, as opposed to an ℓ = 2 decay to the groundstate. Other (higher) spin values would not account forsuch a unique behavior. For the resonance at 996 keV,the momentum distribution, Fig. 3(c), is very well repro-duced by an admixture of ℓ = 2 ( ) and ℓ = 0 ( ),making it another candidate for a positive-parity state,with C S = 0 . .As for the ( − p ) reaction, the four most populatedstates, with energies 204, 940, 1280 and 1840 keV, alldisplay momentum distributions compatible with ℓ = 2 proton removal from the d / orbital, with C S of re-spectively 0.20(3), 0.46(7), 0.50(8) and 0.22(4), summingup to about 1.4, as compared to the maximal expectedoccupancy of 2 for the d / orbital in Ne.
Shell-model calculations.—
These have been performedusing the sdpf-u-mix interaction [54] in order to predictthe energy, J π (Fig. 2, right) and C S values of negative-and positive-parity states in F. In order to assess thesensitivity to the level scheme, the sdpf-mu interaction[55] has also been used. The sdpf-u-mix interaction hasbeen refined in order to reproduce the observed / − and / − level crossing and location of the pf intruder (MeV/c) x P − Y i e l d ( a . u . ) =198keV rel (a) E (MeV/c) x P − Y i e l d ( a . u . ) =406keV rel (b) E (MeV/c) x P − Y i e l d ( a . u . ) =996keV rel (c) E FIG. 3: Experimental transverse-momentum distributions ofthe F + n system following the F ( − n ) reaction comparedto eikonal-model calculations for: (a) removal of a neutronwith ℓ = 1 , (respectively blue, brown lines) for the g.s. at E rel = 198 keV; (b) a pure ℓ = 2 distribution for the resonanceat 406 keV (corresponding to the state at 1321 keV); (c) amixture of ℓ = 0 , (respectively purple, green lines) for thestate at E rel = 996 keV. In (a,c) the red line is the total fit. orbitals in Ne, Mg and Si, and the dripline at F.Both calculations predict about 15 negative- andpositive-parity states below 2 MeV, demonstrating thatthe normal and intruder configurations in F are veryclose in energy. The first 10 states have relatively pureconfigurations (60–80%) mostly originating from the pro-ton d / and neutron d / and p / orbits, with theexception of the − and − levels that arise from aneutron in the f / orbit. The π d / ⊗ ν p / and π d / ⊗ ν d / couplings lead to a multiplet of J = 1 –4states with negative and positive parity, respectively.The calculations predict that four negative-paritystates J π = (4 , , , − are mainly populated in the ( − p ) reaction with dominant ℓ = 1 components and C S values of 0.75, 0.44, 0.35 and 0.19, in rather goodagreement with experiment. We thus think we have pop-ulated this multiplet of states. Among them, a J π = 4 − g.s. is predicted by both calculations, with Γ of about180 keV, in agreement with experiment. Using similararguments, the 940 keV state is proposed to be J π = 2 − .The − level is predicted to decay both to the ground( / + ) and first-excited ( / + ) states of F with ℓ = 1 ,and could correspond to the state identified at 1280 keV.As it has the highest energy in both calculations, the1840-keV resonance is tentatively assigned as J π = 3 − .In the ( − n ) reaction, the − g.s. is calculated to be themost populated among other negative-parity states with C S = 0 . , coming mostly (90%) from an ℓ = 1 removal,to be compared with C S = 0 . , with 79% of ℓ = 1 fraction. As for the positive-parity states, produced onlyin the ( − n ) reaction, both the sdpf-u-mix interactionpredicts the lowest state as J π = 3 + with C S = 0 . , inreasonable agreement with the 996 keV state with C S =0 . . The + state is predicted to decay principallyto the first excited state of F with ℓ = 0 , making the1321 keV state a good J π = 1 + candidate. The calculated C S value of the + state, 0.31, is however much largerthan experiment. The first positive-parity states are predicted too low inenergy, which could be explained by effects of the con-tinuum (not taken into account explicitly in the presentcalculations) that change the effective two-body matrixelements [13, 56] and induce lingering of the ℓ = 1 statescompared to ℓ = 2 [8]. Another feature that could be re-lated to the effects of the continuum, discussed in Ref. [7]as an apparent reduction of pairing, is the damping ofthe | S n ( N ) − S n ( N + 1) | amplitude when approachingthe dripline. While these amplitudes are correctly repro-duced in lighter ( N ) fluorine isotopes by the presentcalculations, our experimental S n ( F ) − S n ( F) valueof 1.82(6) MeV is significantly smaller than the predicted2.8 MeV.
