Exact solution of Calogero model with competing long-range interactions

An integrable extension of the Calogero model is proposed to study the competing effect of momentum dependent long-range interaction over the original $1\text{ov}{r}^2$ interaction. The eigenvalue problem is exactly solved and the consequences on the generalized exclusion statistics, which appears to differ from the exchange statistics, are analyzed. Family of dual models with different coupling constants is shown to exist with same exclusion statistics.