New-generation functionals
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New-generation functionals. Jacek Dobaczewski University of Warsaw & University of Jyväskylä. In collaboration with : Gillis Carlsson, Markus Kortelainen, Jussi Toivanen, and Marcin Borucki, Alessandro Pastore, Francesco Raimondi, Pekka Toivanen,

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New-generation functionals

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New generation functionals

New-generation functionals

Jacek Dobaczewski

University of Warsaw & University of Jyväskylä

In collaboration with:

Gillis Carlsson, Markus Kortelainen, Jussi Toivanen,

and Marcin Borucki, Alessandro Pastore,

Francesco Raimondi, Pekka Toivanen,

and Kazuhito Mizuyama, Rayner Rodriguez-Guzman

UNEDF Annual Workshop, Pack Forest (WA)

June 22-25, 2009


New generation functionals

Nuclear Energy Density Functional


New generation functionals

How to extend the nuclear energy density functional

beyond the current standard form?

Quest for the spectroscopic-quality functional

  • Density dependence of all the coupling constants

  • Derivatives of higher order up to N3LO:

  • Products of more than two densities, for example:


New generation functionals

=

Fits of s.p. energies

EXP: M.N. Schwierz, I. Wiedenhover,

and A. Volya, arXiv:0709.3525

Singular value decomposition

M. Kortelainenet al., Phys. Rev. C77, 064307 (2008)


New generation functionals

Fits of single-particle energies

Before

After

M. Kortelainenet al., Phys. Rev. C77, 064307 (2008)


New generation functionals

Fit residuals for centroids of SO partners (SkP)

Before

After

n

L

n

L

Before

After

M. Kortelainenet al., to be published


New generation functionals

Fit residuals for splittings of SO partners (SkP)

Before

After

n

L

n

L

Before

After

M. Kortelainenet al., to be published


New generation functionals

How to extend the nuclear energy density functional

beyond the current standard form?

Quest for the spectroscopic-quality functional

  • Density dependence of all the coupling constants

  • Derivatives of higher order up to N3LO:

  • Products of more than two densities, for example:


New generation functionals

I. Density dependence of all the coupling constants

M. Kortelainenet al., to be published


New generation functionals

Fit to single-particle energies

SLy5

RMS deviation (MeV)

PRELIMINARY

M. Kortelainenet al., to be published

Number of parameters


New generation functionals

RMS deviation of single-particle energies (MeV)

M. Kortelainenet al., to be published


New generation functionals

PRELIMINARY

Stability of the Hartree-Fock solutions

K. Mizuyamaet al., to be published


New generation functionals

How to extend the nuclear energy density functional

beyond the current standard form?

Quest for the spectroscopic-quality functional

  • Density dependence of all the coupling constants

  • Derivatives of higher order up to N3LO:

  • Products of more than two densities, for example:


New generation functionals

Energy density functional up to N3LO

B.G. Carlssonet al., C 78, 044326 (2008)


New generation functionals

Energy density functional for spherical nuclei (I)

B.G. Carlssonet al., C 78, 044326 (2008)


New generation functionals

EXP-1:

M.N. Schwierz,

I. Wiedenhover, and

A. Volya, arXiv:0709.3525

EXP-2:

M.G. Porquet et al.,

to be published

B.G. Carlssonet al., to be published

  • NM:

  • Nuclear-matter

  • constraints on:

  • saturation density

  • energy per particle

  • incompressibility

  • effective mass


New generation functionals

Galilean invariance

EXP-1:

M.N. Schwierz,

I. Wiedenhover, and

A. Volya, arXiv:0709.3525

EXP-2:

M.G. Porquet et al.,

to be published

B.G. Carlssonet al., to be published

  • NM:

  • Nuclear-matter

  • constraints on:

  • saturation density

  • energy per particle

  • incompressibility

  • effective mass


New generation functionals

Galilean invariance

EXP-1:

M.N. Schwierz,

I. Wiedenhover, and

A. Volya, arXiv:0709.3525

EXP-2:

M.G. Porquet et al.,

to be published

B.G. Carlssonet al., to be published

  • NM:

  • Nuclear-matter

  • constraints on:

  • saturation density

  • energy per particle

  • incompressibility

  • effective mass


New generation functionals

Fast RPA and QRPA + Lanczos method

http://www.jyu.fi/static/fysiikka/saariselka09/

presentations/Toivanen.pdf


New generation functionals

VAP symmetry restoration by the Lipkin method


New generation functionals

Thank You


New generation functionals

Spares


New generation functionals

II. Derivatives of higher order up to N3LO

B.G. Carlssonet al., C 78, 044326 (2008)


New generation functionals

Numbers of terms in the density functional up to N3LO

B.G. Carlssonet al., C 78, 044326 (2008)

Eq. (28) ≡ density dependent CC

Eq. (30) ≡ density independent CC


New generation functionals

Energy density functional for spherical nuclei (II)

B.G. Carlssonet al., Phys. Rev. C 78, 044326 (2008)


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