Conclusions.—
In summary, detailed spectroscopy of F has been undertaken using nucleon removal from sec-ondary beams of F and Ne, with statistics ordersof magnitude higher than the previous study and un-precedented energy resolution. This was made possiblethrough the unique combination of a thick liquid tar-get and state-of-the-art arrays for the detection of high-energy neutrons and charged fragments, as well as de-excitation γ -rays. They proved essential to cope withthe high density of states in F and allowed the identi-fication of the n and n decay modes, including tran-sitions to bound excited states of , F. In addition tomaking comparisons with shell-model calculations, the F transverse-momentum distributions following neu-tron removal, combined with eikonal-model calculations,allowed the ℓ configuration of the removed neutron to bededuced.The F g.s. resonance was unambiguously identified,with S n ( F ) = − keV. It has a negative paritywith an ℓ = 1 content of about 80%, which places Finside the IoI. Based on the comparison to shell-modelcalculations of the decay patterns, resonance widths and C S values, we propose that the multiplet of J π = (1 – − states originating from the π d / ⊗ ν p / configu-ration has been identified. The first positive-parity reso-nance ( + ) is proposed at 996 keV, about 560 keV higherthan shell-model predictions. A candidate for a J π = 1 + resonance is proposed at 1321 keV. As opposed to F,that has well-identified positive-parity states from p - n configurations above a doubly-magic O core, F dis-plays mixed negative- and positive-parity states, with thenegative-parity states being more bound. These featuresstrongly suggest that N = 20 magicity is not restoredat O. Moreover, the single-neutron removal, includingthe strong ℓ = 1 feeding of the negative-parity F g.s.,supports the suggestion, based on mass measurements,that F also lies within the IoI [57].Finally, we propose a very precise value of S n ( F ) =1620(60) keV, as compared to the tabulated valueof keV, which combined with S n ( F ) = − keV leads to a reduced oscillation in the S n val-ues of about 35% at the dripline, as compared to shell-model calculations. This damping in the oscillations hasalso been recently observed in the boron isotopic chain[39], suggesting that a reduced pairing force may be ageneric feature of dripline nuclei.We thank M. Ploszajczak for fruitful discussions, andthe accelerator staff of the RIKEN Nishina Center fortheir efforts in delivering the intense Ca beam. N.L.A.,F.D., J.G., F.M.M. and N.A.O. acknowledge partial sup-port from the Franco-Japanese LIA-International Associ-ated Laboratory for Nuclear Structure Problems as wellas the French ANR-14-CE33-0022-02 EXPAND. J.A.T.acknowledges support from the Science and TechnologyFacilities Council (U.K.) grant No. ST/L005743/1. I.G.was supported by HIC for FAIR and Croatian ScienceFoundation under projects No. 1257 and 7194. Z.D.,Z.E. and D.S. were supported by projects No. GINOP-2.3.3-15-2016-00034 and K128947, and I.K. by projectNo. PD 124717. J.K. acknowledges support from RIKENas short-term International Program Associate. This ma-terial is based upon work supported by the U.S. De-partment of Energy, Office of Science, Office of Nu-clear Physics, under contract No. DE-AC02-06CH11357(ANL). This project was funded in part by the DeutscheForschungsgemeinschaft (DFG, German Research Foun-dation), Project-ID 279384907, SFB 1245, and the GSI-TU Darmstadt cooperation agreement. [1] T. 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[ nu c l - e x ] A p r Supplemental Material for“Extending the Southern Shore of the Island of Inversion to F” A. Revel, O. Sorlin, F.M. Marqués, Y. Kondo, J. Kahlbow,
