Well-dressed repulsive-core solitons and nonlinear optics of nuclear reactions

Abstract

We introduce the concept of nonlinear optics of nuclear reactions and reveal a deep analogy between nonlinear dynamics of the so-called “well-dressed repulsive-core” solitons and the nuclear reactions that take place among atomic nuclei. We derive a nonlinear evolution equation for the Fermi nuclear density and the Woods–Saxon potential based on the inverse problem in the diffraction and dispersion scattering. We obtain a simple formula for the self-interaction (binding) energy, which provides the shape and structural stability of “soliton-like nucleus” with the Fermi density distribution. We find the shape squareness parameter (edge steepness) for “soliton-like nucleus” density distribution and demonstrate its specific quantization related to the conservation of the total number of nucleons. The shape squareness parameter plays a decisive role in increasing the binding soliton energy and appearing the oscillatory side-band spectral structures responsible for the fusion and fission reactions with soliton-like nuclei. We hope that nonlinear-optical analogies found in our work will be able to shed additional light on the fundamental problems of stellar nucleosynthesis. We support our findings with concrete examples of fusion and fission reactions with “well-dressed repulsive-core” nucleus-like solitons: the carbon and oxygen-burning processes, the iron-synthesis, and nuclear fusion–fission reactions induced by alpha particles.