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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

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



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:


=

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)


Fits of single-particle energies

Before

After

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


Fit residuals for centroids of SO partners (SkP)

Before

After

n

L

n

L

Before

After

M. Kortelainenet al., to be published


Fit residuals for splittings of SO partners (SkP)

Before

After

n

L

n

L

Before

After

M. Kortelainenet al., to be published


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:


I. Density dependence of all the coupling constants

M. Kortelainenet al., to be published


Fit to single-particle energies

SLy5

RMS deviation (MeV)

PRELIMINARY

M. Kortelainenet al., to be published

Number of parameters


RMS deviation of single-particle energies (MeV)

M. Kortelainenet al., to be published


PRELIMINARY

Stability of the Hartree-Fock solutions

K. Mizuyamaet al., to be published


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:


Energy density functional up to N3LO

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


Energy density functional for spherical nuclei (I)

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


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


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


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


Fast RPA and QRPA + Lanczos method

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

presentations/Toivanen.pdf





II. Derivatives of higher order up to N3LO

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


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


Energy density functional for spherical nuclei (II)

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


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