Adiabatic time-dependent Hartree-Fock theory of collective motion in finite systems

Journal Article · Fri Sep 01 04:00:00 EDT 1978 · Ann. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1016/0003-4916(78)90265-8· OSTI ID:6498702

Baranger, M; Veneroni, M

We show how to derive the parameters of a phenomenological collective model from a microscopic theory. The microscopic theory is Hartree-Fock, and we start from the time-dependent Hartree-Fock equation. To this we add the adiabatic approximation, which results in a collective kinetic energy quadratic in the velocities, with coefficients depending on the coordinates, as in the phenomenological models. The crucial step is the decomposition of the single-particle density matrix p in the form exp(i/sub chi/) rho/sub omicron/exp(-i/sub chi/), where rho/sub omicron/ represents a time-even Slater determinant and plays the role of coordinate. Then chi plays the role of momentum, and the adiabatic assumption is that chi is small. The energy is expanded in powers of chi, the zeroth-order being the collective potential energy. The analogy with classical mechanics is stressed and studied. The same adiabatic equations of motion are derived in three different ways (directly, from the Lagrangian, from the Hamiltonian), thus proving the consistency of the theory. The dynamical equation is not necessary for writing the energy or for the subsequent quantization which leads to a Schroedinger equation, but it must be used to check the validity of various approximation schemes, particularly to reduce the problem to a few degrees of freedom. The role of the adiabatic hypothesis, its definition, and range of validity, are analyzed in great detail. It assumes slow motion, but not small amplitude, and is therefore suitable for large-amplitude collective motion. The RPA is obtained as the limiting case where the amplitude is also small. The translational mass is correctly given, and the moment of inertia under rotation is that of Thouless and Valatin. For a quadrupole two-body force, the Baranger-Kumar formalism is recovered. The self-consistency brings additional terms to the Inglis cranking formula. Comparison is also made with generator coordinate methods.

• Research Organization: Laboratory for Nuclear Science and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
• OSTI ID: 6498702
• Journal Information: Ann. Phys. (N.Y.); (United States), Journal Name: Ann. Phys. (N.Y.); (United States) Vol. 114:1; ISSN APNYA
• Country of Publication: United States
• Language: English

Related Subjects

653001* -- Nuclear Theory-- Nuclear Structure
Moments
Spin
& Models
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
ADIABATIC APPROXIMATION
COLLECTIVE MODEL
HARTREE-FOCK METHOD
MATHEMATICAL MODELS
NUCLEAR MODELS
NUCLEON-NUCLEON POTENTIAL
POTENTIALS
RANDOM PHASE APPROXIMATION
SKYRME POTENTIAL
SLATER METHOD
TIME DEPENDENCE