P. Quentin

Nuclear deformation energy curves with the constrained Hartree--Fock method.

Abstract Calculations of the deformation energy curves of relatively heavy deformed nuclei — Ce isotopes — have been performed using the constrained Hartree-Fock technique. The two-body interaction is the Skyrme force, and pairing effects are taken into account. Different possible choices for the external field form are investigated and the advantage of a non-linear dependence of the constraint is shown. One of the advantages of this type of calculation is that deformation energy curves can be calculated without making a complete map of the deformation energy surface. A discussion of the numerical techniques and uncertainties, particularly those connected with truncation effects is given. General trends of the deformation energy curves, calculated for the Ce isotopes as a function of the quadrupole moment, are found to be in good agreement with available experimental information. Associated physical quantities are discussed and a comparison is made with the results of phenomenological calculations using the liquid-drop model and the Strutinsky prescription.

An improved pairing interaction for mean field calculations using skyrme potentials

Abstract A zero-range interaction is proposed to calculate nuclear pairing at the Fermi surface. The results of Skyrme calculations using the zero range pairing interaction are compared with those using the constant G model for the pairing, as well as with those of a finite-range calculation. Particular attention is paid to the region of superdeformation and fission.

Self-consistent calculation of the ground state properties of some rare-earth nuclei

Abstract Ground state intrinsic deformation properties of some rare earth nuclei are calculated within the Hartree-Fock approximation using a Skyrme effective interaction. After a careful optimization of basis parameters, calculations have been performed with a basis corresponding to 13 spherical oscillator shells. In order to obtain the multipole moments, good numerical convergence is necessary. Calculated quadrupole and hexadecapole moments are in agreement with available experimental data. Ground state binding energies are also well reproduced.

Superdeformation and shape isomerism at zero spin

Abstract Microscopic Hartree-Fock plus BCS calculations in three-dimensional coordinate space are performed to obtain potential energy surfaces in order to analyse shape isomerism in mass regions other than the well-documented fission isomers in the actinides. Many isotopes of platinum, mercury and osmium exhibit a second minimum with a large deformation and are thus candidates for shape isomerism. The same feature also occurs around the 68 Ni nucleus. The most promising candidates for experimental verification are delineated.

Nilsson's Hamiltonian in the asymptotic basis

Abstract In this work, the set of eigenvectors common to the axially symmetrical deformed harmonic oscillator and to the third component of angular momentum, is used as a basis of representation (asymptotic basis). In this basis, the matrix elements of Nilssons Hamiltonian are calculated by means of creation and destruction operators. A rather simple calculation gives, after a diagonalisation, level diagrams as a function of deformation. The influence of various corrective terms, used instead of l 2 and l · s (particularly l T Nilssons term) is discussed. Within the framework of these approaches and in order to test them, we calculate total energy as a function of deformation for some nuclei. Such a more precise calculation allows also a study of pseudocrossings of levels associated with ΔN = ± 2.

A self-consistent study of triaxial deformations in heavy nuclei

Abstract Lattice Hartree-Fock + BCS calculations for axially asymmetrical solutions have been extended to heavy nuclei. The deformation energy surfaces in a (β, γ) sextant for the 138 Sm and 192 Os nuclei exhibit a shallow triaxial minimum, while a valley connecting smoothly the oblate and prolate minima is found in the 186 Pt nucleus.

Rotational bands in well deformed heavy nuclei

A method for the description of rotational states in nuclei is proposed that takes into account the dynamical stretching of the nuclear mean field, as well the dynamical reduction of pairing correlations due to rotation, and is shown to agree well with the experimental data even up to  = L 30 angular momenta. We also compare our new method with an approach based on an intrinsic vortical motion in rotating nuclei.

Quadrupole collective dynamics of medium–heavy even–even nuclei within the highly truncated diagonalization approach

The seven scalar functions defining a Bohr quadrupole collective Hamiltonian are evaluated from calculations performed within the highly truncated diagonalization approach (HTDA) for four even-even medium-heavy nuclei. The collective nuclear spectra so obtained are discussed and compared with similar previous theoretical results and available experimental data.

Skyrme force-like extension of the nuclear pairing interaction

In this paper, isovector and isoscalar pairing correlations were investigated using generalized Bardeen–Cooper–Shrieffer theory and a Skyrme force-like form of the residual interaction. The calculations are done for even–even N~Z germanium nuclei in an axially symmetric Skyrme–Hartree–Fock + BCS scheme with SIII force and time-reversal invariance. A coexistence of T=0 and T=1 superfluid phases is observed.

β decay of 252Cf in the transition from the exit point to scission

Upon increasing significantly the nuclear elongation, the β-decay energy grows. This paper investigates within a simple yet partly microscopic approach, the transition rate of the β− decay of the Cf252 nucleus on the way to scission from the exit point for a spontaneous fission process. A rather crude classical approximation is made for the corresponding damped collective motion assumed to be one dimensional. Given these assumptions, we only aim in this paper at providing the order of magnitudes of such a phenomenon. At each deformation the energy available for β− decay, is determined from such a dynamical treatment. Then, for a given elongation, transition rates for the allowed (Fermi) 0+⟶0+ β decay are calculated from pair correlated wave functions obtained within a macroscopic-microscopic approach and then integrated over the time corresponding to the whole descent from exit to scission. The results are presented as a function of the damping factor (inverse of the characteristic damping time) in use in our classical dynamical approach. For instance, in the case of a descent time from the exit to the scission points of about 10−20 s, one finds a total rate of β decay corresponding roughly to 20 events per year and per milligram of Cf252. The inclusion of pairing correlations does not affect much these results.