Measurements of keV-Neutron capture cross sections and capture gamma-ray spectra of ^{74,76,78,80,82}Se

ABSTRACT

The neutron capture cross sections and capture $\mathit{\gamma }$-ray spectra of ^{74,76,78,80,82}Se were measured in a region from 15 to 100 keV and around 550 keV. A neutron time-of-flight method was used with a ns-pulsed neutron source based on the ⁷Li(p,n)⁷Be reaction and a large anti-Compton NaI(Tl) $\mathit{\gamma }$-ray spectrometer. A pulse-height weighting technique was applied to the observed $\mathit{\gamma }$-ray pulse-height spectra to obtain capture yields. The capture cross sections of ^74,76,78,80Se were derived with uncertainties from 4.0 to 5.5% and those of ⁸²Se were derived with uncertainties of 6.5–27% by using the standard capture cross sections of ¹⁹⁷Au. The present results of ^78,82Se were the first experimental ones above the resolved resonance region. The present results were compared with previous measurements and the evaluated values in JENDL-5.0 and ENDF/B-VIII.0. The evaluations of JENDL-5.0 differ from the present results of ^74,76,78,80Se and ⁸²Se by 0.9–51% and 6.9–120%, respectively. The capture $\mathit{\gamma }$-ray spectra of ^{74,76,78,80,82}Se were derived by unfolding the observed capture $\mathit{\gamma }$-ray pulse-height spectra. The present results were the first experimental ones in the keV region.

KEYWORDS:

• Neutron capture cross sections
• gamma spectra
• selenium 74
• selenium 76
• selenium 78
• selenium 80
• selenium 82
• anti-compton NaI(Tl) gamma-ray spectrometer
• time-of-flight method
• pulse-height weighting technique

1. Introduction

The nuclear transmutation of long-lived fission products (LLFPs: ⁷⁹Se, ⁹³Zr, ⁹⁹Tc, ¹⁰⁷Pd, ¹²⁶Sn, ¹²⁹I, ¹³⁵Cs, etc.) is one of key issues in the utilization of nuclear fission energy systems [1]. In this situation, the neutron capture cross sections of LLFPs play a very important role in the R&D of the nuclear transmutation systems that utilize neutron capture reactions, because the cross sections directly affect the transmutation performances of systems.

However, the present status of capture cross-section data of LLFPs is very poor both in quality and quantity, because it is difficult to prepare enough of a high-purity sample to make the capture cross-section measurement possible. Moreover, the radiation background from the sample itself is sometimes severe in the measurement, even though the sample preparation is made.

Concerning the stable isotopes corresponding to each LLFP, some of them are also produced in fission reactors. Therefore, the neutron capture cross sections of those stable isotopes are also important for the R&D of transmutation systems without isotope separation, because LLFPs are accompanied by those stable isotopes when LLFPs are loaded into a transmutation system without isotope separation.

Moreover, the keV-neutron capture cross sections and capture $\mathit{\gamma }$-ray spectra of the stable isotopes corresponding to an LLFP contain important information on physical quantities such as $\mathit{\gamma }$-ray strength functions and nuclear level densities, and the information will contribute to the theoretical calculation of keV-neutron capture cross sections of the LLFP.

From the viewpoints described above, we are trying to measure the keV-neutron capture cross sections and $\mathit{\gamma }$-ray spectra of LLFPs and their stable isotopes. So far, we have finished the direct measurements for ⁹⁹Tc [2] and ¹²⁹I [3]. As for ⁹³Zr and ¹²⁶Sn, we have finished the measurements for their stable isotopes, ^90,91,92,94Zr [4,5] and ^{116,117,118,119,120,122,124}Sn [6,7], respectively.

Concerning ⁷⁹Se, which is one of the most important LLFPs [1] and has a half-life of 2.95$\times$10⁵ years [8], there is no experimental data in the whole neutron energy region, and the sample preparation is practically impossible at the moment. As for stable Se isotopes, i.e. ^{74,76,77,78,80,82}Se, the present status of the keV-neutron capture cross section date are poor: there are two data sets and one Maxwellian averaged cross section for ⁷⁴Se [9–11], only one Maxwellian averaged cross section for ⁷⁶Se [12], no data sets for ⁷⁷Se, no data sets for ⁷⁸Se, three data sets for ⁸⁰Se [13–15] and no data sets for ⁸²Se, and there exists discrepancy among the data sets. Therefore, we have carried out a systematic measurement of keV-neutron capture cross sections and $\mathit{\gamma }$-ray spectra of all stable Se isotopes. The cumulative fission yields of ^77,78,80,82Se are comparable to that of ⁷⁹Se [16], although those of ^74,76Se are very small. The keV-neutron capture cross sections and capture $\mathit{\gamma }$-ray spectra of ⁷⁷Se have been reported [17]. The present paper describes the results of ^{74,76,78,80,82}Se.

2. Experimental procedure

Since the experimental procedure has been described in detail elsewhere [18], it will be explained briefly here. The capture cross sections and capture $\mathit{\gamma }$-ray spectra of ^{74,76,78,80,82}Se were measured in a neutron energy region from 15 to 100 keV and at around 550 keV (552 keV for ⁷⁴Se, 545 keV for ⁷⁶Se, 541 keV for ⁷⁸Se, 542 keV for ⁸⁰Se, and 544 keV for ⁸²Se), using the 3 MV Pelletron accelerator at the Tokyo Institute of Technology. Figure 1 shows the experimental setup in the 550 keV measurement.

Figure 1. Experimental setup in the 550 keV measurements.

Pulsed keV neutrons were produced by the ⁷Li(p,n)⁷Be reaction with a pulsed proton beam (1.5 ns width, 4 MHz repetition rate) from the Pelletron accelerator. The incident neutron energy spectrum on a capture sample was measured by using a time-of-flight (TOF) method with a ⁶Li-glass scintillation detector. A small ⁶Li-glass detector (diameter of 5.0 mm and thickness of 5.0 mm) located 30 cm from the ⁷Li neutron-generation target was used in the 15–100 keV measurement, and a large ⁶Li-glass detector (diameter of 102 mm and thickness of 6.4 mm) at 455 cm from the neutron source was used in the 550 keV measurements. The small ⁶Li-glass detector was placed at the average angle of 2.4° or 3.2° and the large ⁶Li-glass detector was placed at 1.4° or 1.9° with respect to the proton beam direction to observe an average energy spectrum of incident neutrons on the capture sample. The small detector was used also in the 550 keV measurements to monitor the neutron production, as shown in Figure 1, where the small detector was placed at an angle of about 30°.

Each of ^{74,76,78,80,82}Se samples with a weight of about 1–3 g was made from isotopically enriched metal powder. The ^74,76,78,80Se powder was formed into a compact under a uniaxial pressure of 5.0 MPa, followed by a cold isostatic pressure of 200 MPa. The compact was sealed by a Mylar film with a thickness of 15 $\mathit{\mu }$m. On the other hand, the ⁸²Se powder was formed into a compact under a uniaxial pressure of 5.0 MPa. The compact was contained in a graphite case with an inner radius of 20 mm. A gold(¹⁹⁷Au) sample was used as a capture cross-section standard. Table 1 shows the characteristics of the samples.

Table 1. Characteristics of samples.

