Basu, D

Bhattacharyya, D P

Sarkar, Kalpana

English

IACS Institutional Repository

Mian J. Phys. 5lA, 2?.l-236 (1971)Cosmic pion spectrum at the top of the atmosphereK aLPANA 8 aRKAB, 1) P . B h ATTACTIAKYYA AT l^) D. B a s I'Indian AssocAation for the Cultivation Science. Jadavpw\ ('alcutia-lKXKKVI (Received 31 March 1911), revised 31 Jvly 1919)llic pion spectmiD in Ihc Rpoolial nuv^ c 10-100 Cc\ ; i  llu‘ lo}- oi tke aline sphere has hcon derived Irom tlu‘ ],rinuiry iiueleuu siMHluim of Tt^ an et aL (1^12) by usiiio Bu^ \acv Jimdel. Tht do!i\(‘d n'suH has been compared will) those expected fn'iii OKP. OE. Dilli'Kiou and Feynman sC(;ling models oi pp intciaetions. U is h-und lhal tlie doiivod results from Bugaev moile] is siix>poj‘led l)y tke sialiiig hypothesis of Feynman and CE model.1. I n t u o  DUCT lowThe study on the production speclnim oi muoiis is ol inter(\s1 io cosmic ray plienomeiiology to got the iiiiorinatit)i] oji the produciiou pjoccvsses. In geiuatd the oxporiment.ai spcctiann oi primary cosmic ray iiuthanis at the lop oi tlu- atniospliere and the. ground level muon spectrum caji h(‘ used to test the validity of t)i,e interaction models in the ])ropagatioii of ct^ smic rays in s]iac(\ The muon spcctrmn can indicate the amoimt of energy trajisferrcd hy Jiucleons tn muons Ol’ Hioio particularly to tlieii' parents. The pion spend rum at th<’ lop oj lh(- atinosphere also gives information about the spectral shape ol muons in the cos­mic lay phenomenology and in the diundopniont oJ high energy jdiysits.Tlie ])ion spectra dmived from thc’ primal y cosmic ray nudc'on sjicctium using tJio soiling hyp(»tliosis o! Jfeyjunan (]9(W). Oonsti.nt. Rjiorgy mo(l('l (Brooko fit cd 1964), Bose tyiie model liave been proseiilod in oui earlier reports (Bliatta- eharyya 1972, Bhattachaiyya &• Basu 197C, Bliatl.acharyya 1975, Bhattachaiyya et al 1975a).In the present paper we have used the pp interaction model ol Bugaev fit id(1970) to derive the pion prodnetiou speetriun at the Inj, of the almospliere irom the measured nucleon spectrum of Byan fit al (1972). The luterseetmg Storage King data on pp collisions reviewed by Erlykin et al (1974) Irave boon used in the present work. T’he derived pion spectrum Im.s been compared with tlu results ohfaiued from vJKl> model (Coeconi fit al 1972), Diffusion model (Bha a- charyya, Koy Chowdhury Basu 1976), Scaling hn>etliosis el I'eynmau (1J(.,ll, Constant Energy model (Brooke el cd 1964).2312. Theoketical Models(i) JhKjmo modelTlit^  H|)(U!truin ol‘ ])ioiis from iho spi'ctrum of primary nuc;loo]is canbu u.stimabid by flio p -p  iriloractioii modd oi‘ Bugaev ei al (1970). Thepioii uuol(i()u flux rali(j ti(E)IN(E) at th(^  energy E at the top of the atmo.splier<) can b(^  ( s^timat(‘d Ifom the folhjwing j‘elatiou232 K a lp a n a  Sa rk a r, D. P. B h a tta c h a ry y a  and D. Basun(li)IN(li) JA„)I .-I - l -<  '(a:"' (])v'liore y'A.