  The systematics of experimental energy differences between the levels of the
ground state band and the gamma-1 band in even-even nuclei are studied as a
function of the angular momentum L, demonstrating a decrease of the energy
differences with increasing L, in contrast to what is seen in vibrational,
gamma-unstable, and triaxial nuclei. After a short review of the relevant
predictions of several simple collective models, it is shown that this decrease
is caused in the framework of the proxy-SU(3) scheme by the same three-body
and/or four body operators which break the degeneracy between the ground state
band and the gamma-1 band, predicting in parallel the correct form of odd-even
staggering within the gamma-1 bands.
