Nucleon microscopy in proton-nucleus scattering via analysis of bremsstrahlung emission

We investigate an idea of how to use analysis of bremsstrahlung photons to study the internal structure of a proton under nuclear reaction with a nucleus. A new model is constructed to describe bremsstrahlung emission of photons which accompanies the scattering of protons off nuclei. Our bremsstrahlung formalism uses a many-nucleon basis that allows us to analyze coherent and incoherent bremsstrahlung emissions. Because a scattered proton can be under the influence of strong forces and produces the largest bremsstrahlung contribution to the full spectrum, we focus on accurate determination of its quantum evolution in relation to the nucleus based on quantum mechanics. For this purpose, we generalize the Pauli equation with an interacting potential describing evolution of a fermion inside the strong field, including the electromagnetic form factors of nucleons based on deep inelastic scattering theory. Anomalous magnetic momenta of nucleons reinforce our motivation to develop such a formalism. The full bremsstrahlung spectrum in our model (after renormalization) is dependent on form factors of the scattered proton. In our calculations we choose the scattering of $p+{}^{197}\mathrm{Au}$ at a proton beam energy of 190 MeV, where experimental bremsstrahlung data were obtained with high accuracy. We show that the full bremsstrahlung spectrum is sensitive to the form factors of the scattered proton. In the limit without such form factors, we reconstruct our previous result (where form factors of the scattered proton were not studied).

Figure 1

The calculated electric and magnetic bremsstrahlung emissions in the scattering of protons off the ${}^{197}\mathrm{Au}$ nuclei at proton beam energy $E_{\mathrm{p}}=190$ MeV in comparison with experimental data [30] [components are defined in Eqs. (52) and (E1, E2, E3, E4, E5, E6, E7, E8)]. (a) Electric emission defined by $p_{\mathrm{el}}$ (blue dashed line), magnetic emission defined by $p_{\mathrm{mag},1}$ (red dash-dotted line), and magnetic emission defined by $p_{\mathrm{mag},2}$ (green dash–double-dotted line). (b) Contributions of the bremsstrahlung emission given by term $p_{\mathrm{q},1}$ with different $Q$ in comparison with electric and magnetic emissions.

Figure 2

Function of errors defined in Eq. (57) in dependence on $Q$ for bremsstrahlung emissions in the scattering of protons off ${}^{197}\mathrm{Au}$ nuclei at a proton beam energy of $E_{\mathrm{p}}=190$ MeV (we calculate the full matrix element as a summation of terms $p_{\mathrm{el}}, p_{\mathrm{mag},1}, p_{\mathrm{mag},2}$, and $p_{\mathrm{q},1}\left(Q\right)$; experimental data used are from Ref. [30]).

Figure 3

The calculated probabilities of emission of the bremsstrahlung photons during $\alpha$ decay of nucleus ${}^{226}\mathrm{Ra}$ in comparison with experimental data [53] (parameters of the model are used in Ref. [53]). Here, black rectangles are experimental data [53], the blue solid line is the full spectrum, the green dashed line is the spectrum of emission from the tunneling region, the red dash-dotted line is the spectrum of emission from the external region (starting from the external turning point), and the short dashed line is the interference term.