Brief introduction to SLEGS beamline

The SLEGS beamline [20-26] at the Shanghai Synchrotron Radiation Facility (SSRF) delivers quasimonochromatic γ rays with maximum scattering energies ($E_{\gamma }$) ranging from 0.66 to 21.7 MeV. This beamline employs inverse Compton scattering technology, wherein photons from a 10,640 nm, 100 W CO₂ laser collide with 3.5 GeV electrons circulating in the SSRF storage ring. The energy of the γ-ray beam is tuned in the slant-scattering mode with a minimum step size of 10 keV, enabling precise mapping of cross sections. This precision surpasses that of γ-ray beams generated under backward scattering at the AIST [7] and NewSUBARU BL01 beamlines [27].

The experiment was conducted using the SSRF storage ring, which operated in top-up mode with a beam current of 160–210 mA and an energy of 3.5 GeV. A CO₂ laser, delivering an average power of 5–20 W at a frequency of 1 kHz and a pulse width of 50 μs, was used to generate γ-rays. These γ-rays were collimated with a C5T2 double collimator. By varying the interaction angle from 102° to 180°, γ-rays with theoretical energies ranging from 13.16 to 21.73 MeV were produced. Within this energy range, 38 energy points of the ²⁷Al(γ, n)²⁶Al reaction cross-sections were measured. The incident γ-ray spectrum on the detector was derived using the direct unfolding method described in [28-30]. Figure 2 presents the detector response spectrum (blue dashed-dotted line) and the unfolded spectra at slant-scattering angles of 103°, 124°, and 155° (red dashed lines). The reconstructed spectrum, obtained by convolving the incident γ-ray spectrum with the simulated detector response matrix [31], is shown as a black line and aligns well with the measured spectrum. The theoretical Compton-edge energies for interactions at 103°, 124°, and 155° were calculated to be 13.37, 16.96, and 20.73 MeV, respectively. These values closely match the energies at the half-peak height on the high-energy side of the incident γ-ray spectrum, confirming the accuracy of the measurements.

Fig. 2Full-screen View

(Color online) A typical γ spectrum obtained by BGO detector (red dash line) and the corresponding unfolded γ spectrum (blue dash-dot line). The reconstructed spectrum is shown as black line. The spectrum is measured with C5T2

Al Target

The aluminum (Al) target consisted of five 10 mm in diameter and 25 mm in thickness of ²⁷Al isotopes with 100% abundance and 99.99% purity. The detailed specifications can be found in Table 1.

The targets were positioned in a polythene sample holder with a 10 mm diameter window. Given that the LCS γ-ray beams had a diameter of approximately 4 mm at the target position, the 10 mm diameter window was sufficient to allow accurate measurement of the target without interference from neutrons originating in the polythene.

Measurements

The details of the measurements and analyses are provided in Ref. [32], and are only briefly summarized here. To determine the cross-sections, the measured quantities included the energy distribution and flux of LCS γ-rays irradiating the sample, as well as the number of neutrons generated from (γ, n) reactions. The energy distribution of the LCS γ-rays was measured using a BGO detector and deduced by unfolding the charge integration spectrum with the BGO response functions.

In the FED system, proportional counters are embedded in moderators such as paraffin or polyethylene to thermalize the emitted neutrons from the reaction. The large neutron capture cross-section of ³He for thermal neutrons makes it an ideal medium for neutron detection. A flat efficiency response is achieved by optimizing the placement of the ³He counters within the moderator. Typically, ³He counters are arranged in concentric rings, with the efficiency of the inner ring being the highest but decreasing rapidly as neutron energy increases. The outer rings compensate for this efficiency loss at higher neutron energies, resulting in a nearly uniform total detector efficiency across a broad energy range. At NewSUBARU [33], the ³He FED, composed of ³He proportional counters, was demonstrated to be an effective tool for studying photoneutron cross-sections.

