Table Of ContentConsistent description of UCN transport properties
S. Wlokkaa,∗, P. Fierlingerb, A. Freia, P. Geltenbortc, S. Paulb, T. P¨oschlb, F. Schmidb,1, W. Schreyerb, D.
Steffenb
aHeinz Maier-Leibnitz Zentrum, Technical University of Munich, Lichtenbergstr. 1, D-85748 Garching
bPhysics Department E18 and Universe-Cluster, Technical University of Munich, James-Franck-Str. 1, D-85748 Garching
cInstitut Laue-Langevin, 71 Avenue des Martyrs, 38000 Grenoble, France
7
1
Abstract
0
2
WehaveinvestigatedthediffusereflectionprobabilitiesofReplicaguidesforultra-coldneutrons(UCN)using
n the so-called helium method. For the first time we could establish a consistent description of the diffuse
a reflection mechanism for different lengths of the guide system. The transmission of the guides is measured
J
depending on the helium pressure inside of the guides. A series of simulations was done to reproduce the
5
experimental data. These simulations showed that a diffuse reflection probability of d = (3.0±0.5)·10−2
2
sufficiently describes the experimental data.
]
t Keywords: ultra-cold neutrons, neutron guides, helium method
e
d
-
s 1. Introduction of(0.990±0.006) m−1 [11]. Theseguidesaremade
n
of a Ni-V alloy and are produced by the so-called
i
s. Ultra-cold neutrons (UCN) [1, 2] are neutrons, “Replika”-technique [12, 13]. In the course of the
c which are reflected from a material surface under described experiment we further investigated the
i all angles of incident due to the Fermi potential
s transmission properties focussing on the diffuse re-
y [3] of the material. Typically they have energies
flectivity applying the helium method.
h lowerthan300neV,whichcorrespondstovelocities
p
smallerthan8m/s. UCNcanbestoredinmaterial
[ 2. The Helium Method
ormagneticbottlesforlongtimes(severalhundreds
1 of seconds). Thus one can determine fundamental
Beginning with the stationary diffusion equation
v
properties of the neutron itself such as its lifetime
1
[4] or its electric dipole moment (EDM) [5]. d2n n
3 = , (1)
4 Currentlynewsourcesforultra-coldneutronsare dz2 L2
D
7 being built. [6–10]. Efficient transport of ultra-
0 cold neutrons requires guides with a high fermi- nbeingtheneutrondensityalongthelengthofthe
1. potential, low absorption and a low diffuse reflec- guideaxisz, onecandeductasolutionfortheneu-
0 tion probability. The latter describes the prob- tron flux J at a given position L within the guide
7 ability for UCN to be reflected non-specularly. [14, 15].
1
This essentially allows backscattering of the UCN
: J(0)
v and strongly increases the loss probability. In J(L)= . (2)
(cid:16) (cid:16) (cid:17) (cid:16) (cid:17)(cid:17)
i order to ensure the delivery of a high amount cosh L +γsinh L
X LD LD
of UCN to the experiments at the Forschungs-
r √
a NeutronenquelleHeinzMaier-Leibnitz(FRMII)we Here, L = Dτ denotes the diffusion length
D
developed UCN guides with relative transmissions with the diffusion constant D and the effective life-
time of the neutron in the guide system τ and
γ = (L v¯)/(4D) with the mean neutron velocity
D
∗Correspondingauthor;Tel.: +498928913739 v¯.
Email address: [email protected](S.Wlokka)
1Presentaddress: Max-Planck-Institutfu¨rQuantenoptik, Diffuse reflections in the guide system decrease
Hans-Kopfermann-Str. 1,D-85748Garching the diffusion constant D and thus the diffusion
Preprint submitted to Elsevier January 27, 2017
Figure1: (Coloronline)Experimentalsetupusedfortheheliummethod. UCNenterfromtheleft. Ashutterisusedtoopen
andclosetheReplikavolumeforUCN.Afterpassingthroughaspectrumshaper[16]theneutronsentertheReplikavolume,
whichisenclosedbyAluminiumfoilsonbothends. ACascadeDetector[17]isusedfortheUCNdetection.
length L effectively reducing the transmission of 3. Experimental Setup
D
the guides. There is still some debate about the
physicsbehindthediffusereflectionmechanismsfor
UCN [18, 19]. In our analysis we will employ the Figure 1 shows the experimental setup of the ex-
Lambert model where the neutrons have a cosine periment. UCN from the PF2/TES beamline [12]
distributionaboutthenormalvectorofthescatter- at the Institute Laue-Langevin enter the experi-
ing surface. ment from the left. A shutter at entrance of the
beam tube controls the flux into the experiment.
