List of Figures

• Muon decay asymmtery $a(\epsilon)$, energy spectrum $\Lambda(\epsilon)$ and the product $a(\epsilon)\Lambda(\epsilon)$ ploted against the reduced positron energy $\epsilon$.
• A polar-coordinate plot of the rate of positron emission from muon decay as a function of angle from the muon spin $\Theta$, at various energies $\epsilon$. The distribution has axial symmetry about the muon spin polarization direction, which points toward the right in this plot.
• A view of the M20 secondary channel and experimental area of the TRIUMF laboratory, configured with a conventional $\mu{\cal SR}$ spectrometer capable of transverse and longitudinal field measurements. (G.D.Morris)
• Schematic diagram showing an arrangment of a sample and five scintillation particle detectors. Each muon triggers the thin muon (TM) detector on entering the experiment. Later, the decay positron triggers one of the positron detectors.
• Schematic logic diagram of the basic fast front-end electronics and signal timing for time-differential $\mu{\cal SR}$ experiments. Two decay positron detectors are shown; more may be added as required by the detector geometry.
• (a) A histogram from the ``Back" positron detector of a time-differential experiment on a sample of liquid Ne. (b) The asymmetry $a_{\rm B}(t)$ extracted from the same histogram according to Eq. (2.8). The oscillations are due to the Larmor precession of the muons' magnetic moments in an externally applied transverse magnetic field of 51.5 G.
• The corrected asymmetry obtained from the Back-Front histogram pair using Eq. (2.13). Error bars shown and all parameter errors obtained in fitting are derived from counting statistics.
• The interior parts of the coldfinger cryostat used for $\mu{\cal SR}$experiments on solidified gases. The samples were condensed from the gas phase and frozen solid in the cell visible at the tip of the cold finger. Sample gas was allowed into the cell through the thin stainless tube, which was equiped with a heater to prevent blockages. (G.D. Morris)
• The sample cell used to condense gases to solids (approximately twice actual size), showing the attachment point to the cold finger and heater on the top of the cell. The flow of heat from top to bottom created a temperature difference of about 1 K down the cell walls. This is necessary to grow void-free crystals by ensuring that the sample freezes from the bottom up. The sample could be seen through the tranparent mylar windows enclosing the front and back faces of the cell. (G.D. Morris)
• A sample of Ne being condensed and frozen; (a) The cell partially full of liquid Ne. (b) The cell full of Ne, some of which has solidified around the edges of the cell. (G.D. Morris)
• Muonium and slowly relaxing diamagnetic asymmetries measured in solid nitrogen.
• Electron mobility in solid nitrogen measured by Loveland et al. [19] using a direct time-of-flight method. Various symbols indicate different samples.
• Slowly relaxing diamagnetic asymmetry $A_{\rm S}$and muonium asymmetry $A_{\rm Mu}$ (boxes and circles respectively) measured in a sample of solid nitrogen at T=20 K with an external electric field applied either along (E>0) or opposite (E<0) to the incoming muon beam direction.
• Total muonium asymmetry measured in liquid nitrogen (T=75 K) at long times where delayed muonium formation has ceased. The solid line represents a fit to theory, yielding a characterictic muonium formation time of 0.014(4)${\mu}$s.
• Phonon density of states in KCl
• Dashed line: $\Omega_{2}(T)$ calculated in the case where $g(\omega)$is the real phonon density of states of KCl. Solid line: the same calculation performed assuming a Debye model.
• Temperature dependence of the exponent $\alpha = \frac{T}{\Omega_2} \frac{d\Omega_2}{dT}$calculated for KCl with the real phonon spectrum (dashed line) and Debye-like phonon density of states (solid line).
• Asymmetries measured in solid N₂ at various temperatures in weak longitudinal magnetic fields of (from bottom to top in each plot) 4, 8 and 12 G.
• Muon spin polarization asymmetries measured in a transverse magnetic field of 5.2 G at temperatures of, from top to bottom, T=3.45, 19 and 54 K in a sample of solid, pure N₂.
• Theoretical muonium spin relaxation functions in transverse field, showing the change from Gaussian to exponential form and reduction in the relaxation rate due to motional narrowing. For all curves $\delta = 1 \mu{\rm s}^{-1}$.
• Muonium spin polarization relaxation rates measured in solid nitrogen. Stars (12G), boxes (8G) and crosses (4G) indicate the LF data and all other points are in TF $\sim$5G for different samples.
• Muonium hop rate $1/\tau_c$ in solid N₂ obtained from the spin relaxation rates 1/T₁ and 1/T₂ measured in LF and TF respectively. Stars indicate the results from LF data; all other points are from TF data. The power-law fit is shown by the solid line; the nearly parallel T⁷ theoretical dependence is shown by the dashed line, offset for clarity.
• Phonon density of states $g(\omega)$ of solid nitrogen at 22 K, data from Ref.[57].
•  $\Omega_{2}(T)$ for solid nitrogen, calculated from both the real (dashed line) and Debye model (solid line) phonon density of states $g(\omega)$.
• Muonium spin relaxation rates 1/T₂ in slowly cooled, solid high-purity N₂(circles), N₂with 0.01% CO (boxes) and N₂with 0.1% CO (triangles).
• Phonon density of states in Xe
• Mu spin relaxation in Xe
• Mu hop rate in Xe
• Example of integral
• Arrhenius law in Xe
• Potential energy map
• Breit-Rabi diagram