1. M. Matsuzaki, RIKEN "Mean-field theories and beyond", Mar. 21, 2006
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. M. Matsuzaki, RIKEN "Mean-field theories and beyond", Mar. 21, 2006
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. M. Matsuzaki, RIKEN "Mean-field theories and beyond", Mar. 21, 2006
Symmetric matter
… preliminary
enhance pairing gap
Finite nuclei
enhance pairing gap
M. Matsuzaki, RIKEN "Mean-field theories and beyond", Mar. 21, 2006

4. M. Matsuzaki, RIKEN "Mean-field theories and beyond", Mar. 21, 2006
Relativistic approach (σ-ω model)
M. Matsuzaki, RIKEN "Mean-field theories and beyond", Mar. 21, 2006

5. M. Matsuzaki, RIKEN "Mean-field theories and beyond", Mar. 21, 2006
Thermodynamics at T=0
Liquid-gas
instability !
M. Matsuzaki, RIKEN "Mean-field theories and beyond", Mar. 21, 2006

6. M. Matsuzaki, RIKEN "Mean-field theories and beyond", Mar. 21, 2006
Quantum mechanics
calculate meson propagator (q =0)
M. Matsuzaki, RIKEN "Mean-field theories and beyond", Mar. 21, 2006

7. ( ) Nucleon propagator k : pha decomposition --- M.Nakano et al.,
: pha decomposition
--- M.Nakano et al.,
PRC56, 3287 (1997)
xxx
xxx
xxx
: FD decompositon --- standard ( ) ,

8. M. Matsuzaki, RIKEN "Mean-field theories and beyond", Mar. 21, 2006
(Longitudinal) dielectric function
pha FD
instability !
instability !
M. Matsuzaki, RIKEN "Mean-field theories and beyond", Mar. 21, 2006

9. Pairing interaction at 1-loop level
ill-defined at instability !

10. (Cross section of dielectric function)
free from instability
infra-red cutoff
is necessary
0.65 is chosen

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

12. M. Matsuzaki, RIKEN "Mean-field theories and beyond", Mar. 21, 2006
Form factor
at every vertex to modulate high mom. interaction
so as to reproduce the result of Bonn-B potential
present
M.M. and T.Tanigawa, NPA683, 406 (2001)
M. Matsuzaki, RIKEN "Mean-field theories and beyond", Mar. 21, 2006

13. σ,longitudinal-ω:attraction, σ-ωmix: repulsionFD
attraction
repulsion
pha
σ,longitudinal-ω:attraction, σ-ωmix: repulsion

14. M. Matsuzaki, RIKEN "Mean-field theories and beyond", Mar. 21, 2006
Neutron matter
instability
M. Matsuzaki, RIKEN "Mean-field theories and beyond", Mar. 21, 2006

15. M. Matsuzaki, RIKEN "Mean-field theories and beyond", Mar. 21, 2006
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. M. Matsuzaki, RIKEN "Mean-field theories and beyond", Mar. 21, 2006
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. M. Matsuzaki, RIKEN "Mean-field theories and beyond", Mar. 21, 2006FD
attraction
pha
M. Matsuzaki, RIKEN "Mean-field theories and beyond", Mar. 21, 2006

18. M. Matsuzaki, RIKEN "Mean-field theories and beyond", Mar. 21, 2006
(Preliminary cal.)
pha FD
OBE
M.M. and P.Ring, nucl-th/
M. Matsuzaki, RIKEN "Mean-field theories and beyond", Mar. 21, 2006