  Photoexcited quasiparticle relaxation dynamics are investigated in a
$YBa_{2}Cu_{3}O_{7-\delta}$ superconductor as a function of doping $\delta$ and
temperature $T$ using ultrafast time-resolved optical spectroscopy. A model
calculation is presented which describes the temperature dependence of the
photoinduced quasiparticle population $n_{pe}$, photoinduced transmission
$\Delta{\cal T}/{\cal T}$ and relaxation time $\tau $ for three different
superconducting gaps: (i) a temperature-dependent collective gap such that
${\bf \Delta}(T)\to 0$ as $T\to T_{c}$, (ii) a temperature-independent gap,
which might arise for the case of a superconductor with pre-formed pairs and
(iii) an anisotropic (e.g. d-wave) gap with nodes. Comparison of the theory
with data of photoinduced transmission $| \Delta{\cal T}/{\cal T} |$,
reflection $| Delta{\cal R}/{\cal R}|$ and quasiparticle recombination time
$\tau$ in $YBa_{2}Cu_{3}O_{7-\delta}$ over a very wide range of doping ($0.1 <
\delta <0.48)$ is found to give good quantitative agreement with a
temperature-dependent BCS-like isotropic gap near optimum doping ($\delta
<0.1)$ and a temperature-independent isotropic gap in underdoped
$YBa_{2}Cu_{3}O_{7-\delta}$ ($0.15<\delta <0.48$). A pure d-wave gap was found
to be inconsistent with the data.
