The asymptotics of matrix elements of Gaussian potential between the basis functions of three-dimensional harmonic oscillator

The asymptotic expression may be used to calculate matrix elements of the Gaussian potential between the basis functions of three-dimensional harmonic oscillator < n l | V0 exp [-r2 / μ2] | ntilde l >, starting with some values of quantum numbers n and n ∼. The asymptotic expression is found, and its behavior is investigated for different values of quantum numbers n, n↓, l and ratio μ/r0. (author). 4 refs., 5 figs