High-accuracy determination of the neutron flux in the new experimental area n_TOF-EAR2 at CERN

Eu . Phys. J. A (2017) 53:X THE EUROPEAN PHYSICAL JOURNAL A epja104154 Please ca e ully ead he P oduc ion que ies a he end o he documen High-accu acy de e mina ion o he neu on flux in he new expe imen al a ea n TOF-EAR2 a CERN M. Saba ´e-Gila e1,2, M. Ba bagallo3,a, N. Colonna3,F.Gunsing 4,P.ˇ Zugec5, V. Vlachoudis1, Y.H. Chen6, A. S ama opoulos7, J. Le endegui-Ma co2, M.A. Co ´es-Gi aldo2, A. Villaco a8, C. Gue e o2, L. Damone3, L. Audouin6, E. Be houmieux4, L. Cosen ino9, M. Diakaki4, P. Finocchia o9,A.Musuma a 9,10, T. Papae angelou4, M. Piscopo9, L. Tassan-Go 6,O.Abe le 1, J. And zejewski11,V.B´eca es12, M. Bacak1,13, R. Baccomi14, J. Balib ea12, S. Ba os15,F.Beˇc ´aˇ 16, C. Bein ucke 17, F. Belloni3,J.Billowes 18,D.Bosna 5,M.B ugge 1, M. Caama˜no19, F. Cal i˜no20, M. Cal iani1, D. Cano-O 12, R. Ca della1, A. Casano as20, D.M. Cas elluccio21,22, F. Ce u i1, E. Chia e i1, G. Co ´es21,K.Deo 19, C. Domingo-Pa do23, R. D essle 24, E. Dupon 4, I. Du ´an19,B.Fe n´andez- Dom´ınguez19, A. Fe a i1, P. Fe ei a15, R.J.W. F os 18, V. Fu man25,K.G¨obel17,A.R.Ga c´ıa12, A. Gawlik11, I. Gheo ghe26,T.Gloda iu 26, I.F. Gon¸cal es15,E.Gonz´alez12,A.Go e do ski 27,E.G iesmaye 13,H.Ha ada 28, T. He ich17,S.Heini z 24,A.He n´andez-P ie o1,20,J.Heyse 29, D.G. Jenkins30, E. Je icha13,F.K¨appele 31, Y. Kadi1, T. Ka abuchi32, P. Ka igin13,V.Ke le o 27, V. Kh yachko 27,A.Kimu a 28,N.Ki el 24,M.Kokko is 7, M. K iˇcka16, E. Leal-Cidoncha19, C. Lede e 33, H. Leeb13, M. Lica a22,34,S.LoMeo 21,22, S.J. Lonsdale33, R. Losi o1, D. Macina1, J. Ma ganiec11,T.Ma ´ınez12, C. Massimi22,34, P. Mas inu35, M. Mas oma co3, F. Ma eucci14,36, E.A. Mauge i24, E. Mendoza12,A.Mengoni 21, P.M. Milazzo14, F. Ming one22,1,M.Mi ea 26, S. Mon esano1, R. Nol e37, A. Op ea26, F.R. Palomo-Pin o38,C.Pa adela 19, N. Pa onis39, A. Pa lik40,J.Pe kowski 11, J.I. Po as41, J. P aena2,41, J.M. Quesada2,K.Rajee 42, T. Rausche 43,44,R.Rei a h 17, A. Riego-Pe ez20, M.S. Robles19, P.C. Rou 42, C. Rubbia1,J.A.Ryan 18, A. Saxena42, P. Schillebeeckx29, S. Schmid 17, D. Schumann24, P. Sedyshe 25, A.G. Smi h18, S.V. Su yana ayana42, G. Taglien e3, J.L. Tain23,A.Ta i e˜no-Saldi ia20,23, A. Tsinganis7, S. Valen a16, G. Vannini22,34, V. Va iale3,P.Vaz 15,A.Ven u a 22, R. Vlas ou7, A. Wallne 45, S. Wa en18, M. Weigand17, C. Wol 17, P.J. Woods33,C.Weiss 1,13, and T. W igh 18 1Eu opean O ganiza ion o Nuclea Resea ch (CERN), Gene a, Swi ze land 2Depa amen o de F´ısica A ´omica, Molecula y Nuclea , Uni e sidad de Se illa, Se illa, Spain 3Is i u o Nazionale di Fisica Nuclea e, Sezione di Ba i, V. O abona 4, 70125 Ba i, I aly 4CEA I u, Uni e si ´e Pa is-Saclay, F-91191 Gi -su -Y e e, F ance 5Depa men o Physics, Facul y o Science, Uni e si y o Zag eb, Zag eb, C oa ia 6Cen e Na ional de la Reche che Scien ifique/IN2P3 - IPN, O say, F ance 7Na ional Technical Uni e si y o A hens (NTUA), A hens, G eece 8Uni e si y o Salamanca, Salamanca, Spain 9INFN Labo a o i Nazionali del Sud, Ca ania, I aly 10 Dipa imen o di Fisica, Uni e si `a di Ca ania, Ca ania, I aly 11 Uni e si y o Lodz, Lodz, Poland 12 Cen o de In es igaciones Ene g´e icas Medioambien ales y Tecnol´ogicas (CIEMAT), Mad id, Spain 13 Technische Uni e si ¨a Wien, Wien, Aus ia 14 Is i u o Nazionale di Fisica Nuclea e, Sezione di T ies e, T ies e, I aly 15 Ins i u o Supe io T´ecnico, Lisbon, Po ugal 16 Cha les Uni e si y, P ague, Czech Republic 17 Goe he Uni e si y F ank u , F ank u , Ge many 18 Uni e si y o Manches e , Manches e , UK 19 Uni e si y o San iago de Compos ela, San iago de Compos ela, Spain 20 Uni e si a Poli `ecnica de Ca alunya, Ba celona, Spain 21 Agenzia nazionale pe le nuo e ecnologie (ENEA), Bologna, I aly 22 Is i u o Nazionale di Fisica Nuclea e, Sezione di Bologna, Bologna, I aly 23 Ins i u o de F´ısica Co puscula , Uni e sidad de Valencia, Valencia, Spain 24 Paul Sche e Ins i u (PSI), Villingen, Swi ze land 25 Join Ins i u e o Nuclea Resea ch (JINR), Dubna, Russia 26 Ho ia Hulubei Na ional Ins i u e o Physics and Nuclea Enginee ing, M˘agu ele, Romania 27 Ins i u e o Physics and Powe Enginee ing (IPPE), Obninsk, Russia 28 Japan A omic Ene gy Agency (JAEA), Tokai-mu a, Japan Page 2 o 13 Eu . Phys. J. A (2017) unline o be inse ed 29 Eu opean Commission, Join Resea ch Cen e, Geel, Re ieseweg 111, B-2440 Geel, Belgium 30 Uni e si y o Yo k, Yo k, UK 31 Ka ls uhe Ins i u e o Technology, Campus No h, IKP, 76021 Ka ls uhe, Ge many 32 Tokyo Ins i u e o Technology, Tokyo, Japan 33 School o Physics and As onomy, Uni e si y o Edinbu gh, Edinbu gh, UK 34 Dipa imen o di Fisica e As onomia, Uni e si `a di Bologna, Bologna, I aly 35 Is i u o Nazionale di Fisica Nuclea e, Sezione di Legna o, Legna o, I aly 36 Dipa imen o di As onomia, Uni e si `a di T ies e, T ies e, I aly 37 Physikalisch-Technische Bundesans al (PTB), Bundesallee 100, 38116 B aunschweig, Ge many 38 Dep o. Ingenie ´ıa Elec ´onica, Escuela T´ecnica Supe io de