Analysis of (π ± ,K + ) and (K - ,K + ) spectra in DWIA HYP06, Friday, Oct. 13, 2006, Mainz, Germany H. Maekawa , K. Tsubakihara, A. Ohnishi Division of Physics, Graduate School of Science, Hokkaido University, Sapporo 060-0810, Japan 1. Introduction and our purpose 2. Model (DWIA with Green function method and Local optimal Fermi averaging) 3. Results(Λ 、 Σ 、 Ξ Quasi-Free spectra) 4. Summary
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Analysis of (π ±,K + ) and (K -,K + ) spectra in DWIA HYP06, Friday, Oct. 13, 2006, Mainz, Germany H. Maekawa, K. Tsubakihara, A. Ohnishi Division of Physics,
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Analysis of (π±,K + ) and (K - ,K + ) spectra in DWIA
HYP06, Friday, Oct. 13, 2006, Mainz, Germany
H. Maekawa, K. Tsubakihara, A. Ohnishi
Division of Physics, Graduate School of Science,
Hokkaido University, Sapporo 060-0810, Japan
1. Introduction and our purpose
2. Model (DWIA with Green function method and Local optimal Fermi averaging)
3. Results(Λ 、 Σ 、 Ξ Quasi-Free spectra)
4. Summary
Do we understand hypernuclear Quasi-Free spectrum ?
Previous DWIA calculation of (K,π), (π,K) and (K,K) reactions Bound state region
Successful expression of the hypernuclear production spectra QF(continuum) region
It is not possible to reproduce QF spectrum well though there are a lot of attempts.(S.W.Hong et al. 1999, M.T.Lopez-Arias 1995)
Auerbach et al., Annals of Physics 148(1983)381.
Traditional Fermi averaging
Recent analysis of hypernuclear Quasi-Free spectrum
Theoretical Cal.
Distorted wave impulse approximation:
T. Harada, Y. Hirabayashi, Nucl. Phys. A 744 (2004) 323.
Semi Classical Distorted Wave model:
M. Kohno, Y. Fujiwara, M. Kawai et al., PTP112 (2004)895.
Cascade model:
Y. Nara, A. Ohnishi, T. Harada and A. Engel, NPA614(1997)433.
T. Harada, Y. Hirabayashi, Nucl. Phys. A 744 (2004) 323
The key in this problem→Fermi averaging with on-shell classical kinematics of t-matrix(Harada and Hirabayashi)
Purpose of our study
・ In optimal Fermi averaging, the t-matrix is averaged under the on-shell kinematics in the free space(no potential effects)
・ We would like to include potential effects with the on-shell condition into the Fermi averaging procedure.
・ To confirm the validity our extension of Fermi averaging with potential effects, we attempt to calculate Λ, Σ and Ξ hypernuclear spectrum on several targets with our modification.
・ In optimal Fermi averaging, the t-matrix is averaged under the on-shell kinematics in the free space(no potential effects)
・ We would like to include potential effects with the on-shell condition into the Fermi averaging procedure.
・ To confirm the validity our extension of Fermi averaging with potential effects, we attempt to calculate Λ, Σ and Ξ hypernuclear spectrum on several targets with our modification.
Λ
ΣRepulsivRepulsivee
-30MeV-30MeV-50MeV-50MeV -50MeV-50MeV
nucleon
nucleon
Model: Green function method by Morimatsu and Yazaki Ref) O.Morimatsu and K.Yazaki, Nucl. Phys. A483(1988)493.S.Tadokoro,Y.Akaishi,H.Kobayashi. Phys.Rev.C51(1995)2656.M.T.Lopez-Arias, Nucl. Phys. A582(1995)440.
)(),';()('Im
1)( ''
* rrrrrr fEGfddES
)()(2
ESd
d
ddE
d
Average
ele
YKnKK
π
σβ
σ
Elementary cross section
Kinematical factor
Meson distorted waves
if NK )()()()( )()*( rrrr
Include the hyperon potential in Green function
iHUTEG
CoreYY
1
KK
MK
MK
K
K
Y
K
pE
pE
p
pp
E
E
cos
1
)()()( )()*( rrr qr iK e
z
zKNN dzzdzz ')'(')'(exp)( ρσρσπr
Strength function
Distortion factor
Double differential cross section
“Green function”
Strength function
Local Optimal Fermi Averaging of t-matrix (LOFAt)
π
N
K
Y
)()( 2*2 rmrE NNN p )(2)( 22* rVmmrm NNNN
)()( 2*2 rmrE YYY p )(2)( 22* rVmmrm YYYY
)()( rEErEE YKN
))()(()(
))()(()(),(),,(
4321)4(
4321)4(
rpprpppd
rpprppptstdrt
NN
NN
δρ
δρω
p
pq
We’d like to include the potential effects in the production points.
Local Optimal Fermi Averaging of t-matrix (LOFALocal Optimal Fermi Averaging of t-matrix (LOFAt)t)
Energy conservation equation
“potential”
→Include the potential effects into Fermi-averaging
・ Σ Quasi-Free analysis(Noumi et al., Harada and Hirabayashi, Kohno et al.): Σ -nucleus pot.:Repulsive (Woods-Saxon),V=+30MeV ~ +90MeV
With potential effect
W0Σ= 20MeV
⇒QF spectrum can be reproduced by small repulsive potential.⇒QF spectrum can be reproduced by small repulsive potential.
-30MeV
+50MeV
Σ hypernucler production spectrum on 28Si target
We consider the two type potentials derived from the Σ atomic data.
1.Batty density dependent potential
2.SCL-RMF model by Tsubakihara, Maekawa, Ohnishi(talk in previous session)
Batty-DD
SCL-RMF1
SCL-RMF2
Is the Quasi-Free data reproduced ??Is the Quasi-Free data reproduced ??
Σ - 27Al:UΣ WΣ
Σ hypernucler production spectrum on 28Si target
Batty’s DD
SCL-RMF1
Derived from Σ - X-ray data potential
⇒QF spectrum can be reproduced well using density dependent potentials derived from atomic data
(rather than the case of simple Woods-Saxon type potentials)
⇒QF spectrum can be reproduced well using density dependent potentials derived from atomic data
(rather than the case of simple Woods-Saxon type potentials)
SCL-RMF2
⇒Σ-nucleus potential is…
Structure of Attractive pocket and Repulsive coreAttractive pocket and Repulsive core is favored.
⇒Σ-nucleus potential is…
Structure of Attractive pocket and Repulsive coreAttractive pocket and Repulsive core is favored.
P. Khaustov et al., Phys. Rev. C61(2000) 054603-1.
Reasonable agreement between the data and theory is achieved by assuming a Ξ-nucleus potential well depth V0 of about 14 MeV within the Woods-Saxon prescription (DWIA calculation).
12C(K - ,K+)
PK=1.80GeV/c
Study of Ξ-nucleus potential by (K - ,K+) reaction
Theoretical curve:
DWIADWIA(Tadokoro et al,PRC51(1995)2656.)
INCINC(Y. Nara et al.,NPA614(1997)433.)
Ξ - hypernuclear production spectra on several targets