Spectroscopy of A=9 hyperlithium by the (e,e^{\prime}K^{+}) reaction
T. Gogami, C. Chen, D. Kawama, P. Achenbach, A. Ahmidouch, I. Albayrak, D. Androic, A. Asaturyan, R. Asaturyan, O. Ates, P. Baturin, R. Badui, W. Boeglin, J. Bono, E. Brash, P. Carter, A. Chiba, E. Christy, S. Danagoulian, R. De Leo, D. Doi, M. Elaasar, R. Ent, Y. Fujii, M. Fujita, M. Furic, M. Gabrielyan, L. Gan, F. Garibaldi, D. Gaskell, A. Gasparian, Y. Han, O. Hashimoto, T. Horn, B. Hu, Ed.V. Hungerford, M. Jones, H. Kanda, M. Kaneta, S. Kato, M. Kawai, H. Khanal, M. Kohl, A. Liyanage, W. Luo, K. Maeda, A. Margaryan, P. Markowitz, T. Maruta, A. Matsumura, V. Maxwell, D. Meekins, A. Mkrtchyan, H. Mkrtchyan, S. Nagao, S.N. Nakamura, A. Narayan, C. Neville, G. Niculescu, M.I. Niculescu, A. Nunez, Nuruzzaman, Y. Okayasu, T. Petkovic, J. Pochodzalla, X. Qiu, J. Reinhold, V.M. Rodriguez, C. Samanta, B. Sawatzky, T. Seva, A. Shichijo, V. Tadevosyan, L. Tang, N. Taniya, K. Tsukada, M. Veilleux, W. Vulcan, F.R. Wesselmann, S.A. Wood, T. Yamamoto, L. Ya, Z. Ye, K. Yokota, L. Yuan, S. Zhamkochyan, L. Zhu
aa r X i v : . [ nu c l - e x ] F e b Spectroscopy of A = 9 hyperlithium by the ( e, e ′ K + ) reaction T. Gogami,
1, 2
C. Chen, D. Kawama, P. Achenbach, A. Ahmidouch, I. Albayrak, D. Androic, A. Asaturyan, R. Asaturyan, ∗ O. Ates, P. Baturin, R. Badui, W. Boeglin, J. Bono, E. Brash, P. Carter, A. Chiba, E. Christy, S. Danagoulian, R. De Leo, D. Doi, M. Elaasar, R. Ent, Y. Fujii, M. Fujita, M. Furic, M. Gabrielyan, L. Gan, F. Garibaldi, D. Gaskell, A. Gasparian, Y. Han, O. Hashimoto, ∗ T. Horn, B. Hu, Ed.V. Hungerford, M. Jones, H. Kanda, M. Kaneta, S. Kato, M. Kawai, H. Khanal, M. Kohl, A. Liyanage, W. Luo, K. Maeda, A. Margaryan, P. Markowitz, T. Maruta, A. Matsumura, V. Maxwell, D. Meekins, A. Mkrtchyan, H. Mkrtchyan, S. Nagao, S.N. Nakamura, A. Narayan, C. Neville, G. Niculescu, M.I. Niculescu, A. Nunez, Nuruzzaman, Y. Okayasu, T. Petkovic, J. Pochodzalla, X. Qiu, J. Reinhold, V.M. Rodriguez, C. Samanta, B. Sawatzky, T. Seva, A. Shichijo, V. Tadevosyan, L. Tang,
3, 12
N. Taniya, K. Tsukada, M. Veilleux, W. Vulcan, F.R. Wesselmann, S.A. Wood, T. Yamamoto, L. Ya, Z. Ye, K. Yokota, L. Yuan, S. Zhamkochyan, and L. Zhu (HKS (JLab E05-115) Collaboration) Graduate School of Science, Kyoto University, Kyoto, Kyoto 606-8502, Japan Graduate School of Science, Tohoku University, Sendai, Miyagi 980-8578, Japan Department of Physics, Hampton University, Hampton, VA 23668, USA Institute for Nuclear Physics, Johannes Gutenberg-University, D-55099 Mainz, Germany Department of Physics, North Carolina A & T State University,Greensboro, NC 27411, USA Department of Physics & Department of Applied Physics, University of Zagreb, HR-10000 Zagreb, Croatia A.I.Alikhanyan National Science Laboratory, Yerevan 0036, Armenia Department of Physics, Florida International University, Miami, FL 27411, USA Department of Physics, Computer Science & Engineering, Christopher Newport University, Newport News, VA, USA 23606 Istituto Nazionale di Fisica Nucleare, Sezione di Bari and University of Bari, I-70126 Bari, Italy Department of Physics, Southern University at New Orleans,New Orleans, LA 70126, USA Thomas Jefferson National Accelerator Facility (JLab), Newport News, VA 23606, USA Department of Physics, University of North Carolina at Wilmington, Wilmington, NC 28403, USA INFN, Sezione Sanit ` a and Istituto Superiore di Sanit ` a , 00161 Rome, Italy Nuclear Physics Institute, Lanzhou University, Gansu 730000, China Department of Physics, University of Houston, Houston, Texas 77204, USA Department of Physics, Yamagata University, Yamagata, 990-8560, Japan Mississippi State University, Mississippi State, Mississippi 39762, USA