Shell-model calculation for masses 27, 28, and 29: general methods and specific applications to 27Al, 28Si, and 29Si

A shell-model calculation for A=27,28, and 29 nuclei has been carried out in a truncated 0d_5/2-1s_1/2-0d_3/2 basis space with a modified-surface-δ-interaction Hamiltonian. A comparison of the calculated results for level energies, single-nucleon spectroscopic factors and E2 and M1 transition strengths in ²⁷Al, ²⁸Si, and ²⁹Si with the corresponding experimental values indicates that a unified and quantitive explanation of nuclear structure around A=28 can be obtained via shell-model techniques.