Mass parameters in the adiabatic time-dependent Hartree-Fock approximation. I. Theoretical aspects; the case of a single collective variable

A self-consistent method for evaluation of mass parameters is presented in the framework of the adiabatic limit of the time-dependent Hartree-Fock approximation, reduced to a single collective variable. The corresponding collective path is assumed to be given either by solving a constrained Hartree-Fock problem with a given time-even constraining operator Q, or by scaling a static Hartree-Fock equilibrium solution. In the former case, once the path is given, a method for solving the equation of motion (of the Hamilton type) is provided, which reduces to a double-constrained Hartree-Fock problem with the time-even constraint Q and with a time-odd constraining operator P. In the case of the scaling path, an analytical solution of the Hamilton equation is discussed and the adiabatic mass for the particular case of an isoscalar quadrupole Q₂₀ mode is given. The operator P, which is uniquely determined from the knowledge of Q, has the physical meaning of a momentum operator; it satisfies, together with Q, a weak quantal conjugation relation. Finally, the connection between the two paths is discussed in terms of generalized random-phase approximation sum rules. NUCLEAR STRUCTURE Evaluation of mass parameters within time-dependent Hartree-Fock approximation in adiabatic limit for single collective variable motion. Discussion and comparison of constrained Hartree-Fock and scaling paths. Expression as a doubly constrained Hartree-Fock problem with momentum operator uniquely defined from coordinate operator. Connection with sum rule and Inglis cranking approaches.