Article

Cluster Expansion of Cold Alpha Matter Energy

Romanian Journal of Physics (Impact Factor: 0.75). 01/2010; 55:933 (20 pp).
Source: arXiv

ABSTRACT In the cluster expansion framework of Bose liquids we calculate analytical
expressions of the two-body, three-body and four-body diagrams contributing to
the g.s. energy of an infinite system of neutral alpha-particles at
zero-temperature, interacting via the strong nuclear forces exclusively. This
is analytically tractable by assuming a density dependent two-body correlation
function of Gaussian type. For the alpha-alpha potential we adopt the
phenomenological Ali-Bodmer interaction and semi-microscopic potentials
obtained from the Gogny force parametrizations. We show that under such
assumptions we achieve a rapid convergence in the cluster expansion, the
four-body contributions to the energy being smaller than the two-body and
three-body contributions by at least an order of magnitude.

1 Bookmark
 · 
78 Views
  • American Journal of Physics 02/1968; 36:279-280. · 0.78 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: The ground state energy of ideal α-matter at T=0 is analyzed within the framework of variational theory of Bose quantum liquids. Calculations are done for three local α–α potentials with positive volume integrals and two-body correlation functions obtained from the Pandharipande–Bethe equation. The energy per particle of α matter is evaluated in the cluster expansion formalism up to four-body diagrams, and using the HNC/0 and HNC/4 approximation for a Bose liquid. At low densities the two methods predict similar EOS whereas at higher densities they are sensitively different, the HNC approximation providing saturation at lower density, bellow the saturation value of nuclear matter. Inclusion of higher-order terms in the cluster expansion of the condensate fraction is leading to a stronger depletion of the alpha condensate with the density compared to the two-body approximation prediction.
    Physics Letters B 09/2009; · 4.57 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: The Euler-Lagrange ground state Jastrow and triplet -Feenberg calculations for liquid ('4)He are generalized to finite temperatures. The thermally excited states are constructed from the generalized Bijl-Feynman functions giving a quasiparticle model, in an occupation-number representation to 4th order in creation and destruction operators, which is approximately orthonormalized within certain truncations of the cumulant expansion of the static multiple density correlation functions. The Gibbs-Bogoliubov inequality, the basis of the T (NOT=) 0 variational calculation, is applied to the 4th order Hamiltonian; three canonical transformations are developed to facilitate this calculation. Qualitative agreement with experiment from this microscopic calculation is obtained for the anomalous temperature dependence of the liquid structure function (delta)(K,T) which shows increasing short range order with increasing temperature below T(,(lamda)), and normal behavior above T(,(lamda)). Contrary to experiment, the roton-roton interaction in this model is repulsive. Semi-empirical calculations using the experimental single particle excitation spectrum as input suggest that significant improvement in the (delta)(K,T) calculation is possible if the attractive roton-roton interaction was to be incorporated in the model.
    05/1981;

Full-text (3 Sources)

Download
64 Downloads
Available from
May 31, 2014