A new ³He Flat Efficiency Detector (FED) was developed at the SLEGS station [32]. Figure 3 illustrates the FED system structure, featuring 26 ³He proportional counters integrated into a polyethylene moderator. These counters were arranged in three concentric rings at distances of 65 mm, 110 mm, and 175 mm from the central beam axis. The moderator included a central tunnel to allow the gamma beam to pass through, with the target positioned at the center of the three rings. The ³He proportional counters had cylindrical sensitive volumes, each 500 mm in length, pressurized with 2 atm of ³He gas. The counters in Ring-1 (inner ring) had a diameter of 1 inch, while those in Ring-2 (middle ring) and Ring-3 (outer ring) had a diameter of 2 inches. The counters were constructed with thin stainless steel walls, ensuring low background noise, high γ resistance, and good pressure tolerance. The inner polyethylene moderator measured 450 mm × 450 mm × 550 mm along the beam direction. To minimize interference from environmental neutrons, 2 mm-thick cadmium (Cd) sheets were used to cover all six surfaces of the moderator. The entire assembly, including the inner moderator and Cd sheets, was sealed with polyethylene plates for added stability and neutron shielding. The ³He proportional counters were powered by a CAEN SY4527LC crate, maintaining a high-voltage deviation of no more than 1 V. Initial signals from the ³He counters were routed to preamplifiers and subsequently processed using a Mesytec MDPP-16 digital pulse processor. Renowned for its high time and amplitude resolution, this processor produced precise reconstructed waveforms. Data acquisition was handled by the MVME DAQ system. Figure 4 shows the simulated efficiency curve based on the Geant4 model of the detector. The total detector efficiency increased from 35.6% at 50 keV to 42.3% at 1.65 MeV, followed by a gradual decrease to 40.7% at 3 MeV for the average neutron energy. Efficiency calibration with a ²⁵²Cf source yielded a value of 42.1 ± 1.3% at 2.13 MeV, the average energy of neutrons emitted by ²⁵²Cf, as indicated on the curve. The uncertainty of the efficiency curve was evaluated by varying parameters such as the moderator density, gas pressure, and counter-sensitive volumes. While the efficiency curve provides an estimate for a range of neutron spectra, precise characterization of neutron detector efficiency for specific energy profiles requires calculation of the weighted average efficiency.

Fig. 3Full-screen View

(Color online) Structure of the FED. The left and right panels denote the front view and the lateral profile of FED

Fig. 4Full-screen View

(Color online) The total detector efficiency and the efficiencies of individual rings. The detector efficiency curves were simulated by neutron-evaporation spectra and monochromatic neutrons. The red dots are given by the neutron spectrum described by the Maxwell-Boltzmann distribution, at the average neutron energy (T = 1.42 MeV) of ²⁵²Cf [34]

The ring-ratio technique, which exploits the energy dependence of the Ring Ratio, was originally developed by Berman et al. [5, 34, 35]. Figure 5 presents the Geant4 simulations illustrating the Ring Ratios as functions of the neutron energy.

Fig. 5Full-screen View

(Color online) The Ring-Ratio curve of the FED array

Monochromatic Approximation

The cross-section in the monochromatic approximation is given by ${\displaystyle {\int }_{S_n}^{E_{\text{max}}}}{n}_{\gamma }\left(E\right)\sigma \left(E\right)\text{d}E=\frac{N_{\text{n}}}{N_{\gamma }{N}_{\text{t}}\xi {ϵ}_{\text{n}}}\mathrm{.}$ (1) By contrast, for $n_{\gamma }\left(E\right)$, the energy distribution of the LCS γ-ray beams was normalized to unity in the energy region of integration. $\sigma (E)$ represents the photoneutron cross section and N_n is the number of detected neutrons. N_t denotes the number of target nuclei per unit area and $N_{\gamma }$ represents the number of γ particles incident on the target with energies above the neutron threshold. The correction factor for a thick target measurement is expressed as $\xi =\left(1-e^{\mu t}\right)/\mu t$, where μ denotes the linear attenuation coefficient of photons in the target material and t represents the thickness of the target. The symbol ${ϵ}_{\text{n}}$ represents the neutron detection efficiency. ${\sigma }_{\left(\gamma \mathrm{,}n\right)}^{E_{\text{max}}}=\frac{N_{\text{n}}}{N_{\gamma }{N}_{\text{t}}\xi {ϵ}_{\text{n}}}\mathrm{.}$ (2) Assuming E_max represents the energy of the LCS γ-ray beams, the photoneutron cross-sections are obtained at the energy in the monochromatic approximation using Eq. (2). The γ beam was collimated to a diameter of 2 mm using a three-hole collimator. However, because of the energy dispersion of the LCS γ-ray beams (see Fig. 2), the monochromatic approximation is inadequate for determining photoneutron cross sections.

In the experiment, the laser pulse period was 1000 μs, consisting of a 50 μs laser on time and a 950 μs off time. This pulse period facilitates inverse Compton scattering between the laser and electron beam, resulting in the production of γ-rays with inherent time broadening. Consequently, the neutrons generated by interaction with the experimental target exhibited time broadening. To accurately count the number of neutrons, an FED array is employed, which involves identifying the flat efficiency zone and measuring the neutron counts within this region. However, the flat efficiency zone varies with the neutron energy as well as other factors such as the size of each ring and ambient conditions such as the counter gas pressure. Therefore, it is necessary to determine the flat efficiency region for each ring at different energy levels, and use the median method to establish the optimal efficiency point. This strategy ensures a more reasonable statistical analysis of the neutron counts.

