Hypernetted Chain Calculations Research Articles

Binding energies of hypernuclei and hypernuclear interactions

In part 1 the effect of nuclear core dynamics cm the binding energies of Λ hy­ pernuclei is discussed in the framework of variational correlated wave functions. In particular, we discuss a new rearrangement energy contribution and its effect on the core polarization. In part 2 we consider the interpretation of the Λ single-particle energy in terms of basic Λ-nuclear interactions using a local density approximation based on a fermi hypernetted chain calculation of the Λ binding to nuclear matter. To account for the data strongly repulsive 3-body AN Ν forces are required. Also in this framework we discuss core polarization for medium and heavier hypernuclei.

Study of the Half-Diagonal Two-Body Density Matrix of Model Nuclear Matter

The half-diagonal two-body density matrix ρ_{2h}/i(r1,r2,r') plays a central role in most theoretical treatments of the propagation of ejected nucléons and their final state interactions (FSI) in the nuclear medium. In this work based on the analysis of Ristig and Clark, we present the results of a Fermi hypernetted-chain calculation ρ_{2h}/i(r1,r2,r') for infinite symmetrical nuclear matter using a Jastrow-correlated model. The dependence of ρ_{2h} on the variables involved has been investigated in detail. Significant departures from ideal Fermi gas behavior in certain domains demonstrate the importance of short-range correlations. A comparison of our results with the predictions of Silver's approximation to ρ_{2h}, which has been employed in some treatments of FSI, reveals certain shortcomings of this approximation. The Fermi hypernetted-chain results obtained here will serve as a key input to an approximate treatment of FSI in inclusive quasielastic electron scattering from nuclear matter.

Revisiting the replica theory of the liquid to ideal glass transition.

The replica theory of the "Random First Order Transition" (RFOT) from a supercooled liquid to an "ideal" glass of a system of "soft spheres" is revisited. Following the seminal work of Mézard and Parisi [J. Chem. Phys. 111, 1076 (1999)], the number m of weakly interacting replicas of the system is varied continuously from m = 2 to m < 1. Relevant order parameters and the free energy of the liquid and glass phases are calculated using the hypernetted chain (HNC) approximation for the pair correlation functions. The scenario observed for all m confirms the existence of two glass branches G1 and G2. The latter has the lowest free energy for all m > 1, while the former has a lower free energy for m < 1 but is shown to be unstable against spinodal decomposition for any nonzero value of the attractive inter-replica coupling. The critical temperature Tcr of the RFOT turns out to depend on m, which may be a by-product of the approximation inherent in the HNC closure. The RFOT is predicted to be weakly first order, characterized by a small jump in density between the coexisting liquid and G2 phases for all m > 1. Estimating Tcr in the limit m → 1 requires a proper extrapolation of high resolution HNC calculations. The present protocol explores the behavior of the free energy of the ideal glass phase below Tcr as a function of m.

Checking the Salpeter enhancement of nuclear reactions at intermediate coupling in asymmetric mixtures

We investigate the plasma enhancement of nuclear reactions in the intermediate coupling regime using orbital free molecular dynamics (OFMD) simulations. Mixtures of H-Cu and H-Ag serve as prototypes of simultaneous weak and strong couplings due to the charge asymmetry. Of particular importance is the partial ionization of Cu and Ag and the free electron polarization captured by OFMD simulations. By comparing a series of OFMD simulations at various concentrations and constant pressure to multi-component hyper-netted chain (MCHNC) calculations of effective binary ionic mixtures, we set a general procedure for computing enhancement factors. The MCHNC procedure allows extension to very low concentrations (5% or less) and to very high temperatures (few keV) unreachable by the simulations. Enhancement factors for nuclear reaction rates extracted from the MCHNC approach are compared with the Salpeter theory in the weak and strong coupling regimes, and a new interpolation is proposed.

Theory of complex fluids in the warm dense matter regime and application to an unusual phase transition in liquid carbon

