Abstract
We motivate and summarise some recent results in the application of formally exact boundary conditions in nuclear time-dependent Hartree-Fock calculations, mak- ing use of Laplace transformations to calculate the values of the wave functions at the boundaries. We have realised the method in the case of giant monopole resonances of spherically-symmetric nuclei, and present strength functions of 16 O and 40 Ca using a sim- plified version of the Skyrme force, showing that no artefacts from discretisation occur as contaminatnts
Highlights
Many nuclear phenomena fall under the general title of collective motion
In the case of time-dependent collective motion, a sufficient amount of wave function is emitted from the nucleus to result in the zeroing of wave functions at the boundaries to have a deleterious effect on observables [2]
The principal problem with zeroing the wave function at boundaries in time dependent problems is that outgoing waves are reflected, in the same way that a wave on a string is reflected by a fixed boundary
Summary
Many nuclear phenomena fall under the general title of collective motion. Examples of collective motion such as giant resonances, rotational states, fusion and deep inelastic collisions may all be simulated computationally by solutions of the time-dependent Schrödinger equation, rendered in its mean-field form of the time-dependent Hartree-Fock equation [1]. The static initialisations have a zero value for the wave functions at the edge of a computational box, typically around a factor 2-10 times the nuclear radius This difference in boundary conditions has little adverse effect on the static ground states of nuclei, thanks to the exponentially descreasing wave function beyond the range of the nuclear potential. Previous applications in nuclear physics include the application of masking functions [2] or the use of complex optical potentials to absorb outgoing flux [3] Either of these techniques can function adequtely, though the size of the masking or absorbing region beyond the physical box can become large and in principle the methods do not absort at all energies.
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