A new unfolding code combining maximum entropy and maximum likelihood for neutron spectrum measurement

Figures & data

Table 1 Parameters for test problem

	Response Function
k	R 1,k	R 2,k	R 3,k	φk,exact
1	3	0	0	2
2	4	2	1	5
3	3	3	2	9
4	2	3	4	13
5	1	0	4	8
ci	87	76	107	37

Table 2 Result of uncertainty estimation by measurement data

k	φ unfold	Δφunfold (1σ)	Δφunfold (%)	φexact
1	2.5	2.2	85.8	2.0
2	4.9	4.5	91.8	5.0
3	8.1	3.6	45.0	9.0
4	13.9	1.3	9.1	13.0
5	7.5	1.3	17.8	8.0

Table 3 Unfolded response

i	c exact	c unfold
1	87.0	87.1
2	76.0	75.9
3	107.0	106.8

Table 4 Probability

χ^2 value	9.78 ×10^−4
Probability	100%

Figure 1 Unfolded spectrum

Figure 2 Comparison of neutron spectra

Table 6 Comparison of reaction rate

	Neutron flux (n/cm^2/s)
Reaction	Measured	MEALU	J-log
^237Np(n,fission)	2.44 × 10^15	2.47 × 10^15	2.44 × 10^15
^235U(n,fission)	8.38 × 10^15	7.80 × 10^15	8.28 × 10^15
^45Sc(n,g)	1.46 × 10^14	1.46 × 10^14	1.49 × 10^14
^46Ti(n,p)	6.21 × 10^12	6.21 × 10^12	6.28 × 10^12
^58Ni(n,p)	7.07 × 10^13	7.07 × 10^13	7.15 × 10^13

Table 5 Comparison of integral value

	Neutron flux (n/cm^2/s)
Value	MEALU	J-log method
φtotal	(5.39 ± 0.21) × 10^15	(5.05 ± 0.31) × 10^15
φE>0.1MeV	(4.17 ± 0.42) × 10^15	(3.70 ± 0.31) × 10^15
φE>1.0MeV	(8.39 ± 1.77) × 10^14	(8.55 ± 0.91) × 10^14

Table 7 Comparison of probability

Value	MEALU	J-log method
χ ^2 value	0.70	0.16
Probability	95.2%	99.5%