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Comprehensive low-temperature specific heat data C(T,H) ofNa_0.35CoO2-1.3H_2O with temperature T down to 0.6 K and the magnetic field Hup to 8 T are presented. For the normal state, the values of gamma_n=13.94mJ/mol K2, and Debye temperature 362 K are reported. At zero field, a verysharp superconducting anomaly was observed at Tc=4.5 K withDeltaC/gamma_nTc=1.45. The superconducting volume fraction is estimated to be47.4 % based on the consideration of entropy balance at Tc for the second-ordersuperconducting phase transition. In the superconducting state, the electroniccontribution C_es at H=0 can be well described by the model of the line nodalorder parameter. In low H, gamma(H) H^1/2 which is also a manifestation of theline nodes. The behaviors of both Tc(H) and gamma(H) suggest the anisotropy ofHc2 or possible crossovers or transitions occurring in the mixed state.Comment: Published as a Rapid Communication in Phys. Rev. B. New measurements  on the new Na_0.35CoO2-1.3H_2O sample. The results in the mixed state are  emphasized. Related to cond-mat/0308031. Another paper cond-mat/0409760 from  Berkeley group also discusses similar issue

physical review. b, condensed matter and materials physics

Evidence of nodal superconductivity in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Na</mml:mi></mml:mrow><mml:mrow><mml:mn>0.35</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi mathvariant="normal">CoO</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msub><mml:mo>·</mml:mo><mml:mn>1.3</mml:mn><mml:mspace width="0.3em" /><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn>2</mml:mn></mml:…

Evidence of nodal superconductivity inNa0.35CoO2·1.3H2