Monte Carlo Mathematical Modeling and Analysis of Optogalvanic Waveforms FOR 1s$_{5}$-2p$_{j}$ (j = 7,8,9) transitions of Neon in a Hollow Cathode Discharge

The laser optogalvanic (OG) waveforms associated with the 1s$_{5}$ -- 2p$_{j }$(j=7,8,9) transitions of neon in a hollow discharge lamp have been investigated as a function of discharge current (2.0 -- 19.0 mA). We have refined a mathematical model in determining the amplitudes, decay constants, and time constants associated with these transitions. Monte Carlo least-squares fitting of these waveforms has helped to specifically determine the decay rate constant (a$_{i})$, exponential rates (b$_{i})$ and time constant ($\tau )$ parameters associated with the evolution of the OG signals. In our investigation of the 1s$_{5}$ -- 2p$_{j }$(j=7,8,9)$_{ }$optogalvanic transitions of neon, we have measured the intensity of each transition (3.65*10$^{-28}$ , 1.43*10$^{-27}$ and 5.82*10$^{-27}$ cm$^{-1}$/mole-cm$^{-2}$, respectively), which in turn has provided insight into the excitation temperature of the plasma (estimated to be 2847$\pm $285 K). The population distribution of the excited neon atoms in the pertinent energy levels has also been estimated using the Heisenberg Uncertainty Principle.