Utilizing PUNITA experiments to evaluate fundamental delayed gamma-ray spectroscopy interrogation requirements for nuclear safeguards

Figures & data

Figure 1. The mean fractional fission product yield mass distribution of ${ }^{235}$U, ${ }^{239}$Pu, and ${ }^{241}$Pu for the declared thermal-neutron energy from the ENDF/B-VII.1 database [15]. See online version for color.

Figure 2. The fission cross section of ${ }^{235}$U, ${ }^{239}$Pu, ${ }^{241}$Pu, and ${ }^{238}$U vs. log-energy from the ENDF/B-VII.1 database [15] as described in the legend. The vertical lines, with various shades of cyan and dash-dot patterns according to the legend, mark energies indicated as the fission yield production energy in the ENDF database. See online version for color.

Figure 3. The graphite and high-density polyethylene infill for the PUNITA cavity (black outline) around the neutron generator and sample shuttle for the later experiments. See online version for color.

Table 1. The list of campaign runs for the associated samples and interrogation as noted in the text used in this study with the ‘0.00’ indicating there was no U and/or Pu, but with additional Al material.

Camp.	Mass (g)			Interrogation
Run	${ }^{235}$U	${ }^{239}$Pu	${ }^{241}$Pu	$t_I$ (s)	$t_D$ (s)	$t_M$ (s)	$t_R$ (s)	$C$
2015Al	0.00	0.00	0.00	50	5.0	150	5	13
201502	3.29	–	–	50	5.0	150	5	13
201503	7.82	–	–	50	5.0	150	5	13
201610	7.82	–	–	50	5.0	150	5	20
201614	–	8.65	0.02	50	5.0	150	5	20
201616	0.53	–	–	50	5.0	150	5	20
201806	0.0	10.44	0.02	50	1.4	50	8	6
201807	0.0	8.26	0.21	50	1.4	50	8	6
201809	0.0	8.26	0.21	50	1.4	50	8	35+15
201810	0.0	8.02	0.10	50	1.4	50	8	35
201811	0.0	10.44	0.02	50	1.4	50	8	33
201813	0.0	8.65	0.02	50	1.4	50	8	12
201814	0.0	8.65	0.02	50	1.4	50	8	50
201815	5.01	1.79	0.003	50	1.4	50	8	50
201816	2.79	4.53	0.01	50	1.4	50	8	3+50
201817	7.82	0.01	0.00002	50	1.4	50	8	50
201818	0.53	8.65	0.02	50	1.4	50	8	50
201819	5.01	4.53	0.01	50	1.4	50	8	50
201821	4.24	4.53	0.01	50	1.4	50	8	5+50
201822	3.29	8.65	0.02	50	1.4	50	8	50
201823	7.82	0.01	0.00002	50	1.4	50	8	50 (18–48 skipped)
201824	7.82	0.01	0.00002	50	1.4	50	8	12
201825	0.53	8.65	0.02	50	1.4	50	8	12+38

Figure 4. The gamma rays produced by the PUNITA deuterium-tritium neutrons from ${ }^{28}$Al, ${ }^{27}$Mg, and ${ }^{28}$Na from the (n,$\gamma$), (n,p), and (n,$\alpha$) reaction modes on the ${ }^{27}$Al in the dummy sample.

Figure 5. The relative positions of the PUNITA deuterium-tritium neutron generator and detector compared to the vertically transferred CBNM U and PuGa samples. See online version for color.

Figure 6. A comparison of Runs 201614 and 201610 between 2700- and 3650-keV. Note, the visible peaks not listed in Table 2 fail at least one quality cut.

Table 2. Gamma-ray peaks fit mean energy and Gaussian counts from the noted short-lived fission products that pass the relative peak significance cut and compared for composition and measurement time ($t_M$) differences as indicated for the Run listed in Table 1. The values are rounded to the uncertainty.