UCN then pass a stainless steel spectrum shaper,
Measurements of the diffuse reflectivity usually
which cuts off most neutrons above ∼ 190neV
employ a slit and collimator system, which reduces
[16]. Downstream the neutrons enter the Replika
the angles accepted by the guide system to a nar-
guide volume, which is enclosed on both sides by
row band of a few degrees. [20] In our case adding
aluminum (AlMg3) windows with a thickness of
helium to the system decreases the lifetime of the
100µm. After the UCN passed the second win-
neutrons in the guide. Since the helium atoms are
dowtheyareguidedtoastandardUCNdetectorof
muchfaster(v ∼1260m/s)thantheUCN,any
RMS theCASCADEtype[17]. Thedetectorsignalswere
interactionoftheneutronswiththegasatomslead
amplifiedwithaCAEN968Amplifierandanalysed
to an upscattering of the UCN and thus to the loss
in the PC by a MCA 3A.
of it. As a higher probability for diffuse reflection
The volume between the two aluminum win-
increases the path length a neutron has to take
dows could be filled with helium with a purity of
through the guide system, the loss probability in
99.996%. Before the helium was put into our sys-
the helium gas is also increased.
tem it was flushed through a liquid nitrogen bath
toeliminatepossiblecontaminants(suchaswater).
Generally one could follow the suggestion of [15] The length of Replika section was varied be-
andmeasuretheheliumpressureneededtodecrease tween 1 − 3m. Every experimental cycle began
theUCNcountrateto1/ewithrespecttovacuum. with a transmission measurement under vacuum
However,inoursetup(cf. Section3)theUCNspec- conditions. Afterwards, helium was filled into the
trumdiffersseverelyfromthespectrumassumedin Replika volume up to pressures ranging between
[15] both in the energy aswell as in the momentum 10−500mbar. The count rate at the detector for
distribution. Therefore we do not use Eq. 2 to different pressures values were normalized to the
extract the diffuse reflectivity but we rely on simu- countrateatzeropressureaftercorrectingthedata
lations, which will be described in Section 5. for the time-varying reactor power.
2
4. Results Our measurements show that the UCN sample
detected at the exit consists of two different pop-
Figure2showstheresultsofourexperimentsfor
ulations. One population has undergone a large
threedifferentlengthsofReplikaguides. Allvalues
number of surface reflections, which leads to an
are normalized to the respective measurements at
increased path length and thus high loss rates in
vacuum conditions. With increasing pressure the
He already at low pressures. The other popula-
transmission decreases owing to an increased in-
tion is characterized by a direct path through the
teraction probability of UCN and helium. As ex-
guidesystem. Thisbehaviourisvisibleforallthree
pected, the transmission decreases for the longer
lengthsbetween100−150mbar,however,itismore
guides.
prominent for the longest guide length since the
Consideringthecaseofnodiffusereflectivityand
probability for zero diffuse scattering events is re-
a gaussian UCN energy distribution, one would ex-
duced.
pect the data to follow an exponential distribution
Using the mean energy from our simulations,
I
=e−nHe(σsc+σabs)L¯ (3) one can calculate the mean path lenghts from the
I
0 double exponential fit. The results are summa-
withtheheliumatomdensitynHe,thetotalscat- rized in table 1. The short characteristic path
teringcross-sectionσsc,theabsorptioncross-section lengths L1 agree with the mean path length ob-
σabs and the mean path length L¯. The mean UCN tainedfromoursimulationsassumingnodiffusere-
energy can be extracted from our simulation to be flectivity (1.27m/m). The longer path length L
1
E¯UCN =185neV (v¯=5.95m/s). for the short Replika piece is due to a change in
Fromfig. 3onecanseethattheheliumcurvesin the momentum spectrum shortly after leaving the
fact do not have a true exponential form indicated spectrum shaper. The lengths L , corresponding
2
by the red line. The blue line shows two separate toUCNscatteredawayfromtheforwarddirection,
exponentials. Forlowdiffuselyreflectingguidesone are an order of magnitude longer than L . The
1
would expect the UCN to undergo very few diffuse weighted mean L¯ (using the factors from the ex-
scattering events. Considering a binomial distribu- ponential fit as weights) does correspond well with
tionofthediffusescatteringeventsonecanestimate themeanpathlengthextractedfromoursimulation
thattherearelessthanfivediffusescatteringevents with diffuse reflection (2.22m).
through the tested guides given a diffuse reflection
probability of 2%.
