Two-body Binding Energy Research Articles

Two-body binding energy calculation using homogeneous and inhomogeneous Lippmann-Schwinger equations within three-dimensional approach

Bound state equations are mostly solved in partial-wave truncated basis. In partial-wave method, we need to consider many partial waves to reach the accurate results. In this paper, we avoid partial-wave decompositions and directly work with vector variables to solve homogeneous and inhomogeneous Lippmann-Schwinger equations. We study binding energies of deuteron and atomic hydrogen using three-dimensional approach.

Spin–orbit coupling adjusting topological superfluid of mass-imbalanced Fermi gas

Topological superfluid state is different from the normal superfluid one due to the excitation energy gap on the boundary. How to obtain the topological superfluid state by using spin–orbit coupling to control the s-waves paired mass-imbalanced Fermi gas is a recent novel topic. In this paper, we study the topological superfluid phase diagram of two-dimensional mass-imbalanced Fermi gas with Rashba spin–orbit coupling at zero temperature. We find that due to the competition among mass imbalance, pairing interaction and spin–orbit coupling, there is a double-well structure in the thermodynamic potential, which affects the properties of the ground state of the system. We comprehensively give the phase diagrams of the system on the plane of spin–orbit coupling and chemical potential, and the phase diagrams on the plane of the reduced mass ratio and two-body binding energy. This study not only points out the stable region of topological superfluid state of mass-imbalanced Fermi gas, but also provides a detailed theoretical basis for better observation of topological superfluid state in experiments.

A New Feature of the Efimov-Like Structure in the Hadron System: Long-Range Force as a Recoil Effect

On the three-body kinematics, we investigate the threshold behavior which appears not only at the three-body break-up threshold (3BT), but also at the quasi two-body threshold (Q2T) for the reactions: A+(BC)rightarrow A+B+C, and (ABC)rightarrow A+(BC), respectively. Recently, the author proposed a generalparticle {transfer} (GPT) potential which appears, not only at the 3BT, but also at the Q2T between A and (BC). The new potential indicates a Yukawa-type potential for short range, but a 1/r^n-type potential for long range. The long range part of the GPT potential for n=1 indicates an attractive Coulomb-like or a gravitation-like potential. While, n=2 indicates the Efimov-like potential between A and (BC). The three-body binding energy: E_n=epsilon +zeta _n with the two-body binding energy epsilon , and the separation energy zeta _n for (ABC)rightarrow A+(BC) satisfies E_n/E_{n+1}=zeta _n/zeta _{n+1}=const for epsilon =0 or the two-body scattering length: arightarrow infty (i.e. the two-body unitary limit). At the Q2T, the condensation of the three-body binding energy is given by the GPT-potential in the form of E_n/E_{n+1}=(zeta _n+epsilon )/(zeta _{n+1}+epsilon )rightarrow 1 (const) for nrightarrow infty (with zeta _nrightarrow 0) which implies the existence of Efimov-like states at the Q2T in the hadron systems, thereby the possibility of “ultra low energy nuclear transformation”, where the three-body binding energies degenerate at zero energy. Finally, the origin of such a long range potential will be clarified.

Stability of the two-dimensional Fermi polaron

A system composed of an ideal gas of N fermions interacting with an impurity particle in two space dimensions is considered. The interaction between impurity and fermions is given in terms of two-body point interactions whose strength is determined by the two-body binding energy, which is a free parameter of the model. If the mass of the impurity is 1.225 times larger than the mass of a fermion, it is shown that the energy is bounded below uniformly in the number N of fermions. This result improves previous, N-dependent lower bounds and it complements a recent, similar bound for the Fermi polaron in three space dimensions.

Equation of state and Kosterlitz–Thouless transition temperature in two-dimensional Fermi gases: An analytical approach

We study Fermi gases in two dimensions at low temperatures with attractive interactions. Analytic results are derived for the equation of state and the Kosterlitz–Thouless transition temperature as functions of the two-body binding energy and the density of the gas. Our results for the equation of state and the pressure of the gas strongly deviate from the mean field predictions. However, they are in reasonable agreement with Monte-Carlo calculations and recent experiments with cold atomic gases.

