Differences between revisions 30 and 34 (spanning 4 versions)
⇤ ← Revision 30 as of 2009-05-19 12:54:31 →
Size: 10440
Editor: UlrikeHeiter
Comment: some clarifications in section Lambda doubling
← Revision 34 as of 2009-05-19 16:27:13 → ⇥
Size: 10602
Editor: UlrikeHeiter
Comment: a number revised
Deletions are marked like this. Additions are marked like this.
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||wavenumber(cm^-1^) ||wavelength(Å) ||
||20997.64 ||4762.440    ||
||11383.24 ||8784.845    ||		 ||wavenumber(cm^-1^) ||||wavelength(Å) ||
|| || vacuum || air ||
||20997.64 ||4762.440 || 4761.109 ||
||11383.24 ||8784.845 || 8782.433 ||
Line 82: Line 83:
The original list is at /h19/ulrike/Molecules/Data/TiO/TiO-Phillips-OBS.dat and has over 35000 lines. The original list is at /h19/ulrike/Molecules/Data/TiO/TiO-Phillips-OBS.dat and has 35584 lines.
Line 89: Line 90:
The converted list (ascii format, same format as calculated list) is at /h19/ulrike/Molecules/Data/TiO/TiO-Phillips-OBS-vald.asc and has 32574 lines. The converted list (ascii format, same format as calculated list) is at /h19/ulrike/Molecules/Data/TiO/TiO-Phillips-OBS-vald.asc and has 35892 lines.
Line 98: Line 99:
P3,Q3,R3 lines in the gamma prime system (H, X-B) are "double", because of resolved lambda doubling in the calculated list (+958 lines). 3341 lines in the gamma prime system where the branch name contains C or D are not in the calculated list. 157 other lines are not in the calculated list (all with J,,low,,<=4). P3,Q3,R3 lines in the gamma prime system (H, X-B) are "double", because of resolved lambda doubling in the calculated list (+958 lines).
The 137 gamma prime P11/Q11/R11 lines have been discarded (not in calculated list).
About 300 gamma prime PQR 1/2 lines have been discarded, where only one component (C or D) is in the observed list.
157 lines from other systems are not in the calculated list (all with J,,low,,<=4).

Contents

  1. TiO data
    1. Transitions in BP's line list
    2. Lambda doubling
    3. Observed wavenumbers
      1. Observed lines in beta system
      2. Observed lines in gamma prime system

TiO data

TiO line lists calculated by Bertrand on 29 May 2008. The files are in Uppsala at /h5/plez/TiOVALD/linelist/linelist??_all.dat.gz
For files with non-resolved lambda-doubled lines merged see below (under "Lambda doubling").

Number of lines:

Isotope

Nmerg

Norig

46

8193347

11140205

47

8194614

11141521

48

8195512

11142777

49

8196355

11143980

50

8197133

11144857

total

40976961

55713340

Norig ... original lists
Nmerg ... non-resolved lambda-doubled lines merged

Transitions in BP's line list

BP_transitions.png

Lambda doubling

-- 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).

-- UlrikeHeiter 2009-02-06 08:37:27 - Lambda-doubled lines with same wavenumbers have been merged according to BP's comment above.

The new files are in Uppsala at /h19/ulrike/Molecules/Data/TiO/linelist??_all_nodoubling.dat.gz

The merging code is at /h19/ulrike/Molecules/Data/TiO/tio_plez_rm_doubling.pro

In the calculated lists, parity is given by the syml and symu quantum numbers, which can be 1 or -1. In the merged lists, syml and symu are set to 0 for the merged lines.

  • lambda doubling in calculated lists in gamma prime system

    • P1,Q1,R1: lambda doubling resolved for all lines

    • P2,Q2,R2: lambda doubling resolved for Jlow>~10

    • P3,Q3,R3: lambda doubling resolved for Jlow>=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 Jlow: wn(syml=-1) > wn(syml=1),

      • for odd Jlow vice versa

    • Q1,Q2: reverse of P

      • for even Jlow: wn(syml=1) > wn(syml=-1),

      • for odd Jlow vice versa

    • PQR 3: reverse of PQR 1,2
    • for the actual values for PQR 1 and 2 see the plots below (the values are the same for each of the three v-v combinations 0-0, 1-0, 0-1), and compare to the plots for observed lambda-doubled lines further down

[ATTACH] [ATTACH] [ATTACH] [ATTACH] [ATTACH] [ATTACH] [ATTACH] [ATTACH]

Observed wavenumbers

A separate list with observed wavenumbers from Phillips (Bertrand Plez, priv. comm. 17 Sep 2008, 14 May 2009) and calculated other values from Plez (from the list with lambda-doubled lines merged), has been generated. Reference: Davis et al. 1986, ApJ 309, 449.

It contains lines in the alpha, beta, gamma, gamma prime systems with range:

wavenumber(cm-1)

wavelength(Å)

vacuum

air

20997.64

4762.440

4761.109

11383.24

8784.845

8782.433

Isotope: 48Ti (see Davis et al. 1986, IV.a p. 452)

The original list is at /h19/ulrike/Molecules/Data/TiO/TiO-Phillips-OBS.dat and has 35584 lines.

Content: "Obs", vupp, vlow, Jlow, "+", branch, ".0000E+00", wavenumber, ".000", system

There are five "double" lines with same quantum numbers and branch names but slightly different wavenumbers. The wavenumbers for these have been averaged for the converted list.

