Isotope effect in chemical shifts of μ+ and H+: MuBr versus HBr and MuHO versus H2O

The isotopic difference between the diamagnetic shielding of a positive muon (μ+) in μ+ HBr and H2O and the analogous shielding of protons is computed from first principles in free space and in Br2 solution, using a self-consistent cellular cluster multiple scattering method (SC-CMS) for condensed matter and for the free molecules. The isotope shift of the chemical shift σis at the μ+ in these molecules dissolved in liquid Br2 is evaluated with the eigenfunctions and eigenvalues obtained using Ramsey's formalism. For HBr the computed chemical shifts σis are comparable with experiment and with the calculations of Breskman and Kanofsky and of Williams, and the solvent effect has the correct sign and order of magnitude. For H2O, σis has also the correct sign and order of magnitude when compared with μ+SR experiments.