Landolt-Brnstein - Group I Elementary Particles, Nuclei and Atoms 
Volume I/3: Numerical Tables for Angular Correlation Computations in a-, -and .-Spectroscopy: 3j-, 6j-, 9j-Symbols, F- and G-Coefficients 
1 Introduction....................................................................................................................................1

2 Angular correlation formalism.......................................................................................................2

3 Definition and properties of the tabulated coefficients...................................................................8

 3.1 The 3j-symbol....................................................................................................................8

 3.2 The 6j-symbol.................................................................................................................. 12

 3.3 The 9j-symbol.................................................................................................................. 17

 3.4 The F-coefficient .............................................................................................................21

 3.5 The G-coefficient .............................................................................................................22

4 Tabulation of 3j-symbols.............................................................................................................. 24
0 0 0 ; 0 0 0............................................................................................................................25
5 5/2 5/2 ; 3 -1/2 -5/2.............................................................................................................39
11/2 5 9/2 ; 7/2 -3 -1/2...........................................................................................................53
6 6 2 ; 1 -1 0...........................................................................................................................67
13/2 6 9/2 ; 3/2 -3 3/2 ............................................................................................................81
7 11/2 9/2 ; 6 -7/2 -5/2...........................................................................................................95
7 7 5 ; 6 -1 -5........................................................................................................................ 109
15/2 13/2 3 ; 3/2 -1/2 -1....................................................................................................... 123
15/2 15/2 6 ; 13/2 -1/2 -6..................................................................................................... 137
8 13/2 5/2 ; 5 -5/2 -5/2......................................................................................................... 151
8 15/2 11/2 ; -5 -1/2 11/2 ..................................................................................................... 165
17/2 5 7/2 ; 5/2 0 -5/2 .......................................................................................................... 179
17/2 7 9/2 ; 7/2 -7 7/2 .......................................................................................................... 193
17/2 8 11/2 ; 3/2 -2 1/2......................................................................................................... 207

5 Tabulation of 6j-symbols............................................................................................................ 221
0 0 0 ; 0 0 0.......................................................................................................................... 222
4 4 2 ; 7/2 7/2 1/2................................................................................................................. 237
5 4 2 ; 1 3 3.......................................................................................................................... 252
11/2 7/2 2 ; 1 3 5/2............................................................................................................... 267
11/2 5 9/2 ; 4 5/2 3............................................................................................................... 282
6 9/2 9/2 ; 4 5/2 9/2.............................................................................................................. 297
6 11/2 7/2 ; 9/2 2 5............................................................................................................... 312
6 6 6 ; 5 4 6.......................................................................................................................... 327
13/2 11/2 3 ; 3 4 9/2............................................................................................................. 342
13/2 6 9/2 ; 1 11/2 5............................................................................................................. 357
13/2 13/2 5 ; 11/2 5/2 4........................................................................................................ 372
7 11/2 5/2 ; 11/2 4 4............................................................................................................. 387
7 6 4 ; 9/2 9/2 5/2................................................................................................................. 402
7 13/2 7/2 ; 3 11/2 9/2.......................................................................................................... 417
7 7 1 ; 5 5 6.......................................................................................................................... 432
7 7 7 ; 7 4 5.......................................................................................................................... 447
15/2 6 5/2 ; 7/2 4 9/2............................................................................................................ 462
15/2 13/2 3 ; 3 5 13/2........................................................................................................... 477
15/2 7 3/2 ; 5/2 3 11/2.......................................................................................................... 492
15/2 7 11/2 ; 3/2 6 11/2........................................................................................................ 507
15/2 15/2 3 ; 11/2 9/2 7........................................................................................................ 522
8 5 3 ; 9/2 7/2 9/2................................................................................................................. 537
8 6 4 ; 13/2 7/2 11/2............................................................................................................. 552
8 13/2 9/2 ; 4 7/2 13/2.......................................................................................................... 567
8 7 3 ; 3 5 4.......................................................................................................................... 582
8 7 6 ; 13/2 13/2 13/2........................................................................................................... 597
8 15/2 7/2 ; 2 7/2 13/2.......................................................................................................... 612
8 15/2 11/2 ; 8 11/2 11/2...................................................................................................... 627
8 8 2 ; 6 6 5.......................................................................................................................... 642
8 8 6 ; 8 5 5.......................................................................................................................... 657
17/2 6 7/2 ; 3 5/2 6............................................................................................................... 672
17/2 13/2 5 ; 7/2 9/2 4.......................................................................................................... 687

17/2 7 7/2 ; 17/2 6 11/2........................................................................................................ 702
17/2 15/2 2 ; 1 2 15/2........................................................................................................... 717
17/2 15/2 5 ; 9/2 9/2 5.......................................................................................................... 732
17/2 8 1/2 ; 7 13/2 3............................................................................................................. 747
17/2 8 7/2 ; 17/2 8 5/2.......................................................................................................... 762
17/2 8 13/2 ; 5 13/2 5........................................................................................................... 777
17/2 17/2 2 ; 13/2 13/2 2...................................................................................................... 792
17/2 17/2 6 ; 6 6 17/2........................................................................................................... 807

6 Tabulation of some selected 9j-symbols .................................................................................... 818

7 Tabulation of F-coefficients.......................................................................................................828
0 1 1 ; 1 1............................................................................................................................. 829
2 5 6 ; 5 7............................................................................................................................. 844
3 4 8 ; 4 5............................................................................................................................. 859
7/2 13/2 8 ; 5 6..................................................................................................................... 874
4 9 1 ; 5 5............................................................................................................................. 889
9/2 21/2 8 ; 6 7..................................................................................................................... 904
5 11 5 ; 6 6........................................................................................................................... 919
11/2 21/2 5 ; 6 7................................................................................................................... 934
6 10 8 ; 4 6........................................................................................................................... 949
13/2 19/2 6 ; 4 6................................................................................................................... 964
7 9 6 ; 3 5............................................................................................................................. 979
15/2 17/2 3 ; 5 6................................................................................................................... 994
8 8 4 ; 6 7 ........................................................................................................................... 1009
17/2 17/2 4 ; 4 5................................................................................................................. 1024
9 9 1 ; 1 2 ........................................................................................................................... 1039
19/2 19/2 4 ; 3 4................................................................................................................. 1054
10 10 5 ; 4 6 ....................................................................................................................... 1069
21/2 23/2 3 ; 5 6................................................................................................................. 1084
23/2 17/2 5 ; 4 4................................................................................................................. 1099

8 Tabulation of Gamma-coefficients........................................................................................... 1107
0 0 0 ; 0 0 ........................................................................................................................... 1108
5/2 3/2 0 ; 2 2..................................................................................................................... 1121
7/2 9/2 3 ; 2 2..................................................................................................................... 1134
9/2 9/2 3 ; 3 3..................................................................................................................... 1147
11/2 9/2 3 ; 2 3 ................................................................................................................... 1160
13/2 9/2 4 ; 3 4 ................................................................................................................... 1173
15/2 11/2 6 ; 5 5................................................................................................................. 1186

9 Useful angular functions .......................................................................................................... 1199

10 References ............................................................................................................................. 1202


