Short-range Two-body Potential Research Articles

Large-N properties of a non-ideal Bose gas

We rigorously discuss the large- thermodynamics of a Bose gas with a short-range two-body potential. Considering the system as a mixture of identical components with a symmetric interaction we calculate numerically the temperature dependence of the leading-order corrections to the depletion of the Bose–Einstein condensate and to the isothermal compressibility.

Exact Evolution versus mean field with second-order correction for Bosons interacting via short-range two-body potential

We consider the evolution of $N$ bosons, where $N$ is large, with two-body interactions of the form $N^{3\beta}v(N^{\beta}\mathbf{\cdot})$, $0\leq\beta\leq 1$. The parameter $\beta$ measures the strength of interactions. We compare the exact evolution with an approximation which considers the evolution of a mean field coupled with an appropriate description of pair excitations, see [25, 26]. For $0\leq \beta < 1/2$, we derive an error bound of the form $p(t)/N^\alpha$, where $\alpha>0$ and $p(t)$ is a polynomial, which implies a specific rate of convergence as $N\rightarrow\infty$.

Harmonically trapped two-atom systems: Interplay of short-ranges-wave interaction and spin-orbit coupling

The coupling between the spin degrees of freedom and the orbital angular momentum has a profound effect on the properties of nuclei, atoms and condensed matter systems. Recently, synthetic gauge fields have been realized experimentally in neutral cold atom systems, giving rise to a spin-orbit coupling term with "strength" $k_{\text{so}}$. This paper investigates the interplay between the single-particle spin-orbit coupling term of Rashba type and the short-range two-body $s$-wave interaction for cold atoms under external confinement. Specifically, we consider two different harmonically trapped two-atom systems. The first system consists of an atom with spin-orbit coupling that interacts with a structureless particle through a short-range two-body potential. The second system consists of two atoms that both feel the spin-orbit coupling term and that interact through a short-range two-body potential. Treating the spin-orbit term perturbatively, we determine the correction to the ground state energy for various generic parameter combinations. Selected excited states are also treated. An important aspect of our study is that the perturbative treatment is not limited to small $s$-wave scattering lengths but provides insights into the system behavior over a wide range of scattering lengths, including the strongly-interacting unitary regime. Our perturbative results are confirmed by numerical calculations that expand the eigenfunctions of the two-particle Hamiltonian in terms of basis functions that contain explicitly correlated Gaussians.

Nonuniversal bound states of two identical heavy fermions and one light particle

We study the behavior of the bound-state energy of a system consisting of two identical heavy fermions of mass $M$ and a light particle of mass $m$. The heavy fermions interact with the light particle through a short-range two-body potential with positive $s$-wave scattering length ${a}_{s}$. We impose a short-range boundary condition on the logarithmic derivative of the hyperradial wave function and show that, in the regime where Efimov states are absent, a nonuniversal three-body state cuts through the universal three-body states previously described by Kartavtsev and Malykh [O. I. Kartavtsev and A. V. Malykh, J. Phys. B 40, 1429 (2007)]. The presence of the nonuniversal state alters the behavior of the universal states in certain regions of the parameter space. We show that the existence of the nonuniversal state is predicted accurately by a simple quantum defect theory model that utilizes hyperspherical coordinates. An empirical two-state model is employed to quantify the coupling of the nonuniversal state to the universal states.

Trapped polarized Fermi gas at unitarity

We consider population-imbalanced two-component Fermi gases under external harmonic confinement interacting through short-range two-body potentials with diverging s-wave scattering length. Using the fixed-node diffusion Monte Carlo method, the energies of the normal are determined as functions of the population-imbalance and the number of particles. The energies of the trapped system follow, to a good approximation, a universal curve even for fairly small systems. A simple parameterization of the universal curve is presented and related to the equation of state of the bulk system.

Stability of inhomogeneous multicomponent Fermi gases

Two-component equal-mass Fermi gases, in which unlike atoms interact through a short-range two-body potential and like atoms do not interact, are stable even when the interspecies $s$-wave scattering length becomes infinitely large. Solving the many-body Schr\"odinger equation within a hyperspherical framework and by Monte Carlo techniques, this paper investigates how the properties of trapped two-component gases change if a third or fourth component are added. If all interspecies scattering lengths are equal and negative, our calculations suggest that both three- and four-component Fermi gases become unstable for a certain critical set of parameters. The relevant length scale associated with the collapse is set by the interspecies scattering length and we argue that the collapse is similar to the collapse of an attractive trapped Bose gas, a many-body phenomenon. Furthermore, we consider a three-component Fermi gas in which two interspecies scattering lengths are negative while the other interspecies scattering length is zero. In this case, the stability of the Fermi system is predicted to depend appreciably on the range of the underlying two-body potential. We find parameter combinations for which the system appears to become unstable for a finite negative scattering length and parameter combinations for which the system appears to be made up of weakly bound trimers that consist of one fermion of each species.

