[ General Glossary, Quantum Glossary, Atomic Glossary ]
The "Lyman-alpha" lines for Hydrogen-Like Ions

The Hydrogen Lyman Series are the series of transitions between the n = 1 shell (ie. the K-shell) and the n > 1 shells (ie L-, M-, N-shells etc). The lines are those allowed by the selection rules Delta l = +/- 1, Delta j = 0, +/- 1. Below we give the energies/wavelengths of the first line (lowest energy; ie n = 1 shell to n = 2 shell transitions) in the series of hydrogen-like ions of the cosmically abundant elements.

In the case of H I, E_scl/E_act is the ratio of the energy of the line assuming a Bohr atom compared to the actual energy of the line. In the case of the other elements E_scl/E_act is the ratio assuming a simple Z² scaling (neglecting small changes due to R_M). For these ions, A_scl/A_act is the ratio between the A_ki assuming a simple Z⁴ scaling using the value for H I compared to the actual value.

Ion	Energy (eV) [Wavelength (nm)]	Aki (s-1)	fki	Notes
H I	10.198834 [121.67000]	4.69x108	4.16x10-1	Escl/Eact=0.999989
He II	40.813419 [30.37822]	7.52x109	4.16x10-1	Escl/Eact=0.999557 Ascl/Aact=0.997872
C VI	367.504180 [3.37360]	6.09x1011	4.16x10-1	Escl/Eact=0.999058 Ascl/Aact=0.998069
N VII	500.301225 [2.47810]	1.13x1012	4.16x10-1	Escl/Eact=0.998884 Ascl/Aact=0.996521
O VIII	653.595346 [1.89689]	1.93x1012	4.15x10-1	Escl/Eact=0.998669 Ascl/Aact=0.995349
Ne X	1021.729366 [1.21339]	4.70x1012	4.15x10-1	Escl/Eact=0.998193 Ascl/Aact=0.997872
Mg XII	1472.188925 [0.84210]	9.75x1012	4.15x10-1	Escl/Eact=0.997584 Ascl/Aact=0.997454
Si XIV	2005.197194 [0.61822]	1.81x1013	4.14x10-1	Escl/Eact=0.996895 Ascl/Aact=0.995420
S XVI	2621.274908 [0.47292]	3.08x1013	4.13x10-1	Escl/Eact=0.996043 Ascl/Aact=0.997935
Fe XXVI	6962.955199 [0.17798]	2.15x1014	4.08x10-1	Escl/Eact=0.990156 Ascl/Aact=0.996845

Things to Note

• There is actually a pair of allowed transitions (ie line components) for each line.
  • These correspond to transitions between the ground-state 1s ²S_1/2 term and the 2p ²P^o_1/2 or 2p ²P^o_3/2 terms (these are permitted dipole transitions)
    • The oscillator strengths are in the ratio of 1:2 (respectively) due to the different number of states see also Oscillator Strengths for H-like Ions)
  (eg see The Hydrogen Lyman series and Lyman-alpha Energies for various Ions)
• The energy of the lines scale as (approx) Z²
• The A_ki values scale as (approx) Z⁴
• The oscillator strengths of the lines are (approx) constant