Hard photodisintegration of ${}^3\mathrm{He}$ into a $pd$ pair

The recent measurements of high energy photodisintegration of a ${}^3\mathrm{He}$ nucleus to a $pd$ pair at ${90}^{\circ }$ center of mass demonstrated an energy scaling consistent with the quark counting rule with an unprecedentedly large exponent of $s^{-17}$. To understand the underlying mechanism of this process, we extended the theoretical formalism of the hard rescattering mechanism (HRM) to calculate the $\gamma {}^3\mathrm{He}\to pd$ reaction. In HRM the incoming high energy photon strikes a quark from one of the nucleons in the target which subsequently undergoes hard rescattering with the quarks from the other nucleons, generating a hard two-body system in the final state of the reaction. Within the HRM we derived the parameter-free expression for the differential cross section of the reaction, which is expressed through the ${}^3\mathrm{He}\to pd$ transition spectral function, the cross section of hard $pd\to pd$ scattering, and the effective charge of the quarks being interchanged during the hard rescattering process. The numerical estimates of all these factors resulted in the magnitude of the cross section, which is surprisingly in good agreement with the data.

Figure 1

(a) Photon energy dependence of invariant momentum transfer $-t$. (b) Laboratory momenta of outgoing proton and deuteron as a function of photon energy. Solid lines denote proton, dashed lines denote deuteron. Calculations are done for ${\theta }_{\mathrm{cm}}={90}^{\circ }$ and ${60}^{\circ }$.

Figure 2

Typical diagram of hard rescattering mechanism of the ${\gamma }^3\text{He}\to pd$ reaction.

Figure 3

Effective center of mass angle vs the incident photon energy.

Figure 4

Fits of elastic $pd\to pd$ scattering cross section. The data in (a) are from [35] and in (b),(c) and (d) are from [36]. The curves are the fits to the data obtained using Eq.(35) with fit parameters from Table 1.

Figure 5

Energy dependence of the differential cross section at ${\theta }_{\mathrm{cm}}={90}^{\circ }$ scaled by an $s^{17}$ factor. The solid curve is the calculation according to Eq. (38). The experimental data are from Refs. [18, 30, 31]. See also the discussion in Ref. [18] on disagreement between DAPHNE and JLAB/CLAS data.

Figure 6

The angular dependence of $s^{17}$ scaled differential cross section for incoming photon energies of 1.3, 1.4, and 1.5 GeV.

Figure 7

Energy dependence of the $s^{17}$ scaled differential cross section for different values of ${\theta }_{\mathrm{cm}}$. The upper curve corresponds to ${\theta }_{\mathrm{cm}}={60}^{\circ }$, with the following curves corresponding to increments of the center-of-mass angle by ${10}^{\circ }$.

Figure 8

Typical quark-interchange mechanism of hard $pd\to pd$ scattering.

Figure 9

Hadronic probe to see baryons in a nucleus.