  A new generation of angular-resolved photoemission spectroscopy (ARPES)
measurements on the cuprate superconductors offer the promise of enhanced
momentum and energy resolution. In particular, the energy and temperature
dependence of the on-shell nodal (k_x=k_y) quasiparticle scattering rate can be
studied. In the superconducting state, low temperature transport measurements
suggest that one can describe nodal quasiparticles within the framework of a
BCS d-wave model by including forward elastic scattering and spin-fluctuation
inelastic scattering. Here, using this model, we calculate the temperature and
frequency dependence of the on-shell nodal quasiparticle scattering rate in the
superconducting state which determines the momentum width of the ARPES momentum
distribution curves. For a zero-energy quasiparticle at the nodal momentum k_N,
both the elastic and inelastic scattering rate show a sudden decrease as the
temperature drops below Tc, reflecting the onset of the gap amplitude. At low
temperatures the scattering rate decreases as T^3 and approaches a zero
temperature value determined by the elastic impurity scattering. For T>T_c, we
find a quasilinear dependence on T. At low reduced temperatures, the elastic
scattering rate for the nodal quasiparticles exhibits a quasilinear increase at
low energy which arises from elastic scattering processes. The inelastic
spin-fluctuation scattering leads to a low energy omega^3 dependence which, for
omega>~Delta_0, crosses over to a quasilinear behavior.
