H Kobeissi and M Korek 1993 J. Phys. B: At. Mol. Opt. Phys. 26 L35 doi:10.1088/0953-4075/26/3/001
H Kobeissi and M Korek
Show affiliationsThe problem of the determination of the diatomic centrifugal distortion constants (CDC) is considered. The previous use of the Rayleigh-Schrodinger perturbation approach (by Hutson) gives analytical expressions of Dnu ,Hnu ,Lnu ,Mnu in terms of psi nu (0) (vibrational wavefunction) and psi nu (1), psi nu (2) (first two rotational harmonics). A similar use (by Kobeissi) gives expressions up to Nnu ,Onu ,. . . In both formulations the analytical expression increases in complexity with increasing order. The present work shows that all CDC of any order are given by one single expression E(n)=( psi nu (0) mod R-Bnu mod psi nu (n-1)) where R=1/r2, Bnu is the rotational constant; psi nu (n) is the solution of the equation y"+f(r)y=sn(r) where just s varies with n, the psi nu (n) initial values at an arbitrary origin r0(0<r0< infinity ) being given by psi nu (n)(r0)=0, d psi nu (n)(r0)/dr= integral nu r0sn(r) psi (0) (r)dr/ psi (0)(r0); sn(r) is given by an exact analytical expression depending on psi nu (0), psi nu (1),. . ., psi nu (n-1).
33.15.Mt Rotation, vibration, and vibration-rotation constants
Issue 3 (14 February 1993)
H Kobeissi and M Korek 1993 J. Phys. B: At. Mol. Opt. Phys. 26 L35
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