Department of Physics and Astronomy, James Madison University, Harrisonburg, VA 22807, USA Divisi´on de Ciencias, Tecnolog´ıa y Ambiente, Universidad Ana G. M´endez, Recinto de Cupey, San Juan 00926, Puerto Rico Department of Physics & Astronomy, Virginia Military Institute, Lexington, Virginia 24450, USA Department of Physics, Xavier University of Louisiana, New Orleans, LA 70125, USA (Dated: February 9, 2021)Missing mass spectroscopy with the ( e, e ′ K + ) reaction was performed at JLab Hall C for theneutron rich Λ hypernucleus Li. The ground state energy was obtained to be B g . s . Λ = 8 . ± . stat . ± . sys . MeV by using shell model calculations of a cross section ratio and an energyseparation of the spin doublet states (3 / +1 and 5 / +1 ). In addition, peaks that are consideredto be states of [ Li(3 + ) ⊗ s Λ = 3 / +2 , / + ] and [ Li(1 + ) ⊗ s Λ = 5 / +2 , / + ] were observed at E Λ ( . ± . stat . ± . sys . MeV and E Λ ( . ± . stat . ± . sys . MeV, respectively.The E Λ ( He + t structure is more developed for the 3 + state than those for the 2 + and 1 + states in a core nucleus Li as a cluster model calculation suggests.
The nucleon-nucleon interaction (
N N ) is informedby a rich data set of scattering and nuclear spec-troscopy experiments. On the other hand, the hyperon-nucleon (
Y N ) and hyperon-hyperon (
Y Y ) interactionsare less understood because experimental data for thestrangeness sector are scarce. Scattering experiments aredifficult for hyperons due to short lifetimes of hyperons.Data from hyperon scattering experiments are still lim-ited [1], although a Σ-proton scattering experiment wasrecently carried out at J-PARC [2]. Therefore, hypernu- clear spectroscopy plays a vital role in investigations of
Y N and
Y Y interactions.The Λ N -Σ N coupling is one of the important effects inthe Λ N interaction. The energy difference between Hand He is firm evidence of the charge symmetry break-ing (CSB) in the Λ N interaction [3–5], and the Λ N -Σ N coupling is considered to be a key to solving the Λ N CSB issue [6–8]. A neutron rich system is a good envi-ronment to investigate the Λ N -Σ N coupling because itis predicted that the Σ mixing probability in a neutronrich system is rather higher and that the energy struc-ture is more affected by the coupling [9] compared to socalled normal Λ hypernuclei. However, there are few dataon neutron rich Λ hypernuclei. For example, superheavyhyperhydrogen H and a superheavy hyperlithium
Liwere investigated via double charge exchange reactionsusing hadron beams. FINUDA Collaboration identifiedthree events that are interpreted as H [10]. Experimentsat J-PARC and KEK, on the other hand, were not ableto determine the Λ binding energies of H [11, 12] and
Li [13] due to either low statistics or insufficient energyresolution. In this article, we report new spectroscopicdata of a neutron rich Λ hypernucleus Li for which weperformed missing mass spectroscopy with the ( e, e ′ K + )reaction at Jefferson Lab’s (JLab) experimental Hall C.A difference of Λ binding energies between mirror hy-pernuclei is a benchmark of CSB in the Λ N interaction.Λ N CSB was discussed in the s -shell hypernuclei [5, 14–16], and an interest is extended to CSB in p -shell hyper-nuclear systems [17–19]. We present new binding energydata of Li which is compared with that of the mirrorhypernucleus B.We performed a series of Λ binding energy measure-ments for several p -shell hypernuclei with a new mag-netic spectrometer system HKS-HES at JLab Hall C (Ex-periment JLab E05-115) [20], and results for He [21],
Be [22] and
B [23] were published. We acquired datawith a Be target to produce Li in the same experimen-tal period. A continuous E e = 2 .
