(飛行 K-, n) 反応による K-pp 生成スペクトルと K--核間有効ポテンシャルのエネルギー依存性 ストレンジネス核物理2010、　ＫＥＫ　小林ホール、　2010年12月3日 (飛行 K-, n) 反応による K-pp 生成スペクトルと K--核間有効ポテンシャルのエネルギー依存性 K-pp formation spectrum via (in-flight K-, n) reaction, and energy dependence of K- -nuclear effective potential Takahisa Koike RIKEN Nishina center Toru Harada Osaka E.C. Univ.　

◆ J-PARC E15 experiment for searching “K-pp” 3He(In-flight K-, n) “K-pp” missing-mass 　 at pK- = 1 GeV/c and qn=0o 　　 spectroscopy 　　　　　　　　　　　+　　　　 “K-pp” →Lp → p-pp invariant-mass detecting decay particles spectroscopy from “K-pp” Simultaneous mesurement Our purpose: theoretical calculation of 3He(In-flight K-, n) inclusive/semi-exclusive spectra within the DWIA framework using Green’s function method. T. Koike & T. Harada, Phys. Lett. B652 (2007) 262-268. T. Koike & T. Harada, Nucl. Phys. A804 (2008) 231-273. T. Koike & T. Harada, Phys, Rev. C80 (2009) 055208. c.f. J. Yamagata-Sekihara et al., Phys, Rev. C80 (2009) 045204.

Why the magnitudes of the calculated cross sections are so different each other? Koike & Harada Inclusive spectra Yamagata-Sekihara et al.

Why the magnitudes of the calculated cross sections are so different each other? Koike & Harada Conversion spectra Yamagata-Sekihara et al.

◆Distorted-Wave Impulse Approximation (DWIA) Strength function Kinematical factor Fermi-averaged ementary cross-section K- + n → N + Kbar in lab. system Morimatsu & Yazaki’s Green function method　 Prog.Part.Nucl.Phys.33(1994)679.　 Green’s function K-pp system → employing K--“pp” effective potential recoil effect Distorted wave for incoming(+)/outgoing(-) particles → Eikonal approximation neutron wave function → (0s)3 harmonic oscillator model

◆ Difference in DWIA formulation Koike & Harada Kinematical factor Fermi-averaged ementary cross-section Yamagata-Sekihara et al. ementary cross-section in free space

◆ Kinematical factor b = 1.5 ~ 2.0 in bound state region. a + “N”→ b + c : Two-body kinematics → subscript (2) a + A → b + A’ : Many-body kinematics b = 1.5 ~ 2.0 in bound state region.

◆ Momentum transfar for (K-, N) reactions p n pK = 1 GeV/c n p K- q pn q = pK - pn < 0 q > 0 → b < 1 e.g. (p, K), (K-, K+) forward q ~ 0 → b ~ 1 e.g. (K, p) recoilless backward q < 0 → b > 1 e.g. (K-, N) The sign of q is important!

◆ KbarN elementary cross sections in lab. system reduced to ~ 60% in Free Space with Fermi-average

◆ Difference in DWIA formulation Koike & Harada Fermi-average ( 1.5 ~ 2.0 ) ×0.6 = 0.9 ~ 1.2 Eventually, b [ds/dW] is not so much different! Yamagata-Sekihara et al. ementary cross-section in free space

◆ Another difference in DWIA formulation --- w/o recoil effect Morimatsu & Yazaki’s Green function method　 Prog.Part.Nucl.Phys.33(1994)679.　 Green’s function K-pp system → employing K--“pp” effective potential Recoil effect Distorted wave for incoming(+)/outgoing(-) particles → Eikonal approximation neutron wave function → (0s)3 harmonic oscillator model

◆ Recoil effect Bound state peak is enhanced by a factor of ~1.8 with recoil factor.

◆ Difference in DWIA formulation Koike & Harada Fermi-average ( with recoil ) ( 1.5 ~ 2.0 ) ×0.6 × 1.8 = 1.6 ~ 2.2 ~ a factor 2 difference --- Not enough? Yamagata-Sekihara et al. ( without recoil ) ementary cross-section in free space

K-pp – Kbar0np coupling should be considered in charge basis. ◆ Yet another difference --- charge basis picture vs. isospin basis picture n 3He p K- K- p p K0 K0 n p - K-pp – Kbar0np coupling should be considered in charge basis.

◆ Charge basis picture + - incoherent sum 3He 3He Yamagata-Sekihara et al. n 3He p K- K- p p + p 3He n K- K0 K0 n p - incoherent sum

◆ Isospin basis picture Koike & Harada - K K- p p - K N N N N N N - - K0 n p - [ K× {NN}I=1]I=1/2 isoscalar transition amplitude

◆Comparison of Fermi-averaged elementary cross sections between charge and isospin basis In charge basis, = 13.9 mb/sr K-+n → n+K- = 7.5 mb/sr K-+p → n+Kbar0 In isospin basis, = 16.4 mb/sr, = 1.2 mb/sr D I = 0 D I = 1

Yamagata-Sekihara et al.

◆Comparison of the calculated inclusive spectra Koike & Harada Inclusive spectra Yamagata-Sekihara et al.

◆Comparison of the calculated inclusive spectra Yamagata-Sekihara et al. Koike & Harada charge basis isospin basis K-pp + Kbar0np [Kbar×{NN} I=1 ] I=1/2 QF-peak height ~ 160 mb/sr ~ 100 mb/sr ~ 160 mb/sr × 0.75 = ~ 120 mb/sr K-pp-Kbar0np coupling effect

◆Comparison of the calculated conversion spectra Koike & Harada Conversion spectra Yamagata-Sekihara et al.

◆Comparison of the calculated conversion spectra Yamagata-Sekihara et al. Koike & Harada charge basis isospin basis K-pp + Kbar0np [Kbar×{NN} I=1 ] I=1/2 Bound state peak height ~ 15 mb/sr ~ 25 mb/sr ~ 15 mb/sr × 0.75 × 1.8 = ~ 20 mb/sr K-pp-Kbar0np coupling effect Recoil effect

◆ Summary on the cross section ・ The magnitudes of the calculated cross sections are rather consistent with each other! Accidental coincidence: b ×[ds/dW] (Fermi-average) ~ [ds/dW] (Free-space) b. Few-body system: Recoil effect enhances a bound-state peak by a factor 1.8. c. ( [ K-pp ] + [K0barpn] in charge basis ) × 0.75 ~ [ KbarNN ] in isospin basis ・ Do NOT directly compare the charge basis calculation with the isospin basis one. Experimentally, K-pp and K0barpn in charge basis can not be distinguished.

The integrated cross section of L = 0 K- conversion part amounts to 3.5 mb/sr. L = 0 component L = 0 K- conversion L = 0 K- escape

L = 0 K- conversion from K- pp bound-state L = 0 component L = 0 other K- conversion process L = 0 K- escape