Hypernuclear photoproduction spectra calculated with multi-configuration wave functions

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1 8th International Conference on Quarks and Nuclear Physics (QNP218) Nov , 218 Hypernuclear photoproduction spectra calculated with multi-configuration wave functions Atsushi UMEYA (Nippon Inst. of Tech.) Toshio MOTOBA (Osaka E-C Univ., YITP) Kazunori ITONAGA (Gifu Univ.) 1

2 Recent (e, e K + ) reaction experiments done at the Jefferson Lab c: " ' 1:) " Fig. 7. dσ/dω K per.3 MeV [nb/sr] (MeV I PRC93, (216) The predicted excitation E Λ [MeV] function for the 5 1 JLab E B(e,e K + ) 1 Be Λ #1 #2 (Fit I) #3 a # B Λ [MeV] Shell-model prediction T. Motoba et al., PTPS117, 123 (1994) Core nucleus calculated with standard p-shell model Λ in s-orbit Recent experimental result T. Gogami et al., This experiment has confirmed the major peaks (#1, #2, #3, #4) predicted in DWIA by emplying the Λ particle in s-orbit coupled with the nuclear core states confined within the p-shell configuration. However, it is interesting to observe extra strengths at E Λ = MeV excitation (a). The extension of the model space is necessary and interesting challenge in view of the present hypernuclear spectroscopy. 2

3 Extension of the model space in the shell model ( 1 Be case) Λ Model space for 9 Be core (A) standard model space J core (s) 4 (p) 5 (p-h) (B) extended model space J + core (s) 3 (p) 6 (s) 4 (p) 4 (sd) 1 (1p-1h) Standard model space for 1 Λ Be (I) J core s Λ 1 Λ Be(J ) (II) J core p Λ 1 Λ Be(J+ ) Extension (1) 1p-1h (1ħω) core excitation is taken into account (a) J core s Λ 1 Λ Be(J ) (b) J core p Λ 1 Λ Be(J+ ) (c) J + core s Λ 1 Λ Be(J+ ) (d) J + core p Λ 1 Λ Be(J ) Extension (2) Configrations mixed by ΛN interaction J core s Λ J + core p Λ 1 Λ Be(J ) J core p Λ J + core s Λ 1 Λ Be(J+ ) 3

4 Configration mixing in 1 Be unnatural parity states Λ 9 Be (J core) + 1 Λ(p) ΛBe (J ) 9 Be (J + core) 1 ω 9 Be (J core) + Λ(s) 9 Be (Jcore) Λ(p) 1 ΛBe (J + ) ΛBe (J + ) 1 Mixing 9 Be (J core) 1 ω 9 Be (Jcore) 1 Λ(s) ΛBe (J ) In the standard shell model, only natural-parity nuclaer-core states (J core ) are taken into account. Λ particle is in the s orbit in 1 Λ Be(J ). In 1 Λ Be(J+ ), the energy difference between Λ(s) and Λ(p) is 1ħω, and the energy difference between 9 Be(J core ) and 9 Be(J + core ) is 1ħω. By ΛN interaction, natural-parity nuclaer-core configurations and unnatural-parity nuclaer-core configurations can be mixed. 4

5 Extended model space for target nucleus 1 B 1 ΛBe (J ) (s) 4 (p) 5 (s Λ ) 1 (s) 3 (p) 6 (p Λ ) 1 (s) 4 (p) 4 (sd) 1 (p Λ ) 1 1 B (J + ) (s) 4 (p) 6 (s) 3 (p) 6 (sd) 1 (s) 4 (p) 5 (fp) 1 (s) 2 (p) 8 (s) 4 (p) 4 (sd) 2 1 ΛBe (J + ) (s) 4 (p) 5 (p Λ ) 1 (s) 3 (p) 6 (s Λ ) 1 (s) 4 (p) 4 (sd) 1 (s Λ ) 1 extended model space for the target nucleus standard model space extended model space for hypernuclei Extension of model space for target nucleus 1 B up to 2p-2h (2ħω) allows the 1 Be production through various configurations. Λ 5

