Configuration Mixing within the Energy Density Functional Formalism: Removing Spurious Contributions from Non-Diagonal Energy Kernels

Abstract

Multi-reference calculations along the lines of the Generator Coordinate Method or the restoration of broken symmetries within the nuclear Energy Density Functional (EDF) framework are becoming a standard tool in nuclear structure physics. These calculations rely on the extension of a single-reference energy functional, of the Gogny or the Skyrme types, to non-diagonal energy kernels. There is no rigorous constructive framework for this extension so far. The commonly accepted way proceeds by formal analogy with the expressions obtained when applying the generalized Wick theorem to the non-diagonal matrix element of a Hamilton operator between two product states. It is pointed out that this procedure is ill-defined when extended to EDF calculations as the generalized Wick theorem is taken outside of its range of applicability. In particular, such a procedure is responsible for the appearance of spurious divergences and steps in multi-reference EDF energies, as was recently observed in calculations restoring particle number or angular momentum. In the present work, we give a formal analysis of the origin of this problem for calculations with and without pairing, i.e. constructing the density matrices from either Slater determinants or quasi-particle vacua. We propose a correction to energy kernels that removes the divergences and steps, and which is applicable to calculations based on any symmetry restoration or generator coordinate. The method is formally illustrated for particle number restoration and is specified to configuration mixing calculations based on Slater determinants.

27 pages, 1 figure, accepted for publication in PRC

References in corpus (15)

• Climbing the Density Functional Ladder: Non-Empirical Meta-Generalized Gradient Approximation Designed for Molecules and Solids
• The Shell Model as Unified View of Nuclear Structure
• Is nuclear matter perturbative with low-momentum interactions?
• Particle-Number Projection and the Density Functional Theory
• Particle-Number Restoration within the Energy Density Functional Formalism
• Particle-Number Restoration within the Energy Density Functional formalism: Nonviability of terms depending on noninteger powers of the density matrices
• Configuration mixing of angular momentum projected self-consistent mean-field states for neutron-deficient Pb isotopes
• Intrinsic-Density Functionals
• Spherical Hartree-Fock calculations with linear momentum projection before the variation.Part I: Energies, form factors, charge densities and mathematical sum rules
• Broken Symmetry in Density-Functional Theory: Analysis and Cure
• Density Functional Theory: Methods and Problems
• Angular-momentum projection of cranked symmetry-unrestricted Slater determinants
• Spherical Hartree-Fock calculations with linear momentum projection before the variation.Part II: Spectral functions and spectroscopic factors
• The generator coordinate method in time-dependent density-functional theory: memory made simple
• Nodal Lines in the Cranked HFB Overlap kernels

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