Muon hyperfine coupling constant

Here this work is continued and extended to C70 where a considerable amount of experimental work is currently in progress. The observation [4] of three electron-muon hyperfine coupling constants in not unexpected since there are five chemically distinct sites for muon to attack. The lower symmetry of C70 makes the molecule much more interesting than Cgo-... 

These are indicated for Mu in Figure 2. The muon hyperfine coupling constant is obtained directly as the sum of the two observed frequencies (or the difference, in fields where -v ] becomes negative). In general is in fact the component of a tensor Aji so its value depends on the orientation of the radical to the magnetic field B however, most experiments are carried out with fluid samples where motion of the radical averages out the anisotropy, so just the isotropic value is observed. 

Figure 2 Breit-Rabi diagram for muonium with transverse-field transitions indicated by arrows. The zero-field splitting corresponds to the muon hyperfine coupling constant (/A = 4463 MHz for Mu). In high fields, the four eigenstates become pure Zeeman states ( 1 >= a a >, 2 >= P a >, 3 > = P P >, 4>= a P .

Af = nuclear hyperfine coupling constant = muon hyperfine coupling constant A f = reduced muon... 

Table 2 Restricted Hartree-Fock energies (Hartrees) for Ceo and C70 and their muon adducts. AE is the difference in energy between the carbon allotrope and its adduct. In all cases, except where indicated by f, only the six carbon atoms in the immediate vicinity of the muon have had there positions optimised, f means that a full geometry optimisation has been carried out. The type specifies the defect and for C70 is identified in Table 1. is the spin density at the muon in atomic units (and the hyperfine coupling constant in MHz). JMuon constrained to lie in equatorial plane. indicates geometry not fully optimized.

An approximate value of the hyperfine coupling constant and hence the type of radical formed can be deduced using repolarization curves. These are plots of the initial amplitude of the muon relaxation signal, which increases as the hyperfine interaction is decoupled by an applied magnetic field. However, these estimates can be distorted by anisotropic terms and motional effects and more accurate values of the hyperfine coupling constants would be given by TF- xSR (transverse field) and ALC- xSR (avoided level crossing) measurements. 

Figure 3 TF- SR spectra for positive muons implanted into benzene (A) the raw time-differential histogram recorded for the experiment (B) the Fourier transform of (A) showing the two transitions due to the CeHeMu radical (218.18 and 295.85 MHz, giving a hyperfine coupling constant of of 514.03 MHz) and the signal from muons in diamagnetic environments (27.1 MHz).

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