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Description
The c^3^{Pi}_u_ state of the hydrogen molecule has the second largest triplet-state excitation cross-section, and plays an important role in the heating of the upper thermospheres of outer planets by electron excitation. Precise energies of the H_2_, D_2_, and HD c^3^{Pi}_u_^-^(v,N) levels are calculated from highly accurate ab initio potential energy curves that include relativistic, radiative, and empirical non-adiabatic corrections. The emission yields are determined from predissociation rates and refined radiative transition probabilities. The excitation function and excitation cross-section of the c^3^{Pi}_u_ state are extracted from previous theoretical calculations and experimental measurements. The emission cross-section is determined from the calculated emission yield and the extracted excitation cross-section. The kinetic energy (Ek) distributions of H atoms produced via the predissociation of the c^3^{Pi}_u_ state, the c^3^{Pi}_u_^-^-b^3^{Sigma}_u_^+^ dissociative emission by the magnetic dipole and electric quadrupole, and the c^3^{Pi}_u_-a^3^{Sigma}_g_^+^-b^3^{Sigma}_u_^+^ cascade dissociative emission by the electric dipole are obtained. The predissociation of the c^3^{Pi}_u_^+^ and c^3^{Pi}_u_^-^ states both produce H(1s) atoms with an average Ek of ~4.1eV/atom, while the c^3^{Pi}_u_^-^-b^3^{Sigma}_u_^+^ dissociative emissions by the magnetic dipole and electric quadrupole give an average Ek of ~1.0 and ~0.8eV/atom, respectively. The c^3^{Pi}_u_-a^3^{Sigma}_g_^+^-b^3^{Sigma}_u_^+^ cascade and dissociative emission gives an average Ek of ~1.3 eV/atom. On average, each H_2_ excited to the c^3^{Pi}_u_ state in an H_2_-dominated atmosphere deposits ~7.1eV into the atmosphere while each H_2_ directly excited to the a^3^{Sigma}_g_^+^ and d^3^{Pi}_u_ states contribute ~2.3 and ~3.3eV, respectively, to the atmosphere. The spectral distribution of the calculated continuum emission arising from the X^1^{Sigma}_g_^+^-c^3^{Pi}_u_ excitation is significantly different from that of direct a^3^{Sigma}_g_^+^ or d^3^{Pi}_u_ excitations.
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