Matching universal behavior with potential models

Two-, three-, and four-boson systems are studied close to the unitary limit using potential models constructed to reproduce the minimal information given by the two-body scattering length $a$ and the two-body binding energy or virtual state energy $E_2$. The particular path used to reach the unitary limit is given by varying the potential strength. In this way the energy spectrum in the three- and four-boson systems is computed. The lowest energy states show finite-range effects absorbed in the construction of level functions that can be used to study real systems. Higher energy levels are free from finite-range effects, therefore the corresponding level functions tend to the zero-range universal function. Using this property a zero-range equation for the four-boson system is proposed and the four-boson universal function is computed.

Two-body physics in quasi-low-dimensional atomic gases under spin–orbit coupling

One of the most dynamic directions in ultracold atomic gas research is the study of low-dimensional physics in quasi-low-dimensional geometries, where atoms are confined in strongly anisotropic traps. Recently, interest has significantly intensified with the realization of synthetic spin–orbit coupling (SOC). As a first step toward understanding the SOC effect in quasi-low-dimensional systems, the solution of two-body problems in different trapping geometries and different types of SOC has attracted great attention in the past few years. In this review, we discuss both the scattering-state and the bound-state solutions of two-body problems in quasi-one and quasi-two dimensions. We show that the degrees of freedom in tightly confined dimensions, in particular with the presence of SOC, may significantly affect system properties. Specifically, in a quasi-one-dimensional atomic gas, a one-dimensional SOC can shift the positions of confinement-induced resonances whereas, in quasitwo- dimensional gases, a Rashba-type SOC tends to increase the two-body binding energy, such that more excited states in the tightly confined direction are occupied and the system is driven further away from a purely two-dimensional gas. The effects of the excited states can be incorporated by adopting an effective low-dimensional Hamiltonian having the form of a two-channel model. With the bare parameters fixed by two-body solutions, this effective Hamiltonian leads to qualitatively different many-body properties compared to a purely low-dimensional model.

Fulde-Ferrell-Larkin-Ovchinnikov state of two-dimensional imbalanced Fermi gases

The ground-state phase diagram of attractively-interacting Fermi gases in two dimensions with a population imbalance is investigated. We find the regime of stability for the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, in which pairing occurs at finite wave vector, and determine the magnitude of the pairing amplitude $\Delta$ and FFLO wavevector $q$ in the ordered phase, finding that $\Delta$ can be of the order of the two-body binding energy. Our results rely on a careful analysis of the zero temperature gap equation for the FFLO state, which possesses nonanalyticities as a function of $\Delta$ and $q$, invalidating a Ginzburg-Landau expansion in small $\Delta$.

Quantum phase transitions and Berezinskii-Kosterlitz-Thouless temperature in a two-dimensional spin-orbit-coupled Fermi gas

We study the effect of spin-orbit coupling on both the zero-temperature and non-zero temperature behavior of a two-dimensional (2D) Fermi gas. We include a generic combination of Rashba and Dresselhaus terms into the system Hamiltonian, which allows us to study both the experimentally relevant equal-Rashba-Dresselhaus (ERD) limit and the Rashba-only (RO) limit. At zero temperature, we derive the phase diagram as a function of the two-body binding energy and Zeeman field. In the ERD case, this phase diagram reveals several topologically distinct uniform superfluid phases, classified according to the nodal structure of the quasiparticle excitation energies. Furthermore, we use a momentum dependent SU(2)-rotation to transform the system into a generalized helicity basis, revealing that spin-orbit coupling induces a triplet pairing component of the order parameter. At non-zero temperature, we study the Berezinskii-Kosterlitz-Thouless (BKT) phase transition by including phase fluctuations of the order parameter up to second order. We show that the superfluid density becomes anisotropic due to the presence of spin-orbit coupling (except in the RO case). This leads both to elliptic vortices and antivortices, and to anisotropic sound velocities. The latter prove to be sensitive to quantum phase transitions between topologically distinct phases. We show further that at a fixed non-zero Zeeman field, the BKT critical temperature is increased by the presence of ERD spin-orbit coupling. Subsequently, we demonstrate that the Clogston limit becomes infinite: $T_{\rm{BKT}}$ remains non-zero at all finite values of the Zeeman field. We conclude by extending the quantum phase transition lines to non-zero temperature, using the nodal structure of the quasiparticle spectrum, thus connecting the BKT critical temperature with the zero-temperature results.

