M. Matsuzaki, RIKEN "Mean-field theories and beyond", Mar. 21, 2006

1

Relativistic study of medium polarization effects on superfluidity in neutron matter

nuclear

Masayuki Matsuzaki(Fukuoka University of Education)

M. Matsuzaki, RIKEN "Mean-field theories and beyond", Mar. 21, 2006

2

Medium polarization effect on superfluidity

Neutron matter

reduce pairing gap significantly

reduction is weak

M. Matsuzaki, RIKEN "Mean-field theories and beyond", Mar. 21, 2006

3

Symmetric matter

enhance pairing gap

Finite nuclei

enhance pairing gap

… preliminary

M. Matsuzaki, RIKEN "Mean-field theories and beyond", Mar. 21, 2006

4

Relativistic approach (σ-ω model)

M. Matsuzaki, RIKEN "Mean-field theories and beyond", Mar. 21, 2006

5

Thermodynamics at T=0

instability !

Liquid-gas

M. Matsuzaki, RIKEN "Mean-field theories and beyond", Mar. 21, 2006

6

Quantum mechanics

calculate meson propagator (q =0)0

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Nucleon propagator

xxxxxx

xxx

k0

: pha decomposition--- M.Nakano et al.,PRC56, 3287 (1997)

: FD decompositon --- standard

hpmed GG

DFmed GG

paF GofpartaGG phD GofpartothertheGG ( , )

M. Matsuzaki, RIKEN "Mean-field theories and beyond", Mar. 21, 2006

8

(Longitudinal) dielectric function

FD pha

instability ! instability !

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Pairing interaction at 1-loop level

ill-defined at instability !

10

(Cross section of dielectric function)

infra-red cutoffis necessary

free from instability

0.65 is chosen

11(corrected using a form factor at tree (OBE) level)

(instability)

M. Matsuzaki, RIKEN "Mean-field theories and beyond", Mar. 21, 2006

12

Form factor

at every vertex to modulate high mom. interaction

present

so as to reproduce the result of Bonn-B potential

M.M. and T.Tanigawa, NPA683, 406 (2001)

13σ,longitudinal-ω:attraction, σ-ωmix: repulsion

FD

pha

repulsion

attraction

OBERPA VV

M. Matsuzaki, RIKEN "Mean-field theories and beyond", Mar. 21, 2006

14

Neutron matter

instability

M. Matsuzaki, RIKEN "Mean-field theories and beyond", Mar. 21, 2006

15

Summary

Liquid-gas instability occurs at medium density

Medium polarization enhances gap at low and medium density

At high density, FD enhances gap whereas pha reduces gap

Characteristic cancellation among σ,ω, and σ-ωmix

Result for neutron matter is similar

M. Matsuzaki, RIKEN "Mean-field theories and beyond", Mar. 21, 2006

16

Acknowledgement

Prof. P. Ring （ Munich) for suggesting the problem

Prof. H.Kouno （ Saga) for useful discussions

M. Matsuzaki, RIKEN "Mean-field theories and beyond", Mar. 21, 2006

17

FD

pha

attraction

M. Matsuzaki, RIKEN "Mean-field theories and beyond", Mar. 21, 2006

18

M.M. and P.Ring, nucl-th/9712060

(Preliminary cal.)

OBE

pha FD