4 ) G. IielletCiini, G. Coccc~rii,A. N. Didderis, E. Lillet:hriri, G. blatthiae,. J. I-'. Scaol.ou, m d A. >l.l\Tet;lereli, Nilci. Piiys. 2,609 (1966). 5) E. L. Androi\.ikashvJ.li, G.
.. ... . I
.
.
.
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.
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I
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. I .
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.
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.
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-5 Such e v e n t s
cosrriic r z y muons were i n c j - d e n t on t h c d e t e c t o r .
were rscl.ectcd by demnntllng t h a t a l t c m a tc end a f t e r eaci? of thc i-nodulea bein:,
poridirrg to t h e passage of a
II!GC:II~.CS
situated before
a n a l y z e d had pubes corre?R
~i.1iglerelativistic
par'ticie.
a
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-9 e x p e c t e d response of tlic d e t e c t o r s ai.c+ r e q v i r c d t o d e f i n e nu i n t e r z c t fori, as a r i m c t i o n of the l>;.ri?her of equ:vxl.cr.c
m u m s nerdeti
LO
def:i.nc an i n t e r a c t i o x , and 2 s i!
f u n c r i o n of ({I f f e r c n t niiubers of rnuoii ec!uival.ent p a r t l c l c L s i n t h e f i r s t a n d secnn,:; k t e r a c t i o n I.iod(!lcs. The s l o p e of t h e i i l t i x r a c t t o n c u r v e was c a I . c u 1 a t e d f o r s e v e r a l
d i f f e r e n t r m s u s i n 3 the rcqijj remcdnt of
OLILIJI~~Sexceed
i.i~g3 th!-i.shoId
i r o x two o r tl?;::-*c c n n s c c u t i v e modules t o cicf-ine a n I n t e r a c t i o n .
For e a c h
ILUI
t?i~ slopcs d e t r m i n e d using
t h e r e q w l - c e m ~ n t o f two
c o n s e c u t i v e nIodul.es a g r e e d we1 1 w i t h i n the e x p e r i m e n t a l u r r c e r t a l n t i c s w i t h the s l o p e s d e t e r m i n e d u s i n g t h e rcquircment of t h r e e c o n s e c u t i v e modules.
1Iowcver. :he
module measui-cnents
s t a t i s t i c a l a c c u r a c y a s s o c . i a t e d w i t h t h e three
i . 7 3 ~
somcvhat less.
T h e d a t a from m e l e s s module
. .
I
I
1111 I 1
I mmm1111.111.111.11-11
1111
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-14 c o u l d be used s i n c e the nuzhcr of i n t e i - a c t l o n s o c c u r r h g i n t h e n e x t - t o - 3 . a s t m o d u l e o b v i o u s l y c o u l d n o t be d e t e r t n i n e d w i t h t h e s a n e r e q u i r e m e n t s p l a c e d on t h e o t h e r modules.
The l o s s
of i n f o r m a t i o n wl?Fch m i g h t h a v e been p r o v i d e d by t h i s one
a d d i t i o n a l rnociule in-rceses ?lip
F t atist-f.cn1.
urcertninly.
Sir\ce
t h e d e t e m i n n t , . o n of t h e sl-ope was irrdcpe1;cient of whet.iier tile t w o ~ , rt h e t h r e c c o n s e c u t i v e - ~ i i o d u l e rcquirc.i:~cnt w;?s u s e d , nrid b e c a u s e g r e a L e r accurac:r
a c h i e v e 3 r i i ~ l . , t h e two m o d u l e requirc,i:icnt , all
1~7as
s u c , c c e d i n g detc.m.inat:.oss
x;-:Ye
n a ; ! ~w 3 . t h t h e
r e q u i r e m e n t t h a t LWO
c o n s e c u t i v e modiilcs had o u t p v t s w l i i c h a c c e d e d t h e s e l e c t e d t h r e s l i o i d s .
'&e :hrcuhold F'-.2y:iicol
t o define! a n i n t e r a c t i o n s e l e c t s t h e
c:hoscn
processi'r; t o L e observr:i.
a n i n t e r a c t i o n is i-.-.is>d, and a l s o f a i l t o ckvei.c;>
As tllc rlirc~sho1.df o r t i e t ~ . ? r . ? : \ j n ~
I n t r r s c f % o n s w h i c h h a y e low i r i i i l t i p l i r i t y ;?
s i g n i f i c a n t s h ~ i i e rare n o t d e t e c t . e 3 .
