A. Kallio

The ground state of rose systems with HNC and BBGKY equations

Abstract The effect of elementary diagrams on liquid 4 He at T = 0 are studied by using two different equations, the hypernetted chain (HNC), not containing the three-body radial distribution function and the Born-Bogoliubov-Green-Kirkwood-Yvon (BBGKY) equation containing it. The asymptotic behaviour of the two-body radial distribution function is determined from the HNC “Schrodinger” equation and the method of trial functions is applied. It is found that the HNC elementary diagram series for the energy converges rather slowly but the lowest-order HNC wave function is surprisingly good. An approximate summation of the elementary diagram series is performed with Pade techniques. The BBGKY equation gives faster convergence for the energy, but predicts wrong large - r behaviour for the Jastrow factor ⨍ 2 . The model energy is shown to be close to the HNC energy. The relative momentum distribution including elementary diagrams is used to study the condensation fraction. We speculate on the possible existence of vortex-like texture in the liquid.

Hypernetted Chain Theory of Charged Impurity

Applying the inhomogeneous hypernetted chain method we formulate the general impurity problem for a correlated Bose or Fermi fluid as a host. In the present paper we apply the method to an impurity in electron gas. From the Euler-Lagrange equation for the induced density one obtains the screening and cusp conditions. It turns out that these two conditions alone are sufficient to give accurate prediction for the positron annihilation in metals. We construct numerical solution for the Euler-Lagrange equation demanding the two conditions to be satisfied. The resulting energies compare well with existing field theoretical calculations for hydrogen and positronium impurities. The uniform limit approximation is used to derive an expression for the dielectric function. In the present theory the linear response to an external field is determined by one characteristic function which is calculable from the ground state quantities alone. Eliminating this function in favour of the dielectric function which is assumed to be known exactly we obtain an equation for the non linear density response which may have more general validity than the approximations made here suggest.

New integral equation for the triplet distribution function

We apply the hypernetted chain theory (HNC) of inhomogeneous systems in the canonical ensemble to derive a new integral equation for the function that corrects the superposition approximation of the triplet distribution function of the homogeneous system. The equation turns out to be an extension of the HNCII equation derived by Verlet with the functional Taylor-expansion technique. A truncation of the new integral equation satisfies the sequential relation for triplet distribution functions far better than the truncated Abe-Stell density-cluster expansions. The method applies to both quantum and classical cases. The theory is used to calculate the triplet distribution function of liquid 4He for equilateral and some isosceles configurations. A possibility to calculate the elementary diagrams (or the bridge function) in the HNC theory of the pair distribution function for liquid 4He are thereafter evaluated with the new HNCII theory and the results are compared to the molecular dynamics simulation data.

On the Optimal Solution of Generalized HNC-Equation for Bose Quantum Liquids and Solids

The properties of two-dimensional liquid 4He film at T = 0 are calculated with HNC-optimization. The effect of elementary diagrams is taken into account with Pade-technique. The agreement is good with Monte Carlo results. Utilizing the HNC-solution for the liquid we construct an approximate solution of the generalized HNC-equation for the corresponding quantum solid. The solidification ρS = 0.087 A-2 is higher than the result for Monte Carlo calculation and close to the experimental value 0.082 A-2. The optimized radial distribution function and the sum of elementary diagrams are given in parametric form for HNC-liquid.

The Temperature Dependence of the Static Structure Factor for Liquid 4He Below Tλ

The temperature dependence of the structure factor S(k, T) is studied based on an assumption that the anomalous behaviour of S(k, T) below Tλ is due to thermally excited rotons and phonons. The calculation of S(k, T) is performed with the help of the HNC-equation from a model density matrix of Penrose which in turn is obtained from a quasiparticle Hamiltonian describing elementary excitations of liquid helium (both phonons and rotons). The results are in qualitative agreement with recent neutron and X-ray scattering experiments below Tλ. The theoretical temperature correction is used to deduce S(k, T = 0) separately from the most recent X-ray and neutron scattering experiments.

The effect of the Δ(1236) on the trinucleon charge form factor

The Δ(1236) is introduced into the wavefunctions of3He and3H and the charge form factor calculated. The effect is to slightly aggravate the already large discrepancy between theory and experiment for q2 ≳ 14 fm−2. However, there are two side benefits —a simple way to understand the d-wave contribution to the CFF, and a simple NΔ correlation function having a very good overlap with a more exact correlation.

Hall-coefficient scaling and chemical equilibrium above Tc

We propose a simple treatment of boson fermion chemical equilibrium reactionB2+⇌2h+ suitable for understanding the normal states of superconductors such as 123 where the bosons may continue to exist as preformed pairs forT>Tc and gradually decay into pairing holes. The densities of bosons and fermions, given by a functionf(T), are temperature dependent. A proper treatment in analogy with ionization using the grand potential Ω(T, V, μ) leads to reduction of free boson contribution to entropy and specific heat nearTc. Large free boson contribution immediately aboveTc, not seen in experiments, has been the main argument against boson models. The treatment explains in a simple fashion also the Hall coefficient scaling law observed experimentally by Hwanget al. InLSCO. The logarithmic behaviour of resistivitiesρab andρc in strong magnetic field by Andoet al is shown to come from bosons which then are 3D rather than 2D.

Towards exact analytic calculation of electron gas

AbstractA new technique for calculation of electron gas radial distribution functiong(r12) and ground-state energy is developed based on the idea that the probability amplitude

Correlations in Fractional Hall Effect

\psi (r_{12} ) = \sqrt {g(r_{12} )}