Repulsive Core of Effective $\alpha$-$\alpha$ Potential and the Pauli Principle

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Abstract
The α-α interaction is a typical one as the interaction between composite particles. The origin of the repulsive core employed in phenomenological α-α potentials is investigated in connection with the characteristic inner oscillation of the relative wave function which is attributed to the Pauli principle and the hard internal structure of the α-particle. It is shown that the elimination of the redundant solutions in the S and D waves leads to a unique description of the inner oscillation and the outer-most energy-independent node plays the role equivalent to the hard core radius. Arguments are developed so that the logical consequences obtained here is applicable to the interaction between the other composite particles. Validity of the effective α-α potential and connection with two nucleon potentials are also discussed. The importance of the angular momentum dependence of the effective potential should be emphasized, because the structural repulsive core disappears beyond some critical value of angular momentum.