  We present a joint experimental and theoretical study of spin coherence
properties of 39K, 85Rb, 87Rb, and 133Cs atoms trapped in a solid parahydrogen
matrix. We use optical pumping to prepare the spin states of the implanted
atoms and circular dichroism to measure their spin states. Optical pumping
signals show order-of-magnitude differences depending on both matrix growth
conditions and atomic species. We measure the ensemble transverse relaxation
times (T2*) of the spin states of the alkali-metal atoms. Different alkali
species exhibit dramatically different T2* times, ranging from sub-microsecond
coherence times for high mF states of 87Rb, to ~100 microseconds for 39K. These
are the longest ensemble T2* times reported for an electron spin system at high
densities (n > 10^16 cm^-3). To interpret these observations, we develop a
theory of inhomogenous broadening of hyperfine transitions of ^2S atoms in
weakly-interacting solid matrices. Our calculated ensemble transverse
relaxation times agree well with experiment, and suggest ways to longer
coherence times in future work.