Ingenie os, Uni e sidad de Se illa, Se illa, Spain 39 Uni e si y o Ioannina, Ioannina, G eece 40 Uni e si y o Vienna, Facul y o Physics, Vienna, Aus ia 41 Uni e si y o G anada, G anada, Spain 42 Bhabha A omic Resea ch Cen e (BARC), Mumbai, India 43 Cen e o As ophysics Resea ch, Uni e si y o He o dshi e, Ha field, UK 44 Depa men o Physics, Uni e si y o Basel, Basel, Swi ze land 45 Aus alian Na ional Uni e si y, Canbe a, Aus alia Recei ed: 30 June 2017 / Re ised: 31 Augus 2017 c Socie `a I aliana di Fisica / Sp inge -Ve lag 2017 Communica ed by T. Mo obayashi Abs ac . A new high flux expe imen al a ea has ecen ly become ope a ional a he n TOF acili y a CERN. This new measu ing s a ion, n TOF-EAR2, is placed a he end o a e ical beam line a a dis ance o app oxima ely 20 m om he spalla ion a ge . The cha ac e iza ion o he neu on beam, in e ms o flux, spa ial p ofile and esolu ion unc ion, is o c ucial impo ance o he easibili y s udy and da a analysis o all measu emen s o be pe o med in he new a ea. In his pape , he measu emen o he neu on flux, pe o med wi h diffe en solid-s a e and gaseous de ec ion sys ems, and using h ee neu on- con e ing eac ions conside ed s anda d in diffe en ene gy egions is epo ed. The esul s o he a ious measu emen s ha e been combined, yielding an e alua ed neu on ene gy dis ibu ion in a wide ene gy ange, om 2 meV o 100 MeV, wi h an accu acy anging om 2%, a low ene gy, o 6% in he high-ene gy egion. In addi ion, an absolu e no maliza ion o he n TOF-EAR2 neu on flux has been ob ained by means o an ac i a ion measu emen pe o med wi h 197Au oils in he beam. 1 In oduc ion The neu on ime-o -fligh acili y n TOF1, ope a ional since 2001 a he Eu opean O ganiza ion o Nuclea Re- sea ch (CERN), is cha ac e ised by a high-in ensi y, high- esolu ion, wide spec um neu on beam mos ly dedica ed o measu emen s o neu on-induced c oss sec ions o in- e es in nuclea echnology [1,2], as ophysics [3,4] and mo e ecen ly o medical applica ions [5,6]. The neu on beam is p oduced by spalla ion o a pulsed p o on beam om he CERN P o on Synch o on accele a o (PS), wi h momen um o 20 GeV/c, impinging on a cylind ical lead a ge su ounded by wa e o cooling and neu on mode a ion pu poses. The neu on beam cha ac e is ics and s a e-o - he-a de ec o s and acquisi ion sys ems make n TOF ideal o measu ing adioiso opes, in pa icula , ac inides, as well as o iden i ying and s udying esonances in neu on c oss sec ions. Fo he fi s 13 yea s o ope a ion, only one ex- pe imen al a ea was a ailable, loca ed a 185 m om he spalla ion a ge along he ho izon al di ec ion. In his a ea, now deno ed as n TOF-EAR1 (he ea e EAR1, Ex- pe imen al A ea 1), he neu on beam is cha ac e ised by a high ins an aneous flux o 106neu ons/bunch, co e ing he ene gy ange om 25 meV o o e 1 GeV, and a neu- on ene gy esolu ion in a la ge pa o he ene gy ange o ΔE/E om 10−3 o 10−4. A mo e de ailed desc ip ion o he neu on beam ea u es in EAR1 can be ound in e . [7]. In 2014, a new expe imen al hall loca ed on he e - ical di ec ion a 20 m dis ance om he spalla ion a - ge , he so-called n TOF-EAR2 [8,9] (he ea e EAR2, Expe imen al A ea 2), was comple ed and became ope a- ional. The main ad an age o his new measu ing s a ion wi h espec o he exis ing one consis s in a flux on a - e age 40 imes highe han in EAR1, a con enien ea u e ha makes i possible o pe o m challenging new mea- su emen s. Combined wi h he sho e ime-o -fligh a a gi en ene gy, 10 imes lowe han EAR1 due o he sho e fligh -pa h, he highe flux esul s in mo e han wo o - de s o magni ude highe signal- o-backg ound a io, when conside ing he backg ound ela ed o he na u al adio- ae-mail: [email p o ec ed] 1www.ce n.ch/n o . Eu . Phys. J. A (2017) unline o be inse ed Page 3 o 13 ac i i y o uns able iso opes, which ep esen s he domi- nan componen o sho -li ed adionuclides. These ea- u es o he EAR2 neu on beam open he way o measu e- men s o neu on-induced eac ions on e y hin samples, adioac i e iso opes wi h sho hal -li e o eac ions o low c oss sec ions [10]. Following he comple ion o he second expe imen al a ea, a la ge effo was de o ed o he commissioning o he new neu on beam, wi h a se ies o dedica ed mea- su emen s pe o med wi h he aim o cha ac e izing i in e ms o flux and i s ene gy dependence, spa ial beam p ofile, esolu ion unc ion and backg ound. An accu a e knowledge o all hese quan i ies is in ac undamen al o he en isaged as expe imen al p og am in EAR2 on neu on-induced eac ion c oss sec ions o undamen al and applied nuclea physics. In his wo k we epo on dedica ed measu emen s o he neu on flux, ca ied ou as pa o he commission- ing o he new expe imen al a ea. To de e mine he flux wi h high accu acy in a wide ene gy ange, om 2 meV o 100 MeV, a combina ion o se e al de ec ion sys ems and neu on con e ing eac ions, conside ed s anda ds, we e used. In his way, he sys ema ic unce ain ies e- la ed o he expe imen al echnique we e minimised. The campaign ex ended o e wo unning pe iods, wi h some measu emen s epea ed wi h diffe en samples o a highe accu acy. This pape is o ganized as ollows: in sec . 