-- (}X])oncuit (>I the jutegral primary iiueleoJi .S])eetruin,- intporaetion free path o f iiudoon.s in aii' — SO g-cni“-,- absorption  fnu'. p a th  rd jhons ni a.ii- — 120 g-cin” “.: nx■'' ■ 7^7,, iL: -  th(^  fiuetioiml ejiergy moments ibr chai'ged ]>ion8 piodueed during p-nnejeiis intcninjliniis,- th(^  kinelie lunistant — 0-(>9J.Rrlykin el al (U371) iiave caJcidaloil the fraetionaJ (‘iieigy mojnenis for ]nons jirodiieed 1‘rom t-lu^  ln1ers(H*,tnig Stora.ge Ring ex[)eriinenls (p~'P collisions).Table-1 shows llu'- values oJ‘ nx'^ ' pTT-h and oj- y 1-75.Tal)h^  i. The vmlues < nx'^ ' ;>i for eliarged piousIrilporatil loii pt‘f>p(ws (i)J> -► “I X(2m+)p-\-p~^  n~-\-X{p7i-):n:Jc'0.0352 0 0220(ii) CKI  ^ atodel'rii(‘ eni[)iriea,l 0KB i'(da,tion formiihited by (^ >eeoni el al (1971) ioi tlu^  number of pi»)iis of one sign emiti-ed in th<^  forward diiection in th(^  C systmn, N(Ej )^dE is given byN {E„)dE,- ,^xvi-EJT,>)dE, (2 )Vwhore E^  ^ is t-lu^  pion energy in L system, A is tlui mean multiplicity of pious of one sign emitted in the forward diriaitioii in the f7-sy.stem and Tp is the mean piou energy. The parameters A, Tp and jiion imdastieity folloAvs tlu* r(‘lationATp — \K^Epwhore Ep is the primary niieleon energy (^ xprf;ssed in (4eV nniis. The prof.on light nmdeus inbnacLion data obiw Fenni JawA — aEp^ '^ ^^ * wherci a — 0-45. (4)Cosmic pion spectrum at the top of (he atmosphere 233F{K^)dE~ at t lir  (oji ul llu  atniuHphojr c-.fiii bo oxprosaod l ‘m m  tlio prim ary iiiicli'ou s]Ma‘1rmJi ul’ llu^ law lit. romiby l,h(^  (5KP rolati«>ii dovolopcd by r f  td  (lb7l) b>)lows a2(ZAV3£  ^ r ‘U'I, ( l-A V p -JJ 7v; -i(0)w Jioro Krp and an  ^ Irlio uuoloon moJaslicit v and pumi JL(-la^ l ioil \ . rosj)(‘0 t iv o ]\- (ill) F i o n  aittKh'ipfmric d i f f u s l o i t  nKxhlTlio  usual dillusiou ocjualiou dc^stuibrd lu j(d 'ounu‘ (J.llialtarluuyva. K in  OlLowdiuiry ct Basil 1970) for tlio [jroj>a.iLralioii ol oliariicil pions in tJir afiuospliriv  aiH'oimt.iug fni‘ loss o1 [uojis liy m torai‘fion dc(-a\ and gain In laodm^tiou iu iLUoloou-iiuoJi'ioii oollisiojis yiold lb(‘. dillorimtiaJ ]>iou sportlum  at tlio lo]i uT tlio atiiiospJioro 7r[E)tW IVom iJii* so>a. Iin'ol muon sjX'olriim /i{E)dE In  1 1h ‘ (dllowmg rojatioji7T{E)dEAv>' ^B^rh(E)!/(E)(7)wdioro r is tiio onoi gy dogradatiou I’aotoi' iu /?—>// di'oay, A is tlw  absoi ptioji moan b'oi paili o f iiuolooiis iu air 120 B-r (iih o a l onorg’> Joj' juoudooay - I IS  (loV . A,, is Uio iiitoraotioii moau l i ‘‘o pat-1) oi nuoji‘oiis in aii' “ 90 g-oiu y IS 1 li(‘. oxponoiit ol iln* diltoroutial oiungN s]Ka‘tjiiin  ol primays oosiuio ray uiiolooiis (‘xpu^ssial as a power law ~  2-7o (Ivyan r/ td IO'/2). /d /’d E a lunotiun dopcjidiui^ oii // — diua^' and t'lioigv loss(^ s ol muons in aij' and y{E) t bo (‘orioo- I'ioji Taotor do[»ondiiig on (lie kaon l.o ]ji(Ui ratio (A/ / / )  a|p prodtiol ion(i \ ) BoaU}iij Juf^olhtuyi'S o f  F e y m m u tFrom  IJio. sealing bypotbosi^ oJ bVymiiaii (19(i0) it is ovudiait Mml tJio