KEK理論センター研究会「ストレンジネス核物理２０１０」
2010年12月2-4日
高エネルギー加速器研究機構,つくば市

２重荷電交換反応によるハイパー核の生成と核成
ハイペロン混合原田 融 (大阪電気通信大学工)平林義治 (北大情報基盤センター）
梅谷篤史 (理研仁科センタ(理研仁科センター))

Contents -1
1.

Introduction

2.

The reactions

2重荷電交換反応

10Li
Production of neutron-rich  hypernuclei --- Σ-

3.

The (K-,K+) reactions
Production of hypernuclei

Production of  hypernuclei
4.

---16
Ξ
Ξ---- 16ΛΛC

C

Summary2２重荷電交換反応
ハイパー核の研究
イパ 核の研究
中性子過剰ハイパー核の研究（,K+), (K,+) S（（K,K+) S
@J-PARCハイパー核の研究（中性子過剰）ダブルハイパー核の研究
バリオン相互作用の解明 → 中性子星の構造
Neutron-rich  hypernuclei

Neutron-rich  hypernuclei

16O(K, K+)16C at p( , K+),((, K0) (K0, )

K=1.65GeV/c-

Neutron-rich nuclei
KEK: J-PARC(K, K+),(K, 0) (0, K+)Neutron star core
“An interesting neutron-rich hypernuclear system”
Hyperon-mixing
Coupling constant ratio;xiY  giY giN (i ,, )U  0U  0U  0U  0

F. Weber, Prog. Part. Nucl. Phys. 54 (2005) 193U  0U  0

R. Knorren, M. Prakash, P.J.Ellis,PRC52(1995)3470

Cassiopeia A nebula
NASA/CXC/SAO.
4

The (,KK+) reactions
Production of neutron-rich  hypernuclei
via  doorways
70 MeV
M V

“Feasibility of extracting a  admixture probability
in the neutron-rich hypernucleus”
10T. Harada, A. Umeya, Y. Hirabayashi, PRC79 (2009) 014603

Li

5

First production of neutron-rich  hypernuclei
10B(  , K  ) 10 Li spectrum by DCX reaction at 1.2GeV/c

Cross sections

KEK-PS-E521 P. K. Saha, et al., PRL94(2005)052502
2.5 MeV FWHM

11.3±1.9 nb/sr

gsg.s.

- p=1.20 GeV/cd
 11 3±1 9 nb/srd  L 11.3±1.9- p=1.05 GeV/c
Lidd  L 5.8±2.2 nb/sr～1/1000
1/1000g.s.

Li

12C(  , K  )12 C (1.2 GeV/c)
17.5±0.6 b/sr

The DCX (,K+) reaction at 1.2GeV/c can produce the neutron-rich  hypernucler
states, whereas the cross section is as small as 1/1000 of the (+,K+) reaction.

6(－, K+) －Double Charge Exchange (DCX) Reaction
Two-step process:-K+  p  K 0
K 0 p  K np p  n
 0 p  K 

0One-stepp pprocess:

pp

pnnK+

-  p  K

 p  nviaby N-N couplingK0K 0 p  K n

  p  K  doorways caused  p K0

pppDoorway
p

n


n7

Results (1) spectrum by DCX reaction at 1.2GeV/cSSpreading
di potentialt ti l dep.
dWfixed P=0.57=0 57%U X  11 MeV
M V is fixed.

10B
Li

W=2
Harada, Umeya,Hirabayashi,
PRC79(2009)014603(s3+(pTwo-step mechanism

The calculated spectrum with WW= 2020-30
30 MeV can reproduce the shape of thedata in the continuum region, and these values of W are consistent with theanalysis of  QF production by the (, K+) reactions.

8Calculation for DCX stopped reactions
If the  admixture probability of ~00.66 % is assumed in 12 Be,Be
we demonstrate the (stopped K,+) spectrum on a 12C target.
12C

Early
KEK data

 4106 / K 
Integrated
production rate

Th result
Thisl is consistent withh recent data
dfform DANE.
NEThe DANE data:

U.L.  (2.00.4)105 / K

M.Agnello, et al.,PLB640(2006)145.
9Remarks
The calculated spectrum by the one-step mechanism
fully explains the 10B(, K+) data.
The  admixture probability
is on the order of 10−1 % for 10Lidue to - couplings.
The (, K+) reactions can provide the ability to extracta production mechanism and  admixture
probabilities of neutron-rich  hypernuclei
from experimental data.
10+Th ( ,  )Thereactions
ti

Production of S = -2 hypernuclei
via  doorways

20 MeV“Production of doubly strange hypernuclei via − doorways
in the 16O(K−, K+) reaction at 1.8GeV/c”
T.Harada, Y.Hirabayashi, A.Umeya, Phys. Lett. B690(2010)363.

