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This paper deals with the solution of the spherically symmetrictime-dependent Hartree-Fock approximation applied to nuclear giant monopoleresonances in the small amplitude regime. The problem is spatially unbounded asthe resonance state is in the continuum. The practical requirement to performthe calculation in a finite-sized spatial region yields an artificial boundary,which is not present physically. The question of how to ensure the boundarydoes not interfere with the internal solution, while keeping the overallcalculation time low is studied. Here we propose an absorbing boundarycondition scheme to handle the conflict. The derivation, via a Laplacetransform method, and implementation is described. An inverse Laplace transformrequired by the absorbing boundaries is calculated using a method of non-linearleast squares. The accuracy and efficiency of the scheme is tested and resultspresented to support the case that they are a effective way of handling theartificial boundary.

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