Alpha Decay in the Complex Energy Shell Model

Abstract

Alpha emission from a nucleus is a fundamental decay process in which the alpha particle formed inside the nucleus tunnels out through the potential barrier. We describe alpha decay of ${}^{212}$Po and ${}^{104}$Te by means of the configuration interaction approach. To compute the preformation factor and penetrability, we use the complex-energy shell model with a separable T=1 interaction. The single-particle space is expanded in a Woods-Saxon basis that consists of bound and unbound resonant states. Special attention is paid to the treatment of the norm kernel appearing in the definition of the formation amplitude that guarantees the normalization of the channel function. Without explicitly considering the alpha-cluster component in the wave function of the parent nucleus, we reproduce the experimental alpha-decay width of ${}^{212}$Po and predict an upper limit of T_{1/2}=5.5x10^{-7} sec for the half-life of ${}^{104}$Te. The complex-energy shell model in a large valence configuration space is capable of providing a microscopic description of the alpha decay of heavy nuclei having two valence protons and two valence neutrons outside the doubly magic core. The inclusion of proton-neutron interaction between the valence nucleons is likely to shorten the predicted half-live of ${}^{104}$Te.

14 two-column pages, 13 figures, 9 tables

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• The R-matrix theory
• Shell Model in the Complex Energy Plane
• Gamow Shell Model Description of Weakly Bound Nuclei and Unbound Nuclear States
• Orbital dependent nucleonic pairing in the lightest known isotopes of tin
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• Super-allowed alpha-decay above doubly-magic 100Sn and properties of 104Te = 100Sn otimes alpha
• Shell model in the complex energy plane and two-particle resonances
• Half-lives of $\alpha$-emitters approaching the N=Z line
• Abrupt changes in alpha decay systematics as a manifestation of collective nuclear modes

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