2 he expe i- men al se ups a e desc ibed, while in sec . 3 he p ocedu e used in he da a analysis is discussed. The final esul s a e p esen ed in sec . 4. 2 The expe imen al se up o neu on flux de e mina ion a n TOF The ime-o -fligh echnique (TOF) is used o de e mine he kine ic ene gy o neu ons (En) om he spalla ion p ocess by he fligh ime be ween he p oduc ion poin and he de ec ion sys em. The neu on beam in a TOF acili y is cha ac e ised by he neu on fluence (FE)and he neu on flux (Φ(En)) spec a ha , acco ding o he ICRU ecommenda ions [11], a e defined as FE=dNE d ·daand Φ(En)=dNE d .(1) dNEdeno es he densi y dis ibu ion o neu ons eaching he sample wi h ene gy be ween Enand En+dEn,d he ime elemen and da he c oss-sec ional a ea o an elemen al sphe e. Ne e heless, when alking abou TOF acili ies he e m flux is used o designa e wha in he ICRU epo is e med fluence a e ( ime-diffe en ial). The e o e, Φ(En) will be he ea e defined as he numbe o neu ons each- ing he sample by elemen o ene gy, a ea and ime. A nTOF, whe e he spa ial p ofile o he neu on beam is no uni o m and neu ons a e deli e ed in bunches a e y low epe i ion a e (<0.8 Hz), i is mo e con enien o Table 1. Neu on induced eac ions used in his wo k o cha - ac e ise he neu on flux in EAR2 a n TOF, and he ene gy ange in which he espec i e c oss sec ions a e conside ed s an- da d. The las eac ion is impo an o ob ain he absolu e alue o he flux by means o an ac i a ion measu emen . Reac ion S anda d ene gy ange 6Li(n, ) 0.0253 eV o 1 MeV 10B(n, α) 0.0253 eV o 1 MeV 235U(n, ) 0.0253 eV and 0.15–200 MeV 197Au(n, γ) 0.0253 eV and 0.2–2.5 MeV conside he o al numbe o neu ons in a bunch in e- g a ed o e he whole beam spa ial p ofile [12]. This mag- ni ude can be only ob ained expe imen ally om FEas a disc e e unc ion by summing-up all he neu on-induced eac ions ha ha e been de ec ed o a e e ence sample in sequen ial fini e ime-slo s (o his og am bins) inside he neu on spills. The knowledge o his quan i y, i.e. he o al numbe o neu ons impinging on he sample in he whole measu emen , is undamen al o he de e mina ion o he eac ion c oss sec ion. The neu on flux is measu ed by means o neu on in- duced eac ions whose c oss sec ions a e smoo h, la ge and accu a ely known in specific ene gy egions, and o his eason gene ally adop ed as s anda d [13,14]. In able 1 he h ee eac ions used in his wo k a e lis ed oge he wi h he c oss sec ion used as a e e ence o he ac i a ion measu emen . The wide ene gy ange o he n TOF neu on beam makes i manda o y o use diffe en s anda ds, co e ing he ull ene gy ange. Fu - he mo e, he combina ion o a ious de ec ion sys ems based on diffe en wo king p inciples allows minimising possible sou ces o unce ain ies such as, o example, he de ec ion efficiency. The ollowing de ec o s ha e been used o he cha ac- e iza ion o he EAR2 neu on flux in wo campaigns. 1) A low-mass Silicon Moni o , SiMon2 [15], simila o he one used in he fi s expe imen al a ea and desc ibed in e . [16]. Apa om he flux measu emen , i is pe - manen ly ins alled in he neu on beam o con inuously moni o he flux and o p o ide he fluence in any mea- su emen . I consis s o a se o ou silicon pad de ec o s loca ed ou side he beam, su ounding a oil wi h a deposi o 6LiF. The sys em is ope a ed inside a acuum chambe . The whole se up is placed a he en ance o EAR2, a a sho dis ance om he las collima o . The silicon de ec- o s, om Mic on Semiconduc o s (MSX09-300), ha e a su ace o 3 ×3cm 2and a hickness o 300 μm. These di- mensions we e selec ed as a comp omise be ween a high efficiency and low capaci ance, o ensu e a low-noise ope - a ion wi h s anda d p eamplifie s. The ene gy esolu ion o he de ec o s esul s in a pe ec sepa a ion be ween i ons and α-pa icles emi ed in he 6Li(n, )α eac ion, and a good ejec ion o he elec onic noise and o he gamma backg ound. Two diffe en samples wi h 6LiF de- posi we e used o he flux measu emen in EAR2: he fi s one, wi h an a eal densi y o 420 μg/cm2, was used Page 4 o 13 Eu . Phys. J. A (2017) unline o be inse ed only o he high-ene gy egion, as i was affec ed by pile- up p oblems a ene gies below 1 eV, whe e bo h he flux and he c oss sec ion a e high. A hinne 105 μg/cm2 hick deposi was la e used in o de o ex end he measu emen down o he meV neu on ene gy egion. 