Summed strength and signature properties of magnetic multipole excitations in a single j shell

Taking the titanium isotopes as an example, the magnetic multipole excitation strengths are calculated in the single j shell model (f7/2). Expressions are derived for the summed strength in this model for the modes with nonvanishing strengthM1, M3, M5, and M7. An approximate expression for this sum is obtained in which only the components of the wave function in which neutrons and protons couple to angular momentum L=0 and 2 (v=2) in the ground state are included. The signature selection rules for the nucleus Ti48 are considered. It is noted that the M1 strength is mostly concentrated in the lowest state (at least 80%). The higher multipole modes are more strongly fragmented. For these modes, there is significant strength in the isobaric analog states, especially for M5. A closed expression for strength to the isobaric analog strength in Ti48 is obtained.