1. VMI-fitting results for V(m+i), i=4-10
Helgi Rafn Hróðmarsson – 31/7/14

2. Two fitting formulas
1) I=A(1+b2P2(cosq))
2) I=A(1+b2P2(cosq)+b4P4(cosq))

3. V(m+4)

4. „Peak A“ – fit 1
I=A(1+b2P2(cosq))

6. „Peak A“ – fit 2
I=A(1+b2P2(cosq)+b4P4(cosq))

8. J‘
b2 (fit 1)
Db2
b2 (fit 2)
b4 (fit 2)
Db4
1,6488
0,017
1,6591
0,0171
-0,02663
0,0132 1
1,0712
0,0628
1,1928
0,039
-0,29651
0,0339 2
1,1306
0,0703
1,1583
0,0758
-0,068
0,0667 3
0,869
0,0301
0,92743
0,0219
-0,13968
0,0204 4
0,54273
0,0458
0,6463
0,0336
-0,23991
0,0338 5
0,38393
0,0433
0,48213
0,0349
-0,22407
0,0366 6
0,41285
0,031
0,49846
0,0165
-0,19587
0,0173 7
0,27025
0,0271
0,33504
-0,14625
0,0238 8
0,01811
0,0331
0,078555
0,0343
-0,13335
0,0393

10. For Peak A, the second fitting formula gives generally better fits (as to be expected). For future references, we will thusly use the results of the second fit.

11. „Peak B“ – fit 1
I=A(1+b2P2(cosq))

13. „Peak B“ – fit 2
I=A(1+b2P2(cosq)+b4P4(cosq))

15. J‘
b2 (fit 1)
Db2
b2 (fit 2)
b4 (fit 2)
Db4
0,78797
0,0321
0,79874
355
-0,02556
0,0345 1
0,18865
0,0413
0,32613
0,0093
-0,30805
0,0101 2
0,2283
0,0303
0,31634
0,0179
-0,19799
0,0195 3
0,24625
0,0375
0,36421
0,0141
-0,2657
0,0152 4
0,07417
0,0276
0,16334
0,0139
-0,19771
0,0156 5
-0,06256
0,034
0,044024
0,0224
-0,2334
0,0258 6
0,039067
0,0322
0,061667
0,0377
-0,04997
0,0434 7
-0,13348
0,0204
-0,1227
0,0245
-0,02345
0,0291 8
-0,07592
0,0437
-0,06621
0,0526
-0,02124
0,0619

17. Again, the fits for the second formula give much better results, so they will be used.

18. „Peak D“ – fit 1
I=A(1+b2P2(cosq))

20. „Peak D“ – fit 2
I=A(1+b2P2(cosq)+b4P4(cosq))

22. J‘
b2 (fit 1)
Db2
b2 (fit 2)
b4 (fit 2)
Db4
1,8545
0,182
1,8923
0,192
-0,10015
0,139 1
1,7377
1,8192
0,2
-0,2131
0,147 2
1,5114
0,138
1,5863
0,143
-0,1912
0,112 3
1,4466
0,21
1,5281
0,224
-0,20664
0,178 4
0,96951
0,251
1,3342
0,232
-0,88042
0,203 5
1,2466
0,209
1,2946
0,227
-0,11906 6
1,2021
0,22
1,2634
0,239
-0,15154
0,204 7
0,9887
0,153
1,1738
0,136
-0,54136
0,127 8
1,2743
0,284
1,243
0,304
0,077825
0,263

24. „Peak G“ – fit 1
I=A(1+b2P2(cosq))

26. „Peak G“ – fit 2
I=A(1+b2P2(cosq)+b4P4(cosq))

28. J‘
b2 (fit 1)
Db2
b2 (fit 2)
b4 (fit 2)
Db4
1,487
0,101
1,5263
0,106
-0,09999
0,0845 1
1,5638
0,123
1,544
0,13
0,050664
0,104 2
1,6289
0,0749
1,6417
0,0795
-0,03304
0,0615 3
1,0447
0,161
1,2737
0,145
-0,55694
0,124 4
1,4149
0,274
1,3527
0,289
0,15713
0,244 5
1,1635
0,227
1,165
0,246
-0,00371
0,217 6
0,89705
0,116
1,0246
0,117
-0,30587
0,107 7
0,68913
0,138
0,85478
0,143
-0,38911
0,137 8
1,0506
0,264
0,88078
0,27
0,4134
0,265