Sample	^74Se	^76Se	^78Se	^80Se	^82Se	^197Au	^197Au
Chemical form	Se	Se	Se	Se	Se	Au	Au
Chemical purity [%]	99.96	99.99	99.95	99.98	99.95	99.99	99.99
Net weight of sample [g]	0.999	1.978	1.983	2.970	1.797	3.427/6.856^a	6.834/12.04^b
Isotopic Composition[%]
^74Se	99.9	0.06	0.04	0.04($\pm$0.02)	0.04
^76Se	0.01	99.67	0.04	$\text{buildrelltover {smash{scriptstyle=}vphantom{\_x}}}$0.01	0.005
^77Se	0.01	0.18	0.17	$\text{buildrelltover {smash{scriptstyle=}vphantom{\_x}}}$0.01	0.005
^78Se	0.01	0.06	99.39	$\text{buildrelltover {smash{scriptstyle=}vphantom{\_x}}}$0.01	0.01
^80Se	0.01	0.02	0.32	99.9($\pm$0.1)	0.01
^82Se	0.01	0.01	0.04	0.06($\pm$0.02)	99.93
^197Au						100	100
Diameter[mm]	14.1	18.4	18.6	17.5	20	15	20
Thickness [mm]	1.7	2.0	2.0	3.3	1.0	1.0/2.0	1.0/2.0
Thickness[atoms/barn]×10^−3	5.18	5.88	5.60	9.29	4.20	5.93/11.9	5.86/11.7
Outer diameter of case [mm]	–	–	–	–	23.8	–	–
Outer thickness of case[mm]	–	–	–	–	2.9	–	–

^aThese were used for the measurements for ⁷⁴Se. 15–100 keV/550 keV

^bThese were used for the measurements for ^76,78,80,82Se. 15–100 keV/550 keV

The capture sample was placed at right angles to the proton beam direction. The distance between the neutron source and the capture sample was adjusted to 12.0 cm in the 15–100 keV measurement and 20.0 cm in the 550 keV measurements from the consideration of the small amount of Se sample and the neutron TOF. The capture $\mathit{\gamma }$ rays emitted from the sample were measured with a large anti-Compton NaI(Tl) spectrometer using a TOF method. The main NaI(Tl) detector of the spectrometer had a diameter of 15.2 cm and a length of 30.5 cm [5]. The detector was centered in a hollow Compton-suppression NaI(Tl) detector with an outer diameter of 33.0 cm and a length of 35.6 cm. The spectrometer was surrounded by a heavy shield which was composed of borated paraffin, borated polyethylene, cadmium, ⁶LiH, and potassium-free lead [19]. The capture $\mathit{\gamma }$ rays were observed at an angle of 125° with respect to the proton beam direction [18]. The signals from the spectrometer were accumulated event by event as two-parameter list data of pulse height (PH) and TOF with a data acquisition system and stored in a personal computer for offline data analysis.

The measurements with the Se sample, the ¹⁹⁷Au sample, and no sample (blank run) were carried out cyclically to average out fluctuations in experimental conditions such as the incident neutron spectrum and the proton beam current. The proton beam currents and the measuring times are summarized in Table 2. The measuring time of 114 hours for the blank run in the 550 keV measurements was the sum of the measuring times of the blank runs for the ^74,76,78,80Se samples. The summed blank data were used for the data processing, described below, because the experimental conditions were assumed to be equivalent in ^74,76,78,80Se measurement at around 550 keV neutron energy region. As for the blank runs for the ⁸²Se sample, the measuring time of 121 hours for the blank run in the 550 keV measurements was the sum of the measuring times of the blank runs for the ^{74,76,78,80,82}Se samples. The measuring time for the blank run in the 550 keV measurement was spent more than that for the ^{74,76,78,80,82}Se sample run, because the time-dependent background described below was determined from the data obtained from the blank run.

Table 2. Average proton beam currents and measuring times.

	Neutron Energy	Beam Current	Measuring Time [hours]
Sample	[keV]	[$\mathit{\mu }$A]	Se Run	^197Au Run	Blank Run
^74Se	15–100	8.5	41	13	6
	550	8.2	36	8	114^a
^76Se	15–100	8.9	48	7	7
	550	9.1	42	5	114^a
^78Se	15–100	9.4	50	10	7
	550	9.4	45	5	114^a
^80Se	15–100	9.4	80	5.5	5.5
	550	8.4	57	4	114^a
^82Se	15–100	7.8	166	9.5	10.5
	550	8.6	74	6	121^b

^aSum of the measuring times of blank runs for the ^74,76,78,80Se samples.

^bSum of the measuring times of blank runs for the ^{74,76,78,80,82}Se samples.

3. Data processing

The data processing has also been described in detail elsewhere [18], so it will be explained briefly here.

3.1. Incident neutron spectra

The incident neutron energy spectra on the capture sample were derived from the TOF spectra measured with the small and large ⁶Li-glass scintillation detector for the blank run. Figure 2 shows the incident neutron energy spectra in the ⁷⁸Se measurement, $\mathit{\eta }(E_n)$, where $E_n$ stands for the incident neutron energy in the laboratory system. Each spectrum in Figure 2 is normalized so that the integration of spectrum with respect to $E_n$ is equal to unity. The regions 1–4 in Figure 2(a) correspond to the neutron energy regions where the capture cross sections were derived. As for the ⁸²Se measurement in the 15–100 keV neutron energy region, different gates were adopted, as described below, because of the resonance structure of the TOF spectrum of capture $\mathit{\gamma }$ rays. The neutron spectra in the ^74,76,80,82Se measurements were similar to those shown in Figure 2

Figure 2. Incident neutron energy spectra, $\mathit{\eta }(E_n)$, in the (a) 15–100 keV and (b) 550 keV measurements for ⁷⁸Se. $⟨E_n⟩$ indicates an average neutron energy in the laboratory system, see Eq. (3)(3) ${⟨E_n⟩}_{\mathit{j}}\equiv \frac{{\int }_{{\mathit{E}}_{\mathit{j},\mathit{min}}}^{E_{\mathit{j},\mathit{max}}}{E}_n\mathit{\eta }(E_n)\mathit{d}{E}_n}{{\int }_{{\mathit{E}}_{\mathit{j},\mathit{min}}}^{E_{\mathit{j},\mathit{max}}}\mathit{\eta }(E_n)\mathit{d}{E}_n},$(3) .

3.2. Net capture $\mathit{\gamma }$-ray Pulse-Height Spectra

Figures 3 and 4 show the TOF spectra measured with the $\mathit{\gamma }$-ray spectrometer for the (a) ⁷⁸Se, (b) ¹⁹⁷Au, and (c) blank runs in the 15–100 keV and 550 keV measurements, respectively.

Figure 3. TOF spectra measured with the $\mathit{\gamma }$-ray spectrometer for the (a)⁷⁸Se, (b)¹⁹⁷Au, and (c) blank runs in the 15–100 keV measurement. Regions 1–4 in the figure correspond to those in Figure 2(a).

Figure 4. TOF spectra measured with the $\mathit{\gamma }$-ray spectrometer for the (a)⁷⁸Se, (b)¹⁹⁷Au, and (c) blank runs in the 550 keV measurements.

The broad peak below 500 ch. in Figure 3(a,b) is due to the neutron capture $\mathit{\gamma }$ rays from the ⁷⁸Se or ¹⁹⁷Au sample, respectively. The sharp peak around 600 ch. in Figs. 3(a–c) is caused by the $\mathit{\gamma }$ rays from the ⁷Li(p,$\mathit{\gamma }$)⁸Be reaction in the neutron production target. We set four regions in the foreground area and one region in the background area, as shown in Figure 3, to obtain the foreground and background PH spectra from the data of the ⁷⁸Se run. Then, net capture $\mathit{\gamma }$-ray PH spectra were obtained by subtracting the background PH spectra normalized with the ratios of the region widths from the foreground PH spectra [18]. As for the ⁸²Se measurement in the neutron energy region from 15 to 100 keV, the foreground area was divided into five regions because of the resonance structure in the foreground area, as shown in Figure 5.

Figure 5. Expansion view of TOF spectrum measured with the $\mathit{\gamma }$-ray spectrometer for the ⁸²Se in the 15–100 keV measurement. Resonance structures were observed in this spectrum.

The peak around 480 ch. in Figure 4(a) or (b) is due to the neutron capture $\mathit{\gamma }$-rays from the ⁷⁸Se or ¹⁹⁷Au sample, respectively. The background in the foreground area in the 550 keV measurements was classified into four components [18]. The time-independent components were evaluated from the data of the ⁷⁸Se run and the time-dependent ones were evaluated from the data of the blank run. After subtracting those background components, the net capture $\mathit{\gamma }$-ray PH spectra were obtained.