		${ }^{239}$Pu (0.62 cm${ }^{-3}$)		${ }^{235}$U (60.78 cm${ }^{-3}$)
E${ }_{fit}$	Primary	(Counts g${ }^{-1}$)		(Counts g${ }^{-1}$)
(keV)	Contrib.	$t_M$ = 150	$t_M$ = 50	$t_M$ = 150	$t_M$ = 50
		201614	201814	201610	201817
2701	${ }^{106}$Tc	18 $\pm$ 6	94 $\pm$ 26	–	–
2716	${ }^{95}$Sr	12 $\pm$ 5	44 $\pm$ 14	23 $\pm$ 6	54 $\pm$ 9
2753	${ }^{27}$Al/${ }^{86}$Br	–	121 $\pm$ 12	134 $\pm$ 13	259 $\pm$ 16
2789	${ }^{106}$Tc	18 $\pm$ 4	67 $\pm$ 8	–	–
2803	${ }^{90m}$Rb-SE	–	–	–	51 $\pm$ 19
2851	${ }^{99m}$Nb	–	50 $\pm$ 10	40 $\pm$ 9	113 $\pm$ 24
2868	${ }^{136}$I	–	–	53 $\pm$ 15	82 $\pm$ 17
2916	${ }^{106}$Tc	–	31 $\pm$ 6	–	–
2933	${ }^{95}$Sr	–	–	–	27 $\pm$ 9
3047	${ }^{106}$Tc	–	16 $\pm$ 6	–	–
3185	${ }^{106}$Tc	10 $\pm$ 4	50 $\pm$ 10	–	–
3259	${ }^{106}$Tc	–	14 $\pm$ 5	–	–
3316	${ }^{90m}$Rb	–	27 $\pm$ 6	34 $\pm$ 8	57 $\pm$ 10
3384	${ }^{90}$Rb	–	–	46 $\pm$ 9	50 $\pm$ 10
3399	${ }^{97}$Y	–	–	–	42 $\pm$ 13
3534	${ }^{90}$Rb	–	–	27 $\pm$ 5	64 $\pm$ 11
3575	${ }^{95}$Y	22 $\pm$ 5	59 $\pm$ 8	55 $\pm$ 8	75 $\pm$ 9
3598	${ }^{91}$Rb	9 $\pm$ 3	31 $\pm$ 6	77 $\pm$ 9	117 $\pm$ 12
3852	${ }^{90}$Rb	–	–	–	32 $\pm$ 11
4077	${ }^{91}$Rb	–	–	39 $\pm$ 9	77 $\pm$ 15
4136	${ }^{90}$Rb	–	12 $\pm$ 4	32 $\pm$ 6	35 $\pm$ 7
4181	${ }^{87}$Br	–	–	14 $\pm$ 4	–
4265	${ }^{91}$Rb	–	–	18 $\pm$ 5	16 $\pm$ 5
4365	${ }^{90}$Rb	–	–	46 $\pm$ 6	60 $\pm$ 9
5405	${ }^{86}$Br	–	–	6 $\pm$ 2	–

Figure 7. A comparison of Runs 201814 and 201817 between 2700- and 3650-keV.

Table 3. A list of many important fission products emitting at least one gamma ray with energy $>$2.7 MeV useful for peak-ratio comparison of delayed gamma-ray spectroscopy or higher-yield parent fission products from the ENDF/B-VII.1 database [15]. Also listed are their associated half-life and fission yields with the numbersin parentheses indicating the uncertainty on the last digit of the value.

Fission	${\tau }_{1/2}$	$Y$ (%)
Product	(s)	${ }^{235}$U	${ }^{239}$Pu	${ }^{241}$Pu
${ }^{86}$Se	14.3 (3)	0.84 (2)	0.3 (2)	0.3 (2)
${ }^{86}$Br	55.1 (4)	0.230 (6)	0.2 (1)	0.13 (8)
${ }^{87}$Br	55.68 (12)	1.27 (4)	0.55 (3)	0.44 (7)
${ }^{90}$Kr	32.32 (9)	4.40 (6)	1.10 (3)	1.00 (6)
${ }^{90}$Rb	158 (5)	0.14 (1)	0.14 (9)	0.06 (4)
${ }^{90m}$Rb	258 (4)	0.71 (45)	0.60 (39)	0.3 (2)
${ }^{91}$Kr	8.57 (4)	3.16 (3)	0.70 (1)	0.92 (4)
${ }^{91}$Rb	58.2 (3)	2.22 (3)	1.38 (44)	0.8 (5)
${ }^{95}$Sr	23.90 (14)	4.54 (9)	2.61 (118)	2.7 (9)
${ }^{95}$Y	618 (6)	1.11 (35)	1.68 (76)	0.7 (4)
${ }^{97}$Sr	0.429 (5)	1.72 (5)	0.8 (5)	1.5 (5)
${ }^{97}$Y	3.75 (3)	1.57 (100)	1.48 (95)	1.4 (9)
${ }^{99}$Zr	2.1 (1)	3.6 (8)	3.8 (12)	3.3 (11)
${ }^{99m}$Nb	150 (12)	0.41 (3)	0.88 (56)	0.2 (1)
${ }^{106}$Mo	8.73 (12)	0.36 (1)	2.2 (10)	3.9 (12)
${ }^{106}$Tc	35.6 (6)	0.03 (2)	1.83 (11)	1.7 (5)
${ }^{133}$Sb	140.4 (3)	2.26 (14)	1.17 (9)	2.5 (8)
${ }^{136}$Te	17.63 (8)	1.32 (11)	0.51 (32)	1.7 (5)
${ }^{136}$I	83.4 (1)	1.32 (11)	1.25 (40)	2.0 (6)
${ }^{140}$Xe	13.6 (1)	3.51 (10)	1.54 (4)	3.1 (1)
${ }^{140}$Cs	63.7 (3)	2.07 (6)	2.28 (36)	2.3 (7)
${ }^{142}$Ba	636 (12)	3.0 (2)	3.1 (5)	1.4 (5)
${ }^{142}$La	5466 (30)	0.10 (3)	0.3 (2)	0.04 (2)

