Ludovic Bonneau

Global microscopic calculations of ground-state spins and parities for odd-mass nuclei

Systematic calculations of ground-state spins and parities of odd-mass nuclei have been performed within the Hartree-Fock-BCS (HFBCS) approach and the finite-range droplet model for nuclei for which experimental data are available. The unpaired nucleon has been treated perturbatively, and axial and left-right reflection symmetries have been assumed. As for the HFBCS approach, three different Skyrme forces have been used in the particle-hole channel, whereas the particle-particle matrix elements have been approximated by a seniority force. The calculations have been done for the 621 nuclei for which the Nubase 2003 data set gives assignments of spins and parities with strong arguments. The agreement of both spin and parity in the self-consistent model reaches about 80% for spherical nuclei, and about 40% for well-deformed nuclei regardless of the Skyrme force used. As for the macroscopic-microscopic approach, the agreement for spherical nuclei is about 90% and about 40% for well-deformed nuclei, with different sets of spherical and deformed nuclei found in each model.

ODD NUCLEI, TIME-REVERSAL SYMMETRY BREAKING, AND MAGNETIC POLARIZATION OF THE EVEN-EVEN CORE

The addition of an extra nucleon to an even-even core generates, in most cases, a polarization of this core which is essentially due to a spin paramagnetic type of coupling. It is shown here that these results (which have been obtained so far only with the SIII Skyrme force) seems to be robust against the change of the Skyrme force parameters for the charge state corresponding to the added nucleon and somewhat less for the other charge state. The consequences drawn from calculations with the SIII force about the effect of the core polarization on the effective spin gyromagnetic factors, hold also for the two other Skyrme force parametrizations (SkM* and SLy4) considered here. A very good reproduction of the average phenomenological quenching of these factors from their free values, is also obtained. Finally, the rare cases where these rules do not hold are discussed.

Ground-state properties of even-even N = Z nuclei within the Hartree-Fock-BCS and higher Tamm-Dancoff approaches

We calculate the ground-state properties of well deformed, even-even N = Z nuclei in the region between 56 Ni and 100 Sn within two different approaches, focusing on the binding energy and deformation and pairing properties. First, we employ the Hartree-Fock-BCS (HFBCS) approximation with the Skyrme effective nucleon-nucleon interaction and discuss how the results depend on the parametrization of the interaction and on the pairing force parameters adjusted in various schemes to reproduce the experimental odd-even mass differences. Then, within the Higher Tamm-Dancoff Approximation (HTDA), which explicitly conserves the particle number, we calculate the same properties starting from the HFBCS solutions. The HTDA treatment of the ground-state correlations is converged within a n-particle-n-hole expansion using up to n =4 particle-hole excitations of the pair type (in the sense of Cooper pairs). We compare the ground-state properties calculated in these two descriptions of pairing correlations and deduce the importance of the particle-number conservation in weak pairing regimes. Finally, we extend the HTDA calculations so as to include the proton-neutron residual interaction and investigate the role of proton-neutron pairing on the above ground-state properties.

EFFECTS OF CORE POLARIZATION AND PAIRING CORRELATIONS ON SOME GROUND-STATE PROPERTIES OF DEFORMED ODD-MASS NUCLEI WITHIN THE HIGHER TAMM–DANCOFF APPROACH

In self-consistent mean-field approaches, the description of odd-mass nuclei requires to break the time-reversal invariance of the underlying one-body hamiltonian. This induces a polarization of the even-even core to which the odd nucleon is added. To properly describe the pairing correlations (in T = 1 and T = 0 channels) in such nuclei, we implement the particle-number conserving Higher Tamm–Dancoff approximation with a residual δ interaction in each isospin channel by restricting the many-body basis to two-particle–two–hole excitations of pair type (nn, pp and np) on top of the Hartree–Fock solution. We apply this approach to the calculation of two ground-state properties of well-deformed nuclei |Tz| = 1 nuclei around 24Mg and 48Cr, namely the isovector odd-even binding-energy difference and the magnetic dipole moment, focusing on the impact of pairing correlations.

