Quantum correlations in one-dimensional Wigner molecules

We studied one-dimensional systems formed by N identical particles confined in a harmonic trap and subject to an inverse power-law interaction potential similar to vertical bar x vertical bar(-d). The correlation properties of a Wigner molecule with the lowest energy are investigated in terms of their dependence on the number N and the power d, including the limit as d -> 0. There are N-particle Wigner molecules with properties such that their correlations are mainly manifested in the N lowest natural orbitals. The values of the control parameters of the system at which such states appear are identified. The properties of Wigner molecules formed in the limit as d approaches infinity are also revealed.