0000000000615097
AUTHOR
R. Guardiola
Variational Study of3HeDroplets
We report variational calculations of energies of ${}^{3}{\mathrm{He}}_{N}$ droplets ( $20\ensuremath{\le}N\ensuremath{\le}40$), using Aziz atom-atom interactions. The trial wave function has a simple structure, combining two- and three-body correlation functions coming from a translationally invariant configuration-interaction description, superimposed to a Jastrow-type correlated wave function with backflow. We find that the smallest bound drop has $N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}35$ atoms, and that for each $N$ the minimum energy states have the highest spin values.
One, Two, Three,…, Infinity
As concluding remarks to the European Few-Body Conference, the author presents a parallelism between the Few-Body and the Many-Body theories along the last years.
Drops of3Heatoms with good angular-momentum quantum numbers
The stability of drops made of ${}^{3}\mathrm{He}$ atoms is studied by means of a Monte Carlo variational method using wave functions with good angular momentum quantum numbers. The number of constituents considered is in the range 34--40. It is found that the minimal bound drop requires 35 atoms (perhaps 34) and that the preferred wave function must have the maximum spin.
On the Lindemann criterion for quantum clusters at very low temperature.
The Lindemann criterion to discern the solid-like or liquid-like nature of a quantum cluster at T = 0 is discussed. A critical analysis of current Lindemann parameters is presented and a new parameter is proposed that is appropriate to study quantum clusters made of identical particles. A simple model wave function is introduced to fix the range of variation of these parameters. The model presents two extreme limits that correspond to either a liquid-like or a solid-like system; besides, it fulfills the Bose symmetry and also permits evaluations without symmetrization. Variational and diffusion Monte Carlo calculations are also performed for clusters of spinless bosons interacting through L…
Diffraction of neutral helium clusters: evidence for "magic numbers".
The size distributions of neutral 4He clusters in cryogenic jet beams, analyzed by diffraction from a 100 nm period transmission grating, reveal magic numbers at N=10-11, 14, 22, 26-27, and 44 atoms. Whereas magic numbers in nuclei and clusters are attributed to enhanced stabilities, this is not expected for quantum fluid He clusters on the basis of numerous calculations. These magic numbers occur at threshold sizes for which the quantized excitations calculated with the diffusion Monte Carlo method are stabilized, thereby providing the first experimental confirmation for the energy levels of 4He clusters.
Small Clusters Made of Helium Atoms
Helium atoms interact very weakly through a van der Waals potential. Nevertheless, they are able to form aggregates or drops with a small number of atoms. This work analyzes the stability of clusters made of 4He atoms, of bosonic nature, clusters made of 3He atoms, of fermionic nature and also mixed aggregates with both kinds of constituents. Some of these drops are predicted to be unstable.
The translationally-invariant coupled cluster method in coordinate space
We study a formulation of the translationally-invariant coupled cluster method in coordinate space. Previous calculations in configuration space showed poor convergence, a problem that the new formulation is expected to remedy. This question is investigated for a system of bosons interacting through the Wigner part of the Afnan-Tang S3 interaction, where previous results exist.
Alpha-cluster model for 8Be and 12C with correlated alpha particles
Abstract An alpha-cluster model is proposed for 8Be and 12C nuclei, within the framework of the resonating group method (RGM). The composing 4He clusters are described using Jastrow-correlated translationally invariant configuration-interaction (Jastrow-TICI2) wave functions. The ground-state energies of the nuclei are computed by means of a Metropolis Monte-Carlo sampling.
Translationally invariant treatment of pair correlations in nuclei: I. Spin and isospin dependent correlations
We study the extension of our translationally invariant treatment of few-body nuclear systems to heavier nuclei. At the same time we also introduce state-dependent correlation operators. Our techniques are tailored to those nuclei that can be dealt with in $LS$ coupling, which includes all nuclei up to the shell closure at $A=40$. We study mainly $p$-shell nuclei in this paper. A detailed comparison with other microscopic many-body approaches is made, using a variety of schematic nuclear interactions. It is shown that our methodology produces very good energies, and presumably also wave functions, for medium mass nuclei.
