Absolute branching fraction measurements of exclusive D+ semileptonic decays

The molecular ions of linear alkanes prefer to fragment at the carbon-carbon bond away from the end of the chain since the cleavage of an inner bond creates a stable carbocation and a stable radical. Consequently, the mass signals of linear alkanes feature intense peaks in the middle of the mass-to-charge ratio plot with weaker peaks on either end. The fragmentation of each carbon-carbon bond with the release of a methyl group in each splitting leads to prominent peaks in the mass spectra...

The skeletal structure of polymers synthesized via radical polymerization is always branched. For example, the polymerization of ethylene by radical polymerization results in a low-density grade of polyethylene with a heavily branched skeletal structure. Here, the radical site abstracts hydrogen from the growing chain, and the radical site shifts from the end (a primary carbon center) to anywhere within the growing chain (a secondary carbon center). Consequently, the part of the chain from the...

Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.

The probability of having two carbon-13 atoms next to each other is negligible because of the low natural abundance of carbon-13. Consequently, peak splitting due to carbon-carbon spin-spin coupling is not observed in spectra. However, protons up to three sigma bonds away split the carbon signal according to the n+1 rule, resulting in complicated spectra.
A broadband decoupling technique is used to simplify these complex, sometimes overlapping, signals. Broadband decoupling relies on a...

This lesson delves into the mass spectrometry of branched alkane fragmentation. Branched alkanes possess secondary or tertiary carbon atoms, which generate relatively stable carbocations if the cleavage occurs at the branching point. The high stability of carbocations drives the instant fragmentation of branched alkanes. Accordingly, the branched alkane's molecular ion peak is very weak or invisible in the mass spectra, especially in comparison to a linear alkane.

A partial fraction is a component of a rational expression represented as the sum of simpler fractions. When a rational function is expressed as a ratio of two polynomials, it can often be decomposed into a sum of fractions whose denominators are simpler polynomials, typically linear or irreducible quadratic factors. This process is called partial fraction decomposition, and it is used to simplify complex expressions for integration, solving equations, or analysis.Partial fraction decomposition...