DWIA calculation of 3 He (In-flight K -, n) reaction RIKEN, Advanced Meson Science Lab. Takahisa Koike KEK 研究会「現代の原子核物理－多様化し進化する原子核の描像」、 2006 年 8 月 3 日

● FINUDA at DA  NE: stopped K - reaction on 6 Li, 7 Li, 12 C “K - pp”→  p invariant-mass spectroscopy Reported: B.E. (K - pp) = 115 MeV,  67 MeV. ● Magas, Oset, Ramos & Toki : critical view Ref. nucl-th/ (2006) FINUDA results: NOT “K - pp” deeply-bound state, BUT FSI after two-nucleon absorption. K - +”NN”→  p p+N→p’  N’ … still controversial. Search for “K - pp” deeply-bound state ● Yamazaki & Akaishi: prediction of “K - pp” deeply-bound state, motivated from chain ;  *= K - p,  *p = K - pp,  *pn = K - ppn, … Predicted: B.E. (K - pp) = 48 MeV,  61 MeV. Ref. PLB535 (2002) 70. Ref. PRL94 (2005)

 Iwasaki et al. (RIKEN): 3 He(In-flight K -, n) “K - pp” proposed for J-PARC, but NO theoretical calculation exists so far. → direct motivation of our present calculation. ● Yamagata, Nagahiro & Hirenzaki Phys. Rev. C74, (2006). 12 C (In-flight K -, p), 16 O (In-flight K -, p) DWIA calculation limitted to midium ~ heavy nuclei Other possible reactions suited for searching “K - pp” ● Yamazaki & Akaishi: DWIA calculation using  * doorway model p(p, K + ) “K - pp” (i.e. p+p → K + +  *+p → K +  ” K - pp”) Falicity : FOPI at GSI nucl-th/ (2006). c.f. Other theoretical calculation of (In-flight K, N) reactions Exp: Kishimoto et al. (Osaka Univ.)

◆ Distorted-Wave Impulse Approximation (DWIA) Kinematical factor Fermi-averaged ementary cross-section n(K -,n)K - in lab. system Strength function Morimatsu & Yazaki’s Green function method neutron hole wave function distorted wave for incoming(+)/outgoing(-) particles K - -“pp” system recoil effect Green’s function of Klein-Gordon eq. for K-K- p n p n p p K-K-

-300 c.f. Klein-Gordon E K = -51 MeV  = 68 MeV Schordinger FINUDA E K = -115 MeV  = 67 MeV

◆ Parameters ●  Distorted wave － Eikonal approximation ●  3 He wave function － (0s) 3 harmonic oscillator model ●  K - -”pp” optical potential ●    Akaishi-Yamazaki ( r.m.s charge radius of 3 He )

Our calculation Yamagata, Nagahiro & Hirenzaki, taken from PRC74, (2006), fig.3 12 C( In-flight K -, p) reaction

Gaussian type Woos-Saxon type Both of these potentials give almost same 0s-state energy & width.

L = 0 K - pp

◆ Problems in the present calculation ●  Simple harmonic oscillator model for 3 He target. Realistic wave function has to be used. ●  The “pp” pair is treated as rigid core. No contraction effect. Internal degree of freedom should be taken into account. ●  Two nucleon absorption process is not considered. Contribution from these must be checked. ●  Single channel calculation with effective KN interaction. Coupled channel between ●  Method of fermi-averaging affects the quasi-free spectrum. ・・・ K - + n → n + K - K - + p → n + K 0

Akaishi, Yamazaki, …Oset, Toki, … cleary distinguishable by 3 He(In-flight K -,n) inclusive spectra. ◆ Summary Deep Shallow preliminary