Figure 6 shows the obtained net capture $\mathit{\gamma }$-ray PH spectra of ⁷⁸Se. The energy calibration was carried out, using the standard $\mathit{\gamma }$-ray sources, i.e. ¹³⁷Cs, ²²Na, ⁶⁰Co, and the background $\mathit{\gamma }$ rays observed in the measurements, i.e. ⁴⁰K: 1.461 MeV, ⁵⁶Fe(${\mathrm{n}}_{\mathit{thermal}},\mathit{\gamma }$)⁵⁷Fe: 7.638 MeV (weighted average of 7.631 and 7.646 MeV $\mathit{\gamma }$ rays). Constant extrapolation below 0.60 MeV was made for these PH spectra, as shown in Figure 6 by referring to average counts around 2.5 MeV. As for the ⁸²Se measurement, the net capture $\mathit{\gamma }$-ray PH spectra with (considerably) large statistical fluctuation were obtained, as shown in Figure 7.

Figure 6. Observed net capture $\mathit{\gamma }$-ray PH spectra of ⁷⁸Se in the incident neutron energy region from 15 to 100 keV (average energy: 48 keV) and around 550 keV. Below 0.6 MeV, constant extrapolation was made.

Figure 7. Observed net capture $\mathit{\gamma }$-ray PH spectra of ⁸²Se in the incident neutron energy region from 15 to 100 keV (average energy: 49 keV) and around 550 keV. Below 0.6 MeV, constant extrapolations were made.

3.3. Capture cross sections

To obtain the capture yields of the individual samples, a PH weighting technique [20] was applied to the net capture $\mathit{\gamma }$-ray PH spectra as follows:

(1) $Y_{\mathit{i},\mathit{j}}=\sum _I\left(W_i\left(\mathit{I}\right)S_{\mathit{i},\mathit{j}}\left(\mathit{I}\right)\right)/\left(B_i+{⟨{\mathit{E}}_{\mathit{n}}^{\mathit{CM}}⟩}_{\mathit{i},\mathit{j}}\right),$(1)

where $Y_{\mathit{i},\mathit{j}}$ is the capture yield for region $\mathit{j}$ of sample $\mathit{i}$, $S_{\mathit{i},\mathit{j}}\left(\mathit{I}\right)$ is the corresponding net PH spectrum, $\mathit{I}$ is the channel number, $B_i$ is the neutron binding energy of sample nuclide $\mathit{i}$, $W_i\left(\mathit{I}\right)$ is the weighting function of the $\mathit{\gamma }$-ray spectrometer with the correction of $\mathit{\gamma }$-ray transportation in sample $\mathit{i}$, and ${⟨{\mathit{E}}_{\mathit{n}}^{\mathit{CM}}⟩}_{\mathit{i},\mathit{j}}$ is an average incident neutron energy for region $\mathit{j}$ of sample $\mathit{i}$ in the center of mass system. The average energy was defined as follows:

(2) ${⟨{\mathit{E}}_{\mathit{n}}^{\mathit{CM}}⟩}_{\mathit{i},\mathit{j}}\equiv {⟨E_n⟩}_{\mathit{j}}\cdot \frac{A_i}{A_i+1},$(2)

where $A_i$ is the mass number of sample $\mathit{i}$ and ${⟨E_n⟩}_{\mathit{j}}$ is an average incident neutron energy for region $\mathit{j}$ in the laboratory system. Here the average energy in the laboratory system was defined as follows:

(3) ${⟨E_n⟩}_{\mathit{j}}\equiv \frac{{\int }_{{\mathit{E}}_{\mathit{j},\mathit{min}}}^{E_{\mathit{j},\mathit{max}}}{E}_n\mathit{\eta }(E_n)\mathit{d}{E}_n}{{\int }_{{\mathit{E}}_{\mathit{j},\mathit{min}}}^{E_{\mathit{j},\mathit{max}}}\mathit{\eta }(E_n)\mathit{d}{E}_n},$(3)

where $E_{\mathit{j},\mathit{max}}$, $E_{\mathit{j},\mathit{min}}$ are the high- and low-energy boundaries of region $\mathit{j}$, respectively.

On the other hand, using the number of incident neutrons ${\varphi }_{\mathit{i},\mathit{j}}$ for region $\mathit{j}$ of sample $\mathit{i}$, the capture yield was expressed as follows:

(4) $Y_{\mathit{i},\mathit{j}}=N_i{⟨\sigma ⟩}_{\mathit{i},\mathit{j}}{\varphi }_{\mathit{i},\mathit{j}},$(4)

where $N_i$ is the number of sample nuclei per barn and ${⟨\sigma ⟩}_{\mathit{i},\mathit{j}}$ is an average neutron capture cross section for region $\mathit{j}$ of sample nuclide $\mathit{i}$. The average capture cross-section was defined as follows:

(5) ${⟨\sigma ⟩}_{\mathit{i},\mathit{j}}\equiv \frac{{\int }_{{\mathit{E}}_{\mathit{j},\mathit{min}}}^{E_{\mathit{j},\mathit{max}}}{\sigma }_i(E_n)\mathit{\eta }(E_n)\mathit{d}{E}_n}{{\int }_{{\mathit{E}}_{\mathit{j},\mathit{min}}}^{E_{\mathit{j},\mathit{max}}}\mathit{\eta }(E_n)\mathit{d}{E}_n},$(5)

where ${\sigma }_i(E_n)$ is the capture cross section of sample nuclide $\mathit{i}$.

Therefore, the number of incident neutrons in the ¹⁹⁷Au run was determined by the capture yield of ¹⁹⁷Au and the average capture cross section ${⟨\sigma ⟩}_{\mathit{Au},\mathit{j}}$ of ¹⁹⁷Au, which was obtained from the standard capture cross sections of JENDL-5.0 [21]. Then, the number of incident neutrons for each region in the Se run was obtained from that in the ¹⁹⁷Au run and the neutron monitor counts of the ⁶Li-glass detector [18].

Finally, the average neutron capture cross-section of Se was derived from the number of incident neutrons and the capture yield for each region in the Se run as follows:

(6) ${⟨\sigma ⟩}_{\mathit{i},\mathit{j}}=\frac{\sum _I{W}_i\left(\mathit{I}\right)S_{\mathit{i},\mathit{j}}\left(\mathit{I}\right)/\left(B_i+{⟨{\mathit{E}}_{\mathit{n}}^{\mathit{CM}}⟩}_{\mathit{i},\mathit{j}}\right)/\left(N_i\cdot {\varphi }_{\mathit{i},\mathit{j}}\right)}{\sum _I{W}_{\mathit{Au}}\left(\mathit{I}\right)S_{\mathit{Au},\mathit{j}}\left(\mathit{I}\right)/\left(B_{\mathit{Au}}+{⟨{\mathit{E}}_{\mathit{n}}^{\mathit{CM}}⟩}_{\mathit{Au},\mathit{j}}\right)/\left(N_{\mathit{Au}}\cdot {\varphi }_{\mathit{Au},\mathit{j}}\right)}\cdot <\mathit{\sigma }{>}_{\mathit{Au},\mathit{j}}.$(6)

The effects of meta-stable states and/or conversion electron process in the residual nucleus (^{75,77,79,81,83}Se or ¹⁹⁸Au) to the capture cross sections derived above should be estimated, because all the excitation energy of capture state is assumed to be promptly released by $\mathit{\gamma }$-ray emission. In the case of ¹⁹⁸Au, a meta-stable state exists at 0.812 MeV and has a half-life of 2.30 d [22]. However, its production cross sections by neutron capture reaction are less than about 0.1% of total neutron capture cross sections in the keV region [23]. Therefore, its effect on the derived capture cross sections is thought to be negligibly small. As for ^{75,77,79,81,83}Se, meta-stable states and/or meaningful conversion electron processes have not been reported.

