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Published byGriffin Wheeler Modified over 9 years ago
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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
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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
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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)
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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
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Procedures for parameter optimization Data: G. Audi et al., NPA729, 3 (2003) exp : 3-point mass difference formula
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Extrapolation: Zone1 → Zone2, 3 - Skyrme SLy4 case -
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Specific examples in Zone3 (outside fitting) Sn Pb
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Verifying for typical Skyrme forces
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Connection to drip-line region (low- limit) (à la Bertsch & Esbensen)
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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. ☺ ☹
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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.
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☹ ☺
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Definition of pairing gap
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Pairing gap: A-dependence only
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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)
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