  London, $\lambda_L (T)$, and Campbell, $\lambda_{C} (T)$, penetration depths
were measured in single crystals of a topological superconductor candidate
$\text{AuSn}_4$. At low temperatures, $\lambda_L (T)$ is exponentially
attenuated and, if fitted with the power law, $\lambda(T) \sim T^n$, gives
exponents $n>4$, indistinguishable from the isotropic single $s-$wave gap
Bardeen-Cooper-Schrieffer (BCS) asymptotic. The superfluid density fits
perfectly in the entire temperature range to the BCS theory. The
superconducting transition temperature, $T_c = 2.40 \pm 0.05\:\text{K}$, does
not change after 2.5 MeV electron irradiation, indicating the validity of the
Anderson theorem for isotropic $s-$wave superconductors. Campbell penetration
depth before and after electron irradiation shows no hysteresis between the
zero-field cooling (ZFC) and field cooling (FC) protocols, consistent with the
parabolic pinning potential. Interestingly, the critical current density
estimated from the original Campbell theory decreases after irradiation,
implying that a more sophisticated theory involving collective effects is
needed to describe vortex pinning in this system. In general, our thermodynamic
measurements strongly suggest that the bulk response of the $\text{AuSn}_4$
crystals is fully consistent with the isotropic $s-$wave weak-coupling BCS
superconductivity.
