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Spectroscopic factors for bound s-wave states derived from neutron scattering lengths

A simple and model-independent method is described to derive neutron single-particle spectroscopic factors of bound s-wave states in $^{A+1}Z = ^{A}Z \otimes n$ nuclei from neutron scattering lengths. Spectroscopic factors for the nuclei ^{13}C, ^{14}C, ^{16}N, ^{17}O, ^{19}O, ^{23}Ne, ^{37}Ar, and ^{41}Ar are compared to results derived from transfer experiments using the well-known DWBA analysis and to shell model calculations. The scattering length of ^{14}C is calculated from the ^{15}C_{g.s.} spectroscopic factor.