Preformation probability inside α emitters having different ground state spin-parity than their daughters

Abstract

ABSTRACT:The ground-state spin and parity of a formed daughter in the radioactive -emitter is expected to influence the preformation probability of the  and daughter clusters inside it. We investigate the  and daughter preformation probability inside odd-A and doubly-odd radioactive nuclei when the daughter and parent are of different spin and/or parity. We consider only the ground-state to ground-state unfavored decays. This is to extract precise information about the effect of the difference in the ground states spin-parity of the involved nuclei far away any influences from the excitation energy if the decays are coming from isomeric states. The calculations are done for 161 -emitters, with and , in the framework of the extended cluster model, with WKB penetrability and assault frequency. We used a Hamiltonian energy density scheme based on Skyrme-SLy4 interaction to compute the interaction potential. The  plus cluster preformation probability is extracted from the calculated decay width and the experimental half-life time. We discussed in detailed steps the effect of angular momentum of the emitted -particle on the various physical quantities involved in the unfavored decay process and how it is finally increases the half-life time. We found that if the ground states spin and/or parity of parent and daughter nuclei are different, then the preformation probability of the -cluster inside parent is less than it would be if they have similar spin-parity. We modified the formula that gives the preformation probability in terms of the numbers of protons and neutrons outside the shell closures of parent, to account for this hindrance in the preformation probability for the unfavored decays between ground states.2

Divergence in the Relativistic Mean Field Formalism: A Case Study of the Ground State Properties of the Decay Chain of 214,216,218U Isotopes

“…Here, our calculated P 0 values are in tune with the shell model, with notable minima around the magic numbers. This conforms with the recent findings of [24,25], in which it was demonstrated that P 0 can be influenced by the isospin asymmetry of the parents, the deformation of the daughter nuclei, and pairing and shell effects and that the minima of P 0 can be ascribed to the presence of proton, neutron shells and sub-shell closures. A careful evaluation of Figure 6, which portrays the relationship between the preformation probability P 0 and the penetrability P, where both parameters are shown as a function of the mass number, reveals that lower P 0 values correspond to a higher P and vice versa, such that their products P 0 P are near to the same order for all the decay chains under study.…”

“…Particularly, some neutron-deficient nuclei around the region Z = 82 in the heavy-ion reaction are often excluded in the in-beam γ-ray experiments [17]. On the other hand, all theoretical probes on this shell closure emanate from either the nuclear fission [18][19][20] or Gamow theory of α-decay [21][22][23][24][25]. The former relegates the idea of preformation; i.e., it is assumed that clusters are formed during the separation/deformation process of the parent nucleus while penetrating the confining interaction barrier.…”

Systematic study of favoredα-decay half-lives of closed shell odd-Aand doubly-odd nuclei related to ground and isomeric states

“…Therefore, α preformation probabilities are usually extracted from rates of experimental α decay half-lives to theoretical results calculated without considering the preformation factors [32][33][34]. Recently a semi-empirical formula of α preformation probabilities taking into account the shell effect, the pairing effect, and the angular momentum effect has been given [35]. Seif et al have proposed that the α preformation probability is proportional to N p N n for even-even nuclei around proton Z = 82, neutron N = 82 and 126 shell closures [36].…”

Ternary fission of 260No in collinear configuration

“…The deformations affect strongly the barrier penetration probability [38,39] and indicate the optimum orientations at which the minimum fragmentation potential takes place. As an example, shown in Fig.…”