Superconducting (SC) gap symmetry and magnetic response of cubic U0.97Th0.03Be13 are studied by means of high-precision heat-capacity and dc magnetization measurements using a single crystal, in order to address the long-standing question of its second phase transition at Tc2 in the SC state below Tc1. The absence (presence) of an anomaly at Tc2 in the field-cooling (zero-field-cooling) magnetization indicates that this transition is between two different SC states. There is a qualitative difference in the field variation of the transition temperatures; Tc2(H) is isotropic whereas Tc1(H) exhibits a weak anisotropy between [001] and [111] directions. In the low temperature phase below Tc2(H), the angle-resolved heat-capacity $C(T,H, phi)$ reveals that the gap is fully opened over the Fermi surface, narrowing down the possible gap symmetry.
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