Even though this is an old question I figured I'd post an answer for people who might have the same question and end up here.
The rotational energy for a specific level J, EJ = J(J+1)[((m1 + m2)*h2)/(8m1m2R2) = J(J+1)B
In this case B = ((m1 + m2)*h2)/(8m1m2R2)
The transition from J = 0...