deuteron diffractive dissociation

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Revista Brasileira de Flsica, Vol. 14, no 2, 19ü4 Deuteron Diffractive Dissociation A.C.B. ANTUNES and F. CARUSO Centro Brasileiro de Pesquisas Fisicas, Rua Dr. Xavier Sigaud 150, Rio de ~aneiro, 22290, RJ, Instituto de Fkica, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, Rio de Janeiro, 21944, RJ and Instituto de Física, Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier 524, Rio de Janeiro, 20550, RJ, Brasil Recebido em 24 de agosto de 1984 Abstract Deiiteron diffractive dissociation is studled in the framework of the Thret? Components Deck Model. The a p p l i c a b i l i t y o f t h i s model t o 1 ight nuclei diffractive dissociation is assumed. The ex l s tence of a slope-mass-cose correlatlon Is pointed out. The relevant distributions are obtained. 1. INTRODUCTION In this paper we present an analysis of the diffractlve dis- sociation oF the deuteron, p+d -+ p+n+p. The descrlption of this reaction i s done thrnugh the Three Components Deck Model (TCDM) ' . Thi s model has been introduced to describe the hadronic dlffractive dissociation re - actions (DDI) as a+b+(1+2)+3. The TCDM has been able t o describe the characteristic features of the DDR and, among these, the model de- scribes very well the slope-mass-correl~tions3~4. The TCDM has been extensively applied to severa1 types of DDR, with differtrnt spin'and parity structures in the dissociative vertex (a + 1+2). In this work we intend to suggest that the TCDM can be ap- plied also .to light nuclei dissociations (in our case the deuteron) . The idea subjacent to our expectation is the principle of nucleardemc- rac y 5 among nucleons and nuclei , proposed for the strong interact ions. In the three components o f the TCDM there appear the dis- sociat lve vertex' of the deuteron 6 d + p+n. Each component has one par - ticle of this vertex off mass shell. In order to find the form of the coupllng in this vertex we make some approximations. We assume t h a t a1 I the particles are on shell and that the deuteron i s an struc- tureless particle. We neglect the mal1 contribution of the D wave t o the wave furiction of the deuteron. The reason for these assumptions i s that the introduct form factors i n the TCDM, to take into account the off mass she ion of 11 ef-

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Revista Brasileira de Flsica, Vol. 14, no 2, 19ü4

Deuteron Diffractive Dissociation

A.C.B. ANTUNES and F. CARUSO Centro Brasileiro de Pesquisas Fisicas, Rua Dr. Xavier Sigaud 150, Rio de ~aneiro, 22290, RJ, Instituto de Fkica, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, Rio de Janeiro, 21944, RJ and Instituto de Física, Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier 524, Rio de Janeiro, 20550, RJ, Brasil

Recebido em 24 de agosto de 1984

Abstract Deiiteron d i f f r a c t i v e d issoc ia t ion i s studled i n the framework o f the Thret? Components Deck Model. The a p p l i c a b i l i t y o f t h i s model t o 1 ight nuclei d i f f r a c t i v e d issoc ia t ion i s assumed. The ex l s t ence o f a slope-mass-cose cor re la t lon I s pointed out. The relevant d i s t r i bu t i ons are obtained.

1. INTRODUCTION

In t h i s paper we present an analysis o f the d i f f r a c t l v e d is -

sociat ion oF the deuteron, p+d -+ p+n+p. The descr lpt ion o f t h i s react ion

i s done thrnugh the Three Components Deck Model (TCDM) ' . Thi s model has

been introduced t o describe the hadronic d l f f r a c t i v e d issoc ia t ion re-

actions (DDII) as a+b+(1+2)+3. The TCDM has been able t o describe the

character is t ic features o f the DDR and, among these, the model de-

scribes very wel l the slope-mass-correl~tions3~4.

