Nuclear beta decay induced by intense electromagnetic fields: Forbidden transition examples

Abstract

A formalism developed earlier for the effect on nuclear beta decay of an intense planewave electromagnetic field is applied to three examples of forbidden beta transitions. The examples represent cases where the nuclear contains one, two, and three nucleons; where the nuclear fragment is defined to be that smallest sub-unit of the nucleus containing the nucleon which undergoes beta decay plus any other nucleons directly angular-momentum coupled to it in initial or final states. The single-nucleon-fragment example is $^{113}\mathrm{Cd}$, which has a fourth-forbidden transition. The two-nucleon-fragment example is $^{90}\mathrm{Sr}$, which is first-forbidden. The three-nucleon-fragment example is $^{87}\mathrm{Rb}$, which is third-forbidden. An algebraic closed-form transition probability is found in each case. At low external-field intensity, the transition probability is proportional to ${z}^{L}$, where $z$ is the field intensity parameter and $L$ is the degree of forbiddenness. At intermediate intensities, the transition probability behaves as ${z}^{L\ensuremath{-}(\frac{1}{2})}$. At higher intensities, the transition probability contains the ${z}^{L\ensuremath{-}(\frac{1}{2})}$. factor, a declining exponential factor, and an alternating polynomial in $z$. This high-intensity transition probability possesses a maximum value, which is found for each of the examples. A general rule, $z={q}^{2}(2L\ensuremath{-}1)$, where $q$ is the number of particles in the fragment, is found for giving an upper limit on the intensity at which the maximum transition probability occurs. Field-induced beta decay half-lives for all the examples are dramatically reduced from natural half-lives when evaluated at the optimum field intensity. Relative half-life reduction is greater the higher the degree of forbiddenness.RADIOACTIVITY $^{87}\mathrm{Rb}$, $^{90}\mathrm{Sr}$, $^{113}\mathrm{Cd}$ intense-field-induced $\ensuremath{\beta}$ decay minimum half-lives, half-life reduction forbiddenness dependence.