The $gamma to alpha$ isostructural transition in the Ce$_{0.9-x}$La$_x$Th$_{0.1}$ system is measured as a function of La alloying using specific heat, magnetic susceptibility, resistivity, thermal expansivity/striction measurements. A line of discontinuous transitions, as indicated by the change in volume, decreases exponentially from 118 K to close to zero with increasing La doping and the transition changes from being first-order to continuous at a critical concentration $0.10 leq x_c leq 0.14$. At the tricritical point, the coefficient of the linear $T$ term in the specific heat $gamma$ and the magnetic susceptibility start to increase rapidly near $x$ = 0.14 and gradually approaches large values at $x$=0.35 signifying that a heavy Fermi-liquid state evolves at large doping. Near $x_c$, the Wilson ratio, $R_W$, has a value of 3.0, signifying the presence of magnetic fluctuations. Also, the low-temperature resistivity shows that the character of the low-temperature Fermi-liquid is changing.
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