  This paper is concerned with the hypercoercivity property of solutions to the
Cauchy problem on the linear Boltzmann equation with a confining potential
force. We obtain the exponential time rate of solutions converging to the
steady state under some conditions on both initial data and the potential
function. Specifically, initial data is properly chosen such that the
conservation laws of mass, total energy and possible partial angular momentums
are satisfied for all nonnegative time, and a large class of potentials
including some polynomials are allowed. The result also extends the case of
parabolic forces considered in [4] to the non-parabolic general case here.
