The energies and ANCs for 5Li resonances deduced from experimental p-$α$ scattering phase shifts using the effective-range and $Δ$ methods

Abstract: Recently a new $\Delta$ method for deducing the energy and asymptotic normalization coefficient (ANC) from phase-shift data has been formulated and applied to resonance states. This differs from the conventional effective-range function (ERF) method by fitting only the nuclear part of the ERF. It also differs from the method which was proposed for bound states by Ram\'irez Su\'arez and Sparenberg (see Ref. below) which also named the $\Delta$ method where a pole condition defines by the Eq. $\Delta_l=0$ ($\Delta_l$ is the function in the ERF determined only by the scattering phase shift). Here the standard pole condition, including the Coulomb part into the relate equation, is used for a resonant state. It has been shown that the ERF method does not work for large-charge colliding nuclei. Moreover, even for lower charges it is not clear that the results of the ERF method are accurately enough. The Coulomb part forms a background, which smooths an ERF energy dependence. Therefore, one needs to find when the ERF method becomes inaccurate and this requires recalculating some published results by the $\Delta$ method. This project has already been started in a paper for resonances in the $\alpha$-$\alpha$ scattering. Here this method is applied using the $\Delta_l$-function fittings to the experimental $p$-${}^4$He scattering phase-shift data in the $P_{3/2}$ and $P_{1/2}$ resonance states. The calculation results are compared with those obtained earlier by the ERF method. The main changes concern resonance energy and width.