Variational approach to anharmonic collective motion

We derive large-amplitude collective equations of motion from the variational principle for the time-dependent Schrodinger equation. These equations reduce to the well-known diabatic formulas for vibrational frequencies in the small-amplitude limit. The finite-amplitude expression allows departures from the harmonic behavior of giant resonances to be simply estimated. The relative shift of the second phonon falls with nuclear mass A as A(-4/3) in the three modes we consider: monopole, dipole, and quadrupole. Numerically, the effect is very small in heavy nuclei, as was found with other approaches.