Search results for "Slater determinant"
showing 10 items of 16 documents
No-core configuration-interaction model for the isospin- and angular-momentum-projected states
2016
[Background] Single-reference density functional theory is very successful in reproducing bulk nuclear properties like binding energies, radii, or quadrupole moments throughout the entire periodic table. Its extension to the multi-reference level allows for restoring symmetries and, in turn, for calculating transition rates. [Purpose] We propose a new no-core-configuration-interaction (NCCI) model treating properly isospin and rotational symmetries. The model is applicable to any nucleus irrespective of its mass and neutron- and proton-number parity. It properly includes polarization effects caused by an interplay between the long- and short-range forces acting in the atomic nucleus. [Metho…
On fermionic shadow wave functions for strongly correlated multi-reference systems based on a single Slater determinant
2015
We demonstrate that extending the Shadow Wave Function to fermionic systems facilitates to accurately calculate strongly-correlated multi-reference systems such as the stretched H2 molecule. This development considerably extends the scope of electronic structure calculations and enables to efficiently recover the static correlation energy using just a single Slater determinant.
Small Clusters Made of Helium Atoms
2003
Helium atoms interact very weakly through a van der Waals potential. Nevertheless, they are able to form aggregates or drops with a small number of atoms. This work analyzes the stability of clusters made of 4He atoms, of bosonic nature, clusters made of 3He atoms, of fermionic nature and also mixed aggregates with both kinds of constituents. Some of these drops are predicted to be unstable.
Gamow-Teller response in the configuration space of a density-functional-theory–rooted no-core configuration-interaction model
2018
Background: The atomic nucleus is a unique laboratory in which to study fundamental aspects of the electroweak interaction. This includes a question concerning in medium renormalization of the axial-vector current, which still lacks satisfactory explanation. Study of spin-isospin or Gamow-Teller (GT) response may provide valuable information on both the quenching of the axial-vector coupling constant as well as on nuclear structure and nuclear astrophysics.Purpose: We have performed a seminal calculation of the GT response by using the no-core configuration-interaction approach rooted in multireference density functional theory (DFT-NCCI). The model treats properly isospin and rotational sy…
A consistent microscopic theory of collective motion in the framework of an ATDHF approach
1978
Based on merely two assumptions, namely the existence of a collective Hamiltonian and that the collective motion evolves along Slater determinants, we first derive a set of adiabatic time-dependent Hartree-Fock equations (ATDHF) which determine the collective path, the mass and the potential, second give a unique procedure for quantizing the resulting classical collective Hamiltonian, and third explain how to use the collective wavefunctions, which are eigenstates of the quantized Hamiltonian.
Evolution of a Quantum System: Lifetime of a Determinant
1976
A measure of the ''dependency'' of a many-particle system is defined and its time dependence is evaluated for systems initially described by a single Slater determinant. An uncertainty product between the energy spread of the initial determinant and the lifetime of a system's independence is established. Numerical estimates of some lifetimes are given. They are not so long as to be reassuring for nuclear time-dependent Hartree--Fock calculations. Each separate case ought to be checked. 1 table.
Quantized ATDHF: theory and realistic applications to heavy ion fusion
1982
The quantized ATDHF theory is reviewed and discussed in the context of the generator coordinate method. This allows for a derivation which does not require an a posteriori quantization process. The ATDHF equations are then solved numerically on a coordinate and momentum grid in fully three dimensional geometry. The theory is applied to various heavy ion systems, where potentials, mass parameters and quantum corrections are evaluated and compared to conventional results from constrained Hartree-Fock. Subbarrier fusion cross sections are calculated and compared with experiment.
Occupation Number Representation
2007
The first two chapters of this book presented angular momentum algebra as the basic tool of nuclear theory. That includes angular momentum coupling coefficients, spherical tensor operators and reduced matrix elements. In the preceding chapter we introduced the mean-field concept, along with associated many-nucleon wave functions, Slater determinants, describing configurations of non-interacting particles in mean-field single-particle orbitals.
Ferromagnetism of the Hubbard Model at Strong Coupling in the Hartree-Fock Approximation
2005
As a contribution to the study of Hartree-Fock theory we prove rigorously that the Hartree-Fock approximation to the ground state of the d-dimensional Hubbard model leads to saturated ferromagnetism when the particle density (more precisely, the chemical potential mu) is small and the coupling constant U is large, but finite. This ferromagnetism contradicts the known fact that there is no magnetization at low density, for any U, and thus shows that HF theory is wrong in this case. As in the usual Hartree-Fock theory we restrict attention to Slater determinants that are eigenvectors of the z-component of the total spin, {S}_z = sum_x n_{x,\uparrow} - n_{x,\downarrow}, and we find that the ch…
Angular momentum projection of cranked Hartree-Fock states: Application to terminating bands inA~44nuclei
2007
We present the first systematic calculations based on the angular-momentum projection of cranked Slater determinants. We propose the Iy --> I scheme, by which one projects the angular momentum I from the 1D cranked state constrained to the average spin projection of =I. Calculations performed for the rotational band in 46Ti show that the AMP Iy --> I scheme offers a natural mechanism for correcting the cranking moment of inertia at low-spins and shifting the terminating state up by ~2 MeV, in accordance with data. We also apply this scheme to high-spin states near the band termination in A~44 nuclei, and compare results thereof with experimental data, shell-model calculations, and res…