A JASTROW CORRELATION FACTOR FOR TWO-DIMENSIONAL PARABOLIC QUANTUM DOTS

One of the standard approaches to calculate the ground-state properties of strongly correlated electronic systems is to use a Jastrow-Slater wavefunction as a starting point. When considering confined electrons in a two-dimensional parabolic quantum dot, one chooses the Slater determinant to be the ground-state wave function of confined independent electrons and the n determines the form of the Jastrow correlation factor in a way that incorporates accurately the spatial correlations of the system. One way to choose a quality Jastrow correlation factor is to consider the two-body problem and search the best possible yet simple approximative solution to such a problem. To achieve this goal, we consider the two-body problem of confined electrons interacting with a Coulomb repulsive potential in zero magnetic field and focus on their relative motion. Based on straight forward theoretical considerations, we suggest a simple two-body Jastrow correlation factor that optimizes very well the overall trial energy. We test the quality of the proposed Jastrow correlation factor by comparing the results to exact numerical diagonalization solutions.