Observation of nuclear dechanneling length reduction for high energy protons in a short bent crystal

Physics Letters B 743 (2015) 440–443

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Observation

of

nuclear

dechanneling

length

reduction

for

high

energy

protons

in

a

short

bent

crystal

W. Scandale

a

,

b

,

e

,

G. Arduini

a

,

M. Butcher

a

,

F. Cerutti

a

,

M. Garattini

a

,

S. Gilardoni

a

,

L. Lari

a

,

k

,

A. Lechner

a

,

R. Losito

a

,

A. Masi

a

,

A. Mereghetti

a

,

E. Metral

a

,

D. Mirarchi

a

,

j

,

S. Montesano

a

,

S. Redaelli

a

,

R. Rossi

a

,

e

,

P. Schoofs

a

,

G. Smirnov

a

,

E. Bagli

c

,

L. Bandiera

c

,

S. Baricordi

c

,

P. Dalpiaz

c

,

G. Germogli

c

,

V. Guidi

c

,

A. Mazzolari

c

,

D. Vincenzi

c

,

G. Claps

d

,

S. Dabagov

d

,

l

,

D. Hampai

d

,

F. Murtas

d

,

G. Cavoto

e

,

F. Iacoangeli

e

,

L. Ludovici

e

,

R. Santacesaria

e

,

P. Valente

e

,

F. Galluccio

f

,

A.G. Afonin

g

,

Yu.A. Chesnokov

g

,

V.A. Maisheev

g

,

Yu.E. Sandomirskiy

g

,

A.A. Yanovich

g

,

I.A. Yazynin

g

,

A.D. Kovalenko

h

,

A.M. Taratin

h

,

Yu.A. Gavrikov

i

,

Yu.M. Ivanov

i

,

L.P. Lapina

i

,

W. Ferguson

j

,

J. Fulcher

j

,

G. Hall

j

,

M. Pesaresi

j

,

M. Raymond

j

,

D. Bolognini

m

,

n

,

S. Hasan

m

,

n

,

M. Prest

m

,

n

,

E. Vallazza

o

a_{CERN,EuropeanOrganizationforNuclearResearch,CH-1211Geneva23,Switzerland} b_{Laboratoiredel’AccelerateurLineaire(LAL),UniversiteParisSudOrsay,Orsay,France} c_{INFNSezionediFerrara,DipartimentodiFisica,UniversitàdiFerrara,Ferrara,Italy} d_{INFNLNF,viaE.Fermi40,00044Frascati(Roma),Italy}

e_{INFNSezionediRoma,PiazzaleAldoMoro2,00185Rome,Italy} f_{INFNSezionediNapoli,Italy}

g_{InstituteofHighEnergyPhysics,MoscowRegion,RU-142284Protvino,Russia} h_{JointInstituteforNuclearResearch,Joliot-Curie6,141980Dubna,MoscowRegion,Russia} i_{PetersburgNuclearPhysicsInstitute,188300Gatchina,LeningradRegion,Russia} j_{ImperialCollege,London,UnitedKingdom}

k_{InstitutodeFisicaCorpuscular(CSIC-IFIC),Valencia,Spain} l_{P.N.LebedevPhysicalInstitute&NRNUMEPhI,Moscow,Russia} m_{Universitàdell’Insubria,viaValleggio11,22100Como,Italy}

n_{INFNSezionediMilanoBicocca,PiazzadellaScienza3,20126Milano,Italy} o_{INFNSezionediTrieste,ViaValerio2,34127Trieste,Italy}

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received8December2014

Receivedinrevisedform16February2015 Accepted28February2015

Availableonline5March2015 Editor:L.Rolandi Keywords: Crystal Channeling Beam Deflection

Deflectionof400GeV/c protonsbyashortbentsiliconcrystalwasstudiedattheCERNSPS.Itwasshown thatthedechannelingprobabilityincreaseswhilethedechannelinglengthdecreaseswithanincreaseof incident anglesofparticlesrelative tothe crystalplanes. Theobservation ofthe dechannelinglength reductionprovidesevidenceoftheparticlepopulationincreaseatthetoplevelsoftransverseenergiesin thepotentialwelloftheplanarchannels.

©2015TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.

