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γ $^{ph}$( x = 0 . 3) gives γ $^{ph}$( x = 0) and γ $^{ph}$( x = 0 . 1). 

The electronic specific heats of the three samples are shown in Figure 2(b). Above 150K, γ is at most only weakly T -dependent and almost independent of doping. At low temperatures γ for the x = 0 and 0.1 samples is heavily reduced by factors of ∼ 11 and 5 respectively due to the opening of a spin density wave (SDW) gap be- low T$_{0}$ ∼ 136K, and increases as ∼ 20 × 10 − $^{6}$T 3 mJ/mol K 2 in the range 40 − 110K. Band splitting and signs of partial gapping of the Fermi surface have been observed in the SDW state of BaFe$_{2}$As$_{2}$ by angle-resolved photoe- mission spectroscopy[16]. γ for the x = 0.3 sample is dominated by the large superconducting anomaly with Δ γ ( T$_{c}$ ) ≈ 48 mJ/mol K $^{2}$, a normal-state γ$_{N}$ (0) of about 47 mJ/mol K 2 and γ (0) = 1.8 mJ/mol K 2 . Measure- ments on a more overdoped crystal with x = 0.4 by Mu et al .[17] show an even larger Δ γ ( T$_{c}$ ) ≈ 100 mJ/mol K 2 and γ$_{N}$ (0) ≈ 63 mJ/mol K $^{2}$, implying a further growth in the density of states with doping. For our x =0.3 sample the superconducting condensation energy U (0) = 10.6 J/mol, as determined from ∫ T$_{c}$ 0 ( S$_{n}$ − S$_{s}$ ) dT , where S$_{n}$ and S$_{s}$ are the normal and superconducting state en- tropies respectively. In Fig. 2(b), the curvature in γ for x =0.3 between 10 and 20K is reduced compared to the raw Δ γ tot data (Fig. 2(a)) by the phonon correction de- scribed above. Evidence that the remaining curvature in γ may reflect a genuine anomalous T -dependence of 

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the electronic term comes from the observation of similar anomalous curvature between 15 and 20K in the field de- pendence Δ γ ( H ) = γ ( H, T ) − γ (0 , T ) shown in the inset to Fig. 4(a). Since the phonon term is H -independent, this anomalous curvature in Δ γ ( H ) can only be of elec- tronic origin, and may signal the presence of a second energy gap as inferred by Mu et al [17]. 

To determine the magnitude and temperature depen- dence of the superconducting gap Δ for x = 0.3 (shown in Fig. 3) we first subtract from γ the small residual γ (0) = 1.8 mJ/mol K 2 and then match the corrected S/T with that calculated assuming the following models for the density of states (see Fig. 3 inset): 

s -wave 

d -wave 

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and s + id -wave 

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where the summations over θ are from 0 to 45 ◦ and N$_{θ}$ is the number of θ values. Although such modelling is too crude to pin down the exact nature of the gap, the rapid increase in Δ below 15K in the case of the as- sumed d -wave gap function, shows that nodes on the Fermi surface are incompatible with the T -dependence of γ observed at low temperature, even in the presence of weak pair breaking. The s + id -wave gap function pro- duces a more reasonable Δ( T ). This function completely gaps the Fermi surface but is strongly anisotropic. Such anisotropy could arise from the presence of multiple gaps 

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