O. Castaños

GROUP THEORY OF THE INTERACTING BOSON MODEL OF THE NUCLEUS

Recently Arima and Iachello proposed an interacting boson model of the nucleus involving six bosons, five in a d and one in an s state. The most general interaction in this model can then be expressed in terms of Casimir operators of the following chains of subgroups of the fundamental group U(6): U(6) ⊆U(5) ⊆O(5) ⊆O(3) ⊆O(2), U(6) ⊆O(6) ⊆O(5) ⊆O(3) ⊆O(2), U(6) ⊆SU(3) ⊆O(3) ⊆O(2). To determine the matrix elements of this interaction in, for example, a basis characterized by the irreducible representations of the first chain of groups, then we only need to evaluate the matrix elements of the Casimir operators of O(6) and SU(3) in this basis as the others are already diagonal in it. Using results of a previous publication for the basis associated with U(5) ⊆O(5) ⊆O(3), we obtain the matrix elements of the Casimir operators of O(6) and SU(3). Furthermore, we obtain explicitly the transformation brackets between states characterized by irreducible representations of the first two chains of groups. Numerical p...

Double-beta decay in the pseudo SU(3) scheme

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. In this approach, we used a recently developed summation procedure, avoiding the closure approximation. We find forbidden decays for five potential double-beta emitters and finite values for the half-life of six other nuclei, one of them strongly inhibited. These forbidden decays represent a possible test of our model and up to now the predictions are in good agreement with the available experimental data.

Neutrinoless double beta decay in heavy deformed nuclei

Abstract The zero-neutrino mode of the double beta decay in heavy deformed nuclei is investigated in the framework of the pseudo-SU(3) model, which has provided an accurate description of collective nuclear structure and predicted half-lives for the two-neutrino mode in good agreement with experiments. In the case of 238U the calculated zero-neutrino half-life is at least three orders of magnitude greater than the two-neutrino one, giving strong support of the identification of the radiochemically determined half-life as being the two-neutrino double beta decay. For 150Nd the zero-neutrino matrix elements are of the order of magnitude of, but lesser than, those evaluated using the QRPA. This result confirms that different nuclear models produce similar zero-neutrino matrix elements, contrary to the two-neutrino case. Using these pseudo-SU(3) results and the upper limit for the neutrino mass we estimate the ββ0ν half-lives for six nuclei. An upper limit for majoron coupling constant is extracted from the experimental data.

Boson realization of sp(4). I. The matrix formulation

Holstein and Primakoff derived long ago the boson realization of a su(2) Lie algebra for an arbitrary irreducible representation (irrep) of the SU(2) group. The corresponding result for su(1,1)≅sp(2) is also well known. This raises the question of whether it is possible to obtain in an explicit, analytic, and closed form, and for any integer d, the boson realization of a sp(2d) Lie algebra for an arbitrary irrep of the Sp(2d) group, which is a problem of considerable physical interest. The case d=2 already illustrates the problem in its full generality and thus in this paper we concentrate on sp(4). The Dyson realization is well known, and the passage to bosons satisfying the appropriate Hermiticity conditions can be done by a similarity transformation through an operator K. What we want, though, is an explicit boson realization for sp(2d) similar to the one that exists for sp(2). In Sec. VI we show how we can get it for sp(4) if the operator K is known. Unfortunately while the matrix form of K2 can be ex...

Double-beta decay of 100Mo: The deformed limit.

The double beta decay of

Transformation to pseudo-SU (3) in heavy deformed nuclei

^{100}Mo

Complete set of states for microscopic nuclear collective models

to the ground state and excited states of

Investigations of rotational nuclei via the pseudo-symplectic model

^{100}Ru

Pseudo-symplectic model for strongly deformed heavy nuclei

is analysed in the context of the pseudo SU(3) scheme. The results of this deformed limit are compared with the vibrational one based on the QRPA formalism. Consistency between the deformed limit and the experimental information is found for various

Generalized coherent states for time-dependent and nonlinear Hamiltonian operators via complex Riccati equations

\beta\beta