Search for O$^{\mathbf{-1}}$ earthquake-like precursors: a MaxEnt-$\mu $SR MgO study

We study O$^{\mathbf{-1}}$ earthquake-like precursor effects [1,2] by analyzing $\mu $SR MgO data using MaxEnt (ME). [3,4] Due to its presence in the Earth's crust, MgO is ideal to study these features: O$^{\mathbf{-1}}$ formation results from a 2-stage break-up in an O anion pair at high-temperatures or high-pressure conditions. [2] As T increases above roomtemperature, a small {\%} is predicted to produce an O$^{\mathbf{-1}}$ state. ME analysis of 100-Oe $\mu $SR data of a pure 3N-MgO single crystal show a broad Gaussian at 1.36 MHz and a sharp signal at 1.4 MHz. The latter could be effects of extended O$^{\mathbf{-1}}$ states, as positive muons probe near negative O ions. There is no sharp 1.4-MHz signal observed in $\mu $SR data of the insulators Al$_{2}$O$_{3}$ [5] and PrBCO6, only the expected 100-Oe Gaussian. We have fitted ME-uSR transforms of MgO to obtain an empirical description of the two peaks. Their T dependences above RT appear to be positive-hole effects. The O-valency effects, related to earthquake-like precursors, are discussed. 1] FT Freund, Nat Hazards Earth Sys Sci \textbf{7} (2007) 1. 2] FT Freund \textit{et al,} Phys Chem Earth \textbf{31} (2006) 389. 3] C Boekema and MC Browne, MaxEnt 2008, AIP Conf Proc {\#}1073 p260. 4] S Lee \textit{et al,} HUIC Educ, Math {\&} Eng Tech Conf, Uo HI (2013). 5] C Boekema \textit{et al}, Hprfn Inter 32 (1986) 667.