Convert damping constant into line width

Convert damping constant into natural line-width.

PyAstronomy.pyasl.convertDampingConstant(gamma, wavelength)

Convert damping constant into line-width in wavelength units.

The inverse lifetime, \(1/\tau\), is related to the damping constant, \(\Gamma\), and the Einstein coefficients, A, according to

\[\frac{1}{\tau_{lu}} = \Gamma_{lu} = \sum_{j<u} A_{lj} + \sum_{j<l} A_{uj}\,,\]

where u and l denote the upper and lower state of the transition (see, e.g., “Der neue Kosmos”, Unsoeld und Baschek, 7th edition). The damping coefficient, gamma, determines the FWHM in units of circular frequency. The natural line width (FWHM of the Lorentzian profile) in wavelength units is then given by

\[\frac{\lambda^2}{2\pi c}\Gamma\,.\]

Parameters

gammafloat

The damping constant [1/s]. The damping constant may be determined by summing all relevant Einstein coefficients as shown above.

wavelengthfloat

Wavelength of the transition in A.

Returns

Natural line-widthfloat

The Full Width at Half Maximum of the Lorentzian [cm].

Example

from __future__ import print_function, division
from PyAstronomy import pyasl

# Einstein coefficient relevant for hydrogen LyA
gLya = 6.258085e8

print("Width of H LyA line at 1215.67 A = %e cm" % \
      pyasl.convertDampingConstant(gLya, 1215.67))