A. A. Raduta

The 2vββ decay rate within a higher RPA approach

Abstract A microscopic hamiltonian consisting of an one-body term and a realistic two-body interaction corresponding to the G matrix of the Bonn potential, is treated within the QRPA formalism including both particle-hole (ph) and particle-particle (pp) channels. The β ± transition operators are expanded up to the first order in terms of the dipole and quadrupole RPA bosons. The influence of the higher RPA terms on the ββ matrix element M GT is studied as function of the strength of the dipole pp interaction. g pp (1) . For any value of g pp (1) , M GT is increased by adding the higher RPA terms. The HRPA terms shift the zero ( g pp (1) = 1) of the RPA function M GT to the region of the QRPA collapse.

Boson description of 190Pt and 192Pt

Abstract A boson model for the major collective bands based on the coherent state formalism is applied to the shape transitional Pt isotopes 190 and 192. A very reasonable description of both spectra and the electromagnetic quadrupole transition rates is obtained.

The 2νββ decay rate within a boson expansion formalism

Abstract A microscopic hamiltonian consisting of a one-body term and a realistic two-body interaction, corresponding to the G-matrix of the Bonn potential, is treated within the QRPA formalism including both particle-hole (ph) and particle-particle (pp) channels. The β± transition operators are expanded up to the first order in terms of the dipole and quadrupole RPA bosons. The influence of the higher RPA terms on the ββ matrix elements MGT(00) and MGT(02), associated with the transitions 0i+ → 0i+ → 0i+ → 2f+ respectively, is studied as a function of the strength of the dipole pp interactions gpp(1). The HRPA terms shift the zero (gpp(1) = 1) of the RPA function MGT(00) to the region where QRPA collapses. The MGT(02) value is an increasing function of gpp(1).

Description of the 2νββ decay within a fully renormalised RPA approach

Abstract The RPA treatment of a many body Hamiltonian describing the states of even-even nuclei involved in a 2νββ decay is revisited. One shows that renormalizing the dipole two quasiparticle operators by accounting for new correlations in the ground state requires a simillar renormalization for the dipole density operators which results in activating new boson degress of freedom. Possible consequences on Ikeda sum rule and Gamow-Teller transition amplitude are suggested. A numerical application for a two levels model is presented

Neutrinoless Double Beta Decay of Ge76, Se82, Mo100 and Xe136 to excited 0^+ states

The neutrinoless double beta decay transition to the first excited 0^+ collective final state is examined for A=76, 82, 100 and 136 nuclei by assuming light and heavy Majorana neutrino exchange mechanisms as well as the trilinear R-parity violating contributions. Realistic calculations of nuclear matrix elements have been performed within the renormalized quasiparticle random phase approximation. Transitions to the first excited two-quadrupole phonon 0^+ state are described within a boson expansion formalism and alternatively by using the operator recoupling method. We present the sensitivity parameters to different lepton number violating signals, which can be used in planning the neutrinoless double beta decay experiments. The half-life of neutrinoless double beta decay to the first excited state 0^+_1 is by a factor of 10 to 100 larger than that of the transition to the ground state.

Unified description of the 2νββ decay in spherical and deformed nuclei

Abstract The Gamow-Teller double-beta decay, with two neutrinos in the final state, is calculated within the QRPA approach. Higher-order corrections to the RPA result are studied within a boson expansion formalism. The specific feature of the present paper is that the single-particle basis is obtained through angular-momentum projection from an orthogonal set of deformed wave functions. The effect of deformation on the Gamow-Teller transition amplitude, as well as on the the single β − and β + strengths distribution is obtained. The Gamow-Teller amplitude is calculated for the transitions 0 + i → 0 + f and 0 + i → 2 + f . The method is applied to the 2νββ d probability 82 34 Se to 82 36 Kr.

Closed formulas for ground band energies of nuclei with various symmetries

A time-dependent variational principle is used to dequantize a second-order quadrupole boson Hamiltonian. The classical equations for the generalized coordinate and the constraint for the angular momentum are quantized and then analytically solved. A generalized Holmberg–Lipas formula for energies is obtained. A similar J(J + 1) dependence is provided by the coherent state model in the large deformation regime, by using an expansion in powers of 1/x for energies, with x denoting a deformation parameter squared. A simple compact expression is also possible for the near-vibrational regime. These three expressions have been used for 44 nuclei covering regions characterized by different dynamic symmetries or in other words belonging to all the known nuclear phases. Nuclei satisfying the specific symmetries of the critical point in the phase transitions O(6) → SU(3), SU(5) → SU(3) have also been considered. The agreement between the results and the corresponding experimental data is very good. This is reflected in very small root mean square values of deviations.

Solvable models for the gamma deformation having X (5) as limiting symmetry. Removing some drawbacks of the existing descriptions

Abstract Two solvable Hamiltonians for describing the dynamic gamma deformation are proposed. The limiting case of each of them is the X ( 5 ) Hamiltonian. Analytical solutions for both energies and wave functions, which are periodic in γ, are presented in terms of spheroidal and Mathieu functions, respectively. For illustration, the case of 152Sm is treated with the spheroidal function method.

Quantum deformation of the Dirac bracket

The quantum deformation of the Poisson bracket is the Moyal bracket. We construct quantum deformation of the Dirac bracket for systems which admit global symplectic basis for constraint functions. Equivalently, it can be considered as an extension of the Moyal bracket to second-class constraints systems and to gauge-invariant systems which become second class when gauge-fixing conditions are imposed.

Quasiparticle random phase approximation with inclusion of the Pauli exclusion principle

Limitations of the Quasiparticle Random Phase Approximation (QRPA) are studied within an exactly solvable model, with a two body interaction of Fermi type. A special attention is paid to the violation of the Pauli exclusion principle (PEP) in solving the QRPA equation. A comparison of the exact solution, obtained by the diagonalization of a schematic nuclear Hamiltonian and those obtained within the standard QRPA, the renormalized QRPA, the QRPA with pertubative treatment of the PEP and the QRPA with exact consideration of the PEP, is presented. The agreement quality is judged in terms of the quasiparticle number operator matrix elements in the ground state and in the first excited states, of the beta transition amplitudes, of the Ikeda sum rule and of the nuclear matrix element for the double beta decay. We have found that restoring the PEP, the QRPA solutions are considerably stabilized and a better agreement with the exact solution is obtained.