344 GeV electron beamwas incident on a 188-mg/cm
Be target. The beamhad an average on target intensity of about 38 µ A with abeam bunch cycle of 2 ns. A total of 5.3 C (= 3 . × electrons) was delivered to the target. The scatteredelectron and K + with central momenta of p e ′ = 0 . p K = 1 .
200 GeV/ c were measured by the HES andHKS [24], respectively. The HES and HKS spectrom-eters have momentum resolutions of ∆ p/p ≃ × − FWHM allowing us to achieve the best energy resolutionin missing mass spectroscopy of hypernuclei [23].In order to calibrate absolute energy in the missingmass spectrum, we used the reactions p ( e, e ′ K + )Λ and p ( e, e ′ K + )Σ on a polyethylene target (CH x ) to pro-duce Λ and Σ hyperons for which we know the masseswith uncertainties of only ± ±
24 keV, re-spectively [25]. The calibration used the same spec-trometer setting as that for hypernuclear productionthanks to large momentum bites of HES and HKS(∆ p accept /p central = ± .
5% and ± . B sys . Λ = 0 .
11 and ∆ E sys . Λ = 0 .
05 MeV,respectively. Refer to Refs. [20, 23] for details about thecalibration method.In the hadron arm of HKS spectrometer, there werebackgrounds of π + s and protons which were rejected toidentify K + s both on-line (data taking trigger) and off-line (data analysis) stages. To reduce the trigger rateto less than 2 kHz, allowing a data acquisition live timeover 90%, we incorporated two types of Cherenkov de-tectors (AC and WC; radiation media of a hydrophobicaerogel and a deionized water with refractive indices of n = 1 .
05 and 1.33, respectively) in the trigger. Off-line,the K + identification (KID) was done by the followingthree analyses: (KID-1) coincidence time analysis, (KID-2) light yield analysis in AC and WC, (KID-3) analysisof particle mass squared. The coincidence time is definedas t coin = t e ′ − t K where t e ′ ,K is the time at target. The t e ′ ,K = t TOF − (cid:16) lv e ′ ,K (cid:17) was calculated event by eventby using the velocity v e ′ ,K , the time at a Time-Of-Flight(TOF) detector t TOF , and the path length ( l ) from thetarget to the TOF detector for each particle. The veloc-ity v e ′ ,K was obtained from a particle momentum whichwas calculated by the backward transfer matrix with as-sumptions of the masses of e ′ and K + for particles in HESand HKS, respectively. A coincidence event of ( e ′ , K + )could be identified with a resolution of 0 .
64 ns (FWHM)in the coincidence time. Peaks of other coincidence re-actions such as ( e ′ , π + ) and ( e ′ , p ) are located at differ-ent positions from that of the ( e ′ , K + ) peak because ofthe wrong assumptions of particle masses for π + s andprotons. The other coincidence events and most of ac-cidental coincidence events could be removed by a coin-cidence time selection with a time gate of ± e ′ , K + ) coincidence peak [20]. With KID-2and 3, survival ratios for π + and proton were suppresseddown to 0 . . >
80% of K + survival ratio [29].Figure 1 shows the missing mass spectrum for thereaction of Be( e, e ′ K + ) Li. The abscissa is − B Λ = − [ M ( Li) + M Λ − M HYP ] where M ( Li) and M Λ aremasses of a core nucleus Li and a Λ which are7471.366 MeV/ c [30] and 1115.682 MeV/ c [25], respec-tively. The mass of M ( Be) = 8392 .
750 MeV /c [30] wasused for a target nucleus Be to calculate M HYP . Theordinate is the differential cross section in the laboratoryframe for the ( γ ∗ , K + ) reaction (cid:16) dσd Ω K (cid:17)(cid:12)(cid:12)(cid:12) HKS that is de-scribed in Refs. [21, 22]. It is noted that Q (= − q where q is the four momentum transfer to a virtual pho-ton) is small [ Q = 0 .
