measurement ofthe refractive index and attenuation length ... · tion light and the refraction...

$: Measurement ofthe refractive index and attenuation length ... · tion light and the refraction index of liquid xenon is schematically depicted in Fig. 1. A source of scintillation$
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Nuclear Instruments and Methods in Physics Research A 516 (2004) 462–474

$This wo

1999 from

Portugal.

*Corresp

238822358.

E-mail a1Support

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0168-9002/$

doi:10.1016

Measurement of the refractive index and attenuation lengthof liquid xenon for its scintillation light$

V.N. Solovova,1, V. Chepela, M.I. Lopesa,*, A. Hitachia,b,2,R. Ferreira Marquesa, A.J.P.L. Policarpoa

aLIP-Coimbra and CFRM of Physics Department, University of Coimbra, P–3004–516 Coimbra, Portugalb Kochi Medical School, Nankokushi, Kochi 783-8505, Japan

Received 21 April 2003; received in revised form 15 July 2003; accepted 9 August 2003

Abstract

The attenuation length and refractive index of liquid xenon for its intrinsic scintillation light ðl ¼ 178 nmÞ have been

measured in a single experiment. The value obtained for the attenuation length is 364718 mm: The refractive index is

found to be 1:6970:02: Both values were measured at a temperature of 17071 K:r 2003 Elsevier B.V. All rights reserved.

PACS: 78.20.Ci; 29.40.Mc; 78.35.+c

Keywords: Liquid xenon; Refractive index; Vacuum ultraviolet; Scintillation

1. Introduction

The scintillation light of liquid xenon occurs inthe vacuum ultraviolet (VUV), with a single bandcentred at l ¼ 178 nm and full-width at half-maximum (FWHM) of about Dl ¼ 14 nm [1]. Therefractive index of liquid xenon for its scintillation,as well as the attenuation length of this light in the

rk was financed by the project CERN/P/FIS/1594/

the Funda@*ao para a Ci#encia e Tecnologia (FCT),

onding author. Tel.: +351 239410657; fax: +351

ddress: [email protected] (M.I. Lopes).

ed by the fellowship PRAXIS XXI/BD/3892/96

ed by a fellowship from Funda@*ao Oriente,

- see front matter r 2003 Elsevier B.V. All rights reserve

/j.nima.2003.08.117

medium, are quantities of prime importance fromboth the practical and theoretical points of view.

Liquid xenon has been proposed as a workingmedium for several large radiation detectors basedon the scintillation induced by radiation. Some ofthose proposals are at the time of writing at thestage of research and development. Several proto-types have been built and are being tested.Detailed information on this issue can be foundsomewhere else in the literature (Refs. [2,3] andreferences therein). For the development of thosedetectors, the knowledge of both the refractiveindex of liquid xenon, n; and the attenuationlength for the scintillation light in the medium, L;is of crucial importance as they influence thescintillation photon transport in the liquid andthus the performance of the detector [4]. Theexisting data on the refractive index of liquid

d.

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V.N. Solovov et al. / Nuclear Instruments and Methods in Physics Research A 516 (2004) 462–474 463

xenon in the VUV region are scarce. To ourknowledge, the only experimental determinationof n for xenon light, is that reported in Ref. [5].The assessment to the real accuracy of the datapresents difficulties, as the authors do not provideenough details on the experiment. In addition tothat value, there are measurements of n in liquidxenon at wavelengths between 361 and 644 nm; fora range of temperature from 178 K down to thetriple-point [6,7]. Some authors have extrapolatedthese values in the visible to the UV, namely to thewavelength of the xenon scintillation, but theresult is very sensitive to the functional form usedfor the extrapolation, which leads to values withvery large uncertainties. This aspect will beaddressed in more detail in Section 5. As regardsthe attenuation length of scintillation (also re-ferred to as the mean free path of scintillationphotons), liquid xenon itself should be transparentto its scintillation light. The excimer emissionoriginates in the transition from the self-trappedexciton states 1Sþ

u and 3Sþu to the repulsive ground

state 1Sþg : The free exciton absorption band is

E1:3 eV above the peak of the emission bandwhose width is E0:6 eV [8]. On the other hand, itis well known that small amounts of impurities canbe very effective in absorbing the light. Therefore,during a long time, the observed attenuation inliquid xenon was attributed to absorption byimpurities. However, in spite of the great progressachieved in purifying the liquid assessed usually bythe measurement of lifetime of free electrons,various authors have reported similar and rela-tively short values of the photon attenuationlength (about 30 cm) almost independently ofpurification processes, apparatuses and measuringmethods [2,9]. This fact has led to the suggestionthat the attenuation length of scintillation mea-sured in liquid rare gases is mainly determined byRayleigh scattering [9], recently supported bytheoretical calculations considering scattering ofthe light on density fluctuations [10]. The calcu-lated values are in reasonable agreement withmeasurements both for pure liquefied rare gasesand their mixtures, although the associated un-certainties are quite large.

