Measurement of the transverse asymmetry of $\gamma$-rays in the ¹¹⁷Sn(n,$\gamma$)¹¹⁸Sn reaction

The experiment was carried out at beamline 04 of the MLF in the J-PARC. The transverse asymmetry for the 1.3-eV resonance of ¹¹⁷Sn was measured with the same setup as the past measurement for the 0.74-eV resonance of ¹³⁹La [6]. In the MLF, the pulsed proton beams accelerated by the 3-GeV Rapid-Cycling Synchrotron of the J-PARC produce the pulsed neutrons by a spallation reaction in a mercury target. The proton beams with a double-bunch structure and an average of 615 kW power were incident upon to the spallation target with a specific repetition ratio of 25 Hz. Therefore, the neutron energy can be determined from the neutron time-of-flight, TOF.

The Ge $\gamma$-ray detector assembly was installed at 21.5-m flight length. There were two types of Ge detectors, cluster and coaxial types. Seven coaxial detectors were arranged to surround the sample on the same plane as the neutron beam. The cluster detectors, bundled with seven Ge detectors, were located at the up-side and down-side of the sample. More details of the beamline are given in Ref. [9, 10]. Figure 1 depicts the detector number definitions.

The angles, $\theta_{\gamma}$ and $\varphi$, were defined as shown in Fig. 2, and the angles of each cluster type detector are listed in Table. 1. The angles of all coaxial type detectors were $\varphi=0$.

The differential cross-section in Eq. (1) can be written in the laboratory system as shown below:

Thus, the effect of the $a_{2}$ term vanishes in coaxial type detectors due to $\varphi=0$. V1724 (14 bits, 100 MHz) modules and the CoMPASS software supported by Costruzionl Apparecchiature Elettroniche Nucleari SpA (CAEN) were used to acquire the difference between proton incident timing and the $\gamma$-ray detection timing, $t^{m}$, corresponding to TOF, and the pulse height corresponding to the deposited $\gamma$-ray energy, $E_{\gamma}$, in a list-mode.

The ³He neutron spin filter was used to produce polarized neutrons. The neutrons are polarized by passing through the ³He spin filter because the neutron capture cross-section of ³He strongly depends on the spin direction. The ³He nuclei were polarized using the Spin Exchange Optical Pumping (SEOP) method with rubidium and potassium [11]. The details of the ³He spin filter at the J-PARC are described in Ref. [12].

The transmitted neutrons were monitored by two types of Li-glass detectors installed at 28.8-m flight length to determine the neutron polarization ratio. One consisted of a ⁶Li enriched ($\geq$95%) Li-glass scintillator, GS20, from Saint-Gobain S.A. and PMT H7195 from Hamamatsu Photonics K.K. This detector can detect neutrons via the ⁶Li(n,$\alpha$)t reaction. The other was a ⁷Li enriched ($\geq$99.9%) Li-glass scintillator, GS30, with slight sensitivity to neutrons because of the small neutron cross-section of ⁷Li. The $\gamma$-ray backgrounds were thus subtracted using neutron spectrum obtained by the ⁷Li enriched detector. A V1720 (12 bits, 250 MHz) module and the CoMPASS software were used for data acquisition.

The natural Sn metal with 40 mm $\times$ 40 mm $\times$ 6 mm was used as the sample. The measurement times for the up- and down-polarized neutrons were 20.5 h and 20.8 h, respectively. The transmission for unpolarized ³He was also measured for 2.0 h to determine the polarization ratio of ³He.

The neutron polarization ratio can be obtained from the transmission measurement. Figure 3 shows the ratio of the neutron TOF spectrum transmitted through the polarized ³He cell divided by that through the unpolarized one.

The polarization ratio of ³He, defined as $P_{\textrm{He}}$, was determined by fitting the ratio with the following function:

where $n_{\textrm{He}}$ is the areal density of ³He; $v$ is the neutron velocity; $v_{\textrm{th}}$ and $\sigma_{\textrm{th}}$ are the velocity and the capture cross-section of ³He at the thermal-neutron energy, respectively. The solid line in Fig. 3 shows the fitting results, and the average ³He polarization ratio was determined as 75% for the first 1.5 h. The ³He polarization relaxes as time proceeds because of the nonuniformity of external magnetic fields or collisions between ³He atoms and so on. Figure 4 presents the ³He polarization ratio against the time, and the solid line represents the fitting results by the following function:

where $t$ is time; and $\tau$ is the relaxation time.

The relaxation time of the ³He was $82.65\pm 0.07$ h. The neutron polarization ratio during the up-polarization measurement was obtained as follows:

The polarization ratios during measurements for each polarization direction were $\overline{P}_{\textrm{n}}^{\textrm{up}}=0.291\pm 0.001$ and $\overline{P}_{\textrm{n}}^{\textrm{down}}=0.296\pm 0.001$ at the 1.3-eV resonance region.

The asymmetry is defined as:

where $n^{\textrm{up}}_{d}$ and $n^{\textrm{down}}_{d}$ are the numbers of events at detector $d$ in each neutron polarization direction. The transverse asymmetry of each detector $d$ is defined as:

Since the capture events after scattering in the Sn sample are not dependent on the polarization direction, the corrected asymmetry $A_{\textrm{LR},d}$ can be written [6] as:

where $n_{\textrm{sct}}$ is the capture events after scattering, and $n_{\textrm{res}}=(n^{\textrm{up}}+n^{\textrm{down}})/2$ is the number of capture reaction events at the resonance.

