17.   Spectral Lines: Selection Rules, Intensities, Transition Probabilities, Values, and Line Strengths

• 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 y_n and z_n 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 S_M 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 - P							D - 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