The absorption cross section of natural Gd and isotopic enriched 157Gd for ultra-cold neutrons (UCN) as a function of the velocity has been measured within a time-of-flight-experiment. Particular attention is paid to small velocities in the region of a few m/s. This is intended to determine the validity of the 1/v-law governing absorption cross sections in this region and the resulting divergence at v=0. The experiment does not show any significant violation of 1/v for v>3 m/s

A. Hollering

H. Rauch

J. Schroffenegger

P. Fierlinger

P. Geltenbort

T. Lauer

T. Zechlau

Physics Letters B

AbstractThe absorption cross section of natural Gd and isotopic enriched 157Gd for ultra-cold neutrons (UCN) as a function of the velocity has been measured within a time-of-flight-experiment. Particular attention is paid to small velocities in the region of a few m/s. This is intended to determine the validity of the 1/v-law governing absorption cross sections in this region and the resulting divergence at v=0. The experiment does not show any significant violation of 1/v for v>3 m/s

Schroffenegger, J.

Fierlinger, P.

Hollering, A.

Geltenbort, P.

Lauer, T.

Rauch, H.

Zechlau, T.

Elsevier - Publisher Connector 

Improved measurement of the neutron absorption cross section for very low velocities 

Physics Letters B 752 (2016) 212–216Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Improved measurement of the neutron absorption cross section for 
very low velocities
J. Schroffenegger a,d,∗, P. Fierlinger b, A. Hollering d, P. Geltenbort c, T. Lauer d, H. Rauch a, 
T. Zechlau d
a Technische Universität Wien-Atominstitut, A-1020 Wien, Austria
b Physik-Department E18, Technische Universität München, D-85748 Garching, Germany
c Institut Laue-Langevin, F-38042 Grenoble, France
d Forschungs-Neutronenquelle Heinz Maier-Leibnitz (FRM-II), 85747 Garching, Germany
a r t i c l e i n f o a b s t r a c t
Article history:
Received 2 March 2015
Received in revised form 26 October 2015
Accepted 11 November 2015
Available online 14 November 2015
Editor: D.F. Geesaman
Keywords:
Neutron transport: diffusion and 
moderation
Protons and neutrons
The absorption cross section of natural Gd and isotopic enriched 157Gd for ultra-cold neutrons (UCN) 
as a function of the velocity has been measured within a time-of-ﬂight-experiment. Particular attention 
is paid to small velocities in the region of a few m/s. This is intended to determine the validity of the 
1/v-law governing absorption cross sections in this region and the resulting divergence at v = 0. The 
experiment does not show any signiﬁcant violation of 1/v for v > 3 m/s.
© 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license 
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3.1. Introduction
The neutron absorption cross section can be described, leaving 
aside resonance phenomena, in the ﬁrst order approximation by a 
1/k or 1/v law [1]:
σa = 4π
k
a′′, (1)
where a′′ is the imaginary part of the scattering length, v is the 
neutron velocity and k is the neutron wave-vector. This equation 
raises the question of the divergent tendency of the absorption 
cross section at low velocities close to v = 0 and of its physical 
meaning. In [2] a deviation of the 1/v law is predicted. The authors 
arrived at this result by theoretical calculation of the interaction 
between an absorbing nucleus and a neutron. It is expected that 
the cross section is proportional to v in the region below 4–5 m/s. 
The authors of [3] however, conclude that the result found in [2]
concerns only the effective cross section for a nucleus occurring in 
a dense medium and not for a single nucleus or for an absorber 
dissolved in a solvent at low concentration. The present work in-
corporates these conclusions. In [4] the authors show the validity 
* Corresponding author at: Forschungs-Neutronenquelle Heinz Maier-Leibnitz 
(FRM-II), 85747 Garching, Germany.
