Collective Oscillations of Atoms in the Hartree-Fock Approximation

Felix M. H. Villars

Sol Wieder, Sidney Borowitz

Received 6 December 1966DOI:https://doi.org/10.1103/PhysRevLett.16.724©1966 American Physical Society

Nobuyuki Fukuda

B.I. Barts, Yu. L. Bolotin, M.I. Kazarinov

Nuclear-matter density oscillations are considered without the assumption that their amplitude is small. The so-called scaling version of the adiabatic time-dependent Hartree-Fock theory is used to find the collective Hamiltonian describing these oscillations. The question of under which conditions the oscillations in question can be studied in the harmonic approximation is investigated in detail.

Seth T. Rittenhouse, M. J. Cavagnero, Javier von Stecher +1 more

We propose an unconventional description for the ground state and collective oscillations of the two-component normal Fermi gas with two-body zero-range interactions. The many-body problem can be accurately reduced to a linear, one-dimensional Schroedinger equation in a single collective coordinate, the hyperradius R of the N-atom system which is the root mean square radius. The calculated properties of the Fermi gas ground state are shown to agree accurately with results from the Hartree-Fock (HF) approximation over a wide range of interspecies scattering lengths. The breathing mode excitation frequency deviates qualitatively from HF predictions, but we show that this reflects a failure of the HF approach for this observable.

Antonios Gonis