The generator coordinate method and quantised collective motion in nuclear systems

Abstract

The generator coordinate method is reviewed from the point of view that it provides a versatile tool for formal development, in particular for the derivation of a consistent microscopic theory of large-amplitude collective motion. The Gaussian overlap approximation is employed to derive the collective mapping of arbitrary microscopic operators which is the starting point for all further derivation, e.g. of collective dynamics and of the equations determining the optimal collective path. The validity of the Gaussian overlap approximation and possible extensions are discussed. it is furthermore pointed out that one needs for nuclear collective motion dynamic paths where a collective mode is expanded by two conjugate parameters. The complications with dynamic paths can be overcome with the help of an adiabatic expansion in powers of the collective momentum. The final outcome is the quantised adiabatic time-dependent Hartree-Fock theory which is then exemplified in various examples.