PARABOLIC RULE FOR THE ENERGY-DEPENDENCE ON X=I(I+1) FOR PROTON-NEUTRON MULTIPLETS IN ODD-ODD NUCLEI

An analytic expression for the energies of the states of the proton-neutron multiplet (jpjn)I = |jp-jn&,...,jp + jn is derived as a quadratic function x = I(I + 1) owing to the exchange of the quadrupole and the spin-vibrational phonon. A discussion of this parabola, its consequences and illustrative applications are presented. The parabolic rule is suggested to serve as a guideline on the classification and investigation of states in odd-odd nuclei. © 1979.