$\gamma$-ray emission in $\alpha$-particle interactions with C, Mg, Si, and Fe at $E_{\alpha }=50\text{–}90$ MeV

Nuclear deexcitation lines are regularly observed in the $\gamma$-ray emission spectra of strong solar flares. The most prominent lines are produced by interactions of protons and $\alpha$ particles, accelerated up to hundreds of MeV, with abundant nuclei of the solar atmosphere. Analysis and interpretation of these lines, which carry valuable information on the solar flare properties, need cross-section data for the $\gamma$-ray line emission in these interactions for a wide particle energy range. To this purpose, we measured the $\gamma$-ray emission in interactions of $\alpha$-particle beams of $E_{\alpha }=50\text{–}90$ MeV with target foils of C, Mg, Si, and Fe at the center for proton therapy of the Helmholtz-Zentrum Berlin. Setups of three high-purity Ge detectors and one $\mathrm{La}{\mathrm{Br}}_3$:Ce detector have been employed to detect the $\gamma$ rays in two experiment campaigns. Relatively large distances of the detectors from the target and pulsed beams with sub-ns-wide pulses allowed the separation of beam-induced prompt $\gamma$-ray emission from the targets from other $\gamma$ rays and neutron-induced background. $\gamma$-ray production cross sections for about 60 deexcitation lines from excited target nuclei or reaction products have been determined. For the strongest deexcitation lines from the major target isotopes, ${}^{12}\mathrm{C}$, ${}^{24}\mathrm{Mg}$, ${}^{28}\mathrm{Si}$, ${}^{56}\mathrm{Fe}$, there are now measured cross-section data from reaction threshold to $E_{\alpha }=90$ MeV that can be directly used for astrophysical applications like solar flares. Comparison of the results with a cross-section compilation for strong $\gamma$-ray lines in solar flare emissions and the predictions of the talys nuclear reaction code were done. They underline the importance of cross-section determinations at accelerator laboratories for the establishment of an accurate cross-section data base in a wide projectile energy range.

Figure 1

Full-energy-peak detection efficiencies of HP-Ge detectors at ${90}^{\circ }$ in the (a) 2015 and (b) 2016 campaign. Measured efficiency data with radioactive sources in the target chamber are shown by blue squares and simulated ones by red circles, connected with the dashed curve. The red upper and lower lines enclosing the simulation efficiencies represent the adopted uncertainty for the detection efficiency. For the HP-Ge detector in 2015, additionally to the standard radioactive sources, data from the decay of ${}^{55}\mathrm{Co}$ and ${}^{56}\mathrm{Co}$ in the activated beam dump could be obtained.

Figure 2

Time vs energy histogram of events in the $\mathrm{La}{\mathrm{Br}}_3$ detector from irradiation of the C target with 60-MeV $\alpha$ particles. The contour for prompt target $\gamma$ rays is shown by the black line. The broad structure inside the contour at $\mathrm{E}2\sim 3000$–4000 contains the full-energy and escape peaks of the 4.439-MeV line. Several other structures from narrow lines between $\mathrm{E}2\sim 150$–3000 can also be distinguished. Below the contour a weaker band extends at $\mathrm{T}2\approx 3680$, which is delayed by about 4 ns relative to prompt target $\gamma$ rays. It contains several narrow $\gamma$-ray lines, nearly exclusively from ${}^{56}\mathrm{Fe}$ and ${}^{52}\mathrm{Cr}$. These lines are most likely produced by interactions of secondary protons and neutrons in the target chamber walls and tubes. There is also some extension of these lines to longer delays, probably produced by the same particles in farther-away beam tubes and support structures. The large, vaguely triangular structure below $\mathrm{T}2\approx 3600$ is from interactions of secondary neutrons in the detector crystal.

