arXiv subjects
Publications and source records attributed to P. -H. Heenen.
We study shape coexistence and low-energy excitation spectra in neutron-deficient Pb isotopes using configuration mixing of angular-momentum and particle-number projected self-consistent mean-field states. The same Skyrme interaction SLy6 is used everywhere in connection with a density-dependent zero-range pairing force.
Self-consistent mean field calculations with the SLy4 interaction and a density-dependent pairing force are presented for nuclei in the Nobelium mass region. Predicted quasi-particle spectra are compared with experiment for the heaviest known odd N and odd Z nuclei. Spectra and rotational bands are presented for nuclei around No252,4 for which experiments are either planned or already running.
Starting from constrained Skyrme-mean-field calculations, the low-energy excitation spectrum of 16O is calculated by configuration mixing of particle-number and angular-momentum projected mean-field states in the framework of the Generator Coordinate Method. Without any adjustable parameters, this approach gives a very good description of those states and their transition moments that can be described with our restriction to axially and reflection-symmetric shapes. The structure of low-lying 0+ states is analyzed in terms of self-consistent 0p-0h, 2p-2h, and 4p-4h Hartree-Fock states.
In order to extract informations on pairing correlations in nuclei from experimental mass differences, the different contributions to odd-even mass differences are investigated within the Skyrme HFB method. In this first paper, the description of odd nuclei within HFB is discussed since it is the key point for the understanding of the above mentioned contributions. To go from an even nucleus to an odd one, the advantage of a two steps process is demonstrated and its physical content is discussed. New results concerning time-reversal symmetry breaking in odd-nuclei are also reported. PACS: 21.10Dr; 21.10.Hw; 21.30.-x. Keywords: Mean-field theories; Pairing correlations; odd nuclei;
We present a microscopic analysis of the collective behaviour of the lead isotopes in the vicinity of Pb208. In this study, we rely on a coherent approach based on the Generator Coordinate Method including exact projection on N and Z numbers within a collective space generated by means of the constrained Hartree-Fock BCS method. With the same Hamiltonian used in HF+BCS calculations, we have performed a comprehensive study including monopole, quadrupole and octupole excitations as well as pairing vibrations. We find that, for the considered nuclei, the collective modes which modify the most the conclusions drawn from the mean-field theory are the octupole and pairing vibrations.
The odd-even mass staggering in nuclei is analyzed in the context of self-consistent mean-field calculations, for spherical as well as for deformed nuclei. For these nuclei, the respective merits of the energy differences $Δ^{(3)}$ and $Δ^{(5)}$ to extract both the pairing gap and the time-reversal symmetry breaking effect at the same time are extensively discussed. The usual mass formula $Δ^{(3)}$, is shown to contain additional mean-field contributions when realistic pairing is used in the calculation. A simple tool is proposed in order to remove time-reversal symmetry breaking effects from $Δ^{(5)}$. Extended comparisons with the odd-even mass staggering obtained in the zero pairing limit (schematic model and self-consistent calculations) show the non-perturbative contribution of pairing correlations on this observable. PACS: 21.10Dr; 21.10.Hw; 21.30.-x. Keywords: Mean-field theories; Pairing correlations; Odd-even mass staggering;
The odd-even mass staggering (OES) of nuclei is analyzed in the context of self-consistent mean-field calculations. The procedure developed allows to understand the OES for spherical as well as for deformed nuclei. Comparison with results at the Hartree-Fock level shows the non-perturbative effect on this observable of the inclusion of pairing correlations.
Rotational bands of $^{252, 253, 254}$No and the fission barriers of $^{254}$No at spin 0$\hbar$ and 20$\hbar$ are calculated with the Hartree-Fock-Bogolyubov theory and the Lipkin-Nogami approximate particle number projection. The SLy4 Skyrme force is used in the particle-hole channel. A zero-range force with and without density-dependence is used in the particle-particle channel. The experimental ground state deformation (${\cal{Q}}_{20}$ = 32.8 b) is reproduced as well as the increase of the dynamical moment of inertia with frequency both for $^{252}$No and $^{254}$No. The rotational band of $^{253}$No is also calculated. Fission barriers of $^{254}$No at spin 0$\hbar$ and 20$\hbar$ show the robustness of shell-corrections against rotation in these heavy nuclei.
Two applications of mean-field calculations based on 3D coordinate-space techniques are presented. The first concerns the structure of odd-N superheavy elements that have been recently observed experimentally and shows the ability of the method to describe, in a self-consistent way, very heavy odd-mass nuclei. Our results are consistent with the experimental data. The second application concerns the introduction of correlations beyond a mean-field approach by means of projection techniques and configuration mixing. Results for Mg isotopes demonstrate that the restoration of rotational symmetry plays a crucial role in the description of 32Mg.
