Selection Rules in the Odd-Even Shift of Certain Nuclear Rotational Bands

A displacement of energy levels has been observed in the $K=0\mathrm{}$ band of odd-odd deformed nuclei. It is shown that this shift is due to a particular type of scattering in which the final state is obtained from the initial state by a rotation of 180°. This circumstance allows one to state certain selection rules on the parts of the $n-p$ residual interaction responsible for the shift. The Wigner component of the force cannot contribute to the shift. In certain cases the contribution of all central forces will be strongly damped allowing observation of the tensor-force scattering contribution. Numerical results are presented.