The formation of heavy fermion bands can occur by means of the conversion of a periodic array of local moments into itinerant electrons via the Kondo effect and the huge consequent Fermi-liquid renormalizations. Leggett predicted for liquid $^3$He th
at Fermi-liquid renormalizations change in the superconducting state, leading to a temperature dependence of the London penetration depth~$Lambda$ quite different from that in the BCS theory. Using Leggetts theory, as modified for heavy fermions, it is possible to extract from the measured temperature dependence of $Lambda$ in high quality samples both Landau parameters $F_0^s$ and $F_1^s$; this has never been accomplished before. A modification of the temperature dependence of the specific heat $C_mathrm{el}$, related to that of $Lambda$, is also expected. We have carefully determined the magnitude and temperature dependence of $Lambda$ in CeCoIn$_5$ by muon spin relaxation rate measurements to obtain $F_0^s = 36 pm 1$ and $F_1^s = 1.2 pm 0.3$, and find a consistent change in the temperature dependence of electronic specific heat $C_mathrm{el}$. This, the first determination of $F_1^s$ with a value~$ll F_0^s$ in a heavy fermion compound, tests the basic assumption of the theory of heavy fermions, that the frequency dependence of the self-energy is much more important than its momentum dependence.
Transverse-field muon spin rotation ($mu$SR) experiments in the heavy-fermion superconductor PrOs$_{4}$Sb$_{12}$ ($T_{c}=1.85$ K) suggest that the superconducting penetration depth $lambda(T)$ is temperature-independent at low temperatures, consisten
t with a gapped quasiparticle excitation spectrum. In contrast, radiofrequency (rf) inductive measurements yield a stronger temperature dependence of $lambda(T)$, indicative of point nodes in the gap. This discrepancy appears to be related to the multiband structure of PrOs$_{4}$Sb$_{12}$. Muon Knight shift measurements in PrOs$_{4}$Sb$_{12}$ suggest that the perturbing effect of the muon charge on the neighboring Pr$^{3+}$ crystalline electric field is negligibly small, and therefore is unlikely to cause the difference between the $mu$SR and rf results.
Zero- and longitudinal-field muon spin relaxation (MuSR) experiments have been carried out in the alloy series Pr(Os1-xRux)4Sb12 and Pr1-yLayOs4Sb12 to elucidate the anomalous dynamic muon spin relaxation observed in these materials. The damping rate
associated with this relaxation varies with temperature, applied magnetic field, and dopant concentrations x and y in a manner consistent with the ``hyperfine enhancement of 141Pr nuclear spins first discussed by Bleaney in 1973. This mechanism arises from Van Vleck-like admixture of magnetic Pr3+ crystalline-electric-field-split excited states into the nonmagnetic singlet ground state by the nuclear hyperfine coupling, thereby increasing the strengths of spin-spin interactions between 141Pr and muon spins and within the 141Pr spin system. We find qualitative agreement with this scenario, and conclude that electronic spin fluctuations are not directly involved in the dynamic muon spin relaxation.
