diff --git a/Code/Mantid/docs/source/interfaces/Muon_ALC.rst b/Code/Mantid/docs/source/interfaces/Muon_ALC.rst index 44496c7921e25d0e3fc4ea2c866ac87332169f62..64cd33a99c3318b199e3157758d9c9ff7bb7a097 100644 --- a/Code/Mantid/docs/source/interfaces/Muon_ALC.rst +++ b/Code/Mantid/docs/source/interfaces/Muon_ALC.rst @@ -7,11 +7,59 @@ Muon ALC Overview -------- -The Muon ALC interface, which is short for Avoided Level Crossing, aims at -handling frequent analysis on e.g. HIFI. It uses simple point-and-click to -analyse a sequence of datasets collected with different parameter values, for -instance different magnetic fields, temperature, etc, and study how this -affects asymmetry. There are currently three steps in the analysis. +The Avoided Level Crossing (ALC) :math:`\mu SR` technique probes the energy levels of a +muoniated radical system, and can be used to elucidate the regiochemistry of +muonium addition, dynamic processes, and reaction kinetics, through measurement +of the muon and proton hyperfine coupling interactions. + +Radical systems are formed during muon thermalisation, during which a portion of +the implanted muons are able to capture electrons to form muonium (:math:`\mu+e`). Muonium +adds to centres of unsaturation in a sample (double or triple bonds) to form a +muoniated radical species. The spins of the muon, unpaired electron, and protons +within the sample interact through the isotropic and anisotropic components of +the hyperfine interaction, forming a quantised system, described by a series of +discrete energy levels. + +In an ALC experiment the magnetic field is incrementally scanned, recording a +specified number of positron events at each step. At certain fields, the energy +levels in the muon and sample system become nearly degenerate, and are able to +interact through the hyperfine coupling interaction. The spins oscillate between +the two energy states resulting in a dip in the polarisation, observed as a +resonance during the magnetic field scan. The three types of ALC resonance +(referred to as :math:`\Delta 0`, :math:`\Delta 1`, and :math:`\Delta 2` resonances) are characterised by the selection +rule :math:`\Delta M=0, \pm 1, \pm 2`, where :math:`M` is the sum of the mz quantum numbers of the spins +of the muon, electron and proton. Isotropic hyperfine coupling interactions +manifest as :math:`\Delta 0` resonances resulting from muon-nuclear spin flip-flop transitions. +The :math:`\Delta 0` resonance field is dependent on the magnitude of both the muon and proton +hyperfine interaction (:math:`A\mu` and :math:`Ak`, respectively) and can occur in gaseous, liquid, +or solid phase samples. The muon spin flip transition that produces the :math:`\Delta 1` +resonance only arises in the presence of anisotropy. Radical systems possessing +complete anisotropy produce a single broad resonance and systems with axial or +equatorial anisotropy produce an asymmetrical resonance line shape known as a +powder pattern. The :math:`\Delta 2` resonance is also observed in radicals from anisotropic +environments. However, these are rarely observed experimentally due to their +characteristically weak intensity line shapes. The magnitude of the hyperfine +interaction is characteristic of the muon binding site, and can result in an +ALC resonance associated with each of the magnetically equivalent nuclei, +for each muoniated radical isomer. + +The magnetic field position, the full width at half height (FWHH), and the +resonance line shape are the important parameters to be extracted from the +ALC spectrum. The field position of a resonance is related to the muon +and/or nuclear hyperfine coupling constant. They often show strong temperature +dependence and can reveal information regarding the structure of the investigated +system. The FWHH of a resonance may indicate any motional dynamics present in the +system, and can also be used to determine muonium addition rates. The anisotropic +environments experienced by radicals in solid samples can produce a variety of +'powder pattern' lineshapes, which are characteristic of the orientation of the +effective hyperfine tensors relative to the magnetic field, and can thus +indicate any reorientational motion present. + +In order to extract these parameters accurately from an ALC spectrum it is +necessary to determine a baseline, perform a baseline subtraction and then +fit the peaks. The Muon ALC interface integrates this sequence of +operations hiding the complexity of the underlying algorithms. + Data Loading ------------