4, 5
T. Nakamura, N.A. Orr, F. Nowacki,
6, 7
J.A. Tostevin, C.X. Yuan, N.L. Achouri, H. Al Falou, L. Atar, T. Aumann,
4, 11
H. Baba, K. Boretzky, C. Caesar,
4, 11
D. Calvet, H. Chae, N. Chiga, A. Corsi, H. L. Crawford, F. Delaunay, A. Delbart, Q. Deshayes, Z. Dombrádi, C. A. Douma, Z. Elekes, P. Fallon, I. Gašparić,
17, 5
J.-M. Gheller, J. Gibelin, A. Gillibert, M. N. Harakeh,
11, 16
W. He, A. Hirayama, C.R. Hoffman, M. Holl, A. Horvat, Á. Horváth, J.W. Hwang, T. Isobe, N. Kalantar-Nayestanaki, S. Kawase, S. Kim, K. Kisamori, T. Kobayashi, D. Körper, S. Koyama, I. Kuti, V. Lapoux, S. Lindberg, S. Masuoka, J. Mayer, K. Miki, T. Murakami, M. Najafi, K. Nakano, N. Nakatsuka, T. Nilsson, A. Obertelli, F. deOliveira Santos, H. Otsu, T. Ozaki, V. Panin, S. Paschalis, D. Rossi, A.T. Saito, T. Saito, M. Sasano, H. Sato, Y. Satou, H. Scheit, F. Schindler, P. Schrock, M. Shikata, Y. Shimizu, H. Simon, D. Sohler, L. Stuhl, S. Takeuchi, M. Tanaka, M. Thoennessen, H. Törnqvist, Y. Togano, T. Tomai, J. Tscheuschner, J. Tsubota, T. Uesaka, Z. Yang, M. Yasuda, and K. Yoneda (SAMURAI21 collaboration) Grand Accélérateur National d’Ions Lourds (GANIL),CEA/DRF-CNRS/IN2P3, Bvd Henri Becquerel, 14076 Caen, France LPC Caen, ENSICAEN, Université de Caen, CNRS/IN2P3, F-14050 CAEN Cedex, France Department of Physics, Tokyo Institute of Technology,2-12-1 O-Okayama, Meguro, Tokyo 152-8551, Japan Institut für Kernphysik, Technische Universität Darmstadt, 64289 Darmstadt, Germany RIKEN Nishina Center, Hirosawa 2-1, Wako, Saitama 351-0198, Japan Université de Strasbourg, IPHC, 23 rue de Loess 67037 Strasbourg, France CNRS, UMR7178, 67037 Strasbourg, France Department of Physics, University of Surrey, Guildford, Surrey GU2 7XH, United Kingdom Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-Sen University, Zhuhai 519082, China Lebanese University, Beirut, Lebanon GSI Helmholtzzentrum für Schwerionenforschung, 64291 Darmstadt, Germany Irfu, CEA, Université Paris-Saclay, 91191 Gif-sur-Yvette, France IBS, 55, Expo-ro, Yuseong-gu, Daejeon, Korea, 34126 Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA Institute of Nuclear Research, Atomki, 4001 Debrecen, Hungary KVI-CART, University of Groningen, Zernikelaan 25, 9747 AA Groningen, The Netherlands Ruđer Bošković Institute, HR-10002 Zagreb, Croatia Physics Division, Argonne National Laboratory, Argonne, Illinois 60439, USA Eötvös Loránd University, Pázmány Péter Sétány 1/A, H-1117 Budapest, Hungary Department of Physics and Astronomy, Seoul National University,1 Gwanak-ro, Gwanak-gu, Seoul 08826, Republic of Korea Department of Advanced Energy Engineering Science,Kyushu University, Kasuga, Fukuoka, 816-8580 Japan Department of Physics, Tohoku University, Miyagi 980-8578, Japan Unversity of Tokyo, Tokyo 1130033, Japan Institutionen för Fysik, Chalmers Tekniska Högskola, 412 96 Göteborg, Sweden Center for Nuclear Study, University of Tokyo, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan Institut für Kernphysik, Universität zu Köln, 50937 Köln, Germany National Superconducting Cyclotron Laboratory,Michigan State University, East Lansing, Michigan 48824, USA Department of Physics, Kyoto University, Kyoto 606-8502, Japan Department of Physics, Osaka University, Osaka 560-0043, Japan (Dated: April 3, 2020)