16C
CC


16



11

Studies of interaction of  hyperon with the nucleus
Studies of -hypernucleiypvia ((K,K+), ) reactions
28Si

C.B. Dover, A.Gal, Ann. Phys. 146 (1989) 309.

V?

Analysis of the nuclear Kp → K+ reaction
The potential depth parameters is obtained byV0  24  4 MeV for r0  1.1 fm (W0  1 MeV)
Data: T.Iijima, et al.,NPA546(1992)588.

Coulomb-assisted  hybrid bound states
T d k
Tadokoro
ett al.,PRC51(1995)2656
l PRC51(1995)2656

Analysis of 12C(K-,K+)
spectrum suggests
BNL-E885V0  16 MeV

12C

DWIA analysis
l i off 12C(K,K+)C(K K+) datad t att 1.8GeV/c
1 8G V/P.Khaustov et al., PRC61(2000)054603

Comparisonpwith the data in the  bound regiongV0  ( 12)-( 14) MeV

Kohno-Fujiwara,
PRC79(2009)054318“ V～0 MeV”

12

(K ,K+) －Double Charge Exchange (DCX) Reactions
K   p  K   

Elementary cross sections
Dover and Gal, Ann. Phys, 146 (1983) 309.
K  p  K 
35 b/sr

Green’ss function method
GreenMorimatsu, Yazaki, NPA483(1988)493

S ( )   | f | Oˆ | i |2  (  EK  E )1

1.8 GeV/cfIm  drdr F†(r )G(  i ; r , r ) F (r )Green’s function
13Momentum transfer to the ,  hyperon
1.8 GeV/c14 spectrum in DCX reactions at 1.8GeV/c
16O

15N+

W0 ( E )  3 MeV
Woods-Saxonr0  1.1
1 1 fmfm, a  00.66 fm

V0  24 MeV
14 MeV
1.5MeV FWHM

• Spin-stretched Ξ– states can be populated due to the high momentum transfer.
d/d[15N(1/2)ٔs ](1= 6 nb/sr, d/d[15N(1/2)ٔp](2+) = 9 nb/sr for V=14 MeV.

15

Recent Theoretical calculationsHeavy  -hypernuclei via (K,K+) reaction
208Pb

Tadokoro et al.,PRC51(1995)2656

Analysis of 12C(K-,K+) spectrum suggests

V0  16 MeV for r0  1.1 fm
Coulomb-assisted hybrid bound state
Semi-Classical Distorted Wave Model Analysis
S. Hashimoto, et al.,PTP119 (2008)1005

V0   50,  20,

12C

 20 MeV

12C

V0  14 MeV
DWIA analysis
l i off theth nuclearl(K,K+)(K K+) reaction
ti att 1.65GeV/c
1 65G V/H. Maekawa, et al., arXiv:0704.3929
16Energy spectrum of Ξ and ΛΛ nuclei on a 16O target16C= 18.4 MeV

16

C. TheTh energy shifts
hif ΔB are not taken
k intoiaccount.
See also Dover, Gal and Millener, NPA572(1994) 85.

17

(,K+) －Double Charge Exchange (DCX) Reactions
・Two-step process:K p  0K  p   0
 0 p  K 

 0 p  K ・One-step process:K  p  K   p  K p  K

- coupling

Doorway(0)† †(0)(0)t K  p  K    G  t K  p  K     tGUGUG    tK pK  K pK   18

Models for calculations

15Single particle shell model wf.
Single-particlewf
16
 -C   [ J ( 14 C) j(1 ) (r1 )]J ''  (j2C  ) (r 2 ) 
JJ '' j2  [ J ( 14 C) jNp (rp )](J ' N)  (j3C   ) (r ) 
JJ ' jN+

18 MeV

15

143C++T 1Hyperon-nucleus potentials

2/3
1/3fm, a  0.6 fmWoods-Saxon + derivative form R  r0 ( A 1)) fm, r0  1.080  0.395 A

U Y  ,  VY f (r , R, a )  iWY (r , R ', a ')  iWY( D ) g (r , R ', a ')-29.34 MeV for Spreading potential: energy-dependent g(E) = excited states

coupling -pot.

zero range interaction:
zero-range0v -N  v)-N  (r  r ')volume integral: v -N 0v

 -N(r )dr19

Coupled-channel Green’s function
Green’s function method

Morimatsu, Yazaki, NPA483(1988)493

12ˆS ()  | f | O | i |  (  EK  E )   Im  drdrF†(r)G(  i ; r, r)F (r)f

The completeness relation including the intermediate states

Coupled-channel Green’s function

Green’s function

T.Harada, NPA672(2000)181

ˆ ( )  G
ˆ (0) ( )  G
ˆ (0) ( ) UGˆ ˆ ( )G(0)Gˆ () G(0) G (0)ˆ   UUUU U ˆ (  )†{Im Gˆ (0) }ˆ ()  
ˆ (  )†{Im Gˆ (0) }ˆ (  )  Gˆ†{W }GˆIm Gˆ  Y ,T escape escapeSpreading (nuclear-core breakup）= Complicated excited states20 spectrum in DCX reactions at 1.8GeV/c
16O

