Laboratorio di Fisica delle Particelle COSMIC MUONS. Giorgia Albani Daniele Cortinovis Alessandra Gaeta Davide Rozza

Transcription

1 Laboratorio di Fisica dll Particll COSMIC MUONS Giorgia Albani Danil Cortinovis Alssandra Gata David Rozza

2 Rlazion di laboratorio di: Giorgia Albani, Danil Cortinovis, Alssandra Gata, David Rozza ABSTRACT Th aim of this laboratory xprinc is to study th muons particls according to: th masur of th fficincy of th dtctor; th masur of th muon liftim; th obsrvation of th muon in a spark chambr. INTRODUCTION Th top of arth s atmosphr is bombardd by a flux of high nrgy chargd particls producd in othr parts of th univrs. Thr ar two typs of cosmic rays which xist. Primary and Scondary. Primary cosmic rays ar particls such as protons and nutrons moving at high nrgis through th intrstllar mdium. Locally, many of ths ar jct from th sun. Whn ths primary cosmic rays com toward arth thy ncountr atmosphric nucli at around 30 km abov th surfac. Ths collisions produc a cascad of scondary cosmic rays which showr down through th atmosphr to th arth s surfac. This showr includ protons, nutrons, pions (both chargd and nutral), kaons, photons, lctrons and positrons. Th impacts caus nuclar ractions which produc pions. Th pions dcay into muons: π ν, π + ν ; this gnrally occurs at around 9 km altitud. Th muons rain down upon th surfac of th arth, travlling at about 0.998c. Many dcay on th way down whil othrs rach th surfac. Th muon dos not intract with mattr via th strong forc but only through th wak and lctromagntic forcs. It travls a rlativly long instanc whil losing its kintic nrgy and dcays by th wak forc into an lctron plus a nutrino and antinutrino. Th flux of sa-lvl muons is approximatly 1 pr minut pr cm with a man kintic nrgy of about 4 GV. Th diagram shows th primary cosmic ray colliding with th nuclus, whr th collision producs a cascad of scondary particls, known as a cosmic-ray showr. MV Th muon () is a chargd lmntary particl with rst mass: m Th muon isn t a stabl particl, it dcays in: ν + ν, + ν + ν with an avrag liftim: τ. s. For this xprimnt w usd: - fiv plastic scintillators of diffrnt dimnsions to dtct th particls; - ach of ths is connct to a high voltag photomultiplirs to convrt th dposd charg into lctric signal; - lctronic units (i.. discriminators, logic units, timing units, dlay units, ADC analogic to digital convrt, TAC tim to amplitud convrtr, MCA multi channl analysr) to laborat th signals of th dtctors; - spark chambr; - a computr for data laboration. c

3 Rlazion di laboratorio di: Giorgia Albani, Danil Cortinovis, Alssandra Gata, David Rozza 3 DETECTORS EFFICIENCY Th aim of th first part of th xprinc is to dtrmin th fficincy of th scintillators, that is to stablish th bst working voltag for th scintillators 1 and. Whn th scintillation countrs ar travrsd by a chargd particl (i.. cosmic ray), th ionisation producd may rcombin, mitting visibl light. Th photons ar dtctd by a photomultiplir tub. This thn convrts this light signal into an analogu lctrical signal. This signal is thn passd into a discriminator whr th analogu signal is convrtd into a digital on. Th dtctors ar arrangd in th following way: N tripl N acc Th fficincy of th dtctor is calculatd in th following way: ε = whr th N doubl coupls ar th coincidnc btwn th dtctors 1 and 3, whil th tripls ar th coincidnc btwn th coupls just calculatd and dtctor. N is th numbr of accidntal counts. Diffrnt kinds of problms aris in this typ of calculation: On dtctor may rgistr an anomalous numbrs of vnts, causd by light raching photomultiplir Natural radioactivity incras th numbr of counts Two diffrnt muons arriving simultanously on two diffrnt dtctor, crating an accidntal coincidnc. Th first two problm ar at most solvd by th coincidnc mthod; furthrmor th dtctors ar bn covrd with som black courtains to protct th photomultiplirs from light. Th third problm, instad, can giv an important rror in th fficincy calculation. acc N doubl N Th rat of th accidntal coincidnc is givn by: Racc = Rdoubl Rsin gl t = t whr T T t is th total tim of th width of th two signals (tripls and coupls). Bcaus a coincidnc unit wasn t availabl, w obtaind th logic function AND with anothr logic function by using NOT and OR; namly, to gain th coupls: ( 1 3). In this way w startd th masurmnt kping th dtctors forming th coupl (1 and 3, th xtrnal ons) at a fixd voltag of 1900 V, to hav a constant and high numbr of counts. Th data ar rportd in th following tabl:

