Showing papers on "Cluster expansion published in 2009"
TL;DR: In this paper, the authors proposed an improved cluster expansion procedure that systematically leads to optimal selections of both clusters and DFT structures to cover as much of the configurational space as possible.
Abstract: The cluster expansion (CE) method has been used to evaluate configurational properties in multicomponent systems based on the density-functional theory (DFT) calculations. Appropriate selections of not only clusters but also structures for DFT calculations (DFT structures) are crucial for the accuracy and the efficiency of the CE. In a conventional procedure to construct the CE, the CE error is reduced mainly through an appropriate selection of clusters. In the present paper, we propose an improved procedure that systematically leads to optimal selections of both clusters and DFT structures. DFT structures are chosen to cover as much of the configurational space as possible. During the iterative process, the predictive power of the out-of-sample structures can be increased up to the accuracy that is required to describe alloy thermodynamics. We apply the procedure to configurational behaviors in a simple MgO-ZnO pseudobinary system and in a complex ${\text{MgAl}}_{2}{\text{O}}_{4}$ system. The CE error is reduced in both systems, in particular, in the complex system, thereby significantly improving configurational properties at high temperatures compared with the conventional CE procedure.
116 citations
TL;DR: The package reduces the need for user intervention, automating the method to reduce human error and judgment, and extends standard cluster expansion formalism to the more complicated cases of ternary compounds, as well as surfaces, including adsorption and inequivalent sites.
Abstract: We present a new implementation of the cluster expansion formalism. The new code, UNiversal CLuster Expansion (UNCLE), consolidates recent advances in the methodology and leverages one new development in the formalism itself. As a core goal, the package reduces the need for user intervention, automating the method to reduce human error and judgment. The package extends standard cluster expansion formalism to the more complicated cases of ternary compounds, as well as surfaces, including adsorption and inequivalent sites.
107 citations
TL;DR: A Bayesian framework for developing cluster expansions that explicitly incorporates physical insight into the fitting procedure is presented and methods that significantly improve the predictive power of cluster expansions for a given training set size are developed.
Abstract: Cluster expansions have proven to be a valuable tool in alloy theory and other problems in materials science but the generation of cluster expansions can be a computationally expensive and time-consuming process. We present a Bayesian framework for developing cluster expansions that explicitly incorporates physical insight into the fitting procedure. We demonstrate how existing methods fit within this framework and use the framework to develop methods that significantly improve the predictive power of cluster expansions for a given training set size. The key to the methods is to apply physical insight and cross validation to develop physically meaningful prior probability distributions for the cluster expansion coefficients. We use the Bayesian approach to develop an efficient method for generating cluster expansions for low-symmetry systems such as surfaces and nanoparticles.
103 citations
TL;DR: The infrared spectrum can be computed, to a very good approximation, within D(2d) symmetry, instead of the G(16) symmetry used before, in which the complete rotation of one water molecule with respect to the other is allowed, thus simplifying the dynamical problem.
Abstract: Quantum dynamical calculations are reported for the zero point energy, several low-lying vibrational states, and the infrared spectrum of the H(5)O(2)(+) cation. The calculations are performed by the multiconfiguration time-dependent Hartree (MCTDH) method. A new vector parametrization based on a mixed Jacobi-valence description of the system is presented. With this parametrization the potential energy surface coupling is reduced with respect to a full Jacobi description, providing a better convergence of the n-mode representation of the potential. However, new coupling terms appear in the kinetic energy operator. These terms are derived and discussed. A mode-combination scheme based on six combined coordinates is used, and the representation of the 15-dimensional potential in terms of a six-combined mode cluster expansion including up to some 7-dimensional grids is discussed. A statistical analysis of the accuracy of the n-mode representation of the potential at all orders is performed. Benchmark, fully converged results are reported for the zero point energy, which lie within the statistical uncertainty of the reference diffusion Monte Carlo result for this system. Some low-lying vibrationally excited eigenstates are computed by block improved relaxation, illustrating the applicability of the approach to large systems. Benchmark calculations of the linear infrared spectrum are provided, and convergence with increasing size of the time-dependent basis and as a function of the order of the n-mode representation is studied. The calculations presented here make use of recent developments in the parallel version of the MCTDH code, which are briefly discussed. We also show that the infrared spectrum can be computed, to a very good approximation, within D(2d) symmetry, instead of the G(16) symmetry used before, in which the complete rotation of one water molecule with respect to the other is allowed, thus simplifying the dynamical problem.