Whenhighenergychargedparticlesentera crystalwithsmall angles relative to the crystal planes,

θ

o

<<

1, their motion is governed by a crystalpotential, U

(

x

)

, averaged along the planes

[1]. If the angles are smaller than the critical angle

θ

o

< θ

c

=

E-mailaddress:alexander.taratin@cern.ch(A.M. Taratin).

(

2Uo

/

pv

)

1/2,where p, v are the particle momentum and veloc-ity, respectively,andUo isthe well depthofthe averagedplanar potential,theparticlescanbecapturedintothechannelingregime.

Channeled particles move in a crystal oscillating between two

neighboringplanes.Channelingisalsopossibleinabentcrystalif

http://dx.doi.org/10.1016/j.physletb.2015.02.072

0370-2693/©2015TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3_.

W. Scandale et al. / Physics Letters B 743 (2015) 440–443 441

itsbendradiusislarger thanthecriticalvalue, R

>

Rc

=

pv

/

e Em

[2],where Emisthemaximumstrengthoftheelectricfieldinthe planarchannel. Ina bentcrystal, theparticle motionisgoverned bytheeffectivepotentialUeff

(

x

,

R

)

=

U

(

x

)

+

x

·

pv

/

R.

Theaveragedplanarpotentialprovidesanapproximate descrip-tionof channeling, inwhich thetransverse energyofparticles is theintegralofmotion.Incoherent(multipleandsingle)scattering bythecrystalelectrons andnucleichanges thetransverseenergy ofchanneledparticlesandtheyleavethechannels,thatis dechan-neling occurs. The density ofatomic nucleireduces quickly with thedistance x from the planes accordingto a Gaussian distribu-tion Pn

(

x

)

∼

exp

(

−

x2

/

u2_⊥

)

, whereu⊥

=

√

2 u1 andu1 isthe am-plitude ofthermal vibrations ofthe crystalatoms. Therefore,the dechanneling process has two stages formost of channeled par-ticlesentering the crystalsufficiently far fromthechannel walls. In the first slow stage particles increase their transverse energy due to multiple scattering on the crystal electrons. The

experi-mental data [3] have shown that a good approximation for the

criticalapproachdistancetothechannelwallsisrc

=

2

.

5u1where thefast dechanneling stage dueto multiple scatteringby atomic nucleibegins(“nuclearcorridor”). Thevalue ofthe planar poten-tial at the distance rc determines the critical transverse energy forthestablechannelingstates Exc

=

Ueff

(

x

=

rc

)

.The dechannel-ing process has an exponential character in the first approxima-tion, Nch

(

z

)

∼

exp

(

−

z

/

Sd

)

, where Sd is the dechanneling length. Thedechannelinglengthmeasuredintheexperiment[4]isabout 10 cmfor200 GeV

/

c protonsinthe (110)channelsof a44 mm longstraightsiliconcrystal.Itdeterminesthereductionofparticles inthe stablechanneling statesdueto multiple scatteringon the crystalelectrons,theelectrondechannelinglength Se.The dechan-nelinglengthisapproximatelyproportionaltotheparticleenergy.

Shortcrystals with length L

<<

Se are requiredto studythe fastmechanismofnucleardechanneling.Thecrystalbendprovides theangularunfoldingofthedechannelingprocess.Thefirst mea-surementofthe nucleardechanneling length was realized inthe experiment[5]using a 2mm long siliconcrystalbent along the

(110) planes with a bend radius R

=

40 m for 400 GeV

/

c

pro-tons.Themeasurednucleardechannelinglengthwasabout1.5mm whichismore than100times smallerthanthe electron dechan-nelinglengthforthisenergyofprotons.

It should be notedthat forthe planar channeling ofnegative particles nuclear multiple scattering is the main mechanism of dechannelingbecausealltheparticles oscillatearoundthecrystal planes.The dechanneling length for 150GeV

/

c

π

− mesons was measuredintheexperiment[6].Itsvalue,Sn

≈

1 mm,isthesame orderofmagnitudeasthenucleardechannelinglengthforpositive particleswiththesameenergy.

Fig. 1showstheeffectivepotentialUeff

(

x

,

R

)

inthesilicon crys-talbent along the (110)planes withthe radius R

=

10

.

