Extension of continuum time-dependent Hartree-Fock method to proton states

This paper deals with the solution of the spherically symmetric time-dependent Hartree-Fock approximation applied to nuclear giant monopole resonances in the small amplitude regime. The problem is spatially unbounded as the resonance state is in the continuum. The practical requirement to perform th...

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Main Authors: Pardi, C, Stevenson, P, Xu, K
Format: Report
Published: APS Physics 2014
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author Pardi, C
Stevenson, P
Xu, K
author_facet Pardi, C
Stevenson, P
Xu, K
author_sort Pardi, C
collection OXFORD
description This paper deals with the solution of the spherically symmetric time-dependent Hartree-Fock approximation applied to nuclear giant monopole resonances in the small amplitude regime. The problem is spatially unbounded as the resonance state is in the continuum. The practical requirement to perform the calculation in a finite-sized spatial region yields an artificial boundary, which is not present physically. The question of how to ensure the boundary does not interfere with the internal solution, while keeping the overall calculation time low is studied. Here we propose an absorbing boundary condition scheme to handle the conflict. The derivation, via a Laplace transform method, and implementation is described. An inverse Laplace transform required by the absorbing boundaries is calculated using a method of non-linear least squares. The accuracy and efficiency of the scheme is tested and results presented to support the case that they are a effective way of handling the artificial boundary.
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spelling oxford-uuid:1304478e-9799-4a75-8ee4-1e5038c8173c2022-03-26T10:11:24ZExtension of continuum time-dependent Hartree-Fock method to proton statesReporthttp://purl.org/coar/resource_type/c_93fcuuid:1304478e-9799-4a75-8ee4-1e5038c8173cMathematical Institute - ePrintsAPS Physics2014Pardi, CStevenson, PXu, KThis paper deals with the solution of the spherically symmetric time-dependent Hartree-Fock approximation applied to nuclear giant monopole resonances in the small amplitude regime. The problem is spatially unbounded as the resonance state is in the continuum. The practical requirement to perform the calculation in a finite-sized spatial region yields an artificial boundary, which is not present physically. The question of how to ensure the boundary does not interfere with the internal solution, while keeping the overall calculation time low is studied. Here we propose an absorbing boundary condition scheme to handle the conflict. The derivation, via a Laplace transform method, and implementation is described. An inverse Laplace transform required by the absorbing boundaries is calculated using a method of non-linear least squares. The accuracy and efficiency of the scheme is tested and results presented to support the case that they are a effective way of handling the artificial boundary.
spellingShingle Pardi, C
Stevenson, P
Xu, K
Extension of continuum time-dependent Hartree-Fock method to proton states
title Extension of continuum time-dependent Hartree-Fock method to proton states
title_full Extension of continuum time-dependent Hartree-Fock method to proton states
title_fullStr Extension of continuum time-dependent Hartree-Fock method to proton states
title_full_unstemmed Extension of continuum time-dependent Hartree-Fock method to proton states
title_short Extension of continuum time-dependent Hartree-Fock method to proton states
title_sort extension of continuum time dependent hartree fock method to proton states
work_keys_str_mv AT pardic extensionofcontinuumtimedependenthartreefockmethodtoprotonstates
AT stevensonp extensionofcontinuumtimedependenthartreefockmethodtoprotonstates
AT xuk extensionofcontinuumtimedependenthartreefockmethodtoprotonstates