3.4. Capture γ-ray spectra

The capture $\mathit{\gamma }$-ray spectra were derived by unfolding the net capture $\mathit{\gamma }$-ray PH spectra with the computer code, FERDOR [24], and the response matrix of the $\mathit{\gamma }$-ray spectrometer [5]. Then, each $\mathit{\gamma }$-ray spectrum was normalized with the following equation:

(7) ${\int }_0^{B_i+{⟨{\mathit{E}}_{\mathit{n}}^{\mathit{CM}}⟩}_{\mathit{i},\mathit{j}}}{E}_{\gamma }{\nu }_{\mathit{i},\mathit{j}}\left(E_{\gamma }\right)\mathit{d}{E}_{\gamma }=B_i+{⟨{\mathit{E}}_{\mathit{n}}^{\mathit{CM}}⟩}_{\mathit{i},\mathit{j}},$(7)

where $E_{\gamma }$ is the $\mathit{\gamma }$-ray energy and ${\nu }_{\mathit{i},\mathit{j}}\left(E_{\gamma }\right)$ is the capture $\mathit{\gamma }$-ray spectrum for region $\mathit{j}$ of sample $\mathit{i}$. Due to the above normalization, the unit of the present $\mathit{\gamma }$-ray spectrum is ‘$\mathit{\gamma }$Rays/MeV/Capture’ and the integration of the $\mathit{\gamma }$-ray spectrum with respect to $E_{\gamma }$ gives the $\mathit{\gamma }$-ray multiplicity of the capture reaction.

3.5. Corrections and uncertainties

The dead time corrections were small (<0.3%), because the count rates of the $\mathit{\gamma }$-ray spectrometer and the ⁶Li-glass neutron detectors were less than about 500 cps.

The extrapolation of the net capture $\mathit{\gamma }$-ray PH spectrum below the discrimination level (0.60 MeV) was required for the application of the PH weighting technique. The contributions of the extrapolation regions to the capture yields were 2.3–7.0% and 2.4–8.0% in the 15–100 keV and 550 keV measurements, respectively. In this correction, 30% of the contributions were estimated to be the uncertainties from the sensitivity of the correction factor to various extrapolation methods [6,7].

The correction for the neutron self-shielding and multiple scattering in each sample was carried out with a Monte Carlo method [25], taking account of the isotopic and chemical impurities in each sample. The nuclear data used in the Monte Carlo calculation were taken from JENDL-5.0 [26]. Table 3 shows the calculated correction factors, where C is the correction factor, defined as the product of the self-shielding correction factor, C_ns, and the multiple-scattering correction factor C_nm.

Table 3. Correction factors for the self-shielding and multiple scattering of neutrons in the sample.

		Neutron energy region [keV]
sample	Correction Factor	region1	region2	region3	region4	region5	550
^74Se	Cns	0.964	0.967	0.970	0.973	–	0.984
	Cnm	1.148	1.118	1.098	1.073	–	1.041
	C=Cns$\times$Cnm	1.106	1.081	1.064	1.043	–	1.024
^76Se	Cns	0.959	0.963	0.965	0.968	–	0.981
	Cnm	1.118	1.106	1.094	1.077	–	1.054
	C=Cns$\times$Cnm	1.072	1.064	1.056	1.042	–	1.033
^78Se	Cns	0.964	0.967	0.969	0.971	–	0.981
	Cnm	1.104	1.094	1.085	1.071	–	1.050
	C=Cns$\times$Cnm	1.064	1.058	1.051	1.040	–	1.030
^80Se	Cns	0.915	0.920	0.923	0.927	–	0.948
	Cnm	1.223	1.201	1.180	1.050	–	1.112
	C=Cns$\times$Cnm	1.119	1.105	1.090	1.066	–	1.055
^82Se	Cns	0.952	0.951	0.952	0.953	0.954	0.966
	Cnm	1.129	1.127	1.154	1.133	1.113	1.087
	C=Cns$\times$Cnm	1.075	1.072	1.099	1.079	1.062	1.049
^197Au^*	Cns	0.956	0.959	0.961	0.964	–	0.962
	Cnm	1.144	1.133	1.120	1.104	–	1.100
	C=Cns$\times$Cnm	1.084	1.078	1.070	1.058	–	1.059

^*Correction factor for the ^76,78,80,82Se measurement. See Table 1.

The neutron cross sections employed in the calculation had uncertainties. Therefore, 10% [5,18] of the corrections were estimated to be the uncertainties from the sensitivity of the correction factor to the variation of the employed cross sections. The resultant uncertainties were 0.5 to 1.5%.

The $\mathit{\gamma }$-ray scattering and absorption in the sample were taken into account in obtaining the weighting function of the $\mathit{\gamma }$-ray spectrometer. The weighting function for each sample was obtained from the response functions of the $\mathit{\gamma }$-ray spectrometer that were calculated for each sample by using a Monte Carlo code [27]. The uncertainty of the weighting function, which was caused by those of response functions and that of a trial function [18] for the weighting function, was estimated to be 4 to 6% [18]. However, since the weighting function appears in both the denominator and numerator of the right-hand side of Eq.(6)(6) ${⟨\sigma ⟩}_{\mathit{i},\mathit{j}}=\frac{\sum _I{W}_i\left(\mathit{I}\right)S_{\mathit{i},\mathit{j}}\left(\mathit{I}\right)/\left(B_i+{⟨{\mathit{E}}_{\mathit{n}}^{\mathit{CM}}⟩}_{\mathit{i},\mathit{j}}\right)/\left(N_i\cdot {\varphi }_{\mathit{i},\mathit{j}}\right)}{\sum _I{W}_{\mathit{Au}}\left(\mathit{I}\right)S_{\mathit{Au},\mathit{j}}\left(\mathit{I}\right)/\left(B_{\mathit{Au}}+{⟨{\mathit{E}}_{\mathit{n}}^{\mathit{CM}}⟩}_{\mathit{Au},\mathit{j}}\right)/\left(N_{\mathit{Au}}\cdot {\varphi }_{\mathit{Au},\mathit{j}}\right)}\cdot <\mathit{\sigma }{>}_{\mathit{Au},\mathit{j}}.$(6) , the contribution of its uncertainty to the capture cross section was about 1%.

The correction for the capture yields due to the chemical and isotopic impurities in the ^{74,76,78,80,82}Se samples was made by using the evaluated capture cross sections of JENDL-5.0 [26]. The corrections for the chemical impurities were less than 0.04%, and those for the isotopic impurities were 0.004–1.5% for ^74,76,78,80Se. As for ⁸²Se, the corrections due to the chemical impurities were 0.1–7.3% and those for the isotopic impurities were 0.46–1.6%. These small corrections were due to the high purity of the ^{74,76,78,80,82}Se samples, as shown in Table 1. In these corrections, there is no information about the uncertainties of the capture cross sections in JENDL-5.0. Therefore, 20% of the corrections were a priori assumed to be the correction uncertainties.

In addition, the following were taken into account for the uncertainties of capture cross sections: the uncertainties due to the standard capture cross sections of ¹⁹⁷Au (3% in the 15–100 keV measurement and 3.5% in the 550 keV measurement) [21] and the number of target nuclei (0.2%).

The uncertainties mentioned above for the derived capture cross sections are summarized in Table 4, together with statistical uncertainties. The total uncertainty was obtained as the square root of the sum of squares of individual uncertainties.

Table 4. Statistical and systematic uncertainties.

	Uncertainty[%]
	Neutron energy region [keV]
	15–25	25–35	35–55	55–100	–	550^b
Uncertainty source	12–18^a	18–22^a	22–32^a	32–46^a	46–100^a
Statistics
^74Se	1.6	1.2	0.9	1.0	–	1.0
^76Se	1.4	1.1	0.8	0.9	–	2.5
^78Se	2.2	1.4	1.0	1.1	–	1.4
^80Se	3.6	2.4	1.6	1.5	–	2.4
^82Se	14	19	4.6	7.8	4.3	27
Neutron self-shielding and multiple scattering
^74Se	1.1	0.8	0.6	0.4	–	0.2
^76Se	0.7	0.6	0.6	0.4	–	0.3
^78Se	0.6	0.5	0.4	0.4	–	0.3
^80Se	1.2	1.0	0.9	0.7	–	0.5
^82Se	0.7	0.7	1.0	0.8	0.6	0.5
^197Au	0.9	0.9	0.8	0.6	–	0.6
^197Au(for ^82Se measurement)	0.9	0.9	0.9	0.8	0.7	0.6
Weighting function	1.0	1.0	1.0	1.0	1.0	1.0
Impurity correction for capture yields
^74Se	<0.01	<0.01	<0.01	<0.01	–	<0.01
^76Se	0.2	0.2	0.2	0.2	–	0.1
^78Se	0.4	0.4	0.4	0.4	–	0.1
^80Se	0.2	0.2	0.2	0.2	–	0.1
^82Se	3.4	1.1	1.3	1.7	2.0	1.1
Standard capture cross sections of ^197Au	3.0	3.0	3.0	3.0	3.0	3.5
Extrapolation of PH spectrum^c
^74Se	1.2	1.2	1.2	1.2	–	0.7
^76Se	1.3	1.3	1.3	1.2	–	0.8
^78Se	1.4	1.3	1.3	1.3	–	0.9
^80Se	1.4	1.4	1.5	1.4	–	1.5
^82Se	0.8	1.2	0.7	0.7	0.2	1.6
^197Au	2.0	1.8	2.0	1.8	–	0.6
^197Au(for ^82Se measurement)	3.5	3.7	4.0	4.1	3.8	0.6
Number of target Nuclei	0.2	0.2	0.2	0.2	0.2	0.2

^aThese regions were set for ⁸²Se in 15–100 keV measurement.

