Nuclear Matrix Elements for Forbidden Beta Decay of Spheroidal-Shaped Nuclei

Abstract

Theoretical expressions for both the nonrelativistic and relativistic nuclear matrix elements for /3 transitions of arbitrary forbiddenness are derived by using the Nilsson model. The /3-decay operators are expressed in terms of irreducible spherical tensors. One-and two-particle intrinsic wave functions are used for odd-and even-mass nuclei, respectively. For even-mass nuclei, the results are found to be strongly dependent on the coupling of the two particles. The results are expected to be applicable to decays involving both intrinsic ground states and excited intrinsic states. The theoretical expressions are used to calculate matrixelement parameters for/? decays in Tm 170 and Re 186 . The theoretical values are compared with experimentally determined values of the Tm 170 and Re 186 parameters.

Nonschematic description of nuclear ?-decay processes

“…[13] and [14]. The one corresponding to the relativistic operator F = ~ was obtained from the CVC theory [18].…”

“…The single-particle matrix elements (pp' I F Inn') correspond to the onebody operators appearing in the fl-decay equations [13,14].…”

Second-class currents in 0−→0+ and unique nuclear β transitions

“…The method for searching the values of the free parameters was based on the minimization of the reduced chi-square function Z 2 defined as 1 mK) (28) …”

Forme des spectres β et éléments de matrice nucléaire s des transitions 1- → 0+ des rhénium s 186 et 188

“…En trait plein la solution obtenue. En traits interrompus les solutions théoriques de Bogdan [15] (B) et de Nguyen Duc Tuong et al [16] (N). Lorsque ces dernières solutions dépendent fortement de la déformation elles sont données pour la valeur admise ô = 0,2 mais aussi pour ô = 0,1 et ô = 0,3.…”

“…Les figures 2, 3 et 4 permettent la comparaison des le modèle de Nilsson par Bogdan (fonction d'onde à une particule [15]) et par Nguyen Duc Tuong et al (fonction d'onde à deux particules [16]). Elles font apparaître pour ces solutions un certain accord avec l'expérience ; en particulier l'allure, croissante avec l'énergie, du facteur de forme est prévue.…”