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Concept
Singlet state
Summary
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 . 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 in this singlet-style terminology has a simple relationship to the spin quantum number: , and .
Singlet-style terminology is also used for systems whose mathematical properties are similar or identical to angular momentum spin states, even when traditional spin is not involved. In particular, the concept of isospin was developed early in the history of particle physics to address the remarkable similarities of protons and neutrons. Within atomic nuclei, protons and neutrons behave in many ways as if they were a single type of particle, the nucleon, with two states. The proton-neutron pair thus by analogy was referred to as a doublet, and the hypothesized underlying nucleon was assigned a spin-like doublet quantum number to differentiate between those two states. Thus the neutron became a nucleon with isospin , and the proton a nucleon with .
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