Explicitly correlated Helium wave function and hyperspherical coordinates

Wave functions of a new functional kind have been proposed for Helium-like atoms in this work . These functions explicitly depend on interelectronic and hyperspherical coordinates. The best ground state energy for the Helium atom $-2.903724376677 a.u.$ has been calculated with variational method with basis set of simple functions with a single exponential parameter. To the author's knowledge, this is the best result with use of hyperspherical coordinates so far. Comparable result has been obtained for the hydrogen anion. For Helium atom, our best wave functions matched the Kato cusp conditions within the accuracy below $6.10^{-4}$. An important feature of proposed wave functions is the inclusion of negative powers of $R=\sqrt(r^{2}_{1}+r^{2}_{2})$ in combination with positive powers of $r_{12}$ into the wave function. We showed that this is necessary condition for proposed wave function to be a formal solution of Schr\"odinger equation.Comment: 18 page

Explicitly correlated trial wave functions in Quantum Monte Carlo calculations of excited states of Be and Be-

We present a new form of explicitly correlated wave function whose parameters are mainly linear, to circumvent the problem of the optimization of a large number of non-linear parameters usually encountered with basis sets of explicitly correlated wave functions. With this trial wave function we succeeded in minimizing the energy instead of the variance of the local energy, as is more common in quantum Monte Carlo methods. We applied this wave function to the calculation of the energies of Be 3P (1s22p2) and Be- 4So (1s22p3) by variational and diffusion Monte Carlo methods. The results compare favorably with those obtained by different types of explicitly correlated trial wave functions already described in the literature. The energies obtained are improved with respect to the best variational ones found in literature, and within one standard deviation from the estimated non-relativistic limitsComment: 19 pages, no figures, submitted to J. Phys.

Excited states of beryllium atom from explicitly correlated wave functions

A study of the first excited states of beryllium atom starting from explicitly correlated wave functions is carried out. Several properties are obtained and discussed focusing on the analysis of the Hund's rules in terms of the single--particle and electron pair intracule and extracule densities. A systematic study of the differences on the electronic distributions of the singlet and triplet states is carried out. The trial wave function used to describe the different bound states consists of a generalized Jastrow-type correlation factor times a configuration interaction model wave function. This model wave function has been fixed by using a generalization of the optimized effective potential method to deal with multiconfiguration wave functions. The optimization of the wave function and the calculation of the different quantities is carried out by means of the Variational Monte Carlo method.Comment: 28 pages, 6 figure

Vortex nucleation in mesoscopic Bose superfluid and breaking of the parity symmetry

We analyze vortex nucleation in mezoscopic 2D Bose superfluid in a rotating trap. We explicitly include a weakly anisotropic stirring potential, breaking thus explicitly the axial symmetry. As the rotation frequency passes the critical value $\Omega_c$ the system undergoes an extra symmetry change/breaking. Well below $\Omega_c$ the ground state is properly described by the mean field theory with an even condensate wave function. Well above $\Omega_c$ the MF solution works also well, but the order parameter becomes odd. This phenomenon involves therefore a discrete parity symmetry breaking. In the critical region the MF solutions exhibit dynamical instability. The true many body state is a strongly correlated entangled state involving two macroscopically occupied modes (eigenstates of the single particle density operator). We characterize this state in various aspects: i) the eligibility for adiabatic evolution; ii) its analytical approximation given by the maximally entangled combination of two single modes; and finally iii) its appearance in particle detection measurements.Comment: 14 pages, 27 figure

Electric dipole response of 6^6He: Halo-neutron and core excitations

Electric dipole ($E1$) response of $^{6}$He is studied with a fully microscopic six-body calculation. The wave functions for the ground and excited states are expressed as a superposition of explicitly correlated Gaussians (CG). Final state interactions of three-body decay channels are explicitly taken into account. The ground state properties and the low-energy $E1$ strength are obtained consistently with observations. Two main peaks as well as several small peaks are found in the $E1$ strength function. The peak at the high-energy region indicates a typical macroscopic picture of the giant dipole resonance, the out-of-phase proton-neutron motion. The transition densities of the lower-lying peaks exhibit in-phase proton-neutron motion in the internal region, out-of-phase motion near the surface region, and spatially extended neutron oscillation, indicating a soft-dipole mode (SDM) and its vibrationally excited mode.Comment: 12 pages, 12 figures, to appear in Phys. Rev.

Beyond Gross-Pitaevskii:local density vs. correlated basis approach for trapped bosons

We study the ground state of a system of Bose hard-spheres trapped in an isotropic harmonic potential to investigate the effect of the interatomic correlations and the accuracy of the Gross-Pitaevskii equation. We compare a local density approximation, based on the energy functional derived from the low density expansion of the energy of the uniform hard sphere gas, and a correlated wave function approach which explicitly introduces the correlations induced by the potential. Both higher order terms in the low density expansion, beyond Gross-Pitaevskii, and explicit dynamical correlations have effects of the order of percent when the number of trapped particles becomes similar to that attained in recent experiments.Comment: Revtex, 2 figure