Fermi hypernetted chain calculations in a periodic box

The Fermi hypernetted chain theory is reformulated to perform calculations with a finite number of fermions in a periodic box. The proposed method is expected to be useful to estimate the finite size effects in Quantum Monte Carlo simulations. Moreover, it can deal with anisotropic correlations as well as with different shaped boxes. Results are given for the neutron matter Bethe homework Hamiltonian and for nuclear matter with spin–isospin dependent central interactions. It is found that finite size effects come from both the kinetic and the potential energy expectation values.     

HNC variational calculations of boson matter

A simple and reliable numerical technique is given for determining the two-body distribution function which minimizes the HNC energy of boson matter. Numerical results are presented for the neutron matter homework problem and the ⁴He Lennard-Jones potential. The resulting distribution function is found to have proper asymptotic behaviour and yields reasonable binding energies.     

Λ-binding to nuclear matter in the fermi hypernetted chain approximation

The Fermi hypernetted chain technique (FHNC) has been extended to the problem of calculating the Λ-binding to nuclear matter. By using graphical techniques and considering the Λ-particle as an impurity, cluster expansions for ΛN and NN distribution functions have been obtained in terms of irreducible graphs. Topological analyses of the graphs have been made to obtain hypernetted chain equations for the two distribution functions for state-independent ΛN and NN correlation factors. Calculations are carried out for the Λ-binding energy including the rearrangement energy terms by employing central, state-independent and spin-averaged hard-core ΛN potentials. Results are in direct contradiction to the reaction matrix results as well as the empirical estimates.     

Pycnonuclear triple-alpha-fusion rate in hypernetted chain Approximation

We have studied the helium plasma in the hypernetted-chain-Approximation considering both short-ranged internuclear and long-ranged Coulomb interactions. The optimal two-particle wave function has been determined in HNC/0 approximation. The two-particle distribution functions, which have been calculated in various orders of HNC/n approximations (n=0, 4, 5), are used to determine the pycnonuclear triple-alpha-fusion rate in the density regime 10⁸ g/cm³≤ρ≤10¹⁰ g/cm³, in which the fusing of three alpha-particles to form a¹²C-nucleus plays an important role in the crust evolution of an accreting old neutron star. Our calculation supports the idea that the helium liquid undergoes a phase transition to stable⁸Be matter at densities slightly lower thanρ≈3×10⁹ g/ cm³ as the plasma induced screening potential then becomes strong enough to bind the⁸Be ground state.     

Liquids in equilibrium: Beyond the hypernetted chain

Density functional techniques are used to derive a charging expression for the non-uniform density of a molecular liquid. In the atomic limit the equation reduces to an exact form due to Fixman. The theory is simplified greatly via a physical approximation that accounts for three-body correlations beyond those included in the hypernetted chain (HNC) closure of the Ornstein-Zernike (OZ) equation. The radial distribution function is obtained as a special case. The theory is tested by examining the phase behavior of two fundamental complex fluids: the homopolymer blend and diblock copolymer melts. For the former it is found, contrary to HNC theory and its molecular generalizations, that a critical temperature T_c is predicted from the structure route. This T_c scales linearly with degree of polymerization N in agreement with Flory theory. The simplest form of the theory can be considered as a way to incorporate attractive interactions within a formalism that is very similar to that of the OZ or reference interaction site model (RISM). The relevance of the theory to charged liquids is also discussed.     

A numerical study of the Fermi hypernetted chain method

We compare several elaborations of the Fermi hypernetted chain (FHNC) method for the calculation of ground-state properties of dense Fermi systems. A variety of simple nuclear potentials is employed. Consistency tests give estimates for the convergence of the resulting FHNC expansions with respect to elementary diagrams, and to antisymmetry corrections.     

Lagrangian submanifolds and the Euler-Lagrange equations in higher-order mechanics

A direct construction of the Euler-Lagrange equations in higher-order mechanics as a submanifold of a higher-order tangent bundle is given, starting from the Lagrangian submanifold defined by the Lagrangian function. This construction uses higher-order tangent bundle geometry, derives the Euler-Lagrange equations as the constraint equations of a submanifold, and makes no assumptions about the regularity of the Lagrangian.     

A definitive test of the Percus-Yevick and hypernetted chain approximations in liquid metals

Pair correlation functions calculated via molecular dynamics (MD) are inverted using the Percus-Yevick and Hypernetted Chain approximations to obtain approximate pair potentials for Li and Al. The results turn out to be quite sensitive to the calculated compressibility. These approximate pair potentials are compared with the ones that were used in the MD calculation. Although some qualitative features of the original potentials are reproduced, the agreement is very poor making it clear that the PY and HNC approximations are of very little use for liquid metal calculations.     

A semi-empirical modified hypernetted chain equation for the one-component plasma

The hypernetted chain (HNC) equation for the one-component plasma is corrected by including a single-parameter expression for the bridge graphs whose functional form ensures that the correct long-wavelength limit of the HNC results is retained. The parameter is chosen to improve the short-range behaviour.     

