Shell-model calculations for masses 27, 28 and 29: electromagnetic transition rates and multipole moments

Abstract

Electromagnetic transition probabilities, multipole moments and log ƒt values have been calculated from many-particle shell-model wave functions in a truncated 1 d 5 2 2 s 1 2 1 d 3 2 config space, with a maximum of four holes in the 1 d 5 2 subshell. The electric quadrupole transition strengths and moments are reproduced very well in a least-squares fit to 74 experimental data with one parameter, for the isoscalar effective charge, yielding the values e p = 1.6 e and e n = 0.6 e. The results for magnetic dipole transition strengths and moments follow from adjusting two effective reduced single-particle matrix elements in separate least-squares fits to 17 experimental data in A = 27 nuclei and 21 data in A = 29 nuclei. The average absolute deviations between theory and experiment for E2 and M1 transition strengths are 3.0 and 0.05 W.u., while the average measured strengths are 7.7 and 0.08 W.u., respectively. Transitions from excited states above E x = 4.8 MeV in 27A1 and from some low-lying states in 27Al and 28Si are poorly reproduced by the present model. Calculated strengths of transitions from analogue states are given. Previous conclusions about the single-particle character of M1 transitions and the collective behaviour of E2 transitions are confirmed. The experimental data of seven A = 27–29 nuclei are well reproduced in one general treatment with an appreciably lower number of free parameters than are required to obtain comparable results in collective model calculations.