1 5M V FWHM
1.5MeV03v
-N  500 MeV  fm

“NSC04a”

03v
-N  250 MeV  fm

“NHC-D”• The shape of the calculated spectrum is quite sensitive to the value of v0 ΞN,ΛΛ.
• Significant peaks of the 11− excited states with14C(0+)ٔs p at ω = 362.1 MeV (BΛ ΛΛΛ = 15.1 MeV)
14C‫(כ‬2+) ٔs p at ω =368.5 MeV (BΛ ΛΛΛ = 8.7 MeV)

21 spectrum in DCX reactions at 1.8GeV/c16OV  14 MeV

12 nb/sr(8 8 %)(8.803v
500
MeV

fm
-N

“NSC04a”

7 nb/sr(5 8 %)(5.81.5MeV FWHM

The large momentum transfer qΞ− ؄ 400 MeV/c leads to the spin-stretched Ξ−
doorways states followed by [15N(1/2−, 3/2−) ٔ sΞ−]1− → [14C(0+, 2+) ٔ sΛpΛ]1−

22

Elementary Cross sections for (K,K+) reactions
K   p  K   K   p   0  ,  0  p  K   

Dover and Gal, Ann. Phys, 146 (1983) 309.

Bando et al., Int.J.Mod.Phys. A5(1990)4021
K   n   

1.1 GeV/c

K  p  K    p  K   

1.8 GeV/c

These different mechanisms are well separated kinematically.

23

Compared with the two-step mechanism“On the formation and spectroscopy
ppy of  hypernuclei”
ypA.J. Baltz, C.B. Dover and D.J. Millener, PLB123(1981)12.
1.1 GeV/c

1.1 GeV/c

The  states populated by the two-step processes are quite different fromthose by the one-step processes.
16K  p  0 L1 0 p K 

16O    N 
 CL216
 L   L1   L2

24

Production of -hypernuclei via 2-step reactions
CB DC.B.
Dover, Nukleonica
N kl
i 25 (1980) 521

EikEikonall approximation
i ti
入射粒子


pKp


pKp

b

標的核

放出粒子





T-matrix elementsiip  b i ( pK   p ) z ' i ( p  pK  ) z(2)Tfi    d b dz '  dz θ( z  z '))eeev 1   1 z
  1 z'
 exp  i
U (b, z)dz  exp  i  U (b, z)dz  exp  i
UK  (b, z)dz 'z v  z K   vK  K  v

Eikonal distortion

 t1 (b)t2 (b) f V (l ) (3) (r  rl )V ( j) (3) (r  rj ) il jA crude estimation for the two-step contributions
Eikonal approximation
ppin a harmonic oscillator model
C.B. Dover, Nukleonica 25 (1980) 521
T. Iijima et al., NPA546(1992)588.

Summed lab cross section at 0oK  p 0 

 d 2 1  d f  d    p20 r 2 1 d   0


0
(2)
fi

1  1  Q0(1) v  N 2  2  1  Q0(2) vK   2dQ t1 (Q ) t2 (Q ) 0.022  0.019fm(2 )2 t1 (0)t2 (0)
K  p  0 

1 ( d / d  ) 0

 1.57  1.26 mb/sr

 0 p K   d 2 d   0PP
Neff

Shadowingg effects

1/ r 2  0.028mb1
 0 pK   2 (d / d )0



 0.070  0.067 mb/sr

Nefppf  1 including the nuclear distortion effects.
Thus,

Bound state production due to q = 400 MeV/c d (2)fi
f  d    0.06  0.04  b/sr   1%  0.6  0.4 nb/sr
0

Doverらの計算値から１桁以上小さくすべき !!

Remarks
One-step mechanism via Ξ− doorways
predicts promising peaks ofthe ΛΛ bound and excited statesin the 16O(K−, K+) reactions at 1.8 GeV/c (0◦).
The (K,K+) reactions can provide the ability to
extract properties of the N- potentials
and  admixture probabilities
in doubly strange hypernuclei.

27

Summaryy
Studies of the double-charge exchange
reactionsti(DCX) ffor hypernuclearhl
productionsd ti
arevery important
it t andd promisingii
at J-PARC.
Future subjects:
jMore microscopic calculations
based on YN,, YY ppotentials areneeded to compare them with theforthcoming experimental data atJ-PARC.
28