MICROWAVE SPECTRAL TABLES Diatomic Molecules

(11)J««-J transition,F^ ; i.j.r)s -' J+FH-Itz"Jtr- I^'i'J-r-tI'' J- F- 1- 1 > UB . (12), J. F; 1. J. F) . ZF(F+1) BandH(I. J.F-l; I. J.F) = -(J+F+I+lKJ+F-IHJ-F+mKJ-F-I) ^ § (M)where co and cx> are normalization constants such that y y H(I, J',F'; I, J", F") equals9unity. Substituting the expressions for the sums given in Condon and Shortley (equations 2 6)shows thatand4(2JU)(2I-fl)(J+l)(2J+3)toA = 14(2J+l)(2I+l)(J-fl)Jco_ = 1JD(Attention is called to a typographical error in Townes and Schawlow's expression for thetransition J, F-*-J-l,F (2: page 152). Since these expressions assume only that the J's andF's are good quantum numbers and that the hyperfine splittings are small compared to kT,they apply for the molecules with unclosed shells as well as with closed shells. These H f sare given in table 2 of this volume for both integral and half-integral values of J (see nextparagraph).For hyperfine splitting associated with two nuclei, the following treatment was used.If the hyperfine splittings are small compared to kT and if the spin I of the first nucleuscombines with J to form a good (angular momentum) quantum number F , the previous Hfactors can be applied with I , J, F substituted for I, J, F, then again with I ? , F , F substituted for I, J, F. In this tabulation, two nuclei contribute to hyperfine splitting only for closedshell molecules; in this case the preceding quantum number condition is obeyed provided thequadrupole coupling constant eQq for I is large in absolute value compared to that for I(and both large compared to the small magnetic couplings) [2: page 172], Rather than carryingout the tedious computations for intermediate coupling [2: page 172] or reporting no hyperfineXV