Measurement of the total prompt neutron spectrum of 235U(nth, f) relative to 252Cf(sf)
А.S. Vorobyev, О.А. Shcherbakov, G.А. Petrov,
Petersburg Nuclear Physics Institute, 188350, Gatchina, Leningrad district, Russia
Introduction
A series of experiments has been performed at the PNPI WWR-M research reactor in Gatchina,
Russia, to measure prompt neutron angular and energy distributions from thermal neutroninduced fission of 235U in correlation with the fission fragments [1].
The obtained angular and energy distributions have been analyzed with the assumption of
neutron emission from accelerated fission fragments. The performed analysis demonstrates that
all obtained experimental results can be described within 5% accuracy using this assumption. It
is to be noted that this conclusion, in a systematic sense, is dependent on the choice of the total
prompt neutron spectrum used for the neutron detector efficiency correction [2]. To exclude this
uncertainty, the additional measurements of prompt neutron angular and energy distribution have
performed recently for 252Cf(sf) and 235U(nth, f) at the same experimental conditions and set-up.
1. Experimental procedure and results
Four measurement cycles have carried out at the PNPI WWR-M research reactor to measure the
total prompt fission neutron spectrum (PFNS) of 235U(nth, f) relative to 252Cf(sf). During data
processing, the following corrections were taken into account: for detector efficiency, for
neutron detector background, for angular and energy resolution, for the fragment detector
efficiency and for complementary fragment contribution. So the PFNS of 235U, NU ( En ) , was
obtained using measured partial spectra, N exp(En, ), by following equation:
NU ( En )  F ( En )  N CfStd ( En ) 
NUexp ( En )
NUexp ( En )
A
E
Std

f
(
E
)

f
(
E
)

I
(
E
)

N
(
E
)

res
n
res
n
n
Cf
n
N Cfexp ( En )
N Cfexp ( En )
(1)
1.2
1.0
0.8
Maslov calc.(2010)
ENDF/B-VII
Neutron detector ND1
Neutron detector ND2
Average
0.6
0.1
1
Neutron energy, En [MeV]
10
Ratio corrected spectrum to uncorrected
Ratio to Maxwellian <En> = 1.971 MeV
where f resA ( E n ), f resE ( E n ) are the coefficients taking into account finite angle and energy
resolution; I ( E n ) is due to summing over angle (because there is experimental histogram instead
of continuous distribution) and N CfStd ( En ) is a reference standard spectrum of 252Cf(sf) [3]. The
obtained PFNS of 235U after efficiency correction and additional corrections are presented in
Figs. 1, 2.
A
1.06
angular resolution - fres (En)
E
energy resolution - fres (En)
due to summing over angle  - I (En)
total correction - F(En)
1.04
1.02
1.00
0.98
0.96
0
2
4
6
8
10
12
14
Neutron energy, En [MeV]
Fig. 1. The total PFNS of 235U as ratio to Fig. 2. The values of corrections taken into account
Maxwellian (T = 1.314) only background and during data processing.
efficiency corrections were applied (log scale).
2. Degree of reliability – experimental errors determination
For 11 fixed angles between the neutron and light fragment direction (from 0 0 to 1800 in 180
interval) the prompt neutron energy spectra were obtained independently for two neutron
detectors as weighted averages of 4 measurement cycles which were analyzed separately.
The errors of the N exp(En, ) spectra are the RMS deviation from weighted means. These
errors include the possible instability of electronic (uncertainties of neutron threshold
determination etc.) as well as the statistical and energy determination uncertainties.
The total prompt neutron spectrum uncertainties were defined as deviation of the perturbed
total spectra from total spectrum obtained by summation of measured angle-energy distribution
over angles. By varying counts in each energy point within obtained errors, twenty perturbed
spectra were obtained for each of two neutron detectors. Herewith, it was assumed that any
correlation between energy points for fixed angle relative to fission fragment direction was
absent. The ratio between the relative errors is presented in Fig. 3.
Result is a weighted average of two total prompt neutron spectra obtained by individual
detectors. The obtained PFNS after all correction is presented in Fig.4 in comparison with
literature data which were normalized to recommended value of the total average neutron
multiplicity, tot = 2.42.
Ratio to Maxwellian <En> = 1.971 MeV
1
due to background uncertainty
252
Relative error [%]
Cf measurements
235
U measurements
Total uncertainty
0.1
0.01
0
2
4
6
8
10
12
1.1
1.0
0.9
Nefedov 1983 (40871008)
Lajtai 1985 (30704003)
Yufeng 1989 (32587002)
HambschKornilov
Present data
Maslov calc.(2010)
ENDF/B-VII
0.8
0.7
14
0.1
1
10
Neutron energy, En [MeV]
Neutron energy, En [MeV]
Fig. 3. The ratio between the relative errors Fig. 4. The PFNS of
(log scale).
summed up into total uncertainties.
235
U as ratio to Maxwellian
3. Results and discussion
The comparison of existing experimental data demonstrates the agreement between them within
their errors in energy range from ~1 MeV to 10 MeV. There is some discrepancy in low energy
region. To verify the assumption about neutron emission from accelerated fragments the PFNS
was calculated using neutron spectra for small angles relative to fission fragment direction
obtained in our earlier experiment. The calculated (method 2) and experimentally obtained
(method 1) spectra are shown in Figs. 5, 6. It is seen that the average of two PFNS obtained from
different experiments and methods is in a good agreement with ENDF/B-VII.
1.2
Maslov calc. (2010)
1.1
error of Cf standard
method 1
method 2
1.2
Maslov calc. (2010)
1.1
error of Cf standard
method 1
method 2
252
Ratio to ENDF/B-VII
Ratio to ENDF/B-VII
252
1.0
0.9
0.1
1
Neutron energy, En [MeV]
235
10
1.0
0.9
0
2
4
6
8
10
12
14
Neutron energy, En [MeV]
235
Fig. 5. The PFNS of U as ratio to ENDF/B-VII Fig. 6. The PFNS of U as ratio to ENDF/B-VII
evaluation (log scale).
evaluation (linear scale).
References
[1] A.S. Vorobyev, O.A. Shcherbakov, Yu.S. Pleva, A.M. Gagarski, G.V. Val’ski, G.A. Petrov,
V.I. Petrova, T.A. Zavarukhina, Nucl. Instr. and Meth. A598 (2009) 795-801.
[2] A.S. Vorobyev, O.A. Shcherbakov, Yu.S. Pleva, A.M. Gagarski, G.V. Val’ski, G.A. Petrov,
V.I. Petrova, T.A. Zavarukhina, IAEA Report INDC(NDS)-0541, Vienna, 2009, p.63.
[3] C.W. Reich, W. Mannhart, T. England, ENDF/B-VII.