The TCDM has been extensively applied t o severa1 types o f DDR,

w i th d i f fe r t rn t spin'and p a r i t y structures i n the d issoc ia t ive v e r t e x

(a + 1+2). In t h i s work we intend t o suggest that the TCDM can be ap-

p l ied a lso .to l i g h t nuclei dissociat ions ( i n our case the d e u t e r o n ) . The idea subjacent t o our expectation i s the p r i nc i p l e of nucleardemc-

racy5 among nucleons and nuclei , proposed f o r the strong in teract ions.

In the three components o f the TCDM there appear t h e d is -

sociat lve vertex' o f the deuteron6 d + p+n. Each component has one par-

t i c l e o f t h i s vertex o f f mass she l l . In order t o f i n d the form o f the

coupllng i n t h i s vertex we make some approximations. We assume that

a1 I the par t i c les are on shel l and that the d e u t e r o n i s an s t ruc-

tureless pa r t i c l e . We neglect the m a l 1 cont r ibut ion o f the D wave t o

the wave furiction o f the deuteron.

The reason f o r these assumptions i s that the introduct

form factors i n the TCDM, t o take i n t o account the o f f mass she

ion o f

1 1 e f -

fects, could destroy the s e n s i t i v e in ter fe rences among the components

of the modell . These in ter fe rences a re the mechani sms t h a t descr i be

the slope rnass co r re la t i ons .

Then the o f f rnass she l l and form f a c t o r e f f e c t s are introduced

by ad jus t i ng the pararneters o f the TCDM, as the e l a s t i c d i f f r a c t i v e

slopes (B) and the asymptotic t o t a l cross sect ions otOt(m), which ap-

pear i n each component. These parameters are f i t t e d w i t h values near

the on she l l experimental ones.

Another rnot ivat ion t o apply the TCDM t o the deuteron d i f f r a c -

t i v e break up i s the inexistence o f proton-neutron resonances, i n the

energy range considered. I n general the TCDM, even i n i t s s i m p l e s t

fo rmula t ion , i s v a l i d on l y f o r low energies (JsT) o f t h e d issoc ia ted

subsystem (1+2), below the threshold o f resonance format ion. For higher

energies the model must be reggeized and dual i ~ e d " ~ , i n order t o de-

scr ibe the h igh energy behaviour o f d i ssoc ia t i on .

As f o r deuteron d i f f r a c t i v e d i s s o c i a t i o n there are no reson-

ances i n the d i ssociated subsystem (proton-neutron) the model i s ex-

pected t o be val i d i n a l a rge r range o f energy than i n those cases i n

which resonances do e x i s t . The TCDM i s constructed w i t h the Born terms

of proton and neutron exchange and deuteron d i r e c t p o l e , w h i c h a r e

s u f f i c i e n t t o descr ibe the low energy b e h a v i o u r o f d i s s o c i a t i o n .

Reggeization and dual i z a t i o n t h a t descr ibe the h igh energy b e h a v i o u r

correspond t o in t roduc ing the necessary co r rec t i ons i n the B o r n a p-

proximat ions.

I n the next sec t ion the h e l i c i t y amplitudes, w h i c h descr ibe

the deuteron d i f f r a c t i v e d i s s o c i a t i o n using the TCDM, a re p r e s e n t e d .

I n sec t ion 3 the numerical resu l t s a re discussed and some conclusions

are presented. In the Appendix we de f i ne ukefu l v a r i a b l e s and ex-

pressions needed t o descr ibe the TCDM.

2. THE APPLICATION OF THREE COMPONENT DECK MODEL TO DEUTERON BREAK UP

The h e l i c i t y amplitude o f deuteron break up, g iven by the TCDM,

i s the coherent sum o f the Born terms showed i n f i g . A2. Fol lowing the 3b p resc r i p t i ons t o w r i t e the components o f the model g iven i n reference ,

and using the k inemat i ca l resu l t s shown i n the Appendix, we have f o r the

s-component:

where

wi t h

and

which i s the d i s s o c i a t i v e ver tex o f deuteron i n t o nucleons6, neg lec t ing

the D wave c o n t r i b u t i o n t o the deuteron wave funct ion. md and m are

r e s p e c t i v e l , ~ the deuteron and nucleon rnasses, and

i s the hel i c i t y conserving Pomeron-deuteron coupl ing4". The u-component

i S

where

and

And the t-component reads

where t

T = i g (t2)/(m2-t,)

and

In the hlgh energy approxirnations, where 6, a,, s, >> Sl, lt, l . l ~ ~ l , lt21, m'$ m2, these components becme

