Hello.
For example, In NIST ASD, it is said that configuration of 1st excited state of neutral Argon is 3s23p5[2P3/2]4s and Term symbol is 2[3/2]2.
It looks there are two term symbols here. One is [2P3/2] and another is 2[3/2]2.
I thought the term symbol represents total orbital (angular) momentum quantum number l, total spin quantum number s, total angular momentum quantum number j. It means there should be only one term symbol in each energy level as term symbol gives "total" angular-related quantum numbers.
How can I understand this? Is 1st one for fully-filled subshells while 2nd is only for rest of outer electrons?
Yes There are two term symbols here , and some times more in other places.
There are various symbol from various coupling in the NIST Atomic Spectra Database
First "LS" coupling:
"Structural entity " " Quantum numbers" " Group of all transitions"
Configuration (nili)Ni Transition array
Polyad (nili)Ni γS1 L1 nl S L, S L′ ... Supermultiplet
Term (nili)Ni γS L Multiplet
Level (nili)Ni γS L J Line
State (nili)Ni γS L J M Line component
The configuration may include several open subshells, as indicated by the i subscripts. The letter γ represents any additional quantum numbers, such as ancestral terms, necessary to specify a particular term.
As an example, the Ca I 3d4p 3D°2 level belongs to the 3D° term which, in turn, belongs to the 3d4p 3(P° D° F°) triplet triad. The 3d4p configuration also has a 1(P° D° F°) singlet triad. The 3d4s configuration has only monads, one 1D and one 3D. The 3d4s 3D2 - 3d4p 3D°3 line belongs to the corresponding 3D - 3D° triplet multiplet, and this multiplet belongs to the great Ca I 3d4s 3D - 3d4p 3(P° D° F°) supermultiplet of three triplet multiplets discussed by Russell and Saunders in their classic paper on the alkaline-earth spectra. The 3d4s - 3d4p transition array includes both the singlet and triplet supermultiplets, as well as any (LS-forbidden) intercombination or intersystem lines arising from transitions between levels of the singlet system and those of the triplet system. The order of the two terms in the transitions as written above, with the lower-energy term on the left, is standard in atomic spectroscopy. Examples of notations for complex configurations are given in Notations for Different Coupling Schemes.
Second "JJ" coupling :
Allowed J values for ljN equivalent electrons (jj coupling).
ljN Allowed J values
l1/2 1/2
l 21/2 0
l3/2 and l 33/2 3/2
l 23/2 0, 2
l 43/2 0
l5/2 and l 55/2 5/2
l 25/2 and l 45/2 0, 2, 4
l 35/2 3/2, 5/2, 9/2
l 65/2 0
l7/2 and l 77/2 7/2
l 27/2 and l 67/2 0, 2, 4, 6
l 37/2 and l 57/2 3/2, 5/2, 7/2, 9/2, 11/2, 15/2
l 47/2 0, 22, 42, 24, 44, 5, 6, 8
l 87/2 0
The allowed levels of the configuration nl N may be obtained by dividing the electrons into sets of two groups , Q + R = N. The possible sets run from Q = N - 2l (or zero if N > 2l) up to Q = N or Q = 2l + 2, whichever is smaller. The (degenerate) levels for a set with both Q and R nonzero have wave functions defined by the quantum numbers (αJ1, βJ2) J, with J1 and J2 deriving from the Q and R groups, respectively. The symbols α and β represent any additional quantum numbers required to identify levels. The J values of the allowed levels for each (αJ1, βJ2) subset are obtained by combining J1 and J2 in the usual way.
Majid,
It looks you suggested me to study http://www.nist.gov/pml/pubs/atspec/index.cfm. I've read contents in this site and I added the obtained knowledge from the site to the Wikipedia (https://en.wikipedia.org/wiki/Term_symbol#Summary_of_various_coupling_schemes_and_corresponding_Term_symbols) for helping other people:)
Dear Aslam,
Firstly, I understand your notation such as [{(l1, l2)L, s1}K, s2]J. This notation means l1 and l2 are coupled to give L, L is coupled with s1 to give K, K and s2 are coupled to give J.
And it is obvious that LK and Jc-K coupling corresponds to LS1 coupling and J1L2 coupling in http://www.nist.gov/pml/pubs/atspec/index.cfm. I've studied this after reading Majid Monajjemi 's comment and I've added summary of the site to the Wikipedia ((https://en.wikipedia.org/wiki/Term_symbol#Summary_of_various_coupling_schemes_and_corresponding_Term_symbols):)
Can I have one question about obtaining total angular momentum quantum number for core electrons, Jc in your process? You suddenly suggested Jc is either 3/2 and 1/2. How could you obtain these values? The core electrons are 3p5. The addtion rule of angular momentums of multiple electrons gives possible L1 = 5,4,3 and possible S1 = 5/2, 3/2 for core electrons. So, possible J1 from coupling of L1 and S1 can be many. I'm wondering how 3/2 and 1/2 comes out.
Oh I see.
You are using concept of "a missing electron from fully filled subshell is equal to a hole start to occupy open subshell". I was shock about how it is cleaver! Thanks to know this smart technique!
I think the inversion of order of J values in arranging them in the order of increasing energy with the same Term can be explained by Hund's 3rd rule.
In terms of applying Pauli Exclusion Principle (PEP), firstly I can imagine that LS coupling Term (2Smax + 1)Lmax is not allowed if at least two electrons are in the same subshell as these electrons have same n, l, ml, ms when mL = Lmax, mS = Smax. In this sense, I understand that Term 3D is not allowed from p2 electronic configuration. And I also think that 3P is not allowed as there is at least one PEP-violating combination of ml1, ml2, ms1, ms2 which make one of possible mL and mS with the given Term. For example, in mL = 0 and mS = 1, there is a combination of ml1 = ml2 = 0, ms1 = ms2 = 1/2 so 3D has potential to violate PEP.
Could you please confirm my approach to apply PEP in Term symbol is right?
I'm just afraid that I've already received too much support from you.
You're really making my eye open:)
Yeah, the reference "R. Liboff, chapter 12.4, Introductory Quantum Mechanics, 4th ed. Addison Wesley, 2003" shows details of what you said, Aslam, although applying Pauli exclusion principle to reduce Terms is not straightforward job, especially for more than 3 electrons.
Thanks for you comment.s. I feel better understanding:)