PACS numbers:
TABLE WITH ENERGIES AND WIDTHS
Tab. S1 contains the resonance energies and widthsobtained from the fit of the F+ n E rel spectra (Fig. 1 of the paper) populated from Ne ( − p ) and F ( − n ) reactions, using a non-resonant component and a set ofrespectively seven and six Breit-Wigner line shapes withan energy-dependent width. Tab. S2 contains the same Ne( p , p ) F F( p , pn ) F E r (keV) Γ (keV) E r (keV) Γ (keV)204 ±
16 180 ±
140 198 ± ± ±
20 150 ±
50 996 ±
13 190 ± ±
21 110 ±
70 *1321 ±
31 50 +90 − *1280 ±
30 170 ±
90 1880 ±
80 10 +220 − ±
30 170 ±
90 *2115 ±
81 200 ± ±
100 660 ±
260 3980 ±
260 700 ± ±
370 470 +610 − *4095 ±
270 320 +670 − TABLE S1: Energies and widths obtained from the fit of the E rel spectra for the F + n system populated from Ne ( − p ) and F ( − n ) reactions. Energies are given with respect to S n ( F). The resonances extracted from the spectra in coin-cidence with a γ -ray in F are marked with the symbol *. Ne( p , p ) F F( p , pn ) F E r (keV) Γ (keV) E r (keV) Γ (keV)245 ±
32 130 ±
98 227 ±
88 6 +310 − ±
70 960 ±
30 1422 ±
89 821 ± ±
50 100 +170 − ±
120 767 ± ±
52 580 ±
160 4390 ±
170 2900 ± ±
43 500 ± ±
240 980 ± F +2 n system.Energies are given with respect to S n ( F). The symbol *refers here to coincidences with a γ -ray in F. information but from the fit of the F+ n + n spectra,using respectively five and four Breit-Wigner line shapes. DECAY SCHEME
The different resonances observed in this work, as wellas their identified decay patterns, are displayed in Fig. S1.We were not only able to obtain a precise spectroscopyof F populated from two different reactions, but also toidentify the way those resonances decayed. This is essen-tial in order to determine their structure, that is relatedto the different decay channels they couple to. However,it is important to keep in mind that F has a known + isomeric state at around 643 keV (see Ref. [12] of thepaper). Even if populated, it would not be observed inour experiment owing to its long lifetime of about 2.2 ms.This could have an impact on our proposed level scheme,if some resonances observed in the F +2 n system weredecaying to this isomer rather than the ground state. PROTON TARGET CONSIDERATIONS
The direct nucleon-removal calculations used are sim-ilar to those for reactions on light nuclear targets (see Ref. [44,45] of the paper), using the eikonal (forward scat-tering) and sudden (fast collision) approximations to thereaction dynamics and shell-model spectroscopic factors.For reactions on a composite light nucleus (e.g. C, Be) thecomplex interaction between the removed nucleon andthe target means that inelastic breakup (or stripping)is the dominant removal mechanism. However, on a pro-ton target the interaction between the struck nucleon andthe proton, and the corresponding S -matrix, describe thenucleon-nucleon (NN) system. Since