+ 4sls2/s]e0 (p,~,) + (ul- t , ) (senciE1(paa) + cos a (p,~,) 11 -i -i

- pl .~(paa)/2m + (sena E'(P,\) - E ' ( ~ ~ \ ) ) Y ' - ~ ~ ( p ~ \ ) y ~

-i

+ C(cos a + I E' (paha) - ( /pals&n o / /B i l ) ~ ' (pala)

-+ - ( 1 + balcos a / J 8 1 ) ~ 3 ( ~ a ~ a l l ~ 3 1 v ( - ~ 2 , - ~ 2 ) ( 14)

and

( t ) lGa i AX A - TÜ(~,Ã,) L, + is - sen cr (sen a 0.03

1 2 , 2Js;.

C a l c u l a t i n g t h e s p l n 1 /2 and s p i n 1 wave functions i n

the Gottfried-Jackson system, defined i n the Appendix, these amplitudes

become.

For Ãa = O

-2iAl$ x [2X2 cos 96A A - sin 9 e

1 2 61, ,-IJ]

- % i l $ - singe 611 , -J -2A2 Cs

x ( /& I - Ea cosa) [sin e sen(2A14)bA - 2iA, (cos2 (0/2) 1 2

(18)

4 4 ~ ~ 4 + sin2(g/2) e

)6A,i-h> + (E, ~ + l $ , [E, cos 9 ) [-i2A2

-i4X14 x [ZA, sin 0 cos(2A1$ oA A + (cos2(0/2) - sin2 (9/2) e

1 2

- i 2x2$ + s i n 8 e +

6 ~ 2 , - ~ , 1 - 2'1 C s I ~ , I s i n ( E ~ - I P ~ I C O S a ) / 2 q l

[(El+m) + 4AlA2 (E1-m)] C-2h2si n 8 c o s (2h2$) 6X 1 2 + ( s i n 2 (8 /2)

-i4A,$ - c o s 2 ( 0 1 2 ) ~ )612,-h! + i ( s ~ & l s i n a / 2 q {-4hl ( h , + h 2 ) I;, I

+ + + (E1 IpaI- I P , I a c o s e C-32Al s i n a@,+m) - 4XlX2(El-m)J [-2A2cos

6h 1 2 h -i2X2$

+ s i n 8 e 6 A,, -h1 1 - 4 ( h ) 1 1 [:siri 8 ~ i n ( 2 h , $ ) 6 ~ 1 2 h

-i4A2$ - 2 i h 2 ( s i n 2 (8 /2) + c o s 2 ( e / 2 ) e ) 6 h 2 , - ~ 1 I

and f o r Ia = I 1

+ i;lQ s i n 8 s i n ( 2 X , $ ~ ) 6 ~ + 2hahl ( c o s 2 (8 /2) 1 2

- i2h1$ - s i n Oe

õ ~ , ,-h I

- i2h1$ x ( 2 X , c 0 s ~ 6 ~ - s i n o e

1 2 6 ~ 1 , -h2 )I + 41, (A,+A,) IP1 I s i n a

x {2iX2 [ ( E ~ ~ Z ) - 411A2 (E, -m)] {-sen a (2X1 c o s 0 1 2

- i2Xl$ - s i n 0 e

,-h2 ) + c o s a [2X1 s i n e c o s (2A1$)6A h

1 2

and (21

-X4h2+ x ( [ -2~ , s in 8 c o s (2A,$)bX h + ( s tn2 (8/2) - c o s 2 (0/2) e

1 2 )6X, , -1J

-22h2@

x (-21, cos 0 6v2 + s i n 0 e 6 1 2 , -1,

I] + 4~~ (A,+x,) 1 s i n a

-i4X2@ G i n 8 ~ i n ( 2 A ~ + ) 6 ~ 1 2 h + 2 ih2(s in2(0 /2) + cos2(8/2)e ) 0 ~ 2 , - ~ 1

