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\sect{The calculation of $Z(T)$ for AB and AA molecules}
Calculate the distribution function of diatomic molecule ${AB}$.
Assume it's possible to relate the molecule, like two "balls" with
${\mathsf{m}}$ mass and ${S}$ spin each one, attached with a spring
length ${r_{0}}$. Assume it's a hard spring so it's possible to
assume that the molecule is in the lowest strip of the vibration. In
other words, we relate the molecule like a rigid body ("rotor").
Relate separately in case of molecule ${AA}$ composed of identical
atoms. Relate specifically in case of identical atoms with spin
${0}$ and identical atoms with spin ${\frac{1}{2}}$. in the last
case, determine what is the probability to find the molecule in
triplet condition and distinguish between the borderline cases of
low temperature and high temperature.