31. V(m+5)

32. „Peak A“ – fit 1
I=A(1+b2P2(cosq))

34. „Peak A“ – fit 2
I=A(1+b2P2(cosq)+b4P4(cosq))

36. J‘
b2 (fit 1)
Db2
b2 (fit 2)
b4 (fit 2)
Db4
1,2189
0,0287
1,2488
0,0276
-0,07404
0,0237 1
0,64142
0,0768
0,84326
0,0296
-0,47193
0,0285 2
0,57808
0,0431
0,69487
0,0171
-0,27143
0,017 3
0,47721
0,0314
0,53331
0,0292
-0,11291
0,0303 4
0,25824
0,0233
0,29722
0,0236
-0,08791
0,0258

38. „Peak B“ – fit 1
I=A(1+b2P2(cosq))

40. „Peak B“ – fit 2
I=A(1+b2P2(cosq)+b4P4(cosq))

42. J‘
b2 (fit 1)
Db2
b2 (fit 2)
b4 (fit 2)
Db4
0,10063
0,0125
0,1072
0,0147
-0,01459
0,0168 1
-0,20745
0,0136
-0,17662
0,0135
-0,06664
0,0162 2
-0,19441
0,0342
-0,10975
0,0324
-0,18324
0,0382 3
-0,10005
0,0138
-0,07613
0,0148
-0,05221
0,0175 4
-0,10907
0,0364
-0,0349
0,0374
-0,16176
0,0436

44. „Peak D“ – fit 1
I=A(1+b2P2(cosq))

46. „Peak D“ – fit 2
I=A(1+b2P2(cosq)+b4P4(cosq))

48. J‘
b2 (fit 1)
Db2
b2 (fit 2)
b4 (fit 2)
Db4
1,5287
0,0992
1,5704
0,104
-0,10649
0,0819 1
1,5877
0,111
1,5964
0,117
-0,02687
0,0969 2
1,429
0,151
1,4587
0,162
-0,07517
0,131 3
1,37
1,3553
0,123
0,044624
0,109 4
1,1182
0,195
1,0675
0,209
0,12423
0,19

50. „Peak G“ – fit 1
I=A(1+b2P2(cosq))

52. „Peak G“ – fit 2
I=A(1+b2P2(cosq)+b4P4(cosq))

54. J‘
b2 (fit 1)
Db2
b2 (fit 2)
b4 (fit 2)
Db4
1,5526
0,0602
1,6443
0,0392
-0,23508
0,0302 1
1,5034
0,0831
1,6248
0,0596
-0,30956
0,0462 2
1,2244
0,099
1,4259
0,0376
-0,49916
0,031 3
1,3671
0,113
1,4871
0,106
-0,30153
0,0854 4
1,2738
0,121
1,2439
0,13
0,07446
0,112

57. V(m+4) & V(m+5)

58. V(m+6), V(m+7), V(m+8), V(m+9), V(m+10) – J‘=0

59. „Peak A“ – fit 1
I=A(1+b2P2(cosq))

61. „Peak A“ – fit 2
I=A(1+b2P2(cosq)+b4P4(cosq))

63. J‘=0
b2 (fit 1)
Db2
b2 (fit 2)
b4 (fit 2)
Db4
V(m+6)
-0,67914
0,00494
-0,69176
0,00508
0,026181
0,00628
V(m+7)
1,3751
0,039
1,4342
0,0287
-0,14865
0,0234
V(m+8)
1,5472
0,0377
1,6107
0,0195
-0,16266
0,0152
V(m+9)
1,5503
0,0745
1,667
0,0461
-0,29896
0,0353
V(m+10)
1,6934
0,042
1,6857
0,0443
0,02006
0,0339

64. „Peak B“ – fit 1
I=A(1+b2P2(cosq))

66. „Peak B“ – fit 2
I=A(1+b2P2(cosq)+b4P4(cosq))