Fixed-node diffusion Monte Carlo study of the BCS-BEC crossover in a bilayer system of fermionic dipoles

We investigate the BCS-BEC crossover in a bilayer system of fermionic dipoles at zero temperature using the fixed-node diffusion Monte Carlo technique. The dipoles are confined on two parallel planes separated by a distance $\lambda$ and are aligned perpendicular to the planes by an external field. The interlayer pairing, which is responsible for the superfluid behavior of the system, crosses from a weak to a strong-coupling regime by reducing the separation distance $\lambda$. For a fixed in-plane density, equal in the two layers, we calculate the ground-state energy, the chemical potential, the pairing gap and the quasiparticle dispersion as a function of the interlayer separation. At large $\lambda$ one recovers the ground-state energy of a single layer of fermions and at small $\lambda$ the one of a single layer of composite bosons with twice the particle mass and the dipole moment. The superfluid gap varies instead from the exponentially small BCS result to half of the large two-body binding energy in the BEC regime of strong interlayer pairing. Results are compared with the predictions of the simplest mean-field theory valid in the low-density limit and deviations are observed both in the BCS regime, where in-plane repulsions are important, and in the BEC regime where the mean-field approach fails to describe the physics of composite dipolar bosons.

Effects of spin-orbit coupling on the Berezinskii-Kosterlitz-Thouless transition and the vortex-antivortex structure in two-dimensional Fermi gases.

We investigate the Berezinskii-Kosterlitz-Thouless (BKT) transition in a 2D Fermi gas with spin-orbit coupling (SOC), as a function of the two-body binding energy and a perpendicular Zeeman field. By including a generic form of the SOC, as a function of Rashba and Dresselhaus terms, we study the evolution between the experimentally relevant equal Rashba-Dresselhaus (ERD) case and the Rashba-only (RO) case. We show that in the ERD case, at a fixed nonzero Zeeman field, the BKT transition temperature T(BKT) is increased by the presence of SOC for all values of the binding energy. We also find a significant increase in the value of the Clogston limit compared to the case without SOC. Furthermore, we demonstrate that the superfluid density tensor becomes anisotropic (except in the RO case), leading to an anisotropic phase-fluctuation action that describes elliptic vortices and antivortices, which become circular in the RO limit. This deformation constitutes an important experimental signature for superfluidity in a 2D Fermi gas with ERD SOC. Finally, we show that the anisotropic sound velocities exhibit anomalies at low temperatures, in the vicinity of quantum phase transitions between topologically distinct uniform superfluid phases.

Scale breaking and fluid dynamics in a dilute two-dimensional Fermi gas

We study two observables related to the anomalous breaking of scale invariance in a dilute two-dimensional Fermi gas, the frequency shift and damping rate of the monopole mode in a harmonic confinement potential. For this purpose we compute the speed of sound and the bulk viscosity of the two-dimensional gas in the high-temperature limit. We show that the anomaly in the speed of sound scales as $(2P\ensuremath{-}\ensuremath{\rho}{c}_{s}^{2})/P\ensuremath{\sim}z/{[\mathrm{ln}(T/{E}_{B})]}^{2}$ and that the bulk viscosity $\ensuremath{\zeta}$ scales as $\ensuremath{\zeta}/\ensuremath{\eta}\ensuremath{\sim}{z}^{2}/{[\mathrm{ln}(T/{E}_{B})]}^{6}$. Here, $P$ is the pressure, ${c}_{s}^{2}$ is the speed of sound, $\ensuremath{\eta}$ is the shear viscosity, $z$ is the fugacity, and ${E}_{B}$ is the two-body binding energy. We show that our results are consistent with the experimental results of Vogt, Feld, Fr\"ohlich, Pertot, Koschorreck, and K\"ohl [Phys. Rev. Lett. 108, 070404 (2012)]. Vogt et al. reported a frequency shift $\ensuremath{\delta}\ensuremath{\omega}/\ensuremath{\omega}$ of the order of a few percent and a damping rate smaller than the background rate $\ensuremath{\Gamma}/{\ensuremath{\omega}}_{0}\ensuremath{\sim}5%$.