However, i n t e r a c t i o n ; v i t h tilgh n u l t i p l L c i t j 7 w i l l c o n t i n u e t o be detected.
bIost i n t , e y n c t i o n s in
1.JhiCh
u ~ i eo r i-iore n o ' s a r e p r o d u c e d
w i l l a l s o b e d e t e c t e d d u e t o ? h c r a p i d b u i l d - u p of t:he eZI?cf:.ro:nag11cCic shower f ~ l i o w i n gt h e d e c a y of t h e n o i n t o t v o p,ciii:~iar;;ys.
A t the
e n e r g i e s i n v e s t i g a t e d i n t h i s work, higher :nultfpl.icf.ty e\Wnts have
luwer p r o b a b i l i t i e s .
S i n c e f n c r e a a i u g tho t l i r e s h o l d r e q u i r e i u e n t will.
5
b i a s ag.r,ins t some l o v m u l t j . p l . i c i t y , higher: p ? : o b a b b l i t y e v e n t s w h i l e continuing t o s e l e c t ti?: h i g h multtplicity, l o w e r p r o b a b i l i t y e v e n t s , t h e i n t e r a c t i o n l e n g t h i s e x p e c t e d t o r i s e a s a f u n c t i o n of i n c r e a s i n j ;
threshold l-'.'quirCnient.
F i g u r e 3 shotis a p l o t o f t h e r.ie.asured i n t e r -
e c t i o n l e n g t h f o r b o t h 9.3-GeV protons a n d positive p i o n s a s a f m c t i o n
b
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-15 of the t h r e s h o l d .
The i n t e r a c t i o n l e n g t h is seen t o 3.ncrease
5y a b o u t 202 a s t h c t h r e s h o l d reqlij.i:ement Is r a i s e d f:rom 2 t o 7 s i n z l e p a r t i c l e equivalents. .
The m e a s u r e d i c t e r a c t i o a l e n g t h
seems t o rcaiain r o u g h l y cow;tzn(l o r dcc.rease s l i g h t l y f o r still
the thresho2.d i s l o x e r e d t'o o n e I o n i z i n E p a r t i c l e the i n t e r a c t i o n w i l l .
3ln:os.t s l w n y c b c d e t e c t e d in thc f i r s t few t u n g s t e n rriodules and no usctfu:! d a t a f o x t!le d e t e r i n i n a t i o n o f t h c ! s l o p e i n t h e i r o n n l o d u e l s w i l l b e a v t i lI n h i e . Not: much d a t a a r c d v n i l a b l c f o r t h e partic1.e 1 n u 1 t i p l i c i t i e s !.o
he e x p e c ~ e dfi-om iiuclt-ar i n t c r c c t i o i i s In i r - c n a t t h e t i g a t e d i n the p r e s e n t w o r k .
was detcrririncd for
ii
,
: . e r g i e s irives
Thus t h e J r i t - c r a c t t o n in3a.n f r e e paell
r a r g e of vnl.ues of the tlirc:,hcl.ds,
F:r,urc
4
s!lous a p l o t of the stntlsticnl u n c e r t a i n t y i n the ine.ln free p a t h
a s a f i i n c r i o n of t l i r e s h o l d . in
t . 3 ~p e r c e n t a g e
F o r t h e s e L9ta there i s
B
very clear rniriimum
u n c e r t a i n t y f o r a t h r e s h o l d r r . q u i r a n e n t of 3 . 0 muon
equival.ent p a r t i c l e s .
The o t h e r d a t a ( 1 3 . 6 and 1 7 . 8 - C e V p r o t o n s ar.d
9.3-GeV p i o n s ) a l s o chow a minimum i n the u n c e r t a i n t y at a thresLo1.d v a l u e of 3 . 0 muon e q u i v a l e n t p a r t i c l e s a l t h o u g h i n t h e s e latter c a s e s
.
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prcnounced.