It is worth to mention that the experimentaldetermination of the attenuation length of photons

in the liquid leads very easily to overestimatedvalues [9,11]. Most of the methods reported in theliterature are based on the measurement of theattenuation of the light after having crossed aknown (and usually variable) thickness of liquid.In most experiments it is assumed that only directlight is detected and the contribution from thereflected light is negligible. Thus, the set-up has tobe designed very carefully in order to fulfil thatrequirement, which has been realised not to beeasy [9,11].

Concerning the theoretical point of view, theprecise knowledge of the refractive index is remark-ably important, among the optical properties, notonly by itself but also because it has been used inevaluating the success of theoretical models andaccurate calculation of other properties, namely thedensity and polarizability of non-polar fluids.

In this paper, we report on simultaneousmeasurements of the attenuation length and therefractive index of liquid xenon for its ownscintillation at the temperature 170 K: The paperis organized as follows. In Section 2 the experi-mental method is explained, while the experimen-tal set-up and procedure are described in Section 3.The data analysis and results are presented inSection 4 and discussed in Section 5.

2. The experimental method

The experimental method used for measuringsimultaneously the attenuation length of scintilla-tion light and the refraction index of liquid xenonis schematically depicted in Fig. 1. A source ofscintillation light pulses is aligned with the axis ofa photomultiplier tube (PMT) at a distance H

from the photocathode of radius r: The source isinside the liquid with refractive index n; whilethe PMT is in the gas (refractive index E1). Thesurface of the liquid is at a distance h above thelight source and parallel to the PMT window.Then, the average number of photoelectronsproduced in the PMT per scintillation pulse maybe written as

N ¼ N0ð1 þ kÞT1T2QO4p

exp �h

L

� �ð1Þ

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h

Hliquidxenon

xenongas

PMT

2r

2 α

α2 ´

Fig. 1. Schematic drawing illustrating the principle of the

experimental method.

V.N. Solovov et al. / Nuclear Instruments and Methods in Physics Research A 516 (2004) 462–474464

where N0 is the average number of photonsemitted into 4p per scintillation pulse, T1 and T2

are the transmitance of the liquid–gas and gas-PMT window boundaries, respectively. Q is thequantum efficiency of the PMT photocathode, O isthe solid angle and L is the attenuation length ofscintillation light (also referred to as mean freepath of the photons) in the liquid. In the case ofexistence of both absorption and Rayleigh scatter-ing, to which are associated mean free paths La

and Ls; respectively, one has

1

L¼

1

Laþ

1

Ls: ð2Þ

In Eq. (1), k is the ratio of the indirect to directphotons collected at the PMT. By indirect photonsone means those photons that are collected at thePMT after undergoing Rayleigh scattering or/andreflection on the surrounding materials. Directphotons are those that did not suffer eitherRayleigh scattering or reflection before beingcollected at the PMT. Hence, k may depend onh; i.e., k ¼ kðhÞ:

From Fig. 1, one sees that if Hbr; then a and a0

are small so that tan aEa and tan a0Ea0: Hence,one can write

rEah þ naðH � hÞ ð3Þ

aEr

Hn � hðn � 1Þð4Þ

O ¼ 2pð1 � cos aÞEpa2Epr

Hn � hðn � 1Þ

� �2

: ð5Þ

Considering that for small incident angles one has

T1E1 �n � 1

n þ 1

� �2

ð6Þ

from Eqs. (1), (5) and (6), one obtains

NðhÞEAð1 þ kðhÞÞr=2

Hn � hðn � 1Þ

� �2

� 1 �n � 1

n þ 1

� �2 !

exp �h

L

� �ð7Þ

where A ¼ N0T2Q; which is constant with respectto h: Therefore, n and L can be determined bymeasuring N as a function of h and fitting Eq. (7)to the data, provided kðhÞ is known. The computa-tion of kðhÞ is discussed in detail in Section 4.