Significance of dressed molecules in a quasi-two-dimensional Fermi gas with spin-orbit coupling

We investigate the properties of a spin-orbit coupled quasi-two-dimensional Fermi gas with tunable $s$-wave interaction between the two spin species. By analyzing the two-body bound state, we find that the population of the excited states in the tightly confined axial direction can be significant when the two-body binding energy becomes comparable to or exceeds the axial confinement. Since the Rashba spin-orbit coupling that we study here tends to enhance the two-body binding energy, this effect can become prominent at unitarity or even on the BCS side of the Feshbach resonance. To study the impact of these excited modes along the third dimension, we adopt an effective two-dimensional Hamiltonian in the form of a two-channel model, where the dressed molecules in the closed channel consist of the conventional Feshbach molecules as well as the excited states occupation in the axial direction. With properly renormalized interactions between atoms and dressed molecules, we find that both the density distribution and the phase structure in the trap can be significantly modified near a wide Feshbach resonance. In particular, the stability region of the topological superfluid phase is increased. Our findings provide a proper description for a quasi-two-dimensional Fermi gas under spin-orbit coupling, and are helpful for the experimental search for the topological superfluid phase in ultracold Fermi gases.

Superfluidity in two-dimensional imbalanced Fermi gases

We study the zero temperature ground state of a two-dimensional atomic Fermi gas with chemical potential and population imbalance in the mean-field approximation. All calculations are performed in terms of the two-body binding energy ϵB, whose variation allows one to investigate the evolution from the BEC to the BCS regimes. By means of analytical and exact expressions we show that, similarly to what is found in three dimensions, at fixed chemical potentials, BCS is the ground state until the critical imbalance hc, after which there is a first-order phase transition to the normal state. We find that hc, the Chandrasekhar–Clogston limit of superfluidity, has the same value as in three-dimensional systems. We show that for a fixed ratio ϵB/ϵF, where ϵF is the two-dimensional Fermi energy, as the density imbalance m is increased from zero, the ground state evolves from BCS to phase separation to the normal state. At the critical imbalance mc, phase separation is not supported and the normal phase is energetically preferable. The BCS–BEC crossover is discussed in balanced and imbalanced configurations. Possible pictures of what may be found experimentally in these systems are also shown. We also investigate the necessary conditions for the existence of bound states in the balanced and imbalanced normal phase.

Finite-temperature phase diagram of quasi-two-dimensional imbalanced Fermi gases beyond mean field

We investigate the superfluid transition temperature of quasi-two-dimensional imbalanced Fermi gases beyond the mean-field approximation, through the second-order (or induced) interaction effects. For a balanced Fermi system the transition temperature is suppressed by a factor $\approx 2.72$. For imbalanced Fermi systems, the polarization and transition temperature of the tricritical point are significantly reduced as the two-body binding energy $|\epsilon_B|$ increases.

Evolution of Fermion Pairing from Three to Two Dimensions

We follow the evolution of fermion pairing in the dimensional crossover from three-dimensional to two-dimensional as a strongly interacting Fermi gas of ^{6}Li atoms becomes confined to a stack of two-dimensional layers formed by a one-dimensional optical lattice. Decreasing the dimensionality leads to the opening of a gap in radio-frequency spectra, even on the Bardeen-Cooper-Schrieffer side of a Feshbach resonance. The measured binding energy of fermion pairs closely follows the theoretical two-body binding energy and, in the two-dimensional limit, the zero-temperature mean-field Bose-Einstein-condensation to Bardeen-Cooper-Schrieffer crossover theory.