- i4A24 + i \ ( -21, s i n 8 cos(2h2@) 6h + ( s i " (0/2) - cos2(0/2)e

1 2 )012,-h1 1

- i2X2+ ;Ia@ + s i n 8 e 6 )I + (I;, 1/2m> si. 0

12 , -1,

-i2A2@ - s i n 0 e 6

1 2 , - 1 1 ) + cos a E-2h2sin 8 cos (2A2@) 61 1 2 A

The subreact ion bd + pn, as appears i n f i g . AI , 1s submitted

t o some cons t ra in t s due t o fso3pIn conservat ion. As the Pomeron has

the vacuum quanturn numbers , and the deuteron i n an i sos ing le t , the i n -

i t i a l s t a t e ] ~ , d > i s a I I = o , I,=0> i sosp in s ta te . Then, by isosp in con-

servat ion, va l i d i n the s t rong i n te rac t l ons , the f i n a l s t a t e Ip,n> must

a l so be an i s o s i n g l e t [1=0, Z3=0>.

As the complete space, sp in and Isosp in wave funct ion, i n t h i s

case, must be antisymmetric under exchange o f the p a r t i c l e s , and the

i s o s i n g l e t i s antisymrnetric, the space and spin p a r t must be symmetric.

Thus, the h e l i c i t y amplitudes (17 t o 22) must be symrnetrized b e f o r e

computing the cross-sect ions. To do t h i s we def ine

and so the symmetric h e l i c i t y amp

way.

150

I i t u d e s are obtained i n as t ra igh fo rward

3. RESULTS AND DISCUSSION

The d i f f e r e n t i a l cross sect

Gott f r ied- Jackson system, whose coord

eq. ( A I O ) .

ions were c a l c u l a t e d i n t h e

ina tes are shown i n f i g . A 3 , using

Figs. 1 and 2 show t h a t the main p a r t o f the events mustoccur

f o r values o f the e f f e c t i v e mass M very near the threshold, and f o r Pn

smal l angle:; symmetrical l y forward and backward i n the GJS. The f i r s t

d i s t r i b u t i o n shows a peak t h a t i s a consequence o f the deuteron p o l e ,

very near the threshold, i n the unphysical region.

Fig.1 - E f f e c t i v e mass (M ) , d i s t r i b u t i o n , Pn

i n tegra ted i n $1(0,27r), cos 9 (-1 .O, 1 . O ) and

t, ( o 9 -1.0).

3 I

Cos e= Figs . 3 t o 6 show t h e s t r o n g

F ig .2 - d u / d c o s e d i s t r i b u t i o n ,

i n t e g r a t e d i n 4(0,27r), t,(O,-1.0)

and M (1.52, 2.22 ( G ~ v ) ) . Pn

F i g s . 4 and 6 show

t h e mass range increases. On

fe rence s t r u c t u r e s , w i t h a d

i ncreases.

The e f f e c t i v e mass

f i g s 7 t o 12. F i g s . 7, 9 and

r e l a t i o n t h a t occur i n t h i s r e a c t i o n . The d i s t r i b u t i o n s presented c o r -

respond t o two e f f e c t i v e mass i n t e r v a l 1.92 ,< M 5 2 . 2 2 ( G ~ v ) a n d Pn

2 .22 ,i M ,< 2.52 (GeV), and t o t h r e e i n t e r v a l s o f cos 9 : -lScosB<,-0.9, Pn

-0.3 6 cos O& 0.3 and 0.9 ,< cos 6 6 1.

d i f f r a c t i v e peaks whose s lope decrease as

t h e o t h e r hand, f i g s . 3 and 5 show i n t e r -

i p a t t, = 0, t h a t become smooth as themass

i n t e r v a l o f f i g s . 3 and 4 i s subd iv ided i n

11 show s e p a r a t e l y the c o n t r i b u t i o n s t o t h e

s t r u c t u r e t h a t appear i n f i g . 3 . These f i g u r e s (7 t o 12) show a l s o t h e

slope-mass-cose c o r r e l a t i o n i n a mass range neares t t h e t h r e s h o l d .

