Investigation of 4He3^{4}He_{3} trimer on the base of Faddeev equations in configuration space

Precise numerical calculations of bound states of a three-atomic Helium cluster are performed. The modern techniques of solution of Faddeev equations are combined to obtain an efficient numerical scheme. Binding energies and other observables for ground and excited states are calculated. Geometric properties of the clusters are discussed.Comment: uses elsart.sty, 9 tables, 5 PostScript figure

Density of Superfluid Helium Droplets

The classical integral cross sections of large superfluid 4He_N droplets and the number of atoms in the droplets (N=10^3-10^4) have been measured in molecular beam scattering experiments. These measurements are found to be in good agreement with the cross sections predicted from density functional calculations of the radial density distributions with a 10-90 % surface thickness of 5.7\AA. By using a simple model for the density profile of the droplets a thickness of about 6-8\AA is extracted directly from the data.Comment: 27 pages, REVTeX, 5 postscript figure

Importance Sampling in Rigid Body Diffusion Monte Carlo

We present an algorithm for rigid body diffusion Monte Carlo with importance sampling, which is based on a rigorous short-time expansion of the Green's function for rotational motion in three dimensions. We show that this short-time approximation provides correct sampling of the angular degrees of freedom, and provides a general way to incorporate importance sampling for all degrees of freedom. The full importance sampling algorithm significantly improves both calculational efficiency and accuracy of ground state properties, and allows rotational and bending excitations in molecular van der Waals clusters to be studied directly.Comment: Accepted for publication in Computer Physics Communication

Low-Energy Universality in Atomic and Nuclear Physics

An effective field theory developed for systems interacting through short-range interactions can be applied to systems of cold atoms with a large scattering length and to nucleons at low energies. It is therefore the ideal tool to analyze the universal properties associated with the Efimov effect in three- and four-body systems. In this "progress report", we will discuss recent results obtained within this framework and report on progress regarding the inclusion of higher order corrections associated with the finite range of the underlying interaction.Comment: Commissioned article for Few-Body Systems, 47 pp, 16 fig

High-quality variational wave functions for small 4He clusters

We report a variational calculation of ground state energies and radii for 4He_N droplets (3 \leq N \leq 40), using the atom-atom interaction HFD-B(HE). The trial wave function has a simple structure, combining two- and three-body correlation functions coming from a translationally invariant configuration-interaction description, and Jastrow-type short-range correlations. The calculated ground state energies differ by around 2% from the diffusion Monte Carlo results.Comment: 5 pages, 1 ps figure, REVTeX, submitted to Phys. Rev.

The helium trimer with soft-core potentials

The helium trimer is studied using two- and three-body soft-core potentials. Realistic helium-helium potentials present an extremely strong short-range repulsion and support a single, very shallow, bound state. The description of systems with more than two helium atoms is difficult due to the very large cancellation between kinetic and potential energy. We analyze the possibility of describing the three helium system in the ultracold regime using a gaussian representation of a widely used realistic potential, the LM2M2 interaction. However, in order to describe correctly the trimer ground state a three-body force has to be added to the gaussian interaction. With this potential model the two bound states of the trimer and the low energy scattering helium-dimer phase shifts obtained with the LM2M2 potential are well reproduced.Comment: 15 pages, 3 figures, submitted to Few-Body System

Universality in the Three-Body Problem for 4He Atoms

The two-body scattering length a for 4He atoms is much larger than their effective range r_s. As a consequence, low-energy few-body observables have universal characteristics that are independent of the interaction potential. Universality implies that, up to corrections suppressed by r_s/a, all low-energy three-body observables are determined by a and a three-body parameter \Lambda_*. We give simple expressions in terms of a and \Lambda_* for the trimer binding energy equation, the atom-dimer scattering phase shifts, and the rate for three-body recombination at threshold. We determine \Lambda_* for several 4He potentials from the calculated binding energy of the excited state of the trimer and use it to obtain the universality predictions for the other low-energy observables. We also use the calculated values for one potential to estimate the effective range corrections for the other potentials.Comment: 23 pages, revtex4, 6 ps figures, references added, universal expressions update

The ^4He trimer as an Efimov system

We review the results obtained in the last four decades which demonstrate the Efimov nature of the $^4$He three-atomic system.Comment: Review article for a special issue of the Few-Body Systems journal devoted to Efimov physic

Supersymmetric isospectral formalism for the calculation of near-zero energy states: application to the very weakly bound 4{^4}He trimer excited state

We propose a novel mathematical approach for the calculation of near-zero energy states by solving potentials which are isospectral with the original one. For any potential, families of strictly isospectral potentials (with very different shape) having desirable and adjustable features are generated by supersymmetric isospectral formalism. The near-zero energy Efimov state in the original potential is effectively trapped in the deep well of the isospectral family and facilitates more accurate calculation of the Efimov state. Application to the first excited state in 4He trimer is presented.Comment: accepte

HACE1 deficiency causes an autosomal recessive neurodevelopmental syndrome

Background: The genetic etiology of neurodevelopmental defects is extremely diverse, and the lack of distinctive phenotypic features means that genetic criteria are often required for accurate diagnostic classification. We aimed to identify the causative genetic lesions in two families in which eight affected individuals displayed variable learning disability, spasticity and abnormal gait. Methods: Autosomal recessive inheritance was suggested by consanguinity in one family and by sibling recurrences with normal parents in the second. Autozygosity mapping and exome sequencing, respectively, were used to identify the causative gene. Results: In both families, biallelic loss-of-function mutations in HACE1 were identified. HACE1 is an E3 ubiquitin ligase that regulates the activity of cellular GTPases, including Rac1 and members of the Rab family. In the consanguineous family, a homozygous mutation p.R219* predicted a truncated protein entirely lacking its catalytic domain. In the other family, compound heterozygosity for nonsense mutation p.R748* and a 20-nt insertion interrupting the catalytic HECT domain was present; Western analysis of patient cells revealed an absence of detectable HACE1 protein. Conclusion: HACE1 mutations underlie a new autosomal recessive neurodevelopmental disorder. Previous studies have implicated HACE1 as a tumour suppressor gene; however, since cancer predisposition was not observed either in homozygous or heterozygous mutation carriers, this concept may require re-evaluation