E-mail address: juri.schroffenegger@tum.de (J. Schroffenegger).http://dx.doi.org/10.1016/j.physletb.2015.11.030
0370-2693/© 2015 The Authors. Published by Elsevier B.V. This is an open access article
SCOAP3.of the 1/v-law for velocities between 6 and 35 m/s by verifying 
the independence of the transmission through an absorbing ﬁlm 
from the neutron velocity component parallel to the sample sur-
face.
Another way for testing the 1/v-law is examined in [5] by us-
ing a time-of-ﬂight-setup. Using this method the absorption cross 
section for all velocities contained in the spectrum of the neutron 
source can be measured simultaneously. The authors show in their 
results a possible violation of the 1/v law. The measurements de-
scribed in the present work can be considered as a continuation of 
the experiments performed in [5].
2. Experimental approach
In this experiment gadolinium, the stable element with the 
highest neutron absorption cross section1 dissolved in heavy water 
(D2O), is used as an absorber. This enables the smallest amount 
of absorbent material to be brought into solution whilst main-
taining ideal proportions for the transmission coeﬃcient. The low 
concentration of the absorber in the D2O-matrix does not notice-
able change the real part of the scattering length density in the 
1 Thermal neutron absorption cross sections: nat. Gd σa = 49700 barn, isotipcal 
enriched 157Gd σa = 259 000 barn. under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by 
J. Schroffenegger et al. / Physics Letters B 752 (2016) 212–216 213Fig. 1. Geometrical form and neutron optical wall potential of the transmission sam-
ples.
transmission sample. The advantage of the method is its large scat-
tering length and the resulting high Fermi-potential. As they enter 
the potential of the D2O neutrons lose a part of their kinetic en-
ergy and decelerate. The velocity inside the sample is given by
v = nv0 =
√
v02 − vc2 with vc2 = 4π h¯
2Nbc
m2
(2)
where n is the refraction index, v0 is the velocity outside the po-
tential, N is the particle density, bc is coherent scattering length 
and m is the mass of the neutron. By decelerating the neutrons 
in the sample it is possible to achieve lower velocities, than those 
present in the neutron source’s spectrum. The liquid solution is 
brought into the neutron beam within a glass cell. In Fig. 1 the po-
tential for a neutron crossing the sample is shown. To determine 
the absorption cross section of the gadolinium, a second identical 
sample without dissolved gadolinium is used. By comparing the 
transmission through both samples the absorption cross section σa
can be calculated as:
T = e−Ndσa → σa = − ln T
Nd
(3)
with T the transmission, N the particle density and d the thick-
ness of the absorber. To calculate the transmission and the related 
absorptions cross section as a function of the velocity, the sam-
ple is installed within a time-of-ﬂight setup. The ratio of the count 
rate for the samples with gadolinium to the count rate without 
gadolinium provides the absorption cross section.
3. Experimental setup
The time-of-ﬂight-measurements (TOF) described were per-
formed at ultra-cold and very-cold neutron facility PF2 of the ILL in 
Grenoble (France). Two different beam ports were used: Pf2/UCN 
and PF2/TES.
In order to soften the spectrum and thus shift the neutron 
velocity spectrum to lower energies, the TOF setup presented in 
Fig. 2 was mounted 60 cm higher than the existing turbine exit of 
the PF2/UCN port. At the PF2/TES port, however, it was mounted 
at the same height as the exit port. An UCN chopper [6] composed 
of two linear motors moving two titanium grids against each other 
forms the ﬁrst element of the TOF setup. The grids in their starting 
position overlap 1 mm. In this position the beam is closed, so that 
no neutron can pass through. Shifting the grids by 2 mm opens 
