We study an atom-phonon coupling model introduced recently for spin-conversion phenomenon. The originality of this model, performed on a linear chain of atoms, is that the elastic force constant values of the spring linking two atoms depends on their electronic states. This leads to introduce naturally in the chain long- and short-range interactions, which appear respectively like a Zeeman and an exchange interactions. The exchange-like interaction can be ferro-, antiferro- or equal to zero. The effects of long-range interactions have already been studied. Here we study those of the short-range interaction. Some parts of the chain phase diagram are analysed and the main features of the experimental behaviours of spin conversion compounds are qualitatively reproduced.