Double beta decay to the first 2+2^+ state within a boson expansion formalism with a projected spherical single particle basis

The Gamow-Teller transition operator is written as a polynomial in the dipole proton-neutron and quadrupole charge conserving QRPA boson operators, using the prescription of the boson expansion technique of Belyaev-Zelevinski type. Then, the $2\nu\beta\beta$ process ending on the first $2^+$ state in the daughter nucleus is allowed via one, two and three boson states describing the odd-odd intermediate nucleus. The approach uses a single particle basis which is obtained by projecting out the good angular momentum from an orthogonal set of deformed functions. The basis for mother and daughter nuclei have different deformations. The GT transition amplitude as well as the half lives were calculated for ten transitions. Results are compared with the available data as well as with some predictions obtained with other methods.Comment: 12 page

New results for the fully renormalized proton-neutron quasiparticle random phase approximation

A many-body Hamiltonian describing a system of Z protons and N neutrons moving in spherical shell model mean field and interacting among themselves through proton-proton and neutron-neutron pairing and a dipole-dipole proton-neutron interaction of both particle-hole and particle-particle type, is treated within a fully renormalized (FR) pnQRPA approach. Two decoupling schemes are formulated. One of them decouples the equations of motion of particle total number conserving and non-conserving operators. One ends up with two very simple dispersion equations for phonon operators which are formally of Tamm-Dancoff types. For excitations in the (N-1,Z+1) system, Ikeda sum rule is fully satisfied provided the BCS equations are renormalized as well and therefore solved at a time with the FRpnQRPA equations. Next, one constructs two operators ${\cal R}^{\dagger}_{1\mu}$, ${\cal R}_{1,-\mu}(-)^{1-\mu}$ which commutes with the particle total number conserving operators, ${\cal A}^{\dagger}_{1\mu}$ and ${\cal A}_{1,-\mu}(-)^{1-\mu}$, and moreover could be renormalized so that they become bosons. Then, a phonon operator is built up as a linear combination of these four operators. The FRpnQRPA equations are written down for this complex phonon operator and the ISR is calculated analytically. This formalism allows for an unified description of the dipole excitations in four neighboring nuclei (N-1,Z+1),(N+1,Z-1),(N-1,Z-1),(N+1,Z+1). The phonon vacuum describes the (N,Z) system ground state.Comment: 24 page

New features of some proton-neutron collective states

Using a schematic solvable many-body Hamiltonian, one studies a new type of proton-neutron excitations within a time dependent variational approach. Classical equations of motion are linearized and subsequently solved analytically. The harmonic state energy is compared with the energy of the first excited state provided by diagonalization as well as with the energies obtained by a renormalized RPA and a boson expansion procedure. The new collective mode describes a wobbling motion, in the space of isospin, and collapses for a particle-particle interaction strength which is much larger than the physical value. A suggestion for the description of the system in the second nuclear phase is made. We identified the transition operators which might excite the new mode from the ground state.Comment: 28 pages and 3 figure

New features of collective motion of intrinsic degrees of freedom. Toward a possible way to classify the intrinsic states

Three exactly solvable Hamiltonians of complex structure are studied in the framework of a semi-classical approach. The quantized trajectories for intrinsic coordinates correspond to energies which may be classified in collective bands. For two of the chosen Hamiltonians the symmetry SU2xSU2 is the appropriate one to classify the eigenvalues in the laboratory frame. Connections of results presented here with the molecular spectrum and Moszkowski model are pointed out. The present approach suggests that the intrinsic states, which in standard formalisms are heading rotational bands, are forming themselves "rotational" bands, the rotations being performed in a fictious boson space.Comment: 33 pages, 9 figure

Description of positive and negative parity dipole bands within the extended coherent state model

AbstractThe extended coherent state model is further extended as to describe two dipole bands of different parities. The formalism provides a consistent description of eight rotational bands. A unified description for spherical, transitional and deformed nuclei is possible. Projecting out the angular momentum and parity from a sole state, the Kπ=1+ band acquires a magnetic character, while the electric properties prevail for the other band. New signatures for a static octupole deformation are pointed out. Interesting features concerning the decay properties of the two bands are found. For illustration the formalism was applied to 172Yb and results are compared with the available data