a 3 mm slit and enables the neutrons to pass. A chopper of this 
type provides variable opening times and duty cycles, in contrast 
to a rotating disk chopper. This allows the open-to-close ratio to be 
optimized and thus increases the number of the usable neutrons. 
The chopper is set to open the beam for 7 ms with a repetition 
rate of 10 Hz. The corresponding opening function, measured with 
light, is shown in Fig. 3. The chopper setup is a well characterized Fig. 2. Sketch of the time of ﬂight setup on the UCN beam port on the PF2 beamline 
at ILL.
Fig. 3. Measured opening function of the linear chopper with t1 = 3.44(14) ms: 
duration of the opening larger than 90%, t2 = 7.47(7) ms: duration of the opening 
larger than 2.5%.
system; the variation of the open function is less than 1%. A cell 
holder for the heavy water samples integrated into the stainless 
steel chopper housing is positioned almost at the beginning of the 
ﬂight path. The chopper vacuum, the UCN feed guide and the ﬂight 
path are separated from the glass cell by two 0.2 mm thick foils of 
AlMg3. By keeping the sample at atmospherical pressure it can be 
changed easily without breaking vacuum.
The glass cell itself is composed of three layers of sodium-glass 
glued together with ultraviolet curing glue. A cavity in the center 
layer forms the ﬁlling volume of the cell. The internal dimensions 
of the cell are 60 ×90 ×1.02 mm3. The thickness of the outer glass 
plates is 0.9 mm. The ﬂight path, a stainless steel tube with a di-
ameter of 100 mm and an effective ﬂight path length of 263.5 mm 
is installed on the backside of the cell holder. A polyethylene foil, 
placed on the inside of the tube acts as an absorber, removing 
neutrons which would otherwise be reﬂected by the tube. This en-
sures that any diffusive scattering, which would falsifying the TOF 
spectrum, is suppressed. This effect was investigated in a sepa-
rate measurement, performed with and without the polyethylene 
foil. The spectra of the neutron passing through the cell ﬁlled with 
D2O were observed. The results shown in Fig. 4, obtained without 
the PE foil, show a relatively increased number of neutron at the 
slow velocity side of the spectrum, caused by diffuse scattering. 
The ﬂight path follows a CASCADE U-100 [8] detector.
The transmission experiment was performed with four differ-
ent gadolinium solutions, varying in particle density and the iso-
topic distribution. The four Gd solutions measured were natural 
gadolinium with a particle density of 6.66 · 1023 1/m3 and of 
4.04 · 1023 1/m3 and isotopic pure 157Gd with a particle density 
214 J. Schroffenegger et al. / Physics Letters B 752 (2016) 212–216Table 1
Measured absorption cross section of the four different gadolinium solutions with Poison type error σP and Gaussian type σG .
N Beamport σ [Mb] σP [Mb] σP /σ [%] σG [Mb] σG/σ [%]
3 m/s
nat. Gd 6.66 UCN 17.28 2.91 16.9 3.3 19.1
nat. Gd 4.04 UCN 29.5 7.33 15.8 5.81 19.7
157Gd 1.40 UCN 96.70 18.85 19.5 21.98 22.7
157Gd 1.39 TST 102.54 20.27 19.8 2.82 2.7
5 m/s
nat. Gd 6.66 UCN 11.33 0.24 2.1 3.30 29.1
nat. Gd 4.04 UCN 18.85 0.54 2.9 5.82 30.9
157Gd 1.40 UCN 77.87 1.50 1.9 21.98 28.2
157Gd 1.39 TST 73.17 1.60 2.2 2.82 3.8
10 m/s
nat. Gd 6.66 UCN 5.36 0.09 1.74 3.30 61.6
nat. Gd 4.04 UCN 10.58 0.21 2.0 5.82 55
157Gd 1.40 UCN 47.69 0.52 1.1 21.98 46.1
157Gd 1.39 TST 40.64 0.49 1.2 2.82 6.9Fig. 4. Time-of-ﬂight (TOF) spectra measured for pure D2O with polyethylene foil ©
in the ﬂight path and without .
of 1.4 · 1023 1/m3 and 1.39 · 1023 1/m3. An acidic environment is 
required to dissolve gadolinium in heavy water. For this reason a 
small amount (<200 ppm) of DCl was added to the D2O. As in all 
the other measurements taken with Gd solutions of this sort, con-
tamination by DCl was found to be insigniﬁcant for further data 
analysis. The reference measurement was performed with pure 