^bFWHM = 81 keV(⁷⁴Se), 84 keV (⁷⁶Se), 91 keV(⁷⁸Se), 95 keV(⁸⁰Se), 96 keV(⁸²Se).

^cDiscrimination level : 0.60 MeV.

As for the uncertainties of the capture $\mathit{\gamma }$-ray spectrum, the statistical uncertainties of the input PH spectrum were taken into account.

4. Results and discussion

4.1. Capture cross sections

The capture cross sections of ^74,76,78,80Se were derived with uncertainties of 4.0–5.5% and those of ⁸²Se were derived with the uncertainties of 6.5–27% in the incident neutron energy region from 15 to 100 keV and at around 550 keV. The derived capture cross sections of ^{74,76,78,80,82}Se are shown in Tables 5–9 and compared with previous measurements and the evaluated values of JENDL-5.0 [26] and ENDF/B-VIII.0 [28] in Figure 8–12. The average neutron energies and the average capture cross sections in Tables 5–9 are those defined by Eqs (3)(3) ${⟨E_n⟩}_{\mathit{j}}\equiv \frac{{\int }_{{\mathit{E}}_{\mathit{j},\mathit{min}}}^{E_{\mathit{j},\mathit{max}}}{E}_n\mathit{\eta }(E_n)\mathit{d}{E}_n}{{\int }_{{\mathit{E}}_{\mathit{j},\mathit{min}}}^{E_{\mathit{j},\mathit{max}}}\mathit{\eta }(E_n)\mathit{d}{E}_n},$(3) and (5(5) ${⟨\sigma ⟩}_{\mathit{i},\mathit{j}}\equiv \frac{{\int }_{{\mathit{E}}_{\mathit{j},\mathit{min}}}^{E_{\mathit{j},\mathit{max}}}{\sigma }_i(E_n)\mathit{\eta }(E_n)\mathit{d}{E}_n}{{\int }_{{\mathit{E}}_{\mathit{j},\mathit{min}}}^{E_{\mathit{j},\mathit{max}}}\mathit{\eta }(E_n)\mathit{d}{E}_n},$(5) ), respectively. In Figures 8–12, the present results are plotted at the average neutron energies, and the horizontal bars show the neutron energy regions in Tables 5–9. The evaluated values of JENDL-5.0 [26] and ENDF/B-VIII.0 [28] are averaged ones with appropriate energy widths for easy comparison with the present results.

Figure 8. Neutron capture cross sections of ⁷⁴Se in the keV region. The horizontal bars show the energy region in Table 5.

Figure 9. Neutron capture cross sections of ⁷⁶Se in the keV region. The horizontal bars show the energy region in Table 6.

Figure 10. Neutron capture cross sections of ⁷⁸Se in the keV region. The horizontal bars show the energy region in Table 7.

Figure 11. Neutron capture cross sections of ⁸⁰Se in the keV region. The horizontal bars show the energy region in Table 8.

Table 5. Derived neutron capture cross sections of ^74.Se.

Average neutron energy[keV](Energy region)	Capture cross section [mb](Relative uncertainty)
20 (15–25)	313$\pm$14 (4.4%)
30 (25–35)	247$\pm$10 (4.2%)
44 (35–55)	220$\pm$9.1 (4.1%)
68 (55–100)	173$\pm$7.0 (4.0%)
552(81)*	109$\pm$5.0 (4.6%)

*FWHM of neutron energy spectrum.

Table 6. Derived neutron capture cross sections of ^76.Se.

Average neutron energy[keV](Energy region)	Capture cross section [mb](Relative uncertainty)
20 (15–25)	198$\pm$9.9 (5.0%)
30 (25–35)	167$\pm$8.6 (5.1%)
44 (35–55)	128$\pm$6.4 (5.0%)
69 (55–100)	103$\pm$4.8 (4.6%)
545(84)*	57.4$\pm$3.0 (5.1%)

*FWHM of neutron energy spectrum.

Table 7. Derived neutron capture cross sections of ^78.Se.

Average neutron energy[keV](Energy region)	Capture cross section [mb](Relative uncertainty)
20 (15–25)	89.5$\pm$4.3 (4.6%)
30 (25–35)	86.6$\pm$3.7 (4.1%)
44 (35–55)	67.5$\pm$2.9 (4.1%)
69 (55–100)	54.1$\pm$2.2 (4.0%)
541(91)*	31.4$\pm$1.4 (4.6%)

*FWHM of neutron energy spectrum.

Table 8. Derived capture cross sections of ^80.Se.

Average neutron energy[keV](Energy region)	Capture cross section [mb](Relative uncertainty)
20 (15–25)	34.8$\pm$1.9 (5.5%)
30 (25–35)	28.4$\pm$1.3 (4.9%)
44 (35–55)	24.7$\pm$1.1 (4.6%)
71 (55–100)	22.7$\pm$1.0 (4.3%)
542(95)*	11.5$\pm$0.6 (5.2%)

*FWHM of neutron energy spectrum.

Table 9. Derived neutron capture cross sections of ^82.Se.

Average neutron energy[keV](Energy region)	Capture cross section [mb](Relative uncertainty)
15 (12–18)	14.0$\pm$2.10 (14.6%)
20 (18–22)	7.66$\pm$1.52 (19.9%)
27 (22–32)	11.8$\pm$0.764 (6.2%)
38 (32–46)	3.91$\pm$0.353 (10.1%)
65 (46–100)	7.65$\pm$0.483 (6.0%)
544(96)*	4.61$\pm$1.25 (27%)

*FWHM of neutron energy spectrum.

Figure 12. Neutron capture cross sections of ⁸⁰Se in the keV region. The horizontal bars show the energy region in Table 8.

4.1.1. ⁷⁴Se

The capture cross sections of ⁷⁴Se were derived with uncertainties of 4.0–4.6% in the energy region of 15–100 keV and at 552 keV, as shown in Figure 8 and Table 5. The present results of ⁷⁴Se are the first measurements as a function of neutron energy and are compared with the previous measurements [9–11] and evaluations of JENDL-5.0 [29] and ENDF/B-VIII.0 [30] in Figure 8. All the previous measurements were performed with neutron activation methods. Siddappa et al. [9] measured the capture cross section at 25$\pm$5 keV, using an Sb-Be neutron source with activities of 20 Ci(740 GBq). Their ⁷⁴Se result is smaller than the present one by 40%. Trofimov [10] et al. measured the capture cross section at around 500 keV using a p-T neutron source with a Van de Graaff accelerator. Their result is smaller than the present one around 550 keV by 20%. Dillmann et al. measured a Maxwellian averaged cross section at kT = 25 keV using a ⁷Li(p,n)⁷Be neutron source. Their result is in good agreement with the present results around 25 keV.

