arXiv subjects

Rodolfo M. Id Betan

Publications and source records attributed to Rodolfo M. Id Betan.

5 recordsLinked to original sources

arXiv2023

Alpha-decay from $^{44}$Ti: A study of the microscopic clusterization

Microscopic determination of alpha-decay half-lives requires structure and reaction calculations. The structure part is given by the microscopic distribution of the constituent nucleons, while the relative motion of the product's decay provides the reaction part. This paper studies the clusterization of the $0^+$ excited states of $^{44}$Ti arising from the nucleonic degrees of freedom. The continuum spectra of proton and neutron are incorporated through the Gamow Shell Model formalism. The alpha-like wave function is calculated in the weak-coupling approximation. Gaussian effective interaction in each pair of nucleons is included. The $0^+$ ground and excited states are compared with experiment and shell model calculations. The wave function amplitudes are obtained and discriminated by their resonant and non-resonant contributions. The influence of a four-body truncated basis is analyzed. Inclusion of the continuum spectra produces a gain in the excited states of a few hundred keV of energy. One candidate for alpha decay was identified near the experimental unresolved state $(0,2)^+$ of 6.8 MeV excitation energy, with a lower limit for the half-life of $\approx 0.8$ ns.

nucl-th↗

arXiv2020

From bound states to the continuum

This white paper reports on the discussions of the 2018 Facility for Rare Isotope Beams Theory Alliance (FRIB-TA) topical program "From bound states to the continuum: Connecting bound state calculations with scattering and reaction theory". One of the biggest and most important frontiers in nuclear theory today is to construct better and stronger bridges between bound state calculations and calculations in the continuum, especially scattering and reaction theory, as well as teasing out the influence of the continuum on states near threshold. This is particularly challenging as many-body structure calculations typically use a bound state basis, while reaction calculations more commonly utilize few-body continuum approaches. The many-body bound state and few-body continuum methods use different language and emphasize different properties. To build better foundations for these bridges, we present an overview of several bound state and continuum methods and, where possible, point to current and possible future connections.

nucl-th↗

arXiv2017

Richardson's solutions in the real- and complex-energy spectrum

The constant pairing Hamiltonian holds exact solutions worked out by Richardson in the early Sixties. This exact solution of the pairing Hamiltonian regained interest at the end of the Nineties. The discret complex-energy states had been included in the Richardson's solutions by Hasegawa et al. [1]. In this contribution we reformulate the problem of determining the exact eigenenergies of the pairing Hamiltonian when the continuum is included through the single particle level density. The solutions with discret complex-energy states is recovered by analytic continuation of the equations to the complex energy plane. This formulation may be applied to loosely bound system where the correlations with the continuum-spectrum of energy is really important. Some details are given to show how the many-body eigenenergy emerges as sum of the pair-energies.

math-ph↗

arXiv2000

Perturbative method for generalized spectral decompositions

Imposing analytic properties to states and observables we construct a perturbative method to obtain a generalized biorthogonal system of eigenvalues and eigenvectors for quantum unstable systems. A decay process can be described using this generalized spectral decomposition, and the final generalized state is obtained.

quant-ph↗

arXiv1999

Subdynamics theory in the functional approach to quantum mechanics

The formalism of subdynamics is extended to the functional approach of quantum systems, and used for the Friedrichs model, in which diagonal singularities in states and observables are included. We compute in this approach the generalized eigenvectors and eigenvalues of the Liouvulle-Von Newmann operator, using an iterative scheme. As complex generalized eigenvalues are obtained, the decay rates of unstable modes are included in the spectral decomposition.

quant-ph↗