ABC effect and resonance structure in the double-pionic fusion to ${}^3\mathrm{He}$

Exclusive and kinematically complete measurements of the double pionic fusion to ${}^3\mathrm{He}$ have been performed in the energy region of the so-called ABC effect, which denotes a pronounced low-mass enhancement in the $\pi \pi$-invariant mass spectrum. The experiments were carried out with the WASA detector setup at COSY (the cooler synchrotron at Forschungszentrum Jülich). Similar to the observations in the basic $pn\to d{\pi }^0{\pi }^0$ reaction and in the $dd\to {}^4\mathrm{He}{\pi }^0{\pi }^0$ reaction, the data reveal a correlation between the ABC effect and a resonance-like energy dependence in the total cross section. Differential cross sections are well described by the hypothesis of $d^{*}$ resonance formation during the reaction process in addition to the conventional $t$-channel $\Delta \Delta$ mechanism. The deduced $d^{*}$ resonance width can be understood from collision broadening due to Fermi motion of the nucleons in initial and final nuclei.

Figure 1

Distribution of the reconstructed neutron momenta in the $dd\to {}^3\mathrm{He}{\pi }^0{\pi }^0+n$ reaction at $T_d=1.4$ GeV (top) and 1.7 GeV (bottom), respectively. Data are given by solid dots. The dashed (dotted) lines show the expected distribution for the quasifree process based on the CD Bonn potential [33] deuteron wave function, if the spectator originates from the target (beam) deuteron. The peak near 0.5 GeV/$c$ originates from ${}^4\mathrm{He}$ contamination, which has been removed in subsequent analysis steps.

Figure 2

Scatter plot of the kinetic energy of the ${}^3\mathrm{He}$ ejectiles in the $dd\to {}^3\mathrm{He}{\pi }^0{\pi }^0+n$ reaction at $T_d=1.7$ GeV versus the ${}^3\mathrm{He}$ laboratory scattering angle ${\Theta }_{{}^3\text{He}}^{lab}$. At the top data are shown and at the bottom the corresponding MC simulation of the processes with either the neutron spectator in the target or in the beam. The high-density area at small angles and large kinetic energies corresponds to the process with the spectator neutron in the target, whereas the distribution at small energies and large scattering angles belongs to spectator neutrons in the beam. The area in between corresponds to coherent processes.

Figure 3

Energy dependence of the total cross section for the double-pionic fusion to ${}^3\mathrm{He}$ with the production of a ${\pi }^0{\pi }^0$ pair. Data obtained in this work by measurements of the $pd\to {}^3\mathrm{He}{\pi }^0{\pi }^0$ reaction at $T_p=1.0$ GeV and of the $dd\to {}^3\mathrm{He}{\pi }^0{\pi }^0+n_{spectator}$ reaction at $T_d=1.7$ GeV are given by the filled cross and the filled circles, respectively. They are compared to previous results from PROMICE/WASA [37] (open circle) and CELSIUS/WASA [27] (open square). The latter has been renormalized; see text. The shaded area denotes the estimated systematic uncertainties. The dotted curve gives the $d^{*}$ contribution, the dashed line the $t$-channel $\Delta \Delta$ process, and the solid line their (coherent) sum.

Figure 4

Dalitz plots of $M_{{}^3\text{He}{\pi }^0}^2$ versus $M_{{\pi }^0{\pi }^0}^2$ of the data at c.m. energies of $\sqrt{s}=3.25$ GeV, $\sqrt{s}=3.31$ GeV, $\sqrt{s}=3.35$ GeV, and $\sqrt{s}=3.41$ GeV (from top to bottom).

Figure 5

Distributions of $M_{{}^{3}He{\pi }^0}$ (left) and $M_{{\pi }^0{\pi }^0}$ (right) at $\sqrt{s}$ = 3.25, 3.31, 3.35 and 3.41 GeV (from top to bottom). Filled circles denote data from the quasifree runs, open crosses those from the $pd$ reaction at $T_p$ = 1.0 GeV ($\sqrt{s}$ = 3.416 GeV). Data from CELSIUS/WASA at $T_p$ = 0.89 GeV ($\sqrt{s}$ = 3.35 GeV) [27] are shown by open squares. The shaded area denotes the phase-space distribution. The dotted curve gives the $d^{*}$ contribution, the dashed line the $t$-channel $\Delta \Delta$ process and the solid line their sum.

Figure 6

Same as Fig. 5, but for the angular distributions of ${}^3\mathrm{He}$ (left) and ${\pi }^0$ (right) ejectiles in the center-of-mass system.