Takuma Matsumoto (Kyushu Univ.) K. Minomo, K. Ogata a , M. Yahiro, and K. Kato b
description
Transcript of Takuma Matsumoto (Kyushu Univ.) K. Minomo, K. Ogata a , M. Yahiro, and K. Kato b
Takuma Matsumoto(Kyushu Univ.)
K. Minomo, K. Ogataa, M. Yahiro, and K. Katob
(Kyushu Univ, aRCNP, bHokkaido Univ)
Description for Breakup Reactions of Three-body Projectiles
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2
4
3
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2
3
Introduction
The Continuum-Discretized Coupled-Channels method (CDCC)Developed by Kyushu group about 20 years ago
M. Kamimura, M.Yahiro, Y. Iseri, Y. Sakuragi, H. Kameyama, and M. Kawai, Prog. Theor. Phys. Suppl. 89, 1 (1986)
Three-body breakup reactions
Four-body breakup reactions
Four-body CDCC method
6He
Target
4He
n
n
The CDCC equation of four-body systems is the same as that of three-body systems.
6He projectile : n + n + 4He (three-body model) S2n ~ 1 MeV
Three-body bound and discretized continuum states
Four-Body Breakup Reactions
Vnn: D. Gogny, et al., PLB32, 591 (1970), Vna: KKNN interaction
Channel 1 Channel 2 Channel 3
n n nn
nn
4He 4He 4He
Gaussian Expansion Method : E. Hiyama et al., Prog. Part. Nucl. Phys. 51, 223 An accurate method of solving few-body problems. A variational method with Gaussian basis functions Take all the sets of Jacobi coordinates
I=0+ I=1- I=2+
Exc
itat
ion
en
ergy
of
6 He
[MeV
]
Ground and breakup states of 6He
6He+12C scattering at 18 MeV 6He+209Bi scattering at 22.5 MeV
Nuclear Breakup
Nuclear & Coulomb Breakup
For elastic scattering, CDCC well reproduces the experimental data.
T.M. Hiyama, Ogata, Iseri, Kamimura, Chiba, and Yahiro, Phys. Rev. C70, 061601 (2004).
T.M. Egami, Ogata, Iseri, Kamimura, and Yahiro,Phys. Rev. C73, 051602 (2006).
Elastic Cross Section
In CDCC breakup cross sections are discrete.
E* (MeV)
(m
b)
6He+12C scattering at 240 MeV/nucl.
How to calculate the continuum breakup cross section
EXP. PRC59, 1252(1999), T. Aumann et al.
CDCC EXP
Breakup Cross Section
Continuous breakup T-matrix element
Smoothing factor :
Discrete T-matrix element
Smoothing factor for 3-body system
Smoothing factor for 4-body system
Smoothing factor :
Three-body continuum wave function Difficult to solveNot good convergency
M.Rodriguez-Gallardo, J. M. Arias, J. Gomez-Camacho,A. M. Moro, I. J. Thompson, and J. A. Tostevin,PRC80, 051601(R) (2009).
T. Egami, T.M., K. Ogata, M.Yahiro, PTP121, 780(2009) T.M., T. Egami, K. Ogata, M.Yahiro, PTP121, 885(2009)
New description of continuum breakup cross section with Complex-scaling method (CSM).
T.M., K. Kato, and M. Yahiro, PRC82, 051602 (2010).
Complex-scaling operator:
Coordinate:
Momentum:
k Im[k]
Re[k]
}Bound states
Resonance
ContinuumUseful for searching many-body resonances
Green’s function with Complex-Scaling Method (CDCS Green’s function)
S. Aoyama, T. Myo, K. Kato, and K. Ikeda,Prog. Theor. Phys. 116, 1 (2006)
Complex-Scaling Method
New Smoothing Procedure with CSM
Final state of the projectileResponse function
T-matrix calculated by CDCC
Green’s function with Complex-Scaling Method (CDCS Green’s function)
T.M., K. Kato, and M. Yahiro, PRC82, 051602 (2010).
New description of differential breakup cross section
Differential Breakup Cross Section
ConvergenceSystem : 6He + 12C scattering @ 40 MeV/A
1. Convergence of T-matrix elements calculated by CDCC
2. Convergence of Green’s function in calculating continuum cross sections.
The number of bases Gaussian range max
Set I 10 10 fm
Set II 15 20 fm
Set III 20 50 fm
We should confirm the convergence with extending the model space
Convergence of T-matrix (2+)
2+ (set II)2+ (set I)
The T-matrix calculated with set I gives good convergence
Convergence of Green’s Function
1-
0+
2+
Dashed : set ISolid : set IIMark : set III
Dashed : set ISolid : set IIMark : set III
The result with set II gives good convergence for Green’s function
6He + 12C and 208Pb scattering at 240 MeV/A T. Aumann et al, PRC59, 1252(1999).
Microscopic optical potential (Double folding model with Melbourne g-matrix)
n - 12C and 4He -12C potentials n – 208Pb and 4He – 208Pb potentials
VnA
VcA
VnAn
n
4He
12C, 208Pb
6He+12C scattering @ 240 MeV/nucl.
Exp. data from PRC59, 1252 (1999), T. Aumann et al.
Underestimation → Inelastic breakup effect ~ 20%
Nuclear Breakup is dominant
Breakup to 3- continuum is negligible
6He+208Pb scattering @ 240 MeV/nucl.
Exp. data from PRC59, 1252 (1999), T. Aumann et al.
Underestimation → Inelastic breakup effect
Overestimation ???
Coulomb Breakup is dominant
In order to obtain continuous breakup cross sections for four-body breakup, we propose a new smoothing method with the complex scaling method.
The convergence of breakup cross sections is confirmed with extending the model space.
The new smoothing method is applied to analyses for 6He breakup reactions on 12C and 208Pb at 240 MeV/A.
In a future work, we will analyse a four-body breakup reaction of 6He, 11Li, 14Be with the new smoothing method.
Summary