root-mean-square end-to-end distance, \(\text{<}r^{2}\text{>}^{1/2}\)

in polymers
The square root of the mean-square end-to-end distance of a @[email protected] chain averaged over all conformations of the chain. For a freely jointed chain consisting of \(N\) segments each of length \(L\), it is given by: \[\text{<}r^{2}\text{>}^{1/2} = \sqrt{N}\ L\] The subscript zero is used to indicate unperturbed dimensions, as in \(\text{<}r^{2}\text{>}_{0}^{1/2}\). If this term is used repeatedly, and if it is not confusing, the abbreviated name 'end-to-end distance' may be used.
Purple Book, 1st ed., p. 49 [Terms] [Book]