Paul-Henri Heenen

Self-consistent study of triaxial deformations: Application to the isotopes of Kr, Sr, Zr and Mo

Abstract Self-consistent mean-field calculations of deformation energy surfaces have been performed for more than 30 exotic isotopes of the Kr, Sr, Zr and Mo elements. Our calculations extend to the proton drip line. We investigate the triaxial stability of the deformed ground states in the deformation regions N ≈ 38 and N ≈ 60. The results are in good agreement with the observed trends.

Generalised meshes for quantum mechanical problems

A new method to discretise Schrodinger equations on a mesh is described. This method is based on an accurate approximation of a variational calculation. The regularly spaced mesh and meshes based on the zeros of orthogonal polynomials are studied in detail. It is shown that with each type of mesh is associated a particular kinetic energy operator and an optimal formula for its discretized form. The applications to some simple potential problems show that the method is very accurate as well as very simple. Applications to many-body problems indicate that the accuracy of the results is improved by an order of magnitude with respect to conventional mesh calculations.

Shell structure of the superheavy elements

Abstract Ground-state properties of the superheavy elements (SHE) with 108 ⩽ Z ⩽ 128 and 150 ⩽ N ⩽ 192 are investigated using both the Skyrem-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, Qα-values, and other observables is given.

Shape coexistence and triaxiality in the superheavy nuclei

Superheavy nuclei represent the limit of nuclear mass and charge; they inhabit the remote corner of the nuclear landscape, whose extent is unknown. The discovery of new elements with atomic numbers Z ≥ 110 has brought much excitement to the atomic and nuclear physics communities. The existence of such heavy nuclei hangs on a subtle balance between the attractive nuclear force and the disruptive Coulomb repulsion between protons that favours fission. Here we model the interplay between these forces using self-consistent energy density functional theory; our approach accounts for spontaneous breaking of spherical symmetry through the nuclear Jahn–Teller effect. We predict that the long-lived superheavy elements can exist in a variety of shapes, including spherical, axial and triaxial configurations. In some cases, we anticipate the existence of metastable states and shape isomers that can affect decay properties and hence nuclear half-lives.

A Hartree-Fock-Bogoliubov mass formula

In order to have more reliable predictions of nuclear masses at the neutron drip line, we here go beyond the recent mass formula HFBCS-1 and present a new mass formula, HFB-1, based on the Hartree-Fock-Bogoliubov method. As with the HFBCS-1 mass formula, we use a 10-parameter Skyrme force along with a 4-parameter δ-function pairing force and a 2-parameter phenomenological Wigner term. However, with the original HFBCS-1 Skyrme force (MSk7), the rms error becomes unacceptably large and a new force fit is required. With the isoscalar and isovector effective masses constrained to be equal, the remaining 15 degrees of freedom are fitted to the masses of all the 1754 measured nuclei with A ≥ 16, N - Z > 2 given in the 1995 Audi-Wapstra compilation. The rms error with respect to the masses of all the 1888 measured nuclei with Z, N ≥ 8 is 0.764 MeV. A complete mass table, HFB-1 (available on the Web), has been constructed, giving all nuclei lying between the two drip lines over the range Z, N ≥ 8 and Z ≤ 120. A comparison between HFB-1 and HFBCS-1 mass tables shows that the HFBCS model is a very good approximation of the HFB theory, in particular for masses, the extrapolated masses never differing by more than 2 MeV below Z ≤ 110. We also find that the behaviour of shell gaps far away from the region of beta stability does not depend on whether the HFBCS or HFB methods are used, in particular, no quenching of astrophysical interest arises from replacing the BCS method by the Bogoliubov method.

Analysis of the generator coordinate method in a study of shape isomerism in 194Hg

Abstract We investigate the properties of the generator coordinate method (GCM) on a collective basis of BCS states. The method is applied to a study of large-amplitude quadrupole dynamics in the nucleus 194 Hg. Among the GCM levels, we discuss candidates for a possible shape isomerism associated with a secondary deformed minimum at large deformation ( Q ≈ 45b). We also analyze standard approximation schemes based on the gaussian overlap approximation which lead to a collective Schrodinger equation. We compare their predictions with the exact GCM results for the particular case of 194 Hg.

Microscopic R-matrix theory in a generator coordinate basis: (III). Multi-channel scattering

The microscopic R-matrix theory presented in two previous papers is extended to the multichannel scattering case. An antisymmetrized wave function is built in the two-centre harmonic oscillator model. This wave function is proved to be equivalent to the resonating group one even if the nuclei have non-zero spin. The method only requires the calculation of numerical values of matrix elements between Slater determinants. The microscopic R-matrix theory may be applied to study both reactions and inelastic scattering.

Deformation of nuclei close to the two-neutron drip line in the Mg region

Abstract We present Hartree-Fock-Bogoliubov (HFB) calculations of the ground states of even Mg isotopes. A Skyrme force is used in the mean-field channel and a density-dependent zero-range force in the pairing channel. 40 Mg and 20 Mg are predicted to be at the two-neutron and two-proton drip lines respectively. A detailed study of the quadrupole deformation properties of all the isotopes shows that the ground states of 36,38,40 Mg are strongly deformed with significantly different deformations for the neutrons and protons. Our study supports the disappearance of the N = 28 shell gap in the Mg and Si isotopes.

Self-consistent calculation of nuclear rotations: The complete yrast line of 24Mg

Abstract We present a method of solution on a three-dimensional mesh of the self-consistent cranked Hartree-Fock + BCS equations. Using several parametrizations of the Skyrme interaction we apply our method to the study of the complete yrast line of 24 Mg. We find that J = 26 is the limiting angular momentum for this nucleus. We have also studied examples of collective rotations along the γ = 60° axis involving hexadecapole deformations. Our work corroborates earlier calculations using the Nilsson-Strutinsky method and extends them to higher spins.

3D solution of Hartree-Fock-Bogoliubov equations for drip-line nuclei

Abstract 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 Hartree-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.