Pion-induced double-charge exchange reactions in the Δ resonance region

We have applied the Giessen BUU (GiBUU) transport model to the description of the double-charge exchange (DCX) reaction of pions with different nuclear targets at incident kinetic energies of 120–180 MeV. The DCX process is highly sensitive to details of the interactions of pions with the nuclear medium and, therefore, represents a major benchmark for any model of pion scattering off nuclei at low and intermediate energies. The impact of surface effects, such as the neutron skins of heavy nuclei, is investigated. The dependence of the total cross section on the nuclear mass number is also discussed. We achieve a good quantitative agreement with the extensive data set obtained at LAMPF. Furthermore, we compare the solutions of the transport equations obtained in the test-particle ansatz using two different schemes: the full and the parallel ensemble methods.

Figure 1

The angular distributions for the charge exchange process ${\pi }^{-}p\to {\pi }^{0}n$ in the CM frame of the pion and proton. The plots are labeled by the kinetic energies of the pions in the laboratory frame. The data are taken from Ref. [38].

Figure 2

Comparison of the full and parallel ensemble methods. Angular distributions for the double-charge exchange process ${\pi }^{\pm }A\to {\pi }^{\mp }X$ at $E_{\mathrm{kin}}=180$ MeV. The error bars denote the $1\sigma$ statistical error of each point of the full ensemble run; the thin lines denote the $1\sigma$ statistical error of the parallel result.

Figure 3

Influence of the density distribution on the angular distributions for the double-charge exchange process ${\pi }^{+}\mathrm{Pb}\to {\pi }^{-}X$ at $E_{\mathrm{kin}}=180$ MeV. The solid line shows the result obtained with our present density distribution [43]; the dashed line was obtained with the previously used one [3, 1, 36], which contains no neutron skin.

Figure 4

The inclusive double-charge exchange total cross section as a function of the nuclear target mass at $E_{\mathrm{kin}}=120,$ 150, and $180$ MeV. The lines connecting our results are meant to guide the eye; the data are taken from Ref. [16] (left panel: $E_{\mathrm{kin}}=120,$ 150, and $180$ MeV; right panel: only $180$ MeV).

Figure 5

The scaling of the total charge exchange cross section according to Eq. (4.1) visualized by dividing ${\sigma }_{\mathrm{tot}}$ by the factor $A^{2/3}Q(Q-1)/(A-1)$ and plotting it as a function of $A-Q$. $Q$ denotes the number of protons in the case of $({\pi }^{-},{\pi }^{+})$ and the number of neutrons in $({\pi }^{+},{\pi }^{-})$. The points are GiBUU results at pion kinetic energies of $180$ MeV; the dashed line denotes a function proportional to $1/(A-Q)$, corresponding to the exact scaling.

Figure 6

Angular distributions for the double-charge exchange process ${\pi }^{\pm }A\to {\pi }^{\mp }X$ at $E_{\mathrm{kin}}=120,$ 150, and $180$ MeV. The data points are taken from [16]; only systematic errors are shown. The solid, dashed, and dotted lines represent the GiBUU results at 120, 150, and 180 MeV, respectively. The bold lines represent the results of the current study; the thin lines represent a $1\sigma$ confidence level for each point based upon our statistics.

Figure 7

Double differential cross sections for the DCX process ${\pi }^{\pm }O\to {\pi }^{\mp }X$ at $E_{\mathrm{kin}}=120,$ 150, and 180 MeV. The results at different angles are shown as function of the kinetic energies of the produced pions. Data are taken from [16], only statistical errors are shown. The GiBUU results are shown as histograms, where the fluctuations indicate the degree of statistical uncertainty.

Figure 8

Same as Fig. 7, but for Ca.

Figure 9

Same as Fig. 7, but for Pb at $E_{\mathrm{kin}}=180$ MeV.