95 citations
TL;DR: A general setting for the cluster expansion method is formulated and sufficient criteria for its convergence is discussed, and the results are applied to systems of classical and quantum particles with stable interactions.
Abstract: We formulate a general setting for the cluster expansion method and we discuss sufficient criteria for its convergence. We apply the results to systems of classical and quantum particles with stable interactions.
77 citations
TL;DR: In this article, first principles phase diagram calculations for the binary systems HfC-TiC, TiC-ZrC, and Hfc-XRC are presented.
Abstract: We report first-principles phase diagram calculations for the binary systems HfC–TiC, TiC–ZrC, and HfC–ZrC. Formation energies for superstructures of various bulk compositions were computed with a plane-wave pseudopotential method. They in turn were used as a basis for fitting cluster expansion Hamiltonians, both with and without approximations for excess vibrational free energies. Significant miscibility gaps are predicted for the systems TiC–ZrC and HfC–TiC, with consolute temperatures in excess of 2000 K. The HfC–ZrC system is predicted to be completely miscibile down to 185 K. Reductions in consolute temperature due to excess vibrational free energy are estimated to be ~7%, ~20%, and ~0%, for HfC–TiC, TiC–ZrC, and HfC–ZrC, respectively. Predicted miscibility gaps are symmetric for HfC–ZrC, almost symmetric for HfC–TiC and asymmetric for TiC–ZrC.
62 citations
TL;DR: In this article, structural disorder in the Co- and Mn-sublattices of the full Heusler alloy Co2 xMn1+xSi ( 1 � x � 2) is investigated with a cluster expansion approach, parametrized using all-electron density functional theory calculations.
Abstract: Previous studies indicated that intrinsic point defects play a crucial role for the density of states of ferromagnetic half-metals in the band gap region: at large concentrations, defect-derived bands might close the gap at the Fermi energy in the minority spin channel. In this work, structural disorder in the Co- and Mn-sublattices of the full Heusler alloy Co2 xMn1+xSi ( 1 � x � 2) is investigated with a cluster expansion approach, parametrized using all-electron density functional theory calculations. By establishing two separate cluster expansions, one for the formation energy and one for the total spin moment, we are in a position to determine the stability of different configurations, to predict new (also half-metallic) ground states and to extend the known SlaterPauling rule for ideally stoichiometric Heusler alloys to non-stoichiometric, Mn-rich compositions. This enables us to identify potentially half-metallic structures in the Mn-rich region. With the help of Monte Carlo simulations based on the cluster expansion, we establish theoretically that Co2 xMn1+xSi close to the stoichiometric composition ought to show a high degree of structural order in thermodynamic equilibrium. Hence, samples prepared with the correct stoichiometry should indeed be half-metallic after thermal annealing. Moreover, we predict that adding a small amount of Mn to stoichiometric Co2MnSi allows suppression of the thermally activated formation of detrimental Co antisites. At Mn-rich compositions (x > 1), the ordered ground state structures predicted for zero temperature are found to be thermally unstable and to decompose into Co2MnSi and Mn3Si above room temperature.
57 citations
TL;DR: Streaming potential changes induced by deposition of particles at solid/liquid interfaces are considered theoretically and a virial expansion of the streaming potential up to the third order of the surface coverage of particles is obtained.
Abstract: Streaming potential changes induced by deposition of particles at solid/liquid interfaces are considered theoretically. The solution is obtained in terms of a virial expansion of the streaming potential up to the third order of the surface coverage of particles, assumed to be distributed according to the hard sphere equilibrium distribution function. Theoretical methods, including the idea of cluster expansion, are adopted from statistical physics. In the cluster expansion, two-body and three-body hydrodynamic interactions are evaluated with a high precision using the multipole method. The multipole expansion algorithm is also used to perform numerical simulations of the streaming potential, valid for the entire surface coverage range met in practice. Results of our calculations are in good agreement with the experimental data for spherical latex particles adsorbed on a mica surface.
47 citations
TL;DR: In this article, a new method for simulating magnetic alloys characterized by configurational disorder, the magnetic cluster expansion, is presented, where each atom in an alloy is assigned a discrete variable denoting the atomic species, and the (continuous) magnetic moment.
46 citations
TL;DR: A new multireference cluster expansion ansatz for the wave operator with the above generally noncommuting cluster operators which essentially has the same physical content as the Jeziorski-Monkhorst ansatz with the commuting cluster operators defined in the spin-orbital basis.