Abnormal boson occupation in alpha matter

A specific example of abnormal boson occupation is given whereby a vacuum state energy lower than the normal one for the case of Ali-Bodmer alpha particle matter is found at physical densities.     

E1 calculations in thesdf-interacting boson model

A simple IBA-sdf form for theE1 transition operator containing an one-body term and a two-body term is tested in a non-analytical case. TheE 1 transition probabilities in the rare-earth region are reproduced rather well.     

On the solutions of the hypernetted chain equation inside the gas-liquid coexistence region

We present a detailed study of the solutions of the hypernetted chain integral equation inside the gas-liquid coexistence region for simple Lennard-Jones fluids. The study is performed by means of a hybrid Newton-Raphson algorithm extended to cope with complex solutions. In this way, we have unequivocally confirmed that the origin of the well-known HNC singular behavior inside the coexistence curve is linked to the onset of complex solutions. As density is increased starting from the vapor phase along isotherms inside the coexistence region, another singularity is encountered (very likely linked with the existence of a complex multiple solution point), and correlations start to diverge. Therefore, with the numerical approach here presented it is not feasible to join the liquid and vapor phases through an analytically continuous path of real and complex solutions. Finally, a study of the transition from the mean spherical approximation behavior (characterized by the presence of a spinodal divergence) to the peculiar hypernetted chain sort of singularity is also presented.     

Effective boson number calculations in Mo and Cd isotopes

The effects of the neutron-proton interaction on the low-lying levels of Mo and Cd isotopes have been considered in the frame of the IBA-1 model by taking into account an effective boson number (N _eff). Both an empirical procedure based on previous IBA-2 mixing calculations and theN _p N _n scheme provide comparableN _eff values. Level spectra and electromagnetic transitions are investigated. The results support the idea that IBA-1 calculations with a suitableN _eff can largely simulate IBA-2 mixing calculations, taking advantage of simplicity and a smaller number of parameters.     

Superfluid nuclear matter calculations

We present a method to calculate nuclear matter properties in the superfluid phase. The method is based on the use of self-consistent off-shell nucleon propagators in the T-matrix equation. Such a complete treatment of the spectral function is required below and around T_c due to a pseudogap formation in the spectral function. In the superfluid phase we introduce the anomalous self-energy in the fermion propagators and in the T-matrix equation, consistently with the strong coupling BCS equations. The equations for the nucleon spectral function include both a contribution of condensed and scattering pairs. The method is illustrated by numerical calculations. Above T_c pseudogap formation is visible in the spectral function and below T_c a superfluid gap also appears.     

Neutralino dark matter in light Higgs boson scenario

Phenomenology of neutralino dark matter in the minimal supersymmetric model is discussed for a scenario where the lightest Higgs boson mass is lighter than 114.4 GeV$114.4\text{GeV}$. We show that the scenario is consistent not only with many collider experiments but also with the observed relic abundance of dark matter. The allowed region may be probed by experiments of Bs→μ⁺μ⁻$B_s\to {\mu }^{+}{\mu }^{-}$ in near future. The scenario predicts a large scattering cross section between the dark matter and ordinary matter and thus it may be tested in present direct detection experiments of dark matter.     

Zero field particle correlations in a ferrofluid using Monte Carlo simulations and the hypernetted chain approximation

A comparison is made between a 3-dimensional model of a ferrofluid using Monte Carlo (MC) and Integral Equation techniques in the absence of an applied field. The MC simulations were performed using standard Metropolis sampling. Pair distribution functions were obtained and compared with those determined using the hypernetted chain (HNC) approximation which for systems with nonspherical potentials entails the expansion of the correlation functions in terms of rotational invariants. At densities applicable to real fluids agreement between the two methods is found to be excellent, and this justifies the use of the HNC approximation to determine thermodynamic data which are free statistical errors in this regime.     

Ground state of an impurity in a homogeneous system in the hypernetted chain approximation

The hypernetted chain theory of the ground state of a homogeneous N-particle medium NM with an impurity particle is presented. The N identical particles are fermions with spin-isospin degeneracy ν, or bosons (in the limit of ν → ∞). The ground-state wave-function of the system is assumed in the Jastrow form with central, state-independent correlation functions. Central, spin-isospin-dependent two-body interactions both in NM and between the impurity particle and the particles of NM are considered. Expressions for the ground-state energy of the system and for the separation energy of the impurity particle are derived. The simplified case of the chain approximation is also considered.     

Lowest-order and hyper-netted-chain calculations of nuclear matter

Employing two model central interactions the binding energy of nuclear matter is calculated within the framework of the Jastrow variational approach using different types of constrains and including all the contributions from hypernetted-chain diagrams.     

N-body integral equations and four-nucleon calculations

N-body extension of the Faddeev three-body theory is formulated in a novel approach. Comparison with other formulations is performed and first numerical results for the⁴He nucleus are briefly discussed.