Radiative orbital electron capture by the atomic nucleus

Abstract

The rate for the photon emission accompanying orbital 1S electron capture by the atomic nucleus is recalculated. While a photon can be emitted by the electron or by the nucleus, the use of the length gauge significantly suppresses the nuclear contribution. Our calculations resolve the long standing discrepancy of theoretical predictions with experimental data for $\Delta J=2$ forbidden transitions. We illustrate the results by comparison with the data established experimentally for the first forbidden unique decays of $^{41}$Ca and $^{204}$Tl.Comment: 18 pages, 2 figures, submitted to Phys. Rev.

Evidence for the virtualβ−γtransition inNi59decay

“…(2) was derived under the approximation Zα 1 and essentially represents the photons emitted by the electron in the IB process. The nuclear contribution is strongly suppressed in this model but only when there are no close-lying excited states in the daughter or in the parent nucleus [28]. We note that for Λ = 1 we obtain the shape factor for the K-capture in 1u transition, which reproduced so well the experimental data [28,29].…”

“…The problem was caused by neglecting the radiation from the nucleus which is not justified in the Coulomb gauge. The length-gauge model, while reproducing exactly the results of Glauber and Martin for allowed decays, was found to describe very well both the shape and the intensity of experimental spectra of 41 Ca and 204 Tl [28] and later also the spectrum of 1u K-capture in 81 Kr [29]. It is because the nuclear radiation is strongly suppressed in this gauge and can be neglected.…”

“…He was able to reproduce the spectrum of 41 Ca at the cost of adding a phenomenological parameter [26], but his model failed in case of 204 Tl [25]. Finally, this conundrum was resolved by Pachucki et al [28] with a crucial insight that the description of the electromagnetic radiation in this case is much more advantageous in the length gauge in contrast to the Coulomb gauge used in all previous calculations. It allowed to expose and to circumvent divergent terms which were the source of wrong approximations in the model of Zon and Rapoport for the ∆J = 2 transitions.…”

“…[28], here we extend the length-gauge model of REC to the 2nu transitions (∆J = 2, no parity change). Conventionally, the emission probability of a photon with energy k per ordinary nonradiative electron capture and per unit energy is expressed in the form:…”

“…[28]. In this case the spectrum depends on the parameter Λ which is a combination of nuclear matrix elements relevant for the direct transition between the initial and the final state:…”