4 Rlazion di laboratorio di: Giorgia Albani, Danil Cortinovis, Alssandra Gata, David Rozza 4 V N1 N doppi 1-3 tripl (1-3)- ff dt (ns) N acc , , , , , , , , , , , , , , , , , , , , , , , , , , , ,017 Tim masurmnt: 00 s. Th procdur to calculat th fficincy of th dtctor 1 is th sam, but th position of th dtctors 1 and must b xchangd. In th following tabl ar rportd th data of th dtctor 1. Again, th xtrnal dtctors and 3 ar supplid with a tnsion of 1900 V V N N1 doppi -3 tripl (-3)-1 ff dt (ns) N acc , , , , , , , , , , , , , , , , , , , , , , , , , , , ,81966

5 Rlazion di laboratorio di: Giorgia Albani, Danil Cortinovis, Alssandra Gata, David Rozza 5 Th graph rprsnts th fficincy of th dtctor ( rd, 1 blu) vs its tnsion. Th graph blow rprsnts th numbr of vnts rgistrd by a singl dtctor ( rd, 1 blu) vs its voltag. From th data w can conclud that th bst working point is about 000 V. Th numbr of th accidntal countrs is ngligibl bcaus in th worst cas is about 1,5 % of th total numbr of coincidnc, hnc it s not rlvant in th calculation of fficincy.

6 Rlazion di laboratorio di: Giorgia Albani, Danil Cortinovis, Alssandra Gata, David Rozza 6 MUON LIFETIME Th purpos of th xprimnt is to masur th muon man liftim. At som tim t w hav N(t) muons. If th probability that a muon dcays in som small tim intrval dt is λdt, whr λ is th dcay constant that charactrizs how rapidly a muon dcays, thn th chang dn in our population of muons is just dn = N( t) λ dt. Intgrating, w hav λt N( t) = N 0 whr N(t) is th numbr of surviving muons at som tim t and N 0 is th numbr of muons at t = 0. 1 Th "liftim" t of a muon is th rciprocal of λ, τ =. This xponntial rlation is typical of λ ν + ν radioactiv dcay. Muons - and antimuons + dcay into: + ν + ν + p n + ν Ngativ muons that stop in th lad or in scintillator can bind to thir own nucli in much th sam way as lctrons do. Sinc th muon is not an lctron, th Pauli xclusion principl dos not prvnt it from occupying an atomic orbital alrady filld with lctrons. Such bound ngativ muons can thn intract with protons bfor thy spontanously dcay. Th probability for nuclar absorption of a stoppd ngativ muon by on of th scintillator nucli is proportional to Z 4, whr Z is th atomic numbr of th nuclus. A stoppd muon capturd in an atomic orbital will mak transitions down to th K-shll on a tim scal short compard to its tim for spontanous dcay. Sinc thr ar now two ways for a ngativ muon to disappar, th ffctiv liftim of ngativ muons in mattr is somwhat lss than th liftim of positivly chargd muons, which do not hav this scond intraction mchanism. Bcaus of m 07m th muon orbit is narr th nuclo. For high Z matrials w can affirm that τ << τ. And th total man liftim is captur = +. That for th formula bcoms:. So th dcay of th muon - is τ tot τ captur τ dcay τ tot τ captur ngligibl. Th xprimntal stup is shown blow: dcay A muon that hits th two scintillators crats a coincidnc btwn 1 and. Th muon coms in th block of lad and hr it maks a dcay. W us lad bcaus it s a high A matrial and it braks th muon. So thr is a highr probability that th muon maks a dcay in th lad than out of thr. Now a positron is cratd in th dcay. It can pass in th scintillators or out of thm. If it pass in 1 and thr is anothr coincidnc. Th tim lapsd btwn thos two coincidnc has an xponntial distribution, whos τ is th liftim of th muon. Th pictur is a viw of th signal of th muon blow, and th sam signal dlayd and strtchd abov.