Description of even-even triaxial Nuclei within the Coherent State and the Triaxial Rotation-Vibration Models

The coherent state model (CSM) and the triaxial rotation-vibration model (TRVM) are alternatively used to describe the ground, gamma and beta bands of 228Th. CSM is also applied to the nuclei 126Xe and 130Ba, which were recently considered in TRVM. The two models are compared with respect to both their underlying assumptions and to their predicted results for energy levels and E2 branching ratios. Both models describe energies and quadrupole transitions of 228Th equally well and in good agreement with experiment, if the 0$_3^+$ level at 1120 keV is interpreted as the head of the beta band. The other two 0$^+$ levels at 832 and 939 keV are most likely not of a pure quadrupole vibration nature as has already been pointed out in the literature.Comment: 31 pages, RevTeX, 6 figure

Ground state particle-particle correlations and double beta decay

A self-consistent formalism for the double beta decay of Fermi type is provided. The particle-particle channel of the two-body interaction is considered first in the mean field equations and then in the QRPA. The resulting approach is called the QRPA with a self-consistent mean field (QRPASMF). The mode provided by QRPASMF, does not collapse for any strength of the particle-particle interaction. The transition amplitude for double beta decay is almost insensitive to the variation of the particle-particle interaction. Comparing it with the result of the standard pnQRPA, it is smaller by a factor 6. The prediction for transition amplitude agrees quite well with the exact result. The present approach is the only one which produces a strong decrease of the amplitude and at the same time does not alter the stability of the ground state.Comment: 23 pages, 7 figure

Analytical description of the Coherent State Model for near vibrational and well deformed nuclei

Analytical formulas for the excitation energies as well as for the electric quadrupole reduced transition probabilities in the ground, beta and gamma bands were derived within the coherent state model for the near vibrational and well deformed nuclei. Numerical calculations were performed for 42 nuclei exhibiting various symmetries and therefore with specific properties. Comparison of the calculation results with the corresponding experimental data shows a good agreement. The parameters involved in the proposed model satisfy evident regularities being interpolated by smooth curves. Few of them, which fall out of the curves, are interpreted as signatures for a critical point in a specific phase transition. This is actually supported also by the figures showing the excitation energy dependence on the angular momentum. The formulas provided for energies and B(E2) values are very simple, being written in a compact form, and therefore easy to be handled to explain the new experimental data.Comment: 9 figures, 50 page

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

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 $\gamma$, are presented in terms of spheroidal and Mathieu functions, respectively. Moreover, the gamma depending factors of the transition operator can be treated.Comment: four two column pages, 1 figur

Non-Scissors-Mode Behaviour of Isovector Magnetic Dipole Orbital Transitions Involving Isospin Transfer

We study the response of isovector orbital magnetic dipole (IOMD) transitions to the quadrupole-quadrupole ($Q \cdot Q$) interaction, to the isospin-conserving pairing interaction (ICP) and to combinations of both. We find qualitatively different behaviours for transitions in which the final isospin differs from the initial isospin versus cases where the two isospins are the same. For $N=Z$ even-even nuclei with $J^{\pi}=0^+, T=0$ ground states such as $^8Be$ and $^{20}Ne$, the summed $T=0 \to T=1$ IOMD from the ground state to all the $J=1, T=1$ states in the $0 \hbar \omega$ space does not vanish when the $Q \cdot Q$ interaction is turned off. The pairing interaction (ICP) alone leads to a finite transition rate. For nuclei with $J=0^+, T=1$ ground states such as $^{10}Be$ and $^{22}Ne$, the summed $T=1 \to T=1$ IOMD $does$ vanish when the $Q \cdot Q$ interaction is turned off, as is expected in a good scissors-mode behaviour. However this is not the case for the corresponding sum of the $T=1 \to T=2$ IOMD transitions. In $^{22}Ne$ (but not in $^{10}Be$) the sum of the $T=1 \to T=2$ IOMD transitions is remarkably insensitive to the strengths of both the $Q \cdot Q$ and the ICP interactions. In $^{22}Ne$ an energy weighted-sum is similarly insensitive. All our calculations were carried out in the $0 \hbar \omega$ space.Comment: 19 pages (including 5 figures). submitted to Nucl. Phys.