In the present work, measurements of NðhÞ werecarried out for two different values of H sothat one has two sets of data taken with thesame sample of liquid but in someway differentgeometries.

In order to enhance the sensitivity of thismethod to n and L; and thus provide accuratedetermination of those quantities, the dependenceof N on h has to be dominated by the exponentialand by the factors dependent on n: For that, kðhÞhas to be 51; i.e. the conditions of light collectionhave to be such that the amount of indirect lightcollected at the PMT is minimal. This wasachieved with a proper design of the liquidcontainer, as described in the next section.

3. Experimental set-up and procedure

A schematic drawing of the experimental set-upis presented in Fig. 2. The whole system ismounted inside a vacuum-tight cylindrical chamber

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45°

Fig. 2. Schematic drawing of the experimental set-up: 1—

chamber; 2—PMT; 3,4,5—floating a-source ð241AmÞ assembly;

6—permanent magnet; 7—diaphragms; 8,9—level-meter; 10—

alcohol cooled with liquid nitrogen; 11—thermosensors.


(1) made of stainless steel. The scintillation light isinduced by a-particles from an 241Am source,8 mm in diameter, deposited on a stainless-steelsubstrate (4). The scintillation light is seen by aphotomultiplier (2) (Hamamatsu R1668) with UVgrade fused silica window and a 25 mm diameterphotocathode, placed 230 mm above the bottomof the chamber.

The source is mounted on top of a magnesiumcylinder (3), which also has a ferromagneticstainless-steel disk (5) screwed to its bottom. Asthe density of magnesium is lower than that ofliquid xenon, the whole assembly can float on theliquid surface. Hence, it is possible to have thesource in two different positions: on the bottom ofthe chamber, holding the source assembly by apermanent magnet (6) placed outside the chamber,

and in an intermediate position between thebottom of the chamber and the PMT with thesource floating in the liquid and hold in place by adiaphragm (see Fig. 2). In these two positions, thedistance between the source and the PMT window,H ; is 187 and 93 mm; respectively.

A stack of stainless-steel diaphragms (7) isintended to minimize the amount of indirectlight reaching the photocathode. The diaphragmsbelow and above the intermediate position of thesource have diameters of 36 and 25 mm; respec-tively, and their edges were shaped as shown inFig. 2.

All the parts were washed in ultrasonic bathbefore assembly. After closing, the chamber washeated up to 353 K and pumped out for severaldays until the pressure decreased to B10�6 mbar:Next, xenon gas was circulated during several daysthrough the chamber and the Oxisorb purifier.

The xenon gas passed through the Oxisorbpurifier before being condensed in the chamber.

The level of liquid xenon was measured bymeans of a capacitance transducer made of astainless-steel rod (8) of 3 mm diameter insertedcoaxially into a stainless-steel tube (9) with innerdiameter of 6 mm: The precision of the levelmeasurement was better than 1 mm resultingfrom an accuracy of the transducer better than0:1 pF:

The chamber was placed inside a dewar withalcohol cooled by liquid nitrogen to approximately170 K (10). Two platinum thermoresistors (11)are attached to the chamber, one at the bottomand the other at the level of the PMT, allowingto monitor the temperature with a precisionof 1 K:

For measuring the mean number of photoelec-trons produced in the PMT per a-particle, theoutput signal of the PMT was amplified by acharge sensitive preamplifier (Canberra 2005) fol-lowed by a spectroscopy amplifier (Canberra 2021)before being fed into a PC-based multichannelanalyzer for pulse height analysis. At the amplifier,a semi-Gaussian shaping with a time constant of1 ms was employed. For converting the pulseheight due to a-particles into number of photo-electrons, the location of the single-photoelectronpeak in the pulse height spectrum was used.

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Fig. 3. Number of photoelectrons, as a function of the

thickness of the liquid xenon layer, measured at two different

positions of the a-source (see Fig. 2). The solid line is the best fit

of Eq. (7) to data with n ¼ 1:69; L ¼ 364 mm; R ¼ 0:21 and

Z ¼ 0:


The single-photoelectron peak was due to thescintillation induced by the 60 keV g-rays alsoemitted by the 241Am source. The position ofsingle-photoelectron peak was permanently mon-itored to check the stability of the PMT gain. Thelinearity and stability of the electronics waschecked by injecting pulses of variable amplitude,from a precision pulse generator, into the pre-amplifier input stage, several times during thecourse of the measurements.