Table 4. Gamma-ray peaks fit mean energy and relative Gaussian counts from Table 2 compared to the 3575-keV peak from ${ }^{95}$Y. The number in parentheses is the uncertainty on the last digit of the value based on the smallest overall digit in the uncertainties.

	${ }^{239}$Pu (0.62 cm${ }^{-3}$)		${ }^{235}$U (60.78 cm${ }^{-3}$)
E${ }_{fit}$	(Rel. Counts)		(Rel. Counts)
(keV)	$t_M$ = 150	$t_M$ = 50	$t_M$ = 150	$t_M$ = 50
2701	0.83 (26)	1.58 (44)	-	-
2716	0.55 (22)	0.73 (24)	0.41 (11)	0.72 (12)
2753	-	2.04 (20)	2.46 (23)	3.47 (22)
2789	0.82 (19)	1.12 (14)	-	-
2803	-	-	-	0.69 (25)
2851	-	0.85 (17)	0.74 (17)	1.52 (32)
2868	-	-	0.97 (28)	1.10 (23)
2916	-	0.52 (11)	-	-
2933	-	-	-	0.37 (12)
3047	-	0.27 (9)	-	-
3185	0.48 (16)	0.84 (16)	-	-
3259	-	0.24 (9)	-	-
3316	-	0.45 (10)	0.62 (14)	0.77 (14)
3384	-	-	0.85 (16)	0.67 (13)
3399	-	-	-	0.57 (17)
3534	-	-	0.49 (10)	0.85 (15)
3575	1.00 (23)	1.00 (14)	1.00 (15)	1.00 (12)
3598	0.40 (14)	0.52 (11)	1.41 (16)	1.56 (15)
3852	-	-	-	0.43 (15)
4077	-	-	0.71 (17)	1.03 (21)
4136	-	0.20 (7)	0.59 (12)	0.47 (10)
4181	-	-	0.26 (8)	-
4265	-	-	0.34 (10)	0.21 (7)
4365	-	-	0.85 (11)	0.80 (12)
5405	-	-	0.12 (4)	-

Figure 8. A comparison of some of the major ${ }^{235}$U fission product peaks in Run 201817 integrated through the cycle time. See online version for color.

Figure 9. A comparison of some of the major ${ }^{239}$Pu fission product peaks in Run 201814 integrated through the cycle time. See online version for color.

Figure 10. A comparison of peak-ratios of the major ${ }^{235}$U fission product peak counts in Figure 8 proportional to the 3575-keV peak. Additionally, the same peak ratios from Run 201610 are shown for comparison. See online version for color.

Figure 11. A comparison of peak-ratios of the major ${ }^{239}$Pu fission product peak counts in Figure 9 proportional to the 3575-keV peak. Additionally, the same peak ratios from Run 201614 are shown for comparison. See online version for color.

Table 5. Gamma-ray peaks fit mean energy, Gaussian counts, and t-test CDF results from different ${ }^{235}$U content and interrogated as Runs 201502 and 201503 (see Table 1). Also listed are the 201502 mass values scaled (201502’) to the 201503 mass and mass with self-shielding correction. The CDF is noted to the first different digit in the integrated values.

