Measurement of the low energy 25 Mg( p , γ ) 26 Al resonances

. The cosmic 1.809 MeV γ -ray emitted by the radioactive nucleus 26 Al in the Galaxy is one of the key observation targets of the γ -ray astronomy. The 26 Al is mainly produced by the 25 Mg(p ,γ ) 26 Al reaction in the stellar Mg-Al reaction cycle. At the astrophysical relevant temperatures, the reaction rates of 25 Mg(p ,γ ) 26 Al are dominated by several narrow resonances at low energy. This work reports a measurement of the low energy 25 Mg(p ,γ ) 26 Al resonances at Jinping Underground Nuclear Astrophysics experimental facility (JUNA) in the China Jinping Underground Laboratory (CJPL).


Introduction
The 1.809 MeV γ-ray emitted from the radioactive decay of 26 Al in the interstellar medium of the Galaxy has been observed by several satellites [1][2][3]. The half-life of 26 Al (7.17 × 10 5 y) is modest for the observation of the γ-ray astronomy. It is long enough that 26 Al synthesized in the interior of the star can survive and transfer to the interstellar medium. On the other hand, it is much shorter than the evolution time of the Galaxy so the observation of 26 Al decay is direct evidence of the ongoing nucleosynthesis in the Galaxy. Therefore, 26 Al is expected to be a tracer for stellar nucleosynthesis and a thermometer for its production site [4]. 26 Al can be synthesized by Mg-Al reaction cycle in the H burning environments, e.g., asymptotic giant branch (AGB) stars, Wolf-Rayet stars, O-Ne-Mg novae and core collapse supernovae. It is believed that 26 Al in the interstellar medium of the Galaxy is mainly from massive stars and partly from AGB stars and novae [4]. In the Mg-Al reaction cycle, 26 Al is produced via the 25 Mg(p, γ) 26 Al reaction and destroyed by β-decay or other reactions, e.g., 26 Al(p, γ) 27 Si, 26 Al(n, p) 26 Mg, 26 Al(n, α) 23 Na, depending on the astrophysical sites. Hence, the 25 Mg(p, γ) 26 Al reaction plays an important role in the study of the 1.809 MeV cosmic γ-ray and the origin of 26 Al in the Galaxy.
At astrophysical relevant temperatures, the reaction rates of 25 Mg(p, γ) 26 Al are characterized by several narrow resonances at low energy, among which the main contributors are 58, 92, 189, and 304 keV resonances. Due to its extremely low resonance strength, the 58 keV resonance has been only investigated by indirect method [5,6]. The 304 keV resonance has been directly measured in several works [7][8][9] thus its resonance strength is well determined. Strieder et al. [10] performed the first direct underground measurement of the 25 Mg(p, γ) 26 Al reaction and obtained the 92 and 189 keV resonance strengths. However, the 189 keV resonance strength result of the underground experiment [10] is larger than those obtained by ground measurement [11] and accelerator mass spectrometer(AMS) method [12].
In the present work, we performed a new direct measurement of the low energy resonances of 25 Mg(p, γ) 26 Al at the 400 kV accelerator of Jinping Underground Nuclear Astrophysics experimental facility (JUNA) [13]. Since the result of the 92 keV resonance has already been published elsewhere [14], we present some supplementary results here. Figure 1 shows the experimental setup. The proton beam provided by the 400 kV accelerator was collimated by two apertures and then bombarded on the 25 Mg enriched isotopic target which was directly cooled by flowing water. In the upstream of the target, a cold trap cooled by liquid nitrogen was used to suppress the carbon deposition on the target. The target and the end of the vacuum tube composed a Faraday cup, which was used to measure the beam current. A ring electrode applied with a voltage of −300 V was installed between the target and cold trap to suppress secondary electrons. 25 Mg isotopic targets made by 25 Mg enriched magnesium metal (98.81 ± 0.02% abundance) were used. The thickness of targets was set to be ∼60 μg/cm 2 . A Cr layer with a thickness of ∼40 μg/cm 2 was sputtered on the surface of each target to enhance the radiation resistance of the target. A near 4π BGO detector array was used to detect the γ-rays. The BGO detector array was calibrated by 137 Cs and 60 Co gamma sources. The single spectrum (sum of the spectra obtained by eight segments) and the sum spectrum (sum of the energies of all eight BGO segments) were obtained. The Monte Carlo simulation based on the GEANT4 software [15] was performed for the BGO detector array, which reproduced the calibration spectra well.