We present in this paper the general framework of a method which permits to restore the rotational and particle number symmetries of wave functions obtained in Skyrme HF+BCS calculations. This restoration is nothing but a projection of mean-field intrinsic wave functions onto good particle number and good angular momentum. The method allows also to mix projected wave functions. Such a configuration mixing is discussed for sets of HF+BCS intrinsic states generated in constrained calculations with suitable collective variables. This procedure gives collective states which are eigenstates of the particle number and the angular momentum operators and between which transition probabilities are calculated. An application to 24Mg is presented, with mean-field wave functions generated by axial quadrupole constraints. Theoretical spectra and transition probabilities are compared to the experiment.
The yrast line of the N=Z nucleus 48Cr is studied up to high spins by means of the cranked Hartree-Fock-Bogoliubov method including the T=0 and T=1 isospin pairing channels. A Skyrme force is used in the mean-field channel together with a zero-range density-dependent interaction in the pairing channels. The extensions of the method needed to incorporate the neutron-proton pairing are summarized. The T=0 pairing correlations are found to play a decisive role for deformation properties and excitation energies above 16hbar which is the maximum spin that can be obtained in the f7/2 subshell.
Recent experimental observation of the direct links between superdeformed and normal-deformed structures in the A~190 mass region offers a unique information on the absolute nuclear binding energy in the 2:1 minima, and hence on the magnitude of shell effects in the superdeformed well. In the present paper, the self-consistent mean-field theory with density-dependent pairing interaction is used to explain at the same time the two-particle separation energies in the first and second wells, and the excitation energies of superdeformed states in the A~190 and A~240 mass regions.
Ground state energies and decay widths of particle unstable nuclei are calculated within the Hartree-Fock approximation by performing a complex scaling of the many-body Hamiltonian. Through this transformation, the wave functions of the resonant states become square integrable. The method is implemented with Skyrme effective interactions. Several Skyrme parametrizations are tested on four unstable nuclei: 10He, 12O, 26O and 28O.
We perform the Hartree-Fock-Bogoliubov (HFB) calculations for ground states of even Mg isotopes using the Skyrme force and a density-dependent zero-range pairing force. The HFB equation is solved in a three-dimensional cartesian mesh, and a convergence of deformation is carefully examined with respect to a cut-off radius for a check of the calculations. We discuss systematics of the two-neutron separation energy, deformation and root-mean-square radius. We have found that 36,38,40Mg have appreciable static deformation, where 40Mg is a two-neutron drip-line nucleus in our calculation, and the deformations of the neutron and proton are different in these three nuclei. The deformation property is analyzed on the basis of the single-particle diagram. It is shown that N=28 is not a closed shell in Mg as well as Si.
Ground state properties of the superheavy elements (SHE) with Z from 108 to 128 and N from 150 to 192 are investigated using both the Skyrme-Hartree-Fock method with a density-independent contact pairing interaction and the macroscopic-microscopic approach with an average Woods-Saxon potential and a monopole pairing interaction. Detailed analysis of binding energies, separation energies, shell effects, single proton and neutron states, equilibrium deformations, alpha-decay energies, and other observables is given.
We study the properties of the superdeformed (SD) bands of 195Pb and 193Hg by the cranked Hartree-Fock-Bogoliubov method. Our calculations reproduce the flat behavior of the dynamical moment of inertia of two of the SD bands of 195Pb measured recently. We discuss possible configuration assignments for the observed bands 3 and 4 of 195Pb. We also calculate the two interacting SD bands of 193Hg. Our analysis confirms the superiority of a density-dependent pairing force over a seniority pairing interaction.
We investigate the possibility of describing triaxial quadrupole deformations for nuclei close to the two-neutron drip line by the Hartree-Fock Bogoliubov method taking into account resonances in the continuum. We use a Skyrme interaction to describe the Hartee-Fock hamiltonian and a density-dependent zero-range interaction to evaluate the pairing field. The mean-field equations are solved in a three-dimensional cubic mesh. We study the stability of the two-neutron separation energies and of the description of the nuclear surface as a function of the number of active mean-field orbitals and of the size of the mesh. The even Ni isotopes are used as a test case and the accuracy as a function of quadrupole deformation is studied by performing constrained calculations. A first application to the study of the two-neutron separation energies in Ni isotopes up to the drip line is presented.
The cranked Hartree-Fock-Bogoliubov method presented in previous studies of superdeformed bands in Hg and Pb isotopes is applied to the study of superdeformed bands in Gd150, Dy152, Dy151 and Tb151. The same density-dependent zero-range pairing interaction used in the A=190 mass region leads to a similarly good agreement with the experimental data. In particular, our results confirm the importance of a correct treatment of pairing correlations in Gd150 to reproduce its experimental dynamical moment of inertia. The quasi-particle spectra obtained for all the nuclei studied here are compatible with the experimental results obtained for excited bands in this mass region. The quality of our results opens the possibility of studying microscopically very subtle phenomena like the properties of identical bands.