1.0 1
0.9 0.9
nt rate0.8 nt rate0.8
u u
o o
e c0.7 e c0.7
v 1m v
elati0.6 elati
R R
0.6
0.5 2m
0.4 3m 0.5
0.3
0 100 200 300 400 500 0 100 200 300 400 500
Pressure [mbar] Pressure [mbar]
Figure2: (Coloronline)Normalizedcountratesfordifferent Figure 3: (Color online) Normalized UCN count rate for
pressuresusingReplikaguidelengthsbetween1−3m. The L =2masfunctionoftheHepressureinlogarithmic
Replika
errorbarsarestatisticaluncertaintiesplusuncertaintiesfrom scale. Thesolidlinerepresentsafitusingtwoexponentials.
areactorpowercorrection. Allcountratesareshownrelative Forcomparisonwealsoshowthebestsingleexponentialfit
tothevacuumcountrate. inadashedline.
3
Table1: CalculatedvaluesforthemeanpathlengthsofUCN.
Guide length L [m/m] L [m/m] L¯[m/m]
1 2
1m 1.47±0.04 35.60±13.49 2.66±0.53
2m 1.22±0.03 11.46±1.29 2.33±0.17
3m 1.28±0.01 23.43±2.65 3.30±0.26
5. Simulation
1.0
In order to extract values for the diffuse reflec-
tivity of the Replika guides, a GEANT4 [21] sim- 0.9 Simulation
ulation was used. This simulation incorporated all e Experiment
parts of the experimental setup. The simulated ve- nt rat0.8 Two-exp Fit
locity spectrum had a gaussian shape with a peak cou 1m
at10m/sandaspreadof5m/sroughlycorrespond- ve 0.7
ingtothesituationatthePF2/TESbeamline[22]. elati
R0.6
The velocity vectors were generated following a co-
2m
sine distribution around the guide axis. The sim-
0.5
ulation incorporated the TES beam aluminum exit
3m
window as well as our shaper.
0.4
Thefollowingexpressionwasusedtodescribethe
0 100 200 300 400 500
interaction cross section between UCN and the he-
Pressure [mbar]
lium gas [23]:
Figure4: (Coloronline)Simulated(squares)andexperimen-
(cid:114)
k T 4m M tal (triangle) data. The experimental data are shown with
σ (E )=2σ B × n . (4)
up UCN 0 AπEUCN (M +mn)2 tahreerreelsapteivcteivtoedthoeubcoleunextproanteesntwiaitlhfintso(hdealsiuhmedilninteh)e. sCimouunlats-
Here, σ is the thermal scattering cross-section tion.
0
(1.34barn in the case of helium), A = 4 is the
massratioofheliumatomsandaneutrons,mn and Fig. 4showsthesimulationtogetherwiththeex-
M are the masses of neutrons and helium atoms perimentaldata. ThediffusereflectivityoftheRep-
respectively and EUCN is the energy of the UCN. likapiecesinthesimulationwassettod=3.0·10−2.
AnyinteractionofaUCNwithaheliumatomleads Simulated and experimental data match well. We
to the UCN being upscattered to thermal energies. define an error number (cid:15)2 number in the following
Thus,inthesimulation,theUCN,whichinteracted way
with the helium were removed from the ensemble.
To describe diffuse scattering of the neutrons on (y −y )2
thewalls,weusedamodifiedLambertianreflection (cid:15)2 = dat sim (5)
σ2 +σ2
mechanism, where the neutrons are scattered with dat sim
a cosine law around the axis of specular reflection withtherelativecountsfortherealdataandsim-
instead of an axis normal to the surface. ulation (y , y ) and their respective errors. We
dat sim
Inthesimulationswealsoassumedthealuminum receivea(cid:15)2/DOF-valuesof0.91. Byvaryingthedif-
foils to be covered by a layer of Fombline oil due fuse reflectivity in the simulation we determine the
to a contamination of the facility by previous ex- uncertainty of the value for the diffuse reflectivity
periments, which in turn alters the Fermi potential to be σ =0.5·10−2.
d
of the foils (i.e. V = 106neV, V = 54neV). Themeasurementsaredescribedconsistentlyand
Fom Al
Thus, the energy spectrum of UCN at the entrance our model could be applied to different lengths of
of the Replika volume is significantly altered, es- a given guide material with a unique set of param-
pecially their angular distribution, which is much eters in the simulation. We thus conclude that the
more forward peaked than for pure aluminum and modified Lambert model is the correct description
consequently enhances the relative transmission. for diffuse scattering on very smooth surfaces.