(99.98%) D2O from the same batch as used for the Gd solution.
4. Experimental results and their analysis
The time-of-ﬂight-spectra time resolution is given by the 
brought of the detector time channels, which was set to 250 μs. 
A single spectrum was measured for 130 s, what was repeated up 
to 1500 times. The small peak shortly after the start, i.e. 0 s, is 
caused by UCN up-scattered in cells glass and in the heavy water. 
After subtracting a constant background (caused by the thermal 
neutron background in the reactor environment), the velocity-
dependent transmission is obtained by comparing the counts for 
a single time bin for measurements with the gadolinium solu-
tion and pure D2O. Finally, the absorption cross section can be 
extracted as a function of the neutron velocity, presented in Fig. 5, 
by applying three important corrections:
• the position of the sample behind the chopper. The time of 
ﬂight is changed because the neutrons are decelerated in the 
potential of the sample. Fig. 6 shows the correlation of the 
time neutrons need to cross the ﬂight path with and without 
sample inserted.• neutrons, reﬂected at the D2O surface, leading to multiple 
crossing of the sample [7]. Considering this effect, the trans-
mission coeﬃcient is given as
τ = αT
2
1− α2R2 (4)
with α = e−Nσd , T = 4v0Re(v ′)|v0+v ′ |2 and R = |
v0−v ′
v0+v ′ |2 where T is the 
transmissivity and R is the reﬂectivity of the D2O surface. Both 
values depend on the UCN velocity outside the sample, v0 and 
on the, in general complex, velocity v ′ inside the sample. σ is 
the sum of the inelastic and incoherent scattering cross sec-
tion, which is dominated by the absorption. Without multiple 
crossings the transmission coeﬃcient would reduce to α as 
expected.
• the UCN velocity within the potential of the D2O, calculated 
according eqn. (2).
The results of the measurements performed at the UCN beam pro-
vide no absolute value for the absorption cross section within ac-
ceptable error limits, because the total count rate for the single 
130 s spectra is ﬂuctuating, as shown in Fig. 7. This ﬂuctuation 
produces an additional Gaussian type error for the calculation of 
the absolute value. In Table 1 absolute values and error limits for 
the different performed measurements are listed. Hereby the error 
limits are distinguished in the mentioned Gaussian error and the 
error given by Poison statistics, which depends on the total counts 
of a single measurement. The results of the two measurements, 
performed on different beams, match and yield Poisson-type errors 
in the same region. But in contrast to the TST beam measurement, 
the UCN beam measurement shows very large Gaussian type er-
rors, with relative errors up to 46.1%. Nevertheless the dependence 
of the absorption cross section on the velocity can be calculated. 
The results shown in Fig. 5 a)–c) do not include the additional 
error caused by the ﬂuctuation. The measurement performed at 
the TST beam port does not show a signiﬁcant ﬂuctuation of the 
count-rate. For that reason the absolute value of the cross section 
can be calculated and are within acceptable error limits, shown in 
Fig. 5 d).
To evaluate the behavior of the absorption cross section the 
measured data can be ﬁtted with different functions, like 1/v , be-
coming constant or proportional to v at a certain velocity. The 
different models can be compared using the reduced χ2 values 
and the corresponding p values. In Table 2 the such values are 
listed for the ﬁt models mentioned.
J. Schroffenegger et al. / Physics Letters B 752 (2016) 212–216 215Fig. 5. Extracted absorption cross section as function of the velocity; line: 1/v-law, a) Gd(nat) 6.66 · 1023 1/m3, b) Gd(nat) 4.04 · 1023 1/m3, c) 157Gd 1.40 · 1023 1/m3, 
d) 157Gd 1.39 · 1023 1/m3.Fig. 6. Correlation of the measured time of ﬂight and the theoretical without sample.
5. Conclusion
In the measurement described, we measured the neutron ab-
