• ### Relative Strengths for Lines of Multiplets in LS Coupling

This table lists relative line strengths for frequently encountered symmetrical (P → P, D → D) and normal (S → P, P → D) multiplets in LS coupling. The strongest, or principal, lines are situated along the main diagonal of the table and are called x1, x2, etc. Their strengths normally diminish along the diagonal. The satellite lines yn and zn are usually weaker and deviate more from the LS values than the stronger diagonal lines when departures from LS coupling are encountered. The total multiplet strengths SM are also listed in this table. A discussion of their normalization as well as more extensive tables are given in Ref. [33].

### Relative Strengths for Lines of Multiplets in LS Coupling

Normal multiplets S - P, P - D, D - F, etc.   Symmetrical multiplets P - P, D - D, etc.

Jm Jm - 1 Jm - 2 Jm - 3 Jm - 4   Jm Jm - 1 Jm - 2 Jm - 3

Jm - 1 x1 y1 z1     Jm       x1 y1
Jm - 2   x2 y2 z2   Jm - 1 y1 x2 y2
Jm - 3     x3 y3 z3 Jm - 2   y2 x3 y3
Jm - 4       x4 y4 Jm - 3     y3 x4

Multiplicity

Multiplicity

1 2 3 4 5   1 2 3 4 5

S - PD - D
SM = 3 6 9 12 15 SM = 25 50 75 100 125

x1 3.00 4.00 5.00 6.00 7.00 x1 25.00 28.00 31.11 34.29 37.50
y1   2.00 3.00 4.00 5.00 x2   18.00 17.36 17.29 17.50
z1     1.00 2.00 3.00 x3     11.25 8.00 6.25
x4       5.00 1.25
P - P
SM = 9 18 27 36 45 y1   2.00 3.89 5.71 7.50
y2     3.75 7.00 10.00
x1 9.00 10.00 11.25 12.60 14.00 y3       5.00 8.75
x2   4.00 2.25 1.60 1.25 y4         5.00
x3       1.00 2.25
D - F
y1   2.00 3.75 5.40 7.00 SM = 35 70 105 140 175
y2     3.00 5.00 6.75
x1 35.00 40.00 45.00 50.00 55.00
P - D x2   28.00 31.11 34.29 37.50
SM = 15 30 45 60 75 x3     21.00 22.40 24.00
x4       14.00 14.00
x1 15.00 18.00 21.00 24.00 27.00 x5         7.00
x2   10.00 11.25 12.60 14.00
x3     5.00 5.00 5.25 y1   2.00 3.89 5.71 7.50
y2     3.89 7.31 10.50
y1   2.00 3.75 5.40 7.00 y3       5.60 10.00
y2     3.75 6.40 8.75 y4         7.00
y3       5.60 6.75
z1     .11 .29 .50
z1     .25 .60 1.00 z2       .40 1.00
z2       1.00 2.25 z3         1.00
z3         3.00