State-dependent Jastrow correlation functions for 4He nuclei
We calculate the ground-state energy for the nucleus 4He with V4 nucleon interactions, making use of a Jastrow description of the corresponding wavefunction with state-dependent correlation factors. The effect related to the state dependence of the correlation is quite important, lowering the upper bound for the ground-state energy by some 2 MeV.
Jastrow-Correlated Configuration-Interaction Description of Light Nuclei
This work describes recent progress of the UMIST-VALENCIA collaboration on the ab initio study of ground states of light nuclei using realistic forces. The method presented here constructs trial variational wave functions by superimposing a central Jastrow correlation on a state-dependent translationally invariant linearly correlated state, with very promising results.
Translationally invariant treatment of pair correlations in nuclei - II. Tensor correlations
We study the extension of our translationally invariant treatment of few-body nuclear systems to include tensor forces and correlations. It is shown that a direct application of our method is not as successful for realistic V6 interactions as our previous results for V4 potentials suggested. We investigate the cause in detail for the case of $^4$He, and show that a combination of our method with that of Jastrow-correlated wave functions seems to be a lot more powerful, thereby suggesting that for mildly to strongly repulsive forces such a hybrid procedure may be an appropriate description.
The spectra of mixed $^3$He-$^4$He droplets
The diffusion Monte Carlo technique is used to calculate and analyze the excitation spectrum of $^3$He atoms bound to a cluster of $^4$He atoms, by using a previously determined optimum filling of single-fermion orbits with well defined orbital angular momentum $L$, spin $S$ and parity quantum numbers. The study concentrates on the energies and shapes of the three kinds of states for which the fermionic part of the wave function is a single Slater determinant: maximum $L$ or maximum $S$ states within a given orbit, and fully polarized clusters. The picture that emerges is that of systems with strong shell effects whose binding and excitation energies are essentially determined over configur…
Cluster Expansions and Variational Monte Carlo in Medium Light Nuclei
The B1 Brink-Boeker effective interaction is used to compute variational upper bounds for the ground state energy of nuclei from 16 O up to 40 Ca. The calculations are carried out by means of the Variational Monte Carlo method and with a multiplicative cluster expansion up to fourth order.
Quantum Thermodynamic Perturbation Theory for Fermions
The quantum version of classical thermodynamic perturbation theory is applied to the ground state of a fluid of spin-1/2 fermions interacting via the Aziz interatomic potential, as a model for liquid 3He. Results from the rapidly-convergent sixth-order calculation about the unperturbed hard-sphere fluid for energy, density and sound velocity at the zero-pressure liquid equilibrium point, lie within a few percent of computer-simulation values and appreciably closer than the most elaborate recent variational calculation. The procedure explicitly avoids crossing phase boundaries and is relatively insensitive to varying the close-packing density up to a value somewhat below the maximum possible…
Total muon-capture rate. Application to11B
A study of the total muon-capture rate in nuclei is presented, with the aid of the impulse and closure approximations and under the assumption that the initial nucleus can be described by a mixing of states in theJ-scheme. The theory is applied to the process of muon capture in11B, with a discussion on the value of the average neutrino momentum.
Minimal mass size of a stable He-3 cluster
The minimal number of 3He atoms required to form a bound cluster has been estimated by means of a Diffusion Monte Carlo procedure within the fixed-node approximation. Several importance sampling wave functions have been employed in order to consider different shell-model configurations. The resulting upper bound for the minimal number is 32 atoms.
STABILITY AND SPECTRA OF SMALL 3He-4He CLUSTERS
Diffusion Monte Carlo calculations have been systematically performed to analyze the stability of small mixed 3 He -4 He clusters, as well as their excitation spectra. The picture that emerges is that of systems with strong shell effects whose binding and excitation energies are essentially determined by the monopole properties of an effective Hamiltonian.
