Rotation harmonics for a numerical diatomic potential

The problem of the determination of the rotation harmonics 03A61, 03A62, ... for the case of a numerical diatomic potential is considered. These harmonics defined in a recent work by 03C8vJ = 03C8v0 + 03BB03A61 + 03BB2 03A62 + ··· (where 03C8vJ is the wave function of the vibration level v and the rotation level J, and 03BB = J(J + 1)) are studied for the case of the Dunham potential and for a numerical potential defined by the coordinates of its turning points with polynomial interpolations and extrapolations. It is proved that the analytic expressions of the harmonics 03A61, 03A62, ... reduce to polynomials where the coefficients are simply related to those of the potential in the case of the Dunham potential, and to the coordinates of the turning points in the case of the numerical potential. The numerical application is simple. The examples presented show that the vibration-rotation wave function 03C8vJ calculated by using two harmonics only is « exact » up to eight significant figures. J. Physique 44 (1983) 1257-1262 NOVEMBRE 1983, 1 Classification Physics Abstracts 31.00