Data from recent laser‐shock experiments or from simulations using density functional theory (DFT), molecular dynamics (MD), path integrals etc. that are available for warm dense carbon are compared with the corresponding results predicted using the neutral pseudo‐atom [NPA] method. The NPA results are in good agreement not only with the 3–12 g/cm3 regimes that have been studied via path‐integral Monte Carlo methods but even at low densities and low temperatures where transient covalent bonding dominates ionic correlations. Thus, the “prepeak” due to the C–C bond at ∼1.4 Å and other features found in the pair distribution function g[r] from DFT + MD simulations at 0.86 eV and 3.7 g/cm3 and other densities etc. are recovered accurately in the NPA + HNC (hypernetted‐chain) calculations. The exploration of regimes not covered by previous studies is presented together with evidence of an unusual phase transition of carbon in the liquid state to a vapour, as seen from the loss of ion–ion correlations. An abrupt decrease in the number of free electrons per ion occurs simultaneously. A metallic liquid with strong ionic correlations arising from transient C–C bonds becomes a metallic vapour. This occurs when carbon at the density of ∼1.0 g/cm3 and mean ionization Z = 4 transits abruptly to a disordered mono‐atomic vapour at 7 eV, with Z ≃ 3. The behaviour of the pressure, compressibility and the electrical conductivity as well as physical quantities available from X‐ray Thomson scattering are presented across the tentatively proposed phase transition.

Density-wave instability and collective modes in a bilayer system of antiparallel dipoles

We consider a bilayer of dipolar particles in which the polarization of dipoles is perpendicular to the planes, in the antiparallel configuration. Using accurate static structure factor data from hypernetted-chain (HNC) and Fermi HNC calculations, respectively for an isolated layer of dipolar bosons and dipolar fermions, we construct effective screened intralayer interactions. Adopting the random-phase approximation for interlayer interactions, we investigate the instability of these homogeneous bilayer systems towards the formation of density waves by studying the poles of the density–density response function. We have also studied the collective modes of these systems and find that the dispersion of their antisymmetric collective mode signals the emergence of the density wave instability as well.

Variational Approach to Nuclear Matter

We calculated the energies of asymmetric nuclear matter at zero and finite temperatures with the cluster variational method. At zero temperature, the expectation value of the two-body Hamiltonian composed of the kinetic energies and the AV18 two-bo dy forces is calculated with the Jastrow wave function in the two-body cluster approximation. The obtained two-body energy is in good agreement with the result with the Fermi Hypernetted Chain (FHNC) calculation by Akmal et al. The energy caused by the UI X three-body forces is treated somewhat phenomenologically so that the total energy reproduces the empirical saturation point. Furthermore, the parameters included in the three-body energy are readjusted so that the Thomas-Fermi (TF) calculations with use of the obtained energy of nuclear matter reproduce the gross feature of the experimental data on atomic nuclei. The nuclear species in the neutron star crust obtained by the TF calculation are reasonable. The free energies of asymmetric nuclear matter at finite temperatures are calculated with an extension of the method proposed by Schmidt and Pandharipande. The obtained free energies are in good agreement with those with the FHNC method, and it is also found that the present variational method is self-c onsistent. It is remarkable that the symmetry free energy is not proportional to (1 - 2x)(2), where x is the proton fraction. With use of the obtained thermodynamic quantities, we are constructing a new nuclear equation of state for supernova simulations.

Particle-in-cell and hypernetted chain models of two-component, two-temperature coupled classical plasmas

Three-dimensional simulations of moderately to strongly coupled electron-ion and multicomponent classical plasmas using the particle-in-cell method are presented. The simulations resolve sub-Debye-length interparticle spacing to accurately model the dynamics of these systems. We consider realistic mass ratios and quasiequilibrium conditions with different component temperatures which are relevant on short time scales. The simulation results are in very good agreement with classical hypernetted chain calculations for dense electron-ion and ion-ion plasmas. Our results demonstrate the feasibility and utility of large-scale particle-in-cell simulations for the modeling and analysis of multicomponent moderately and strongly coupled plasmas.

Equation of state of classical Coulomb plasma mixtures

We develop analytic approximations of thermodynamic functions of fully ionized nonideal electron-ion plasma mixtures. In the regime of strong Coulomb coupling, we use our previously developed analytic approximations for the free energy of one-component plasmas with rigid and polarizable electron background and apply the linear mixing rule (LMR). Other thermodynamic functions are obtained through analytic derivation of this free energy. In order to obtain an analytic approximation for the intermediate coupling and transition to the Debye-Hückel limit, we perform hypernetted-chain calculations of the free energy, internal energy, and pressure for mixtures of different ion species and introduce a correction to the LMR, which allows a smooth transition from strong to weak Coulomb coupling, in agreement with the numerical results.

Ion structure in warm dense matter: Benchmarking solutions of hypernetted-chain equations by first-principle simulations

We investigate the microscopic structure of strongly coupled ions in warm dense matter using ab initio simulations and hypernetted chain (HNC) equations. We demonstrate that an approximate treatment of quantum effects by weak pseudopotentials fails to describe the highly degenerate electrons in warm dense matter correctly. However, one-component HNC calculations for the ions agree well with first-principles simulations if a linearly screened Coulomb potential is used. These HNC results can be further improved by adding a short-range repulsion that accounts for bound electrons. Examples are given for recently studied light elements, lithium and beryllium, and for aluminum where the extra short-range repulsion is essential.