2) A gaseous de ec o , based on he Mic oMegas mic o- bulk echnology [17–19]. This ype o de ec o s is being used a n TOF since many yea s o a ious pu poses, due o hei high signal- o-backg ound a io, high adia ion e- sis ance and low mass, which minimises pe u ba ion o he neu on beam. A Mic omegas is defined by wo gas olumes: he d i olume, ypically o a ew millime e hickness, and he amplifica ion egion, 50 μm, sepa a ed by a 5 μm mic o-mesh laye . The neu on-con e ing ma- e ial is deposi ed on he ca hode, in he d i egion, de- limi ed by he ca hode and he mesh. In his egion he ioniza ion om he cha ged p oduc s o he neu on e- ac ions akes place. The seconda y elec ons d i h ough he elec ic field, ∼1kV/cm, o he mesh. Due o he high elec ic field in he second gap, ≥10 kV/cm, an a alanche mul iplica ion o he p ima y elec ons akes place. Two diffe en de ec o geome ies we e implemen ed. In he fi s one, he ea e e e ed o as MGAS, elec odes 9.5 cm in diame e we e used equipped wi h deposi s o 93 μg/cm2en iched 235U and wi h 20 nm- hick deposi o 10B4C, on 30 and 18 μm- hick aluminium backings espec- i ely. The en ance and exi windows o he aluminium chambe which con ains he se up we e made o 25 μm- hick kap on oils. The second chambe , e e ed o as monMGAS, con ains elec odes 6 cm in diame e and alu- minized myla windows; i was loaded wi h a 281 μg/cm2- hick deposi o 235U wi h an en ichmen o 99.9% on a 30 μm hick aluminium oil. In bo h cases, he chambe was filled wi h a mix u e o 88% A , 10% CF4and 2% iC4H10 a a mosphe ic p essu e. 3) Finally, a se o posi ion-sensi i e Pa allel Pla e A alanche Coun e s (PPAC [20,21]) equipped wi h a 70 μg/cm2 hick 235U deposi on an aluminium backing o 0.7 μm hickness we e employed. The de ec o s a e moun ed on bo h sides o he deposi o de ec fission agmen s in coincidence, a echnique ha esul s in a e y low backg ound om α-pa icles om he na u al adioac i i y o he sample, and allows one o econs uc he neu on in e ac ion posi ion. Each PPAC consis s o a cen al anode, o iming, flanked by wo posi ion-sensi i e ca hodes. Th ee PPACs wo king a low gas p essu e we e de eloped in o de o measu e he flux and he beam p o- file. The de ec o s we e hos ed in a chambe specifically designed o ope a ion in EAR2. The fission agmen s a e iden ified by a coincidence window o 20 ns. Mo e de ails on he de ec o s and on he analysis p ocedu e can be ound in e s. [22,23]. In fig. 1 he wo adop ed expe imen al se ups a e p e- sen ed. The ull wa e o ms o de ec o signals we e acqui ed by he s anda d n TOF Da a Acquisi ion Sys em, based on SPDe ices ADQ412DC-3G ca ds o 2 GS/s maximum sampling a e, 12 bi s esolu ion and 175 MBy es on-boa d memo y. The special ea u es o hese ca ds ensu e he col- lec ion o da a o a ime-o -fligh co esponding o neu- Fig. 1. Scheme o he expe imen al se up when mic omegas (le ) and PPAC ( igh ) we e used o measu e he neu on flux. The SiMon2 chambe was always in place, loca ed a 18.42 m om he spalla ion a ge . The fligh pa hs o each neu on con e e wi h espec o he spalla ion a ge a e also indi- ca ed. on ene gies well below he he mal ene gy. The signals om SiMon2 and mic omegas de ec o s a e econs uc ed by means o a Pulse Shape Analysis ou ine desc ibed in [24], while in he case o PPAC a dedica ed ou ine was used. In all cases, in o ma ion was ex ac ed on he ampli ude, a ea, iming and o he pe inen quan i ies o he signals. Toge he wi h hese de ec ion sys ems, wo ci cula gold oils we e also exposed o he beam in o de o de e - mine he absolu e alue o he neu on flux by ac i a ion. The wo oils, placed back- o-back and co e ing ully he beam spo , we e 100 μm hick. 3 Da a analysis The eac ion yield ep esen s he p obabili y o a neu on o unde go ha eac ion inside he sample. Fo hin a - ge s, whe e he sca e ing in he deposi is negligible, he heo e ical yield is defined by Y h(En)=1−e−n·σ (En)·σ (En) σ (En),(2) whe e nis he a eal densi y (a oms/ba n) o he a ge deposi , σ and σ a e, espec i ely, he eac ion and o al c oss sec ions o he iso ope used as neu on con e e . In his wo k, he e alua ed c oss sec ions om he ENDF- /B-VII.1 lib a y [25] we e used o all he samples up o 20 MeV, while he IAEA e e ence file o he 235U(n, ) c oss sec ion was adop ed abo e his ene gy [14]. Expe i- men ally, he yield is Yexp(En)=C(En)−B(En) ε(En)·Φ(En).(3) Eu . Phys. J. A (2017) unline o be inse ed Page 5 o 13 The expe imen al alue inside an ene gy bin is he in e- g al o he de ec ed e en s (coun s), di ided by he bin- wid h, and his alue is assigned o he bin-cen e in he his og am. Taking his in o accoun , in eq. (3), C(En) ep esen s he o al eco ded numbe o coun s pe bunch and B(En) he backg ound con ibu ion in he bin cen- e ed a En, while ε(En) is he efficiency o de ec ing he p oduc o he neu on in e ac ion. This ac o includes he geome ical efficiency, he angula dis ibu ion and he kinema ic effec s o a gi en eac ion. The unce ain y o he ene gy dependence o he neu on flux depends on all quan i ies ha a e a unc ions o he neu on ene gy, En (such as he efficiency), while he absolu e alue o he flux is affec ed by ene gy-independen ac o s, such as he a eal densi y o he deposi . The ela ionship be ween he heo e ical (2) and he expe imen al (3) eac ion yield p o ides he neu on flux, Φ(En): Φ(En)= C(En)−B(En) ε(En)·1−e−n·σ (En)σ (En) σ (En) .