Skip to main content
Open Access Publications from the University of California

UC San Diego

UC San Diego Previously Published Works bannerUC San Diego

Polynomial coefficients. Application to spin-spin splitting by N equivalent nuclei of spin I > 1/2.

Published Web Location

The NMR intensity pattern of a nucleus split by N identical nuclei of spin 1/2 is given by the binomial coefficients. These are conveniently obtained from Pascal's triangle, equivalent to the chemist's branching diagram. Much less well-known is the pattern from splitting by N identical nuclei of spin I > 1/2. This was originally presented in terms of multinomial coefficients, but polynomial coefficients are more convenient. These describe the number of ways that N objects can be distributed to 2I + 1 numbered boxes. They arise in the polynomial expansion and are conveniently obtained from generalizations of Pascal's triangle. Examples and predictions are given.

Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you.

Main Content
For improved accessibility of PDF content, download the file to your device.
Current View