ast403_saha equation notes

ast403_saha equation notes - IONIZATION SAHA EQUATION Let...

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IONIZATION, SAHA EQUATION Let the energies of two states, A and B , be E A and E B , and their statistical weights g A and g B , respectively. In LTE (Local Thermodynamic Equilibrium) the number of particles in the two states, N A and N B , satisfies Boltzman equation: N A N B = g A g B exp [ ( E A E B ) /kT ] . (i . 1) Now, we shall consider two ions, “i” and “i+1”, of the same element. The ionization potential, i.e. the energy needed to ionize “i” from the ground state is χ , and the statistical weights of the ground states of the two ions are g i and g i +1 , respectively. The number densities, [ cm - 3 ], of the two types of ions and free electrons are n i , n i +1 , and n e , respectively. We shall use the Boltzman equation (i.1) to estimate the number ratio n i +1 /n i . The statistical weight of an ion in the lower ionization state to be used in the equation (i.1) is just g i . The statistical weight of an ion in the upper ionization state is g i +1 multiplied by the number of possible states in which a free electron may be put. As we know, in every cell of a phase space with a volume h 3 there are two possible states for an electron, because there are two possible orientations of its spin. h = 6 . 63 × 10 - 27 erg s is the Planck constant. The energy of a free electron with a momentum p with respect to the ground state of an ion in a lower ionization state is E = χ + p 2 / 2 m . The number of cells available for free
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