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Global fitting of pairing density functional; the isoscalar-density dependence revisited

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.

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Global fitting of pairing density functional; the isoscalar-density dependence revisited

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  1. Global fitting of pairing density functional;the isoscalar-density dependence revisited MasayukiYAMAGAMI (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) Determination of r–dependence (Not new problem, but one of bottlenecks in DF calc.) Connection to drip-line regions

  2. Our discussion Density dependence of pairing in nuclei • NN scattering of 1S0 (strong @low-r) • Many-body effects (e.g. phonon coupling) Standard density functional for pairing phonon coupling Our question:How to determine h0 ??

  3. Difficulty for h0 (r -dependence) Mass number A dependence of pairing J. Dobaczewski, W. Nazarewicz, Prog. Theor. Phys. Supp. 146, 70 (2002) h0=1 h0=0 Neutron excess a=(N-Z)/Adependence (same dependence for proton pairing) Mass data: G. Audi et al., NPA729, 3 (2003) Dn,exp: 3-point mass difference formula

  4. Our model Pairing density functional with isoscalar & isovector density dep. 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 Parameter optimization

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

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

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

  8. Verifying for typical Skyrme forces

  9. Connectionto drip-line region (low-r limit) (à laBertsch & Esbensen)

  10. Validity of assumption V0=Vvac Comparison Procedure 1;V0=Vvac + optimized (h0, h1, h2) Procedure 2;Optimized (h0, h1, h2, V0) Results ☺ m*/m=0.7~0.8 ⇒ Good coincidence Procedure 1 ~Procedure 2 ☹ m*/m=1.0⇒ stotof 1 & 2 are comparable, although the minimum positions are different.

  11. Conclusion r-dependence of the pairing part of local energy density functional is studied. All even-even nuclei with experimental data are analyzed by Skyrme-HFB. Strong r–dep. (h0～0.8) for typical Skyrme forces r1–tems should be included. Connection todrip-line regions, if m*/m=0.7~0.8.

  12. ☺ ☹

  13. Definition of pairing gap

  14. Pairing gap: A-dependence only

  15. Survey of h1(opt.) : pairing and effective mass 12 Skyrme parameters SKT6 (k=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) a -dependence of effective masses

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