  The statistical mechanics of a treelike polymer in a confining volume is
relevant to the packaging of the genome in RNA viruses. Making use of the
mapping of the grand partition function of this system onto the statistical
mechanics of a hard-core gas in two fewer spatial dimensions and of techniques
developed for the evaluation of the equilibrium properties of a one-dimensional
hard rod gas, we show how it is possible to determine the density and other key
properties of a collection of rooted excluded-volume tress confined between two
walls, both in the absence and in the presence of a one-dimensional external
potential. We find, somewhat surprisingly, that in the case of key quantities,
the statistical mechanics of the excluded volume, randomly branched polymer map
exactly into corresponding problems for an unrestricted linear polymer.
