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

Figures & data

Figure 1. Experimental setup in the 550 keV measurements.

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

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.

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) .

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.

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.

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.

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.

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.

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.

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.

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

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)

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)

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)

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.