sorption cross section for Gd. The results show values, depending 
on velocity, up to 100 Mb. The 1/v-law was also examined. Con-
trary to [5], no signiﬁcant violation in the region above 3 m/s was 
visible. One possible explanation for this is the improved experi-
mental setup, and the polyethylene absorber foil in particular. This 
foil eliminates non-angular reﬂected neutrons. The pollution of the 
spectrum due to these neutrons is shown in Fig. 8 for a ﬂight path 
of 263.5 mm. A longer ﬂight path, as used in the previous experi-
ments, inﬂuences the results even more strongly. More speciﬁcally Table 2
Reduced χ2 and p values (117 degrees of freedom) for different ﬁtting models. 
4.46 m/s and 3.66 m/s are the optimized velocities for the corresponding ﬁtting 
model.
Fitting function v0 [m/s] χ2 p value
σa ∝ 1v 1.78 1.3 · 10−6
σa ∝ 1v , v > v0
σa ∝ const, v < v0
5 1.57 1.9 · 10−4
4 1.37 9.5 · 10−3
3 1.67 2.2 · 10−5
4.46 1.35 1.5 · 10−2
σa ∝ 1v , v > v0
σa ∝ v , v < v0
5 3.6 2.4 · 10−24
4 1.32 2.0 · 10−2
3 1.58 1.5 · 10−4
3.66 1.27 4.8 · 10−2
it leads to an overrating of the neutron transmission on the lower 
ﬂanks of the spectrum.
By ﬁtting models to the data measured, we obtained slightly 
better reduced χ2 values than those obtained with the 1/v-law; 
this was not suﬃcient, however, to demonstrate any signiﬁcant 
violation of the 1/v-law. The lack of data in the velocity region 
below 3 m/s inhibits any further extrapolation of the absorption 
cross section. Further investigations would be needed to obtain 
more precise results at even lower velocities. Nevertheless the 
possibilities of this approach are rather limited and signiﬁcant im-
provements on the error limits in the lower velocity range are not 
216 J. Schroffenegger et al. / Physics Letters B 752 (2016) 212–216Fig. 7. Total count rate for UCN beam and TST beam experiments. UCN beam: 
black: pure D2O ﬂuctuation for the full spectrum 20%, red: Gd(nat) 6.66 · 10231/m3
ﬂuctuation 10.3%, green: Gd(nat) 4.04 · 1023 1/m3 ﬂuctuation 13.3%, blue 157Gd, 
1.40 · 1023 1/m3 ﬂuctuation 24.4% TST beam: black: pure D2O ﬂuctuation 3%, blue 
157Gd, 1.39 · 1023 1/m3 ﬂuctuation 2.6%.
to be expected. Another approach will be necessary for future in-
vestigations.Fig. 8. Time-of-ﬂight (TOF) spectra measured for pure D2O © and Gd-solution 
normalized to their total measurement time.
Acknowledgements
This experiment beneﬁted from the technical support by 
T. Brenner and D. Hess from the ILL and J. Weber form the neutron 
optic group of the FRM II. The kind hospitality of the ILL is grate-
fully acknowledged. This work was supported by the DFG under 
the contract number La 2835/1-1.
References
[1] V.F. Sears, Neutron Optics, Oxford University Press, 1989.
[2] V.V. Lomonosov, A.I. Gurevich, Capture of ultracold neutrons in thin absorbing 
ﬁlms, J. Exp. Theor. Phys. 95 (5) (2002) 800–804.
[3] A.I. Frank, V.I. Bodnarchuk, P. Geltenbort, et al., Phys. At. Nucl. 66 (10) (2003) 
1831–1845.
[4] A.I. Frank, P. Geltenbort, G.V. Kulin, et al., JETP Lett. 3 (2006) 105–109.
[5] H. Rauch, M. Zawisky, C. Stellmach, P. Geltenbort, Phys. Rev. Lett. 83 (24) (1999) 
4955–4958.
[6] T. Lauer, Investigation of a superthermal ultracold neutron source based on a 
solid deuterium converter for the TRIGA Mainz reactor, Dissertation, 2010.
[7] A. Steyerl, Nucl. Instrum. Methods 101 (1972) 295–314.
[8] http://www.n-cdt.com.


Directory of Open Access Journals

Improved measurement of the neutron absorption cross section for very low velocities

file:///data/remote/core/dit/data/elsevier/pdf/b4e/aHR0cDovL2FwaS5lbHNldmllci5jb20vY29udGVudC9hcnRpY2xlL3BpaS9zMDM3MDI2OTMxNTAwODc4Mw==.pdf

Improved measurement of the neutron absorption cross section for very low velocities

Abstract

Similar works

Full text

Available Versions

Elsevier - Publisher Connector

Elsevier - Publisher Connector

Directory of Open Access Journals