68. J‘=0
b2 (fit 1)
Db2
b2 (fit 2)
b4 (fit 2)
Db4
V(m+6)
0,69321
0,0316
0,65747
0,0322
0,083996
0,0326
V(m+7)
1,2832
0,098
1,2096
0,0981
0,18342
0,0863
V(m+8)
0,97405
0,0919
0,91639
0,0968
0,13927
0,0918
V(m+9)
0,57049
0,0549
0,62749
0,0586
-0,13039
0,0593
V(m+10)
1,3592
0,0458
1,3263
0,0441
0,099806
0,0394

69. „Peak D“ – fit 1
I=A(1+b2P2(cosq))

71. „Peak D“ – fit 2
I=A(1+b2P2(cosq)+b4P4(cosq))

73. J‘=0
b2 (fit 1)
Db2
b2 (fit 2)
b4 (fit 2)
Db4
V(m+6)
2,0183
0,177
1,99
0,182
0,091099
0,137
V(m+7) 2
0,347
0,337
0,44249
0,235
V(m+8)
1,661
0,244
1,7725
0,255
-0,289
0,19
V(m+9)
1,8085
0,201
1,6281
0,164
0,56971
0,141
V(m+10)
1,9017
0,186
1,8866
0,196
0,040398
0,142

74. „Peak G“ – fit 1
I=A(1+b2P2(cosq))

76. „Peak G“ – fit 2
I=A(1+b2P2(cosq)+b4P4(cosq))

78. J‘=0
b2 (fit 1)
Db2
b2 (fit 2)
b4 (fit 2)
Db4
V(m+6)
1,8527
0,127
1,9483
0,122
-0,25303
0,0869
V(m+7)
1,5703
0,276
1,9131
0,229
-0,8802
0,172
V(m+8)
1,8235
0,217
1,627
0,191
0,51842
0,155
V(m+9)
1,9747
0,12
2,0244
-0,15953
0,0886
V(m+10)
1,5868
0,139
1,7724
0,0807
-0,57386
0,0645

81. Summary figures:

82. b2 vs i and J´ V(m+4); J´= 0-8; fit 2 V(m+5); J´= 0-4; fit 2
V(m+i); i = 6-10 (J´= 0); fit 2

83. See explanation
below
See explanation
below
See explanation below

84. Comment:
1) The drop in b2 from i= 4 to i = 5 (and from i = 8 to i = 9), for the„H*+Br“ channel (peak B), i.e. an
increasing perpendicular transition contribution, is for those V(m+i) states which experience largest interactions with the E(0) (and E(1)) state(s),See: :

85. -hence those states which experience largest E state character, but according to
Fig. from HBr-VMI manuscript

86. -an increased E character will result in an enhanced perpendicular transition contribution
The perpendicular transition contribution is even larger for J´s larger than zero (J´>0) :
: ) The drop (enhanced perpendicular contribution) in the „H* + Br*“ for i = 6 is a bit of a surprise and could possibly be because of a signal overlap or interaction with the f3D1(1) state(?). …SEE below

87. More about V(m+6) and f3D1(v):

88. https://notendur.hi.is/~agust/rannsoknir/papers/jcp93-4624-90.pdf::
These look like
Q lines of a Rydberg
state
H81Br+
H79Br+
81Br+
79Br+ H+
V(m+6);Q
J´= ?

89. It does not look as if there is any overlap between V(m+6), J´= 0 and f3D1(1) peaks
-anyway the KER for V(m+6) fits nicely into the trend of the KER´s for V(m+i); i = 4-10 (see Fig. below)
BUT: possibly there is a strong near –resonanace interaction between V(m + 6), J´= 0 and f3D1(v´=1), J´= 0 resulting in an
enhanced perpendicular character of the V(m + 6) photodissociation! NB according to C&G (see slide 87 above) the
energy difference is only DE J´= 9.4 cm-1!....
: Fig. from HBr-VMI manuscript

90. https://notendur.hi.is/~agust/rannsoknir/papers/jcp93-4624-90.pdf:

91. …NB: J´= 0 level of V(m+6) should not be affected by
f3D1(v´=1) since W = 1, hence J´= 0 does not exist!
BUT:
79Br+
V(m+6);Q
# = peak measured in Crete
Possibly this is the J´= 0 peak and that peak # is J´= 1 but not J´=0 H+
x103/cm-1