Strong-coupling expansion for the anharomonic oscillators −d2/dx 2+x 2+λx 2N
A perturbation expansion based on a modified and scaled harmonic oscillator combined with Pade extrapolation techniques has been used to determine the expansion of the ground-state energy in fractional and negative powers of the coupling constant, valid for large values of λ.
Excitation spectra of aHe3impurity onHe4clusters
The diffusion Monte Carlo technique is used to calculate and analyze the excitation spectrum of a single $^{3}\mathrm{He}$ atom bound to a cluster with $N$ $^{4}\mathrm{He}$ atoms, with the aim of establishing the most adequate filling ordering of single-fermion orbits to the mixed clusters with a large number of $^{3}\mathrm{He}$ atoms. The resulting ordering looks like the rotational spectrum of a diatomic molecule, being classified only by the angular momentum of the level, although vibrational-like excitations appear at higher energies for sufficiently large $N$.
Stability chart of small mixed4He−3Heclusters
A stability chart of mixed ${}^{4}\mathrm{He}$ and ${}^{3}\mathrm{He}$ clusters has been obtained by means of the diffusion Monte Carlo method, using both the Aziz HFD-B and the Tang-Toennies-Yiu atom-atom interaction. The investigated clusters contain up to eight ${}^{4}\mathrm{He}$ atoms and up to 20 ${}^{3}\mathrm{He}$ atoms. One single ${}^{4}\mathrm{He}$ binds 20 ${}^{3}\mathrm{He}$ atoms, and two ${}^{4}\mathrm{He}$ bind 1, 2, 8, and more than 14 ${}^{3}\mathrm{He}$ atoms. All clusters with three or more ${}^{4}\mathrm{He}$ atoms are bound, although the combinations ${}^{4}{\mathrm{He}}_{3}^{3}{\mathrm{He}}_{9,10,11}$ and ${}^{4}{\mathrm{He}}_{4}^{3}{\mathrm{He}}_{9}$ are metastable. …
Excitation levels and magic numbers of small parahydrogen clusters (N⩽40)
The excitation energies of parahydrogen clusters have been systematically calculated by the diffusion Monte Carlo technique in steps of one molecule from 3 to 40 molecules. These clusters possess a very rich spectra, with angular momentum excitations arriving up to L=13 for the heavier ones. No regular pattern can be guessed in terms of the angular momenta and the size of the cluster. Clusters with N=13 and 36 are characterized by a peak in the chemical potential and a large energy gap of the first excited level, which indicate the magical character of these clusters. From the calculated excitation energies the partition function has been obtained, thus allowing for an estimate of thermal e…
Translationally-Invariant Coupled-Cluster Method for Finite Systems
The translational invariant formulation of the coupled-cluster method is presented here at the complete SUB(2) level for a system of nucleons treated as bosons. The correlation amplitudes are solution of a non-linear coupled system of equations. These equations have been solved for light and medium systems, considering the central but still semi-realistic nucleon-nucleon S3 interaction.
Microscopic and translationally-invariant calculations with tensor forces and tensor correlations
In this paper we discuss an approach to the ab initio study of ground states of light nuclei using realistic forces. The method constructs trial variational wavefunctions by superimposing state-dependent translationally-invariant pair correlations on a state-independent Jastrow-correlated wavefunction, with very promising results.
High-quality variational wave functions for small4Heclusters
We report a variational calculation of ground state energies and radii of ${}^{4}{\mathrm{He}}_{N}$ droplets $(3l~Nl~40),$ using the Aziz HFD-B (HE) atom-atom interaction. 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.
The spiked harmonic oscillatorV(r)=r 2+λr −4 as a challenge to perturbation theory
The standard weak- and strong-coupling perturbation series are interpreted as extreme special cases of expansions obtainable within the framework of Rayleigh-Schroedinger perturbation theory with non-diagonal propagators and unspecified zero-order energies. The formalism of the latter type is then tested by our strongly singular example. It proves suitable for applications in the domain of virtually arbitrary couplings. A few related technicalities and especially the quadruple problem of convergence are also discussed.