Abstract: In this paper, we present a comprehensive account of an explicitly spin-free compact state-universal multireference coupled cluster (CC) formalism for computing the state energies of simple open-shell systems, e.g., doublets and biradicals, where the target open-shell states can be described by a few configuration state functions spanning a model space. The cluster operators in this formalism are defined in terms of the spin-free unitary generators with respect to the common closed-shell component of all model functions (core) as vacuum. The spin-free cluster operators are either closed-shell-like n hole-n particle excitations (denoted by Tμ) or involve excitations from the doubly occupied (nonvalence) orbitals to the singly occupied (valence) orbitals (denoted by Seμ). In addition, there are cluster operators with exchange spectator scatterings involving the valence orbitals (denoted by Sreμ). We propose a new multireference cluster expansion ansatz for the wave operator with the above generally noncommu...
41 citations
TL;DR: In this article, two-dimensional cluster expansions are used to extend a small density functional theory database of oxygen adsorption energies on Au and Pt (111) surfaces to explore a wide range of configurational space in larger unit cells than can be conveniently examined by DFT.
Abstract: We utilise two-dimensional cluster expansions in order to extend a small density functional theory (DFT) database of oxygen adsorption energies on Au and Pt (111) surfaces to explore a wide range of configurational space in larger unit cells than can be conveniently examined by DFT. We calculate adsorption energies and heats of formation for all configurations of up to 15 adsorption sites using the cluster expansions. We show how the cluster expansion adsorption energies obey the configurational correlation previously observed for the DFT results. The ramifications of figure selection are considered and the use of cross-validation scores to weigh figure sets and determine predictive power is examined. Finally, we show that there are only a small number of structural motifs needed to describe the most relevant structures in the phase diagram on these metals.
TL;DR: In this paper, the authors consider Gibbs measures for which the reference measure is Wiener measure and the interaction is given by a double stochastic integral and a pinning external potential, and prove existence and basic properties of such Gibbs measures in the small coupling regime by means of cluster expansion.
Abstract: Motivated by applications to quantum field theory we consider Gibbs measures for which the reference measure is Wiener measure and the interaction is given by a double stochastic integral and a pinning external potential. In order properly to characterize these measures through DLR equations, we are led to lift Wiener measure and other objects to a space of configurations where the basic observables are not only the position of the particle at all times but also the work done by test vector fields. We prove existence and basic properties of such Gibbs measures in the small coupling regime by means of cluster expansion.
TL;DR: The resulting fully six-dimensional potential energy function reproduces the correct symmetry under permutation of identical atoms and predicts the main stationary points of the molecule in the valence and long-range regions in good agreement with available experimental and theoretical data on the diazene molecule.
Abstract: A global single-sheeted double many-body expansion potential energy surface is reported for the ground electronic state of N(2)H(2). Starting from an approximate cluster expansion of the molecular potential that utilizes previously reported functions of the same family for the triatomic fragments, four-body energy terms have been calibrated from extensive accurate ab initio data so as to reproduce the main features of the title system. The switching function formalism previously suggested for three-body systems [A. J. C. Varandas and L. Poveda, Theor. Chem. Acc. 116, 404 (2006)] has been generalized to approximate the true multisheeted nature of N(2)H(2) potential energy surface, thus allowing the correct behavior at the N((2)D) + NH(2)((2)A(")) and N((4)S) + NH(2)((4)A(")) dissociation limits. The resulting fully six-dimensional potential energy function reproduces the correct symmetry under permutation of identical atoms and predicts the main stationary points of the molecule in the valence and long-range regions in good agreement with available experimental and theoretical data on the diazene molecule.
TL;DR: Clustering estimates for the truncated correlations, i.e., cumulants of an unbounded spin system on the lattice, are proved and a unified treatment of four different regimes is provided, based on cluster expansion techniques, of large mass, small interaction between sites, large self-interaction, as well as the more delicate small self-Interaction or near massive Gaussian regime.
Abstract: We prove clustering estimates for the truncated correlations, i.e., cumulants of an unbounded spin system on the lattice. We provide a unified treatment, based on cluster expansion techniques, of four different regimes: large mass, small interaction between sites, large self-interaction, as well as the more delicate small self-interaction or near massive Gaussian regime. A clustering estimate in the latter regime is needed for the Bosonic case of the recent result obtained by Lukkarinen and Spohn on the rigorous control on kinetic scales of quantum fluids.