26 m for 400GeV

/

c protons.Theinterval oftransverseenergies (Exc

,

Exm), whereExm

=

Ueff

(

0

,

R

)

isthepotentialwelldepth,determinesthe particlefraction undergoing dechanneling dueto strong multiple scattering by the crystal nuclei. One would expect that dechan-nelingshouldbe fasterforparticles whentheirtransverseenergy isclosertothe well depth Exm.Thenumber ofsuchnear-barrier particlesshouldincreasewithanincreaseofthebeamorientation anglerelativetotheplanesatthecrystalentrance.

In thispaper, the results of the experiment atthe CERN SPS on the deflection of 400 GeV

/

c protons by a short bent silicon crystalareconsidered.Theanalysisofdifferentbeamfractionsfor thecrystalorientationoptimalforchannelingallowstoobservethe reductionofthe nucleardechanneling length withan increaseof theorientation angleof the considered beamfraction relative to theplanesatthecrystalentrance.

Fig. 1. (Coloronline.) TheeffectivepotentialUeff(x,R)inthebentsiliconcrystalfor

400GeV/c protonsasafunctionofarelativecoordinatex/dp,wheredp=1.92 Å

isthedistancebetweentwoplanes.Thecrystalisbentalongthe(110)planeswith theradiusR=10.26 m.HereExmisthemaximaltransverseenergyforchanneled

particles,Exm=Ueff(0,R)isthepotentialwelldepth,Excisthecriticaltransverse

energyforstablechanneling,Exc=Ueff(x=2.5u1).Theinterval(Exc,Exm)

deter-minestherangewheredechannelingofparticlesoccursduetomultiplescattering bytheatomicnucleiofthecrystal.

Fig. 2. (Color online.) The intensity distribution of 400GeV/c protons passed throughthebentsiliconcrystalwhenitsorientationisoptimalforchannelingin thedeflectionanglesθxasafunctionofincidenceangleθinofparticlesrelativeto

the(110)planesatthecrystalentrance.

The experimental setup was the same described in [7]. Four microstripsilicondetectors,twoupstreamandtwodownstreamof the crystal, were used to detect the particle trajectories withan angularresolutionof3μrad,whichislimitedbythemultiple scat-teringofparticlesinthedetectorsandair.A70

×

1

.

94

×

0

.

5 mm3 silicon strip crystal with the largest faces parallel to the (110) crystallographicplaneswasfabricated accordingtothe methodol-ogydescribed in[8,9].The strip-crystalwas bentalong itslength andplacedvertically,sothattheinducedanticlasticbendingalong the crystal width was used to deflect particles in the horizon-tal plane (see Fig. 2b in [7]). The beam of 400 GeV

/

c protons hadthe RMS value of the horizontalangular divergence of

σ

x

=

(

9

.

34

±

0

.

06

)

μrad.Ahighprecisiongoniometer,withan accuracy of2μrad,wasusedtoorientthe(110)crystalplanesparalleltothe

beamdirection. An angular scan was performedandthe optimal

orientationwasfound,whichgivesthemaximumofthedeflected beamfraction.

Fig. 2 shows the intensity distribution of 400 GeV

/

c protons passed through the bent silicon crystal when its orientation is optimal for channeling in the deflection angles

θ

x as a function of incidence angle

θ

in of particles relative to the (110) plane at

442 W. Scandale et al. / Physics Letters B 743 (2015) 440–443

the crystal entrance. The beam divergence value allows to

ob-servethedifferentinteractionmechanismswiththecrystalforthe different beam fractions. The fraction 1 consists of the particles

passed through the crystal which experienced the same

multi-plescatteringasintheamorphoussubstance.Theparticleswhich passedthefulllengthofthecrystalinthechannelingregime and deflected by the bend angle represent the fraction 2. The frac-tion 3 consists of the particles deflected to the side opposite to thecrystalbendduetovolumereflection. Thedechanneled parti-cles,which are found in the angular interval betweenthe initial direction and that of the channeled fraction, represent the frac-tion 4.

Letusconsiderthe differentbeamfractionswiththe incident angles

θ

in

± θ

in, where

θ

in

=

1

.

