Abstract
The Fourier transform of single particle wave functions in cylindrical coordinates is applied to the study of neutrons released during scission. We propagate the neutron wave packets in time through the bi-dimensional time dependent Schrödinger equation with time dependent potential. We separate the parts of these wave packets that are in the continuum and calculate their Fourier transforms at different times: immediately after scission (T = 1×10-22 s) and at several intervals afterwards (until T = 50×10-22 s). The momentum distributions corresponding to these Fourier transforms are then estimated. The evolution of these distributions in time provides an insight into the separation of the neutron from the fissioning system and asymptotically gives the kinetic energy spectrum of that particular neutron.
Highlights
The Fourier transform (FT) appears in many nuclear physics applications
The momentum distribution of the scission neutrons is given by the FT of the tail of their wave packets that is in the continuum
The nuclei involved in the direct reactions are often deformed, the calculations have been performed in spherical coordinates neglecting the, undoubtedly important, role of the deformation
Summary
The Fourier transform (FT) appears in many nuclear physics applications. For example, FT is required in theoretical approaches of direct nuclear reactions of stripping, pick-up and knock-out types. The FTs of the single-particle wave-function (WF) represent the momentum transfers that occur during the reaction and give the probability that such an event takes place. Another application of the FT of a WF is in the field of nuclear fission. The nuclei involved in the direct reactions are often deformed, the calculations have been performed in spherical coordinates neglecting the, undoubtedly important, role of the deformation. This is mainly because a deformed WF is commonly expressed in cylindrical coordinates and the procedure to calculate its FT is quite complicated. After a short description of the numerical methods used, we apply them to scission neutrons and present some physical results in the frame of the Dynamical Scission Model [2, 3]
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