Analytical proposal for the assessment of the molecular excitation levels contribution to the mean excitation energy: Application to the water molecule

Abstract

The mean excitation energy 〈I〉 is a fundamental quantity in radiation physics, concerning energy deposition in matter and absorbed dose analytical estimations for charged particles. The stopping of charged particles in different materials strongly depends on this parameter among others. This work intends to contribute with insights for some issues, usually treated not in detail in the theory of stopping power, as the analytic and theoretic assessment of 〈I〉-value for different relevant materials. A methodology is proposed and described aimed at providing the procedure for the 〈I〉 calculation framework, based on the definition of the mean excitation energy using the dielectric response function is analytically integrable if the inelastic cross section parameters are known. Some dielectric models were studied, aimed at calculating the 〈I〉-value for liquid water by theoretical means, reaching the conclusion that a decay at least of the order of ω−2 in frequency (energy) is needed as weak condition of the optical energy-loss function for the integrals to converge. Afterwards, the first four discrete excitation levels and the diffuse bands for water are treated in a fully analytical scheme, and further compared with numerical results, providing the contribution of these levels to 〈I〉, with the aim of testing the proposed analytical model.