J. G. Hirsch

M1 strengths in deformed nuclei

The Elliott SU(3) model, extended via pseudo-spin for heavy nuclei, is used to study low-lying magnetic dipole excitations in deformed nuclei. Proton and neutron degrees of freedom are handled explicitly and the system Hamiltonian includes single-particle energies as well as quadrupole-quadrupole and pairing two-body interactions. The calculated excitation spectra and M1 strength distribution of the strongly deformed even-even Gd isotopes are shown to be in good agreement with experimental results. Results for the -unstable (soft rotor) nucleus and the even-odd system are also reported and found to compare favourably with the available experimental data, demonstrating the ability of the model to describe very different types of systems.

Pseudo‐spin symmetry and its applications

The pseudo‐spin symmetry is reviewed. A mapping that produces the separation of the total angular momentum into pseudo‐orbital and pseudo‐spin degrees of freedom is discussed, together with the analytic transformations that take us from the normal parity space to the eigenstates of a pseudo‐oscillator with one quanta less. The many‐particle version of the unitary transformation to the pseudo‐SU(3) space is established. As an example, these symmetries are used to describe the double beta decay phenomenon in heavy deformed nuclei.

Renormalized QRPA and double beta decay: a critical analysis of double Fermi transitions

The proton-neutron monopole Lipkin model, which exhibits some properties which are relevant for those double beta decay (

Comparative studies of the 2νββ decay

beta beta

SHELL MODEL CALCULATIONS FOR HEAVY DEFORMED NUCLEI

) transitions mediated by the Fermi matrix elements, is solved exactly in the proton-neutron two-quasiparticle space. The exact results are compared with the ones obtained by using the Quasiparticle Random Phase (QRPA) and renormalized QRPA (RQRPA) approaches. It is shown that the RQRPA violates the Ikeda Sum Rule and that this violation may be common to any extension of the QRPA where scattering terms are neglected in the participant one-body operators as well as in the Hamiltonian. This finding underlines the need of additional developments before the RQRPA could be adopted as a reliable tool to compute

Pseudo SU(3) approach to the ββ decay

beta beta

Interplay between the quadrupole-quadrupole and spin-orbit interactions in nuclei

processes.

Scissors mode and the pseudo-SU(3) model

The microscopic description of nuclear double beta decay transitions is presented in the framework of a schematic model. The comparison between these results and the ones corresponding to realistic calculations shows that the physics of the double beta decay may be dominated by non-perturbative effects.

Microscopic description of the scissors mode and its fragmentation

The pseudo SU(3) model is shown to be a powerful scheme for describing the excitation spectra as well asB(E2) andB(M1) transition strengths in heavy deformed nuclei. It is also useful for describing double beta decay amplitudes for transitions from the ground state of an even-even nucleus to the ground and excited states of the daughter nucleus, both for the two and zero neutrino emitting modes. The existence of selection rules which strongly restricts the decays is discussed. Anti-correlations between the quadrupole deformation and the Gamow-Teller (GT+) strength are found in an extension of the pseudo SU(3) model which explicitly includes pairing, which is also able to describe the fragmentation of the scissors mode. The projected shell model is introduced and proposed as an alternate means for studying single and double beta decay processes.

Spontaneous and dynamical breaking of mean field symmetries in the proton-neutron quasiparticle random phase approximation and the description of double beta decay transitions

Abstract We estimate the double beta half-life in the two neutrino mode of several heavy deformed nuclei using the pseudo SU(3) shell model scheme, together with a summation procedure. We find forbidden decays for five potential emitters and finite values for the half-life of other six nuclei.