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Renormalized Interactions for CI constrained by EDF methods

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Renormalized Interactions for CI constrained by EDF methods Alex Brown, Angelo Signoracci and Morten Hjorth -Jensen. Wick’s theorem for a Closed-shell vacuum filled orbitals. Closed-shell vacuum filled orbitals. EDF (Skyrme Phenomenology). Closed-shell vacuum filled orbitals.

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slide1

Renormalized Interactions for CI constrained by EDF methods

Alex Brown, Angelo Signoracci and MortenHjorth-Jensen

slide7

Wick’s theorem for a

Closed-shell vacuum

filled orbitals

slide8

Closed-shell vacuum

filled orbitals

EDF (Skyrme

Phenomenology)

slide9

Closed-shell vacuum

filled orbitals

NN potential with V_lowk

EDF (Skyrme)

phenomenology

slide10

Closed-shell vacuum

filled orbitals

“tuned” valence

two-body matrix elements

EDF (Skyrme)

phenomenology

slide11

Closed-shell vacuum

filled orbitals

Monopole from EDF

EDF (Skyrme)

phenomenology

slide12

Closed-shell vacuum

filled orbitals

Monopole from EDF

A3 A2 A 1

slide14

Aspects of evaluating a microscopic two-body Hamiltonian (N3LO + Vlowk+ core-polarization) in a spherical EDF (energy-density functional) basis (i.e. Skyrme HF)

TBME (two-body matrix elements): Evaluate N3LO + Vlowk with radial wave functions obtained with EDF.

TBME: Evaluate core-polarization with an underlying single-particle spectrum obtained from EDF.

TBME: Calculate monopole corrections from EDF that would implicitly include an effective three-body interaction of the valence nucleons with the core.

SPE for CI: Use EDF single-particle energies – unless something better is known experimentally.

slide15

Why use energy-density functionals (EDF)?

Parameters are global and can be extended to nuclear matter.

Effort by several groups to improve the understanding and reliability (predictability) of EDF – in particular the UNEDF SciDAC project in the US.

This will involve new and extended functionals.

With a goal to connect the values of the EDF parameters to the NN and NNN interactions.

At this time we have a reasonably good start with some global parameters – for now I will use Skxmb – Skxm from [BAB, Phys. Rev. C58, 220 (1998)] with small adjustment for lowest single-particle states in 209Bi and 209Pb.

slide17

What do we get out of (spherical) EDF?

Binding energy for the closed shell

Radial wave functions in a finite-well (expanded in terms of harmonic oscillator).

gives single-particle energies for the nucleons constrained to be in orbital (n l j)a where BE(A) is a doubly closed-shell nucleus.

4)

gives the monopole two-body matrix element for nucleons constrained to be in orbitals (n l j)a and (n l j)b

slide20

Theory (ham) from Skxmb with parameters adjusted to reproduce

the energy for the 9/2- state plus about 100 other global data.

slide24

x = experiment

CI with N3LO

CI (ham) N3LO with EDF constraint

EDF (or CI) with

no correlations

208Pb

218U

slide25

Skyrme (Skxmb) +

Vlow-k N3LO (second order)

210Po

slide26

Skyrme (Skxmb) +

Vlow-k N3LO (first order)

210Po

slide27

Skyrme (Skxmb) +

Vlow-k N3LO (second order)

213Fr

slide28

214Ra

Skyrme (Skxmb) +

Vlow-k N3LO (second order)

slide30

Theory (ham) from Skxmb with parameters adjusted to reproduce

the energy for the 9/2+ state plus about 100 other global data.

slide31

210Pb

Skyrme (Skxmb) +

Vlow-k N3LO (second order)

slide32

210Bi

Skyrme (Skxmb) +

Vlow-k N3LO (second order)

slide33

212Po

Skyrme (Skxmb) +

Vlow-k N3LO (second order)

slide34

210Pb

Skyrme (Skxmb) +

Vlow-k N3LO (second order)

slide35

210Pb

Skyrme (Skxmb) + exp spe

Vlow-k N3LO (second order)

slide36

Skyrme (Skxmb) for 208Pb (closed shell)

+ Vlow-k N3LO (second order)

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