Figure 3

$\gamma$-ray spectra recorded by the (a) $\mathrm{La}{\mathrm{Br}}_3$ at $\mathrm{\Theta }={76}^{\circ }$ and the (b) HP-Ge detector at $\mathrm{\Theta }={90}^{\circ }$ during irradiation of the carbon target by a 60-MeV $\alpha$-particle beam in the 2016 campaign. The blue lines show the spectra for events selected by the contour around the prompt $\gamma$ rays from the target (see Fig. 2), red lines are the spectra for all events with energy and timing signal. The green line for the $\mathrm{La}{\mathrm{Br}}_3$ detector are events dominated by interactions of secondary particles in the target chamber walls and tubes.

Figure 4

Spectrum with a ${}^{152}\mathrm{Eu}$ source at the target position, recorded by the Eurisys HP-Ge detector (blue symbols) and geant simulation with a detailed model of the experimental setup and all ${}^{152}\mathrm{Eu}$ decay lines with branching ratio $>0.1$% (red line).

Figure 5

Examples of measured differential $\gamma$-ray emission cross sections (blue symbols) and Legendre-polynomial fits (black lines). Data from (a) irradiation of the C target at $E_{\alpha }=75$ MeV, (b) irradiation of the Mg target at $E_{\alpha }=50$ MeV, (c) irradiation of the Si target at $E_{\alpha }=60$ MeV, and (d) irradiation of the Fe at target $E_{\alpha }=90$ MeV, the $\gamma$-ray line energies being indicated on the figures.

Figure 6

Compton-suppressed spectrum of the HP-Ge detector at $\mathrm{\Theta }={90}^{\circ }$ from the irradiation of the C target with 60-MeV $\alpha$ particles in the 2016 experiment with 1-keV/channel resolution below 1 MeV and 5-keV/channel resolution above. The lines listed in Table 4 are marked with their energy in keV, as well as lines due to interactions of secondary particles in the chamber walls and tubes (red numbers in parentheses).

Figure 7

Cross section for emission of the 4.44-MeV line in $\alpha$-particle reactions with natural carbon targets in the present experiment and in Belhout et al. [10] and with enriched ${}^{12}\mathrm{C}$ targets in Dyer et al. [11]. The dotted cyan line shows the values of the MKKS compilation [4], the dot-dashed black line is the result of calculations with the talys-1.6 code [5] with default parameters, including $\gamma$-ray lines in the window $E_{\gamma }=4439\pm 140$ keV, while the dashed magenta line shows the contribution of the 4439-keV line of ${}^{12}\mathrm{C}$.

Figure 8

Symbols show the 4.44-MeV line complex in Compton-suppressed spectra of the Ge detectors sitting at $\mathrm{\Theta }={90}^{\circ }$ for (a) $E_{\alpha }=50$ MeV and (b) $E_{\alpha }=75$ MeV. The different lines show calculated lineshapes for the 4439-keV line of ${}^{12}\mathrm{C}$ from inelastic scattering (dashed green), the 4319-keV line of ${}^{11}\mathrm{C}$ (dotted red), and the 4445-keV line of ${}^{11}\mathrm{B}$ (dot-dashed blue), the solid black line showing the sum of the calculated lines. Inelastic scattering off ${}^{12}\mathrm{C}$ accounts here to about 60% and 30% of the line complex at $E_{\alpha }=50$ and 75 MeV, respectively.

Figure 9

Symbols show measured cross-section data for four different lines emitted in $\alpha$-particle reactions with C (see Fig. 7 for more details). $\gamma$-ray line energies indicated in the panels refer to the lines listed in Table 4. The dotted cyan line show the values from the cross-section compilation [4] and the dot-dashed black lines are the results of talys calculations.

Figure 10

Compton-suppressed spectrum of the HP-Ge detector at $\mathrm{\Theta }={90}^{\circ }$ from the irradiation of the Mg target with 60-MeV $\alpha$ particles in the 2016 experiment in 1-keV/channel resolution below 3 MeV and 5-keV/channel resolution above. A selection of strong lines listed in Table 5 are marked with their energy in keV, as well as lines due to interactions of secondary particles in the chamber walls and tubes (red numbers in parentheses).

