Spin singlet

In quantum mechanics, a singlet state usually refers to a system in which all electrons are paired. The term singlet originally meant a linked set of particles whose net angular momentum is zero, that is, whose overall spin quantum number ${\displaystyle s=0}$. As a result, there is only one spectral line of a singlet state. In contrast, a doublet state contains one unpaired electron and shows splitting of spectral lines into a doublet; and a triplet state has two unpaired electrons and shows threefold splitting of spectral lines.

Singlets and the related spin concepts of doublets and triplets occur frequently in atomic physics and nuclear physics, where one often needs to determine the total spin of a collection of particles. Since the only observed fundamental particle with zero spin is the extremely inaccessible Higgs boson, singlets in everyday physics are necessarily composed of sets of particles whose individual spins are non-zero, e.g. 1/2 or 1.

The origin of the term "singlet" is that bound quantum systems with zero net angular momentum emit photons within a single spectral line, as opposed to double lines (doublet state) or triple lines (triplet state). The number of spectral lines ${\displaystyle n}$ in this singlet-style terminology has a simple relationship to the spin quantum number: ${\displaystyle n=2s+1}$, and ${\displaystyle s=(n-1)/2}$.

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