Analytic Solutions of the Reference Spectrum Equation

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Abstract
Analytic solutions of the fundamental equation of the reference spectrum method for nuclear matter are obtained in the cases of the square well and exponential potentials with hard cores. In the former case analytic wavefunctions are obtained for every partial wave L. These wavefunctions are expressed in terms of spherical Bessel and Hankel functions or in terms of spherical Bessel, Hankel, and Newmann functions of order L. In the latter case an analytic expression is obtained for the swavefunction only. This is given in terms of the transcendental functions G ±v (r) and M ±v (r) which are defined as series of well‐known functions. Finally an application is made of our results to the calculation of the well depth of a Λ particle in its ground state in nuclear matter.

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