01 (GeV /c ) ] with our experimen-tal setup, and thus, the virtual photon may be treatedas almost a real photon. A distribution of accidentalcoincidence events shown in Fig. 1 was obtained by themixed event analysis in which the missing mass was re-constructed with random combinations of e ′ and K + ( nb / s r) / . M e V d σ d Ω -40 -30 -20 -10 0 10 20 30 40 -B Λ (MeV)JLab E05-115 Be (e,e’K + ) Li Λ Region of interest Q u a s i - f r e e Λ Accidental coincidence
FIG. 1. An obtained spectrum for the Be( e, e ′ K + ) Li re-action with an abscissa of − B Λ . Events that exceeded overthe accidental coincidence background in the bound region( − B Λ <
0) were analyzed in the present work. in the analysis [26]. The accidental background distri-bution was subtracted as shown in Fig 2, and residualevents in a region of − B Λ < Li. Three doublet states for which a Λ re- -B Λ (MeV) ( nb / s r) / . M e V d σ d Ω Be (e,e’K + ) Li Λ FIG. 2. A fitting result on the Be( e, e ′ K + ) Li spectrum bythree Voigt functions. A distribution of the accidental coin-cidence events that was obtained by the mixed event analysis(Fig. 1) was subtracted from the original spectrum. siding in the s -orbit couples with the 2 + (ground state),1 + and 3 + states of the core nucleus Li are expectedto be largely populated in the Li spectrum [31, 32]. Inaddition, the energy spacings between each spin doubletstates are theoretically expected to be about 0.6 MeVat most making them difficult to separate given the ex-pected experimental resolution. Therefore, we used threeVoigt functions with the same width for fitting to thespectrum. The fitting result with χ / n . d . f . = 22 . / . ± . . ± .
13 and0 . ± .
15, respectively while ratios of the correspond-ing spectroscopic factors C S are respectively 0.60 and0.65 that were measured in the Be( t, α ) Li reaction [33].Peak Li(2 + ; g . s . ) ⊗ s Λ = 3 / +1 , / +1 . It is predicted that theproduction cross section of the 5 / +1 state is larger thanthat of the ground state 3 / +1 by a factor of 5–7 and thedoublet separation is 0.5–0.7 MeV [9, 31, 34]. Assum-ing the above cross section ratio and the doublet separa-tion, the ground state binding energy is evaluated to begreater than that of the mean value of peak . ± .
10 MeV [= ∆ B Λ (g . s . − B Hall-CΛ ( Li; g . s . ) = 8 . ± . stat . ± . sys . MeV. The obtained B Λ agrees with B emul . Λ ( Li; g . s . ) = 8 . ± .
12 MeV [35], the mean bind-ing energy of 13 emulsion events, and B Hall-AΛ ( Li; g . s . ) =8 . ± . stat . ± . sys . MeV from the measurementin JLab Hall A [36, 37] within ± σ of the uncertainty.The weighted average of the above three measurementsincluding our result is found to be B meanΛ ( Li; g . s . ) =8 . ± .
08 MeV.The excitation energies ( E Λ ) for peaks B Hall-CΛ ( Li; g . s . ), and are shown in Table I. Figure. 3shows a comparison of the obtained E Λ with those of shellmodel predictions [9, 34, 38] and the experimental datafrom JLab Hall A [36, 37]. Experimental energy levelsof the core nucleus Li taken from Ref. [39] are shown aswell. The excitation energy of E Λ ( . ± . stat . ± . sys . MeV is consistent with those of the theoreticalpredictions of 3 / +2 and 1 / + and the experimental resultof JLab Hall A. For the third doublet which is consideredto correspond to peak / + ispredicted to be larger than that of 5 / +2 by a factor of 2–3 [31, 34], and thus peak / + state. The energy of peak E Λ ( . ± . stat . ± . sys . MeV. It isfound that E Λ ( / + by a few hundred keV. An E Λ could be larger if acore nucleus is deformed due to a development of clustersbecause a spatial overlap between the core nucleus and aΛ gets smaller [40]. A cluster model calculation suggeststhat a He + t structure is more developed for the 3 + state than for the 2 + and 1 + states in Li [41]. The largerenergy compared to the shell model predictions for peak + state of the core nucleus Li as suggested.A peak in the highest excitation observed in the ex-periment at JLab Hall A was at 2 . ± .
09 MeV [36, 37]that differs from E Λ ( TABLE I. Fitting result of the Be( e, e ′ K + ) Li spectrum in JLab E05-115. Three Voigt functions were used for the fitting. TheΛ binding energy of the ground state B g . s . Λ and the excitation energy E Λ were evaluated with an assumption that the cross sectionratio of the first excited state 5 / +1 to that of the ground state 3 / +1 is 5–7 and the doublet separation is 0.5–0.7 MeV [9, 31, 34].Peak ID Possible states B Λ (MeV) E Λ (MeV) (cid:16) dσd Ω K (cid:17)(cid:12)(cid:12)(cid:12) HKS (nb/sr) Li(2 + ) ⊗ s Λ . ± . ± . sys . [∆ B Λ (g . s . − . ± . sys . ] 7 . ± . stat . ± . sys . = 3 / +1 , / +1 ( B g . s . Λ = 8 . ± . stat . ± . sys . ) Li(1 + ) ⊗ s Λ . ± . ± . sys . . ± . stat . ± . sys . . ± . stat . ± . sys . = 3 / +2 , / + Li(3 + ) ⊗ s Λ . ± . ± . sys . . ± . stat . ± . sys . . ± . stat . ± . sys . = 5 / +2 , / + JLabE05-115 JLab
Hall A (Present data)
Assumption ⁸Li Li Λ + + + E Λ ( M e V ) + + + + + + + + + + + + M ill e n e r G ogny + + + + + + U m e y a Theoretical calc.
