Global fitting of pairing density functional the isoscalar density dependence revisited
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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.

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

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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

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


Our discussion

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 ??


Difficulty for h 0 r dependence

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


Our model

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


Procedures for parameter optimization

Procedures for parameter optimization

Data: G. Audi et al., NPA729, 3 (2003)

Dexp: 3-point mass difference formula


Extrapolation zone1 zone2 3

Extrapolation: Zone1 → Zone2, 3

- Skyrme SLy4 case -


Specific examples in zone3 outside fitting

Specific examples in Zone3 (outside fitting)

Pb

Sn


Verifying for typical skyrme forces

Verifying for typical Skyrme forces


Connection to drip line region low r limit

Connectionto drip-line region (low-r limit)

(à laBertsch & Esbensen)


Global fitting of pairing density functional the isoscalar density dependence revisited

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.


Conclusion

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.


Global fitting of pairing density functional the isoscalar density dependence revisited


Definition of pairing gap

Definition of pairing gap


Pairing gap a dependence only

Pairing gap: A-dependence only


Survey of h 1 opt pairing and effective mass

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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