TL;DR: In this article, the stability of anyonic models on lattices to perturbations was studied and the spectral gap was shown to be stable when the model is defined on a sphere, so that there is no ground state degeneracy.
Abstract: We study the stability of anyonic models on lattices to perturbations. We establish a cluster expansion for the energy of the perturbed models and use it to study the stability of the models to local perturbations. We show that the spectral gap is stable when the model is defined on a sphere, so that there is no ground state degeneracy. We then consider the toric code Hamiltonian on a torus with a class of abelian perturbations and show that it is stable when the torus directions are taken to infinity simultaneously, and is unstable when the thin torus limit is taken.
TL;DR: In this article, the Van Kampen cluster expansion method is adapted to the problem of resuming the commutator expansion arising in a canonical transformation upon the Hamiltonian operator of a many-electron system.
Abstract: The Van Kampen cluster expansion method is adapted to the problem of resuming the commutator expansion arising in a canonical transformation upon the Hamiltonian operator of a many-electron system. The canonical transformation generates effective interactions which in the cluster formalism may be grouped in a natural way according to the number of interacting particles. A practical scheme is developed for exhibiting the many-body terms with explicit formulas given for the two-body effective interactions.
The formalism is applied to the σ-π separability problem for planar molecules, with the generator of the transformation chosen to eliminate, to a certain approximation, the σ-π interactions. This procedure yields an effective π-π interaction which is exhibited explicitly as an expansion over the spectrum of two-particle a states. The results closely resemble those of Harris though the procedure arising from the cluster expansion approach is somewhat more straightforward to carry out.
Abstract: High ionic conductivity of lithium in LixLa(2-x)/3TiO3 with A-site deficient type perovskite structure has attracted considerable attention owing to both the range of practical usage (e.g., all-ceramics Li secondary batteries) and the fundamental fascination of fast lithium ion transport in crystalline solids. In present paper, we investigated the arrangement of La and vacancies in La2/3TiO3 by means of first-principles computations combined with cluster expansion approach, since it has caused a difficulty of atomistic level discussion due to numerous freedoms of configuration. The computational results predicted the alternate La concentrated and diluted layers stacking along c-axis, which agreed with the previous structural analyses. In addition, La cluster formation within ab plane is indicated. Using predicted La/vacancy arrangement, we demonstrated to calculate the Li migration path and energy profiles during Li jump by nudged elastic band method, which showed diagonal pathways to avoid passing A-site center.
TL;DR: The CE-CVM has been used for computing phase equilibria as discussed by the authors, where the effects of local order and vibrational and electronic mixing contributions to the Gibbs function are taken into account.
Abstract: The cluster expansion method (for configurational enthalpy of mixing) and cluster variation method (for configurational entropy of mixing) (CE–CVM) together offer a systematic hierarchy of approximations for representation of phase diagram, thermochemical, thermophysical and structural data as opposed to the traditional CALPHAD methods which neglect the effects of local order and vibrational and electronic mixing contributions to the Gibbs function. The CE–CVM has not been very widely used for computation of phase equilibria since it is algebraically complex. A procedure has been developed for simultaneous nonlinear optimization of all the relevant data under the framework of CE–CVM. Vibrational and electronic mixing contributions have also been included using the CE method. The procedure has been successfully utilized for computing the solid-state regions of the phase diagrams of Sc–Zr and Sc–Ti. Debye temperatures and short-range order (sro) parameters have been calculated for these systems.
TL;DR: In this paper, the mixed diamond chain composed of spins 1 and 1/2 when the exchange interaction is alternatingly distorted is investigated and the ground state is determined by numerically analyzing each spin cluster.
Abstract: We investigate the mixed diamond chain composed of spins 1 and 1/2 when the exchange interaction is alternatingly distorted. Depending on the strengths of frustration and distortion, this system has various ground states. Each ground state consists of an array of spin clusters separated by singlet dimers by virtue of an infinite number of local conservation laws. We determine the ground state phase diagram by numerically analyzing each spin cluster. In particular for strong distortion, we find an infinite series of quantum phase transitions by the cluster expansion method and conformal field theory. This leads to the infinite series of steps in the behavior of the Curie constant and residual entropy.
TL;DR: In this paper, the metastable phase diagram of the BCC-based ordering equilibria in the Ti-Fe system has been calculated using a truncated cluster expansion, through the combination of FP-LAPW and cluster variation method (CVM) in the irregular tetrahedron cluster approximation.