FIG. 3. A comparison of the obtained excitation energy E Λ of Li with those of theoretical calculations [9, 34, 38] andan experimental data taken at JLab Hall A [36, 37]. E Λ wasobtained with the assumption that the cross section ratio ofthe 5 / + state to that of the ground state 3 / + is 5–7 andthe doublet separation is 0.5–0.7 MeV [9, 31, 34]. ( B emul . Λ ). Accordingly, the excitation energies are re-duced by 0.34 MeV [= 0 . − (8 . − .
31) MeV] fromthose shown in Table I and Fig. 3, and E Λ ( ,
3) becomemore consistent with the theoretical predictions. How-ever, E Λ ( Q and the K + scattering angle with respectto the virtual photon. However, the relative strength ofthe cross section for each state in the present experimentis predicted not to differ so much from that of JLab HallA in DWIA calculations [42] in which elementary ampli-tudes of the Saclay-Lyon and BS3 models [43] are used.Further studies are necessary to consistently understandthese experimental spectra.Three events of B were identified in the emulsionexperiment, and the mean value was reported to be B Λ ( B; g . s . ) = 8 . ± .
18 MeV [35]. The difference of Λbinding energies between the A = 9 isotriplet hypernu-clei was found to be B Λ ( B; g . s . ) − B Hall-CΛ ( Li; g . s . ) = − . ± .
29 MeV while a prediction is − .
054 MeV [18].There might be an unexpectedly large CSB effect in the A = 9 isotriplet hypernuclei. However, the current ex-perimental precision is not sufficient for Li as well as B to discuss the Λ N CSB in the system. In order toprecisely determine the ground state energy by an experi-ment with the ( e, e ′ K + ) reaction, the first doublet stateswould need to be resolved. The doublet separation of Li (between 3 / + and 5 / + states) is predicted to be0.5–0.7 MeV which is much larger than for other p -shellhypernuclei (e.g. the separation between 1 − (g.s.) and2 − states of C was measured to be 0 . ± . N -Σ N coupling [9]. Therefore, an ( e, e ′ K + ) experimentwith an energy resolution of 0.5 MeV (FWHM) or bet-ter would be a promising way to precisely determine theground state energy of Li.To summarize, we measured Li by missing mass spec-troscopy with the ( e, e ′ K + ) reaction at JLab Hall C. Weobserved three peaks ( s Λ states coupling with a Li nucleus in the 2 + , 1 + and 3 + states. Peak Li(2 + ) ⊗ s Λ (= 3 / +1 , / +1 )] was analyzed to obtainthe ground state energy. The ground state energy wasdetermined to be B Hall-CΛ ( Li; g . s . ) = 8 . ± . stat . ± . sys . MeV with assumptions that the cross section ra-tio of the fist excited state (5 / +1 ) to that of the groundstate (3 / +1 ) is 5–7 and the doublet energy separation is0.5–0.7 MeV [9, 31, 34]. Peaks Li(1 + ) ⊗ s Λ (= 3 / +2 , / + )] and [ Li(3 + ) ⊗ s Λ (=5 / +2 , / + )] states, respectively. We obtained excitationenergies to be E Λ ( . ± . stat . ± . sys . MeVand E Λ ( . ± . stat . ± . sys . MeV by usingthe obtained B Hall-CΛ ( Li; g . s . ). E Λ ( N N and Λ N interactions are used while E Λ ( He + t structureis more developed for the 3 + state than for the 2 + and 1 + states of the Li nucleus, as a cluster model calculationsuggests [41].We thank the JLab staff of the physics, accelerator,and engineering divisions for support of the experiment.We thank T. Motoba, A. Umeya, P. Bydˇzovsk´y, M. Isaka,and D.J. Millener for valuable exchanges for this work.This work was partially supported by the Grant-in-Aid for Scientific Research on Innovative Areas “Towardnew frontiers Encounter and synergy of state-of-the-art astronomical detectors and exotic quantum beams.”The program was supported by JSPS KAKENHIGrants No. JP18H05459, No. 18H01219, No. 17H01121,No. 12002001, No. 15684005, No. 16GS0201, No. 24 · ∗∗