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

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

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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

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 ??

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

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

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

Dexp: 3-point mass difference formula

- Skyrme SLy4 case -

Pb

Sn

(à laBertsch & Esbensen)

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.

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 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