  Gravitational radiation reaction forces and balance equations for energy and
momenta are investigated to 3/2 post-Newtonian (1.5PN) order beyond the
quadrupole approximation, corresponding to the 4PN order in the equations of
motion of an isolated system. By matching a post-Newtonian solution for the
gravitational field inside the system to a post-Minkowskian solution (obtained
in a previous work) for the gravitational field exterior to the system, we
determine the 1PN relativistic corrections to the ``Newtonian" radiation
reaction potential of Burke and Thorne. The 1PN reaction potential involves
both scalar and vectorial components, with the scalar component depending on
the mass-type quadrupole and octupole moments of the system, and the vectorial
component depending in particular on the current-type quadrupole moment. In the
case of binary systems, the 1PN radiation reaction potential has been shown to
yield consistent results for the 3.5PN approximation in the binary's equations
of motion. Adding up the effects of tails, the radiation reaction is then
written to 1.5PN order. In this paper, we establish the validity to 1.5PN
order, for general systems, of the balance equations relating the losses of
energy, linear momentum, and angular momentum in the system to the
corresponding fluxes in the radiation field far from the system.
