α-decay calculations of heavy nuclei using an effective Skyrme interaction

Abstract

Background: For nuclei heavier than 208 Pb α decay is a dominating decay mode, and in the search of new superheavy elements one often observes chains of α decays.Purpose: Explore and test microscopic descriptions of α decay based on theories with effective nuclear interactions.Methods: The nuclear ground states are calculated with the Hartree-Fock-Bogoliubov (HFB) method using the Skyrme interaction. Microscopic α-decay formation amplitudes are calculated from the HFB wave functions, and the R-matrix formalism is utilized to obtain decay probabilities.Results: Using a large harmonic-oscillator basis we obtain converged α-decay widths. A comparison with experiment including all spherical even-even α emitting nuclei shows that the model consistently predicts too small formation amplitudes while relative values are in good agreement with experiment. Conclusions:The method was found to be numerically practical even with a large basis size. The comparison of formation amplitudes suggests that the pairing type correlations included in the HFB approach cannot produce sufficient α-particle clustering.

Systematics of nucleon density distributions and neutron skin of nuclei

“…The nuclear energy density functional is optimized to provide an adequate approximation of the total energy and the local nuclear local. The SLy4 parameterization of the Skyrme-like force is widely used in different nuclear studies such as the nuclear structure [36,37,38], the nuclear reactions [39,40,41] as well as the decay processes of heavy nuclei [42,43,44]. One of the advantages of the Skyrme force is that it gives simple analytic expressions which are easy to handle with straight forward calculations.…”

Alpha-particle formation and decay rates from Skyrme–HFB wave functions

“…We use the same decay formalism and Skyrme-HFB nuclear structure model as in the previous work [12], where several aspects of the approach and the introduced approximations are discussed in detail. Here we recapitulate only the ingredients necessary for the discussion of the current results.…”

“…In the case of 212 Po this means [12] that the formation amplitude should be converged for separations R ≤ 10 fm. As seen in Fig.…”

How to calculate α-decay rates in the future?

“…A microscopic description of the emission is obtained from the R-matrix approach [9]. The combination of these two frameworks was recently explored for decay of spherical even-even [10] and odd nuclei [5]. The results show that within this formalism the nuclei are predicted to be much too long lived.…”

“…This implies that the missing correlation effects always increase the probability for the particle to form with the same percentage. This assumption was tested by comparing calculations for all even-even [10] and odd spherical nuclei with experimental data [5]. Figure 2 shows the ratio of theoretical and experimental partial decay widths ( =h ln (2) /t 1/2 ).…”