1.92SMpnS 2 . 2 2 ( ~ e ~ ; 0.9 S I Cos 0 1 S 1.0

I I I

I 02 0:4 0.6 c 1 I

- t, (Ge v2 Fig .3 - du/dt, d i s t r i b u t i o n , in -

tegra ted iri 4(0 ,2n) , Mp, (1 .92 ,

2 .22 ( G ~ v ) ) and Icos 01 (0 .9 , l .o ) . F ig .4 - da/&, d i s t r i b u t i o n ,

i n t e g r a t e d in 4 ( 0 , 2 , r r ) ,

M ( 1 . 9 2 , 2 . 2 2 ( G e V ) ) a n d P n

I c o s 81 ( 0 , O . j ) .

2 . 2 2 ~ ~ ~ , ~ 2 . 5 2 ( ~ e ~ ) 0.9 5 l Cos 8 1 1 1.0 d F i g . 5 - d o / d t , d i s t r i b u t i o n , i n - ' O2 O4 t e g r a f e d i " 41(0 ,2n) , M p , ( 2 . 2 2 ,

-t2('e v2) 2 . 5 2 ( G ~ v ) ) a n d [ c o s e 1 ( 0 . 9 , 1 .O).

F i 9 . 6 - d a / d t , d i s t r i b u t i o n , i n -

3 t e g r a t e d i n $ ( 0 , 2 n ) , M ( 2 . 2 2 , Pn

2 . 5 2 ( G e V ) ) a n d l c o s 0 1 ( 0 , 0 . 3 ) .

1.925 ~ ~ , 1 2 . 0 2 ( ~ e ~ : 0.951 Cos e 15 1.0

Fig .7 - du/dt, d i s t r i b u t i o n , . i n -

t e g r a t e d i n $ ( 0 , 2 ~ ) , M (1.92, Pn

2.02 ( G ~ v ) ) and Icose l (0 .9 , l .O).

1.925 M,,,,s~.o~(G~v: I Cos 0Ii0.3

F ig .8 - du/dt, d i s t r i b u t i o n , i n -

t e g r a t e d i n $ ( 0 , 2 ~ ) , M' (1.92, Pn

2.02 ( G ~ v ) ) and Icose l (0,0.3).

F ig .9 - da/dt2 d i s t r i b u t i o n , i n -

t e g r a t e d i n $~(0 ,2 í~ ) , Mpn (2.02,

2.12 (GeV)) and i cos e1 (0.9,l.o).

2.02 6 Mp,62.12 (G~v : I Cos 8 1 ' 0.3

Fig.10 -da/dt , d i s t r i b u t i o n , i n -

t e g r a t e d i n $ ( 0 , 2 ~ ) , M (2 .02 ,

2.12 (GeV)) and c o r Br?0,0.3).

F ig .1 l - da/dt2 d i s t r i b u t i o n ,

i n t e g r a t e d i n 4 ( 0 , 2 n ) , Mpn

(2.12, 2.22 (GeV)) and IcosOl

(0.9, 1.0).

Fig.12 - du/dt, d i s t r i b u t i o n , in tegra ted

3.8 i n $(0,21~), M (2.12,2.22(GeV) and Icosel pn

- t 2 ( ~ e v Z ) (0,0.3).

This c o r r e l a t i o n i s a consequence o f d i s t r u c t i v e in ter fe rences

among the th ree components o f the model. A d e t a i l e d discussion o f these

in ter fe rences e f f e c t s i s d i scussed e1 ~ e w h e r e ~ ~ ' ~ . The present r e s u 1 t s

were ca lcu la ted f o r 24 GeV protons i n the labora tory system. This en-

ergy value i s a t y p i c a l one t o assure the v a l i d i t y o f the model. Not-

wi thstanding, the amplitudes given here could be used t o ca l cu la te the

cross sect ions a t o ther energies, i n order t o compare our r e s u l t s w i t h

experimental ones. We were unable t o f i n d experimental r e s u l t s t o make

t h i s comparison.