A genetic algorithm for the 1D electron gas

We show how to apply a genetic algorithm to describe the homogeneous electron gas. For simplicity we consider just the 1D case. The pair correlation function so obtained is compared with those found by using variational Monte Carlo and quantum hypernetted chain calculations and reported for the first time in this paper.

Thermodynamic Functions for Plasmas Beyond Montroll Ward

AbstractWe present an approach to the equation of state of fully ionized plasmas with any coupling strength. For this reason we go beyond the Montroll‐Ward contribution. The latter describes the thermodynamic functions at any degeneracy, but it only includes terms up to the order e4 with respect to the coupling strength. Therefore, we combine the Montroll‐Ward contribution and the corresponding exchange contribution up to the order e4 with classical hypernetted chain (HNC) calculations. The improvements made by the application of quantum pseudo‐potentials in the latter approach are discussed. Furthermore, a detailed analysis shows which terms must be omitted in the combined approach since they are included in both the Montroll‐Ward and the classical HNC contribution. Results for a hydrogen plasma are finally compared with simulation data and other theoretical results. (© 2007 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Fluid–fluid and fluid–solid phase separation in nonadditive asymmetric binary hard-spheremixtures

Very asymmetric mixtures of hard spheres naturally arise in the modellization of colloidaldispersions. Effective potentials have emerged as a powerful tool for describing thesesystems and have often been employed to extract the phase diagram in both theadditive and nonadditive cases. However, most theoretical investigations havebeen carried out by means of mean-field-like approaches, so their quantitativeaccuracy remains to be assessed. Here we employ previously determined effectivepotentials for nonadditive hard-sphere mixtures to study the fluid–fluid phasetransition by the hierarchical reference theory (HRT), which is designed to takerealistically into account the effects of long-range fluctuations on phase separation.Fluid–solid equilibrium is addressed by supplementing HRT with thermodynamicperturbation theory for the solid phase. We apply this approach both to a potential withadjustable nonadditivity parameter (Louis et al 2000 Phys. Rev. E 61 R1028) and to theAsakura–Oosawa (AO) potential, which represents an extreme case of nonadditivity. Ourresults for the phase diagram, including modified hypernetted chain (MHNC)calculations, are compared to those of other liquid-state theories and are found toagree nicely with available simulation data. Unlike commonly adopted liquid-statetheories, HRT is capable both of getting arbitrarily close to the fluid–fluid criticalpoint, and of giving nontrivial critical exponents. In particular, the fluid–fluidcoexistence curve is much flatter than that obtained via perturbation theory, inagreement with a recent finite-size scaling Monte Carlo analysis of the AO model.

Thermodynamic properties of charge asymmetric mixed electrolytes in the primitive model

Theoretical results for the structure and thermodynamics of charge asymmetric but equal size electrolyte mixtures obtained by the hypernetted-chain (HNC) integral equation are presented. The electrolytes are modeled as charged hard spheres in a dielectric continuum. The results for the excess energies, osmotic and activity coefficients for mixtures of +2:−1 and +1:−1 electrolytes with a common ion were calculated as a function of composition in the range of ionic strength from I=10 −4 to 1.2 M. From these data, the first two mixing coefficients for the excess internal energy ( q i ) and excess osmotic pressure ( w i ) were determined. The hypernetted-chain results were used to analyze experimental data for mixtures of NaCl and MgCl 2 in water. The zeroth mixing coefficient w 0 for the excess osmotic pressure was compared with the experimental data for this quantity, obtained from osmotic pressure measurements of MgCl 2 and NaCl mixtures in water. In addition, the Harned coefficients for the activity coefficients were calculated and compared with the experimental values. The agreement between theory and experiment for the w 0 results and Harned coefficients α ij is fair. In addition, the hypernetted-chain calculations were compared with existing and new Monte Carlo (MC) data for the excess energies and osmotic coefficients as functions of composition of the model mixture.

Activity coefficients of electrolyte solutions in the modified mean spherical approximation

The Helmholtz free energy of ionic solutions is calculated in the dressed-ion theory (DIT) using a Gibbs–Helmholtz relation. The obtained expression naturally takes into account the occurrence of a process of renormalization of charges and screening length in the bulk which is described by means of the modified mean spherical approximation (MMSA). This process is shown to provoke a decreasing of the electrostatic attractions in the bulk. The chemical potentials and activity coefficients are also a matter of study and a c 3/2 dependence on molar concentration is predicted for the deviations from Debye–Hückel limiting law (DHLL) values of these magnitudes, recovering the classical results of Fowler and Guggenheim. Finally, theoretical predictions for the mean activity coefficients of 1:1 restricted primitive model (RPM) electrolytes are seen to fit actual hypernetted chain calculations (HNC) and first- and second-order mode expansions.

