Isovector rotational model

Abstract

The explicit form of the canonical angle operator is found and the isovector rotor is quantized in canonical relative variables ensuring the exact separation of the spurious mode. The main characteristics of the resulting joint mode, together with the low- and high-frequency parts of the split mode are obtained. It is found that the isovector rotational mode exhausts all the non-spurious M1 strength at low and high energy, providing a strong support for the interpretation of all the orbital 1 + excitations as a scissors mode. Self-consistent residual interactions do not change the non-spurious restoring force of the deformed potential. Simple numerical estimates, derived from a schematic deformed oscillator, are in a good qualitative agreement with microscopic RPA results. Relationships with the results of the two-rotor model and the microscopic realization of the scissors state are established.