6 ΛN interaction and Λ single-particle energy NΛ V NΛ Nijmegen NSC97e Th. A. Rijken, V. G. J. Stoks, Y. Yamamoto, PRC59, 21 (1999) ε Λ s and ε Λ p are determined to reproduce the #1 (2 ) and #6 ( ) peaks in 12 Λ B production cross-section. ε Λ s and ε Λ p are applied to 1 Λ Be. JLab Hall C, E5-115 L. Tang et al., PRC9, 3432 (214) Theoretical calculation T. Motoba et al., PTPS185, 224 (21) e K ) 12 B experimental spectrum (top) taken from JLab E5-115 experiment [9 6

7 Results : Energy levels of 9 Be and 1 Λ Be Energy (MeV) /2 9/2 + 7/2 3/2 3/2 + 1/2 5/2+ 1/2 + 3/2 9 Be (exp.) 9 1 Be (cal.) ΛBe (cal.) dominant configurations blue J ; 9 Be(J core) Λ(s) green J + ; 9 Be(J + core) Λ(p) magenta J + ; 9 Be(J core) Λ(p) red J + ; 9 Be(J + core) Λ(s)

8 Results : Energy levels of 1 Be (comparison with JLab experiments) Λ Energy (MeV) /2 9/2 + 7/2 3/2 3/2 + 1/2 5/2+ 1/2 + 3/ New bump Be (exp.) 9 1 Be (cal.) Λ Be (cal.) 1 Λ Be (exp.) T. Gogami et al., PRC93, (216) 8

9 Results : Spectroscopic factors of the pickup reaction, 1 B 9 Be Energy (MeV) /2 + 5/2 7/2 3/2 7/2 3/2 + 1/2 5/2 + 1/2 + 3/ /2 9/2 + 7/2 3/2 3/2 + 1/2 5/2+ 1/2 + 3/ C 2 S rel (Exp.) 1 2 C 2 S rel (Cal.) 9

10 Results : Cross sections of the 1 B (γ, K + ) 1 Be reaction (1) Λ 5 Eγ= L 1.5 GeV,θγ= L 7 Cross Section d 2 σ/dωde (nb/sr/mev) B (γ, K + ) 1 Λ Be Hypernuclear Energy E Λ (MeV) QF 1

11 Results : Cross sections of the 1 B (γ, K + ) 1 Be reaction (2) Λ dσ/dω K per.3 MeV [nb/sr] JLab E B(e,e K + ) 1 Be Λ #1 #2 (Fit I) #3 a E Λ [MeV] #4 T. Gogami et al., PRC93, (216) Cross Section d 2 σ/dωde (nb/sr/mev) B Λ [MeV] Eγ= L 1.5 GeV,θγ= L 7 1 B (γ, K + ) 1 Λ Be Hypernuclear Energy E Λ (MeV) QF Our new calculation reproduces the four major peaks (#1, #2, #3, #4). Our new calculation explains the new bump (a) as a sum of cross sections of some J + states. 11

12 Results : Cross sections of the 1 B (γ, K + ) 1 Be reaction (3) Λ Eγ = 1.5 GeV EXP = T. Gogami et al, PRC93 (216) 9 Be (Ji) Λ 1 Be (Jk) CAL θ = 7 deg EXP Fit I Ji Ei (exp) Ei (cal) Jk Ex BΛ dσ/dω exp Ex BΛ dσ/dω C2S C2S [MeV] [MeV] [nb/sr] peak [MeV] [MeV] [nb/sr] 3/ (rel) 1.(rel) # ±.7 17.± / #2 2.78± ± ± #3 6.26± ± ± (3) (3) (2) (4) (5) (3) (29.37) #a 8.34±.41.2± ±.7 7/ (5) (3) (5) #4 1.83± ± ± (51.44) 12