The data-taking procedure was as follows.Initially, the floater with the source lied on thebottom of the chamber. The magnet, placedoutside the chamber, just below its bottom, keptthe floater in this position while xenon wascondensed into the chamber. The condensationwas performed in steps, the level of liquidincreasing by 10–15 mm each time. After tempera-ture stabilization, which typically took about30 min; the difference between the readings ofthe two thermoresistors was about 2–3 K; depend-ing on the liquid level. After that, the meanamplitude of the PMT signal obtained from thepulse height spectrum, and the level of liquidxenon were recorded every minute during 10 min:The procedure was repeated until the liquid hadreached the surface of the PMT which wasrecognized by an abrupt change of the signalamplitude. In order to obtain a set of measure-ments of NðhÞ with the source in the upperposition (shown in Fig. 2 in dashed lines), themagnet was removed slowly. A second stepwiseprocedure was then followed, with the differencethat, in each step, the level of liquid was decreasedby allowing some amount of liquid to evaporate.The two sets of measurements were repeatedseveral times.

The experimental results are plotted in Fig. 3. Ateach value of h; the mean value of the readings ofthe peak position in 10 spectra accumulatedsequentially was taken as the best estimate of N :The standard deviation of that set of readings wastaken as the uncertainty in N : The uncertainty inthe data points ranges from about 0.5% to 1%,with the exception of the data point correspondingto the smallest value of h and the source at thebottom of the chamber ðH ¼ 187 mmÞ for whichthe uncertainty is 1.5%.

4. Data analysis

In order to determine the refractive index, n; andthe attenuation length, L; Eq. (7) was fitted to theexperimental data on NðhÞ; the number of photo-electrons detected per a-particle. The difficulty ofthe fit lies in the fact that the parameter k can alsodepend on the adjusted parameters n and L; as wellas on other unknown quantities involved in thetransport of the light in the chamber, such asthe reflectivity of the chamber materials and theprobability of photon scattering in liquid xenon.This dependence can not be expressed in a simpleanalytical form, and therefore, it can only beassessed numerically by Monte-Carlo simulation.As every intermediate step of the fit requiresthe knowledge of k for every experimental pointat the current values of the adjustable parameters,its calculation by simulation during the fittingprocedure would be extremely time consuming.To overcome this problem, the Monte-Carlosimulation was decoupled from the fitting proce-dure in the following way: First, for each experi-mental value of h and a finite set of theinput parameters, a detailed Monte-Carlo simula-tion of scintillation light propagation in thechamber was carried out, producing a kind oflook-up-table with information that allows to

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Table 1

The boundary processes taken into account in the simulation of

light transport in the chamber and their probabilities: R was

regarded as unknown quantity, m was set equal to 0:5(Ref. [13]), RPM and Rlg were calculated using Fresnel equation

Boundary Processes Probability

SS/liquid and SS/gasa Specular reflection R�m

Diffuse reflection R�ð1 � mÞAbsorption 1 � R

Gas/PMT window Specular reflection RPM

Transmission 1 � RPM

Liquid/gas Specular reflection Rlg

Transmission 1 � Rlg

aSS stands for stainless-steel.

3This value of m was obtained in a separate experiment by

fitting the results of Monte-Carlo simulation, with m as an

adjustable parameter, to experimental data on the light

collection in a stainless-steel cell. However, it was concluded

that the present results are quite insensitive to the value of m:


compute the value of k for any set of values of theparameters at the fitting stage, without the need ofrunning the simulation program. In the next twosubsections, this procedure is described in detail.

4.1. Monte-Carlo simulation

The chamber was represented by a cylindricalvolume where all the rings were included, as wellas the source support. Details concerning theshape of the rings were also taken into account.

The emission of a-particles from the source wasassumed to be uniform over the surface of thesource and isotropic in 2p: As the range of an a-particle in liquid xenon is small compared with thedimensions of the chamber (for Ea ¼ 5:49 MeVand T ¼ 170 K; this range is of the order of a fewtens of mm), it was neglected and the scintillationphotons were simulated as being emitted isotropi-cally from the emission point of the a-particle.

