Two-body Potential Research Articles

Ground State Energy of Dense Gases of Strongly Interacting Fermions

AbstractWe study the ground state energy of a gas of N fermions confined to a unit box in d dimensions. The particles interact through a two-body potential with strength scaled in an N-dependent way as $$N^{-\alpha }v$$ N - α v , where $$\alpha \in \mathbb {R}$$ α ∈ R and v is a function of positive type satisfying a mild regularity assumption. Our focus is on the strongly interacting case $$\alpha <1-\frac{2}{d}$$ α < 1 - 2 d . We contrast our result with existing results in the weakly interacting case $$\alpha >1-\frac{2}{d}$$ α > 1 - 2 d and the transition happening at the mean-field scaling $$\alpha =1-\frac{2}{d}$$ α = 1 - 2 d . Our proof is an adaptation of the bosonization technique used to treat the mean-field case.

Mutual information sums and relations with interaction energies in N-particle quantum systems.

The sums of position- and momentum-space mutual information measures are used to examine the pairwise and higher-order statistical correlation in the ground states of N-particle coupled oscillators. Analytical expressions for these measures are shown to be related to the logarithmic interaction energies of these states, plus those of mirror states where the intensities of the one- and two-body potentials are interchanged, and the nature of the attractive or repulsive interaction is opposite to that in the original state. The measures separate the contributions from the interactionsand those from the effective interactions due to marginalization into different terms. The pairwise mutual information sum is linearly related to the Shannon entropy sum in two particle systems, while the total correlation sum exhibits a similar relationship in three particle ones. In the latter instance, the interaction information sum can be related to entropy differences. This illustrates how entropy sums are connected to correlation measure sums in these systems. All measures approach zero with large N, when the magnitudes of the one- and two-body potentials are fixed. The pair mutual information and total correlation sums decay monotonically with N in the presence of an attractive potential and monotonically increase with a repulsive potential. On the other hand, the interaction information sum exhibits a minimum at small N, with an attractive potential. This is a consequence of the higher-order correlations governing behavior at smaller N while the pairwise ones dominate at larger N. Results are presented when the magnitude of the one-body potential is set to N.

Λ6He (1−, 2−) spin doublet in a Λ + n + α cluster model

The spin singlet and spin triplet states of the helium-6-lambda hypernucleus are studied in configuration space as a three-body problem, using the hyperspherical method. This hypernucleus is treated as a Λ + n + α cluster model. Since the α particle core has a spin of 0, this is an ideal hypernucleus from which to understand spin dependence in hyperon-nucleon potentials. In this paper, the hyperon-nucleon potential considered is the GLM-YN0 Λ-n potential, which is a simulation of the NSC97f potential obtained through inverse scattering theory. Due to violations of the cluster structure, two-body potentials underbind the helium-6-lambda hypernucleus. This issue is addressed by including a three-body force to complement these two-body forces. A three-body force, whose strength is spin dependent, is used to guide predictions of the spin triplet state of helium-6-lambda which is not yet known experimentally.

Third density and acoustic virial coefficients of helium isotopologues from abinitio calculations.

Improved two-body and three-body potentials for helium have been used to calculate from first principles the third density and acoustic virial coefficients for both 4He and 3He. For the third density virial coefficient C(T), uncertainties have been reduced by a factor of 4-5 compared to the previous state of the art; the accuracy of first-principles C(T) now exceeds that of the best experiments by more than two orders of magnitude. The range of calculations has been extended to temperatures as low as 0.5K. For the third acoustic virial coefficient γa(T), we applied the Schlessinger point method, which can calculate γa and its uncertainty based on the C(T) data, overcoming some limitations of direct path-integral calculation. The resulting γa are calculated at temperatures down to 0.5K; they are consistent with available experimental data but have much smaller uncertainties. The first-principles data presented here will enable improvement of primary temperature and pressure metrology based on gas properties.