Non-Debye screening in a formally consistent version of the modified mean spherical approximation

The non-Debye decay length of ionic solutions ( κ) is analyzed combining the dressed ion theory route with a new version of the modified mean spherical approximation (MMSA) [Varela et al., J. Chem. Phys. 109, 1930 (1998)]. Seeking formal consistency, the MMSA short-range direct correlation function is naturally extended to include a linear term in radial distance whose effect on the screening predictions is analyzed. This behavior is derived from soft-core considerations and the concentration-dependent slope is related to the penetrability of the ions by means of a Tosi–Fumi-type potential. A limit is established for the slope of c( r) in order to predict the correct behavior of the decay constant in the low concentration regime ( κ→ k D +, k D being Debye's parameter). This limit is shown to be violated by the classical mean spherical approximation (MSA) for a one-component charged spheres fluid. Thus, it is confirmed that the MSA effective decay constant tends to Debye's one from below in the limit of vanishing concentration, in accordance with the recent hypernetted chain (HNC) calculations, a behavior which has been the object of some controversy in the literature. Finally, the HNC calculations of κ are analyzed for various ionic species and the behavior of the calculated slope of c( r) discussed in terms of ionic coupling.

Hypernetted-chain study of broken rotational symmetry states for theν=13fractional quantum Hall effect and other fractionally filled Landau levels

We investigate broken rotational symmetry (BRS) states for the fractional quantum Hall effect (FQHE) at 1/3-filling of the valence Landau level (LL). Recent Monte Carlo calculations by Musaelian and Joynt [J. Phys.: Condens.\ Matter {\bf 8}, L105 (1996)] suggest that Laughlin's state becomes unstable to a BRS state for some critical finite thickness value. We study in detail the properties of such state by performing a hypernetted-chain calculation that gives results in the thermodynamic limit, complementing other methods which are limited to a finite number of particles. Our results indicate that while Laughlin's state is stable in the lowest LL, in higher LLs a BRS instability occurs, perhaps indicating the absence of FQHE at partial fillings of higher LLs. Possible connections to the newly discovered liquid crystalline phases in higher LLs are also discussed.

Fermi hypernetted-chain calculation of the half-diagonal two-body density matrix of model nuclear matter

The half-diagonal two-body density matrix ρ2h(r1,r2,r1′) is a key quantity in theoretical descriptions of nucleon knockout reactions at intermediate energies, due to its central role in treatments of the propagation and final-state interactions of ejected nucleons in the nuclear medium. This quantity is calculated for a simple model of the ground state of infinite symmetrical nuclear matter, based on a Jastrow-correlated wave function and a Fermi hypernetted-chain analysis. The dependence of ρ2h on the variables r11′=|r1−r1′|, r12=|r1−r2|, and the angle θ between r1−r1′ and r1−r2 is investigated in some detail. Significant departures from ideal Fermi gas behavior in certain domains reflect the importance of short-range correlations and their interplay with statistical correlations. The quality of approximations to ρ2h proposed by Gersch et al., Rinat, and Silver is assessed by comparison with the Fermi hypernetted-chain results.

Molecular dynamics studies of strongly coupled charged particle bilayers at finite temperatures.

The structure of strongly coupled charged particle bilayers was investigated using molecular dynamics simulation, in a wide range of the plasma coupling parameter Gamma=20-100. The simulations showed the existence of a series of structural transformations, controlled by the separation of the layers. At high values of Gamma a pronounced long-range order was found to develop at intermediate layer separations, with staggered square lattice configuration. The results show a fair agreement with those obtained by hypernetted chain calculations, in terms of intralayer and interlayer pair correlation functions and structure functions.

A CONSTRAINED PATH MONTE CARLO METHOD FOR NUCLEON SYSTEMS

By combining diffusion Monte Carlo for the spatial degrees of freedom and auxiliary field Monte Carlo to separate the spin-isospin operators, we can solve for the ground state of many-nucleon systems. We use a path constraint to control the fermion sign problem and apply the method to neutron systems interacting with the Argonne v′8 two nucleon potential and the Urbana IX three-nucleon potential. We compare our results with fermion hypernetted chain calculations.