$\alpha$-decay from ${}^{44}\mathrm{Ti}$: A study of microscopic clusterization

Background: 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.

Purpose: This paper studies the clusterization of the $0^{+}$ excited states of ${}^{44}\mathrm{Ti}$ arising from the nucleonic degrees of freedom.

Methods: 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.

Results: 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 nonresonant contributions. The influence of a four-body truncated basis is analyzed.

Conclusions: 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.

Figure 1

Experimental and calculated two-body energies for the complete basis.

Figure 2

Low-lying $0^{+}$ states of ${}^{44}\mathrm{Ti}$. The results for the three single-particle model spaces are shown. The experimental values are from Ref. [26].

Figure 3

Two-neutron correlated bound states. The quantum number $E_{J^{\pi }}$ of each line is not stated for simplicity.