Efficient circular Dyson Brownian motion algorithm

Circular Dyson Brownian motion describes the Brownian dynamics of particles on a circle (periodic boundary conditions), interacting through a logarithmic, long-range two-body potential. Within the log-gas picture of random matrix theory, it describes the level dynamics of unitary (“circular”) matrices. A common scenario is that one wants to know about an initial configuration evolved over a certain interval of time, without being interested in the intermediate dynamics. Numerical evaluation of this is computationally expensive as the time-evolution algorithm is accurate only on short time intervals because of an underlying perturbative approximation. This work proposes an efficient and easy-to-implement improved circular Dyson Brownian motion algorithm for the unitary class (Dyson index β=2, physically corresponding to broken time-reversal symmetry). The algorithm allows one to study time evolution over arbitrarily large intervals of time at a fixed computational cost, with no approximations being involved. Published by the American Physical Society 2024

Atomistic insights into argon clusters and nucleation dynamics

Accurate predictions of nucleation and atomic-level estimates of cluster properties in gas-phase chemical physics have proven challenging. These challenges arise from two primary sources: finite-size effects associated with nanoscopic particles and the emergence of non-standard thermodynamics, particularly at elevated temperatures. This study reexamines the formation of argon clusters using established methodologies such as atomistic simulations, configurational sampling, and statistical thermochemistry. To enhance the representation of condensed-phase argon, we employ an ab initio-based two-body potential, complemented by a three-body Axilrod–Teller potential. Additionally, we address the impact of anharmonicities on cluster stabilities using a recently developed extension to the standard statistical cluster model. The employed anharmonic model is rigorously benchmarked against molecular dynamics simulations. The subsequent analysis demonstrates a robust and consistent agreement between our model and experimental data. Our analysis covers nearly every experimental data point collected between 1971 and 2010, offering valuable insights into the predictive capabilities of the model. Moreover, in contrast to previous studies, our findings indicate that individual measurements are consistently in alignment with each other.

New alternatives to the Lennard-Jones potential

We present a new method for approximating two-body interatomic potentials from existing ab initio data based on representing the unknown function as an analytic continued fraction. In this study, our method was first inspired by a representation of the unknown potential as a Dirichlet polynomial, i.e., the partial sum of some terms of a Dirichlet series. Our method allows for a close and computationally efficient approximation of the ab initio data for the noble gases Xenon (Xe), Krypton (Kr), Argon (Ar), and Neon (Ne), which are proportional to r-6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r^{-6}$$\\end{document} and to a very simple depth=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$depth=1$$\\end{document} truncated continued fraction with integer coefficients and depending on n-r\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n^{-r}$$\\end{document} only, where n is a natural number (with n=13\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n=13$$\\end{document} for Xe, n=16\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n=16$$\\end{document} for Kr, n=17\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n=17$$\\end{document} for Ar, and n=27\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n=27$$\\end{document} for Neon). For Helium (He), the data is well approximated with a function having only one variable n-r\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n^{-r}$$\\end{document} with n=31\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n=31$$\\end{document} and a truncated continued fraction with depth=2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$depth=2$$\\end{document} (i.e., the third convergent of the expansion). Also, for He, we have found an interesting depth=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$depth=0$$\\end{document} result, a Dirichlet polynomial of the form k16-r+k248-r+k372-r\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k_1 \\, 6^{-r} + k_2 \\, 48^{-r} + k_3 \\, 72^{-r}$$\\end{document} (with k1,k2,k3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k_1, k_2, k_3$$\\end{document} all integers), which provides a surprisingly good fit, not only in the attractive but also in the repulsive region. We also discuss lessons learned while facing the surprisingly challenging non-linear optimisation tasks in fitting these approximations and opportunities for parallelisation.

Statistical theory of fluids confined in quenched disordered porous media.

We develop a theory to calculate structural correlations and thermodynamic properties of a fluid confined in a random porous solid medium (matrix). We used density functional formalism to derive an annealed averaged expression for the density profile and excess free energy of fluid arising due to random fields of a particular realization of the matrix. After performing the second average over the quenched-disordered variables, the excess free energy is organized to give one- and two-body potentials for fluid particles. The average over disorder reduces the system to an effective one-component system of fluid in which particles feel one-body (external) potential and interact via effective pair potential. The effective pair potential is a sum of the bare (the one in the pure fluid) and the matrix-induced potential. The resulting partition function involves only fluid variables. Equations are derived for fluid-fluid and fluid-matrix correlation functions and for free energy, pressure, and chemical potential of the fluid. The theory is applied to a model system of hard spheres and results for the effective pair potential, correlation functions, and thermodynamic properties are reported. The effective pair potential is found to be attractive at the contact and develops a repulsive peak before decaying to zero. Results for pair correlation function and structure factor are compared with simulation results for several fluid densities at two matrix densities. In all the cases, a very good agreement has been found.

