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Pair Correlation Functions
In this section, we compare the pair correlation functions for
different densities and temperatures from PIMC simulations using free
particle and VDM nodes. The pair correlation function is defined as
(Allen and Tildesley, 1987),

(202) 
Figure:
Protonproton pair correlation functions multiplied by the density from PIMC
simulations of hydrogen using free particle nodes. The
columns correspond to different values and the rows to
different temperatures .

Figure:
Protonproton pair correlation functions multiplied by the density
as in Fig. but for deuterium at higher
densities.

It goes to 1 in the limit of large in an infinite system and to
in a system of particles. The protonproton pair
correlation functions from PIMC simulations with free particle nodes
are shown in Figs. and
. For
a peak at the bond length of emerge,
which clearly demonstrates the formation of molecules. In the low
density region, we find it useful to multiply the pair correlation
function by an extra density factor
so that the area under
the peak is proportional to the molecular fraction. For
,
the peak height gets smaller with decreasing density as a result of
entropy dissociation. Thermal dissociation reduces the number of
molecules with increasing temperature. For
, pressure
dissociation diminishes the peak with increasing density. For PIMC
with free particle nodes, this process occurs within a small density
interval, in which the system undergoes a transition from a molecular
to a metallic regime (see Fig. ).
Figure:
Protonproton pair correlation function from PIMC
simulations of deuterium using VDM nodes. The
columns correspond to different values and the rows to
different temperatures .

Figure:
Protonproton pair correlation function as in Fig.
but for higher densities.

Fig. and show the
protonproton pair correlation functions from PIMC simulations with VDM
nodes using the standard normalization from Eq. . We also
included simulations at higher densities corresponding to . The
molecular peak disappears gradually with increasing density,
indicating that pressure dissociation leads to a smooth transition to a
metallic regime.
Figure:
Protonelectron radial correlation
function multiplied by the density,
from PIMC with free particle nodes. The columns correspond to
different values and the rows to different temperatures
.

Figure:
Protonelectron pair correlation function from PIMC
simulations of deuterium using VDM nodes. The
columns correspond to different values and the rows to
various temperatures.

Figure:
Protonelectron pair correlation function as in Fig.
but for higher densities.

Figure:
Electronelectron pair correlation function from PIMC
simulations of deuterium using VDM nodes. Solid lines
correspond to pairs with parallel spins and dashed lines to
antiparallel spins. The columns belong to different
values and the rows to various temperatures .

Figure:
Electronelectron pair correlation function as in Fig.
but for higher densities.

The protonelectron radial distribution function
from different simulations using free particle nodes is shown in
Fig. . For noninteracting particles, this function
would be identical to zero. The first peak shows an increased
probability of finding a electron near a proton due to the attractive
forces. At low temperature, the size of peak can also be interpreted
as the occupation of bound electronic states. Also the unbound,
scattering states lead to a smaller but nonzero contribution to this
peak. However, one can still deduce that the degree of ionization,
inversely related to the peak size, increases with temperature.
Alternatively, one can study the protonelectron pair correlation function
as shown in Fig. and
from simulations using VDM nodes, where the
same overall behavior is represented in a different form.
Fig. and show the
electronelectron paircorrelation functions. The peak for pairs with
antiparallel electron spins indicates the formation of molecules, in
which two electrons get very close, in cases where they realize the
molecular binding. For same spin electrons, one always finds a strong
repulsion due to the Pauli exclusion principle.
Next: Equation of State
Up: Thermodynamic Properties of Dense
Previous: Comparison of Variational and
Contents
Burkhard Militzer
20030115