In case (b), the spin-orbit coupling is weak or non-existent (in the case ).  In this case, we take  and  and assume  precesses quickly around the internuclear axis.
The good quantum numbers in case (b) are , , , and .  We express the rotational energy operator as , where  is a rotational constant.  The rotational levels therefore have relative energies  starting with . For example, a Σ state has rotational levels  = 0, 1, 2, 3, 4, ..., and each level is divided by spin-orbit coupling into two levels  =  ± 1/2 (except for  = 0 which corresponds only to  = 1/2 because  cannot be negative).
Another example is the Σ ground state of dioxygen, which has two unpaired electrons with parallel spins. The coupling type is Hund's case b), and each rotational level N is divided into three levels  = , , .
For case b) the selection rules for quantum numbers , ,  and  and for parity are the same as for case a). However for the rotational levels, the rule for quantum number  does not apply and is replaced by the rule .