Bremsstrahlung during $\alpha$-decay: quantum multipolar model

TL;DR

This paper introduces an improved quantum multipolar model for bremsstrahlung during alpha decay, providing absolute scale calculations of photon emission probabilities and comparing them with experimental data for various nuclei.

Contribution

The paper presents a new definition of angular photon emission probability in alpha decay, enabling absolute scale predictions without experimental normalization, and extends analysis to proton emission and fission.

Findings

Model accurately reproduces bremsstrahlung spectra for multiple nuclei.

New angular probability definition improves prediction accuracy.

First quantum estimates of bremsstrahlung in proton emission and fission.

Abstract

In this paper the improved multipolar model of bremsstrahlung accompanied the $\alpha$-decay is presented. The angular formalism of calculations of the matrix elements, being enough complicated component of the model, is stated in details. A new definition of the angular (differential) probability of the photon emission in the $\alpha$-decay is proposed where direction of motion of the $\alpha$-particle outside (with its tunneling inside barrier) is defined on the basis of angular distribution of its spacial wave function. In such approach, the model gives values of the angular probability of the photons emission in absolute scale, without its normalization on experimental data. Effectiveness of the proposed definition and accuracy of the spectra calculations of the bremsstrahlung spectra are analyzed in their comparison with experimental data for the $^{210}{\rm Po}$, $^{214}{\rm Po}$, $^{226}{\rm Ra}$ and $^{244}{\rm Cm}$ nuclei, and for some other nuclei predictions are performed (in absolute scale). With a purpose to find characteristics taking influence on the bremsstrahlung probability strongly, a dependence of the bremsstrahlung probability on effective charge of the decaying system is analyzed. As a natural result, as supposed type of decaying system the emission of proton from nucleus is studied, for which the effective charge is essentially larger in a comparison with $\alpha$-decay. For some proton emitters estimations of the bremsstrahlung probability are obtained (at first time, in fully quantum approach). Also the bremsstrahlung in fission of the $^{252}{\rm Cf}$ nucleus is analyzed.