Thfo minfmum in the
u n c e r t a i n t y o c c u r s e v e n though t h e total nuniber of i n t e r a c t t o n s f o u n d i n t h e iron modules is a r i ~ o n ~ i t c ~ ~ l ~i nacJr.el e>s~i n g f u n c t i o n of t h e t h r e s h o l d value u n t i l t h e t h r e s h o l d i s approximately muor, e q u i v a l e n t psrti c l e s .
of t h e s l . o p c dep'ndc;
,
e
The u n c e r t a i n t y In ti-.e d e t c n ; i n n t i o u
j o t t i Eycn t h e s t a t i s t i c a l a c c r ; r a c y of t h e d a t a
of the. fit b c c o x e s worse r~P1il.et h e t o t a l number 02 interastdoum 12
detccLcd i n c r c a s c s , i n d i c a t e f i
tliitt
data f o r t h e s e I i i g h e r t h r e s h o l d s
d o n o t fit t h e Iiypot.Ires5.s of a slmplc e x p o n e n t f a l d e c a y
60
well.
The
thresV.old w?:fch result:ed f n Che rinimum s t a t i s t i c a l u n c e r t a i n t y i n h was
Ci1092Ll.
f i r s t a t 3 was i n v e s t - i g s t e d .
For some cases, p a r c i c u l a r 1 . y f'or F n t c r
a c t i o n s ~ I i i c hi n i t i a t x r.Icctro,r.apriet-j.c c a s c a d e s , t h e s i g n a l 3 . c u e l i n t h e s e c o n d r!oJul.e is h i g h e r t h a n i n t h e f i r s t .
I t was t h o u g h t t h e t a. h i g h e r
t h r e s h o l d f o r d e t e c t i o n i n the scdcond module would niare n e a r l y r e p r e s e n t t r u e e v e n t s and b e a b e t t - e r c r i ' ; e i - i o n f o r e v c n t s e l e c t i o n .
The G a t s f o r
9.3-GeV I . r o t o n s were a n a l y z e d b y v a r y i n g the t h r e s h o l d f o r t h c s e c o n d module from 1 to 5 muon e q u i v a l e r t t p a r t l c l e s u ' n i l e t h e t h r e s h o l d fox t h e f i r s t module w:i.s he1.d const:int: a t 3 muon e q u t v a l e n c p a r t i c l e s .
As
can be seen in F i g . 5 , the,miniuwic n n t e r t o i n t y irk t h e d e t e r c n i n a t i o n 02 t h e s l o p e o c c u r s with t h e same threshold f o r b o t h the f!.rst
While a d j u s t i n g t h e t h r e s h o l d v a l u e in t h e second nodule changed
modules.
I
and s e c o n d
~
I
i n the val.iie of t h e i n r e r s c t i o n 1 9 n E t h was c i c t a c t c d . f i n a l . results on t h e d e t e r m i n a t i o n
0%
Thus all
inzeraction l e n g t h s presented
h e r e arc b a s e d on the +cqu%reinent of Erao s u c c e o s i v e t n o d u 1 . e ~wlth n
.. .. l e n g t h s c o n ; sins
33
addit:cna9.
212 duc t o the i i n c a r t a i n t y
I m c e r t d n t y of
i n t h e mean d r : i t ; i t y of the d e t e c t o r r w i t < : r i a l . I t iiccds t o be r;ti-c~-t~,Jy strrriscd ( h a t .
Crt
of ';he i n t e r a c t i o n I . o n g t h s , ~ n c i t h e c!;:;ucia'ied
Tables '5
uncert:lfnti.es
f o r o u r bast-fit d c f i n i t - i m o f an i n t - c r n c c j o n p a r t i c l e s i n esch of two consecutive?
aiid
nodules).
(3
ill\iarl
T I the values are givcri
equf.vnI.cnt
As �.a:; beezi d i s c u s r ; e d
f
p r e v i o u s l y , the value of the i r t e r a c t i o n 1eiigt.h c a n b e chenged coil , d e r a b l y
i o u t s i d e t h e s t a t e d e r r o r s by a p p r o p r i a t e changes i n the d e f i n i t i o n o f a n interaction.
