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Doublets continue to play an important role in physics. For example, the healthcare technology of magnetic resonance imaging is based on nuclear magnetic resonance. In this technology, a spectroscopic doublet occurs in a spin-1/2 atomic nucleus, whose doublet splitting is in the radio-frequency
The spectrum would have two signals, each being a doublet. Each doublet will have the same area because both doublets are produced by one proton each. The two doublets at 1 ppm and 2.5 ppm from the fictional molecule CH−CH are now changed into CH 2 −CH: The total area of the 1 ppm CH 2 peak will be twice that of the 2.5 ppm CH peak.
The two-Higgs-doublet model (2HDM) is an extension of the Standard Model of particle physics. [1] [2] 2HDM models are one of the natural choices for beyond-SM models containing two Higgs doublets instead of just one. There are also models with more than two Higgs doublets, for example three-Higgs-doublet models etc. [3]
Coupling to additional spins leads to further splittings of each component of the multiplet, e.g. coupling to two different spin-1/2 nuclei with significantly different coupling constants leads to a doublet of doublets (abbreviation: dd). Note that coupling between nuclei that are chemically equivalent (that is, have the same chemical shift ...
A classic example is the 1 H-NMR spectrum of 1,1-difluoroethylene. [5] The single 1 H-NMR signal is made complex by the 2 J H-H and two different 3 J H-F splittings. The 19 F-NMR spectrum will look identical. The other two difluoroethylene isomers give similarly complex spectra. [6]
Left: when 2 J-coupling constants are sufficiently unequal (Jab>Jbc) for spin ½ nuclei, a doublet of doublets with an intensity ratio of about 1:1:1:1 is seen in NMR spectra. Right: when Jab=Jbc for spin ½ nuclei, a triplet (collapsed or overlapping doublet of doublets) with an intensity ratio of about 1:2:1 is always seen in NMR spectra.
The ability of positronium to form both singlet and triplet states is described mathematically by saying that the product of two doublet representations (meaning the electron and positron, which are both spin-1/2 doublets) can be decomposed into the sum of an adjoint representation (the triplet or spin 1 state) and a trivial representation (the ...
Simulated pake doublet. A Pake Doublet (or "Pake Pattern") is a characteristic line shape seen in solid-state nuclear magnetic resonance and electron paramagnetic resonance spectroscopy. It was first described by George Pake. It arises from dipolar coupling between isolated two spin-1/2 nuclei, or from transitions in quadrupolar nuclei such as ...