75 μrad. Fig. 3a showsthe de-flection angle distribution of protons for the optimal casewhen

θ

in

=

0. The peak on the right consists of the particles passed throughthewholecrystalinthechannelingregime. Thepeakhas a well visiblecentral partbecause the consideredfraction ofthe incidentbeamconsistsofparticleswithalltransverseenergies sat-isfyingthechannelingconditionsincludingthesmallestones.The maximumofthepeak isatanangle

θ

ch

=

189 μrad andits posi-tioncorrespondstothecrystalbendangle

θ

ch

=

α

.Thepartof par-ticlesdeflectedbytheangleslargerthan

θ

ch

−

3

σ

ch(theboundary isshownbythedot–dashedline),where

σ

ch istheRMSdeviation ofaGaussian fitofthepeak, determinesthedeflection (channel-ing)efficiency,itis Pch

=

77%. Thepeak onthe leftis formedby theparticles,whichwerenotcapturedintothechannelingregime. The peak is shifted to the side opposite to the crystal bend by theangle of

θ

VR dueto volumereflection. The peak boundary at

θ

VR

+

3

σ

VR, where

σ

VR is the RMS deviation ofa Gaussian fit of thispeak,isshownbythedot-dashedline.

Theparticleswithdeflectionangleswithintheangularinterval indicated in Fig. 3 by two dot-dashed lines are the dechanneled ones Ndc.The particle deflectionangle isdetermined by the dis-tance S passed in the channeling regime,

θ

xs

=

S

/

R. The total

number of particles in the channeling peak and the

dechannel-ingregionrepresentsthoseparticlescapturedintothechanneling regimeatthecrystalentrance Nch

(

0

)

.Thedechanneling probabil-ity is defined as the ratio Pdc

=

Ndc

/

Nch

(

0

)

. For the case under consideration, Pdc

=

7.2%.The solid lineshowsan exponentialfit ofthe centraldechanneling region,which givesthedechanneling lengthvalue,Sn

=

1

.

38

±

0

.

24 mm.

Fig. 3bshowsthedistributionofdeflectionanglesforthebeam fractionwithan incident angle

θ

in

=

8

.

75 μrad, which iscloseto the critical channeling angle,

θ

cb

(

R

)

=

9

.

8 μrad, for the consid-ered bend radius R. In this case, the channeling peak is addi-tionallyshifted because ofthe angle

θ

in relative to theplanes at

the crystal entrance. The upper part of the peak becomes more

flat because the number of particles with small oscillation am-plitudesdecreases (thesimulationsactuallyshow thetwo-headed peak, whichisalso justvisiblehere).The dechanneling probabil-itybecomessignificantlyhigher,Pdc

=

23

.

5% andthedechanneling lengthbecomessmaller,Sn

=

0

.

81

±

0

.

09 mm.

Fig. 4 shows the experimental dependence of the dechan-neling probability of 400 GeV

/

c protons on the incident angle of the beam fraction

θ

in. The dechanneling probability increases monotonouslywithincreasing

θ

in.The dependencebecomes close tolinearforlargeorientationangles.Fig. 5showsthedependence of the dechanneling length of protons on the incident angle

θ

in. The dechanneling length decreases approximately by a factor of twointheangularrangeconsidered.

Simulationoftheprotonbeampassagethroughthebentsilicon crystalforthe conditionsofthe considered experimenthasbeen carried out using theCRYD model suggested in[10]. The proton trajectorieswere foundby numericalsolutionoftheequations of

Fig. 3. (Coloronline.) Thedistributionsofdeflectionanglesfor400GeV/c protonsin thesiliconcrystalbentalong(110)planesforthebeamfractionswiththeincident anglesθin± θin,whereθin=1.75 μrad.(a)for θin=0,(b)forθin=8.75 μrad.

Thechannelingpeakisontheright.Thedistributionofdechanneledparticlesis lo-catedbetweentwodot-dashedlines.Thesolidlineshowstheexponentialfit,which determinesthedechannelinglength.

Fig. 4. (Coloronline.) Theexperimentaldependenceofthedechannelingprobability of400GeV/c protonsinthebentsiliconcrystalontheincidentangleofthebeam fractionθin(filledcircles).Thesimulationresultsareshownbytheemptycircles

anddot-dashedline.

motion in the effective bent planar potential. The change of the transverse velocityofa particledueto multiplescatteringonthe crystalelectronsandnucleiwascalculatedusingtherealistic dis-tributionsofelectronsandnucleiineachstepalongthetrajectory, whichwasmuchsmallerthanthespatialperiodoftheparticle os-cillationsintheplanarchannels.Thecalculateddependenceofthe dechannelingprobabilityisshownbythedot-dashedlineinFig. 4.

