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Frontiers in nuclear and particle physics

Numerical Calculations of TDHF

P. D. Stevenson

Published Jun 27, 2019• 3 citations
Publisher

Abstract

We discuss some aspects of implementing the time-dependent Hartree-Fock method in the case of nuclear physics. Topics discussed include implementation of the time-stepping algorithm, considerations involving the effective interaction, and the use (or not) of particular optional terms in the energy density functional, and boundary conditions. Examples of application of the technique to giant resonances and reactions are given, concentrating on issues to do with numerical and conceptual interpretation.

DOI
10.2174/9781681087641119020005

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We discuss some aspects of implementing the time-dependent Hartree-Fock method in the case of nuclear physics. Topics discussed include implementation of the time-stepping algorithm, considerations involving the effective interaction, and the use (or not) of particular optional terms in the energy density functional, and boundary conditions. Examples of application of the technique to giant resonances and reactions are given, concentrating on issues to do with numerical and conceptual interpretation.
A tractable method is presented for the study of the adiabaticity of a given time-dependent Hartree-Fock solution. In terms of the Baranger-V\'en\'eroni approach, this amounts to extracting the two operators ${\ensuremath{\rho}}_{0}$ and $\ensuremath{\chi}$, for which rather simple expressions are derived. These explicit formulas are exploited to illustrate some implications of the adiabatic approximation itself and several related approximations. In particular, the incompatibility of two current hypotheses for the $\ensuremath{\chi}$ operator (locality and absence of particle-particle, hole-hole matrix elements) is pointed out. Finally, the whole discussion is exemplified by the simple case of uniform translational motion.NUCLEAR STRUCTURE Discussion of adiabatic limit of TDHF approximation, derivation of practical method of study adiabaticity of collective motion from TDHF solutions.
A particle-number projection technique is used to calculate transfer probabilities in the 16O+208Pb reaction below the fusion barrier. The time evolution of the many-body wave function is obtained with the time-dependent Hartree-Fock (TDHF) mean-field theory. The agreement with experimental data for the sum of the proton-transfer channels is good, considering that TDHF has no parameter adjusted on the reaction mechanism. Some perspectives for extensions beyond TDHF to include cluster transfers are discussed.
The long‐time classical behavior of many‐body systems is examined using time‐dependent Hartree–Fock (TDHF) theory. Detailed computer simulations for the formation of a nuclear molecule in low‐energy 12C+12C collisions are discussed at length. The representation of effective classical coordinates, and their correspondence to physical observable for systems which undergo large‐amplitude quasi‐periodic and chaotic motion is briefly summarized. The relationship between these calculations and new methods, which allow the calculation of quasiperiodic solutions to the TDHF equations under more general circumstances, is summarized.