1. (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.　

2. ◆ 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)
T. Koike & T. Harada, Nucl. Phys. A804 (2008)
T. Koike & T. Harada, Phys, Rev. C80 (2009)
c.f. J. Yamagata-Sekihara et al., Phys, Rev. C80 (2009)

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

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

5. ◆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

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

7. ◆ 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.

8. ◆ Momentum transfar for (K-, N) reactionsp 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!

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

10. ◆ 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

11. ◆ 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

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

13. ◆ 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

14. 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.

15. ◆ 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

16. ◆ 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

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

18. Yamagata-Sekihara et al.

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

20. ◆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 × = ~ 120 mb/sr
K-pp-Kbar0np
coupling effect

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

22. ◆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 × × 1.8 = ~ 20 mb/sr
K-pp-Kbar0np
coupling effect
Recoil
effect

23. ◆ 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.

24. 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

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