Abstract
We present general analytical solutions to the nuclear dynamics-related Neutron Boltzmann Transport Equation inside nanoenergy reactors. Finding a particular solution to the neutron equation by making use of boundary conditions and initial conditions may be too much for the present study and reduce the generality of the solutions. Some simple assumptions have been introduced in the main system thanks to the Boubaker Polynomial Expansion Scheme, BPES, in order to make the general analytical procedure simple and adaptable for solving similar real-life problems.
Highlights
Several choices are possible for describing neutron behavior in a medium filled with nuclei
When a neutron collides with the nucleus, its strong force interacts with all of the individual nucleons 2, 4
The analytical solution of the neutron transport equation applying the method of separation of variable has been presented
Summary
Several choices are possible for describing neutron behavior in a medium filled with nuclei. A quantum mechanical description seems appropriate, leading to an involved system of Schrodinger equations describing neutron motion between and within nuclei 1–7. A neutron posses wave and classical particle properties simultaneously and a collective description like that of Maxwell’s equations seems appropriate. When a neutron collides with the nucleus, its strong force interacts with all of the individual nucleons 2, 4. Neutrons with energies above 20 Mev with speeds of more than 20% the speed of light exhibit relativistic motion, but most in a reactor are rarely above 0.17 c. Classical neutral particle description with quantum mechanics describing collisions energies is the most appropriate for the investigation of neutron motion within a nuclear reactor. The statistically large number of neutrons interacting in a reactor allows for a continuum-like description through averaging resulting in the linear Boltzmann equation. A statistical mechanics formulation, first attempted by Boltzmann for interacting gases, provides appropriate descriptions
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