b,*

In this work, solid helium is studied within the framework of the static fluctuation approximation. The closed set of nonlinear coupled equations, which is an inherent feature of this approximation, is derived for one-dimensional solid 4 He. This set is solved numerically by an iteration method for a realistic interhelium potential. The central aim is to determine the chemical potential µ, condensate fraction N0/N, total energy U, heat capacity C, and entropy S of the system. The effects of temperature T, total number of particles N, frequency ω and lattice constant R on these properties are emphasized and explained. Below 80 mK: (1) as N or ω increases, µ increases; (2) as N increases, U, C, and S increase; whereas N0/N, U/N, C/NkB and S/NkB decrease (kB being Boltzmann's constant); (3) as ω increases, N0/N, U, C, and S increase; whereas U/N, C/NkB and S/NkB are hardly affected; and (4) as T → 0, the effect of R on N0/N increases. These results are presented in a set of figures