Systematic study of $\mathrm{\Delta }$(1232) resonance excitations using single isobaric charge-exchange reactions induced by medium-mass projectiles of Sn

The fragment separator FRS has been used for the first time to measure the $(n,p)$- and $(p,n)$-type isobaric charge-exchange cross sections of stable ${}^{112,124}\mathrm{Sn}$ isotopes accelerated at $1A$ GeV with an uncertainty of $3\%$ and to separate quasielastic and inelastic components in the missing-energy spectra of the ejectiles. The inelastic contribution can be associated to the excitation of isobar $\mathrm{\Delta }$(1232) resonances and to the pion emission in $s$ wave, in both the target and projectile nuclei, while the quasielastic contribution is associated with the nuclear spin-isospin response of nucleon-hole excitations. The data lead to interesting results, where we observe a clear quenching of the quasielastic component, and their comparisons to theoretical calculations demonstrate that the baryonic resonances can be excited in the target and projectile nuclei. To go further in this investigation, we propose to study the excitation of baryonic resonances, taking advantage of the combination of high-resolving power magnetic spectrometers with the Wide Angle Shower Apparatus (WASA) calorimeter. These new measurements will allow us to determine the momenta of the ejectiles and pions emitted in coincidence after the single isobaric charge-exchange collisions, providing us unique opportunities to study the evolution of the baryonic resonance dynamics with the neutron-proton asymmetry through the use of exotic radioactive ion beams.

Figure 1

Schematic view of the FRS experimental setup used in the present work with the reaction target located at the entrance of the FRS spectrometer to induce the single isobaric charge-exchange reactions.

Figure 2

Identification matrix at the final focal plane of the FRS obtained from reactions induced by ${}^{112}\mathrm{Sn}$ impinging on the carbon target, where one can identify the single isobaric charge-exchange residues ${}^{112}\mathrm{Sb}$ and ${}^{112}\mathrm{In}$. In addition, the single electron charge state of ${}^{112}\mathrm{Sn}$ is marked by a dotted ellipse.

Figure 3

Missing-energy spectra obtained from the Pb, Cu, ${}^{12}\mathrm{C}$, and proton targets for the single isobaric charge-exchange reactions (${}^{112}\mathrm{Sn},{}^{112}\mathrm{Sb}$) and (${}^{112}\mathrm{Sn},{}^{112}\mathrm{In}$). The quasielastic and inelastic contributions are displayed with gray and brown histograms, respectively.

Figure 4

Missing-energy spectra obtained from the ${}^{12}\mathrm{C}$ (a) and proton (b) targets for the single isobaric charge-exchange reaction (${}^{124}\mathrm{Sn},{}^{124}\mathrm{Sb}$). The quasielastic and inelastic contributions are displayed with gray and brown histograms, respectively.

Figure 5

Total, quasielastic (qe), and inelastic cross sections as a function of the neutron excess of target nuclei for the (${}^{112}\mathrm{Sn},{}^{112}\mathrm{In}$) (a) and (${}^{112}\mathrm{Sn},{}^{112}\mathrm{Sb}$) (b) reactions. We also compare these data to the cross sections obtained for the (${}^{124}\mathrm{Sn},{}^{124}\mathrm{Sb}$) reaction. Lines represent the best data fit.

Figure 6

Direct contributions to the quasielastic [diagrams (a) and (b)], and inelastic [diagrams from (c) to (f)] $(n,p)$ and $(p,n)$ elementary processes. The emitted pion in the final state is assumed to come either from the decay $\mathrm{\Delta }\to N\pi$ [diagrams (c) and (d)] or to be produced in $s$ wave without the excitation of any resonance [diagrams (e) and (f)]. Exchange contributions are obtained by interchanging the lines of the incoming neutron or proton of the projectile and the nucleon $\tau$ of the target.

Figure 7

Missing-energy spectra obtained from the Pb, Cu, ${}^{12}\mathrm{C}$, and proton targets for the single isobaric charge-exchange reactions (${}^{112}\mathrm{Sn},{}^{112}\mathrm{Sb}$) and (${}^{112}\mathrm{Sn},{}^{112}\mathrm{In}$) compared to the theoretical calculations described in Ref. [31]. See the legend displayed in the upper left panel for explanation.

Figure 8

Inelastic cross sections as a function of the neutron excess of target nuclei for the (${}^{112}\mathrm{Sn},{}^{112}\mathrm{In}$) (a) and (${}^{112}\mathrm{Sn},{}^{112}\mathrm{Sb}$) (b) reactions. The lines represent the contributions from $np$, $pp$, $pn$, and $nn$ interactions predicted by our theoretical model (see Tables 2 and 3). (c) Quasielastic cross sections for the (${}^{112}\mathrm{Sn},{}^{112}\mathrm{In}$) and (${}^{112}\mathrm{Sn},{}^{112}\mathrm{Sb}$) reactions compared to our calculations.

Figure 9

Schematic illustration of the WASA calorimeter at the intermediate focal plane of Super-FRS. This setup consists of a miniature drift chamber made of straw tubes, a counter barrel made of plastic scintillators, a superconducting solenoid magnet, and an external iron yoke. Upstream of the WASA device we will install tracking detectors to identify the incoming projectiles.