7 Rlazion di laboratorio di: Giorgia Albani, Danil Cortinovis, Alssandra Gata, David Rozza 7 W us a scalr bcaus it s a count masur. Th input ar th coincidnc btwn 1 and and th sam signal dlayd and strtchd. Th dlay is diffrnt for vry channls: it incrass of 1s for ach channl, whil th width is always 1s. W nglct th first intrval bcaus thr ar bad signal du to th scintillators. Aftr som days of masur w obtain a graph with six bins filld with data. ch count rror count/tim rr tim (s) ,16 0, , ,69 0, , ,0 0, , tim (s) ,6 0,0035 0, ,91 0, , ,33 0, , W hav fittd this graph with an xponntial function w obtain: Th man liftim of muons is: τ = ( 1.59 ± 0.1) s ; our rsult isn t satisfactory bcaus it isn t in agrmnt with th xpctation valu τ = ( ± ) s. Our masur diffrs from th tru valu of 5.1 σ: σ σ s + σ = = 0. 1 = t τ t τ s t = = = 5.1. To stablish th agrmnt of our data with xponntial σ 0.1 function w us th χ tst: χ = and ~ χ χ =. 1 with a ~ ~ Pr ob ( χ χ ) = 10% > 5%. d 0 = Our masur is scintifically accptabl but not satisfactory. Th dtctor rsponds to any particl that producs nough scintillation light to triggr its radout lctronics. Ths particls can b ithr chargd, lik lctrons or muons, or nutral, lik photons, that produc chargd particls whn thy intract insid th scintillator. Th dtctor has no knowldg of whthr a pntrating particl stops or not insid th scintillator and so has no way of distinguishing btwn light producd by muons that stop and dcay in th lad, from light 0

8 Rlazion di laboratorio di: Giorgia Albani, Danil Cortinovis, Alssandra Gata, David Rozza 8 producd by a pair of through-going muons that occur on right aftr th othr. W can stimat th background lvl by looking at larg tims in th dcay tim histogram/graph whr w xpct fw λt vnts from gnuin muon dcay. Th law of dcay is: N( t) = N + bg whr bg is th count background of th masur. From th fit of th data w s that: bg = ( ± ). s In th scond part of this xprinc, th countr is rplacd with a TAC (tmporal unity containing 819 channls). Th TAC taks as start signal th coincidnc btwn th two scintillators dlayd by 1s, whil th stop signal is th coincidnc itslf. Th output of th TAC is connctd with th input of th MCA that, in turn, is connctd with th computr. Th rang of data gathring of th TAC is st 10s. Th tmporal unity bgins to rad whn it rcivs a signal from th start, to b mor prcis, whn a muon gos through th two scintillators, and it finishs whn it rcivs a stop signal, that it s th muon dcay. Th dcay of th muon, in fact, rlass an lctron that, capturd by th dtctors, stops th masur and rstart. Th logic schm is hr shown: 0 First of all w hav calibratd th TAC: tim (ns) channl Th graph is:

