Towards a self-consistent microscopic α-decay theory

We show that for osmium, platinum and mercury isotopes the α-particle preformation factors given by the standard shell model are not consistent with the barrier penetrabilities. The internal cluster formation amplitude and the outgoing Coulomb wavefunction should have the same logarithmic derivatives for the experimental Q-value. The usual shell model wavefunctions are not able to satisfy this condition along any isotopic chain. In order to correct this deficiency we use an effective procedure. We diagonalize the mean field using a single particle basis with two harmonic oscillator parameters, as proposed in a previous paper. In order to obtain correct tails of the wavefunctions, the second harmonic oscillator parameter should increase with the mass number. This is consistent with the suppression of α-clustering by increasing the proton–neutron asymmetry. A parabolic fit of this parameter versus the mass number enables us to ensure a consistency in experimental Q-values within a mean deviation of 300 keV.