(4) I is con enien o exp ess he neu on flux as he o al numbe o neu ons o a nominal p o on pulse. The e o e, in eq. (4) he backg ound-sub ac ed numbe o coun s eco ded in he whole measu emen is di ided by he o- al numbe o inciden p o ons and mul iplied by 7 ·1012, a alue ha ep esen s he nominal p o on in ensi y o a dedica ed pulse deli e ed by he PS o he n TOF expe - imen . The neu on kine ic ene gy in he equa ions abo e is de e mined om he ime-o -fligh acco ding o he ol- lowing exp ession: En(T)=mn·c2·⎛ ⎝ 1 1−(L+λ(T) c·T)2 −1⎞ ⎠,(5) whe e Tis he calib a ed ime-o -fligh econs uc ed om he signal, c he speed o ligh and mn he neu on mass. The ime-o -fligh is de e mined ela i e ei he om a pick-up signal o om he signal o he so-called γ-flash, gene a ed in he de ec o by he p omp γ- ays and ela- i is ic pa icles p oduced in he spalla ion p ocess. The quan i y λ(T) eflec s he esolu ion unc ion o he n TOF neu on beam, i.e. he sp ead o he ue neu- on ene gy o a gi en ime-o -fligh , o equi alen ly he sp ead in ime-o -fligh o a gi en ue neu on ene gy. Such a sp ead, caused by he s ochas ic mode a ion p o- cess neu ons unde go inside he spalla ion sou ce and mode a ion ci cui , can be exp essed as an addi ional e - ec i e fligh pa h ha neu ons ha e o a el inside he lead a ge and he mode a o sys em be o e en e ing he beam line. This quan i y is no easily accessible expe i- men ally, bu can be de e mined as a unc ion o he neu- on ene gy by means o Mon e Ca lo simula ions o he spalla ion p ocess. S udies o he esolu ion unc ion o he second ex- pe imen al a ea a n TOF ha e been pe o med wi h FLUKA [26,8] and GEANT4 [27,28]. They indica e ha in he ela i ely wide ene gy ange om a ew eV o se e al ens o keV, he a e age alue o λ emains app oxima ely cons an , so ha a fixed alue o he o al effec i e fligh pa h L+λcan be used in eq. (5). On he con a y, be- low 1 eV and abo e 100 keV he esolu ion unc ion shows la ge a ia ions, bo h in e ms o a e age alue and wid h o he λdis ibu ion. I no p ope ly included in he analy- sis, his beha iou would affec he econs uc ed neu on ene gy and, as a consequence, he neu on flux. Fo he fi s expe imen al a ea he effec o he esolu ion unc ion is ela i ely small a low and epi he mal neu on ene gies, being ΔE/E o he o de o 10−3–10−4, hanks o he long fligh pa h o EAR1 (200 m). Fo his eason, i was no conside ed in he neu on flux de e mina ion, while i is ou inely included in esonance shape analysis, see o example [29]. On he con a y, in EAR2 he effec o he esolu ion unc ion is much la ge , eaching app oxi- ma ely 2% a he mal neu on ene gy, and has he e o e o be aken in o accoun in he flux de e mina ion. The only way o p oceed in his espec is o con olu e he heo e - ical yield o he h ee e e ence eac ions, i.e. 235U(n, ), 6Li(n, )and10B(n, α), wi h he simula ed esolu ion unc- ion, be o e using i in eq. (4). The me hod ollowed in his wo k is based on he e- sampling and p opaga ion o neu ons sco ed on a ally su ace jus abo e he spalla ion a ge . Mo e de ails on he p opaga ion p ocedu e can be ound in [8,28]. Neu- ons on he sco ing plane a e eco ded wi h hei ue en- e gy and ime elapsed since he s a o he spalla ion p o- cess (i.e., hei ime-o -fligh inside he a ge -mode a o assembly). When hey a e anspo ed o he expe imen- al a ea, only he ime-o -fligh is changed acco ding o he geome ical dis ance be ween he sco ing plane and he sample posi ion in EAR2. Fo a gi en e e ence eac- ion, he yield is calcula ed on he basis o he ue neu- on ene gy and co esponding e e ence c oss sec ion, bu assigned o an ene gy bin calcula ed on he basis o he ime-o -fligh . The esul ing dis ibu ion, which akes in o accoun he shi o sp ead in he econs uc ed ene gy ela ed o he esolu ion unc ion, can a his poin be used in eq. (4), ins ead o he poin -wise c oss sec ions, o ex ac he neu on flux. Be o e, howe e , an accu a e alue o he effec i e fligh pa h o be used in he ime- o-ene gy con e sion o he expe imen al da a has o be de e mined. This is done by compa ing he simula ed yield wi h he expe imen al one: he alue o he fligh pa h is adjus ed and he simula ed yield is ecalcula ed in an i - e a i e p ocedu e un il he posi ion o he esonances in ime-o -fligh pe ec ly ma ches he expe imen al ones. In fig. 2, he expec ed yield o 235U(n, ) based on he ENDF da a lib a y and he FLUKA-based esolu ion unc ion is compa ed wi h he final expe imen al yield measu ed wi h monMGAS; he same compa ison was pe o med o MGAS and PPAC. Fo he eac ions ha do no ha e any esonance in he ange o in e es , i.e. o he 10B(n, α) and 6Li(n, ) eac ions, he effec i e fligh pa h is calcu- la ed by simply conside ing, i.e. adding o sub ac ing, he geome ical dis ance be ween he posi ion o he co - esponding samples and he 235U sample. Page 6 o 13 Eu . Phys. J. A (2017) unline o be inse ed Fig. 2. Expe imen al (g een) and calcula ed ( ed) 235U(n, ) eac ion yield in he esol ed esonance egion as a unc ion o he neu on ime-o -fligh . The ag eemen be ween he wo yields, ob ained o a p ope choice o he fligh pa h leng h, demons a es he accu acy o he ime- o-ene gy calib a ion. Fig. 3. Sca e plo o he ene gy deposi ed in a silicon de ec o o he SiMon2 appa a us, e sus he econs uc ed neu on ene gy. The ed line co esponds o he cu applied o sepa a e i ons and α-pa icles om he backg ound and he elec onic noise o he de ec o . 