I'm trying to find the paramagnetic susceptibility on an ideal gas with spin = 1, and magnetic moment $\mu$ in the high-temperature regime.

The paramagnetic susceptibility is given by $$ \chi = \frac{N}{V} \frac{\mu_0\mu_B^2g_J^2J(J+1)}{3K_BT} $$ where $\mu_B$ is Bohr's magneton, it's obvious that $S = 1$, but in the case for the L and J what would be the values? I assumed it was set to 1, but then the values of J would go from $[2, 1, 0]$ because of $J = [L+S, ..., L-S].

Is my approximation to this gas correct?


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