Simple regularization scheme for multireference 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 26 Al. 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.PACS numbers: 21.60.Jz, 21.30.Fe,

Beta-Decay Studies in N ≈ Z Nuclei Using No-Core Configuration-Interaction Model

“…This was because of the anomalously large ISB correction, caused by uncontrolled mixing of the 2s 1/2 and 1d 3/2 orbits, which for the SV T Skyrme true interaction are almost degenerate. The SV T interaction is the SV functional [7] augmented with the tensor terms, see discussion in [8].…”

No-core configuration-interaction model for the isospin- and angular-momentum-projected states

“…An alternative way of building a nonsingular MR theory, the one that we use in the present work, relies on employing the EDFs derived from a true interaction, which then acquires a role of the EDF generator [12]. The results presented here were obtained using in this role the density-independent Skyrme interaction SV [13], augmented by the tensor terms (SV T ) [11].…”

“…Unfortunately, the resulting MR EDFs are, in general, singular and require regularization, which still lacks satisfactory and practical solution; see, e.g., Refs. [9][10][11]. An alternative way of building a nonsingular MR theory, the one that we use in the present work, relies on employing the EDFs derived from a true interaction, which then acquires a role of the EDF generator [12].…”

Gamow-Teller response in the configuration space of a density-functional-theory–rooted no-core configuration-interaction model

“…The intensive work to overcome this problem of projection-induced singularities is currently under way. The attempts to regularize the kernels [30,31] have not provided a satisfactory solution so far. Hence, at present, the theory can be safely carried on only for true interaction such as SV T [32], used in the present work, or the SLyM0 [33], which both are density-independent Skyrme pseudopotentials.…”