In the evaluation of JENDL-5.0 for the capture cross sections of ⁷⁴Se, a statistical model calculation with a coupled-channel optical potential was performed, and the $\mathit{\gamma }$-ray strength function was adjusted to reproduce the present ones. The evaluations of JENDL-5.0 have larger than present results by 0.96–11% in the region from 15 to 55 keV, but smaller than present ones by 0.01% and smaller than present ones by 5.4% at 552 keV. The ENDF/B-VIII.0 adopted the values of JENDL-3.3 [31,32] in the unresolved and continuous regions. In the evaluation of JENDL-3.3 for the capture cross sections of ⁷⁴Se, a statistical model calculation with a spherical optical potential was performed, and the $\mathit{\gamma }$-ray strength function was adjusted to reproduce capture cross section of 198 mb at 25 keV measured by Sriramachandra et al. (Siddappa et al.). Comparing the evaluated values of JENDL-3.3 with the present results, the evaluated values are smaller than the present results by 13–31% in the region from 15 to 100 keV, and by about 34% at 552 keV.

4.1.2. ⁷⁶Se

The capture cross sections of ⁷⁶Se were derived with uncertainties of 4.6–5.1% in the energy region of 15–100 keV and at 545 keV, as shown in Figure 9 and Table 6. The present results are compared with a previous measurement and evaluations of JENDL-5.0 [33] and ENDF/B-VIII.0 [34] in Figure 9. Beer et al. [12] measured Maxwellian cross sections in the region of kT = 10–100 keV using a ⁷Li(p,n)⁷Be neutron source and two C₆D₆ scintillation counters for capture $\mathit{\gamma }$-ray detection. Their result is in agreement with the present ones up to 50 keV within the uncertainty.

In the evaluation of JENDL-5.0 for the capture cross sections of ⁷⁶Se, a statistical model calculation with a coupled-channel optical potential was performed, and the $\mathit{\gamma }$-ray strength function was adjusted to reproduce the present ones. The evaluations of JENDL-5.0 are larger than the present results by 2.8–16% in the region from 15 to 100 keV, and by about 13% at around 545 keV. Since the ENDF/B-VIII.0 adopted the values of JENDL-3.3 [35] in the unresolved and continuous regions, the evaluated values of ENDF/B-VIII.0 are identical to those of JENDL-3.3. In the evaluation of JENDL-3.3 for the capture cross sections of ⁷⁶Se, a statistical model calculation with a spherical optical potential was performed, and the $\mathit{\gamma }$-ray strength function was assumed to be 1.59$\times$10⁻⁴. Comparing the evaluated values of JENDL-3.3 with the present results, the evaluated values are smaller than the present results by 34–48% in the region from 15 to 100 keV, and by about 30% at around 545 keV.

4.1.3. ⁷⁸Se

The capture cross sections of ⁷⁸Se were derived with uncertainties of 4.1–4.7% in the energy region of 15–100 keV and at 541 keV, as shown in Figure 10 and Table 7. As mentioned before, no previous measurements can be compared with the present results. The evaluations of JENDL-5.0 [36] and ENDF/B-VIII.0 [37] are compared with the present results in Figure 10.

In the evaluation of JENDL-5.0 for the capture cross sections of ⁷⁸Se, a statistical model calculation with a coupled-channel optical potential was performed, and the $\mathit{\gamma }$-ray strength function was adjusted to reproduce the present results. The evaluations of JENDL-5.0 are larger than the present ones by 0.9–30% in the region from 15 to 55 keV, but smaller than 0.7% in the region from 55 to 100 keV, and larger than the present one by 12% at 541 keV. Since the ENDF/B-VIII.0 adopted the values of JENDL-3.3 [38] in the unresolved and continuous regions, the evaluated values of ENDF/B-VIII.0 are identical to those of JENDL-3.3. In the evaluation of JENDL-3.3 for the capture cross sections of ⁷⁸Se, a statistical model calculation with a spherical optical potential was performed, and the $\mathit{\gamma }$-ray strength function was determined from the average radiation width (0.23 eV) and the average spacing (1390 eV) of s-wave neutron resonances which were based on the evaluation of Mughabghab et al. [39]. Comparing the evaluations of JENDL-3.3 are larger than present results by 2.5–51% in the region from 15 to 100 keV and larger than present on by about 34% at around 541 keV.

4.1.4. ⁸⁰Se

The capture cross sections of ⁸⁰Se were derived with uncertainties of 4.3–5.5% in the energy region of 15 to 100 keV and at 542 keV, as shown in Figure 11 and Table 8, are compared in with previous measurements [13–15] and evaluations of JENDL-5.0 [40] and ENDF/B-VIII.0 [41] in Figure 11. There are relatively more previous measurements than other Se isotopes because the appropriate half-life(18.45 min) of the residual nuclide ⁸¹Se makes it easier to apply an activation method to the capture cross-section measurement. Tolstikov et al. [13], and Sriramachandra Murty et al. [14] adopted neutron activation methods. Their result is smaller than the present ones by a factor of two. Tolstikov et al. [13] measured the capture cross sections in the energy region from 11 keV to 3 MeV using a p-T neutron source with a Van de Graaff accelerator. Their results are larger than the present ones in the energy region from 15–55 keV by 40–60%, but in agreement with the present ones in the energy region from 55–100 keV and at around 550 keV. Sriramachandra et al. [14] measured the capture cross sections at 25 keV using an Sb-Be neutron source. Their result is larger than the present ones by a factor of two. Walter et al. [15] measured the capture cross sections in the energy region of 3–220 keV with a ⁷Li(p,n)⁷Be neutron source and a pair of C₆D₆ scintillation counters by means of a TOF method. Their results have fluctuations due to the resonance structure. Therefore, for easy comparison, their measurements are averaged in each energy region of present data processing, as shown in Figure 11. Consequently, their measurements are larger than the present ones by 3–45%.

In the evaluation of JENDL-5.0 for the capture cross sections of ⁸⁰Se, a statistical model calculation with a coupled-channel optical potential was performed, and the $\mathit{\gamma }$-ray strength function was adjusted to reproduce the present results. The evaluations of JENDL-5.0 are larger than the present ones by 9.7–28% in the region from 15–55 keV, but smaller than the present one by 7.8%, but larger than the present one by 11% at around 542 keV. Since the ENDF/B-VIII.0 adopted the values of JENDL-3.3 [42] in the unresolved and continuous regions, the evaluated values of ENDF/B-VIII.0 are identical to those of JENDL-3.3. In the evaluation of JENDL-3.3 for the capture cross sections of ⁸⁰Se, a statistical model calculation with a spherical optical potential was performed, and the $\mathit{\gamma }$-ray strength function was adjusted to reproduce the capture cross section of 16 mb at 200 keV measured by Walter et al. [15]. The evaluations of JENDL-3.3 are larger than present results by 12–39% in the region from 15 to 55 keV, but smaller than present one in the region from 55 to 100 keV by 8.5%, but larger than present by 43% at around 542 keV.

4.1.5. ⁸²Se

The capture cross sections of ⁸²Se were derived with uncertainties of 6.3–27% in the energy region of 12–100 keV and at 544 keV, as shown in Figure 12 and Table 9. The present results are the first measurements in the keV region. Therefore, no previous measurements are to be compared with the present results. The evaluations of JENDL-5.0 [43] and ENDF/B-VIII.0 [44] are compared with the present results in Figure 12. The present results have large fluctuations due to the resonance structure in Figure 12.

In the evaluation of JENDL-5.0 for the capture cross sections of ⁸²Se, a statistical model calculation with a coupled-channel optical potential was performed, and the $\mathit{\gamma }$-ray strength function was adjusted to reproduce the present results. The evaluations of JENDL-5.0 are smaller than the present results by 69% in the region from 12 to 18 keV, but larger than the present one in the region from 18 to 22 keV by 73%, and smaller than the present one by about 6.9% in the region from 22 to 32 keV, but larger than present one by 120% in the region from 32 to 46 keV, and smaller than the present one by 25%, and smaller than the present one by 31% at 544 keV. Since the ENDF/B-VIII.0 adopted the values of JENDL-3.3 [45] in the unresolved and continuous regions, the evaluated values of ENDF/B-VIII.0 are identical to those of JENDL-3.3. In the evaluation of JENDL-3.3 for the capture cross sections of ⁸²Se, a statistical model calculation with a spherical optical potential was performed, and the $\mathit{\gamma }$-ray strength function was adjusted to reproduce the capture cross section of 0.045 b at 25 keV which was a somewhat larger value than a meta-stable state production cross section of 0.045 b at 24 keV measured by Chaubey et al. [46]. The evaluations of JENDL-3.3 are smaller than present results by 44–84% in the region from 12 to 22 keV, but larger than present ones in the region from 18 to 100 keV by 213–750%, and by about 310% at 544 keV.

