Skyrme energy density functional approach to nuclear collective - - PowerPoint PPT Presentation

Kenichi Yoshida Skyrme energy‐density functional approach to nuclear collective dynamics: Small amplitude to large amplitude

24‐26/10/10@YITP Workshop on Microscopic Theory of Large‐Amplitude Collective motion

Contents

Why DFT? Formalism Small‐amplitude collective dynamics Applicability of DFT to nuclear dynamics Large‐amplitude collective dynamics Collectivity of neutron‐rich Cr isotopes Quadrupole mass of fissioning 256Fm Summary

http://www.unedf.org/

DFT for all nuclei

Skyrme Energy Density Functional (EDF)

zero range: local densities finite range: gradient terms

EDF for superfluid systems

M.V. Stoitsov et al., PRC68(2003) 054312 Neutron Number Proton Number Deformation Mass explorer http://www.massexplorer.org/

Nuclear DFT for ground states

SkM*

(MeV)

Weakly binding Continuum coupling

HFBTHO

Skyrme-HFB-QRPA (at the equilibrium point)

Mean‐field Hamiltonian Pairing field

J.Dobaczewski, H.Flocard and J.Treiner, NPA422(1984)103 A.Bulgac, FT-194-1980 (Institute of Atomic Physics, Bucharest)

The coordinate‐space Hartree‐Fock‐Bogoliubov theory Minimizing the energy density

HFB equations solved directly on the 2D lattice.

13‐point formula for derivative

Simple Appropriate for describing the spatially extended structure of wave functions

H.O. basis

z

ρ

Skyrme-HFB-QRPA (at the equilibrium point)

Quasiparticle basis (i,j,k,l) HFB equations

The QRPA equation in a matrix form

particle‐hole channel: We neglect only the two‐body Coulomb interactions. particle‐particle channel: Residual interactions KY, N.V.Giai, PRC78 78(2008)064316 Strength distributions

# of 2qp excitation: about 50,000 Matrix elements: 590 CPU hours Diagonalization: 330 CPU hours 512 CPUs@RICC Matrix elements: 69 minutes Diagonalization: 38 minutes

Dipole responses in actinides

Box: Cut‐off: HFB calc. (using 64 CPUs) QRPA calc. Cut‐off:

SkM* functional

P.Carlos et al., NPA225 A225(1974)171

Evolution of nuclear deformation in GDR

spherical deformed transitional

144Sm 154Sm

Skyrme-QRPA photoabsorption cross sections

SkM* functional

Intrinsic Q moment KY, T.Nakatsukasa, arXiv:1008.1520

Collective Hamiltonian approach

The classical collective Hamiltonian in 1+2D: The collective Schrödinger equation:

Requantization with the Pauli’s prescription: Collective wf in the Lab. frame Collective wf in the intrinsic frame

Skyrme-EDF based Collective Hamiltonian

Mean‐field Hamiltonian Pairing field

The coordinate‐space Hartree‐Fock‐Bogoliubov theory with constraint

At each point, we define the vacuum; and the field operator;

Thouless‐Valatin moment of inertia

Skyrme-EDF based Collective Hamiltonian

The local QRPA on top of the constrained HFB state QRPA equation in the PQ representation

Neutron-rich Cr isotopes around N=40

Skyrme‐HFB with SkM*

Volume‐pairing: H.Oba and M.Matsuo, PTP120 120(2008)143

Collectivity of neutron-rich Cr isotopes

Exp.:

58Cr,60Cr:S.Zhu et al., PRC74(2006)064315 62Cr:N.Aoi et al., PRL102(2009)012502 64Cr: A.Gade et al.,PRC81(2010)051304R

Effects of time-odd components in mean fields

Skyrme‐HFB with SkM*

Mixed‐pairing

Comparison with HFODD

Fission pathway in 256Fm

A.Baran et al., arXiv:1007.3763

Collective inertia on fission pathway in 256Fm

ATDHFB‐C: Baran et al. Cranking mass: Local QRPA mass

Summary

Applicability of Skyrme EDFs to excited states

First application to photoabsorption cross sections in rare‐earth nuclei with shape transitions

Shape changes in neutron‐rich Cr isotopes around N=40

Low‐lying states well described in the framework of the Skyrme EDF‐ based collective Hamiltonian approach Large‐amplitude excited 0+ states

Quadrupole mass of 256Fm

First calculation of the quadrupole vibrational mass of 256Fm including the time‐odd components of mean fields

Acknowledgements

Collaborations with

Nguyen Van Giai (IPNO) Takashi Nakatsukasa (RNC) Nobuo Hinohara (RNC)

for the Skyrme‐EDF based deformed QRPA for the collective Hamiltonian approach Facilities

T2K-Tsukuba