Example of Collapsing Energy Levels

An example of collapsing levels is shown below. The example is for the relatively simple 1s(1) 3l(1) configuration of a He-like ion.

The table shows how a single base superconfiguration, composed of 1 K-shell electron and 1 M-shell electron, splits into configuration-averaged levels (in this case 3 levels), then into term split levels (6 levels), and finally fine structure split levels (10 levels).

Since the number of atomic transitions in a calculation is ~ (# levels)², collapsing levels can result in significant reductions in computational requirements.

Base Superconfiguration	Configuration-Averaged	L-S Term Split	Fine Structure Split
1K(1) 3M(1)	1s(1) 3s(1)	1s(1) 3s(1) 1S	1s(1) 3s(1) 1S 0
		1s(1) 3s(1) 3S	1s(1) 3s(1) 3S 1
	1s(1) 3p(1)	1s(1) 3p(1) 1P	1s(1) 3p(1) 1P 1
		1s(1) 3p(1) 3P	1s(1) 3p(1) 3P 0
			1s(1) 3p(1) 3P 1
			1s(1) 3p(1) 3P 2
	1s(1) 3d(1)	1s(1) 3d(1) 1D	1s(1) 3d(1) 1D 2
		1s(1) 3d(1) 3D	1s(1) 3d(1) 3D 1
			1s(1) 3d(1) 3D 2
			1s(1) 3d(1) 3D 3