Application of the nonlinear Schrödinger equation with a logarithmic inhomogeneous term to nuclear physics.

Abstract

Recently a nonlinear Schr\odinger equation (NLSE) with an inhomogeneous term proportional to $b\mathrm{ln}({|\ensuremath{\psi}|}^{2}|{a}^{3})\ensuremath{\psi}$ has been put forward. It has been proposed to apply it to atomic physics. Subsequent neutron interferometer experiments designed to test the physical reality of such a nonlinearity were not conclusive, thus rejecting it as unphysical. In the present paper it is pointed out that the different length scales $a$ associated with atomic and nuclear physics, for example, lead to different typical energies $b$ for these systems. Guided by the experience with phenomenological NLSE's, the constant $b$ is for the following applications to nuclear physics identified with the compressibility of finite nuclear matter, $C=\frac{K}{9}$, i.e., $b\ensuremath{\equiv}C$. Thus we obtain consistent qualitative and quantitative answers related to the concepts of microworlds and mesoworlds as well as, e.g., the prediction $130l~Kl~250$ MeV. However, this necessitates the interpretation of the respective NLSE as an equation for extended objects.