= Cristiano Fantini
{c}
\b[Cristiano Fantini] coauthored the 2015 <graphene> isotope study using <Raman spectroscopy>; the paper gives his UFMG physics affiliation.<Probing carbon isotope effects on the Raman spectra of graphene with different ¹³C concentrations by Bruno R. Carvalho and others>[byline and affiliation 1]{ref}
A useful measurement issue is how a spectral width relates to time-dependent motion. For an original model, suppose a vibrational coherence decays as $e^{-t/T_2}$. Its corresponding homogeneous <Lorentzian line shape> has frequency full width at half maximum $\Delta\nu=1/(\pi T_2)$, or wavenumber width
$$
\Gamma=\frac1{\pi cT_2}.
$$
With stipulated $\Gamma=10\,\mathrm{cm^{-1}}$ and $c=2.998\times10^{10}\,\mathrm{cm\,s^{-1}}$, the coherence time is about $1.06\,\mathrm{ps}$. The units of $c$ must match the inverse-centimetre linewidth.
A measured linewidth does not automatically give an energy-relaxation lifetime. In a simple relaxation model, $1/T_2=1/(2T_1)+1/T_\phi$, where $T_1$ describes population relaxation and $T_\phi$ pure dephasing. Only when the latter contribution is negligible does $T_1=T_2/2$. Instrumental broadening or spatially varying frequency can additionally widen a recorded <Raman spectrum>.
This example explains why spectral fitting, instrument characterization and the physical relaxation model matter together. Its linewidth and times are hypothetical; they are not measured values or individually assigned results from Fantini's paper.
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