Show that for a gas composed of particles with spin (J) [hbar_{2}^{S}(J)=(J+1)(2 J+1) hbar_{2}^{S}(0)+J(2 J+1){varpi_{2}^{A}}^{A}(0)] and [bar{b}_{2}^{A}(J)=J(2
Question:
Show that for a gas composed of particles with spin \(J\)
\[\hbar_{2}^{S}(J)=(J+1)(2 J+1) \hbar_{2}^{S}(0)+J(2 J+1){\varpi_{2}^{A}}^{A}(0)\]
and
\[\bar{b}_{2}^{A}(J)=J(2 J+1) \hbar_{2}^{S}(0)+(J+1)(2 J+1) \hbar_{2}^{A}(0) .\]
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