Concerning the transport of the scintillationphotons, each photon was followed, using the ray-tracing technique, until it was either collected atthe PMT or absorbed, either in the liquid or at anysurface of the chamber. In the liquid, the photontransport was simulated as follows: (1) At eachphoton location, the distance to the next interac-tion point in the liquid, di; is computed accordingto the exponential distribution

di ¼ �L logðxÞ ð8Þ

x being a random number uniformly distributed in[0,1]. (2) The distance, db; from the presentlocation to the nearest boundary along the photondirection was calculated. (3) The photon wastransported along the present photon directionby the distance d equal to di or db whichever issmaller. (4) If d ¼ di; then an interaction in theliquid took place, else a boundary surface wasreached. In the gas, the attenuation of scintillationlight was neglected.

In the liquid, the interaction processes consid-ered for the photons were the Rayleigh scatteringand the absorption, with associated mean freepaths Ls and La; respectively. These processesoccur with probabilities L=Ls and L=La ¼ 1 �L=Ls; respectively, L being related with La and Ls

by Eq. (2). Henceforth, the probability of occur-

rence of Rayleigh scattering, L=Ls; will be referredto as Z for the sake of simplicity.

In the case of occurrence of an interaction in theliquid, the type of the interaction was sampledaccording to the probabilities referred above. Inthe case of scattering, the new photon directionwas generated according to the cross section of theprocess [12], with a probability distribution func-tion given by

dP ¼3

8ð1 þ cos2 yÞ sin y dy

dj2p

ð9Þ

y and j being the polar and azimuthal anglesrelative to the photon initial direction. The photonenergy is unchanged and its transport continues.

The processes taken into account at eachboundary and their probabilities are listed inTable 1. Regarding any metal surface (wall, ringor source support surface), reflection, specular aswell as diffuse, and absorption were considered.The probabilities of these processes were takenequal to R�m; R�ðm � 1Þ and ð1 � RÞ; respectively,R being the reflectance of the surface at thewavelength of the scintillation light and m thefraction of specular reflection at the surface. Forthe simulation, R was regarded as a variable inputparameter, while m was set to 0:53 [13]. In the caseof photon impact on the PMT window surface,

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n1.4 1.6 1.8 2.0

L (

mm

)

150

300

450

600

1000

Fig. 4. Grid of points in the ðn;LÞ-plane where the matrix C

was calculated by Monte-Carlo simulation.

4The true upper limit of R is 1 but it is extremely improbable

that the reflectance of stainless steel to VUV radiation of l ¼178 nm is higher than 0:6 (see Ref. [17]).


only specular reflection was considered withprobability RPM; which is the reflectance of thePMT window in contact with the gas. The balance,ð1 � RPMÞ; is assumed to correspond to thetransmission of the photon through the windowtowards the photocathode. The detection of thephoton requires its conversion into an electron,process whose average probability is given by thequantum efficiency of the photomultiplier, Q;which is taken into account explicitly in Eq. (1),thus outside the simulation. At the liquid–gasinterface, it was considered that the photon couldundergo either specular reflection or refraction,with probabilities Rlg and ð1 � Rlg), respectively,Rlg being the reflectance of the liquid/gasboundary. Both RPM and Rlg were calculatedusing Fresnel equation [14], which takes intoaccount the dependence of the reflectance on theincidence angle. The refractive index of the xenonvapour in equilibrium with the liquid wasapproximated to 1 and that of the PMT window,which is made of UV grade fused silica, was takenequal to 1.6 [15,16]. The refractive index of liquidxenon, n; was regarded as a variable inputparameter.

When a boundary surface is reached, thecompetitive processes that can occur at thatsurface are sampled taking their respective prob-abilities as listed above. In case of specularreflection and refraction the direction of thephoton is changed accordingly. In case of diffusereflection, the direction of the reflected photon wassampled from an angular uniform distributioncovering 2p according to Lambert law [14].

For a given set of values of n; L; Z; R and h; 108

photons were emitted isotropically from randompoints uniformly distributed over the a-sourcesurface and followed until they are lost or detectedby the PMT, as described above. The number ofreflections, r; and the number of scatteringinteractions, s; undergone by each photon col-lected at the PMT were counted. The matrix C;defined such that the element Crs is equal to thenumber of photons reaching the PMT photo-cathode after suffering r reflections and s scatter-ing processes, was computed.