9 Rlazion di laboratorio di: Giorgia Albani, Danil Cortinovis, Alssandra Gata, David Rozza 9 W hav fittd this graph with a linar function y = mx with th fit paramtr channl m = ( ± ) ; in this way 819 channls corrspond to s. ns Thn w hav rcordd th data for a wk to calculat th man liftim. Th p1 paramtr is th man liftim xprssd in channl. Th convrsion givs th valu of: 134 τ = = (1.565 ± 0.040)s, whr th rror arrivs from th propagation of th rrors: σ p1 σ m σ τ = τ + = s p1. m In th graph you can s a pak in channl W rpatd th masurmnts svral tims but this problm prsistd. W suppos that it is du to lctronic instrumnts. Conclusions: In both cass w hav obtaind a valu that is about 5σ lowr than th tru on. Thrfor w suppos that thr is a sistmatic rror, probably causd by th following problm. W obsrvd by an analogic oscilloscop that th scintillator oftn dtcts som rstart, that is a doubl signal for a singl vnt givn in diffrnt tims. This ffct may b causd by th high spd of photomultiplir s raction. Although w dlayd th signal of start to protct th masurmnts by nois, spcially rstarts, w hav noticd an xcssiv numbr of counts just aftr th start. Supporting with hypothsis w hav calculatd th man liftim nglcting th first data.

10 Rlazion di laboratorio di: Giorgia Albani, Danil Cortinovis, Alssandra Gata, David Rozza 10 Th fit paramtr p1 givs a man liftim of τ = ( ± 0.35) s. This rsult is satisfactory with th xpctation valu τ = ( ± ) s. RANGE AND ENERGY OF THE MUON IN THE LEAD To masur th muon liftim, w ar intrstd in only thos muons that ntr, slow, stop and thn dcay insid th lad. Such muons hav a total nrgy of only about 10 MV as thy ntr th lad. In ordr to know how much th muon pntrat in th lad and its initial nrgy w must do som approximations: Muon arrivs prpndicular to th ground; MV Muon looss nrgy at th minimum of ionisation: Muon gos through th lad dcays insid. Dcays undr th lad ar ngligibl bcaus th positron cratd can t cross th 5 cm of lad; Muon dcays stationary; convrsly, du to momntum consrvation th positron would go in th sam dirction of th muon so th dtctor couldn t collct it; Th dcay taks plac so that th configuration of positron and nutrino is back to back; If th muon dcays stationary its nrgy is From rlativity thory, th four-momntum is: q E c E r r = p = m 0c. = p c E = m c. g cm E c q = r and its squar valu is p

11 Rlazion di laboratorio di: Giorgia Albani, Danil Cortinovis, Alssandra Gata, David Rozza 11 Th momntum consrvation of dcay + = + + ν + ν implis ( q ( q 0 = ( q E + E + + ) = + c + q + m + c m + c c r ν p + + q ν ) q = q q q ν ν + 0. Th lctron nrgy is largst, if ν + qν ) tak on a minimum valu. For vanishing nutrino masss this mans that th lctron r r qν qν Eν Eν pν pν =. This quation is satisfid for p rν p r ν = gts a maximum nrgy, if: 0 Thrfor th positron Enrgy is: ( m + + m + ) c m + E + = = 5. 83MV. m + //. Th positron is dtctd by th scintillators only if it dosn t intract with mattr and so it must b vry fast. Usually, whn it slows down it dosn t annihilat but it bounds with an lctron forming a positron. For this particl th loss of nrgy in th lad is causd by irradiation according to: de E Z E = =. d( ρx) x 170A g [ ] 0 cm From rlativistic modl for high nrgis th ratio btwn th loss of nrgy du to irradiation and Sirr Z E[ MV ] collision is: = 5.4 Scoll Thrfor th total loss nrgy is givn by th sum of th two contributs in this way: de 1 de Z E 6.4 = Stot = Sirr + Scoll = 1 + =. g d( ρx) 5.4 d( ρx) 170A[ ] 5. 4 tot cm 143.5A E0 Intgrating and solving rspct to x w obtain x = ln. ρz E W know that E 0 is half of th muon rst nrgy. On th othr hand E is th minimum nrgy ncssary to positron so that it can cross th two scintillators. mm Th xtrapolatd rang is R MV, th total thicknss of th two scintillators is 4 cm; so th positron nds 0 MV at last to cross thm. So w obtaind x cm. Th dcaying muon can pntrat to a maximum xtnt of 0.4 cm and it loss MV g E = cm 9. 04MV. g cm cm Insid th scintillators (dnsity = 1.03 g/cm 3 ) muon loss MV g E = cm 8. 6MV. g At th and w can affirm that muons obsrvd in this xprimnt hav an nrgy about E 130 MV. cm cm