at the collision en-ergies of interest these NN collisions are entirely elastic,the removal cross section is now determined only by theelastic breakup (or diffraction dissociation) mechanism(see Ref. [45] of the paper).This required NN S -matrix for the system formed bythe removed nucleon and the proton target is written S jp ( b ) , with j the species of the removed nucleon, j = n, p . The NN scattering operator, a function of the NNimpact parameter b , is conventionally written [1]: S jp ( b ) = 1 − Γ jp ( b ) (1)where Γ jp , called the NN profile function, is parameter-ized as: Γ jp ( b ) = σ jp i ( i + α jp ) g ( β jp , b ) (2)Here g ( b ) , a normalized 2D Gaussian form factor: g ( β, b ) = 12 πβ exp( − b / β ) (3)approximates the finite range of the NN interactions. The σ jp are the np and pp total cross sections, calculated herefrom the Charagi and Gupta parameterization of the ex-perimental NN data [2] at the mid-target energy. Theparameters α jp , the ratios of the real to the imaginaryparts of the NN forward-scattering amplitudes, are inter-polated from the tabulation of Ray [3].For the associated range parameters, β jp , as in Ref. [4]we require that the total and total elastic cross sectionsderived from the S jp are equal, since the NN scatteringis entirely elastic, giving: β jp = σ jp (cid:0) α jp (cid:1) π (4)The remaining dynamical input, the eikonal S -matrixthat describes the interaction of the mass A − reac-tion residue with the proton target, is computed in theoptical limit (or tρ folding approximation) to the proton-residue optical potential with the above NN parameters.This potential and S -matrix includes effects of the sizeand asymmetry of the reaction residue through its point-neutron and proton densities, approximated using spheri-cal Skyrme SkX Hartree-Fock (HF) calculations [5]. Suchcalculations have been shown to provide a very goodglobal description of the root mean squared sizes [6] and (4 − ) 0.204(2 − ) 0.940(1 − ) . . (3 − ) .
840 1 . .
648 3 . .
608 4 .
044 3 . . + g.s. 1/2 + + g.s. 1/2 + + g.s. 2 + + g.s. 2 + . . . . . . . . Ne(–1 p ) F F+ n F+2 n Ne(–1 p ) F F+ n F+2 n (4 − ) 0.198(3 + ) 0.996(1 + ) 1.3212.115 . . . . . + g.s. 1/2 + + g.s. 1/2 + + g.s. 2 + + g.s. 2 + . . . . . . F(–1 n ) F F+ n F+2 n F(–1 n ) F F+ n F+2 n FIG. S1: The detailed decay scheme of the different states observed in F, populated from Ne and F, is shown in thetop and bottom panels, respectively. The widths of the levels correspond to the uncertainty on their centroid value, while theplacement of the levels marked with a filled orange circle is derived from their observed coincidence with a γ -ray in the F or F spectra from the n or n emission, respectively. The level scheme of F has been divided into two regions (left and right)for better clarity. radial forms of the matter and charge [7] distributions ofboth stable and neutron-proton asymmetric nuclei. [1] J.S. Al-Khalili and J.A. Tostevin, Phys. Rev. C , 1846(1998).[2] S.K. Charagi and S.K. Gupta, Phys. Rev. C , 1610 (1990).[3] L. Ray, Phys. Rev. C , 1857 (1979).[4] B. Abu-Ibrahim et al. , Phys. Rev. C , 034607 (2008).[5] B.A. Brown, Phys. Rev. C , 220 (1998).[6] B.A. Brown, S. Typel, and W.A. Richter, Phys. Rev. C , 014612 (2002).[7] W.A. Richter and B.A. Brown, Phys. Rev. C67