  Inspired by recent experiments and simulations on pattern formation in
biomolecules by optical tweezers, a theoretical description based on reference
interaction site model (RISM) integral equation method is developed to
calculate the equilibrium density profiles of small polyelectrolytes in an
external potential. The formalism is applied to the specific case of a finite
number of polyelectrolytes trapped in a harmonic potential. The density
profiles of flexible Gaussian and rigid rod-like polyelectrolytes are studied
over a range of lengths and numbers of polyelectrolytes in the trap and the
Coulomb coupling parameter. For smaller polymers we recover the results for
point charges. In the mean field limit the point particles do not form shells
for any values of the coupling parameter whereas the longer polymers form a
shell at the boundary at moderate coupling. When the inter-polymer cor-
relations are included the density profile of the polymers shows sharp shells
even at weak coupling. The implications of these results are also discussed.
