Crystal rainbow channeling potential for 〈1 0 0〉 and 〈1 1 1〉 cubic crystallographic crystals

In this work we show a way how the crystal rainbow channeling effect can be applied for obtaining the interaction potential between 2 MeV protons and the cubic crystallographic crystals, in the cases of axial channeling of protons along (001) and (111) crystal directions. The procedure for construction of this potential has been based on our previous work in which the rainbow morphology was crucial for their determination. However, important improvements have been made. As a result, the two axial channeling directions can be treated using the same physical arguments leading to more consistent values of the fitting parameters in the ion-atom interaction potential.