NONINTEGRAL EXPRESSIONS FOR THE DIATOMIC CENTRIFUGAL-DISTORTION CONSTANTS

The problem of the centrifugal distortion constants (CDC), D-nu, H-nu, ... for a diatomic molecule is considered. It is shown that a new form ulation of the standard Rayleigh-Schrodinger perturbation theory can g ive simple and compact analytical expressions of the CDC (up to any or der). Thus, the constants e(1) = B-nu, e(2) = -D-nu, e(3) = H-nu,...,e (n), are all of the form e(n) = lim sigma(n)(r)/sigma(0)(r) as r --> i nfinity. sigma(0) is the particular solution of the nonhomogeneous equ ation y'' + k(E(nu) - U)y = s, with s = psi(nu), where (E(nu),psi(nu)) is the eigenvector corresponding to the rotationless potential U(r) a nd to the vibrational level nu; and where sigma(0)(0) = sigma'(0),(0) = 0. sigma(n) is the particular solution of the above equation, where s is known for each order of n. The numerical application to the stand ard Lennard-Jones model potential shows that good results are obtained for D-nu, H-nu, L(nu),..., O-nu, P-nu, for nu, = 0 to 22, which is on ly at 2 x 10-4 of the well depth. The program uses one routine (the in tegration of the equation y'' + fy = s) repeated for different s; it i s quite simple and gives no difficulties at the boundaries and there i s no need to use any mathematical or numerical artifices.