d ifi’oj'oiiUaJ cross section Jbr tbo production ol a. oliaiyod paj'laelo ol a givcm type in  higli ojiorgy badron-hadron oollisions tends l,o a lim itlim E(dA(rld^ ]j) - - /{x.'Pt) •**S—>Q0w'lxoi‘0  .S’ IS t b(‘. scpiaro o f tbo oont in* cd iiiass onorgy, E. p ,  ai o niorgy, momentum  (iiid tT^a.nsvorso niomonlLUU of tlio secondary jiartick in tbo ccjitoi oJ mass lia im  and the Foyiuuaii variable x - wboji^ pj ,  is tbo logitudinal oompoiuailo f p  j)aralloJ Lo tbo iiiomontum pu , c  ‘>1 pibm^O^ part-ido At a vo]-\ liigb (morgy pj^ o(|nation (8) can be written asd(T^  -- nf(x, Pt) dpT". (b)234  K a lp a n a  S a rk a r, D. P, J ih a tta c h a ry y a  and D. B asuTill? produtjtioii .spoclruin ot'ulmigecl pious 7i(!CJtdE  ^ can be 1‘ound IVoiii tli(‘ folloM - relation (Blmtiaehaiyya 1975).VV dhj p j . ,-a±x-)V^(AV)|r^ <;6(7. rt.,H CL(/>iy, a.J\ wlioj‘0 (piy. a) ()-5rd^  I'Ky-- l)/21.( 10)The iut.ei ai'tiou pcU auK^ ters C\ , , r/, a  ^ liave been iouiid irom the nieasuie-iiieuts ()1 Bali d al (1970) and \vei(^  0-47, 0-97, 7*4 and 12-], lespeclively.(v) (‘Ondani Enuyu modelBi‘(K)ke el (190^ 1) have assumcal in tliii C-oJislant Enej'^y jiiodt^ J (to be leferred to as CE) that pious are (UiiitUal vith (ajieal t‘u(agy iit tlie ('-system, lialf biding iiL the forward direc^ i ion ajid halt lu t h(‘ bac^ lvAvard diieetiou, and th<i euerijfy (if the I'ast^  jMouM iii llu‘ L system is lak(Mi as K^Epj'AA, H‘ one assiuiies the jiiieleiui iiielastieity /k^T and pioii inelastieity K  ^ as ('oustauis ioj- eaeh interaction at a ])art ieulai' (Mier^ y, the, production S|)eelrum of ehai'p;ed pious can 1k‘, fouJid Iroiu lh(' (JE Jiiodi'l bv iisijLu: the relat ionn{E,)dE,  ^ - - n.1 (1  ^ /vr) -^'J (I( 11)wheiv, H -y)( l -a )^( y - a - l )(1-^)2a y)-  /I \1 -- a 0*25.‘{. RKsui/rs AJicn Dist usiONTlie diflercntial sjuudra (d‘ cosmic^  juimaj v protons jmaisiireil upto 200(> 0e\ by Ryan el al (1972/ has b(‘en used in the present eaieulatioiis. Ihey used ionisa­tion spectiometers al balbm altitudt s^. The primary nueleoji speetJiuu can be est iinat/cd on assiiuiiu  ^ the, nuel(‘oii proton llu\ ratio to h(5 1-33 and the spectrum folloAN.s th(' I'elatioJLN(Ep)dEp -- 2-G(>AV dEp (12)where Ep is (‘xpiess(^ d in GeV and tlu' intensity in (em“ sec sr GoV^ )~h 4he solid line in iigure 1 shows t]u‘, primarv nucleon spectrum estimated from the Goddard Spac(‘ Eli^ dit. data (Ryan el al 1972). Tln^  relation (12) yields th(^  values of B and y ol‘ ri l^ation (5) arc* of 2*(i(i and 2-75 , jespectiveljr. Using this iiucleoji spectrum, the pion nuclemi dux ratio at energ^  ^E at production has been estimated by rtdation (1). The derived pion spectrum at the t.op of tlie atmosphere has btam estimated and follows the rehtionrr(E,)dE, 0-158  ^ dE .