Unfolding Photoneutron Cross Sections

Approximating the integral in Eq. (1) with a summation of each γ-beam profile, the unfolding problem can be expressed as a set of linear equations. The unknown cross section σ can be determined by solving the equations for the system ${\sigma }_{\text{f}}=\text{D}\sigma$, where ${\sigma }_{\text{f}}$ represents the folded cross section with beam profile D. This approach solves the unfolding problem by formulating it as a linear algebraic problem. ${\left(\begin{array}{c}{\sigma }_1\\ {\sigma }_2\\ ⋮\\ {\sigma }_N\end{array}\right)}_{\begin{array}{c}\text{f}\end{array}}=\left(\begin{array}{cccc}{D}_{11}& D_{12}& \cdots & D_{1M}\\ D_{21}& D_{22}& \cdots & D_{2M}\\ ⋮& ⋮& \ddots & ⋮\\ D_{N1}& D_{N2}& \cdots & D_{NM}\end{array}\right)\left(\begin{array}{c}{\sigma }_1\\ {\sigma }_2\\ ⋮\\ ⋮\\ {\sigma }_M\end{array}\right)\mathrm{.}$ (3) Matrix D is composed of the normalized incident gamma energy distributions from S_n to E_max at the discrete beam energies ($E_{\gamma }$). The system of linear equations presented in Eqs. (3) is underdetermined, making it impossible to directly extract the true vector σ by matrix inversion. To determine σ, the following folding iteration method was employed [36, 37]:

The process starts at the zeroth iteration of a constant trial function ${\sigma }_0$. This initial vector is multiplied with D, and the zeroth folded vector is obtained ${\sigma }_{\text{f}}^0=\text{D}{\sigma }^0$. The next trial input function is denoted as ${\sigma }_1$. This is realized by adding the difference between the experimentally measured ${\sigma }_{\text{exp}}$ and folded spectrums ${\sigma }_{\text{f}}^0$ to $\text{D}{\sigma }^0$. To enable the addition of folded and input vectors, spline interpolation is initially performed on the folded vector to ensure that both vectors have matching dimensions. The new input vector is ${\sigma }^1={\sigma }^0+\left({\sigma }_{\text{exp}}-{\sigma }_{\text{f}}^0\right)\mathrm{.}$ (4) The above steps are iterated i times, yielding ${\sigma }_{\text{f}}^i=\text{D}{\sigma }^i\mathrm{,}$ (5) and ${\sigma }^{i+1}={\sigma }^i+\left({\sigma }_{\text{exp}}-{\sigma }_{\text{f}}^i\right)\mathrm{.}$ (6) The updated input vector is determined iteratively until convergence is achieved. The convergence criterion is satisfied when ${\sigma }_{\text{f}}^{i+1}$ approximates ${\sigma }_{\text{exp}}$ within statistical error limits. Convergence was quantitatively assessed by computing the reduced χ² between ${\sigma }_{\text{f}}^{i+1}$ and ${\sigma }_{\text{exp}}$ at the end of each iteration. Typically, approximately three iterations are adequate to achieve convergence, which is characterized by a reduced χ² value approaching one.

The monochromatic cross sections of the ²⁷Al(γ, n)²⁶Al reaction were derived using the unfolding iteration method. Figure 6 compares the quasimonochromatic and monochromatic cross sections for ²⁷Al. Statistical uncertainties are attributed solely to neutron counts, as a high number of γ-ray counts results in negligible uncertainties. The total uncertainty encompasses statistical, systematic, and methodological components. The total uncertainty estimate for ²⁷Al(γ, n)²⁶Al is less than 4%, except for the data points corresponding to lower cross-sectional values and energies of 21.7 MeV. The cross sections for the SLEGS experiment were comparable to or even higher than some of the datasets in the EXFOR database. The conclusions regarding systematic uncertainties are as follows:

Fig. 6Full-screen View

(Color online) Cross sections of ²⁷Al(γ, n)²⁶Al measured at SLEGS. The dots are the folded cross section and the line with shaded area is the unfolded (monochromatic) cross section

• The total uncertainty in the efficiency of the neutron detector is 3.0%.