Two‐step evaluation of binding energy and potential energy surface of van der Waals complexes

Evaluation of intermolecular distance and binding energy (BE) of van der Waals complex/cluster at ab initio level of theory is computationally demanding when many monomers are involved. Starting from MP2 energy, we reached a two-step evaluation method of BE of van der Waals complex/cluster through reasonable approximations; BE = BE(HF) + sum Mi> Mj{BE (Mi- Mj)(MP2 or MP2.5) - BE(Mi-Mj)(HF)} where HF represents the Hartree-Fock calculation, Mi, Mj, etc. are interacting monomers, and MP2.5 represents the arithmetic mean of MP2 and MP3. The first term is the usual BE of the complex/cluster evaluated at the HF level. The second term is the sum of the difference in two-body BE between the correlated and HF levels of theory. This equation was applied to various van der Waals complexes consisting of up-to-four monomers at MP2 and MP2.5 levels of theory. We found that this method is capable of providing precise estimate of the BE and reproducing well the potential energy surface of van der Waals complexes/clusters; the maximum error of the BE is less than 1 kcal/mol and 1% in most cases except for several limited cases. The origins of error in these cases are discussed in detail.

Improving the volume dependence of two-body binding energies calculated with lattice QCD

Volume modifications to the binding of two-body systems in large cubic volumes of extent L depend upon the total momentum and exponentially upon the ratio of L to the size of the boosted system. Recent work by Bour et al determined the momentum dependence of the leading volume modifications to nonrelativistic systems with periodic boundary conditions imposed on the single-particle wavefunctions, enabling them to numerically determine the scattering of such bound states using a low-energy effective field theory and Luscher's finite-volume method. The calculation of bound nuclear systems directly from QCD using Lattice QCD has begun, and it is important to reduce the systematic uncertainty introduced into such calculations by the finite spatial extent of the gauge-field configurations. We extend the work of Bour et al from nonrelativistic quantum mechanics to quantum field theory by generalizing the work of Luscher and of Gottlieb and Rummukainen to boosted two-body bound states. The volume modifications to binding energies can be exponentially reduced from ~ e^{-kappa L}/L to ~ e^{-2 kappa L}/L in nonrelativistic systems (where kappa is the binding momentum of the state) by forming particular combinations of the binding energies determined in the four lowest-lying boosted systems. Relativistic corrections to this combination, and others, that violate the exponential reduction are determined. An analysis of what can be expected from Lattice QCD calculations of the deuteron is performed, the results of which are representative of a generic loosely bound system.

Efimov effect in 2-neutron halo nuclei

This paper presents an overview of our theoretical investigations in search of Efimov states in light 2-neutron halo nuclei. The calculations have been carried out within a three-body formalism, assuming a compact core and two valence neutrons forming the halo. The calculations provide strong evidence for the occurrence of at least two Efimov states in 20C nucleus. These excited states move into the continuum as the two-body (core-neutron) binding energy is increased and show up as asymmetric resonances in the elastic scattering cross-section of the n-19C system. The Fano mechanism is invoked to explain the asymmetry. The calculations have been extended to 38Mg, 32Ne and a hypothetical case of a very heavy core (A = 100) with two valence neutrons. In all these cases the Efimov states show up as resonances as the two-body energy is increased. However, in sharp contrast, the Efimov states, for a system of three equal masses, show up as virtual states beyond a certain value of the two-body interaction.

Quantum chemical study of dissociation of H2 on C3 H3 V organometallic compound

We have studied H2 adsorption on C3H3V organometallic compound using density functional method at B3LYP/LanL2Dz level of theory. It was found that H2 molecule dissociates and adsorbed in dihydride form on this organometallic compound. Potential energy surface for H2 dissociation process was obtained and different properties such as HOMO–LUMO gap, dipole moment, interaction energies between different molecules and atoms, vibrational frequencies, and atomic charges during the dissociation process were studied. It was found that the C3H3V(H2) structure is most stable at HVH angle of 66.3°. Many-body analysis was also carried out to determine the two-body energies, three-body energies, relaxation energy, and binding energy of the structures for each point on the potential surface. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010