Ruby R-line shift
= Ruby R-line shift
{title2=$\Delta E=hc\,\Delta(1/\lambda)$}
The <ruby R-line shift> compares the same emission feature under two conditions. It is distinct from the <Stokes shift>, which compares absorption and emission features. In <ruby>, <chromium> <ions> in the <corundum> <crystal> provide the <electronic transitions>; compression changes their local environment and transition <energies>.<Stress Measurements in Alumina by Optical Fluorescence: Revisited by Robert F. Cook and Chris A. Michaels>[Introduction and hydrostatic-pressure discussion: chromium fluorescence in alumina and stress-sensitive R lines]{ref}
For consistently defined <vacuum> <wavelengths>, the reciprocal relation gives
$$
\Delta(1/\lambda)=\frac{1}{\lambda_0+\Delta\lambda}-\frac1{\lambda_0}
=-\frac{\Delta\lambda}{\lambda_0(\lambda_0+\Delta\lambda)}.
$$
Thus a positive <wavelength> shift means a negative reciprocal shift, and $E=hc/\lambda$ gives lower <photon> <energy>; $h$ is the <Planck constant> and $c$ the <speed of light>. For <spectroscopic wavenumber>, use <vacuum> <wavelength> and keep that convention consistent. A calibration specified in air <wavelength> must retain its convention or be converted consistently. The reciprocal relation is nonlinear: a line exactly linear in $\Delta\lambda$ is not exactly linear in $\Delta(1/\lambda)$.
For a purely mathematical check with chosen <vacuum> <wavelengths> $\lambda_0=700.0\,\mathrm{nm}$ and $\Delta\lambda=2.0\,\mathrm{nm}$, the reciprocal shift is $-40.7000\,\mathrm{cm^{-1}}$. The small-shift approximation $-\Delta\lambda/\lambda_0^2$ gives $-40.8163\,\mathrm{cm^{-1}}$, about $0.286\%$ too large in magnitude. These chosen values illustrate the conversion; they are not measured <ruby> lines or an additional <pressure calibration>.