Numerical Study of $\alpha$-$\alpha$ Phase Shifts Using the Phase Function Method

The $\alpha$--$\alpha$ scattering phase shifts are calculated using the phase function method with several pair potentials. We consider the interactions proposed in Ref. [1] (Morse-type potentials) and Ref. [2] (Gaussian-type potentials). The Coulomb interaction is included by employing the Bessel-function asymptotic form within the phase function method. A direct solution of the Schr\"{o}dinger equation with the Coulomb-function asymptotic form is also applied. The phase shifts obtained from these two approaches are compared for the partial-wave channels $l = 0^+$, $2^+$, and $4^+$. Experimental data from Refs.~\cite{Ref1,Ref2} are used to verify the results. The finite size of the $\alpha$ particles is discussed in relation to the short-range behavior of the pair potentials.





[1] A. Khachi, L. Kumar, and O. S. K. S. Sastri, Phys. Atom. Nucl. 85, 382 (2022)

[2] S. Ali, A. R. Bodmer, Nucl. Phys. 80, 99 (1966).