0000000000143634
AUTHOR
Rafael Guardiola
Magic numbers, excitation levels, and other properties of small neutral 4He clusters (Nor = 50).
The ground-state energies and the radial and pair distribution functions of neutral 4He clusters are systematically calculated by the diffusion Monte Carlo method in steps of one 4He atom from 3 to 50 atoms. In addition the chemical potential and the low-lying excitation levels of each cluster are determined with high precision. These calculations reveal that the "magic numbers" observed in experimental 4He cluster size distributions, measured for free jet gas expansions by nondestructive matter-wave diffraction, are not caused by enhanced stabilities. Instead they are explained in terms of an enhanced growth due to sharp peaks in the equilibrium concentrations in the early part of the expa…
A universal relation for power-law confining interactions
Abstract Power-law ( r α ) confining interactions are considered in the Schrodinger equation with a hyperangular momentum, which corresponds to the lowest order of the hyperspherical harmonic expansion for an N -particle system. It is shown that the product of the first odd-parity excitation energy times the mean square radius is independent of the exponent α of the potential within a few percent. This universal relation is extended to other states.
Riccati-Padé quantization and oscillatorsV(r)=grα
We develop an alternative construction of bound states based on matching the Riccati threshold and asymptotic expansions via their two-point Pad\'e interpolation. As a form of quantization it gives highly accurate eigenvalues and eigenfunctions.
A diffusion Monte Carlo study of small para-Hydrogen clusters
Abstract An improved Monte Carlo diffusion model is used to calculate the ground state energies and chemical potentials of parahydrogen clusters of three to forty molecules, using two different p-H2-p-H2 interactions. The improvement is due to three-body correlations in the importance sampling, to the time step adjustment and to a better estimation of statistical errors. In contrast to path-integral Monte Carlo results, this method predicts no magic clusters other than that with thirteen molecules.
QUANTIZATION CONDITION FOR HIGHLY EXCITED STATES
We develop a quantization condition for the excited states of simple quantum-mechanical models. The approach combines perturbation theory for the oscillatory part of the eigenfunction with a rational approximation to the logarithmic derivative of the nodeless part of it. We choose one-dimensional anharmonic oscillators as illustrative examples.
Thermal effects on small para-hydrogen clusters
A brief review of different quantum Monte Carlo simulations of small (p-H2)N clusters is presented. The clusters are viewed as a set of N structureless p-H2 molecules, interacting via an isotropic pairwise potential. Properties as superfluidity, magic numbers, radial structure, excitation spectra, and abundance production of (p-H2)N clusters are discussed and, whenever possible, a comparison with 4HeN droplets is presented. All together, the simulations indicate that temperature has a paradoxical effect of the properties of (p-H2)N clusters, as they are solid-like at high T and liquid-like at low T, due to quantum delocalization at the lowest temperature. © 2010 Wiley Periodicals, Inc. Int …
Monte carlo methods in quantum many-body theories
This is an introduction of Monte Carlo methods for beginners and their application to some quantum many-body problems. Special emphasis is done on the methodology and the general characteristics of Monte Carlo calculations. An introduction to the applications to many-body physics, specifically the Variational Monte Carlo and the Green Function Monte Carlo, is also included.