Where a is the scattering length, k is the wave number, and \ delta ( k ) is the s-wave phase shift . The elastic cross section, \ sigma _ e, at low energies is determined solely by the scattering length,
2.
In fact the shape resonance occurs where the integral number of wavelengths of the particle sit within the potential of the nucleus of radius R . Therefore, the measure of the energies of the shape resonances in the neutron-nucleus scattering have been used in the years from 1947 to 1954 to measure the radii R of the nuclei with the precision of ??0 " 13 cm as it can be seen in the chapter " Elastic Cross Sections " of " A Textbook in Nuclear Physics " by R . D . Evans.
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