^ (13)Thn rosult has lieoii in i111 CKP model (relation (1) the l)o,st e,stinmte<l value (»l Brooke vl nl (llHiJ) on the mideoji inelastieity Kt PdT mid pioir im^ last ieit> /v„ 0‘ar> has beenused in the present oaleulations. The pion spoetrum has Ikmui estimated in \hv speetral ran«:o 10-^100 OeV and the lesidi is ^m^ smited m tiai.n' 1Cosmic pion spectrum at the top of the atmosphere 235t'"ip: I Tlvi full lino (/!,) 8ho\VK the y>rima.ry nuclMnn H]K'i;trinn after Kyau r,( uL Thetlorivud pion spocira at th(' top of the atmosphore.......... (B) at tor Bngu^ 'V moch»l(Bugaovcl!a? 1 9 7 0 ,------(OKlb aflor (flocooni o,l al 1971);........(1>) after DitTusionmodel d^luittacharyya r/ at 1970) ....... .. (F) nfier non,ling nmdel (Foynmai. 1999):_____  (CE) after OE model (Brooke rt al 1904).Til the pion atmospheric diffusion model (lolation 7) tlu^  experimental different tial sea level muon spectrum fi{E)dE of Ayre ct al (1075) has hfon used. Tlu‘ dorivt^d pion spectrum from the diffusion inodel has also been presented in figure 1.Using the mteraution parameters t a . , , a ol Baii ot al (10/1) the pion spectrum from the primary nucleon spectrum of Ryan et al (1072) has been estimated by Scaling model of Feynman (1960) and the rosnlt has been plotted in figure 1Pitifillv Ironi Iho riuoloou soiirrc sj)P(*tnim of Itvaii p/ al, (11)72) th(  ^ ]iion spppliuni ill ilin top (»| tlio almoHpliorn has 1)pojl doi’ivod by iisirug (Vaislaiil m(Kl(d. I lio \'^ ailuns ol hrp aiid A „ l)(duj  ^ chosen from tlu ‘ Avork of Brofdtc rt al (H)M) which an. 0-47 ami ivspncli\(‘lyll- IS (‘vidmit iron) | tlia( the d('riA(‘d jiiou spccli’iim from BupiatTniodol ,iioe('s wjI h th(^  result (*\jMa*1(‘d irom scalini:; liypothesis of roynmaiii (IDH!)) and lli(^ (amsianl Energy model ol lh'ook(‘ r/ al (Il3b4)236 Kalpana Sarkar, D. P. Bhattacharyya and D. BasuReI'^eiikncksAyi'o n A., ltiA(UL(ln,l(‘ . Iluiiir P. ,L, Nnurli i; C , Tli<au]>um M (\ ^ VVluillcv W. Ik l!)7a , f .  Phifs. ( ;  N r k / V , l , ; , S lRail N Ik, Hrowii I., S.. IVcpoi :il D. iV P i m^.oi ), ,\ m7() f ! rr  / . r / / . 23, r.n7,HliiiMHf'haiyyiM) R IM72 Zr/7 . / .  PA//,s 257, 2!l2.RhaUm'harvyii, 1). P. lB7r, .J, Phi s^. (i , Nurl p/nps, 1 . 77:;.Rhniiiidiaryyii I). It  liasu 1) lt)7a Tmlinn 7V<//.s\ 49. :;+(jlUuittadmvyyji 1). ] t ,  Miiklim’jr,- M, tSc Rasii I>. 1075 ^uh Phusi t  liuiuf 32. iS UU. \ HliaitacliiM vyii I). V . liny r'lmW(lhuiy ]l. K. Ikisn I) 1!I7H ./ Ph/,s, (;  ^ PJnp^ . 2. Hrooko (k, Hayinjiu k ,1., Kaiuiya 5' (V. Wnlfcuidalr A. W MUM /Vor. kW 83, 85:;. ' ikigaoN^  K. \ l\nj.('v \  Ti. I), tkj Iii.i 1 |j. lt)7u (to.sniK M'lifVifi aiiil A fV/.U/7?oa' (ih K iismuui). Mikthui (k. Kons((M‘ r  iV, IVHsiiis I) H. MI7 I Nurl. Pln/y. B28. :)7l.Kriykm A. I)., Ng k K k WnlUwluIo A W. 1074 ■/. I • iUr//A. Anri. (l<n, 7. iMif.O.I'oytunan II. k MKIO 7V///v L ( l l .  23. 1 115.Ilyari AT. JOr ' mcs ,J V A MuIusuImahnifiuyini \ K. L072 J'hifs f } n , L t t l  28, I'Sf)

Cosmic Pion Spectrum at the Top of the Atmosphere

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Cosmic Pion Spectrum at the Top of the Atmosphere

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