Analyses of low energy $\pi^+ -^{12}$C, $^{16}$O elastic scattering data using inverse scattering theory and suggested scaling method

Abstract

The elastic scattering data for low-energy ($ T_\pi \leq 80 $ MeV) positive pions from carbon-12 and oxygen-16 nuclei has been successfully analyzed by using our local optical potential based on the inverse scattering theory within the framework of the full Klein-Gordon equation. It is found that the same potential parameters used in the $\pi^- - ^{12}$C, cases are still valid for $\pi^+ - ^{12}$C with a need to change the three parameters $R_0$, $V_1$ and $W_3$ with the pion's incident kinetic energy $ T_\pi $. This is also found to hold in analyzing successfully the measured angular distributions for $\pi^+ - ^{16}$O in the same energy region. The systematic trends in the changed three free potential parameters $R_0$, $V_1$ and $W_3$ with $ T_\pi $ are compared to their counterparts for $\pi^+ - ^{12}$C. The different relations obtained for the two cases under consideration, $\pi^+ - ^{12}$C and $\pi^+ - ^{16}$O, reveals their dependence on the atomic weight of the target nucleus. As such, this suggests the use of a scaling method to obtain the potential parameters for a certain pion-nucleus system, as $\pi^+ - ^{16}$O, from a similar nearby one, as $\pi^+ - ^{12}$C. Further studies are needed to confirm our new findings.