ON NONINTEGRAL E CORRECTIONS IN PERTURBATION-THEORY - APPLICATION TO THE PERTURBED MORSE OSCILLATOR

A new formulation of the Rayleigh-Schrodinger perturbation theory is a pplied to the derivation of the vibrational eigenvalues of the perturb ed Morse oscillator (PMO). This formulation avoids the conventional pr ojection of the PSI corrections on the basis of unperturbed eigenfunct ions {PSI(nu)(0)}, or the projection of the nonhomogeneous Schrodinger equations on PSI(nu)(0); it gives simple expressions for each E corre ction E(nu)(p) free of summations and integrals. When the PMO is chara cterized by the potential U = U(M) + U(P) (where U(M) is the unperturb ed Morse potential), the eigenvalue of a vibrational level nu is given by: E(nu) = E(nu)M + E(nu)(1) + E(nu)(2) +.... According to the new f ormulation the correction E(nu)(p) is given by E(nu)(p) = lim(r --> in finity) sigma(p)(r)/sigma0(r), where sigma(p)(r) is a particular solut ion of the nonhomogeneous differential equation y'' + fy = s(p); here f = E(nu)M - U(M) (r), s(p) is well known for each p: for p = 0, s0 = PSI(nu)(0); for p = 1, s1 = U(p)PSI(nu)(0)... For the numerical applic ation one single routine is used, that of integrating y'' + fy = s, wh ere the coefficients are known as well as the initial values. An examp le is presented for the Huffaker PMO of the (carbon monoxide) CO-X1SIG MA+ state. The vibrational eigenvalues E(nu) are obtained to a good ac curacy (with p = 4) even for high levels. This result confirms the val idity of this new formulation and gives a semianalytic expression for the PMO eigenvalues.