12 Rlazion di laboratorio di: Giorgia Albani, Danil Cortinovis, Alssandra Gata, David Rozza 1 SPARK CHAMBER Our spark chambr consists of 4 moduls. At th top and bottom of th spark chambr, covring th activ ara of th moduls, ar locatd plastic scintillation countrs. Whn th scintillation countrs ar travrsd by a chargd particl, th passag producs an lctrical signal. Th cosmic ray has by now passd through th 4 moduls, laving th H-N gas ionisd. On xiting th chambr th cosmic ray passs through th scond scintillator countr, which lik th first countr, mits a photon which is dtctd by th phototub, which thn convrts th light puls into an analogu signal. This signal is thn passd through th discriminator which convrts th signal into a digital on. Th signal will thn pass into th coincidnc unit. Th coincidnc unit givs an output whn it rcivs th digital signals from th two discriminators within a crtain tim intrval. Ths ssntially simultanous signals indicat th passag of a chargd particl through th spark chambr. If th coincidnc unit rcivs th signal from th top and bottom scintillator togthr, thn it will pass a signal to th triggring unit. Th triggring unit is ssntially a capacitor chargd up to a voltag of 4.5KV. This is an unstabl situation, of which th moduls can t stay lik it for any lngth of tim. Th plats must discharg. This discharg will occur along th asist path possibl. Th asist path is through th ionisd track lft bhind in th H-N by th passag of a cosmic ray. Thrfor th plats will discharg down th ionisd track of th cosmic ray, and hnc th charactristic spark is obsrvd. Shown on th diagram abov is th sparks (rd circls) along th track of th cosmic ray which th spark chambr has dtctd. Th spark chambr in th laboratory. A basic xplanation of how th spark chambr works

13 Rlazion di laboratorio di: Giorgia Albani, Danil Cortinovis, Alssandra Gata, David Rozza 13 Origin of a spark Th spark chambr is mad up of mtal plats, and a mixtur of H-N gas filling th spac insid. In its initial stat, th gas in th chambr is mad up of atoms that ar lctrically nutral. Whn th muon particl travls through th chambr, it knocks lctrons off thir orbit around th nuclus. Sinc lctrons hav a ngativ charg, whn thy ar knockd off th atom, it lavs th atom with a nt positiv charg. Du to having a nt charg, th atom is now calld an ion. As th muon gos through th chambr, it knocks lctrons off numrous atoms. Thrfor, a trail of ions and fr lctrons ar lft along th muon s path. Aftr th muon passs through th spark chambr, a larg potntial diffrnc is applid to th plats by oppositly charging th plats as sn in th diagram. This arrangmnt crats an lctric fild in th spac btwn th plats. Th fr lctrons ar attractd toward th positivly chargd plats, whil th positiv atoms ar attractd to th ngativly chargd plats. As th lctrons fall, thy spd up and gain nough nrgy so that whn thy ncountr anothr atom, it knocks an lctron off, crating anothr lctron and ion pair. This continus to happn, crating an avalanch of fr lctrons and ions. Along this path, a discharg occurs, forming visibl light. Through th spark chambr, th travl of a particl that is invisibl to us in daily lif is rndrd visibl. Unfortunatly th gas in th chambr is not only H-N, but thr is also air. This air arrivs from th hols in th spark chambr. For this rason w will not hav sparks in th whol chambr, but only in th lowr part, whr th gas ntrs. Blow thr ar som photos of spark in a spark chambr. Instad of this spark, w should hav had photos as this:

14 Rlazion di laboratorio di: Giorgia Albani, Danil Cortinovis, Alssandra Gata, David Rozza 14 Indx: Introduction Dtctors Efficincy Muon Liftim Rang and Enrgy of th muon in th lad Spark Chambr Rfrncs: Knnth S. Kran: Introductory Nuclar Physics G.F. Knoll: Radiation Dtction and Masurmnts David Griffiths: Introduction to Elmntary Particls Claus Grupn: Astroparticl Physics Stopping-Powr and Rang Tabls for Elctrons, Protons, and Hlium Ions