Effects of Shape of Potential Energy Wells Detectable by Experiments on Proton-Proton Scattering

Abstract

The shapes of several types of potential wells giving approximate agreement with proton-proton scattering experiments are discussed. The somewhat poor agreement of the $K_0$, $E$ curve for the exponential well with experimental data is shown to be due to the "tail" of the well at large radii. In the case of the meson potential well the effect of very large values of the potential at small distances counteracts the effect of the tail. The experimental dependence of phase shift on energy is not reproduced by the inverse square potential well. The maximum theoretically admissible depth of this potential fits experiment at about 1 Mev. A series expansion is developed which gives the change of the phase shift caused by a given change in the potential well, and an example of the use of the formula is given. The approximate equality of the proton-proton and proton-neutron interactions is discussed, and the close agreement in the case of the meson potential is shown to be due to the large attraction at small distances.