The d i f f r a c t i v e deuteron break up pd -t p(np) i n the s i mpl e s t

example o f l i g h t nuc le l DDR. I n the a p p l i c a t i o n o f TCDM t o t h i s reac-

t i on , the deuteron i s t rea ted as an elementary p a r t i c l e . I f the pred ic -

t i o n s o f the model presented here were confirmed, they would show the

small c o n t r l b u t i o n o f the deuteron s t ruc tu re t o the d i f f r a c t i v e d i s -

soc ia t ion , as expected. Th is study could a l s o be used t o c l a r i f y some

aspects concerning the a p p l i c a t i b i l i t y o f nuclear democracy p r i n c i p l e

t o the DDR.

The d i f f r a c t i v e d i s s o c i a t i o n o f deuteron i s character ized by

the k inemat ical region where i t occurs, t ha t i s , h igh energy ( s > l D G e ~ ~ ) ,

and small niomentum t rans fe r (-t, < 1 Gev2). A t t h i s k inemat ical r e g i o n

the reac t i on i s per iphera l and the Regge phenomenology may be used. The

small momentum t rans fe r a1 lows us t o presume tha t the pomeron exchange

dominates the process.

The d i f f r a c t i v e cross sec t ion f o r deuteron break-up, obtained

i n teg ra t i ng the d i s t r i b u t i o n o f f i g . 1 i n the i n t e r v a l 1.92 < M < 2.52 Pn

GeV, i s udif e 2.33 mb.

An es t imat ion o f the non -d i f f r ac t i ve cross s e c t i o n f o r t h i s

process, using a s ing le sca t te r i ng approximation and n e g l e c t i n g s p i n

e f f e c t s , g ives a 13 mb. non- d l f f

Using a naive impulse approximation model w i thout sp in e f f e c t s , w i th t e l a s t i c -Bt2

(t,) = e , t o ca l cu la te the e f f e c t i v e mass d i s t r i b u t i o n Pn

due t o the non d i f f r a c t i v e con t r i bu t i on ,weob ta in apeak a t the threshold.

The he ight o f t h i s peak i s about 10 mb/GeV, which may be cornpared w i t h

the 39 mb/GeV of the peak due t o f ig.1. The peak i n donon-dif /dMpn be - haver l i k e ( ~ , - r n ~ ) - ~ , s i m i l a r i y t o t h a t o f dodif /dMpn near the threshold,

but i s broader, g i v i n g s i m i l a r c o n t r i b u t i o n t o the i n t e g r a t e d cross sec-

t i o n . To observe the d i f f r a c t i v e e f f e c t s , use should be made o f the d i f -

ference i n the shapes o f the two peaks.

F i n a l l y we would l i k e t o s t ress t h a t t h i s i s the f i r s t a p p l i -

ca t i on o f the TCDM t o l i g h t nuc le i d i f f r a c t i v e d i ssoc ia t i on , which en- . .

la rge the range o f a p p l i c a b i l i t y o f the inodel.

We would l i k e t o thank very much Profs. C. Alvear, J. Benuzzi,

A. Santoro, M. Souza and S . Wulk f o r f r u i t f u l d iscussions and a l s o thank

Pro f . J . Tiomno fo r a c r i t i c a 1 reading o f the manuscrlpt.

APPENDIX

Tti is Appendix contains a sumnary o f the k inemat ical var iab les

and expressions usefu l t o descr ibe the deuteron d i f f r a c t i v e break up.

The DDR a+b + (l+2)+3, i n general, and d+p + (p+n)+p i n p a r t i c u-

l a r , may be represented as i n f i g . ( A I ) .

The TCDM which descrlbes these react ions i s represented by the

diagrams o f f i g . ( ~ 2 ) .

Fig.AI - d+p -+ p+n+p DDR, fac to r i zed by

Pomeron exchange i n t o the e l a s t i c vertex

pPp and t h e d i ssoc ia t i on subreaction

P + d + p+n.