Thermophysical properties of argon gas from improved two-body interaction potential

Thermophysical properties of argon gas from improved two-body interaction potential

Insights on the structure and properties of sodium iron phosphate glasses from molecular dynamics simulations

Iron phosphate glasses are promising nuclear waste forms while more detailed understanding of their structures and structure-property relations are still needed to better design waste glass compositions. In this work we report studies of three series of sodium iron phosphate (NFP) glasses: 60P2O5-(40-x)Fe2O3-xNa2O (x = 0→40), (100–2x)P2O5-xFe2O3-xNa2O (x = 5→17.5) and one with different iron redox ratio, to understand the composition as well as the iron redox effects on the structure and properties of these glasses using molecular dynamics simulations with effective two-body and three-body potentials. Structural analyses, including pair distribution function, bond angle distribution, Qn distribution, and polyhedral connectivity, were performed to obtain in-depth information on short-range and medium-range structural features. The P-O pair distributions showed a first peak splitting with phosphorus-bridging and non-bridging oxygen contributions. This and the average P-O and other cation-oxygen bond distances are in excellent agreement with experiments. The coordination number of P5+ remained four while that of Fe3+ increased from 4.30 to 4.72 with decreasing Fe/Na ratio. Polyhedral linkage analysis showed [PO4] units linked with [PO4] and [FeOx] through corner-sharing while the [PO4]-[FeOx] linkages become dominant for compositions with Fe2O3 larger than 15 mol%. The effect of iron redox ratio on the structure of NFP glasses was also studied and it was found that bond lengths and coordination numbers were not strongly affected, while the reduction of iron introduced higher network distortions, as evident by O-P-O bond angle and Qn distribution. The glass transition temperature (Tg) showed a monotonic increase with Fe2O3 in the first series, in good agreement with experiments, while those of the second series showed a maximum at P2O5 = 82 mol%. Calculated elastic moduli were found to increase with Fe2O3 in the first glass series, which was be explained by the increase of network connectivity, while those of the second series decrease with Fe2O3 due to decrease of P2O5.

The Ground State Energy of a Two-Dimensional Bose Gas

We prove the following formula for the ground state energy density of a dilute Bose gas with density ρ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\rho $$\\end{document} in 2 dimensions in the thermodynamic limit e2D(ρ)=4πρ2Y(1-Y|logY|+(2Γ+12+log(π))Y)+o(ρ2Y2),\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} e^{\ ext {2D}}(\\rho ) = 4\\pi \\rho ^2 Y\\Big (1 - Y \\vert \\log Y \\vert + \\Big ( 2\\Gamma + \\frac{1}{2} + \\log (\\pi ) \\Big ) Y \\Big ) + o(\\rho ^2 Y^{2}), \\end{aligned}$$\\end{document}as ρa2→0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\rho a^2 \\rightarrow 0$$\\end{document}. Here Y=|log(ρa2)|-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Y= |\\log (\\rho a^2)|^{-1}$$\\end{document} and a is the scattering length of the two-body potential. This result in 2 dimensions corresponds to the famous Lee–Huang–Yang formula in 3 dimensions. The proof is valid for essentially all positive potentials with finite scattering length, in particular, it covers the crucial case of the hard core potential.

How close are the classical two-body potentials to abinitio calculations? Insights from linear machine learning based force matching.

In this work, we propose a linear machine learning force matching approach that can directly extract pair atomic interactions from abinitio calculations in amorphous structures. The local feature representation is specifically chosen to make the linear weights a force field as a force/potential function of the atom pair distance. Consequently, this set of functions is the closest representation of the abinitio forces, given the two-body approximation and finite scanning in the configurational space. We validate this approach in amorphous silica. Potentials in the new force field (consisting of tabulated Si-Si, Si-O, and O-O potentials) are significantly different than existing potentials that are commonly used for silica, even though all of them produce the tetrahedral network structure and roughly similar glass properties. This suggests that the commonly used classical force fields do not offer fundamentally accurate representations of the atomic interaction in silica. The new force field furthermore produces a lower glass transition temperature (Tg ∼ 1800K) and a positive liquid thermal expansion coefficient, suggesting the extraordinarily high Tg and negative liquid thermal expansion of simulated silica could be artifacts of previously developed classical potentials. Overall, the proposed approach provides a fundamental yet intuitive way to evaluate two-body potentials against abinitio calculations, thereby offering an efficient way to guide the development of classical force fields.

