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

Recently a nonlinear Schroedinger equation (NLSE) with an inhomogeneous term proportional to b ln(Vertical BarpsiVertical Bar/sup 2/a/sup 3/)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 = K/9, i.e., bequivalentC. Thus we obtain consistent qualitative and quantitative answers related to the concepts of microworlds and mesoworlds as well as, e.g., the prediction 130< or =K< or =250 MeV. However, this necessitates the interpretation of the respective NLSE as an equation for extended objects.

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