This paper applies the phase-integral method to the stationary theory of α-decay. The rigorous form of the connection formulas, and their one-directional nature that was not widely known in the physical literature, are applied. The condition for obtaining s-wave metastable states affects the stationary state at large distance from the nucleus, which is dominated by the cosine of the phase integral minus π/4. Accurate predictions for the lowest s-wave metastable state and mean life of the radioactive nucleus are obtained in the case of uranium. The final part of the paper describes the phase-integral algorithm for evaluating stationary states by means of a suitable choice of freely specifiable base function.Within this framework, original approximate formulas for the phase integrand with arbitrary values of the angular momentum quantum number are obtained.
A phase-integral perspective on alpha-decay / Esposito, G. - In: THE EUROPEAN PHYSICAL JOURNAL PLUS. - ISSN 2190-5444. - 135:9(2020), pp. 692-1-692-17. [10.1140/epjp/s13360-020-00719-8]
A phase-integral perspective on alpha-decay
ESPOSITO GPrimo
2020
Abstract
This paper applies the phase-integral method to the stationary theory of α-decay. The rigorous form of the connection formulas, and their one-directional nature that was not widely known in the physical literature, are applied. The condition for obtaining s-wave metastable states affects the stationary state at large distance from the nucleus, which is dominated by the cosine of the phase integral minus π/4. Accurate predictions for the lowest s-wave metastable state and mean life of the radioactive nucleus are obtained in the case of uranium. The final part of the paper describes the phase-integral algorithm for evaluating stationary states by means of a suitable choice of freely specifiable base function.Within this framework, original approximate formulas for the phase integrand with arbitrary values of the angular momentum quantum number are obtained.File | Dimensione | Formato | |
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