In view of the data analysis, namely the fitting ofEq. (7) to data, the matrix C was computed for the

values of n and L forming the rectangular grid inthe ðn;LÞ-space represented in Fig. 4, and for everyvalue of h at which experimental data were taken.This kind of look-up table of values of the matrixC was computed for the upper limits of theparameters R and Z; which were taken equal to 0.6and 1, respectively.4 In so doing, for the values ofh; n and L mentioned above, the elements of thematrix C allow the analytical calculation of k forany other values of R and Z in the intervals [0,0.6]and [0,1], respectively, using the relation

kðh; n;L;R; ZÞ

¼Xsmax

s¼0

Xrmax

r¼0

Crsðh; n;LÞC00ðh; n;LÞ

R

Rmax

� �r

Zs

!� 1: ð10Þ

During the fitting procedure, the value of k for anyset of values of the parameters ðn;L;R; ZÞ and thevariable h was obtained by linear interpolation ofthe values of k between the closest vertices of theðn;LÞ-grid (see Fig. 4) which, in turn, had beencomputed for the current values of R and Z usingEq. (10).

4.2. Fitting and results

As it was referred in Section 3, two sets ofexperimental values of NðhÞ were measured

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Table 2

Domain of search, best estimate and uncertainty of the adjusted

parameters

Parameter Domain Best estimate Uncertainty

n 1:4;y; 2:0 1.69 0.02

L (mm) 150;y; 1000 364 17.7

R 0;y; 0:6 0.21 0.02

Z 0;y; 1 a

aSee Section 5.


corresponding to the two different positions of thea-source, at H ¼ 187 and 93 mm: To determinethe refractive index and attenuation length of thescintillation photons, Eq. (7) was fitted to theexperimental data of both sets by using the methodof least squares, i.e., by minimizing the function

w2 ¼X2

j¼1

XMj

i¼1

NexpðhijÞ � NðhijÞsij

� �2

: ð11Þ

Here, the index j refers to the dataset(H1 ¼ 187 mm and H2 ¼ 93 mm), Mj being thenumber of points in the j dataset. Hence, hij is thethickness of the liquid layer above the source (seeFig. 1) at data point i of the dataset j; and NexpðhijÞis the number of photoelectrons measured with anuncertainty sij : NðhijÞ was calculated using Eq. (7),with kðhij) computed by Monte-Carlo simulationas described in the previous section. As it wasdiscussed therein, k can depend not only on n andL but also on two additional unknown parameters,R and Z; i.e., the reflectance of the inner surfaces ofthe chamber and the probability of scattering ofphotons in the liquid, respectively. Therefore, thefitting was done with six independent adjustableparameters: n; L; Z; R; A1 and A2; A1 and A2 beingthe multiplicative constants of Eq. (7) for the set ofdata corresponding to H1 and H2; respectively.

The minimization was carried out using thedownhill simplex method [18] as it does notrequire derivatives. The starting point for definingthe initial simplex was chosen randomly in theparameter space. Once the minimization routinehas terminated, it was restarted at the point whereit claimed to have found a minimum in order toensure that it was not trapped in a false minimum.The whole fitting procedure was repeated 1000times with different starting points randomlydistributed in the parameter domain (seeTable 2). Figs. 5 and 6 show the distributions ofthe parameters and the w2 of the fits, respectively,obtained with one and three restarts. From thesefigures, the importance of performing more thanone restart in each fitting procedure is evident. Nosignificant changes were observed by furtherincreasing the number of restarts. For the bestestimate of the parameters one took the set ofvalues of the fit performed with three restarts that

gave the smallest value of w2: That fit is shown inFig. 3, together with the data points, and thevalues of the adjusted parameters are listed inTable 2.

For the estimation of the confidence limits, themethod known as Monte-Carlo simulation ofsynthetic datasets [18] was used. Essentially, themethod comprises the following steps: Firstly,from the experimental dataset ðNexpðhijÞ; sjiÞ sev-eral new synthetic datasets are generated, such asNsynðhijÞ ¼ NexpðhijÞ þ sijG; where G is a randomvalue, distributed normally with zero mean anddispersion equal to 1. Secondly, for every syntheticdataset the minimization procedure describedabove was performed giving rise to a set of fittedparameters. The uncertainty in each parameterwas calculated as the standard deviation of thedistribution of the values of the parameterobtained by performing the fitting over 1000synthetic datasets. The distributions of the para-meter values are shown in Fig. 7 and theuncertainties are listed in Table 2. As it shouldbe expected, the mean values of these distributions(n ¼ 1:69; L ¼ 362 mm and R ¼ 0:20) agree, with-in the uncertainties, with the values of theparameters corresponding to the best fit to theexperimental data (n ¼ 1:69; L ¼ 364 mm andR ¼ 0:21).

