A NONRELATIVISTIC QUANTUM-MECHANICAL TREATMENT OF A SYSTEM OF SELF-GRAVITATING PARTICLES

By making an intuitive choice for the single-particle density of a sys tem of N self-gravitating particles, without any source for the radiat ion of energy, we have been able to calculate the binding energy of th e system by treating these particles as fermions. Our expression for t he ground state energy of the system shows a dependence of N-7/3 on th e particle number, which is in agreement with the results obtained by other workers. We also arrive at a compact expression for the radius o f a star following which we correctly reproduce the nucleon number to be found in a typical star. Using this value, we obtain the well-known result for the limiting value of the mass, M, of a neutron star (M si milar or equal to 3.12M., M. being the solar mass) beyond which the bl ack hole formation should take place. Generalizing the present calcula tion to the case of white dwarfs, we have been able to obtain the so c alled Chandrasekhar limit for the mass, M-Ch, (M-Ch similar or equal t o 1.44M.) below which the stars are expected to go over to the white d warf state. We reproduce this by introducing a radius, equivalent to S chwarzschild radius, at the interface of the neutron stars and white d warfs. This is justified by considering the fact that it gives rise to the correct value for the degree of ionization mu(e)(mu(e) approximat e to 2) for heavy nuclei.