,
The m e a n . h t e r a c t i o n l e n g t h s are o b s e r v e d t o b e i n d e p m d e n t .
of the nnmber of i r o n m o d u l e s eniployed to
tl! :'niii
t h e s t a t i o t l c a l uncer
1' t
i
.!
.'i.
t a i n t i e s i n t h e measi.tre,..srit.
No s i g n j . f i c a n t d e p e n d e a c e of t h e i n t e r a c t i o n
I -18
t
l e n g t h on energy is d e t e c t e d .
On t h e h y p o t h e s i s t h a t the i n t c s
a c t i o n leiigt?: i s i11depe12dcilt of eneirgy '?
P = 0.95 f o r pions.
0.0s f o r p r o t o n s azrd
The mean interection l e n g t h f o r pions 10
apprc)xi.wat
L:.
, the sinal1 c h m g e I n incidrnt errs-rgy s h o u l d not a p p r e c i a b l y a f f c c t the dctcr".nation
of t h e n3ari I n c e r a c t i o i i l e n g r f i .
Contiiiilination of t h e p r o t o n b ? m by o t h e r hadrons was small.
E f f i c i e n c y for r e j e c t i o n of n m.d K was metlsurc.d t o b e Getter t h a n
V
Ilieao4s
98M.
by t h e gas C e r c ~ k o vdetector
S i n c e thc f l r i i c of p r o t o n s nlriays
represented inore than h a l f of the trJtal f l u x , t h e c o n t a m i n t i t i o n in t h e p r o t o n beam w a s R l w i y s less than 2%.
,
-19-
1
-
:.
- .
.
.
.
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5 -
I
. . .
.
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,
I
.
.
.
. .... . .... . , . . . , . . . . . . .'
.. . .
-
.
:_
I
. .
,
.
-23
runs was p l o t t e d a s a f u n c t i o n of module number. included i n the data a n a l y s i s the
flu!\
For e a c h module
of t h e i n t e r n c f i o n s d i f f e r e d by
no m r e t h m 2'% from the e x p " c t e d f i t ts t h e d a t a .
We t h u s c o n c l u d e
t h a t all detecLoro have t h e s'me e f f i c i e n c y f c r t h e d e t e c t i o n of an i n t e r a c t i o n t o wfthin a fer4 p e r c e n t .
S e c o n d l y , t h e muon e q u i v a l e n t
p a r t i c j . e c c ; l i b i n t l . u n fcjr thc? first u s e f u l i r o n iitodule wzs a r b i t r a r i l y
val.ue o b t a i n e d d e g e n d s somewhat upon t h e s i g n a t u r e required t o d e f i n e ..
....
an i n t e r a c t i o n .
C x a c t comparl. son v F t h t h e o t h e r aetcm.inot.i,oris air
L\\C
... . .
.i
O v c n t s , the precision of t h e p r e s e n t ircsiil.ts i s g e n c r n l J y g r c l n t t r . 140
s t a t l a t i c a l 1 . y s j g n J . i i c o n t \TarjotLon of
t h e mean i n t e r a c t i o n
l e n g t h f o r p r o t o n s o r p i o n s as n f u n c r i o r i of c?ncry;y 'i.:as ...
. .
t h i s work.
observed i n
Hoxcver, w i t h o n l y two exccptl.onr;, the d a t a p r e s e n t e d i n
T a b l e I11 r;how a , 2 y s t e m a t i c 5% d i f f e r e n c e berween measurements of the mean
:-?! . L
i n t e r a c t i o n l m g , t h made w i t l i cofimic r a y s and t h o s e i n a d c w i t h a c c e l e r a t o r
:.i
produced p r o t o n s .
A c o n - e c t i a n f o r p i o n cori: m i n a t i o n i n t h e cosinic
r a y f l u x ~ i o u l dlower t h e v a l u e o b t a i n e d
111
u n c o r r e c t e d c o s m i c r a y experi-
- .. . .. . ,
I
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-
*:.-;..L
.
.
.
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.
.
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./, i
.
,
-
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-.