E${ }_{fit}$	201502	201503	201502’		CDF
(keV)	3.29 g ${ }^{235}$U	7.82 g ${ }^{235}$U	Mass	Mass$\times$SSF	Mass	Mass$\times$SSF
2705	127 $\pm$ 55	-	300 $\pm$ 130	259 $\pm$ 112	-	-
2753	509 $\pm$ 58	646 $\pm$ 68	1207 $\pm$ 138	1041 $\pm$ 119	0.000	0.002
2850	–	247 $\pm$ 68	–	–	–	–
2868	–	222 $\pm$ 75	–	–	–	–
2934	–	101 $\pm$ 36	–	–	–	–
3088	113 $\pm$ 45	-	267 $\pm$ 106	230 $\pm$ 91	–	–
3317	79 $\pm$ 24	161 $\pm$ 36	186 $\pm$ 56	161 $\pm$ 49	0.354	0.504
3383	–	180 $\pm$ 41	–	–	–	–
3533	–	129 $\pm$ 34	–	–	–	–
3575	105 $\pm$ 26	195 $\pm$ 37	248 $\pm$ 62	214 $\pm$ 53	0.229	0.382
3599	242 $\pm$ 38	421 $\pm$ 54	574 $\pm$ 89	495 $\pm$ 77	0.071	0.216
3624	103 $\pm$ 40	–	244 $\pm$ 95	210 $\pm$ 82	–	–
4077	–	136 $\pm$ 46	-	-	–	–
4134	105 $\pm$ 23	199 $\pm$ 34	249 $\pm$ 55	215 $\pm$ 47	0.218	0.392
4365	109 $\pm$ 22	186 $\pm$ 30	258 $\pm$ 53	222 $\pm$ 46	0.118	0.252
$\ge$2700	21,266	35,200	50,469 $\pm$ 346	43,528 $\pm$ 299	0.999	0.997
$\ge$3300	9316	15,365	22,109 $\pm$ 229	19,068 $\pm$ 199	0.997	0.996

Table 6. Gamma-ray peaks fit mean energy, Gaussian counts, and t-test CDF results from different ${ }^{235}$U content and interrogated as Runs 201616 and 201610 (see Table 1). Also listed are the 201616 mass values scaled (201616') to the 201610 mass and mass with self-shielding correction. The CDF is noted to the first different digit in the integrated values.

E${ }_{fit}$	201616	201610	201616’		CDF
(keV)	0.53 g ${ }^{235}$U	7.82 g ${ }^{235}$U	Mass	Mass$\times$SSF	Mass	Mass$\times$SSF
2716	-	176 $\pm$ 46	-	-	-	-
2753	656 $\pm$ 59	1047 $\pm$ 99	9736 $\pm$ 877	7351 $\pm$ 662	0.969	0.000
2850	-	316 $\pm$ 73	–	–	–	–
2868	–	414 $\pm$ 118	–	–	–	–
3317	–	264 $\pm$ 59	–	–	–	–
3383	–	362 $\pm$ 67	–	–	–	–
3533	–	208 $\pm$ 42	–	–	–	–
3575	63 $\pm$ 20	426 $\pm$ 63	931 $\pm$ 300	703 $\pm$ 226	0.834	0.126
3599	90 $\pm$ 20	602 $\pm$ 67	1341 $\pm$ 294	1012 $\pm$ 222	0.886	0.041
4077	–	302 $\pm$ 71	–	–	–	–
4134	58 $\pm$ 15	250 $\pm$ 49	866 $\pm$ 223	654 $\pm$ 168	0.896	0.022
4181	–	111 $\pm$ 35	–	–	–	–
4262	66.9 $\pm$ 0.3	144 $\pm$ 41	993 $\pm$ 4	750 $\pm$ 3	0.985	0.000
4365	–	361 $\pm$ 49	–	–	–	–
5405	–	51 $\pm$ 17	–	–	–	–
$\ge$2700	13,537	69,464	201,041 $\pm$ 1728	151,789 $\pm$ 1301	0.997	0.996
$\ge$3300	6331	32,216	94,023 $\pm$ 1182	70,989 $\pm$ 897	0.995	0.994

Table 7. Gamma-ray peaks fit mean energy and Gaussian counts from increasing U mass with the same Pu sample base and interrogated with the same periodic time pattern and scaled to the total fissile mass (see Table 1). Also shown are the relative increase of those peaks appearing in multiple spectra for sequentially greater U.

