  We investigate the energy eigenstate R\'enyi entropy of generic bipartition
in the fermionic, bosonic, and spin-1/2 XY chains. When the gap of the theory
is large or all the momenta of the excited quasiparticles are large, the
R\'enyi entropy takes a universal form, which is independent of the model, the
quasiparticle momenta, and the subsystem connectedness. We calculate
analytically the R\'enyi entropy in the extremely gapped limit and find
different additional contributions to the universal R\'enyi entropy in various
models. The corrections to the universal R\'enyi entropy cannot be neglected
when the momentum differences of the excited quasiparticles are small. The
R\'enyi entropy derived in the extremely gapped limit is still valid in the
slightly gapped and even critical chains as long as all the momenta of the
excited quasiparticles are large. In the case of double interval in the XY
chain we find new universal results and their corrections. We call the result
universal even though it is only valid for double interval in the spin-1/2 XY
chain. In the case of the bosonic chain in the extremely massive limit we find
analytically a novel formula for the R\'enyi entropy written as the permanent
of a certain matrix. We support all of our analytical results with numerical
calculations.
