One of the tools used to study high temperature superconducting materials involves the use of muons as magnetic probes. Positive muons with a mass ~ 207 times that of an electron are fired into a sample where they rapidly lose their kinetic energy and wind up in a stable site. A muon spin rotation measurement is then performed which provides information about the distribution of charge near the muons. However, this information is only useful if one knows where within the unit cell the muons happen to be. That is, one needs to know the location of the stable muon sites within the material being studied.
The stable sites occur at minima in the potential energy suface. However, trying to treat such a large system in a fully quantum mechanical way is extremely difficult, even with modern quantum chemistry/solid state techniques. Thus, we proposed to treat only the muon and its nearest neigbors in a fully quantum mechanical way. For this scheme the muon and nearest neighbors are treated as a "molecule" embedded in a crystal lattice of point charges that represent the rest of the unit cell. Self-consistent-field energy values for a variety of muon locations are then calculated so that the minima can be located.
A few representative results from the dissertation of Dr. Terry R. Adams are available below:
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