3.1 Analysis o SiMon2 wi h 6Li con e e The use o op imized elec onics, in pa icula o speci - ically designed p eamplifie s, in combina ion wi h he hin deposi esul s in a e y good sepa a ion be ween i ons and α-pa icles om he 6Li(n, )α eac ion, as well as be ween en i onmen al backg ound o elec onic noise o he de ec o . Due o kinema ic effec s, he en- e gy o he eac ion p oduc s inc eases wi h he neu on ene gy. The e o e, he selec ion o i ons and α-pa icles equi es a non-linea cu on he 2D plo o he ene gy deposi ed in he silicon de ec o e sus neu on ene gy. Figu e 3 shows an example o he sca e 2D plo o he ene gy deposi ed by de ec ed pa icles e sus neu on en- e gy o one o he silicon de ec o s, whe e he solid ed line ep esen s he 2-dimensional condi ion used in he analysis. The efficiency o SiMon2 was es ima ed by means o GEANT4 simula ions, on he basis o he geome ical de- Fig. 4. (Top panel) SiMon2 efficiency o he de ec ion o p od- uc s om he 6Li(n, )α eac ion. (Bo om panel) Efficiency o de ec ing he p oduc s o he 10B(n, α)7Li eac ion in he MGAS de ec o . Fig. 5. Spec um o he signal a ea o he 235U(n, ) eac ion measu ed wi h he monMGAS. The wo bumps co espond o he ligh and hea y fission agmen s. The α-pa icles om he na u al adioac i i y o he sample a e elimina ed by he elec onic h eshold indica ed by he ed line. ails desc ibed in e . [15]. As shown in he op panel o fig. 4, he efficiency is cons an below 1 keV (∼9%) while a highe ene gies he o wa d peaked angula dis ibu ion o i ons causes an inc ease o he efficiency. The in insic unce ain y in he angula dis ibu ion o he p oduc s o he 6Li(n, )α eac ion esul s in a ela i ely la ge unce - ain y, o he o de o 9%, on he efficiency and hence o he ex ac ed neu on flux abo e 10 keV. 3.2 Flux de e mina ion wi h 235U con e e In o de o de e mine he flux om he 235U(n, ) eac- ion, h ee complemen a y de ec ion sys ems we e used: MGAS, monMGAS and PPAC. The high Q- alue o he neu on induced fission eac ion on 235U esul s in a good disc imina ion o he fission agmen s om he elec onic noise and he backg ound, due o he α-ac i i y o he u a- nium sample. Fo he monMGAS, he sepa a ion is shown in fig. 5, whe e he ypical double-bump dis ibu ion is Eu . Phys. J. A (2017) unline o be inse ed Page 7 o 13 Fig. 6. Spec um o he signal a ea om he 10B(n, α) eac ion measu ed wi h he MGAS de ec o . The peaks co esponding o he α-pa icles and o 7Li a e well abo e he elec onic noise, which is supp essed by he elec onic h eshold indica ed by he ed line. The ene gy esolu ion o he de ec o does no allow o sepa a e he wo final s a es o he eac ion. also isible. An ene gy-independen cu on he signal am- pli ude is sufficien o ejec he backg ound and selec he fission agmen s. The h eshold is chosen o ensu e maximum efficiency. Due o he p esence o a s ong p omp signal, he so- called γ-flash, mos ly induced by p omp γ- ays p oduced in he spalla ion a ge [7,8], he maximum ene gy ha can be eached wi h he mic omegas de ec o s is o a ew MeV. On he con a y, PPACs a e a he insensi i e o γ- ays. Conside ing also ha PPAC signals a e e y as , he eco e y ime o he de ec o o he γ-flash is almos immedia e (a ew ns). These ea u es bes ow he sys em he possibili y o ex ending he ange o he measu ed flux up o 100 MeV neu on ene gy. Acco ding o Mon e Ca lo simula ions o he se up, he efficiency o mic omegas de ec o s is close o 95% in he ene gy ange up o a ew MeV, while o he PPAC he efficiency is ∼60% up o a ew MeV, and changes abo e his alue due o co ec ions o he angula aniso opy o he agmen emission [22]. As men ioned be o e, he calib a ion o he neu on ene gy, om he ime-o -fligh , is based on he analysis o he esonances in he 235U(n, ) c oss sec ion. 3.3 Analysis o MGAS wi h 10B a ge The 10B(n, α)7Li eac ion was measu ed wi h he MGAS. The ene gy esolu ion o he de ec o u ned ou o be no sufficien o sepa a ing he wo exi channels o he eac ion, i.e. he g ound s a e (6%) and he fi s exci ed s a ed (94%), whose decay o he g ound s a e is accompa- nied by he emission o a 478 keV γ- ay. Ne e heless, bo h eac ion p oduc s a e well sepa a ed om he elec onic noise and he backg ound, as indica ed by he ed line in fig. 6. As in he case o SiMon2, an ene gy-dependen cu has been applied on he deposi ed ene gy o selec he α-pa icles and he 7Li ions abo e 1 keV. The efficiency o he de ec o was es ima ed by means o Mon e Ca lo simula ions o he ene gy loss in he sample and in he gas olume. The angula dis ibu ion o bo h p oduc s, epo ed in e . [30], as well as he effec o he bleed- h ough o 7Li below he h eshold we e aken in o accoun in he efficiency calcula ion. As shown in he bo - om panel o fig. 4, he efficiency emains cons an , ∼98%, up o ew keV when he backwa d/ o wa d aniso opy in he angula dis ibu ion s a s o play an impo an ole. 3.4 Dead ime and o he co ec ions The dead ime is he minimum ime be ween wo consec- u i e e en s ha can be iden ified and sepa a ely econ- s uc ed. Since he ne effec o he dead