An analytical potential energy function to model protonated peptide soft-landing experiments. The CH3NH3+/CH4 interactions

To model soft-landing of peptide ions on surfaces, it is important to have accurate intermolecular potentials between these ions and surfaces. As part of this goal, ab initio calculations at the MP2/aug-cc-pVTZ level of theory, with basis set superposition error (BSSE) corrections, were performed to determine both the long-range attractive and short-range repulsive potentials for CH(4) interacting with the -NH(3)(+) group of CH(3)NH(3)(+). Potential energy curves for four different orientations between CH(4) and CH(3)NH(3)(+) were determined from the calculations to obtain accurate descriptions of the interactions between the atoms of CH(4) and those of -NH(3)(+). A universal analytic function was not found that could accurately represent both the long-range and short-range potentials for collision energies as high as those obtained in surface-induced-dissociation (SID) experiments. Instead, long-range and short-range analytic potentials were developed separately, by simultaneously fitting the four ab initio potential energy curves with a sum of two-body interactions between the atoms of CH(4) and -NH(3)(+), and then connecting these long-range and short-range two-body potentials with switching functions. Following a previous work [J. Am. Chem. Soc., 2002, 124, 1524], these two-body potentials may be used to describe the interactions of the N and H atoms of the -NH(3)(+) group of a protonated peptide ion with the H and C atoms of alkane-type surfaces such as alkyl thiol self-assembled monolayers and H-terminated diamond. Accurate short-range and long-range potentials are imperative to model protonated peptide ion soft-landing experiments. The former controls the collision energy transfer, whereas the latter describes the binding of the ion to the surface. A comparison of the ab initio potential energy curves for CH(3)NH(3)(+)/CH(4) with those for NH(4)(+)/CH(4) shows that they give nearly identical two-body interactions between the atoms of -NH(3)(+) and those of CH(4), showing that the smaller NH(4)(+)/CH(4) system may be used to obtain the two-body potentials. A comparison of the four ab initio potential energy curves reported here for CH(3)NH(3)(+)/CH(4), with those given by the AMBER and CHARMM molecular mechanical potentials, show that these latter potentials "roughly" approximate the long-range attractions, but are grossly in error for the short-range repulsions. The work reported here illustrates that high-level ab initio calculations of intermolecular potentials between small model molecules may be used to develop accurate analytical intermolecular potentials between peptide ions and surfaces.

Three-body halos: Gross properties.

Three-body bound systems are investigated in the limit of very weak binding by use of hyperspherical harmonics. The short-range two-body potentials are assumed to be unable to bind the binary subsystems. Then the mean square radius always converges for vanishing binding except for the most spherical wave function, where all angular momenta involved are zero, which diverges logarithmically. Universal scaling properties are suggested. Any additional long-range repulsive potential, like, for example, the Coulomb potential, leads to finite radial moments even for vanishing binding. Spatially extended charged halos are only possible for very low charges. The spatial extension of three-body systems is in the asymptotic region more confined than for corresponding two-body systems, where the divergences are stronger and more abundant. Numerical examples and transitions to the asymptotic region are shown for square well and Gaussian two-body potentials. The results are applied to several drip-line nuclei.

Phonon dispersion curves and densities of lithium-intercalated iron phosphorus trisulfide

The lattice dynamics of Li-intercalated FePS3 has been studied by means of a force constant model generated by a set of short-range two-body potentials. The intercalated phases have been investigated for the three stoichiometric compositions: Li0.5FePS3, LiFePS3, Li1.5FePS3, with the aim of analysing the evolution of the host lattice normal modes as a function of the concentration, and of finding the dispersion of the new phonon branches induced by lithium. The above special values of lithium concentration have been chosen because the size of the unit cell keeps the same as in the host material. The force constants are fitted to the infrared data and the phonon dispersion curves and the phonon energy densities have been calculated. A spectroscopic method for monitoring lithium migration in the host material is proposed.

Lattice dynamics of lithium-intercalated iron phosphorus trisulphide

We review the recent investigations on the lattice dynamics of lithium-intercalated FePS 3. These studies represent an extension of those made for the pure material and have been performed by means of a force-constant model generated by a set of short-range two-body potentials. The intercalated phases have been investigated for the three stoichiometric compositions Li 0.5FePS 3, LiFePS 3 and Li 1.5FePS 3 with the aim of analysing the evolution of the host lattice normal modes as a function of the concentration, and finding the dispersion of the new phonon branches induced by lithium. The above special values of lithium concentration have been chosen because the size of the unit cell remains the same as in the host material. The interaction between lithium and sulphur includes only nearest neighbours and is also described by a two-body potential. The Li-Li interaction is described by a Born-Mayer potential. The choice of this simplified model is dictated by the limited number of experimental data: these are the Raman and infrared data for the host material and only the infrared data for the intercalated phases. The force constants of lithium are fitted to these data and the phonon dispersion curves are calculated along the symmetry directions of the Brillouin zone. A spectroscopic method for monitoring lithium migration in the host material is proposed.

The ground state for soft disks

We consider some two-dimensional models of point particles interacting through short-range two-body potentials and prove that their zero temperature, zero pressure states are crystalline.