Measurement and analysis of nuclear $\gamma$-ray production cross sections in proton interactions with Mg, Si, and Fe nuclei abundant in astrophysical sites over the incident energy range $E=30–66$ MeV

The modeling of nuclear $\gamma$-ray line emission induced by highly accelerated particles in astrophysical sites (e.g., solar flares, the gas and dust in the inner galaxy) and the comparison with observed emissions from these sites needs a comprehensive database of related production cross sections. The most important reactions of protons and $\alpha$ particles are those with abundant target elements like C, O, N, Ne, Mg, Si, and Fe at projectile energies extending from the reaction threshold to a few hundred MeV per nucleon. In this work, we have measured $\gamma$-ray production cross section excitation functions for 30, 42, 54, and 66 MeV proton beams accelerated onto ${}^{\mathrm{nat}}\mathrm{C}$, $\mathrm{C}+\mathrm{O}$ (Mylar), ${}^{\mathrm{nat}}\mathrm{Mg}, {}^{\mathrm{nat}}\mathrm{Si}$, and ${}^{56}\mathrm{Fe}$ targets of astrophysical interest at the Separated Sector Cyclotron (SSC) of iThemba LABS (near Cape Town, South Africa). The AFRODITE array equipped with eight Compton suppressed high-purity (HPGe) clover detectors was used to record $\gamma$-ray line energy spectra. For known, intense lines previously reported experimental data measured up to $E_p\simeq 25$ MeV at the Washington and Orsay tandem accelerators were thus extended to higher proton energies. Our experimental data for the last three targets are reported here and discussed with respect to previous data and to the Murphy et al. compilation [Astrophys. J. Suppl. Ser. 183, 142 (2009)], as well as to the predictions of the nuclear reaction code talys. The overall agreement between theory and experiment obtained in first-approach calculations using default input parameters of talys has been appreciably improved by using modified optical model potential (OMP), level deformation, and level density parameters. The OMP parameters have been extracted from theoretical fits to available experimental elastic and inelastic nucleon scattering angular distribution data by means of the coupled-channels reaction code optman. Experimental data for several new $\gamma$-ray lines are also reported and discussed. The astrophysical implications of our results are emphasised.

Figure 1

Calibrated $\gamma$-ray spectra produced by the scattering of 42 MeV protons off the ${}^{\mathrm{nat}}\mathrm{Mg}$ target. The blue histograms correspond to the raw spectrum of one clover crystal without background suppressions, while the red spectrum is background subtracted.

Figure 2

Absolute $\gamma$-ray efficiencies for a single HPGe crystal. The green data points correspond to experimental values measured using standard radioactive sources of ${}^{60}\mathrm{Co}, {}^{137}\mathrm{Cs}$, and ${}^{152}\mathrm{Eu}$. The black data points represent the results obtained via geant4 simulations at various $\gamma$-ray energies that were normalised to experimental data. The red solid line is the result of the fit of the efficiency function of Eq. (1) [34] to the experimental data and to the normalized geant4-simulated values.

Figure 3

$\gamma$-ray angular distributions. Top: for main lines produced in interactions of 42 MeV protons with the ${}^{\mathrm{nat}}\mathrm{Mg}, {}^{\mathrm{nat}}\mathrm{Si}$, and ${}^{56}\mathrm{Fe}$ targets. Bottom: for the line at $E_{\gamma }=1368$ keV emitted by the ${}^{24}\mathrm{Mg}$ isotope upon inelastic scattering of 30 MeV protons.

Figure 4

Total production cross sections for $\gamma$-ray lines produced in proton reactions with the ${}^{24}\mathrm{Mg}$ (open circles) and ${}^{\mathrm{nat}}\mathrm{Mg}$ (filled circles) targets (see Table 3 for more details and Table 1 for the properties of targets used in this and previous works). The experimental data are shown with full circles: in blue color (this work), in red (Dyer et al. [8]), in green (Belhout et al. [11, 12]), and in orange (Lesko et al. [13]). The dashed-dotted curves correspond to predictions of the Murphy et al. semiempirical compilation [16]. The results of talys calculations performed with default parameters are shown by grey curves; those performed with our modified OMP and level structure parameters are depicted by black curves for $\gamma$-ray lines emitted by the most abundant isotope, and by red curves for $\gamma$-ray lines from the target of natural composition.

Figure 5

Same as in Fig. 4 but for $\gamma$-ray lines produced in proton reactions with the Si targets. The same symbols are used, except that here the green circles represent the experimental data of Benhabiles et al. [18, 19].

Figure 6

Same as in Fig. 4 but for $\gamma$-ray lines produced in proton reactions with the ${}^{56}\mathrm{Fe}$ target.

Figure 7

Illustrative examples of results from our theoretical analyses of experimental angular distribution cross section data for elastically scattered protons off ${}^{24}\mathrm{Mg}$ taken from the literature and considered in the optman code [40] for extracting new OMP and nuclear level deformation parameters used in our talys code calculations of $\gamma$-ray line production cross sections.

Figure 8

Same as in Fig. 7 but for scattered protons off the ${}^{28}\mathrm{Si}$ target

Figure 9

Same as in Fig. 7 for scattered protons off the ${}^{56}\mathrm{Fe}$ target.

Figure 10

Calculated nuclear $\gamma$-ray line emission spectra for LECRs produced by shock acceleration with the parameter $E_c=60$ MeV [26] interacting with interstellar matter in the inner Galaxy. The energies of $\gamma$-ray lines analyzed in this work are indicated by vertical labels in units of keV. The four spectra are calculated for various assumptions for the cross section data and the metallicity of the ambient medium. Black: cross section data derived with our modified parameters in the talys code and $M=3$, i.e., three-times solar metallicity; red: same, but $M=1$; green: cross section data derived with the default parameters of talys and $M=3$; blue: cross section data from the compilation of Murphy et al. [16] and $M=3$.