  The class of R-diagonal *-distributions is fairly well understood in free
probability. In this class, we consider the concept of infinite divisibility
with respect to the operation $\boxplus$ of free additive convolution. We
exploit the relation between free probability and the parallel (and simpler)
world of Boolean probability. It is natural to introduce the concept of an
eta-diagonal distribution that is the Boolean counterpart of an R-diagonal
distribution. We establish a number of properties of eta-diagonal
distributions, then we examine the canonical bijection relating eta-diagonal
distributions to infinitely divisible R-diagonal ones. The overall result is a
parametrization of an arbitrary $\boxplus$-infinitely divisible R-diagonal
distribution that can arise in a C*-probability space, by a pair of compactly
supported Borel probability measures on $[ 0, \infty )$. Among the applications
of this parametrization, we prove that the set of $\boxplus$-infinitely
divisible R-diagonal distributions is closed under the operation $\boxtimes$ of
free multiplicative convolution.
