https://doi.org/10.1140/epjp/s13360-020-00719-8
Regular Article
A phase-integral perspective on 
-decay
Istituto Nazionale di Fisica Nucleare, Sezione di Napoli, Complesso Universitario di Monte S. Angelo, Via Cintia Edificio 6, 80126, Napoli, Italy
a
giampiero.esposito@na.infn.it
Received:
21
June
2020
Accepted:
27
August
2020
Published online:
4
September
2020
This paper applies the phase-integral method to the stationary theory of -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 
. 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.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
