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N. Sandulescu

Publications and source records attributed to N. Sandulescu.

At least 55 records · Page 3Linked to original sources
arXiv2009

Density Matrix Renormalization Group study of $^{48}$Cr and $^{56}$Ni

We discuss the development of an angular-momentum-conserving variant of the Density Matrix Renormalization Group (DMRG) method for use in large-scale shell-model calculations of atomic nuclei and report a first application of the method to the ground state of $^{56}$Ni and improved results for $^{48}$Cr. In both cases, we see a high level of agreement with the exact results. A comparison of the two shows a dramatic reduction in the fraction of the space required to achieve accuracy as the size of the problem grows.

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arXiv2008

Accuracy of BCS-based approximations for pairing in small Fermi systems

We analyze the accuracy of BCS-based approximations for calculating correlation energies and odd-even energy differences in 2-component fermionic systems with a small number of pairs. The analysis is focused on comparing BCS and projected BCS treatments with the exact solution of the pairing Hamiltonian, considering parameter ranges appropriate for nuclear pairing energies. We find that the projected BCS is quite accurate over the entire range of coupling strengths in spaces of up to about 20 doubly degenerate orbitals. It is also quite accurate for two cases we considered with a more realistic Hamiltonian, representing the nuclei around 117Sn and 207Pb. However, the projected BCS significantly underestimates the energies for much larger spaces when the pairing is weak.

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arXiv2008

The Density Matrix Renormalization Group and the Nuclear Shell Model

We summarize recent efforts to develop an angular-momentum-conserving variant of the Density Matrix Renormalization Group method into a practical truncation strategy for large-scale shell model calculations of atomic nuclei. Following a brief description of the key elements of the method, we report the results of test calculations for $^{48}$Cr and $^{56}$Ni. In both cases we consider nucleons limited to the 2p-1f shell and interacting via the KB3 interaction. Both calculations produce a high level of agreement with the exact shell-model results. Furthermore, and most importantly, the fraction of the complete space required to achieve this high level of agreement goes down rapidly as the size of the full space grows.

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arXiv2007

Equation of state in the inner crust of neutron stars: discusion of the unbound neutron states

In this paper, we calculate the stable Wigner-Seitz (W-S) cells in the inner crust of neutron stars and we discuss the nuclear shell effects. A distinction is done between the shell effects due to the bound states and those induced by the unbound states, which are shown to be spurious. We then estimate the effects of the spurious shells on the total energy and decompose it into a smooth and a residual part. We propose a correction to the Hartree-Fock binding energy in Wigner-Seitz cell (HF-WS).

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arXiv2007

Nuclear Superfluidity and Cooling Time of Neutron-Star Crust

We analyse the effect of neutron superfluidity on the cooling time of inner crust matter in neutron stars, in the case of a rapid cooling of the core. The specific heat of the inner crust, which determines the thermal response of the crust, is calculated in the framework of HFB approach at finite temperature. The calculations are performed with two paring forces chosen to simulate the pairing properties of uniform neutron matter corresponding respectively to Gogny-BCS approximation and to many-body techniques including polarisation effects. Using a simple model for the heat transport across the inner crust, it is shown that the two pairing forces give very different values for the cooling time.

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arXiv2007

Pairing interactions and the vanishing pairing correlations in hot nuclei

Finite temperature Hartree-Fock-Bogoliubov calculations are performed in Sn isotopes using Skyrme and zero-range, density-dependent pairing interactions. For both stable and very neutron-rich nuclei the critical temperature at which pairing correlations vanish is independent of the volume/surface nature of the pairing interaction. The value of the critical temperature follows approximatively the empirical rule T$_c$ $\simeq$ 0.5 $Δ_{T=0}$ for all the calculated isotopes, showing that the critical temperature could be deduced from the pairing gap at zero temperature. On the other hand, the pairing gap at temperatures just below T$_c$ is strongly sensitive to the volume/surface nature of the pairing interaction.

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arXiv2006

Physical Origin of Density Dependent Force of the Skyrme Type within the Quark Meson Coupling Model

A density dependent, effective nucleon-nucleon force of the Skyrme type is derived from the quark-meson coupling model -- a self-consistent, relativistic quark level description of nuclear matter. This new formulation requires no assumption that the mean scalar field is small and hence constitutes a significant advance over earlier work. The similarity of the effective interaction to the widely used SkM$^*$ force encourages us to apply it to a wide range of nuclear problems, beginning with the binding energies and charge distributions of doubly magic nuclei. Finding acceptable results in this conventional arena, we apply the same effective interaction, within the Hartree-Fock-Bogoliubov approach, to the properties of nuclei far from stability. The resulting two neutron drip lines and shell quenching are quite satisfactory. Finally, we apply the relativistic formulation to the properties of dense nuclear matter in anticipation of future application to the properties of neutron stars.

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arXiv2006

Giant neutron halos in the non-relativistic mean field approach

Giant neutron halos in medium-heavy nuclei are studied in the framework of the Hartree-Fock-Bogoliubov (HFB) approach with Skyrme interactions. The appearance of such structures depends sensitively on the effective interaction adopted. This is illustrated by comparing the predictions of SLy4 and SkI4 in the Ca and Zr isotopic chains. The former force gives no halo effect, the latter predicts a neutron halo in the Zr chain with A>122 due to the weakly bound orbitals 3p1/2 and 3p3/2. The structure of the halo is analyzed in terms of the occupation probabilities of these orbitals and their partial contributions to the neutron density. The anti-halo effect in Ni and Zr isotopes is also discussed by comparing the occupation probabilities of Hartree-Fock neutron single-particle states near the Fermi energy with the corresponding HFB quasiparticle states.