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I
r
-
:
xim2nko, A . E . Piorosov, A . G. P:o7.ikov, 0 . F. Ogurzov, V. S . P~:chkov, D. 1'. X.3!l.l\Tet;lereli, Nilci. Piiys. 2, 609 ( 1 9 6 6 ) . 5)
E. L. Androi\.ikashvJ.li, G. 2 . C h i k o v a n i , D . I . G a r i b a s h v i l i , G a b u n i a , Li. B . K a l c a v r i d z e , D. M. K o t l y a r e v s k i , 2 . S h . N a n j a v i d z e , L. .4. R a z d o l s k a y a , and E . N. S h e r e r , Can. J . Pliys. 3, S 6 8 3 ( 1 9 6 8 ) . L . I,.
14. N. K o i i > J s h v i l i ,
6 ) W. ZG
H . Schniidt. (Dissertation Glcl. < 1 ? 6 8 ) unpublis!ied:.
1;.
-
Christlan-Albrcchts
-
Universitat
7 ) W. V. .Tones, K . Pjiikau, U. P o l l . v o g t , W . K. 13. S c h m i d t , R r i d 1.: W. Hi!:;i;ett, A c t a k'liysics H i i n g a r i c a ? 2S u p p l . 4 , 5 2 1 ( 1 9 7 0 ; Nuovo' CFciento Ei;, 5 7 5 , ( 1 9 7 2 ) . L
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G. L. Bashi!i~lj!i;;g;.an, V. X. Isclokopytov, P.. I . Demimov, V. S . Muryin, L. I. S a x y c i : c v a , a n d N . E . S i n y o v , p a p e r HE-24 1 2 t h I n t e r n a t i o n a l Co;:ference o n Cosmic i i x y s , H o b a r t , 5, 221.1 (1971).
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I,. Id. J o n e s , A . E. L'u.c sta n, G . 1). Dtt!eestel-, R . C!. Loo, D. E. Lyon, 1'. V. R m a n a Eiurthy, 1:. 17. K n t b , .'1 R . VJsliwanath, J. G. L e a r n e d , 1'. D. Reederr, l?. J. Wilkes, IC. N. E r i c k s o n , E'. E . Mllls, a n d D . Cork, L h i v e r s i t y of Michigan R e p o r t HE 71-46 R e v i s e d ( 1 9 7 2 ) .
b
> I
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I i
i I
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1
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i'
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lo)
J. F. O~?r,cs, V. K. Ualasuhrnhiiianpan, R. D. P r i c e , 14.. 2 . Ryan, a n d K. F. S i l v e r b e r g , I E E E ?cans. Nucl. S c i iL2, 1 7 (1970).
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._.
._
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S. P. k n i s o v , S. V. Donokov, Y u . P. Gorin, A . I. P c t r u k h i n , Yu. D. Prokoshkin, D. A . S t o y a n o v a , J . V. A l l a b y , a n d G. G i a c o m e l l i , Pliys. Lett. 415 (1971).
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Fig.
1
A scliematic Y i o n i z a t i o n calorj.meter tlsed i n i h i s e x p e r i n t e n t .
Fig.
2a
P l o t of p u l s e l i e i g h t a s a f u n c t i o n of module number. Xn [.his c a s e t h e modr8l.r i n which the i n t e r a c r i o n o c c u r r e d i s clc-ar1.y Fe 3 .
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Fig.
3
P l o t of tlie nicasurrid i n l c r a c t i o n i c n g t h as a f u n c t i o n of t h r e s l i o l d r e q u i r e m e n t s .
Fig.
4
P l o t of st;r?-isti.cnl uncertainty i n the determination of the m(!,ln i n t e r a c t i o n l e n g t h as a f u n c t i o n of threslioid requirement.
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Table I1
&an
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I n t e r a c t l c n Ler?~rkhsof Picns in Iron
A in p.lm2
1'1.8
1
9
I G X / A :i
Percent
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Table III
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Compariscn of E x p e r i c e n t a l 3 e t e m h s t i o n s of K c a n I n t e r a c t i c n L?;..gth.-, of %rr;tcm in Iron
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Experirenters
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A ? h o r e et al.(c) (1960)
24.2
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Accelerator
Bellettiai e t al. (1966)
(4
Cosmic Xays
.
15227
I n t e g r a t e d a l l ha-'-ons i n cosiilic r a y f l u x ( b ) TJalue i n t e r p o l a t e d from measurezents O i i A I and Cu
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