Figure 11

Symbols show (a) the 1.37-MeV line complex in Compton-suppressed spectra of the Ge detectors sitting at $\mathrm{\Theta }={147}^{\circ }$ for $E_{\alpha }=75$ MeV and (b) the 1.63-MeV line complex at $\mathrm{\Theta }={43}^{\circ }$ for $E_{\alpha }=60$ MeV. The dashed, dotted, and dot-dashed lines show calculated lineshapes for the strongest components. The sum of all components is shown by the solid black lines. Two separated calculations were done for the 1369-keV line of ${}^{24}\mathrm{Mg}$, one for the inelastic-scattering component, and one for the fusion-evaporation component, labeled “fev” in panel (a).

Figure 12

Symbols show measured cross-section data for four different lines emitted in $\alpha$-particle reactions with natural Mg target from the present experiment, and with enriched ${}^{24}\mathrm{Mg}$ targets from Belhout et al. [10] and Seamster et al. [23]. $\gamma$-ray line energies indicated in the panels refer to the lines listed in Table 5. The dotted cyan lines show the values from the cross-section compilation [4] and the dot-dashed black lines are the results of talys calculations. talys cross sections up to 45 MeV are the results for a ${}^{24}\mathrm{Mg}$ target, and above 45 MeV for a natural Mg target.

Figure 13

Compton-suppressed spectrum of the HP-Ge detector at $\mathrm{\Theta }={90}^{\circ }$ from the irradiation of the Si target with 60-MeV $\alpha$ particles in the 2016 experiment in 1-keV/channel resolution below 2.4 MeV and 5-keV/channel resolution above. A selection of lines listed in Table 6 are marked with their energy in keV, as well as the 847-keV line of ${}^{56}\mathrm{Fe}$ line produced in interactions of secondary particles in the chamber walls and tubes.

Figure 14

Symbols show (a) the 1.78-MeV and (b) the 1.27-MeV line complexes in Compton-suppressed spectra of the Ge detector sitting at $\mathrm{\Theta }={90}^{\circ }$ for $E_{\alpha }=60$ MeV. The dashed, dotted and dot-dashed lines show calculated lineshapes for the strongest components. The sum of all components is shown by the solid black lines. Two separated calculations were done for the 1779-keV line of ${}^{28}\mathrm{Si}$, one for the inelastic-scattering component and one for the fusion-evaporation component, labeled “fev” in panel (a).

Figure 15

Symbols show measured cross-section data for four different lines emitted in $\alpha$-particle reactions with natural Si target from the present experiment, and with enriched ${}^{28}\mathrm{Si}$ targets from Seamster et al. [23]. $\gamma$-ray line energies indicated in the panels refer to the lines listed in Table 6. The dotted cyan lines show the values from the cross-section compilation [4] and the dot-dashed black lines are the results of talys calculations. talys cross sections up to 45 MeV are the results for a ${}^{28}\mathrm{Si}$ target, and above 45 MeV for a natural Si target.

Figure 16

Compton-suppressed spectrum of the HP-Ge detector at $\mathrm{\Theta }={90}^{\circ }$ from the irradiation of the Fe target with 60-MeV $\alpha$ particles in the 2016 experiment in 1-keV/channel resolution below 2.0 MeV and 5-keV/channel resolution above. A selection of lines listed in Table 7 are marked with their energy in keV.

Figure 17

Symbols show measured cross-section data for six different lines emitted in $\alpha$-particle reactions with natural Fe target from the present experiment and from Belhout et al. [10], and with enriched ${}^{56}\mathrm{Fe}$ targets from Seamster et al. [23]. $\gamma$-ray line energies indicated in the panels refer to the lines listed in Table 7. The dotted cyan lines show the values from the cross-section compilation [4] and the black lines are the results of talys calculations, dashed for enriched ${}^{56}\mathrm{Fe}$ target and dot-dashed for natural Fe target.