Data analysis
The resonance strength ωγ of a narrow resonance can be determined by measuring the maximum yield Y max of a thick target where λ R is the de Broglie wavelength and ε eff (E R ) is the effective stopping power of proton in the target. The effective stopping power is related to the concentration of 25 Mg in the target, which changed with the bombardment of the proton beam on the target. Therefore, in the measurement with high-intensity beam, such as 92 keV resonance measurement, the effective stopping power was monitored by measuring the maximum yield of the 304 keV resonance regularly. The maximum yield was calculated by Y max = A sum /η sum , where the A sum is the sum peak count and the η sum is the sum peak efficiency. The sum peak efficiency is related to γ-ray decay scheme as well as the primary γ-ray branching ratios of the resonance. Figure 2(a) shows the sum spectrum of the 304 keV resonance obtained by BGO detector array, in which the sum peak at E sum = 6610 keV is clearly visible. Figure 2(b) shows the single spectrum obtained by putting a 6400-6800 keV gate on the sum peak shown in Fig. 2(a). In contrast to the sum spectrum, many individual γ peaks, which are closely related to the decay scheme of the resonance, appear in the single spectrum.  A fitting program based on the expectation-maximization method [16] was developed to extract the decay scheme of the resonance from the experimental single spectrum, in which the primary γ-ray branching ratios were set as adjustable input parameters. The fitting process is 1) Initial primary γ-ray branching ratios were fed in the GEANT4 simulation to produce a single spectrum, and 2) The simulation result was compared with the experimental data and the deviations were fed back to adjust the input parameters. After thousands of iterations, the primary γ-ray branching ratios will converge to a final result. By using this program, the primary γ-ray branching ratios of the 304 keV resonance were extracted by fitting the single spectrum shown in Fig. 2(b). The result is in good agreement with those reported by the previous measurements with HPGe detector [8,9]. The GEANT4 simulation based on primary γ-ray branching ratios reproduced the sum spectrum obtained well, as shown in Fig. 2(a).
The experimental data of the 92 keV resonance were analyzed via the same process as the 304 keV resonance. Figure 3 shows the sum spectrum and single spectrum of the 92 keV resonance. The primary γ-ray branching ratios of the 92 keV resonance were extracted by fitting the single spectrum.
in which A R , η R , and N R are the sum peak count, sum peak efficiency, and proton numbers of the corresponding resonance measurements, respectively. The sum peak efficiency ratio η 304 /η 92 is deduced to be 1.3 ± 0.04. The effective stopping power ratio ε eff (92)/ε eff (304) is calculated to be 1.50 ± 0.01 over a large range of 25 Mg content in the target. With the ωγ 304 =(3.1±0.1)×10 −2 eV value reported in Ref. [9], the resonance strength of 92 keV resonance is determined to be ωγ 92 =(3.8±0.3)×10 −10 eV [14].

Summary
In summary, the 25 Mg(p, γ) 26 Al reaction was directly measured at JUNA in CJPL. The primary γ-ray branching ratios of the 92 and 304 keV resonance were extracted from the single spectrum. The 92 keV resonance strength was determined with improved precision. The data analysis of other low energy resonances including the 189 keV resonance is in process and the results will soon be published.

Acknowledgements
The present work is supported by the National Natural Science Foundation of China (Grant Nos. 11490563, U1867211, 12125509, 11961141003, 11775133, and 12175152), and the Continuous Basic Scientific Research Project No. WDJC-2019-13.