arXiv subjects
Publications and source records attributed to M. V. Stoitsov.
The Density Matrix Renormalization Group (DMRG) method is developed for application to realistic nuclear systems. Test results are reported for 24Mg.
The volume and surface effects in the nuclear local energy density and the volume and surface components of the pairing interaction are discussed in the context of the mean-field, Hartree-Fock-Bogoliubov description of atomic nuclei. Predictions of properties of exotic nuclei close to the particle drip lines are presented.
The particle-hole Density Matrix Renormalization Group (p-h DMRG) method is discussed as a possible new approach to large-scale nuclear shell-model calculations. Following a general description of the method, we apply it to a class of problems involving many identical nucleons constrained to move in a single large j-shell and to interact via a pairing plus quadrupole interaction. A single-particle term that splits the shell into degenerate doublets is included so as to accommodate the physics of a Fermi surface in the problem. We apply the p-h DMRG method to this test problem for two $j$ values, one for which the shell model can be solved exactly and one for which the size of the hamiltonian is much too large for exact treatment. In the former case, the method is able to reproduce the exact results for the ground state energy, the energies of low-lying excited states, and other observables with extreme precision. In the latter case, the results exhibit rapid exponential convergence, suggesting the great promise of this new methodology even for more realistic nuclear systems. We also compare the results of the test calculation with those from Hartree-Fock-Bogolyubov approximation and address several other questions about the p-h DMRG method of relevance to its usefulness when treating more realistic nuclear systems.
Properties of density-dependent contact pairing interactions in nuclei are discussed. It is shown that the pairing interaction that is intermediate between surface and volume pairing forces gives the pairing gaps that are compatible with the experimental odd-even mass staggering. Results of the deformed Hartree-Fock-Bogoliubov calculations for this `mixed' pairing interaction, and using the transformed harmonic oscillator basis, are presented.
We introduce a local-scaling point transformation to allow for modifying the asymptotic properties of the deformed three-dimensional Cartesian harmonic oscillator wave functions. The resulting single-particle bases are very well suited for solving the Hartree-Fock-Bogoliubov equations for deformed drip-line nuclei. We then present results of self-consistent calculations performed for the Mg isotopes and for light nuclei located near the two-neutron drip line. The results suggest that for all even-even elements with $Z$=10--18 the most weakly-bound nucleus has an oblate ground-state shape.
The cross sections of the ($e,e'N$) and ($γ,p$) reactions on $^{16}$O are calculated, for the transitions to the $1/2^{-}$ ground state and the first $3/2^{-}$ excited state of the residual nucleus, using single-particle overlap functions obtained on the basis of one-body density matrices within different correlation methods. The electron-induced one-nucleon knockout reaction is treated within a nonrelativistic DWIA framework. The theoretical treatment of the ($γ,p$) reaction includes both contributions of the direct knockout mechanism and of meson-exchange currents. The results are sensitive to details of the different overlap functions. The consistent analysis of the reaction cross sections and the comparison with the experimental data make it possible to study the nucleon--nucleon correlation effects.
The two-body density matrix for $^{4}He,^{16}O$ and $^{40}Ca$ within the Low-order approximation of the Jastrow correlation method is considered. Closed analytical expressions for the two-body density matrix, the center of mass and relative local densities and momentum distributions are presented. The effects of the short-range correlations on the two-body nuclear characteristics are investigated.
Single-particle overlap functions and spectroscopic factors are calculated on the basis of the one-body density matrices (ODM) obtained for the nucleus $^{16}O$ employing different approaches to account for the effects of correlations. The calculations use the relationship between the overlap functions related to bound states of the (A-1)-particle system and the ODM for the ground state of the A-particle system. The resulting bound-state overlap functions are compared and tested in the description of the experimental data from (p,d) reactions for which the shape of the overlap function is important.
