The investigation of exotic particle capture in complex media is studied in this thesis. An investigation into the best one-step Born-type approximation for the Auger capture rate of mu-is made for a H target. It is concluded that a distorted Born-approximation in which the shielding effect of the atomic electrons is included in the determination of the Coulomb continuum wavefunctions is the most appropriate and computationally efficient method of calculation. Generalisation of this method for Auger capture in light atoms is then studied with the ejection of 1s, 2s, 2p, 3s and 3p electrons examined. The focus of the investigation is on the dependence of the Auger rate on the type of electron, the final mu-bound state, and the collision centre of mass energy. It is discovered that the outermost electrons of an atom are the most effective capture electrons with Auger rate maxima as a function of the principal quantum number n occurring at approximately n = 14, n = 30 and n = 40 for the K, L and M-shell s and p electrons. The Auger rate curves as a function of the angular momentum I reach a maximiim between I = 10 and I = 20 dropping rapidly thereafter. An attempt is also made at predicting pi-Auger capture rates into (pppi-)+ molecular orbitals, however the results are schematic and serve only as an example of the method of calculation. Differences between the initial distributions required by the cascade code EXCAS to fit the X-ray data from essentially atomic targets and molecular targets have been determined. A modified statistical distribution with small positive a's is required for the noble gas atoms with a very highly ionised atom resulting at the n = 14 stage for mu-. The oxygen and carbon atoms in simple molecules require a small negative a with again a depleted electron population at the n = 17 stage for pi-. By extending the cascade code EXCAS to larger starting values and inputing a population of mu- for every bound quantum state the properties and de-excitation behaviour of the Ne muonic atom is studied. Results show that depending upon if electron refilling rates are fast or slow an approximate modified distribution with a positive a at the n = 14 state can be attained by a statistical input distribution of mu- or a distribution peaked in I around I = n/2 respectively. The second distribution agrees with the previous results for Auger capture in light atoms.