13 Results : Configrations of J + states corresponding to the new bump J π n( B Λ [MeV]) [J π core] j Λ [J π core] j Λ [J π core] j Λ XS [nb/sr] (.739) (.665) (.228) (.42) (.112) (.459) 2.43 [5/2 + 2 ]sλ 1/2 87.5% [5/2 + 2 ]sλ 1/2 11.3% [5/2 + 2 ]sλ 1/2 31.6% [5/2 + 2 ]sλ 1/2 67.5% [3/2 1 ](p 3/2 p 1/2 )Λ 82.5% [3/2 1 ](p 3/2 p 1/2 )Λ 79.5% [3/2 1 ](p 3/2 p 1/2 )Λ 9.4% [3/2 1 ](p 3/2 p 1/2 )Λ 7.9% [3/2 1 ]pλ 3/2 55.4% [3/2 1 ]pλ 3/2 27.1% [ 1 ](p 3/2 p 1/2 )Λ 15.8% [ 1 ]pλ 3/2 17.9% [ 1 ](p 3/2 p 1/2 )Λ 2.4% [ 1 ](p 3/2 p 1/2 )Λ 1.8% [ 1 ](p 3/2 p 1/2 )Λ 9.7% [ 1 ](p 3/2 p 1/2 )Λ 2.7% 13

14 Results : Cross sections of the 1 B (K, π ) 1 Λ B reaction Cross Section d 2 σ/dωde (µb/sr/mev) Cross Section d 2 σ/dωde (nb/sr/mev) B (K,π ) 1 Λ B p L K =.8 GeV/c,θL γ= p n Hypernuclear Energy Ep Λ (MeV) Λ 5 Eγ= L 1.5 GeV,θγ= L 7 α B (γ, K + ) 1 Λ Be α Be Λ Hypernuclear Energy Eα Λ (MeV) α α Λ Be α [p 1 p Λ ] QF p In the (K, π ) reaction, the large peak at E Λ = 4.4 MeV is a p-substitutional state via the p N 3/2 pλ 3/2, which is strongly excited by recoilless reaction. The small peak at E Λ = MeV corresponds to the new bump and is explained as a mixture of s Λ and p Λ states. The large peak at E Λ = 4.4 MeV in 1 Λ Be corresponds to the [p 1 p Λ ] state in 9 Λ Be (9 Be analog state). The small peak at E Λ = MeV in 1 Λ Be corresponds to the [p 1 p Λ // ] state in 9 Λ Be. [p 1 p Λ // ] 14

15 [p 1 p Λ ] and [p 1 p Λ // ] states of 9 Λ Be 9Be (K, π ) 9 Λ Be T. Motoba et al., PTPS81, 42 (1985) R. Bertini et al. (H-S-S Collaboration), NPA368, 365 (1981) 15

16 Summary We have calculated the cross sections in 1 ΛBe productions by using the extended shell model to describe the unnatural-parity nuclear core. dσ/dω K per.3 MeV [nb/sr] JLab E B(e,e K + ) 1 Be Λ #1 #2 (Fit I) #3 a E Λ [MeV] # B Λ [MeV] Cross Section d 2 σ/dωde (nb/sr/mev) B (γ, K + ) 1 Λ Be E L γ= 1.5 GeV,θ L γ= Hypernuclear Energy E Λ (MeV) Our new calculation explains the new bump in the JLab experimental results as a sum of cross sections of some J + states. These states have a large mixture of unnatural- and natural-parity nuclear-core states. The new bump in 1 Λ Be corresponds to the [p 1 p Λ // ] state in 9 Λ Be. 16 QF

Multi-configuration calculations of hypernuclear photoproduction spectra to shed light on new capability

Multi-configuration calculations of hypernuclear photoproduction spectra to shed light on new capability T. Motoba (Osaka E-C Univ. / Yukawa Inst., Kyoto Univ.) A. Umeya (Nippon Institute of Technology)