Relationships are obtained connecting the two-nucleon overlap function of the eigenstates in the (A-2) particle system with the asymptotic behavior of the two-body density matrix for the ground state of the A-particle system.This makes it possible to calculate the two-body overlap functions, spectroscopic factors and separation energies on the basis of a realistic two-body density matrix. The procedure can be used in describing the (e,e'NN) and (γ, NN) reactions where the two--body overlap functions are a key ingredient in the analysis.
A complete discrete set of spherical single-particle wave functions for studies of weakly-bound many-body systems is proposed. The new basis is obtained by means of a local-scale point transformation of the spherical harmonic oscillator wave functions. Unlike the harmonic oscillator states, the new wave functions decay exponentially at large distances. Using the new basis, characteristics of weakly-bound orbitals are analyzed and the ground state properties of some spherical doubly-magic nuclei are studied. The basis of the transformed harmonic oscillator is a significant improvement over the harmonic oscillator basis, especially in studies of exotic nuclei where the coupling to the particle continuum is important.
Slater determinants built from the single-particle wave functions of the analytically solvable Ginocchio potential are used to approximate the self-consistent Hartree-Fock solutions for the ground states of nuclei. The results indicate that the Ginocchio potential provides a good parametrization of the nuclear mean field for a wide range of nuclei, including those at the limit of particle stability.
An asymptotic restoration procedure is applied for analyzing bound--state overlap functions, separation energies and single--nucleon spectroscopic factors by means of a model one--body density matrix emerging from the Jastrow correlation method in its lowest order approximation for $^{16}O$ and $^{40}Ca$ nuclei . Comparison is made with available experimental data and mean--field and natural orbital representation results.
A phenomenological method based on the natural orbital representation is applied to construct the ground state one-body density matrix which describes correctly both density and momentum distributions in $^{4}He$, $^{16}O$ and $^{40}Ca$ nuclei. The parameters of the matrix are fixed by a best fit to the experimental density distribution and to the correlated nucleon momentum distribution. The method allows the natural orbitals, the occupation probabilities and the depletion of the Fermi sea to be obtained. Ground-state characteristics of $^{4}He$, $^{16}O$ and $^{40}Ca$ nuclei, such as rms radii and mean kinetic energies are calculated, as well.
Proton momentum distributions of the $^{12}C$, $^{16}O$, $^{40}Ca$, $^{56}Fe$ and $^{208}$Pb nuclei are calculated by a model using the natural orbital representation and the experimental data for the momentum distribution of the $^{4}He$ nucleus. The model allows realistic momentum distributions to be obtained using only hole-state natural orbitals (or mean-field single-particle wave functions as a good approximation to them). To demonstrate the model two different sets of wave functions were employed and the predictions were compared with the available empirical data and other theoretical results.
A method to calculate the hole spectral function in the discrete part of the spectrum is suggested within the natural orbital representation of the one-body density matrix of $A$-nucleon system using its relationship with the overlap functions of the eigenstates in the $(A-1)$-nucleon system.
The breathing-mode giant monopole resonance is studied within the framework of the relativistic mean-field (RMF) theory. Using a broad range of parameter sets, an analysis of constrained incompressibility and excitation energy of isoscalar monopole states in finite nuclei is performed. It is shown that the non-linear scalar self-interaction and the resulting surface properties influence the breathing-mode considerably. It is observed that dynamical surface properties respond differently in the RMF theory than in the Skyrme approach. A comparison is made with the incompressibility derived from the semi-infinite nuclear matter and with constrained nonrelativistic Skyrme Hartree-Fock calculaions.
The breathing-mode giant monopole resonance is studied within the framework of the relativistic mean-field (RMF) theory. Using a broad range of parameter sets, a systematic analysis of constrained incompressibility and excitation energy of isoscalar monopole states in finite nuclei is performed. A comparison is made with the incompressibility derived from the semi-infinite nuclear matter and with constrained nonrelativistic Skyrme Hartree-Fock calculations. Investigating the dependence of the breathing-mode energy on the nuclear matter incompressibility, it is shown that dynamical properties of surface respond differently in the RMF theory than in the Skyrme approach.