4.2. Capture γ-ray spectra

The keV-neutron capture $\mathit{\gamma }$-ray spectra of ^{74,76,78,80,82}Se were obtained for the first time, and are shown in Figures 13, 14, 15, 16, 17, respectively, where low-lying states of the residual nucleus, ^{75,77,79,81,83}Se, are also shown as vertical bars. The energies of low-lying states correspond to the spectra in the 15–100 keV measurements, i.e., each state is shown at the energy of ($B_i+<E_n^{\mathit{CM}}{>}_i-E_x$), where $<E_n^{\mathit{CM}}{>}_i$ is the average incident neutron energy in the 15–100 keV measurement for sample $\mathit{i}$ in the center of the mass system and $E_x$ is the excitation energy of the state. Since the statistical uncertainty of the PH spectrum of ⁸²Se at 545 keV was large, as shown in Figure 7, we tried to perform 3-point smoothing without weighting to the PH spectrum and then unfolded it. However, the obtained spectrum of ⁸²Se was not meaningful. So we omit to show the unfolded spectrum of ⁸²Se at 545 keV in Figure 17.

Figure 13. Neutron capture cross sections of ⁸²Se in the keV region. The horizontal bars show the energy region in Table 9.

Figure 14. Obtained capture $\mathit{\gamma }$-ray spectra of ⁷⁴Se in the incident neutron energy region from 15 to 100 keV and around 550 keV. Low-lying states of ⁷⁵Se are shown as vertical bars. As for the energy positions of states, see the text.

Figure 15. Obtained capture $\mathit{\gamma }$-ray spectra of ⁷⁶Se in the incident neutron energy region from 15 to 100 keV and around 550 keV. Low-lying states of ⁷⁷Se are shown as vertical bars. As for the energy positions of states, see the text.

Figure 16. Obtained capture $\mathit{\gamma }$-ray spectra of ⁷⁸Se in the incident neutron energy region from 15 to 100 keV and around 550 keV. Low-lying states of ⁷⁹Se are shown as vertical bars. As for the energy positions of states, see the text.

Figure 17. Obtained capture $\mathit{\gamma }$-ray spectra of ⁸⁰Se in the incident neutron energy region from 15 to 100 keV and around 550 keV. Low-lying states of ⁸¹Se are shown as vertical bars. As for the energy positions of states, see the text.

The multiplicities of observed capture $\mathit{\gamma }$ rays ($E_{\gamma }\ge$ 0.60 MeV) were derived by integrating the $\mathit{\gamma }$-ray spectra with respect to the $\mathit{\gamma }$-ray energy, and are shown in Table 10, where our results [17] for ⁷⁷Se are also shown. The reduced multiplicities obtained by dividing the multiplicities by the corresponding excitation energy of capture states (the neutron binding energy plus the incident neutron energy) are also shown in Table 10. Each multiplicity of ^{74,76,77,78,80,82}Se seems to increase with the excitation energy of capture states, but each reduced multiplicity seems to be constant with respect to the excitation energy, considering the experimental uncertainties. This tendency is similar to those observed for lanthanide nuclides [18,47–49].

Table 10. Multiplicities of observed capture $\mathit{\gamma }$-rays (MP:E${ }_{\gamma }\ge 0.6$ MeV) and reduced multiplicities.

Target Nuclide	^74Se	^76Se	^77Se	^78Se	^80Se	^82Se
Bn^a [MeV]	8.028	7.419	10.50	6.963	6.701	5.818
MP [$\mathit{\gamma }$ Rays/Capture]
15–100 keV measurement	2.69$\pm$0.10	2.48$\pm$0.06	3.92$\pm$0.12(4.04$\pm$0.08)^d	2.54$\pm$0.07	2.30$\pm$0.10	2.29$\pm$0.23
$⟨E_n⟩$^b [MeV]	0.046	0.047	0.045	0.048	0.050	0.048
550 keV measurement	2.87$\pm$0.11	2.59$\pm$0.09	4.06$\pm$0.18	2.60$\pm$0.12	2.26$\pm$0.14	–
$⟨E_n⟩$^b [MeV]	0.544	0.538	0.509	0.535	0.536	–
Reduced MP^c
15–100 keV measurement	0.334$\pm$0.012	0.333$\pm$0.008	0.384$\pm$0.012	0.362$\pm$0.010	0.341$\pm$0.014	0.390$\pm$0.039
550 keV measurement	0.335$\pm$0.013	0.326$\pm$0.011	0.369$\pm$0.016	0.347$\pm$0.016	0.312$\pm$0.019	–

^aNeutron binding energy of target nuclide.

^bAverage incident neutron energy in the center of mass system.

^cDefined by (multiplicity)/(B_n+$⟨E_n⟩$). The unit is ($\mathit{\gamma }$ Rays/1-MeV excitation energy/Capture).

^d${\mathrm{E}}_{\gamma }\ge 0.5\mathrm{MeV}$.

4.2.1. ⁷⁴Se

In Figure 13, the primary transitions from the neutron capture states to the ground (E_x = 0 MeV, ${\mathrm{J}}^{\pi }$ = ${\frac{5}{2}}^{+}$), first (E_x = 0.112 MeV, ${\mathrm{J}}^{\pi }$ = ${\frac{7}{2}}^{+}$), nor second (E_x = 0.133 MeV, ${\mathrm{J}}^{\pi }$ = ${\frac{9}{2}}^{+}$) states [22] were not clearly observed in the spectrum obtained in the 15–100 keV measurement. This indicates that the capture reaction in the region from 15 to 100 keV is mainly due to the s-wave neutron capture, assuming a predominant electric dipole (E1) transition. On the other hand, the primary transitions from the capture states to the third (E_x = 0.287 MeV, ${\mathrm{J}}^{\pi }$ = ${\frac{3}{2}}^{-}$), fourth (E_x = 0.293 MeV, ${\mathrm{J}}^{\pi }$ = ${\frac{1}{2}}^{-}$), sixth (E_x = 0.586 MeV, ${\mathrm{J}}^{\pi }$ = ${\frac{3}{2}}^{-}$) states and so forth were observed in the spectrum obtained in the 15–100 keV measurement. In the spectrum obtained at around 550 keV measurements, the primary transitions from the capture states to the ground state start to be observed. This suggests that the p-wave neutron capture component increases at 550 keV.

4.2.2. ⁷⁶Se

In Figure 14, the primary transitions from the neutron capture states to the low-lying states, that is, the ground (E_x = 0 MeV, ${\mathrm{J}}^{\pi }$ = ${\frac{1}{2}}^{-}$) and third (E_x = 0.239 MeV, ${\mathrm{J}}^{\pi }$ = ${\frac{3}{2}}^{-}$) states [22] are observed above 7 MeV in the spectrum obtained in the 15–100 keV measurement, assuming the s-wave capture and the E1 transition. On the other hand, the primary transitions from the neutron capture states to the ground state are not observed, but the primary ones from the neutron capture states to the third-excited state are clearly observed in the spectrum obtained at around 550 keV measurements. The intensities of the peak above 7 MeV due to these primary $\mathit{\gamma }$-ray transitions are shown in Table 11.

Table 11. Intensities of primary transitions of the neutron capture of ^76.Se.