ime is a educ- ion in he numbe o eco ded e en s, a co ec ion has o be applied in o de o compensa e o he loss o coun s. A nTOF, he use o flash ADCs o da a acquisi ion, com- bined wi h a powe ul pulse shape analysis p ocedu e (see e . [24]) a e educing he effec o he dead ime o a ew pe cen , p o ided ha he sample hickness is p ope ly chosen. The minimum ime diffe ence ha allows iden i- ying wo consecu i e signals is be ween 150 ns and 350 ns, depending on he de ec ion sys em. Ne e heless, consid- e ing he high coun - a e and he need o eaching a high accu acy on he measu ed flux, a co ec ion is necessa y. To his end, consecu i e e en s wi hin a ime window τ we e disca ded; hen he esul ing his og am was subse- quen ly co ec ed o his fixed dead ime τ, assuming he non-pa alyzable model [31] o neu on ime-o -fligh mea- su emen s. Acco ding o his model, when he coun ing losses a e small, he numbe o co ec ed e en s, C (T)as a unc ion o ime-o -fligh T, is ela ed o he measu ed one, Cm(T), by means o C (T)= Cm(T) 1−T =T−τ Cm( ) n ,(6) whe e nis he numbe o neu on pulses o bunches and he sum uns o he p eceding ( ac ional) bins co e ing a ime τ. Due o he high ins an aneous flux a EAR2, a co - ec ion on he dead ime mus be included in he case o SiMon2 and o bo h mic omegas, al hough he sample mass we e selec ed in o de o minimise his effec . Only he PPACs a e as enough (τ<10 ns) o ha e negligible dead- ime co ec ions in he ene gy ange co e ed wi h hese de ec o s. Figu e 7 shows he alue o he dead- ime co ec ion o hese de ec o s as a unc ion o he neu on ime-o -fligh . A he he mal peak (≈6 ms), he co ec- ion is close o 1% while abo e 200 keV (3 μs) he co ec- ions inc ease up o 10%. The unce ain y on he dead ime co ec ion is ea ed as an ene gy-dependen effec . I has been es ima ed by calcula ing he dead- ime co - ec ion o a ificially inc eased ime sepa a ions be ween wo pile-up signals. O he co ec ions ha ha e o be conside ed in he ex- ac ion o he flux a e ela ed o he a enua ion o he Page 8 o 13 Eu . Phys. J. A (2017) unline o be inse ed Fig. 7. Dead ime co ec ion ac o o MGAS, monMGAS and SiMon2 de ec o s. The coun a e o he de ec o is mul iplied by his ac o in o de o ge he eal numbe o e en s p oduced in he sample. neu on beam in he a ious windows, elec odes and de- posi s placed ups eam o he sample unde analysis, as well as he sel -shielding effec in he espec i e deposi . The neu on beam a enua ion, es ima ed by means o Mon e Ca lo simula ions, is small, ypically less han 2% a he mal ene gy i only he windows and elec odes a e in he beam. Howe e , i becomes highe , al hough ne e exceeding a ew pe cen , when hick 6Li o 10B deposi s a e in he beam, due o he high (n, o ) c oss sec ions o hese iso opes. Sel -shielding effec s we e co ec ed by means o he classical analy ical o mula, aking in o ac- coun he abula ed o al c oss sec ion. Apa om he ene gy independen ac o s, like he sample mass, he un- ce ain ies on he ansmission and sel -abso p ion co ec- ions a e included in he unce ain y due o sys ema ic effec s associa ed wi h he Mon e Ca lo simula ions, o a mos 2%, conside ing also ha all c oss sec ions in ol ed a e con olu ed, h ough he yield, wi h he esponse unc- ion using he me hod desc ibed in sec . 3. 3.5 Analysis o he ac i a ion measu emen An al e na i e o de e mine he absolu e alue o he neu- on flux a a specific ene gy is he double oil ac i a ion me hod. I elies on he use o wo iden ical oils made o he same ma e ial (iso ope) which p esen s one la ge and isola ed esonance; he oil hickness is selec ed in such a way ha he fi s one deple es en i ely he neu on flu- ence a he posi ion o he esonance lea ing he es o he spec um un ouched [32]. In he p esen ac i a ion measu emen , wo gold oils we e exposed a he same ime o he neu on beam o ≃1 hou . A e he ac i a ion he numbe o coun s co e- sponding o he 411.8 keV γline we e measu ed sepa a ely in he same geome y o he wo oils using a LaB 3scin- illa o de ec o . The numbe o 198Au nuclei p oduced by ac i a ion was ob ained and he neu on flux deduced om he diffe ence in coun s, aking in o accoun he di - e ence in coun s o each sample, he geome ic efficiency o he se up used and he ime o exposu e o he neu on beam. The 100 μm hick oils esul ed in a flux-in eg a ed ac- i a ion o he fi s oil by he inciden neu on flux, and ac i a ion o he second oil by he ansmi ed neu on flux. F om he calcula ed expec ed flux-dependen diffe - ence in ac i a ion we obse ed ha abou 80% o he di - e ence was due o he s ong 197Au(n, γ) esonance a 4.9 eV, and oughly 10% due o he lowe ene gy neu ons down o sub he mal ene gies, and 10% due o highe en- e gy neu ons. 4Resul s The compa ison and combina ion o all measu emen s de- sc ibed abo e allowed us o de e mine he neu on flux in EAR2, in pa icula i s ene gy dependence, om 2 meV o 100 MeV. The esul s o all measu emen s a e shown in fig. 8. Fo con enience, he flux is exp essed in uni s o le ha gy and pe nominal pulse o 7 ·1012 p o ons. Since each measu emen is affec