Fig. 8 shows the confidence regions for twoparameters of interest jointly, n and L; defined bycurves of constant w2 of the fit to the experimentaldata. The pairs of values ðn;LÞ obtained byperforming the fit to the synthetic datasets arealso represented in Fig. 8 by dots. Their fractioninside each confidence region fully agrees with thevalue predicted on the basis of the w2 cont-ours. Moreover, the projections of the curve

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(a) (b)

0

50

100

150

200

250

300

1.64 1.66 1.68 1.7 1.720

100

200

300

400

500

350 400 450

n

(c) (d)

0

100

200

300

400

500

600

700

0.15 0.2 0.25 0.3 0.350

100

200

300

400

500

600

700

800

900

0 0.25 0.5 0.75 1

R η

L

Fig. 5. Distribution of the adjusted parameters obtained by carrying out the fitting with 1000 starting points randomly distributed in

the parameter domain. The number of restart points considered in each fitting was equal to one (dashed lines) and three (solid lines).


corresponding to a confidence level equal to 68.3%for one parameter, agree with the standarddeviations of the distributions of the parametersn and L obtained by performing the fits tothe synthetic datasets (i.e., the distributions plottedin Fig. 7).

The discussion of the absolute values of n; L

and Z obtained from the fit will be given inSection 5. As for R; it is consistent with thedata on the reflectance of stainless-steel in theVUV region that could be found in the litera-ture [17]. The fitted value of the constant A inEq. (7) was also found to be consistent with theexpected one from an estimate assuming N0 ¼

Ea=Wph ¼ 3:37 � 105; Q ¼ 0:2 and T2 ¼ 0:95:Ea is the energy of the alpha particles(Ea ¼ 5:49 MeV) and Wph the mean energyfor producing a photon (Wph ¼ 16:3 eV [19,20]).The value of the quantum efficiency of thephotocathode, Q; was taken equal to the onequoted by the manufacturer at l ¼ 178 nmand T2 was calculated using Fresnel equationwith the refraction index of UV grade fusedsilica and xenon vapour equal to 1.6 and 1,respectively.

It is worth to mention that the condition k51referred in Section 2 is fulfilled in the presentexperimental situation. In fact, for the values of

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(a)

(b)

Fig. 6. Distribution of the w2 values of the fits to experimental

data obtained with 1000 different starting points randomly

distributed in the parameter domain. The number of restarts in

each fit was set equal to one (a) and three (b).


the parameters corresponding to the best fit, onehas kE0:03 for h > 15 mm: It increases for smallervalues of h; attaining its maximum value of 0.1 forh ¼ 1 mm:

5. Discussion

The attenuation length of scintillation light inliquid xenon obtained in this work is very similarto most of the values reported in literature,ranging from 300 to 400 mm [9,21,22]. Anapparent longer attenuation has also been ob-tained in some measurements where the collectionof the reflected light was not taken into account[11,23]. So, in this type of measurements, it iscrucial to suppress the collection of reflected lightby a proper design of the set-up or to take it intoaccount in the data analysis.

In the present work, the lower limit for theelectron lifetime in the liquid measured in aseparate chamber was found to be at least 20 ms;being limited by the sensitivity of the method used

for the measurement. This lifetime corresponds toa concentration of oxygen equivalent impurities ofabout 0:05 ppm; showing that the liquid is verypure at least with respect to electron attachingimpurities.

The measurement of a similar value of L bydifferent authors using different purification meth-ods, contrary to the significant improvementachieved in the mean free path with respect tothe attachment of free electrons, has led to thesuggestion that L was mainly determined by theRayleigh scattering [9]. Moreover, the observationthat the attenuation length of scintillation in liquidargon increases significantly with the addition ofsmall quantities of Kr or Xe, shifting thewavelength of the emitted photons from 128 to147 nm and 174 nm; respectively, has also beencited in support of that hypothesis [9]. Indeed, asthe cross-section of the Rayleigh scattering processis proportional to l�4; the shift to longerwavelength would account for the observedincrease of the attenuation length.

The theoretically estimated scattering mean freepath of scintillation photons in both liquid xenonand liquid argon doped with Kr and Xe agreesfairly well with the experimental values of thescintillation photon attenuation lengths [10]. How-ever, the hypothesis of the dominant role ofRayleigh scattering was not yet confirmed experi-mentally.