The converted list (ascii format, same format as calculated list) is at /h19/ulrike/Molecules/Data/TiO/TiO-Phillips-OBS-vald.asc and has 35892 lines.

The conversion code is at /h19/ulrike/Molecules/Data/TiO/tio_phillips_to_vald_ascii.f

The list has been sorted by wavelength after running the conversion code.

Differences between observed and calculated wavelengths, O-C: min=-5.4Å, max=1.7Å.

Explanation for different numbers of lines in original and converted list: P3,Q3,R3 lines in the gamma prime system (H, X-B) are "double", because of resolved lambda doubling in the calculated list (+958 lines). The 137 gamma prime P11/Q11/R11 lines have been discarded (not in calculated list). About 300 gamma prime PQR 1/2 lines have been discarded, where only one component (C or D) is in the observed list. 157 lines from other systems are not in the calculated list (all with Jlow<=4).

Observed lines in beta system

v-v

branch

Jlow,min

Jlow,max

Jlow missing

0-0

P

4

99

94

1-1

P

2

100

66,88,91,92,93,95

2-2

P

2

90

8,10,12,14,76,81,83

0-0

Q

2

100

4

1-1

Q

1

100

2,4,96

2-2

Q

3

100

7,78,82,83,84,89,90,91

0-0

R

2

100

1-1

R

2

98

7

2-2

R

2

92

5,26,42,62,64,70,74,75,84

Observed lines in gamma prime system

observed lines in gamma prime system, P1,Q1,R1 branches (C/D pairs for each v-v and Jlow), Jlow values:

vupp-vlow

branch

Jlow,min

Jlow,max

Jlow missing C+D

Jlow missing C

Jlow missing D

0-0

P1

3

131

3,4,5,6,13,23

29,104,130,131

1-0

P1

2

107

98

21,77

15,63,103,107

0-1

P1

2

145

89,93,109,110,120,123

2,10,14,28,29,63,104, 126,131,135,138,139, 140,144,145

23,62,68,71,72,77,84,98, 99,111,125,129,130,136

0-0

Q1

1

141

2

1,12,119,138,139,140,141

4,7,118

1-0

Q1

1

120

1,104,105,112,114,118

0-1

Q1

2

144

94,138

11,104,107,114,125,127, 128,129,130,132,133,143,144

8,77,100,102,122,124

0-0

R1

1

122

96

5,6,19,64,87

1,2,76,83,84,90,94,100, 107,>=110

1-0

R1

1

135

126

28,43,78,82,95

116,119,121,128,131

0-1

R1

1

150

119,122,124,148

22,58,78,87,100,105,106, 108,111,114,115,130, 137,>=144

5,38,39,53,81,103,116, 117,121,125,128,141 (7 double)

observed lines in gamma prime system, P1,Q1,R1 branches, wavenumber differences between C and D lines:

[ATTACH] [ATTACH] [ATTACH]

observed lines in gamma prime system, P2,Q2,R2 branches (C/D pairs for each v-v and Jlow), Jlow values:

vupp-vlow

branch

Jlow,min

Jlow,max

Jlow missing C+D

Jlow missing C

Jlow missing D

0-0

P2

11

106

16

51, >=85

1-0

P2

3

88

3,4,6,15,34,35

5,16,82,88

0-1

P2

5

90

7,9,13,16

60,67,85

69,71,74,76, >=84

0-0

Q2

7

107

28

>=84

1-0

Q2

2

91

90

<=9, 35,74,91

0-1

Q2

4

85

8,19,75

78,82,84

72,76,79,80,82,83,84,85

0-0

R2

11

106

19,27,32

83,96,97

48,80, >=82

1-0

R2

4

90

18,36,81

4,5,6,8,22,25,37,41,50,61,75,89,90

0-1

R2

1

91

88

18,20,67,76

44,48,82,83, >=85

observed lines in gamma prime system, P2,Q2,R2 branches, wavenumber differences between C and D lines:

[ATTACH] [ATTACH] [ATTACH]

vupp-vlow

branch

Jlow,min

Jlow,max

wn(C)-wn(D) = delta

0-0

P2

11

45

= 0

46

84

< 0

1-0

P2

7

12

|delta| < 0.07

13

42

> 0

43

51

|delta| < 0.07

52

87

< 0

0-1

P2

5

44

= 0 (39: -0.81)

45

83

< 0

0-0

Q2

7

44

= 0

45

83

< 0

1-0

Q2

10

37

> 0

38

50

|delta| < 0.07

51

89

< 0

0-1

Q2

4

43

= 0

44

81

< 0

0-0

R2

11

45

= 0 (36: +0.19)

46

81

< 0

1-0

R2

13

44

> 0

59

88

< 0

0-1

R2

1

42

= 0

43

84

< 0

observed lines in gamma prime system, P3,Q3,R3 branches:

vupp-vlow

branch

Jlow,min

Jlow,max

Jlow missing

0-0

P3

4

121

10,14,19,31,68

1-0

P3

7

95

63,89,93

0-1

P3

4

103

7,19,20,52,79,82,93,97

0-0

Q3

11

130

1-0

Q3

4

109

5,10,14,17,19

0-1

Q3

6

112

10,25,54,87,94,102,104,110

0-0

R3

11

139

21,25,30,65,77,118,119,123,124,134,138

1-0

R3

5

124

99,100,103,119,122

0-1

R3

3

127

5,14,20,70,94,95,96,98,100,113,123

ValdWiki: TiO (last edited 2012-05-04 17:16:40 by UlrikeHeiter)