1. Global fitting of pairing density functional; the isoscalar-density dependence revisited Masayuki YAMAGAMI (University of Aizu) Motivation Construction of energy density functional for description of static and dynamical properties across the nuclear chart ⇒ Focusing on the pairing part (pairing density functional) a.Determination of  –dependence (Not new problem, but one of bottlenecks in DF calc.) b.Connection to drip-line regions

2. Our discussion Density dependence of pairing in nuclei NN scattering of 1 S 0 (strong @low-  Many-body effects (e.g. phonon coupling) Standard density functional for pairing Our question: How to determine  0 ?? phonon coupling

3. Difficulty for  0 (  -dependence) Mass number A dependence of pairing J. Dobaczewski, W. Nazarewicz, Prog. Theor. Phys. Supp. 146, 70 (2002)  0 =1  0 =0 Neutron excess  =(N-Z)/A dependence Mass data: G. Audi et al., NPA729, 3 (2003)  n,exp : 3-point mass difference formula (same dependence for proton pairing)

4. Our model Pairing density functional with isoscalar & isovector density dep. Parameter optimization Theoretical framework Hartree-Fock-Bogoliubov theory ( Code developed by M.V. Stoitsov et al. ) Axially symmetric quadrupole deformation Skyrme forces (SLy4, SkM*, SkP, LNS) Energy cutoff = 60 MeV for pairing

5. Procedures for parameter optimization Data: G. Audi et al., NPA729, 3 (2003)  exp : 3-point mass difference formula

7. Extrapolation: Zone1 → Zone2, 3 - Skyrme SLy4 case -

8. Specific examples in Zone3 (outside fitting) Sn Pb

9. Verifying for typical Skyrme forces

10. Connection to drip-line region (low-  limit) (à la Bertsch & Esbensen)

11. Validity of assumption V 0 =V vac Comparison Procedure 1; V 0 =V vac + optimized (  0,  1,  2 ) Procedure 2; Optimized (  0,  1,  2, V 0 ) Results m*/m=0.7~0.8 ⇒ Good coincidence Procedure 1 ~ Procedure 2 m*/m=1.0 ⇒  tot of 1 & 2 are comparable, although the minimum positions are different. ☺ ☹

12. Conclusion a.Strong  –dep. (  0 ～ 0.8 ) for typical Skyrme forces b.  1 –tems should be included. c.Connection to drip-line regions, if m * /m=0.7~0.8. 1.  -dependence of the pairing part of local energy density functional is studied. 2. All even-even nuclei with experimental data are analyzed by Skyrme-HFB.

13. ☹ ☺

14. Definition of pairing gap

15. Pairing gap: A-dependence only

16. Survey of  1 (opt.) : pairing and effective mass  -dependence of effective masses 12 Skyrme parameters SKT6 (  =0.00), SKO’ (0.14), SKO (0.17), SLy4 (0.25), SLy5 (0.25), SKI1 (0.25), SKI4 (0.25), BSK17 (0.28), SKP (0.36), LNS (0.37), SGII (0.49), SkM* (0.53)