ed by a ew pe cen unce ain y on he absolu e alue o he flux, all measu emen s we e e-no malized a he mal neu on ene gy, whe e he c oss sec ions o all h ee eac ions used in he measu emen s a e well known, he e o e conside ed s anda d. I was de- cided o ake he SiMon2 measu emen as he e e ence because he sample mass and he efficiency, which affec he absolu e alue o he flux, a e bes cha ac e ised in his case. In addi ion, a compa ison be ween he absolu e alue de e mined by he ac i a ion measu emen and he esul s om he SiMon2 de ec o has been pe o med, showing an ag eemen wi hin he quo ed e o ba s o 5% (fig. 9). The a ious expe imen al esul s shown in fig. 8 we e combined, a e e-no maliza ion a he mal neu on en- e gy, in o de o ex ac an e alua ed neu on flux. The weigh ed a e age was pe o med aking in o accoun he s a is ical unce ain y as he weigh ing ac o , while unce - ain ies due o sys ema ic effec s we e ea ed sepa a ely (as discussed la e on). The da a o be included in he combina ion in diffe en neu on ene gy egions we e cho- sen mos ly on he basis o he unde lying c oss sec ion, i.e. whe he i is conside ed s anda d in ha egion. In able 2, a summa y o measu emen s included in he e al- ua ion o se e al ene gy egions is p esen ed. The ag ee- men be ween he a ious measu emen s below 10 keV is in gene al e y good. Sys ema ic effec s o he ene gy de- pendence ha e been es ima ed om he compa ison o he diffe en measu emen s. As an example, he a io be- ween MGAS(10B) and SiMon2 shows a smoo h beha iou wi hin he s a is ical unce ain ies (fig. 10), wi h he a io ne e depa ing om he 2% ma k in he whole ene gy egion o he compa ison. Abo e 10 keV, in p inciple he flux ex ac ed om he 235U(n, ) eac ion should no be conside ed in he anal- ysis, as he c oss sec ion o his eac ion is no consid- e ed s anda d om he mal up o 150 keV. Ne e heless, in o de o inc ease he s a is ical accu acy in his egion, hose da a ha e been included in he flux e alua ion a Eu . Phys. J. A (2017) unline o be inse ed Page 9 o 13 Fig. 8. Resul s om all measu emen s pe o med o he neu on flux de e mina ion and conside ed in he p esen analysis. The hick blue line co esponds o he e alua ed flux. Each esul has been no malized close o he he mal poin o he alue p o ided by SiMon2 measu emen , while he cyan do ep esen s he in eg al measu emen om he flux-a e aged ac i a ion measu emen . Fig. 9. Compa ison o he ac i a ion measu emen (cyan do ) wi h he alue o he e alua ed flux ( ed do ) a 4.9 eV. Resul s a e in ag eemen wi hin o e all unce ain ies o 5%. he expenses o a sligh ly highe unce ain y. In ac , as can be no ed in fig. 8, he flux based on he 235U(n, ) eac ion in he 10–30 keV neu on ene gy ange is sys- ema ically lowe han he one ob ained om he o he wo eac ions. This effec was al eady obse ed in e . [12] and i is associa ed wi h an o e es ima ion o he e alu- a ion c oss sec ion in he ENDF/B-VII.1 lib a y which is pending o co ec ions o he nex coming ENDF/B-VIII elease. A 100 keV, he SiMon2 de ec o s a s o be limi ed by he γ-flash. The e o e, abo e his ene gy he neu on flux is e alua ed on he basis o he mic omegas and PPAC esul s alone. A simila a gumen applies o he MGAS and monMGAS de ec o s, which s a o be affec ed by he γ-flash a ound 5 MeV. Hence, he only de ec o ha allows eaching 100 MeV neu on ene gy is he PPAC (see fig. 11), hanks o he low sensi i i y o he γ-flash and i s e y as signals. Figu e 12 shows he dependence o he s a is ical un- ce ain ies wi h he neu on ene gy. Up o 5 MeV i u ns o be less han 2% excep a he posi ion o he dips in he flux; while abo e his ene gy he s a is ical unce ain y in- c eases up o 8.5% because only he PPAC da a ha e been included. An in e es ing ea u e is obse ed a e y low ene gy. Fo he fi s ime a n TOF i was in ac possible o de- ec neu ons wi h an ene gy as low as 2 meV, hanks o he combina ion o a la ge memo y on he Flash ADC and he sho e ime-o -fligh , which p o ides he possi- bili y o pe o m measu emen s a sub- he mal neu on ene gies. The flux a hose ene gies shows he ypical solid s a e effec o neu on diff ac ion, i.e., he B agg sca e - ing o neu ons in he sou ce and he beam line ma e ials. Figu e 13 exhibi s a s uc u e in he e alua ed flux e- la ed wi h his effec hanks o he good ene gy esolu ion o he neu on beam and de ec ion sys ems. The B agg- edge ansmission dips in he flux, ela ed o he sca e ing off a c ys al plane, like polyc ys alline me al, is isible a a ound 3.7 and 5.0 meV. They a e due o he in-beam alu- minum windows nea he spalla ion a ge . The posi ions co espond o he measu ed ansmission o Al [33]. 4.1 Unce ain ies due o sys ema ic effec s The unce ain ies on se e al ene gy-dependen co ec ions a e unco ela ed o he de ec o alues a a gi en ene gy, bu co ela ed o a pa icula de ec o o e he en i e en- e gy ange. We e e o hem as sys ema ic unce ain ies. The sys ema ic unce ain ies in he shape o he flux a e a combina ion o se e al ene gy-dependen con ibu- ions. The main ones a e he unce ain y on he e alua ed