By Robert G. Sachs
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CHAP. (3-36) Insertion of 7 from Eq. (3-36) into Eq. (3-35) provides an approximate relationship between it and £ which is the desired connection between range and depth, since TJ = K2a2 and £ = kga. Results thereby obtained are presented in Table 3-2 for those values of £ given in Table 3-1. The close agreement with the direct numerical this very simple method. shows the accuracy of integrations Although an accurate value of 7j is easily obtained, it does not follow that the corresponding wave function «(1) is also accurate.
3-2] WELL SQUARE 29 sensitivity to shape is a direct consequence of the large ratio of wavelength of the eigenfunction to range of the forces, a condition shown, in Section The wave function is 2-2, to be satisfied by the ground state function. capable of "seeing" only those effects which extend over a distance some what longer than a wavelength. We shall find that none of the potentials, Eqs. (3-3) to (3-6), as they stand, is adequate for a complete description of the ground state of the deuteron; the forces must be taken to be noncentral.
The saturation property can now be ascribed to the following character istic of the nuclear interaction : (c) Nucleons attract each other strongly only if they are in the same orbital state. According to the Pauli principle, only two neutrons and two protons be found in the same orbital state. Therefore strong attraction will will The binding energy of a occur between only four particles at a time. nucleus will be given roughly by the sum of the binding energies of the This means, of course, that for a sets of four nucleons contained in it.