Shell model study of p-shell X hypernuclei (12XBe) 杉本聡 京都大学 元場俊雄 大阪電通大 山本安夫 都留文科大
Introduction Up to now, the experimental information are limited for X hyper nuclei as compared to L hyper nuclei. Theoretically, a pioneer work was done by Dover and Gal (Ann. Phys. 146 (1983)) using the existent data at that time. VX~-21~24MeV The experiments of (K-,K+) reaction were performed at KEK (Fukuda et al. PRC 58 (1998)) and AGS (Khaustov et al. PRC 61 (2000)) UX~-14MeV (Assuming a simple WS potential) At JPARC, the experiment of (K-,K+) reaction is planned to explore X hypernuclei.
Purpose of our study This method has been quite successful To study the structure of X hypernuclei using the shell model with effective interactions deduced from realistic NY interaction model. To perform a reaction calculation with the wave function from the shell model to explore what can be obtained from the experimental data. DWIA for (K-,K+) This method has been quite successful in the study of L hypernuclei!
12C(p+,K+)12LC Experiment Experiment Shell model +DWIA Hotchi et al., PRC 64 (2001) Experiment Chrien et al., NPA 478 (1988) Shell model +DWIA Itonaga et al., PRC 49 (1994) Woods-Saxon (K-P)+DWIA Motoba et al., PRC 38 (1988) From Hashimoto et al., PPNP 57
Shell model calculation 12XBe (11B+X-) (12C(K+,K-)12XBe) Active space for nucleons: p-shell X is fixed to the 0s1/2 orbit. Effective interaction for nucleons: Cohen-Kurath Effective interaction for N-X: YNG interaction by Yamamoto (G matrix, kF dependence) YN interaction model (VN-Xが引力的) ESC04d (Rijken and Yamamto PRC 73 044008 (2006)) NHC-D (Nagels et al. PRD 15 2547 (1977)) Non-central part is not included.
Single particle energy 12XBe Jp T kF tY UY tY+UY E BE (Y) ESC04d (X) 1-1 1 1.08 11.8 -16.1 -4.4 -57.4 4.5 NHC-D(X) 1.05 -15.3 -3.5 NS97f(L) 1/2 1.24 10.5 -22.5 -11.9 -65.1 12.2 kF in YNG is determined by the condition BE(X,1-1)~4.5 MeV. UX is comparable to the experimental data. UX ~ 14MeV (Fukuda et al., Khaustov et al)
p-shell matrix element of YNG Vb D(ss) h (D/Vb) N-X ESC04d 4.98 -15.81 -3.18 1 0.30 -2.96 -9.88 N-X NHC-D 2.14 4.75 2.23 1.55 0.79 0.51 N-L NSC 1/2 1.05 0.04 D for N-X is larger than that for N-L. ESC04d gives quite large D. D for ESC04d and NHC-D have opposite signs.
12XBe(11B+X) 11B+X The spectra for ESC04d and NHC-D show different behavior. The orders of the lowest two levels are different because of the sign changes of spin-spin part between ESC04d and NHC-D. ESC04d: intermediate (strong) coupling NHC-D: weak coupling (at least in the T=0 channel)
DWIA計算 12C(K-,K+)12XBe 殻模型計算で得られた波動関数を用いてDWIA計算を行った。 (K-,K+)反応 運動量移行が大きい（~500MeV/c@pK-=1.6GeV/c)のでJ-stretchedの状態が強く励起される。 アイソスピン移行は1
T=1, 1- state in 12XBe T=1/2 12C(K-,K+)12XBe反応で強く励起されるのはT=1,1-の状態。 (P(3/2-1Xs1/2),P(1/2-1Xs1/2), P(3/2-2Xs1/2)) 12C(K-,K+)12XBe反応で強く励起されるのはT=1,1-の状態。 ESC04dとNHC-Dでは波動関数の中身が大きく違う。（相互作用の違いを反映）
Exicitation Function NHC-D Smearing factor: 2MeV
Excitation Function ESC04d Smearing factor: 2MeV
Excitation Functionの比較 ESC04d NHC-D 波動関数（NY相互作用）の違いが励起関数に反映される。 X0p1/2 Woods-Saxon potential (Khaustov et al, PRC 61) X0s1/2
Summary 12XBeに対してN-X相互作用として ESC04dとNHC-Dに基づいたものを用いて殻模型計算を行った。 殻模型波動関数を用いて12C(K-,K+)12XBe反応に対する励起関数を求めた。 励起関数は波動関数の違いを反映しESC04dとNHC-Dとで大きく異なる。 →N-X相互作用の情報を得られる可能性？ 今後の課題 Xp→LLに対する幅 連続状態の影響（p状態) 他のN-X相互作用を用いた計算 fss2 etc.