18.   ATOMIC LIFETIMES

(27)

(28)

If only one branch (i ) exists (or if all other branches may be neglected), one obtains A_ki  k = 1, and

k = 1/Aki .

(29)

Precision lifetime measurement techniques are discussed in Atomic, Molecular, & Optical Physics Handbook, Chaps. 17 and 18, ed. by G.W.F. Drake (AIP, Woodbury, NY, 1996).

19.   REGULARITIES AND SCALING

   

• Transitions in Hydrogenic (One-Electron) Species

  The nonrelativistic energy of a hydrogenic transition [Eqs. (1), (10)] is

  (30)

  Hydrogenic Z scaling. The spectroscopic quantities for a hydrogenic ion of nuclear charge Z are related to the equivalent quantities in hydrogen (Z = 1) as follows (neglecting small differences in the values of R_M):

  (E)Z = Z2(E)H ,	(31)
  (vac)Z = Z-2(vac)H ,	(32)
  SZ = Z-2 SH ,	(33)
  fZ = fH ,	(34)
  AZ = Z4 AH ,	(35)

  For large values of Z, roughly Z > 20, relativistic corrections become noticeable and must be taken into account.

  f-value trends. f values for high series members (large n values) of hydrogenic ions decrease according to

  f(n,l n, l ± 1) (n)-3 .

  (36)

  Data for some lines of the main spectral series of hydrogen are given in the table below.

  Some transitions of the main spectral series of hydrogen

  Transition	Customary namea	b  (Å)			gic		gk	Aki (108 s-1)
  1-2	(L)	1 215.	67		2		8
  1-3	(L)	1 025.	73		2		18		5.575(-1)d
  1-4	(L)	972.	537		2		32		1.278(-1)
  1-5	(L)	949.	743		2		50		4.125(-2)
  1-6	(L)	937.	80		2		72		1.644(-2)
  2-3	(H)	6 562.	80		8		18		4.410(-1)
  2-4	(H)	4 861.	32		8		32		8.419(-2)
  2-5	(H)	4 340.	46		8		50		2.530(-2)
  2-6	(H)	4 101.	73		8		72		9.732(-3)
  2-7	(H)	3 970.	07		8		98		4.389(-3)
  3-4	(P)	18 751.	0		18		32		8.986(-2)
  3-5	(P)	12 818.	1		18		50		2.201(-2)
  3-6	(P)	10 938.	1		18		72		7.783(-3)
  3-7	(P)	10 049.	4		18		98		3.358(-3)
  3-8	(P)	9 545.	97		18		128		1.651(-3)

  ^aL is often called Lyman , H = Balmer , P = Paschen , etc.
  ^bWavelengths below 2000 Å are in vacuum; values above 2000 Å are in air.
  ^cFor transitions in hydrogen, g_i(k) = 2(n_i(k))², where n_i(k), is the principal quantum number of the lower (upper) electron shell.
  ^dThe number in parentheses indicates the power of 10 by which the value has to be multiplied.

  
  

• Systematic Trends and Regularities in Atoms and Ions with Two or More Electrons

  Nonrelativistic atomic quantities for a given state or transition in an isoelectronic sequence may be expressed as power series expansions in Z^-1:

  Z-2 E = E0 + E1 Z-1 + E2 Z-2 + ...   ,	(37)
  Z2 S = S0 + S1 Z-1 + S2 Z-2 + ...   ,	(38)
  f = f0 + f1 Z-1 + f2 Z-2 + ...   ,	(39)

  where E₀, f₀, and S₀ are hydrogenic quantities. For transitions in which n does not change (n_i = n_k), f₀ = 0, since states i and k are degenerate.

  For equivalent transitions of homologous atoms, f values vary gradually. Transitions to be compared in the case of the "alkalis" are [31]

  Complex atomic structures, as well as cases involving strong cancellation in the integrand of the transition integral, generally do not adhere to this regular behavior.