TL;DR: Theory of dilution effect in orbital ordered system is presented in this paper, where the authors analyzed the orbital model without spin degree of freedom and spin-orbital coupled model in a three-dimensional simple-cubic lattice.
Abstract: Theory of dilution effect in orbital ordered system is presented. The ${e}_{g}$ orbital model without spin degree of freedom and the spin-orbital coupled model in a three-dimensional simple-cubic lattice are analyzed by the Monte Carlo simulation and the cluster expansion method. In the ${e}_{g}$ orbital model without spin degree of freedom, reduction in the orbital ordering temperature due to dilution is steeper than that in the dilute magnet. This is attributed to a modification of the orbital wave function around vacant sites. In the spin-orbital coupled model, it is found that magnetic structure is changed from the A-type antiferromagnetic order into the ferromagnetic one. Orbital-dependent exchange interaction and a sign change in this interaction around vacant sites bring about this phenomenon. Present results explain the recent experiments in transition-metal compounds with orbital dilution.
TL;DR: In this article, a new code called VAAQP (variational average atom in quantum plasmas) is briefly described and its first results in the case of aluminium at solid density and temperatures between 0.05 and 12 eV are reported.
Abstract: A new code called VAAQP (variational average atom in quantum plasmas) is briefly described and its first results in the case of aluminium at solid density and temperatures between 0.05 and 12 eV are reported. The code is based on a new fully variational approach to plasmas at local equilibrium with both bound and free electrons treated quantum mechanically. This model which is derived from two first terms of the cluster expansion appears to be the quantum extension of the well-known atom-in-cell model based on the Thomas–Fermi theory (Thomas–Fermi average atom) that has been proposed in 1949 by Feynman, Metropolis and Teller. Similar to the case of Feynman et al's model the VAAQP approach, due to its fully variational character, respects the virial theorem and uses a simple formula for the electronic pressure. Comparisons to results obtained using other approaches are also shown and discussed in the aluminium case. The results confirm the feasibility of the quantum variational model in the warm dense matter regime. Effects of the variational treatment can lead in this regime to significant differences with respect to existing non-variational models.
TL;DR: In this article, the ground state energy of ideal α -matter at T = 0 is analyzed within the framework of variational theory of Bose quantum liquids, and the energy per particle of α matter is evaluated in the cluster expansion formalism up to four-body diagrams.
01 Jul 2009
TL;DR: In this paper, a Bayesian framework for cluster expansion is presented, which explicitly incorporates physical insight into the fitting procedure and uses cross validation to develop physically meaningful prior probability distributions for the cluster expansion coefficients.
Abstract: Cluster expansions have proven to be a valuable tool in alloy theory and other problems in materials science but the generation of cluster expansions can be a computationally expensive and time-consuming process. We present a Bayesian framework for developing cluster expansions that explicitly incorporates physical insight into the fitting procedure. We demonstrate how existing methods fit within this framework and use the framework to develop methods that significantly improve the predictive power of cluster expansions for a given training set size. The key to the methods is to apply physical insight and cross validation to develop physically meaningful prior probability distributions for the cluster expansion coefficients. We use the Bayesian approach to develop an efficient method for generating cluster expansions for low-symmetry systems such as surfaces and nanoparticles.
TL;DR: In this article, the ground state and phase equilibria at finite temperatures of the ternary system Fe-Al-Ti have been investigated by combining first-principles density functional total energy calculations and statistical mechanics.
Abstract: By combining first-principles density functional total energy calculations and statistical mechanics the ground state and the phase equilibria at finite temperatures of the ternary system Fe–Al–Ti have been investigated. Total energy calculations have been performed by means of the Wien 2k code to establish the ground state energetic. A cluster expansion method was therewith used to describe solid solutions. At several chosen finite temperatures the cluster variation method in the irregular tetrahedron approximation was employed in order to calculate the iron rich ternary bcc equilibria. It is confirmed that there are two kinds of phase separations of the bcc phase, A2+L2 1 and B2+L2 1 .
TL;DR: In this paper, the pressure components of soft disks in a two-dimensional narrow channel were analyzed in the dilute gas regime using the Mayer cluster expansion and molecular dynamics, and it was found that when the two-body potential, u(r), is singular at some distance r0, the dependence of the pressure component on the channel width exhibits a singularity at one or more channel widths which are simply related to r0.
