171 research outputs found

### A Microscopic Look at Liquid Helium: the 3He Impurity Case

The description of the properties of liquid Helium is a challenge for any
microscopic many-body theory. In this context, we study the ground state and
the excitation spectrum of one $^3$He impurity in liquid $^4$He at T=0 with the
aim of illustrating the power of the correlated basis function formalism in
describing heavily correlated systems. The strong interatomic interaction and
the large density require the theory to be pushed to a high degree of
sophistication. A many-body correlation operator containing explicit two- and
thre-particle correlation functions is needed to obtain a realistic ground
state wave function, whereas a perturbative expansion including up to two
phonon correlated states must be enforced to study the impurity excitation
energies. The theory describes accurately the experimental spectrum along all
the available momentum range. As empirically shown by the experiments, a marked
deviation from the quadratic Landau-Pomeranchuck behavior is found and the
momentum dependent effective mass of the impurity increases of $\sim50~%$ at
$q\sim1.7~\AA^{-1}$ with respect to its q=0 value. Although the main emphasis
is given to the Correlated Basis Function theory, we present also comparisons
with other methods, as diffusion Monte Carlo, variational Monte Carlo with
shadow wave functions and time dependent correlations.Comment: 16 pages, 2 figs, world-scientific latex style. Proceedings of Many
Body X, Seattle, 10-15 Sept. 199

### Energy and structure of dilute hard- and soft-sphere gases

The energy and structure of dilute hard- and soft-sphere Bose gases are
systematically studied in the framework of several many-body approaches, as the
variational correlated theory, the Bogoliubov model and the uniform limit
approximation, valid in the weak interaction regime. When possible, the results
are compared with the exact diffusion Monte Carlo ones. A Jastrow type
correlation provides a good description of the systems, both hard- and
soft-spheres, if the hypernetted chain energy functional is freely minimized
and the resulting Euler equation is solved. The study of the soft-spheres
potentials confirms the appearance of a dependence of the energy on the shape
of the potential at gas paremeter values of $x \sim 0.001$. For quantities
other than the energy, such as the radial distribution functions and the
momentum distributions, the dependence appears at any value of $x$. The
occurrence of a maximum in the radial distribution function, in the momentum
distribution and in the excitation spectrum is a natural effect of the
correlations when $x$ increases. The asymptotic behaviors of the functions
characterizing the structure of the systems are also investigated. The uniform
limit approach results very easy to implement and provides a good description
of the soft-sphere gas. Its reliability improves when the interaction weakens.Comment: Accepted in Phys. Rev.

### Deuteron distribution in nuclei and the Levinger's factor

We compute the distribution of quasideuterons in doubly closed shell nuclei.
The ground states of $^{16}$O and $^{40}$Ca are described in $ls$ coupling
using a realistic hamiltonian including the Argonne $v_{8}^\prime$ and the
Urbana IX models of two-- and three--nucleon potentials, respectively. The
nuclear wave function contains central and tensor correlations, and correlated
basis functions theory is used to evaluate the distribution of neutron-proton
pairs, having the deuteron quantum numbers, as a function of their total
momentum. By computing the number of deuteron--like pairs we are able to
extract the Levinger's factor and compare to both the available experimental
data and the predictions of the local density approximation, based on nuclear
matter estimates. The agreement with the experiments is excellent, whereas the
local density approximation is shown to sizably overestimate the Levinger's
factor in the region of the medium nuclei.Comment: 26 pages, 8 figures, typeset using REVTe

### Spin-orbit and tensor interactions in homogeneous matter of nucleons: accuracy of modern many-body theories

We study the energy per particle of symmetric nuclear matter and pure neutron
matter using realistic nucleon--nucleon potentials having non central tensor
and spin--orbit components, up to three times the empirical nuclear matter
saturation density, $\rho_0=0.16$ fm$^{-3}$. The calculations are carried out
within the frameworks of the Brueckner--Bethe--Goldstone (BBG) and Correlated
Basis Functions (CBF) formalisms, in order to ascertain the accuracy of the
methods. The two hole--line approximation, with the continuous choice for the
single particle auxiliary potential, is adopted for the BBG approach, whereas
the variational Fermi Hypernetted Chain/Single Operator Chain theory, corrected
at the second order perturbative expansion level, is used in the CBF one. The
energies are then compared with the available Quantum and Variational Monte
Carlo results in neutron matter and with the BBG, up to the three hole--line
diagrams. For neutron matter and potentials without spin--orbit components all
methods, but perturbative CBF, are in reasonable agreement up to $\rho\sim$ 3
$\rho_0$. After the inclusion of the LS interactions, we still find agreement
around $\rho_0$, whereas it is spoiled at larger densities. The spin--orbit
potential lowers the energy of neutron matter at $\rho_0$ by $\sim$ 3--4 MeV
per nucleon. In symmetric nuclear matter, the BBG and the variational results
are in agreement up to $\sim$ 1.5 $\rho_0$. Beyond this density, and in
contrast with neutron matter, we find good agreement only for the potential
having spin--orbit components.Comment: 18 pages, 4 tables. Accepted in PL

### Momentum distributions in ^3He-^4He liquid mixtures

We present variational calculations of the one-body density matrices and
momentum distributions for ^3He-^4He mixtures in the zero temperature limit, in
the framework of the correlated basis functions theory. The ground-state wave
function contains two- and three-body correlations and the matrix elements are
computed by (Fermi)Hypernetted Chain techniques. The dependence on the ^3He
concentration (x_3) of the ^4He condensate fraction $(n_0^{(4)})$ and of the
^3He pole strength (Z_F) is studied along the P=0 isobar. At low ^3He
concentration, the computed ^4He condensate fraction is not significantly
affected by the ^3He statistics. Despite of the low x_3 values, Z_F is found to
be quite smaller than that of the corresponding pure ^3He because of the strong
^3He-^4He correlations and of the overall, large total density \rho. A small
increase of $n_0^{(4)}$ along x_3 is found, which is mainly due to the decrease
of \rho respect to the pure ^4He phase.Comment: 23 pages, 7 postscript figures, Revte

### A model of short-range correlations in the charge response

The validity of a model treating the short-range correlations up to the first
order is studied by calculating the charge response of an infinite system and
comparing the obtained results with those of a Fermi Hypernetted Chain
calculation.Comment: 6 pages, 3 Postscript figures, to be published on Phys. Rev.

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