• The uncertainty in the reconstructed incident energy spectrum due to the external copper attenuator and the target is 0.50%.

• The uncertainty in the target thickness is estimated to be less than 0.10%.

The uncertainties associated with data processing for the cross-sectional calculations are summarized below.

• The neutron count extraction algorithm introduces an uncertainty of approximately 2%.

• The BGO detectors exhibit 100% efficiency; when combined with the modeled BGO reaction matrix, the overall uncertainty is approximately 1%.

First, the measured cross-sections for the ²⁷Al(γ, n)²⁶Al reaction were compared with TENDL-2021 [38] and available experiments from various γ ray sources. In Fig. 7, data from Baglin [39] and Mutsuro [40], originate from gamma sources induced by bremsstrahlung γ beams, while the data from Fultz [41] and Veyssiere [42] are derived from gamma sources associated with PAIF. It can be visually discerned that there are distinct segmented characteristics in the differences between the datasets.

Fig. 7Full-screen View

(Color online) The measured cross section for ²⁷Al(γ, n)²⁶Al (solid circles) at SLEGS and comparison with existing data. The solid line denotes the TENDL-2021 evaluation. Results measured with bremsstrahlung γ rays (Baglin 1961 and Mutsuro 1962) are shown by filled inverted triangles and filled triangles, respectively. Results measured with PAIF γ rays (Fultz 1966 and Veyssiere 1974) are indicated by squares and diamonds, respectively

The uncertainty of the specific data is shown, as the measured data in the energy region below 16.3 MeV are in good agreement with the data obtained by Fultz using a PAIF gamma source. In the energy region above 16.3 MeV, the measured data are significantly higher than the data obtained by Fultz and Veyssiere using PAIF γ sources but agree with the data obtained by Baglin et al. using bremsstrahlung γ sources. With respect to the global structure of the data, this dataset shows high consistency with the TENDL-2021 [38] data and exhibits more uniform smoothness, whereas the Fultz and Veyssiere datasets display multiple oscillations during the increased cross-section. These oscillations show worse agreement with the calculations from relevant nuclear reaction models, such as the quasiparticle random phase approximation (QRPA) [43], and are particularly pronounced during the ascent of the QRPA ²⁷Al(γ, n)²⁶Al cross section. The implications of this work are significant for both the evaluation of nuclear data and the optimization of the parameters of the theoretical model.

As discussed in Ref. [44], the ratios of the integral cross sections provide a clear indication of the systematic differences among the various data compilations. The integral cross sections in the S_n and S_max regions are as follows: ${\sigma }^{\text{int}}={\displaystyle {\int }_{S_n}^{S_{\text{max}}}}\sigma (E)\text{d}E\mathrm{.}$ (7) Experiments on the reactions ¹⁹⁷Au(γ, n) and ¹⁵⁹Tb(γ, n) were performed using SLEGS [32]. Comparison of ¹⁹⁷Au(γ, n) reaction data with the findings of Itoh et al [33] revealed an integrated cross-sectional difference of approximately 0.4%, which underscores the reliability of SLEGS in both measurement procedures and data analysis. Based on these reliable experimental data, the integral ratios of the photoneutron cross sections were calculated for energy ranges from S_n to 16.3 MeV, 16.3 MeV to E_max and S_n to E_max, as shown in Table 2. In the energy range from S_n to 16.3 MeV, the experimental results in this study differ from the Fultz data by only 4%, whereas the discrepancy with other datasets exceeds 30%. In the energy range of 16.3 MeV to E_max, the results from this work show a difference of 3% compared to Baglin's results and 4% compared to TENDL, with discrepancies from other datasets ranging between 8% and 28%. In general, the TENDL evaluated data agree with the measured data in this work across the energy range of 13–20 MeV. However, the rapid decrease in cross-section values after 20 MeV observed in the TENDL data is not physically reasonable. The differences between the data from this measurement and those from other laboratories range from 3% to 25%. Notably, after the energy exceeded 20 MeV, the relatively large energy intervals between the TENDL data points and the unusually rapid decline in the high-energy segment make the discrepancies between TENDL and the data from other laboratories more pronounced. The cross-section rise observed in this work was smooth, with no resonance structure peaks detected. This suggests that the resonance structures measured in other laboratories may be artifacts arising from the process of solving single-energy cross-sections. Considering the variations in the data structure between the measured results, the data presented here have significant implications for refining nuclear data evaluations, optimizing theoretical model parameters, resolving discrepancies in the ²⁷Al(γ, n)²⁶Al reaction cross-section, and improving the understanding of its underlying nuclear structure.