Target Nuclide(${\mathrm{J}}^{\pi }$)	^76Se(0^+)
Neutron Binding Energy [MeV]	7.419
Residual Nuclide	^77Se
Ex(${\mathrm{J}}^{\pi }$) of low-lying state of residual nuclide[MeV]
Ground-state	0(${\frac{1}{2}}^{-}$)
First-excited state	0.162(${\frac{7}{2}}^{+}$)
Second-excited state	0.175(${\frac{9}{2}}^{+}$)
Third-excited state	0.239(${\frac{3}{2}}^{-}$)
Highest-energy peak intensity
15–100 keV experiment	0.0671$\pm$0.0024
550 keV experiment	0.0556$\pm$0.0040
Intensity ratio^a	0.83$\pm$0.07

^a(550 keV experiment)/(15–100 keV experiment)

4.2.3. ⁷⁸Se

In Figure 15, the primary transitions from the neutron capture states to the first (E_x = 0.096 MeV, ${\mathrm{J}}^{\pi }$ = ${\frac{1}{2}}^{+}$) and second (E_x = 0.128 MeV, ${\mathrm{J}}^{\pi }$ = ${\frac{1}{2}}^{+}$) states and the fifth (E_x = 0.499 MeV, ${\mathrm{J}}^{\pi }$ = ${\frac{3}{2}}^{-}$) and sixth (E_x = 0.528 MeV, ${\mathrm{J}}^{\pi }$ = ${\frac{3}{2}}^{-}$) states [22] are observed as two composite peaks in the spectra obtained both in the 15–100 keV and 550 keV measurements. The intensities of these two peaks are shown in the Table 12. The cascade transitions among low-lying states are observed as a strong peak around 0.8 MeV in both spectra.

Table 12. Intensities of primary $\mathit{\gamma }$-rays transitions of the neutron capture ^78.Se.

Target Nuclide(${\mathrm{J}}^{\pi }$)	^78Se(0${ }^{+}$)
Neutron Binding Energy [MeV]	6.963
Residual Nuclide	^79Se
Ex(${\mathrm{J}}^{\pi }$) of low-lying state of residual nuclide[MeV]
Ground State	0(${\frac{7}{2}}^{+}$)
First-excited state	0.096(${\frac{1}{2}}^{-}$)
Second-excited state	0.128(${\frac{1}{2}}^{-}$)
Third-excited state	0.137(${\frac{9}{2}}^{+}$)
Fourth-excited state	0.365(${\frac{5}{2}}^{-}$)
Fifth-excited state	0.499(${\frac{3}{2}}^{-}$)
Sixth-excited state	0.528(${\frac{3}{2}}^{-}$)
First-peak intensity^a
15–100 keV experiment	0.0417$\pm$0.0026
550 keV experiment	0.0524$\pm$0.0066
Intensity Ratio	1.26$\pm$0.18
Second-peak intensity^b
15–100 keV experiment	0.1012$\pm$0.0039
550 keV experiment	0.0593$\pm$0.0065
Intensity ratio^c	0.58$\pm$ 0.07

^aComposed of the transitions to the first- and second-excited states.

^bComposed of the transitions to the fifth- and sixth-excited states.

^c(550 keV experiment)/(15–100 keV experiment)

4.2.4. ⁸⁰Se

In Figure 16, the primary transitions from the neutron capture states to the ground (E_x = 0 MeV, ${\mathrm{J}}^{\pi }$ = ${\frac{1}{2}}^{-}$) state and the third (E_x = 0.468 MeV, ${\mathrm{J}}^{\pi }$ = ${\frac{3}{2}}^{+}$) state [22] are observed as two peaks around 6.8 MeV and 6.3 MeV in the spectrum obtained in the 15–100 keV measurement, respectively. In the spectrum obtained in the 550 keV measurement, the peak around 6.8 MeV becomes broader in comparison with the corresponding peak around 6.3 MeV in the spectrum obtained in the 15–100 keV measurement. This may be caused by the transitions to the fifth (E_x = 0.616 MeV, ${\mathrm{J}}^{\pi }$ = ${\frac{3}{2}}^{+}$) [22] state as well as the third state. The intensities of these two peaks are shown in the Table 13.

Table 13. Intensities of primary $\mathit{\gamma }$-ray transitions of neutron capture of ^80.Se.

Target Nuclide(${\mathrm{J}}^{\pi }$)	^80Se(0${ }^{+}$)
Neutron Binding Energy [MeV]	6.701
Residual Nuclide	^81Se
Ex(${\mathrm{J}}^{\pi }$) of low-lying state of residual nuclide[MeV]
Ground State	0(${\frac{1}{2}}^{-}$)
First-excited state	0.103(${\frac{7}{2}}^{+}$)
Second-excited state	0.294(${\frac{9}{2}}^{+}$)
Third-excited state	0.468(${\frac{3}{2}}^{-}$)
Fourth-excited state	0.491(${\frac{5}{2}}^{-}$)
Fifth-excited state	0.616(${\frac{3}{2}}^{+}$)
First-peak intensity^a
15–100 keV experiment	0.0751$\pm$0.0046
550 keV experiment	0.0655$\pm$0.0106
Intensity Ratio^c	0.87$\pm$0.17
Second-peak intensity^b
15–100 keV experiment	0.0856$\pm$0.0045
550 keV experiment	0.0985$\pm$0.0118
Intensity ratio^c	0.87$\pm$ 0.10

^aTransition to the ground state.

^bComposed of the transitions to the third- and fifth-excited states.

^c(550 keV experiment)/(15–100 keV experiment)

4.2.5. ⁸²Se

In Figure 17, the primary transitions from the neutron capture states to the third (E${ }_x$ = 0.430 MeV, ${\mathrm{J}}^{\pi }$ = ${\frac{3}{2}}^{+}$), fourth (E_x = 0.539 MeV, ${\mathrm{J}}^{\pi }$ = ${\frac{1}{2}}^{+}$), and fifth (E_x = 0.582 MeV, ${\mathrm{J}}^{\pi }$ = ${\frac{5}{2}}^{+}$) states [22] are observed as a peak around 5.4 MeV in the spectrum obtained in the 15–100 keV measurement. This suggests that the primary transitions are due to the p-wave neutron capture, considering the E1 transition and the spins and parities of these states. The intensity of this peak is shown in the Table 14.

Table 14. Intensities of primary $\mathit{\gamma }$-ray transitions of neutron capture of ^82.Se.

Target Nuclide(${\mathrm{J}}^{\pi }$)	^82Se(0^+)
Neutron Binding Energy [MeV]	5.818
Residual Nuclide	^83Se
Ex(${\mathrm{J}}^{\pi }$) of low-lying state of residual nuclide[MeV]
Ground State	0(${\frac{9}{2}}^{+}$)
First-excited state	0.229(${\frac{1}{2}}^{-}$)
Second-excited state	0.360(${\frac{1}{2}}^{+}$)
Third-excited state	0.430(${\frac{3}{2}}^{+}$)
Fourth-excited state	0.539(${\frac{1}{2}}^{+}$)
Fifth-excited state	0.582(${\frac{5}{2}}^{+}$)
First-peak intensity*
15–100 keV experiment	0.178$\pm$0.015

*Composed of the transitions to the third- fourth- and fifth-excited states.

5. Conclusion

We have measured the $\mathit{\gamma }$ rays from the neutron capture reaction ^{74,76,78,80,82}Se in the incident neutron energy region from 15 to 100 keV and around 550 keV, using the 1.5-ns pulsed neutron source based on the ⁷Li(p,n)⁷Be reaction and the large anti-Compton NaI(Tl) $\mathit{\gamma }$-ray spectrometer.

The neutron capture cross sections of ^74,76,78,80Se have been derived with the uncertainties of 4.0–5.5% and those of ⁸²Se were derived with the uncertainties of 6.5–27%. The evaluations of JENDL-5.0 differ from the present results of ^74,76,78,80Se and ⁸²Se by 0.9–51% and 6.9–120%, respectively. On the other hand, the evaluations in the ENDF/B-VIII.0 have differences of 6–150% and 20–450% with the present results of ^74,76,78,80Se and ⁸²Se, respectively.

The keV-neutron capture $\mathit{\gamma }$-ray spectra of ^{74,76,78,80,82}Se have been derived for the first time. The spectra show the primary transitions from the neutron capture states to low-lying states and the cascade transitions among low-lying states. The multiplicities of observed capture $\mathit{\gamma }$ rays as well as the intensities of these primary transitions have been derived from the capture $\mathit{\gamma }$-ray spectra. The multiplicities seem to increase with neutron binding energies of target nuclides.

Acknowledgments

The present study was supported by a Grant-in-Aid (No. 19360423) of the Japan Ministry of Education, Culture, Sports, Science and Technology. This work was also supported by KAKENHI Grant-in-Aids (21K04580).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.