Many-body potential for simulating the self-assembly of polymer-grafted nanoparticles in a polymer matrix

Many-body interactions between polymer-grafted nanoparticles (NPs) play a key role in promoting their assembly into low-dimensional structures within polymer melts, even when the particles are spherical and isotropically grafted. However, capturing such interactions in simulations of NP assembly is very challenging because explicit modeling of the polymer grafts and melt chains is highly computationally expensive, even using coarse-grained models. Here, we develop a many-body potential for describing the effective interactions between spherical polymer-grafted NPs in a polymer matrix through a machine-learning approach. The approach involves using permutationally invariant polynomials to fit two- and three-body interactions derived from the potential of mean force calculations. The potential developed here reduces the computational cost by several orders of magnitude, thereby, allowing us to explore assembly behavior over large length and time scales. We show that the potential not only reproduces previously known assembled phases such as 1D strings and 2D hexagonal sheets, which generally cannot be achieved using isotropic two-body potentials, but can also help discover interesting phases such as networks, clusters, and gels. We demonstrate how each of these assembly morphologies intrinsically arises from a competition between two- and three-body interactions. Our approach for deriving many-body effective potentials can be readily extended to other colloidal systems, enabling researchers to make accurate predictions of their behavior and dissect the role of individual interaction energy terms of the overall potential in the observed behavior.

Molecular dynamics simulation of 100 keV argon ion radiation effects in metals and comparison with stopping and range of ions in matter code

Simulation is essential to analyse radiation-induced effects because energetic ions have short transit times within materials (Ar ions of 1 keV and 100 keV have transit times of 0.29 picoseconds and 29 femtoseconds respectively, through a 25 nm Al film). The binary collision approximation (BCA) is extensively used in simulations to study damage caused by energetic ions due to its computational efficiency. Stopping and Range of Ions in Matter (SRIM), a widely used Monte Carlo software using BCA, provides accurate ion ranges consistent with experiments. Molecular dynamics simulations are powerful computational method, where classical equations of motion are solved to track atomic movements from radiation damage, but computational resources required are heavier for this method. In our current effort, the energy transfer from 100 keV Ar+ to metal targets is analysed as a function of target properties, including melting temperature and atomic density, using these two methodologies. A detailed investigation of 100 keV Ar+ ion impact on metal targets is done using the classical Molecular Dynamics simulation program ‘MDRange’, which uses the Recoil Interaction Analysis (RIA) approximation, where the interaction between the ion and its closest neighbours is considered via a two-body potential. The correlation of energy transferred to the metal with the target properties is examined considering the physical approximations of each technique.

Simulations of the thermodynamic properties of the helium fluid from the state-of-the-art ab initio potentials and their uncertainty estimation

ABSTRACT The molecular dynamics simulation method is used to study the internal energy, pressure, isochoric heat capacity, and sound speed of helium based on the state-of-the-art ab initio potentials. The simulations cover a wide temperature and density range of (20–2000) K and (0.0005–70) m o l L − 1 . The uncertainty of simulation data are evaluated based on the uncertainty of the potential and the uncertainty of the simulation method. At temperatures below 300 K, the quantum Feynman-Hibbs modified potential and the Wigner-Kirkwood modified potential are introduced and the results are almost the same as those by the original ab initio potential. The modified potentials can not reasonably describe the quantum effects for the helium fluid at low temperatures, which become obvious below 200 K. The two-body ab initio potential is combined with the three-body ab initio potential to evaluate the influence of multi-body interactions at high densities. When the density is lower than 45 m o l L − 1 , the contribution of the three-body term to our simulation data is not significant. As a result, the three-body potential is omitted in our calculations to improve the overall computational efficiency. The thermodynamic property data of this work show agreement with the experimental data in the literature as well as the NIST Refprop 10.0 data at temperatures above 200 K and densities below 45 m o l L − 1 .

Quantum mechanics based non-bonded force field functions for use in molecular dynamics simulations of materials and systems: The nitrogen and oxygen columns.

Accurate Force Fields (FFs) are essential for Molecular Dynamics (MD) simulations of the dynamics of realistic materials in terms of atomic-level interactions. The FF parameters of short-range valence interactions can be derived through Quantum Mechanical (QM) calculations on model systems practical for QM (<300 atoms). Similarly, the dynamic electrostatic interactions can be described with methods such as QEq or PQEq that allow charges and polarization to adjust dynamically. However, accurately extracting long-range van der Waals (vdW) interactions from QM calculations poses challenges due to the absence of a definitive method to distinguish between the different energetic components of electrostatics, polarization, vdW, hydrogen bonding, and valence interactions. To do this we use the Perdew-Burke-Ernzerhof flavor of Density Functional Theory, including empirical D3 vdW corrections, to predict the Equation of State for each element (keeping any covalent bonds fixed), from which we obtain the two-body vdW nonbond potential. Here, we extend these calculations to include non-bonded parameters for the N and O columns of the periodic table so that we now describe columns 15 (N), 16 (O), 17 (F), and 18 (Ne) of the periodic table. For these 20 elements, we find that the two-body vdW potentials can all be mapped to a single universal two-body curve, with just three scaling parameters: Re, De, and L. We refer to this as the Universal NonBond (UNB) potential. We expect this to be useful for new MD simulations and a helpful starting point to obtain UNB parameters for the remainder of the periodic table.