THE HIGHER TAMM–DANCOFF APPROXIMATION: THEORETICAL CONTEXT AND PHENOMENOLOGICAL ASPECTS

We present the key aspects of the theoretical foundations of the Higher Tamm–Dancoff Approximation which can be interpreted as a truncated shell-model approach based on a Hartree–Fock solution, ensuring the conservation of the particle number. Then we discuss some phenomenological aspects of the residual interactions used, namely the delta interaction to describe the neutron–neutron and proton–proton pairing correlations and the quadrupole–quadrupole interaction to describe vibrational correlations.

ISOSPIN MIXING IN THE HIGHER TAMM-DANCOFF APPROXIMATION

We present a formalism to study the isospin content of a nuclear state in the framework of the Higher Tamm-Dancoff Approximation. This formalism is then applied to the description of even-even N = Z nuclei. Finally a schematic two-level model provides some insight into the isospin-mixing mechanism at work and the impact of the pairing correlations on the isospin-mixing parameter.

EFFECTS OF VIBRATIONAL AND PAIRING CORRELATIONS ON ISOSPIN MIXING IN THE HIGHER TAMM-DANCOFF APPROXIMATION

In the framework of the Higher Tamm-Dancoff Approximation which allows for a consistent treatment of pairing and quadrupole vibrational correlations preserving the particle-number symmetry and the Pauli principle, we compare the isospin content of ground and excited Kπ = 0+ states including either type of the above mentioned correlations using an approximate projection-after-variation technique for isospin. The pairing correlations are described with a delta interaction using the same strength in the T = 0 and T = 1 channels, whereas the vibrational correlations are treated with an isoscalar quadrupole-quadrupole interaction. As a first study, we apply this approach in the N = Z, even-even 16O nucleus. For the same amount of correlations measured by the diffusivity of Fermi surface or depletion of particle-hole vacuum in the ground-state solution, we find very similar isospin mixing in the ground state for both types of correlations, but different patterns for the distribution in the calculated solutions of the expectation value of the square of the isospin operator.

Microscopic calculations of Qp-values in well-deformed odd-Z proton emitters

Within the Hartree–Fock–BCS and Highly Truncated Diagonalization microscopic approaches we have calculated the ground‐state binding energies of axially‐deformed odd‐Z, even‐N nuclei in the A ∼ 130 region and of the even‐even daughter nuclei resulting from one‐proton emission. The deduced Qp values are in fair agreement with available experimental data.

EFFECTS OF PAIRING CORRELATIONS ON THE ISOSPIN-SYMMETRY-BREAKING CORRECTION TO SUPER-ALLOWED 0+ → 0+ FERMI TRANSITIONS WITHIN THE HIGHER TAMM–DANCOFF APPROACH

Super-allowed 0+ → 0+ Fermi transitions provide a test at low energy of the Standard Model of elementary interactions. The isospin-symmetry breaking due to the electromagnetic interaction at a nuclear level is a fundamental theoretical tool for the understanding of weak processes beyond the Standard Model. Within the Higher Tamm–Dancoff description of correlated nuclear states, we calculate the isospin-symmetry breaking correction δc to the Fermi transition matrix element. A sensitivity study on the T = 0 pairing correlations is carried out and some tests of model ingredients are performed. The obtained correction is of the order of 0.15~0.2% for plausible strengths in the T = 1 and T = 0 channels of the residual interaction. This is expected to constitute a lower bound.

Quantum preequilibrium multistep direct calculations for nucleon scattering on deformed nuclei: a microscopic approach

An introduction of the different quantum mechanics models is given for the calculation of pre‐equilibrium multistep direct process for nucleon induced reaction. A practical application is presented for 238U neutron induced reaction at medium energy (10–20 MeV). The double differential cross‐sections are calculated with no adjustable parameter and reproduced the data very well. The cross‐sections are expressed as a sum of DWBA transition amplitudes computed with a microscopic two‐body interaction. The exited states of the target are expressed as particle‐hole excitations built from single particle states obtained with the HF+BCS calculation with a Skyrme force. We also perform a sensitivity study our calculations with respect to the ingredients of the model, namely the two‐body interaction which generates the transitions and the target states description.