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arXiv2006

Density Matrix Renormalization Group and the Nuclear Shell Model

We describe the use of the Density Matrix Renormalization Group method as a means of approximately solving large-scale nuclear shell-model problems. We focus on an angular-momentum-conserving variant of the method and report test results for the nucleus $^{48}Cr$. The calculation is able to reproduce both the ground state energy and the energy of the first excited state, by diagonalizing matrices much smaller than those of the full shell model.

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arXiv2005

A Complex Shell Model Representation Including Antibound States

A generalization of the Complex Shell Model formalism is presented which includes antibound states in the basis. These states, together with bound states, Gamow states, and the continuum background, represented by properly chosen scattering waves, form a representation where all states are treated on the same footing. Two-particle states are evaluated within this formalism and observable two-particle resonances are defined. The formalism is illustrated in the well known case of $^{11}$Li in its bound ground state and in $^{70}$Ca(gs), which is also bound. Both cases are found to have a halo structure. These halo structures are described within the generalized Complex Shell Model. We investigated the formation of two-particle resonances in these nuclei, but no evidence of such resonances was found.

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arXiv2005

Quasiparticle Resonances in the BCS Approach

We present a simple method for calculating the energies and the widths of quasiparticle resonant states. The method is based on BCS equations solved in the Berggren representation. In this representation the quasiparticle resonances are associated to the Gamow states of the mean field. The method is illustrated for the case of neutron-rich nuclei $^{20-22}$O and $^{84}$Ni. It is shown that the contribution of the continuum coupling to the pairing correlations is small and largely dominated by a few resonant states close to the continuum threshold.

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arXiv2005

Convergence of Particle-Hole Expansions for the Description of Nuclear Correlations

The convergence properties of a multiparticle-multihole (mp-mh) configuration mixing approach whose purpose is to describe ground state correlations in nuclei without particle number and Pauli violations is investigated in the case of an exactly solvable pairing hamiltonian. Two different truncation schemes are tested by looking at quantities as correlation energies and single-particle occupation probabilities. Results show that pairing correlations present in usual superfluid nuclei can be accurately described using up to 6 particle-6 hole excitations, a convergence fast enought for envisaging extensions to fully microscopic calculations.

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arXiv2005

Nuclear Pairing: Surface or Bulk ?

We analyse how the spatial localisation properties of pairing correlations are changing in a major neutron shell of heavy nuclei. It is shown that the radial distribution of the pairing density depends strongly on whether the chemical potential is close to a low or a high angular momentum level and has very little sensitivity to whether the pairing force acts in the surface or in the bulk. The averaged pairing density over one major shell is however rather flat, practically independent of the pairing force. Hartree-Fock-Bogoliubov calculations for the isotopic chain $^{100-132}$Sn are presented for demonstration purposes.

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arXiv2004

Collective excitations in the inner crust of neutron stars : supergiant resonances

We investigate the nuclear collective excitations of Wigner-Seitz cells containing nuclear clusters immersed in a gas of neutrons. This baryonic non-uniform system is specific to the structure of inner crust matter of neutron stars. The collective excitations are studied in the framework of a spherical Hartree-Fock-Bogoliubov + Quasiparticle Random Phase Approximation, formulated in coordinate representation. The calculations are done for two representative Wigner-Seitz cells with baryonic density equal to 0.02 fm$^{-3}$ and 0.08 fm$^{-3}$. It is shown that the excitations with low multipolarities are concentrated almost entirely in one strongly collective mode which exhausts a very large fraction of the energy-weighted sum rule. Since these collective modes are located at very low energies compared to the giant resonances in standard nuclei, they may affect significantly the specific heat of baryonic inner crust matter of neutron stars.

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arXiv2004

Superfluid Properties of the Inner Crust of Neutron Stars

Superfluid properties of the inner crust matter of neutron stars, formed by nuclear clusters immersed in a dilute neutron gas, are analysed in a self- consistent HFB approach. The calculations are performed with two pairing forces, fixed so as to obtain in infinite nuclear matter the pairing gaps provided by the Gogny force or by induced interactions. It is shown that the nuclear clusters can either suppress or enhance the pairing correlations inside the inner crust matter, depending on the density of the surrounding neutrons. The profile of the pairing field in the inner crust is rather similar for both pairing forces, but the values of the pairing gaps are drastically reduced for the force which simulates the polarisation effects in infinite neutron matter.

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arXiv2004

Nuclear Superfluidity and Specific Heat in the Inner Crust of Neutron Stars

We analyse the temperature dependence of pairing correlations in the inner crust matter of neutron stars. The study is done in a finite-temperature HFB approach and by using a zero range pairing force adjusted to the pairing properties of infinite neutron matter. Within the same approach we investigate how the specific heat of the inner crust depends on temperature, matter inhomogeneity, and the assumption used for the pairing force. It is shown that in a physical relevant range of densities the pairing properties of inner crust matter depend significantly on temperature. The finite-temperature HFB calculations show also that the specific heat is rather sensitive to the presence of nuclear clusters inside the inner crust. However, the most dramatic change of the specific heat is determined by the scenario used for the neutron matter superfluidity.

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arXiv2003

Antibound and Resonant States in Halo Nuclei

An unified shell model scheme to evaluate simultaneously the contribution of antibound states and Gamow resonances to the nuclear halos is presented. The calculations, performed in the complex energy plane, are applied to the case of $^{11}$Li. It is found that $^{11}$Li may develop a resonant state excitation near the breakup threshold.

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