Calculation of beta spectral shapes

Abstract

-Classical beta spectra calculations are briefly described, highlighting the usual assumptions and limitations. To go beyond these usual assumptions, the numerical resolution of the Dirac equation for the atomic and beta electrons is necessary. This allowed us to determine the parameters λ i involved in the theoretical shape factors exactly. A systematic comparison between theoretical and experimental shape factors led us to disqualify the usual λ i = 1 assumption for all forbidden transitions. The usual ξ-approximation was proved to be incorrect for numerous first forbidden non-unique transitions, and for all higherorder non-unique transitions. A more accurate screening correction was defined and the atomic exchange effect was taken into account, an effect which is always neglected in usual calculations. The beta spectra of 63 Ni and 241 Pu, recently measured down to very low energies, are well reproduced in our calculations. The exchange effect was demonstrated to have a great influence on the spectral shape within this energy range.

A Model for Ni-63 Source for Betavoltaic Application

“…Each radioisotope material have a continuous energy probability distribution known as beta energy spectrum. The beta spectra emitted by Ni-63 radioisotope recently measured down to very low energies, are well reproduced by the calculations of X. Mougeot et al [16,22]. It is characterised by emission of electron (β-particle) having average energy 17.4 keV and a maximum energy of 66.9 keV diffusing in random directions.…”

“…Most of the available simulators were developed for monoenergetic electron beam, whereas in a real beta source the spectrum of emitted particle energy is rather complex. In our simulation we adopted the beta spectra data obtained by [16], which reproduced well the measured beta spectra of Ni-63. The simulated source consisted of a thin Ni-63 active layer, with a varying thickness, deposited onto Ni metallic foil as a substrate and a protective Ni layer was optionally added.…”

Can we use heavy nuclei to detect relic neutrinos?

“…Finally, to get a rough idea of the feasibility of the relic neutrino capture experiment based on 171 Tm (Q = 96.5 keV, τ = 2.77 years) or 151 Sm (Q = 76.6 keV, τ = 130 years), we estimate the corresponding cross sections using the β-decay spectra computed in BetaShape [24,25]. For 171 Tm and 151 Sm, this code uses the so-called ξ-approximation, whose validity has to be established on the case to case basis.…”

Calculations of dose point kernels of 64Cu in different media with PENELOPE Monte Carlo code

“…For 64 Cu, the end‐point energies of the beta plus and β − decay are 653.0 and 579.4 keV, respectively. The shape of the beta energy spectrum has been thoroughly studied over the years for beta‐emitting radionuclides and it can be numerically modeled, taking into account of the Coulomb interactions between the positively charged nucleus and the outgoing charged particles ( β − or β +) and whether the transition is forbidden or allowed …”

“…The shape of the beta energy spectrum has been thoroughly studied over the years for betaemitting radionuclides and it can be numerically modeled, taking into account of the Coulomb interactions between the positively charged nucleus and the outgoing charged particles (bÀ or b+) and whether the transition is forbidden or allowed. 22 The number of beta particles emitted per unit time, N T ð Þ, in the normalized energy range between T and T + dT can be expressed as:…”