W. Scandale et al. / Physics Letters B 743 (2015) 440–443 443

Fig. 5. (Coloronline.) Thedependence ofthe dechannelinglengthof400GeV/c protonsinthebentsiliconcrystalontheincidentangleofthebeamfractionθin.

Fig. 6. (Coloronline.) Thecalculatedparticledistributionsinthetransverseenergy Ex atthecrystalentrance (1)and exit(2)forthedifferentbeam fractionswith

theincidentanglesθin± θin,whereθin=1.75 μrad.(a)forθin=0,(b)forθin=

8.75 μrad.

The dependence is in good agreement with the experiment, the

discrepancyisnotlargerthan10%.

Fig. 6shows thecalculated particledistributions in the trans-verse energy Ex at the crystalentrance (1) and exit (2) for the sameangles of thebeam fractionorientation as inFig. 3.In the case of

θ

in

=

0 (Fig. 6a) the distribution has a large peak near Ex

=

0 and two small peaks for the transverse energies corre-sponding to the effective potential values at the channel walls

where its changes are minimal. Two dot-dashed lines show the

rangeoftransverseenergies at which particlescan enterthe

nu-clearcorridorof thechannels. The initial distributionofparticles in this range of nuclear dechanneling is approximately uniform. Inthe caseof

θ

in

=

8

.

75 μrad theinitialdistribution in Ex is sig-nificantly wider. The distribution maximum is near Ex, which is close tothe potential well depthof the planar channel. The dis-tribution of particles inthe nuclear dechanneling range of Ex is stronglynon-uniform.Theparticledensitywiththetransverse en-ergiesclosetothepotentialwelldepthvalueismaximal.

Simulation for protons with transverse energies from narrow layers withthe widthof1eVwas madetoestimate the dechan-nelingrateofparticleswithdifferentEx fromthenuclear dechan-neling range (Exc

,

Exm). The dechanneling lengthsfor Ex

=

15 eV and18eV,whichcorrespondtothemiddleandtheupperpartof the nucleardechanneling range,were foundto be Sn

=

1

.

49 mm and0.61mm,respectively.Thelastvalueisclosetothe dechannel-inglengthobservedintheexperimentforthebeamfractionwith thelargeincidentangle,

θ

in

=

10

.

5 μrad.

Thus, when the beam fraction enters the crystal at an angle relativetotheplanesclosetothecriticalone,thepopulationofthe upperpartofthenucleardechannelingrangeismaximalandonly thoseparticlesdetermine thedechannelinglengthvalueobserved intheexperiment.Thedistributionsofparticletransverseenergies atthecrystalexitclearlyshowthatdechannelingoccursonlyfrom thenuclearcorridorrange.

The experiment showedthat thedechanneling probability in-creases with an increase of the incident angle of particles rela-tive tothe planeswhichcan be explainedby theincrease ofthe particle population in the whole range of nuclear dechanneling. Moreover, the observation of the dechanneling length reduction providesevidence ofan increaseoftheparticlepopulation atthe toppartofthisnucleardechannelingrange.Itisimportanttotake thesechangesofdechannelinglengthforprotonsintoaccountfor experimentsonthecolliderbeamhalocollimationwithusingbent crystals.

Acknowledgements

WewishtoacknowledgethestrongsupportoftheCERNEN-STI

andBE-AOP groups. We alsoacknowledge the partialsupport by

theRussianFoundationforBasicResearchGrants05-02-17622and 06-02-16912, the RF President Foundation Grant SS-3383.2010.2, theLHCProgramofPresidiumofRussianAcademyofSciencesand

the grant RFBR-CERN 12-02-91532. G. Cavoto, F. Iacoangeli and

R. Santacesaria acknowledge the support fromMIUR (grantFIRB

RBFR085M0L_001/I11J10000090001).S.Dabagovacknowledgesthe

support by the Ministryof Educationand Scienceof the Russian

Federation in the framesof Competitiveness Growth Program of

NRNUMEPhI, Agreement 02.A03.21.0005.Work supported by the

EuCARD program GA 227579, within the “Collimators and

Mate-rialsforhighpower beams”work package (Colmat-WP).The

Im-perialCollegegroup gratefullyacknowledgessupportfromtheUK ScienceandTechnologyFacilitiesCouncil.

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