Atomic level description in VALD3

Each level is characterized by energy E in cm-1, principal quantum number J, electronic configuration and term designation (name).

Electronic configuration is separated from term name by one or more spaces. If space occurs inside an electronic configuration, it is marked by a leading back slash "\ " (see examples below). In case when the term is known but not the electronic configuration the latter is replaced by a dash "-".

Odd parity levels have * in term names. Other information (quantum numbers) can be extracted from term names and electronic configurations. In VALD we consider 4 types of coupling schemes with the notations adopted by the NIST (see Atomic Spectroscopy, part 9, Notations for different coupling schemes), and described in XSAMS.

LS coupling

In LS coupling term name contains one block letter other than A and B. This block letter gives the value of the orbital quantum number L

S P D F G H I K L M N .... =

0 1 2 3 4 5 6 7 8 9 10 ....

A number in front of the block letter is multiplicity and it is equal to 2S+1, where S is spin. Any small letters in front of the multiplicity are ignored. Any numbers or block letters A, B after block letter containing L information are seniority indices and can be ignored when extracting quantum numbers.

Examples:

The first four levels have odd parity. For the last level number "2" after "D" is seniority. All these levels have the following sets of quantum numbers:

L, S vectors are coupled to give J = from L-S to L+S.

JJ coupling

In JJ coupling scheme term name contains two J values in (J1,J2), separated by comma. As usual, J1 and J2 have already been given in electronic configuration in <>. In this coupling scheme each level has the following quantum numbers: J, J1 and J2

Examples:

J=7.5, J1=6, J2=3.5

J1, J2 are coupled to give J = abs(J1-J2), ..., J1+J2. Number of levels is 2*min(J1,J2)+1.

JK coupling

In JK coupling scheme each level is characterized by the following set of quantum numbers: J, Jc, S2 and K. The latter two can be extracted from term name, where number in [ ] gives K, and number in front of [ ] is 2*S2+1. Jc is J-value of the parent term and is usually given in <> inside electronic configuration.

Examples:

K and S2 are coupled to give J: J=K+/-S2, the multiplicity of [K] term arises from the spin of the external electron(s). In first example we have one external electron, 6g, therefore S2=0.5, and each term produces pairs of levels with J=K+/-0.5 and we have two levels with J=5.0 and 6.0. Here Jc=1.5 = 3/2. In the second example S2=1 (spin of 3D), Jc=3.5, K=3.5, and this term produces 3 levels with J=4.5, 3.5, 2.5. Vector K is a sum of Jc and l of the external electron(s).

A space inside electronic configuration is noted as "\ ", and it emphasize the order of coupling: 4s electron first is coupled to 5D grandparent term to produce 6D<3/2>, and then 6g electron is coupled to 6D<3/2> parent to give a resulting term 2[11/2].

LK coupling

In LK coupling scheme each level is characterized by the following set of quantum numbers: J, L, S2 and K. S2 and K can be extracted from term name, where number in square brackets [] gives K, and number in front of the [] is 2*S2+1. L is extracted from the block letter at the end of electronic configuration, separated from it by en escaped space "\ ".

Example:

"D" gives us L=2 (sum of orbital angular momenta of the core and spin of the external electron), while S2 and K are extracted from term name as in JK connection. Here vector K is a sum of L and S1 - spin of the core (S1=1/2 in example).

Unknown coupling

In this case there is no term name. Sometimes electronic configuration exists. In this case Term Type = 'Unknown', and energy level is characterized by energy value, J and parity.

In VALD all J for individual levels are written in the form 1.0, 1.5, etc, while J-numbers inside configuration and in term names (J1,J2,K) are usually written as 1, 3/2, etc, although sometimes 1, 1.5, ... may be used.