The correction factor $n_{\textrm{sct}}/n_{\textrm{res}}$ was calculated using the Monte Carlo simulation code, PHITS [13]. The resolution function of beamline 04 obtained by Kino et al. [14] and Doppler broadening were considered in the correction factor, $n_{\textrm{sct}}/n_{\textrm{res}}$, as shown in Fig. 5 with the capture reaction rate, $n_{\textrm{res}}$, which corresponds to the capture cross-section considering effects of self-shielding and multiple scattering.

Notably, the correction factor depends on the neutron energy because neutrons with higher energies than resonance are captured by the decrease in energy due to scattering. Thus, the correction factor was increased at higher energy, or lower TOF, than the resonance.

Figure 6 depicts the obtained $\gamma$-ray deposit energy spectrum of detector 1 in Sn measurement.

The vertical solid line indicates the 9327.5 keV transition to the ground-state of ¹¹⁸Sn from the compound state of ¹¹⁷Sn+n, and the dotted lines represent its single and double escape peaks. The neutron capture reaction of ¹¹⁵Sn is responsible for the 9563.1 keV peak. The other peaks are derived from the scattered neutron capture reaction of iron contained in the guide magnet and shield of the Ge detector assembly. Since the transition to the first excited state of ¹¹⁸Sn from the compound-state emits 8069.8 keV $\gamma$-ray, it is considered that $\gamma$-rays above the double escape peak, 8305.5 keV photo-peak, contain the only transition to the ground-state of ¹¹⁸Sn, including backgrounds derived from other nuclei. Furthermore, backgrounds by iron and ¹¹⁵Sn do not affect the transverse asymmetry because their cross-sections have no resonance or unique structure around 1.3 eV. Therefore, the $\gamma$-ray gate region was set from 8250 keV to 9400 keV, and Fig. 7 shows the gated histogram of $\gamma$-ray counts as a function of $t^{m}$ with the open circle.

To remove the s-wave component of ¹¹⁷Sn and the backgrounds from other nuclei, the histogram was fitted using the following function:

with $700\ \mu s\leq t^{m}\leq 1200\ \mu s$ and $1700\ \mu s\leq t^{m}\leq 2500\ \mu s$. Figure 7 presents the fitting result with the solid line. The histogram after subtracting the fitting function is also shown in Fig. 7 with the closed circle.

Figure 8 shows the histograms for each polarization direction after background subtraction and calculated transverse asymmetry $A_{\textrm{LR}}$.

Table 2 lists $A_{\textrm{LR}}$ in a neutron energy region $E_{\textrm{p}}-2\Gamma_{\textrm{p}}\leq E_{\textrm{n}}\leq E_{\textrm{p}}+2\Gamma_{\textrm{p}}$ for each detector.

Here, the resonance parameters were used, as shown in Table 3.

The $A^{90^{\circ}}_{\textrm{LR},d}$ is the transverse asymmetry converted to 90^∘, calculated by $A^{90^{\circ}}_{\textrm{LR},d}=A_{\textrm{LR},d}/(\sin\theta_{\gamma}\sin\varphi)$. It is found that the average of $A^{90^{\circ}}_{\textrm{LR},d}$ is consistent between up- and down-side detectors. The transverse asymmetry averaged over up- and down-side detectors was obtained as $A^{90^{\circ}}_{\textrm{LR}}=-1.07\pm 0.23$. Furthermore, the average of $A_{\textrm{LR},d}$ of the coaxial detector was consistent with 0 due to $\sin\varphi=0$.

In the previous study of the left-right asymmetry measurements of ¹¹⁷Sn, the asymmetry $\varepsilon_{\textrm{LR}}$ was reported in Fig. 13 in Ref. [8]. Notably, the asymmetry $\varepsilon_{\textrm{LR}}$ was defined, including the s-wave components around the p-wave resonance. Conversely, the aforementioned analysis removed the s-wave components with backgrounds in the present definition of $A_{\textrm{LR}}$. To compare the present result with the previous study, $\varepsilon_{\textrm{LR}}$ was also calculated and plotted in Fig. 9 with the previous results. In the present analysis, the $\varepsilon_{\textrm{LR}}$ was calculated for all detectors and divided by $\sin\theta_{\gamma}\sin\varphi$, and average values of all detectors were plotted in Fig. 9, consistent with the previous study, which implies that the background conditions for our and Skoy’s cases were comparable. The result of $\gamma$-ray identification suggested that the asymmetry was influenced by backgrounds such as iron isotopes. Therefore, it was necessary to evaluate the asymmetry without backgrounds, $A_{\textrm{LR}}$.

To discuss the angular dependence of $a_{2}$ term, $A_{\textrm{LR}}$ is plotted for $\sin\theta_{\gamma}\sin\varphi$ in Fig. 10. The weighted average of $A_{\textrm{LR}}$ was calculated and plotted for each angle. According to Eq. (II.1), the transverse asymmetry could be written as:

where $A_{i}$ is

Here, $a_{0,\textrm{p}}$ is the $a_{0}$ term only considering the 1.4-eV p-wave resonance. Furthermore, $a_{1}$ term can be ignored by integral in Eq. (11) because its energy-dependence is odd function of energy centered at the p-wave resonance [4, 7]. In this study, the angular dependence of the transverse asymmetry was little sensitive to $A_{3}$ because the Ge detectors were placed around $\cos^{2}\theta_{\gamma}\sim 0$. If the angular dependence of the $a_{3}$ term was ignored, the angular dependence of the transverse asymmetry can be written as:

where $\tilde{A}_{\textrm{LR}}=\frac{A_{2}}{1-A_{3}/3}$.

The solid line in Fig. 10 shows the fitting results by Eq. (12), and $\tilde{A}_{\textrm{LR}}=1.07\pm 0.23$ was obtained. The transverse asymmetry depending on $\sin\theta_{\gamma}\sin\varphi$ was evaluated, and it is caused by the $a_{2}$ term.