Simple regularization scheme for multi-reference density functional theories

Abstract

Background: Extensions of single-reference (SR) energy-density-functionals (EDFs) to multi-reference (MR) applications involve using the generalized Wick theorem (GWT), which leads to singular energy kernels that cannot be properly integrated to restore symmetries, unless the EDFs are generated by true interactions. Purpose: We propose a new method to regularize the MR EDFs, which is based on using auxiliary quantities obtained by multiplying the kernels with appropriate powers of overlaps. Methods: Regularized matrix elements of two-body interactions are obtained by integrating the auxiliary quantities and then solving simple linear equations. Results: We implement the new regularization method within the self-consistent Skyrme-Hartree-Fock approach and we perform a proof-of-principle angular-momentum projection (AMP) of states in odd-odd nucleus 26Al. We show that for EDFs generated by true interactions, our regularization method gives results identical to those obtained within the standard AMP procedure. We also show that for EDFs that do not correspond to true interactions, it gives stable and converging results that are different than unstable and non-converging standard AMP values. Conclusions: The new regularization method proposed in this work may provide us with a relatively inexpensive and efficient tool to generalize SR EDFs to MR applications, thus allowing for symmetry restoration and configuration mixing performed for typical nuclear EDFs, which most often do not correspond to true interactions.

8 pages, 5 figures, submitted to Physical Review C

References in corpus (15)

• Particle-Number Projection and the Density Functional Theory
• Particle-Number Restoration within the Energy Density Functional Formalism
• Configuration Mixing within the Energy Density Functional Formalism: Removing Spurious Contributions from Non-Diagonal Energy Kernels
• Beyond Mean-Field Calculations for Odd-A Nuclei
• Solution of the Skyrme-Hartree-Fock-Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis. (VII) HFODD (v2.49t): a new version of the program
• Solution of the Skyrme-Hartree-Fock-Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis. (VI) HFODD (v2.38j): a new version of the program
• Microscopic calculations of isospin-breaking corrections to superallowed beta-decay
• Remarks on the use of projected densities in the density dependent part of Skyrme or Gogny functionals
• Skyrme pseudo-potential-based EDF parametrisation for spuriousity-free MR-EDF calculations
• New parameterization of Skyrme's interaction for regularized multi-reference energy density functional calculations
• Large amplitude pairing fluctuations in atomic nuclei
• Density Dependence of Two-Body Interactions for Beyond Mean-Field Calculations
• Density-Dependence of Two-Body Interactions Beyond the Mean-Field Approximation. Part 1: Generalized Brueckner G-Matrix in the Local Approximation
• Angular-momentum projection of cranked symmetry-unrestricted Slater determinants
• New density-independent interactions for nuclear structure calculations

Cited by in corpus (15)

• The Nuclear Symmetry Energy
• Symmetry restoration in mean-field approaches
• Isospin-symmetry breaking in masses of $N\simeq Z$ nuclei
• Projection on particle number and angular momentum: Example of triaxial Bogoliubov quasiparticle states
• Effective density functionals beyond mean field
• Solution of universal nonrelativistic nuclear DFT equations in the Cartesian deformed harmonic-oscillator basis. (IX) HFODD (v3.06h): a new version of the program
• No-core configuration-interaction model for the isospin- and angular-momentum-projected states
• Isobaric Multiplet Mass Equation within nuclear Density Functional Theory
• Complex-energy approach to sum rules within nuclear density functional theory
• Ab initio-driven nuclear energy density functional method. A proposal for safe/correlated/improvable parametrizations of the off-diagonal EDF kernels
• Isospin effects in N~Z nuclei in extended Density Functional Theory
• Gamow-Teller response in the configuration space of DFT-rooted no-core configuration-interaction model
• Mirror energy differences in T=1/2 f7/2-shell nuclei within isospin-dependent DFT
• Symmetry-restored Skyrme-Random-Phase-Approximation calculations of the monopole strength in deformed nuclei
• Beta-decay Studies in N~Z Nuclei Using No-Core Configuration-Interaction Model