G. Karl, COUNTING THE NUMBER OF VIBRATIONAL-STATES OF A MOLECULE TO IMPROVE THE BORN-OPPENHEIMER ESTIMATE, Physical review. A, 49(2), 1994, pp. 799-802
I derive an approximate estimate for the number N of states in a vibra
tional band of a diatomic molecule. The number N may be used to redefi
ne and improve by a factor pi a well-known estimate of Born and Oppenh
eimer [Ann. Phys. (Leipzig) 84, 457 (1927)]. The formulas for N are co
mpared to data for H-2 and a few other molecules.