Theoretical Half-Lives of Forbiddenβ-Transitions

摘要: Fermi's theory of $\ensuremath{\beta}$-decay is extended to the "nth forbidden" approximation. Precise formulas for distribution in energy emitted $\ensuremath{\beta}$-rays are derived arbitrarily charged nuclei, according five possible invariant forms interaction, so-called scalar, polar vector, tensor, axial and pseudo-scalar interactions, respectively. The nuclear matrix elements transitions, made up components certain irreducible tensors, constructed. selection rules appropriate these given Table II. magnitudes estimated by a simple averaging process depending only on directional properties tensors from which they constructed order magnitude tensor components. Theoretical half-lives "forbidden" $\ensuremath{\beta}$-decays RaE, ${\mathrm{P}}^{32}$, ${\mathrm{K}}^{40}$, ${\mathrm{Rb}}^{87}$ calculated numerical integration dependent electron emission probabilities. Upon comparing with experimental determinations half-lives, most satisfactory agreement seems be obtained form interaction. evidence favor Gamow-Teller somewhat inconclusive case ${\mathrm{K}}^{40}$ decay because uncertainty determination maximum energy.