Editing Percus Yevick
Jump to navigation
Jump to search
The edit can be undone. Please check the comparison below to verify that this is what you want to do, and then publish the changes below to finish undoing the edit.
Latest revision | Your text | ||
Line 1: | Line 1: | ||
If one defines a class of | If one defines a class of diagrams by the linear combination (Eq. 5.18 Ref.1) | ||
(See G. Stell | (See G. Stell \cite{P_1963_29_0517_nolotengoElsevier}) | ||
:<math>\left.D(r)\right. = y(r) + c(r) -g(r)</math> | :<math>\left.D(r)\right. = y(r) + c(r) -g(r)</math> | ||
one has the exact | one has the exact integral equation | ||
<math>y(r_{12}) - D(r_{12}) = 1 + n \int (f(r_{13})y(r_{13})+D(r_{13})) h(r_{23})~dr_3</math> | |||
The Percus-Yevick integral equation sets ''D(r)=0''. | The Percus-Yevick integral equation sets ''D(r)=0''. | ||
Percus-Yevick (PY) proposed in 1958 | Percus-Yevick (PY) proposed in 1958 \cite{PR_1958_110_000001} | ||
<math>h-c=y-1</math> | |||
The | The {\bf PY} closure can be written as (\cite{PR_1958_110_000001} Eq. 61) | ||
<math>f [ \gamma (r) ] = [e^{-\beta \Phi} -1][\gamma (r) +1]</math> | |||
or | or | ||
<math>c(r)= {\rm g}(r)(1-e^{\beta \Phi})</math> | |||
or (Eq. 10 | or (Eq. 10 \cite{MP_1983_49_1495}) | ||
:<math>\left.c(r)\right.= \left( e^{-\beta \Phi } -1\right) e^{\omega}= g - \omega - (e^{\omega} -1 -\omega)</math> | :<math>\left.c(r)\right.= \left( e^{-\beta \Phi } -1\right) e^{\omega}= g - \omega - (e^{\omega} -1 -\omega)</math> | ||
or (Eq. 2 of | or (Eq. 2 of \cite{PRA_1984_30_000999}) | ||
:<math>\left.g(r)\right. = e^{-\beta \Phi} (1+ \gamma(r))</math> | :<math>\left.g(r)\right. = e^{-\beta \Phi} (1+ \gamma(r))</math> | ||
or in terms of the bridge function | |||
:<math>\left.B(r)\right.= \ln (1+\gamma(r) ) - \gamma(r)</math> | |||
Note: the restriction $-1 < \gamma (r) \leq 1$ arising from the logarithmic term \cite{JCP_2002_116_08517}. | |||
The HNC and PY are from the age of {\it `complete ignorance'} (Martynov Ch. 6) with | |||
respect to bridge functionals. | |||
A critical look at the PY was undertaken by Zhou and Stell in \cite{JSP_1988_52_1389_nolotengoSpringer}. | |||
==References== | ==References== | ||
[ | #[RPP_1965_28_0169] |