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Questions tagged [term-symbols]

Term symbol are abbreviated descriptions of the (total) angular momentum quantum numbers in a multi-fermion system: atom, molecule, nucleus, meson. Each energy level of a composite system with a given constituent configuration is described by not only the constituent configuration but also its own term symbol, as the energy level also depends on the total angular momentum, including spin. Generalized usage is welcome.

In quantum mechanics, the term symbol is an abbreviated description of the (total) angular momentum quantum numbers in a multi-electron atom. Each energy level of an atom with a given electron configuration is described by not only the electron configuration but also its own term symbol, as the energy level also depends on the total angular momentum, including spin. Beyond atomic physics, they are also useful for molecules, nuclei, and mesons.

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What do term symbols with a half-integer "$L$" like $^3[3/2]_{1/2}$ mean?

Atomic term symbols are used to notate the angular momentum content of the electronic states of an atom, and are normally written down as $$^{2S+1}L_J$$ where the state has total spin $S$, spin multiplicity $2S+1$, total angular momentum $J$, and…
Emilio Pisanty
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Why is the specific notation used for term symbols useful?

This has bugged me for a long time. Term symbols describe electronic states of atoms which have well-defined total electronic angular momentum $J$ as well as total spin and orbital angular momenta $S$ and $L$; this is often a good description. My…
Emilio Pisanty
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Spectroscopic Notation - Does $n^{2S+1} L_J$ describe a Single Electron, or the state of multiple Electrons?

I was introduced to spectroscopic notation as $n^{2S+1} L_J$ (with L = "S, P, D.."). And the meaning that n stands for the principal quantum number (energy level, as known from the hydrogen atom), L being the orbital angular momentum (as known from…
Quantumwhisp
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Molecular orbital notation

I'm reading about papers about atom-ion interaction. There are some states as showned above. The notations of the states look like molecular orbital since $\Sigma$ and $\Pi$ is usually used in orbital hybridization to denote the different…
Han Bao
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Term symbols and the role of antisymmetrization

In the Hartree-Fock method for many-electron atoms, for a given eigenspace $\mathscr{E}$ of the unperturbed Hamiltonian (in a.u.) $$\hat{H}=\sum_{i=1}^Z \Big(-\frac{1}{2}\nabla^2_i-\frac{Z}{|\vec{r}_i|}+V_H(|\vec{r}_i|)\Big)$$ corresponding to the…
Simone
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What does degeneracy and multiplicity in Term symbol mean?

$^{2S+1}L_J$ was the term symbol. I watched a video online saying $2J+1$ was the fold of degeneracy to the term symbol. Specifically, for nitrogen, the term symbol for the lowest energy was $^4S_{3/2}$ which means it has 4 fold degeneracy. But I…
ShoutOutAndCalculate
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How to determine symmetry of the system from the term symbol?

I'm studying term symbols. I can derive them mechanically from the electron configuration using the complete table of microstates. Let's consider a typical example - an atomic carbon with the electron configuration $1s^22s^22p^2$. It has states…
Eenoku
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Ground state of Beryllium (${\rm Be}$)

Why is the ground state of Beryllium (${\rm Be}$) with electronic configuration $[{\rm He}]2s^2$ is $^1S_0$ and not $^3S_1$? The state $^3S_1$ has higher spin multiplicity.
Solidification
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The Existence of the $^1D$ term and the non-existence of the $^3D$ term?

Yesterday I asked this question concerning the existence of terms. This question is on the same topic. I have been looking at some tables (in Yang and Hamilton (2010), pg 199) at the terms that exist for two electrons in the same configuration. I…
Quantum spaghettification
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What's the relationship between Term Symbol and Wave Functions?

I'm trying to represent the Term Symbols in terms of wavefunctions and/or arrows for the excited state of hydrogen atom $2p^1$: $^2P_{3/2}$ and $^2P_{1/2}$. Ideas I have: The sum of $2J+1=4$ and $2J+1=2$ says how many different configurations…
Ang
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Nuclear physics notation

This is probably a very basic question about notation. If we have the following notation for Boron nuclei: $$^{12}_5 B(1^+)\;\text{or}\; ^{10}_3B(3^+)$$ What does the number in the parentheses mean? I guess $1$ and $3$ correspond to a spin number…
GeorgePhys
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Using symmetry and Group theory argumens to explain $\rm Fe^{2+}$ in a tetrahedral $\rm Td$ crystal field

I am trying to figure out how to explain $1s \rightarrow 3d$ spectroscopic transitions for $Fe^{2+}$ in $T_d$ symmetry. These transitions make up the pre edge region in K edge X-ray absorption spectroscopy (XAS). My goal is to rely on groupy theory…
Silverwilly
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What does the notation $^1 S_0$ represent in particle physics?

I'm coming across the notation $^1 S_0$, $^3 P_1$, $^1D_2$ etc. in relation to particle states. What do the two numbers and the letter represent? I've tried googling to no avail and it just appears in the lecture notes with no explanation. It's…
P4PL4
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How to determine possible term symbols in case there are more than 2 electrons?

I'm doing some exercises on $LS$ coupling during my self-study of atomic physics. I understand how to construct a table of possible microstates. I also understand how to map term symbols to those cells of microstates: the total wave function must be…
Eric
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When creating term symbols, how do you know if the angular momentum $L$ is antisymmetric of symmetric?

For example I'm trying to get the term symbol of $(1s)^{2}(2s)^{2}(2p)^2$ . In the answers they state the following: The combination of angular momenta $L_1 = L_2 = 1$ gives $L = 2$ (symmetric), $L = 1$ (antisymmetric) and $L = 0$ (symmetric).…
Caspertijmen1
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