The Faddeev and Schrödinger approaches to Efimov states—a numerical comparison

We compare effective hyperradial three-body potentials calculated using the S-wave part of the Faddeev equations to calculations using the full Schrödinger equation. As two-body model potential we test both a short-range potential and a Lennard-Jones potential with van der Waals tail. In the former case we find excellent agreement between the two methods for the lowest adiabatic state, indicating that the Faddeev method can be a useful tool also for numerical computations. For excited states the two methods show important differences, but agree for hyperradii larger than about five times the range of the potential (independent of the value of the scattering length and of the number of bound states). For the van der Waals potential, we focus on how well the Faddeev method reproduces the so-called van der Waals universality. We find that indeed the universality is manifest also using this method, but at a slightly different value of the universal parameter . We further derive an efficient method to solve the integro-differential equation arising in the Faddeev method.

Third-order corrections to the ground-state energy of the gas of spin- s fermions with arbitrary densities of different spin projections

Recently, we computed third-order corrections to the ground-state energy of an arbitrarily polarized diluted gas of spin-$\frac{1}{2}$ fermions interacting through a spin-independent repulsive two-body potential. Here we extend this result to the gas of spin-$s$ fermions [a system whose Hamiltonian has an accidental $\text{SU}(2s+1)$ symmetry] with arbitrary densities of fermions having different spin projections. The corrections are computed semianalytically using the effective-field-theory approach and are parametrized by the $s$- and $p$-wave scattering lengths ${a}_{0}$ and ${a}_{1}$ and the $s$-wave effective radius ${r}_{0}$, measurable in the low-energy fermion-fermion elastic scattering. The result is used to study the impact the higher-order corrections can have on the characteristics of the phase transition (at zero temperature) to the ordered phase (on the emergence of the itinerant ferromagnetism).

Hyperspherical Cluster Model for Bosons: Application to Sub-threshold Halo States in Helium Drops

To describe long-range behaviour of one particle removed from a few- or a many-body system, a hyperspherical cluster model has been developed. It has been applied to the ground and first excited states of helium drops with five, six, eight and ten atoms interacting via a two-body soft gaussian potential. Convergence of the hyperspherical cluster harmonics expansion is studied for binding energies, root-mean-squared radii and overlaps of the wave functions of two helium drops differing by one atom. It was shown that with increasing model space the functional form of such overlaps at large distances converges to the correct asymptotic behaviour. The asymptotic normalization coefficients that quantify the overlaps’ amplitudes in this region are calculated. It was also shown that in the first excited state one helium atom stays far apart from the rest forming a two-body molecule, or a halo. The probability of finding the halo atom in the classically-forbidden region of space depends on the definition of the latter and on the valence atom binding energy. The total norm of the overlap integrals, the spectroscopic factor, represents the number of partitions of a many-body state into a chosen state of the system with one particle removed. The spectroscopic factors have been calculated and their sum rules are discussed giving a further insight into the structure of helium drops.

An intermolecular potential for hydrogen: Classical molecular simulation of pressure-density-temperature behavior, vapor-liquid equilibria, and critical and triple point properties.

An intermolecular potential is reported for molecular hydrogen that combines two-body interactions from abinitio data with three-body interactions. The accuracy of the two-body potential is validated by comparison with experimental second virial coefficient data. Experimental pressure-density-temperature data are used to validate the addition of three-body interactions, often yielding very accurate predictions. Classical Monte Carlo simulations that neglect quantum effects are reported for the vapor-liquid equilibria (VLE), critical properties, and the triple point. A comparison with experimental data indicates that the effect of quantum interactions is to narrow the VLE phase envelope and to lower the critical temperature. The three-body interactions have a considerable influence on the phase behavior, resulting in good agreement with the experimental density. The critical properties of the two-body + three-body potential for hydrogen provide an alternative set of input parameters to improve the accuracy of theoretical predictions at temperatures above 100K. In the vicinity of the critical point, the coexistence densities do not obey the law of rectilinear diameters, which is a feature that has largely been overlooked in both experimental data and reference equations of state.