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== Lambda doubling - calculated TiO lines ==

-- BertrandPlez 28 Jan 2009:

Some transitions are affected by Lambda-doubling. In that case there are 2 sublevels that give rise to transitions, and if the separation is large enough, they appear in the list as 2 lines with the same parameters except for the parity of the upper and lower level, and a slightly different wavenumber. The degeneracy of these sublevels is 2*J+1. When the Lambda-doubling is too small there are 2 lines with exactly the same data (except the parities). One way to compact the list is to merge these lines and double the gf-value 2*(2*J+1)*f.

For some transitions Lambda-doubling does not exist (if Lambda=0, i.e if one of the states is a Sigma state).

 * lambda doubling in Plez 2008 calculated lists in '''gamma prime system'''
  * P1,Q1,R1: lambda doubling resolved for all lines
  * P2,Q2,R2: lambda doubling resolved for J,,low,,>~10
  * P3,Q3,R3: lambda doubling resolved for J,,low,,>=3 
  * "resolved" here means: wavenumber difference >=0.001
 
 * wavenumber (wn) difference for calculated lambda-doubled lines in '''gamma prime system'''
  * P1,P2,R1,R2 (all v-v):
   * for even J,,low,,: wn(syml=-1) > wn(syml=1),
   * for odd J,,low,, vice versa
  * Q1,Q2: reverse of P
   * for even J,,low,,: wn(syml=1) > wn(syml=-1),
   * for odd J,,low,, vice versa
  * PQR 3: reverse of PQR 1,2
  * for the actual values and comparisons to observed wn difference see the plots below (the values are the same for each of the three v-v combinations 0-0, 1-0, 0-1)

{{attachment:TiO-Phillips-OBS-H-P1CD-wn.png}}
{{attachment:TiO-Phillips-OBS-H-Q1CD-wn.png}}
{{attachment:TiO-Phillips-OBS-H-R1CD-wn.png}}

{{attachment:TiO-Phillips-OBS-H-P2CD-wn.png}}
{{attachment:TiO-Phillips-OBS-H-Q2CD-wn.png}}
{{attachment:TiO-Phillips-OBS-H-R2CD-wn.png}}

{{attachment:TiO-calc-H-PQR1CD-wn.png}}
{{attachment:TiO-calc-H-PQR2CD-wn.png}}
{{attachment:TiO-calc-H-PQR3CD-wn.png}}