	201814	201818		201822
	8.65 g ${ }^{239}$Pu	8.65 g ${ }^{239}$Pu	2x$\frac{201818}{201814}$	8.65 g ${ }^{239}$Pu	2x$\frac{201822}{201818}$
E${ }_{fit}$ (keV)	0.0 g ${ }^{235}$U	0.53 g ${ }^{235}$U	+6%g	3.29 g ${ }^{235}$U	+30%g
2702	94 $\pm$ 26	49 $\pm$ 10	0.52 (18)	31 $\pm$ 7	0.62 (19)
2716	44 $\pm$ 14	27 $\pm$ 7	0.62 (25)	19 $\pm$ 7	0.71 (30)
2753	121 $\pm$ 12	130 $\pm$ 13	1.08 (15)	139 $\pm$ 11	1.07 (14)
2789	67 $\pm$ 8	64 $\pm$ 8	0.96 (17)	32 $\pm$ 6	0.49 (12)
2851	50 $\pm$ 10	42 $\pm$ 8	0.83 (23)	24 $\pm$ 7	0.56 (20)
2869	–	29 $\pm$ 8	–	–	–
2916	31 $\pm$ 6	–	–	–	–
2932	–	19 $\pm$ 6	–	23 $\pm$ 5	1.23 (48)
2946	–	29 $\pm$ 7	–	17 $\pm$ 4	0.60 (20)
3047	16 $\pm$ 6	–	–	–	–
3186	50 $\pm$ 10	35 $\pm$ 6	0.70 (19)	16 $\pm$ 4	0.46 (13)
3259	14 $\pm$ 5	19 $\pm$ 6	1.36 (65)	–	–
3316	27 $\pm$ 6	20 $\pm$ 6	0.74 (27)	46 $\pm$ 8	2.30 (78)
3535	–	13 $\pm$ 4	-	14 $\pm$ 6	1.10 (62)
3575	59 $\pm$ 8	38 $\pm$ 6	0.64 (14)	48 $\pm$ 6	1.26 (26)
3599	31 $\pm$ 6	35 $\pm$ 6	1.13 (30)	67 $\pm$ 7	1.91 (38)
3741	–	–	–	18 $\pm$ 5	–
4076	–	18 $\pm$ 5	–	34 $\pm$ 7	1.89 (62)
4136	12 $\pm$ 4	9 $\pm$ 3	0.78 (36)	18 $\pm$ 4	1.99 (77)
4366	–	–	–	34 $\pm$ 5	–
$\ge$2700	20,665	23,743	1.15 (0.01)	38,209	1.61 (0.01)
$\ge$3300	5662	6532	1.15 (0.02)	10,474	1.60 (0.03)

Figure 12. A comparison of total counts above the indicated energy in Table 8 compared to the total fissile mass of the combined samples.

Figure 13. A comparison of peak-ratios of the fission product peak counts in Table 8 compared to the mass-volume of the combined samples for those peaks that are in all four spectra. See online version for color.

Table 8. Gamma-ray peaks fit mean energy and Gaussian counts from increasing Pu mass interrogated with the same interrogation pattern (see Table 1). These values are integrated through the maximum of Run 201811 that stopped at 33 cycles.

	201810	201809	201814	201811
	0.87 cm${ }^3$	0.70 cm${ }^3$	0.63 cm${ }^3$	0.75 cm${ }^3$
E${ }_{fit}$ (keV)	8.12 g ${ }^{fiss}$Pu	8.47 g ${ }^{fiss}$Pu	8.67 g ${ }^{fiss}$Pu	10.46 g ${ }^{fiss}$Pu
2702	–	34 $\pm$ 9	40 $\pm$ 14	25 $\pm$ 11
2718	–	17 $\pm$ 5	–	20 $\pm$ 6
2754	49 $\pm$ 9	48 $\pm$ 10	69 $\pm$ 9	66 $\pm$ 9
2790	44 $\pm$ 7	43 $\pm$ 7	45 $\pm$ 7	36 $\pm$ 5
2852	18 $\pm$ 9	30 $\pm$ 8	28 $\pm$ 8	23 $\pm$ 5
2869	18 $\pm$ 5	22 $\pm$ 7	–	20 ($\pm$ 6
2916	–	–	20 $\pm$ 6	–
2946	31 $\pm$ 8	16 $\pm$ 6	–	15 $\pm$ 5
3187	30 $\pm$ 7	30 $\pm$ 6	38 $\pm$ 11	13 $\pm$ 4
3260	12 $\pm$ 5	–	13 $\pm$ 4	–
3318	–	18 $\pm$ 6	14 $\pm$ 4	–
3402	–	–	–	19 $\pm$ 6
3535	–	–	–	16 $\pm$ 4
3577	20 $\pm$ 5	24 $\pm$ 5	41 $\pm$ 6	10 $\pm$ 3
3602	16 $\pm$ 4	23 $\pm$ 4	23 $\pm$ 6	24 $\pm$ 6
4079	12 $\pm$ 4	–	–	11 $\pm$ 4
4137	–	–	9 $\pm$ 4	–
$\ge$2700	10,404	13,493	13,737	13,645
$\ge$3300	2792	3757	3805	3826

Chadwick MB, Herman M, Obložinský P, et al. ENDF/B-VII.1 nuclear data for science and technology: cross sections, covariances, fission product yields and decay data. Nucl Data Sheets. 2011;112(12):2887–2996.

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