Importance of accurate calculation of average reaction rate in thermonuclear reactions is introduced. Two types of nuclear involved in thermonuclear reactions are assumed in thermal equilibrium state under same temperature. With comparison between analytical expressions of average reaction rate and average rate of thermonuclear reaction using MC method directly, correctness of MC method is obtained. Finally, MC method is extended to calculation of average thermonuclear reaction rate in several typical distributions.

A nonlinear optimizing method is applied to study the ground state configurations of a two-dimensional charged particle system in a hard-wall confining potential.We find that the circular shell configurations in a circular hard wall confinement are similar to that in a parabolic confining potential.With a hard-wall square boundary,the Wigner crystal lattice is square as the number of particles N<66,but becomes a hexagon as N≥66 since the boundary effect is weak for inner particles.The influence of the elliptic and rectangular boundary on the wigner crystal lattice is analyzed.