dorsal/arxiv
View SchemaMean Field Methods for Atomic and Nuclear Reactions: The Link between Time--Dependent and Time--Independent Approaches
| Authors | J. Uhlig, J. C. Lemm, A. Weiguny |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9806083 |
| URL | https://arxiv.org/abs/nucl-th/9806083 |
| DOI | 10.1007/s100500050131 |
| Journal | Eur.Phys.J. A2 (1998) 343-354 |
Abstract
Three variants of mean field methods for atomic and nuclear reactions are compared with respect to both conception and applicability: The time--dependent Hartree--Fock method solves the equation of motion for a Hermitian density operator as initial value problem, with the colliding fragments in a continuum state of relative motion. With no specification of the final state, the method is restricted to inclusive reactions. The time--dependent mean field method, as developed by Kerman, Levit and Negele as well as by Reinhardt, calculates the density for specific transitions and thus applies to exclusive reactions. It uses the Hubbard--Stratonovich transformation to express the full time--development operator with two--body interactions as functional integral over one--body densities. In stationary phase approximation and with Slater determinants as initial and final states, it defines non--Hermitian, time--dependent mean field equations to be solved self--consistently as boundary value problem in time. The time--independent mean field method of Giraud and Nagarajan is based on a Schwinger--type variational principle for the resolvent. It leads to a set of inhomogeneous, non--Hermitian equations of Hartree--Fock type to be solved for given total energy. All information about initial and final channels is contained in the inhomogeneities, hence the method is designed for exclusive reactions. A direct link is established between the time--dependent and time--independent versions. Their relation is non--trivial due to the non--linear nature of mean field methods.
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"abstract": "Three variants of mean field methods for atomic and nuclear reactions are\ncompared with respect to both conception and applicability: The time--dependent\nHartree--Fock method solves the equation of motion for a Hermitian density\noperator as initial value problem, with the colliding fragments in a continuum\nstate of relative motion. With no specification of the final state, the method\nis restricted to inclusive reactions. The time--dependent mean field method, as\ndeveloped by Kerman, Levit and Negele as well as by Reinhardt, calculates the\ndensity for specific transitions and thus applies to exclusive reactions. It\nuses the Hubbard--Stratonovich transformation to express the full\ntime--development operator with two--body interactions as functional integral\nover one--body densities. In stationary phase approximation and with Slater\ndeterminants as initial and final states, it defines non--Hermitian,\ntime--dependent mean field equations to be solved self--consistently as\nboundary value problem in time. The time--independent mean field method of\nGiraud and Nagarajan is based on a Schwinger--type variational principle for\nthe resolvent. It leads to a set of inhomogeneous, non--Hermitian equations of\nHartree--Fock type to be solved for given total energy. All information about\ninitial and final channels is contained in the inhomogeneities, hence the\nmethod is designed for exclusive reactions. A direct link is established\nbetween the time--dependent and time--independent versions. Their relation is\nnon--trivial due to the non--linear nature of mean field methods.",
"arxiv_id": "nucl-th/9806083",
"authors": [
"J. Uhlig",
"J. C. Lemm",
"A. Weiguny"
],
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"nucl-th"
],
"doi": "10.1007/s100500050131",
"journal_ref": "Eur.Phys.J. A2 (1998) 343-354",
"title": "Mean Field Methods for Atomic and Nuclear Reactions: The Link between Time--Dependent and Time--Independent Approaches",
"url": "https://arxiv.org/abs/nucl-th/9806083"
},
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