Chebyshev approximations for the transmission integral for one single line in Mössbauer spectroscopy

An analytic expansion, to arbitrary accuracy, of the transmission integral (TI) for a single Mössbauer line is presented. This serves for calculating the effective thickness ( T_a) of an absorber in Mössbauer spectroscopy even for T_a > 10. The new analytic expansion arises from substituting in the TI expression the exponential function by a Chebyshev polynomials series. A very fast converging series for TI is obtained and used as a test function in a least squares fit to a simulated spectrum. The test yields satisfactory results. The area and height parameters calculated were found to be in good agreement with earlier results. The present analytic method assumes that the source and absorber widths are different.