Exchange effects in β decays of many-electron atoms

Abstract

The effect on the P spectrum of exchange between bound and continuum electrons is discussed for decay of a many-electron atom R.esults of calculations of the exchange distortion of the P spectrum are presented using both a screened hydrogenic and a Hartree-Fock approximation for the electron wave functions. The results of the two approaches agree well and show that the inclusion of exchange leads to an enhancement of the P spectrum, particularly at low electron energy. This corrects an error in a previous calculation that found that exchange decreased the P intensity. For the low-energy P emitters Ru and 'Pu, the present calculation indicates that the enhancement due to exchange is of the order of several percent over much of the spectrum, becoming larger at very low electron energy. Exchange with 1s electrons dominates in the high-energy part of the spectrum, but exchange with ns (n~2) electrons becomes significant in the low-energy region. The inclusion of exchange leads to an increase in the phase-space integral by 6.4% for ' Ru and 7.5% for 'Pu. Results are presented for exchange effects in other P spectra, including those of ' C and S, in which experimentally measured distortions have been interpreted as evidence for a heavy antineutrino of mass 17 keV. The distortions due to exchange are found to be significantly smaller than the measured distortions.

Calculation of beta spectral shapes

“…A formalism for the exchange effect has already been set out in detail in (Harston and Pyper, 1992) for allowed transitions. Indeed in this case, only the ns orbitals are reachable by the beta electron, which greatly simplifies the calculations.…”

Effets atomiques sur les émissions bêta à basse énergie : calcul et mesure

“…Comme exposé en détail dans [7], l'effet d'échange peut s'exprimer comme un facteur de correction modifiant la probabilité d'émission P à une énergie donnée E de l'électron bêta : Dans le cas des transitions permises, seuls les élec-trons bêta créés dans un état lié « s » de l'atome fils contribuent à η T ex . En effet, une transition bêta est classée selon les propriétés des états nucléaires initiaux et finaux à travers les variations de moment angulaire total ΔJ et de parité Δπ.…”

“…Harston [7] souligne que l'effet d'écrantage doit dé-former les fonctions d'ondes et peut donc contribuer au recouvrement de façon significative. Il prend cet effet en compte en utilisant des charges nucléaires effectives lors du calcul des fonctions d'ondes radiales.…”

Evaluation of the beta spectral shapes

“…Harston and Pyper [19] pointed out that the screening must distort the wave functions and contribute significantly to their overlap. They took this effect into account using effective nuclear charges for the calculations of the wave functions involved.…”

“…This does not concern the wave functions evaluated at the nuclear radius, for which the full nuclear charge has to be used. Following [19], the effective nuclear charges were determined from the mean radii of the orbitals, which were taken from [20] and [21] in the non-relativistic case (Hartree-Fock calculations), and from [22] in the relativistic case (Dirac-Fock calculations).…”