We have measured the heat capacities of $delta-$Pu$_{0.95}$Al$_{0.05}$ and $alpha-$Pu over the temperature range 2-303 K. The availability of data below 10 K plus an estimate of the phonon contribution to the heat capacity based on recent neutron-scattering experiments on the same sample enable us to make a reliable deduction of the electronic contribution to the heat capacity of $delta-$Pu$_{0.95}$Al$_{0.05}$; we find $gamma = 64 pm 3$ mJK$^{-2}$mol$^{-1}$ as $T to 0$. This is a factor $sim 4$ larger than that of any element, and large enough for $delta-$Pu$_{0.95}$Al$_{0.05}$ to be classed as a heavy-fermion system. By contrast, $gamma = 17 pm 1$ mJK$^{-2}$mol$^{-1}$ in $alpha-$Pu. Two distinct anomalies are seen in the electronic contribution to the heat capacity of $delta-$Pu$_{0.95}$Al$_{0.05}$, one or both of which may be associated with the formation of the $alpha-$ martensitic phase. We suggest that the large $gamma$-value of $delta-$Pu$_{0.95}$Al$_{0.05}$ may be caused by proximity to a quantum-critical point.
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