On the Matrix Element in Fermi's Theory of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>β</mml:mi></mml:math>-Decay

Abstract

It is investigated how the Fermi theory of $\ensuremath{\beta}$-decay has to be formulated for a complex nucleus containing many particles. By symmetrizing the problem in all particles (neutrons and protons) a general prescription is obtained which would allow one to calculate the transition probabilities when the wave functions for the nucleus in its initial and final state are known. The discussion of the heavy particle matrix element which is involved shows that a considerable decrease of the transition probability with the complexity of the nucleus is to be expected. A new reduction of the empirical data shows that the influence of the Coulomb field on the $\ensuremath{\beta}$-disintegration probability is larger than heretofore assumed. The difference obtained in reduced lifetimes of light and heavy nuclei (of the order of a factor 50 to 100) is of the same order of magnitude as estimated from the theoretical considerations.