Correlated one-body momentum density for helium to neon atoms

Abstract

Abstract. Starting from explicitly correlated wavefunctions, the one-body momentum density, γ ( p), and the expectation values δ( p) and p n , with n = −2 to +3, have been obtained for the atoms helium to neon. All the calculations have been carried out by using the Monte Carlo algorithm. An analysis of the numerical accuracy of the method has been performed within the HartreeFock framework. The effects of the electronic correlations have been systematically studied by comparing the correlated results with the corresponding Hartree-Fock ones.

Momentum space densities for the beryllium isoelectronic series

“…8,13 Once the Monte Carlo momentum densities are obtained, one can evaluate the expectation values ͗t n ͘ defined as This distribution function has been shown to work properly to calculate the momentum distributions of four-electron atoms.…”

“…1 We shall denote its spherical average by ⌸(p). 7 Explicitly correlated wave functions have been used to obtain ␥(p ជ ) using the Monte Carlo algorithm, 8 due to the difficulties which appear in solving the different integrals involved in the evaluation of the momentum space wave function. [2][3][4][5] Correlated calculations have been performed in a configuration interaction ͑CI͒ scheme by expanding the single particle wave functions in either a Slater-type basis set 6 or by using Gaussiantype orbitals.…”

One- and two-body densities for the beryllium isoelectronic series

“…In doing so not only the behavior at large distances of the one-and two-body position densities is amended 8,9 but also the low range behavior of single-particle momentum density. 34 To obtain the best set of parameters that determines the wave function, the variational Monte Carlo ͑VMC͒ method has been used. The random walk in the VMC has been performed by using the Metropolis algorithm.…”

Angular versus radial correlation effects on momentum distributions of light two-electron ions

“…Conversely, the only angular correlation mechanism slightly shifts the momentum distributions towards high momenta and allows the electron cloud to get closer to the nucleus. The correlation contributions to the Compton profile are in all cases positive at large momenta, which reflects the fact that correlation makes electrons move faster in average [36]. The angular correlation mechanism is shown to bring a negative contribution to ∆J(0).…”

“…Conversely, the only angular correlation allows the electron cloud to get closer to the nucleus in average, brings a negative contribution to J(0) and slightly shifts the Compton profile towards higher momenta. Thus, angular and radial correlation mechanisms have opposite effects on J(0) but the deformations in momentum space are in all cases positive at large q [35,36].…”