  The low-temperature specific heat (SH) of overdoped La_{2-x}Sr_{x}CuO_{4}
single crystals (0.178=<x=<0.290) has been measured. For the superconducting
samples (0.178=<x=<0.238), the derived gap values (without any adjusting
parameters) approach closely onto the theoretical prediction
\Delta_{0}=2.14k_{B}T_{c} for the weak-coupling d-wave BCS superconductivity.
In addition, the residual term \gamma(0) of SH at H=0 increases with x
dramatically when beyond x~0.22, and finally evolves into the value of a
complete normal metallic state at higher doping levels, indicating growing
amount of unpaired electrons. We argue that this large \gamma(0) cannot be
simply attributed to the pair breaking induced by the impurity scattering,
instead the phase separation is possible.
