Correlation effects in a few-particle one-dimensional Coulomb-interacting system

A model of the one-dimensional Coulomb-interacting few-particle system is studied in detail. The model is similar to a many-electron system which in a zero-order approximation of the non-interacting particles has only singly occupied one-electron levels. Such model cancels the divergencies in the Coulomb and exchange interaction energies found regularly for a conventional one-dimensional system which is built up of the doubly occupied one-electron levels and is submitted to the Coulomb perturbation. In the present case, the correlated wave functions for the system can be obtained from the Slater determinants constructed for the sets of the one-electron levels and combined according to the rules given by the standard perturbation theory. The calculations allow us to discuss the correlation influence and the effect of the size of the model on: (i) the excitation energies including the criterion corresponding to the metal-insulator transition (the Mott transition), (ii) the distribution of the correlated charge along the model, (iii) the average velocity of a two-particle system being in different states, and (iv) the dipole moments and transition probabilities. In the last case, the lifetime of the uncorrelated and correlated excited states obtained in the situation of the allowed one-photon transitions can be compared with the lifetime obtained for a similar system in the case when the one-photon transitions are forbidden and two-photon transitions should be taken into account. No data other than the length of the model and the fundamental constants of nature enter the calculations.