In the present work, the possibility of occur-rence of Rayleigh scattering was introduced in thedata analysis and was parameterised in terms ofthe fitted parameter Z (see Section 4.1). Accordingto its definition, Z ¼ 0 means that the only processresponsible for the finite value of L is theabsorption and, conversely, the upper limit, Z ¼1; corresponds to L entirely determined byscattering. From Fig. 7 one can see that the mostprobable value of Z is 0. In Fig. 9(a), the w2 of thefit to experimental data is plotted as a function ofthe parameter Z: Fig. 9(b) shows similar plot butwhen the three data points corresponding to thesmaller values of h for H ¼ 193 mm were notincluded in the fit. In both figures the horizontalline corresponds to the confidence level of 68.3%.Therefore, we consider that the experimental datado not allow a confident conclusion about the

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(a)

29.99 / 32Constant 77.06Mean 1.692

Sigma 0.2011E-01

0

10

20

30

40

50

60

70

80

90

1.6 1.65 1.7 1.75 1.8n

(c)

18.88 / 18

Constant 117.6Mean 0.2011Sigma 0.2005E-01

0

20

40

60

80

100

120

140

0 0.1 0.2 0.3R

(b)

18.66 / 20Constant 110.8Mean 361.5

Sigma 17.69

0

20

40

60

80

100

120

140

300 400 500

(d)

0

50

100

150

200

250

300

350

400

450

0 0.25 0.5 0.75 1η

L

Fig. 7. Distributions of the fitted parameters obtained by the method of the synthetic datasets.


value of Z: It should be stressed that the values of n

and L obtained from the fits with and withoutthose three data points are the same.

Regarding the refractive index of liquid xenonfor its scintillation, the result obtained in thepresent work ðn ¼ 1:6970:02Þ is in good agree-ment with the value recently calculated ðn ¼1:6870:01Þ using a free exciton model based ona dispersion relation reported for xenon gas in theUV [24]. Significantly lower value of the refractiveindex ðn ¼ 1:565570:002470:0078Þ has been mea-sured in Ref. [5] at xenon triple point. Regretfully,the paper does not provide enough details toenable discussion of possible reasons for thediscrepancy. Similar low value, n ¼ 1:59 at l ¼

175 nm; was obtained earlier by Braem et al. [21]from experimental data [6] at l > 350 nm byextrapolation with a non-specified modified formof the Lorentz–Lorenz equation. However, theauthors stressed that the extrapolation is verysensitive to the functional form of the extrapola-tion and to small changes in the values of therefractive index at the longer wavelengths.

6. Conclusions

The refractive index of liquid xenon for its ownscintillation at 170 K was measured to be1:6970:02: This result is in good agreement with

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Fig. 8. Confidence regions in the ðn;LÞ domain defined by

contours of w2 ¼ const: Curves B and C delimit confidence

regions of 68% and 95%, respectively, for the two parameters

jointly. The projections of curve A on the axes define a 68%

confidence interval for each parameter separately. The dots

correspond to the ðn;LÞ-pairs obtained by performing the fit to

the synthetic datasets.

(a)

(b)

Fig. 9. w2 of the best fit of Eq. (7) to experimental data as a

function of the value parameter Z: (a): with all the data points;

(b): without the three data points taken at H ¼ 187 mm and

with hp22 mm (see Fig. 3).


n ¼ 1:68 obtained using a free exciton model basedon a dispersion relation reported for xenon gas inthe UV [24].

The attenuation length of the scintillationphotons in liquid xenon was also measured. Thevalue obtained, L ¼ 364718 mm; is comparablewith most of the published data. The possibility ofoccurrence of both absorption and Rayleighscattering of the photons in the liquid was takeninto account in the analysis. However, the dataobtained at the present experimental conditions donot allow to conclude about the relative contribu-tion of these processes. A dedicated experiment isneeded to clarify this issue.

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[13] V. Solovov, Ph.D. Thesis, unpublished.

[14] M. Born, E. Wolf, Principles of Optics, Pergamon Press,

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[15] I.H. Malitson, J. Opt. Soc. Am. 55 (1965) 1205.

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Flannery, Numerical Recipes in Fortran, the Art

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[19] M. Miyajima, S. Sakai, E. Shibamura, Nucl. Instr. and

Meth. B 63 (1992) 297.

[20] V.Yu. Chepel, M.I. Lopes, R. Ferreira Marques, A.J.P.L.

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[22] I.M. Obodovsky, in: Proceedings of the International

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measurement ofthe refractive index and attenuation length ... · tion light and the refraction...

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