We consider the hypothesis that cosmic rays are emitted from the surfaces of neutron stars by a process of evaporation from an internal nuclear liquid to a dilute external gas which constitutes the “ vacuum ” . On this basis , we find an inverse power in the energy distribution with a power law exponent of 2.701178 in excellent agreement with the experimental value of 2.7 . The heat of nuclear matter evaporation via the entropy allows for the computation of the exponent . The evaporation model employed is based on the entropy considerations of Landau and Fermi that have been applied to the liquid drop model of evaporation in a heavy nucleus excited by a collision . This model provides a new means of obtaining power law distributions for cosmic ray energy distributions and , remarkably , an actual value for the exponent which is in agreement with experiment and explains the otherwise puzzling smoothness of the cosmic ray energy distribution over a wide range of energies without discontinuities due to contributions from different sources required by current models .