Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSimple regularization scheme for multi-reference density functional theories
138
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic 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.
rate research
Read More
[Background] Symmetry restoration and configuration mixing in the spirit of the generator coordinate method based on energy density functionals have become widely used techniques in low-energy nuclear structure physics. Recently, it has been pointed out that these techniques are ill-defined for standard Skyrme functionals, and a regularization procedure has been proposed to remove the resulting spuriosities from such calculations. This procedure imposes an integer power of the density for the density dependent terms of the functional. At present, only dated parameterizations of the Skyrme interaction fulfill this condition. [Purpose] To construct a set of parameterizations of the Skyrme energy density functional for multi-reference energy density functional calculations with regularization using the state-of-the-art fitting protocols. [Method] The parameterizations were adjusted to reproduce ground state properties of a selected set of doubly magic nuclei and properties of nuclear matter. Subsequently, these parameter sets were validated against properties of spherical and deformed nuclei. [Results] Our parameter sets successfully reproduce the experimental binding energies and charge radii for a wide range of singly-magic nuclei. Compared to the widely used SLy5 and to the SIII parameterization that has integer powers of the density, a significant improvement of the reproduction of the data is observed. Similarly, a good description of the deformation properties at $Asim 80$ was obtained. [Conclusions] We have constructed new Skyrme parameterizations with integer powers of the density and validated them against a broad set of experimental data for spherical and deformed nuclei. These parameterizations are tailor-made for regularized multi-reference energy density functional calculations and can be used to study correlations beyond the mean-field in atomic nuclei.
Pioneering study of Gamow-Teller (GT) and Fermi matrix elements (MEs) using no-core-configuration-interaction formalism rooted in multi-reference density functional theory is presented. After successful test performed for 6He -> 6Li beta-decay, the model is applied to compute MEs in the sd- and pf-shell T=1/2 mirror nuclei. The calculated GT MEs and the isospin-symmetry-breaking corrections to the Fermi branch are found to be in a very good agreement with shell-model predictions in spite of fundamental differences between these models concerning model space, treatment of correlations or inclusion of a core. This result indirectly supports the two-body current based scenarios behind the quenching of axial-vector coupling constant.
The results of systematic calculations of isospin-symmetry-breaking corrections to superallowed beta-decays based on the self-consistent isospin- and angular-momentum-projected nuclear density functional theory (DFT) are reviewed with an emphasis on theoretical uncertainties of the model. Extensions of the formalism towards no core shell model approach with basis cutoff scheme dictated by the self-consistent particle-hole DFT solutions will be also discussed.
The nonrelativistic reduction of the self-consistent covariant density functional theory is realized for the first time with the similarity renormalization group (SRG) method. The reduced nonrelativistic Hamiltonian and densities are calculated by solving the corresponding flow equations with a novel expansion in terms of the inverse of the Dirac effective mass. The efficiency and accuracy of this newly proposed framework have been demonstrated for several typical spherical nuclei. It is found that the exact solutions of the total energies, traces of vector and scalar densities, and the root-mean-square radii are reproduced quite well for all nuclei. This allows one to directly compare and bridge the relativistic and nonrelativistic nuclear energy density functional theories in the future.
We discuss anharmonicity of the multi-octupole-phonon states in $^{208}$Pb based on a covariant density functional theory, by fully taking into account the interplay between the quadrupole and the octupole degrees of freedom. Our results indicate the existence of a large anharmonicity in the transition strengths, even though the excitation energies are similar to those in the harmonic limit. We also show that the quadrupole-shape fluctuation significantly enhances the fragmentation of the two-octupole-phonon states in $^{208}$Pb. Using those transition strengths as inputs to coupled channels calculations, we then discuss the fusion reaction of $^{16}$O+$^{208}$Pb at energies around the Coulomb barrier. We show that the anharmonicity of the octupole vibrational excitation considerably improves previous coupled-channels calculations in the harmonic oscillator limit, significantly reducing the height of the main peak in the fusion barrier distribution.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
