ISSN:
1572-9613
Keywords:
Percus-Yevick correlation function
;
moments
;
shell expansions
;
asymptotic forms
;
residue series
;
hybrid approximations
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract A simple recursive relation is derived for the momentsM n ,n=1, 2,..., of the Percus-Yevick correlation functionh(r) for identical hard spheres. TheM n are rational functions of the volume fractionw occupied by the spheres; the first ten are given explicitly, and a single-term asymptotic form is obtained to suffice for the rest. Applications of theM n(w) include testing different approximations forh by numerical integration ofh(r) r n . We compare exact moments with shell approximationsM n [h s ] corresponding to integration fromr=0 tos+1 fors=3−8, and with hybrid approximationsM n [h s +h a ] which supplement the shell approximations with integrals of an asymptotic tail froms+1 to ∞. For a givens, the hybrid approximation is better forw increasing than the shell approximation, andM n [h 3+h a ] is even better thanM n [h 8]
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01014371
