Description:
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<jats:title>Abstract</jats:title>
<jats:p>The relaxation of free electron–hole pairs generated after proton irradiation is modelled by means of a simplified set of hydrodynamic equations. The model describes the coupled evolution of the electron–hole pair and self-trapped exciton (STE) densities, along with the electronic and lattice temperatures. The equilibration of the electronic and lattice excitations is based on the two-temperature model, while two mechanisms for the relaxation of free electron–hole pairs are considered: STE formation and Auger recombination. Coulomb screening and band gap renormalisation are also taken into account. Our numerical results show an ultrafast (<jats:inline-formula><jats:alternatives><jats:tex-math>$${\ll }\,{\mathrm {1}}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mrow>
<mml:mo>≪</mml:mo>
<mml:mspace />
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:math></jats:alternatives></jats:inline-formula> ps) free electron–hole pair relaxation time in amorphous <jats:inline-formula><jats:alternatives><jats:tex-math>$${{\mathrm {SiO}}_{\mathrm {2}}}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:msub>
<mml:mi>SiO</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:math></jats:alternatives></jats:inline-formula> for initial carrier densities either below or above the exciton Mott transition. Coulomb screening alone is not found to yield the long relaxation time (<jats:inline-formula><jats:alternatives><jats:tex-math>$${\mathrm {\gg }}{\mathrm {10}}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mrow>
<mml:mo>≫</mml:mo>
<mml:mn>10</mml:mn>
</mml:mrow>
</mml:math></jats:alternatives></jats:inline-formula> ps) experimentally observed in amorphous <jats:inline-formula><jats:alternatives><jats:tex-math>$${{\mathrm {SiO}}_{\mathrm {2}}}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:msub>
<mml:mi>SiO</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:math></jats:alternatives></jats:inline-formula> and borosilicate crown glass BK7 irradiated with high-intensity laser pulses or BK7 irradiated by short proton pulses. Another mechanism, <jats:italic>e.g.</jats:italic> thermal detrapping of STEs, is required to correctly model the long free electron–hole pair relaxation time observed experimentally.
</jats:p>
</jats:sec><jats:sec>
<jats:title>Graphical Abstract</jats:title>
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