By Dopita M.A., Sutherland R.S.

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1 Resonance Line Absorption by Heavy Elements Consider an excited state, j = 2, and the corresponding resonance transition to the ground state, j = 1. The width in energy (or frequency) of an excited state is not a perfect delta function. 5): ∆t = 1/A21 . ∆t ≥ ¯ h. Thus, this energy uncertainty translates to a natural line width in terms of frequency (full width half maximum; FWHM), ∆νN =A21 /2π. Since the frequency dependence of the absorption proﬁle can be represented as the Fourier transform of an exponentially decaying harmonic oscillator, the eﬀective absorption coeﬃcient at frequency ν has a natural line shape which is Lorentzian, centered at the frequency of the transition ν0 and having a FWHM ∆ν .

This function declines as a power law with frequency for frequencies which lie far away from the line core. These are often referred to as the damping wings of the proﬁle. 0169f1j ∆ν −1 cm2 . In most cases, near the line core, the line broadening is not dominated by the natural width, but by the Doppler broadening caused by the thermal motions of the atoms along the line of sight, vx . The Doppler shift in frequency produced by this velocity relative to the line center is given by (ν − ν0 ) = ν0 vx /c.

This is presumably related to the intrinsic symmetry of the nuclei before the molecule formation and the symmetry of the process that forms them. In the case of H2 , the nuclei have non–zero spin – namely ±1/2. The nuclear spin of the molecule can take on values according to the vector sums of the two spins, either 1 (both +1/2, or parallel, anti–symmetric) or 0 ( one +1/2 and the other −1/2, anti–parallel , symmetric). 33) where I is the spin number of each nucleus. Also each value of N has a statistical weight of 2N + 1 in the usual manner.

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