The next step was to check how the independent fits can be improved by fitting
the
and the
transition
together by keeping the value for 
identical for both spectra.
This has been done for the intensity value of 10000 and 20000 entries each.
As a result a reduction of the relative error from 3.3(3.4) % to 2.4% is obtained
with a statistics of 10000 entries. The higher statistics of 20000 results in
a reduction of the relative error from about 2.4 % to 1.9 %.
The only modest gain shows again how the accuracy of the fit results is influenced by the unknown Doppler broadening.