Abstract: The pressure components of 'soft' disks in a two-dimensional narrow channel are analyzed in the dilute gas regime using the Mayer cluster expansion and molecular dynamics. Channels with either periodic or reflecting boundaries are considered. It is found that when the two-body potential, u(r), is singular at some distance r0, the dependence of the pressure components on the channel width exhibits a singularity at one or more channel widths which are simply related to r0. In channels with periodic boundary conditions and for potentials which are discontinuous at r0, the transverse and longitudinal pressure components exhibit a 1/2 and a 3/2 singularity, respectively. Continuous potentials with a power-law singularity result in weaker singularities of the pressure components. For channels with reflecting boundary conditions the singularities are found to be weaker than those corresponding to periodic boundaries.
TL;DR: In this article, the ground state structures of binary transition metal carbides such as (Ti1-xMox)C have attracted much attention for use in increasing the strength of steels.
Abstract: Recently, binary transition metal carbides such as (Ti1-xMox)C have attracted much attention for use in increasing the strength of steels. This study aims to understand the ground state structure of various compositions of that carbide. Using a combined approach of first-principles calculation and the cluster expansion method, ground state structures of the compositions of TiC and MoC were determined. Only 29 symmetrically inequivalent structures were sufficient to determine the ground state structures of (Ti1-xMox)C for the whole range of the composition. The linear chains of solute atoms predicted by calculation were favored when the compositions of MoC were between 20 at.% and 70 at.%. When the composition of MoC was 50 at.%, an alternating layer of Ti and Mo formed along the direction. This layered structure is expected to show peculiar mechanical and electronic properties.
TL;DR: In this article, the thermodynamic properties of normal liquid helium 3 were calculated by using the lowest order constrained variational (LOCV) method, and it was found that the critical temperature for the existence of the pure gas phase is about 4.90 K (4.45 K), which is higher than the experimental prediction of 3.3 K.
Abstract: The thermodynamic properties of normal liquid helium 3 are calculated by using the lowest order constrained variational (LOCV) method. The Landau Fermi liquid model and Fermi–Dirac distribution function are considered as our statistical model for the uncorrelated quantum fluid picture and the Lennard–Jones and Aziz potentials are used in our truncated cluster expansion (LOCV) to calculate the correlated energy. The single particle energy is treated variationally through an effective mass. The free energy, pressure, entropy, chemical potential and liquid phase diagram as well as the helium 3 specific heat are evaluated, discussed and compared with the corresponding available experimental data. It is found that the critical temperature for the existence of the pure gas phase is about 4.90 K (4.45 K), which is higher than the experimental prediction of 3.3 K, and the helium 3 flashing temperature is around 0.61 K (0.50 K) for the Lennard–Jones (Aziz) potential.
TL;DR: In this paper, an extended van der Waals equation of state (EOS) is derived by statistical mechanics on the perturbation approximation of a hard sphere system, where the attraction energy term in the canonical ensemble partition function is extended by a cluster expansion.
Abstract: Molecular dynamics simulations on the Lennard-Jones system are performed to obtain the pVT and UVT relations. An extended van der Waals equation of state (EOS) is derived by statistical mechanics on the perturbation approximation. A hard sphere system is used as the reference system. The attraction energy term in the canonical ensemble partition function is extended by a cluster expansion. The new EOS includes three parameters, two of which are the interaction parameters in the Lennard-Jones interaction. The last parameter is the effective volume of the hard sphere system. The extended van der Waals EOS reproduces the pVT and UVT relations, at least qualitatively, whereas the original van der Waals EOS can explain only the pVT relation.
TL;DR: In this article, the normal liquid helium 3 one-body momentum distribution, n(k), at zero and finite temperature is evaluated by using the cluster expansion theory for the occupation probability of Ristig-Clark formalism.
Abstract: The normal liquid helium 3 one-body momentum distribution, n(k), at zero and finite temperature is evaluated by using the cluster expansion theory for the occupation probability of Ristig-Clark formalism The lowest order constrained variational (LOCV) and the extended LOCV (ELOCV) method are used to calculate the correlation functions at zero and finite temperatures The input inter-atomic potential is the familiar 6–12 Lennard-Jones interaction The gap in n(k) at the Fermi surface is found to be about 041 comparing to 10 (072) for the noninteracting (dilute hard-sphere) Fermi gas model at zero temperature and it decreases by increasing the temperature It is also demonstrated that the high-momentum tail of n(k) gets larger as we increase the temperature and finally, we find a good agreement between present calculated n(k) and those coming from more sophisticated approaches such as Diffusion and Green-function Monte Carlo techniques