Universal expression for the lowest excitation energy of natural parity even multipole states

We present a new expression for the energy of the lowest collective states in even–even nuclei throughout the entire periodic table. Our empirical formula holds universally for all of the natural parity even multipole states and describes the overall trends. This formula depends only on the mass number and the valence nucleon numbers with six parameters. The parameters are determined unambiguously from the data for each multipole state. We discuss the validity of our empirical formula by comparing our results with those of other studies and also by estimating the average and the dispersion of the logarithmic errors of the calculated excitation energies with respect to the measured ones.