F i g . A 2 - TCDM componen ts w h i c h c o n t r i b u t e t o the DDR d+p -+ p+n+p.

159

The fourmomenta correspond i ng t o the externa1 1 ines a re pi (&= =a,b,1,2,3), and f o r the interna1 l i n e s we de f i ne

q=Pa-P l , k=Pa-P2 and P = P , + P 2 (A. 1 )

At the d i f f r a c t i v k v e r t i c e s the fo l l ow ing fourmomenta are used

K = (pa+p)/2 and R = (pb+p,)/2

Some inva r i an ts required t o descr ibe the TCDM are

2 2 s , = (P,+P,)~ , t1 = (pa-pl) . Ul = (pa-p2)

and

t2 = (pb-p3) * (A.3)

-f

The energies (Ei) and the mornenta lpZl (i=a,b,1,2,3) i n the -+ -+

12 system (pi+pp=l)), as í unc t i ons o f the i nva r i an ts are

where

and X(x,y,z) i s def ined by

h(x,y,z) = x2+y2+z2 - 2 ( q j + xz + yz)

I n the R12 system we de f i ne the Gott f r ied- Jackson system (GJS).

The o r i en ta t i ons o f the axes a re glven by

The angular coordinates o f the momenta a r e

The GJS i s shown I n f i g s . (~3).

X

I

I m

Y Fig.A3 - Angular coordinates o f

the momenta def ined i n the GJS.

High energy approximations a re v a l i d a t the k inemat ical reg ion

charac ter i s t i c o f the DDR. They correspond t o

Wi,thi n these approximat ions we have

2Q.R = s2 , 2P.R s , and 2K.R s ( A . 8 )

For a th ree p a r t i c l e s f i n a l s ta te reac t i on the c r o s s - sect ion

i s g iven by9

where

REFERENCES

1 . G. Cohen-Tannoudji, A. Santoro and M. Souza, Nuc l . Phys. 8125, 445

(1977) ; G. Cohen-Tannoudj i, D. Levy and M. Souza, Nucl . Phys. 8229, 286

( 1 977) . 2 . G. A l b e r i and G. Goggi, Phys. Rep. 74, 1 (1981).

3. a) A. End le r , M.A.R. Monte i ro , A. Santoro and M. Souza, Z. f u r Phys ik

C7, 137 (1981); b) A.C. Antunes, A. Santoro and M . Souza, Rev. B r a s . d e

F í s i c a 13, 415 (1983) and i b i d 13, 601 (1983).

4. A.C. Antunes, A. Santoro and M. Souza, "Systematlc o f t h e slope-rnass-

- c o r r e l a t i o n s i n d i f f r a c t i v e d i s s o c i a t i o n reac t ions" , i n p r e p a r a t i o n .

5 . G . F . Chew , S-Matriz Theory of Strong Interactions, (w. A. Benjarni n I nc

( N . Y. ) , 1961), and references t h e r e i n ; i n B. de W i t t and M. Jacob (eds.),

High energy physics, Les Houches Lec tu res (Gordon and Breah, 1965) . 6. M. Gourdin et aZ . , Nuovo Cim. 37, 3240 (1965); G.W. Bar ry , Ann. o f

Phys. 73, 482 (1 972).

7. M.D. Scadron, Phys. Rev. 165, 1640 (1968).

8. P.D.B. C o l l i n s , An -Introduc~ion to Regge Theory & Hcgh Energy Physics,

(~arnb. Un iv . Press. 1977).

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Resumo

A d issoc iação d l f r a t i v a do deu te ron é estudada no c o n t e x t o do Modelo Deck a Três Componentes. Admite-se a a p l i c a b l l i d a d - des te modelo à d i s s o c i a ç ã o d i f r a t i v a de núcleos leves. Observa-se a e x i s t ê n c i a de uma c o r r e l a ç ã o massa- inc l I n a ç ã o - d i f r a t i v a - c o s e . Obtém-se as d i s t r i b u i çÕes r e l e v a n t e s .