4
6. Conclusions [7] B. Lauss, Journal of Physics: Conference Series 312,
052005(2011).
Guides for ultra-cold neutrons made from a NiV [8] J. Martin, L. Buchmann, J. Bowman, L. Clarke,
C. Davis, B. Filippone, M. Gericke, R. Golub,
alloy have been studied before with a different
K.Hatanaka,M.Hayden,etal.,Tech.Rep.,TRIUMF
method[20]. Atchisonet. alobtainedvaluesforthe Vancouver,BC(2008).
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samples. However,thisvaluehasbeenextractedus- A. Gschrey, E. Gutsmiedl, R. Hackl, G. Hampel,
F. Hartmann, W. Heil, et al., Eur. Phys. J. A 34, 119
ing the original Lambertian scattering mechanism.
(2007).
Under these circumstances our results are compa- [10] A. Frei, Ucn quelle (im auf-
rable. bau) (2014), http://www.mlz-
garching.de/instrumente/teilchenphysik/ucn.html.
We have successfully applied the helium method
[11] T. Huber, Master’s thesis (2011), diploma The-
to our Replika guides. We determined a diffuse re-
sis, Physics Department E18,Technische Universtitt
flectivity of d = (3.0±0.5)·10−2 using a modified Mnchen.
Lambertian scattering mechanism. It is the first [12] A.Steyerl,H.Nagel,F.X.Schreiber,K.A.Steinhauser,
R.Ghler,W.Glser,P.Ageron,J.M.Astruc,W.Drexel,
time that a UCN guide system could be charac-
G.Gervais,etal.,Phys.Lett.A116,347(1986).
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the NiV Replika guides and this work, we arrive at [14] I. Groshev, V. Dvoretsky, A. Demidov, Y. Panin,
V. Lushchikov, Y. Pokotilovsky, A. Strelkov, and
a good understanding of their transmission proper-
F.Shapiro,Phys.Lett.34B,293(1971).
ties. [15] V.Ignatovich,Physics-Uspekhi39,283(1996).
The helium method itself is rather easy to pre- [16] M. Daum, A. Frei, P. Geltenbort, E. Gutsmiedl,
pare and conduct, thus it provides a cheap means P. Hbel, H. C. Koch, A. Kraft, T. Lauer, A. R. Mller,
S.Paul,etal.,Nucl.Instr.Meth.A675,103(2012).
of testing guides for ultra-cold neutrons on their
[17] M. Klein, Cascade (2014), http://www.physi.uni-
reflection properties. heidelberg.de/Forschung/ANP/Cascade/.
[18] A.Steyerl,S.Malik,A.Desai,andC.Kaufman(2010),
arXiv:0911.4115v2[cond-mat.other].
7. Acknowledgement [19] A. Serebrov, A. Fomin, and V. Varlamov (2010),
arXiv:1001.3210v1[nucl-ex].
[20] F.Atchison,M.Daum,R.Henneck,S.Heule,M.Horis-
We thank T. Brenner and T. Deuschle for their
berger,M.Kasprzak,K.Kirch,A.Knecht,M.Kuzniak,
support in the preparation of the experimental B.Lauss,etal.,Eur.Phys.J.A44,23(2010).
setup and during the beamtime. We also thank [21] S. Agostinelli, J. Allison, K. Amako, J. Apostolakis,
H. Araujo, P. Arce, M. Asai, D. Axen, S. Banerjee,
C. Morkel for the helpful discussions during data
G.Barrand,etal.,Nucl.Instr.Meth.A506,250(2003).
analysis.
[22] T.Zechlau(2015),PrivateCommunication.
This work was funded by the DFG Excellenz- [23] K. Beckurts and K. Wirtz, Neutron Physics (Springer
Cluster EXC153 ”Origin and Structure of the Verlag,1964).
Universe” and the Maier-Leibnitz-Laboratorium
(MLL) of the TU and LMU Munich.
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