Projectile and target delta excitation in the (3He, t) and (3He, 3He) reactions

Nuclear Physics A5 North-Holland

r®ject e

(1992) 793-810

target delta excitation in the 3 e) reactions (

(3

He, t)

P. Fernândez de Côrdoba and E. ®set

Departamento de Fisica Te6rica and IFIC, Centro Mixto Universidad de Valencia-CSIC, 46100 Burjassot (Valencia), Spain

Received 27 January 1992 (Revised 5 March 1992) Abstracts We study simultaneously the (3 He, t) and ( 3 He, 3 He) reactions on proton and neutron targets in the region of the delta excitation resonance . We observe that the mechanism of delta excitation in the target dominates the (; He, t) reaction on the proton, but the mechanism of delta excitation in the projectile is important in the (3 He, t) reaction on the neutron, and largely dominates the (3 He, 3 He) reaction on proton and neutron targets . The two mechanisms give rise to different shapes in the energy distributions of the t or 3 He outgoing particles and the weights and shapes of the mechanism change appreciably with the energy of the projectile . The combined experimental study of both reactions as a function of energy is thus a much richer source of information on the dynamics of these problems than the study of the (3 He., t) reaction alone, where the experimental efforts have so far concentrated .

l . Introduction

The charge exchange reactions of the (p, n) type, either induced by proton beams or light ions, like the ( ; He, t) reaction, are receiving increased experimental and theoretical attention ' -h ) . The famous shift of the delta peak from the ('He, t) reaction on the proton to the reaction on nuclei''{ ) has been the subject of intense debate [see refs. '_a) for recent reviews] . In ref. '), a part of the shift of the peak is attributed to collective effects in the pion channel . In ref. "'), the idea of delta excitation in the projectile was exploited and it was shown to lead to some shift of strength in nuclei . Meanwhile, further experimental research 4) is showing that the shift is selective and depends on the reaction channel : while no appreciable shift is seen in the irN final-state channel, an appreciable shift is observed in the NN emission channel . This detailed information represents a challenge for theory, which will have to come down to details on the dynamical mechanisms of the reaction. The fact that the shift is seen in the 2N emission channel probably indicates that two-step mechanisms may lay some role too.

o far, all theoretical approaches rely upon one-step excitation of the delta.

(`o,respondence to : l'rof. F. ()set, Dept . de, Ikica Tecirica, Universidcrd de V.,Ileircia, 46100 110r,j , ~~ rtrt V".alencia ), Spain. 0375-9474/92/$05 .00 (C) 1992 - 1 1%evier Science l'ublisher% I1 .V . All ri ht% te%erved

794

de Cordoba, E. Oset / â- excitation E Aniàn&z 1

ur aim here is to pay attention to the mechanisms of delta excitation in the target and the projectile and to suggest an experimental method to extract relevant information on these mechanisms . It is important to have a good control of these mechanisms . Indeed, the most important finding of ref. ") was the fact that the

He, t) reaction on the proton and on the neutron had a very different shape . The reason is that the A -excitation in the target and the projectile lead to different energy distributions and the weight of these two mechanisms is quite different in the (; He, t) reaction on the proton or the neutron . As a consequence, the comparison of the e, t) reaction on nuclei with the one on the proton is rather unfair because nuclei are made out of protons and neutrons . This is, however, what is done in most theoretical studies, which also neglect the excitation in the projectile . A fairer approach is to compare with the deuteron . Indeed, the deuteron already shows a displacement of the strength of the energy distribution towards higher energies of the outgoing tritium . This distribution, both in size and shape was well reproduced in the work of ref. '°) . (3 ,3 What we do in the present work is to show that the related He He) reaction, which can be performed with minor modifications on the presently running experiments, stresses the mechanism of A-excitation in the projectile to the point that it becomes dominant at energies around TH, = 2 GeV. As a consequence, both the magnitude and shape of the energy distribution are quite different than in the (He, t) (3 reaction. The study of the (3 He, 'He) reaction, in connection with the He, t) reaction, is thus a very important tool in order to learn about the dynamical excitation of deltas in nuclei . (3

2. The

odel for NN - NNw

The basic model for the N N - N N 7r interaction used in ref. "'), and which we use here again, is depicted in fig. 1 : a pion is produced in the NN7r vertex and it rescatters with a second nucleon via an s-wave (1a) or a p-wave (1c) in the TrN- 7TN scattering matrix . The p-wave amplitude is given in our model by the A-pole. On the other hand, we can have the pion production in the second nucleon and the rescattering in the first one . The corresponding terms with s-wave and p-wave rescattering are depicted in figs . l b and Id, respectively . The basic couplings we need in order to construct these amplitudes are the NNrcoupling, theAN7coupling and the -aN- ,7rN s-wave amplitude . The NN7 coupling is given by f5

NN7r

A

where q is the momentum of an incoming pion in the NN7r vertex, and ju the pion mass. The structure of eq. (1) holds exactly from a pseudovector coupling, which we implicitly assume, in a frame with q"=O . Since this is not the case here, one

P. Ferncindez de Côrdoba, E. Oser / .1-excitation

795

Fig. l . Feynman diagrams for NN - NN z with pion production in the target (a), (c) or the projectile (b), (d) induced by the s-wave (a), (b) or p-wave (c), (d) TrN- 7rN interaction .

must replace q, coming from the vertices in the final results by - q`', the corresponding invariant magnitude. We also need the s-wave 7rN-> iTN amplitude given by - tSH lrr7rNN - - t 4Îr8 ,

r11,

2A1

Unt,m ;VAA'+ iE,,AA'

2A,

\m~f T mll ce I

where m,, m ;, m,, m, are the spin and isospin variables of the incoming and outgoing nucleons, and A,, A, the isoscalar and isovector couplings . The N®7r is given by -t (5 HN _1 ,r

=f

+ . qT +A +h .c .

in a frame where for art incoming pion with momentum q. Once again, eq. (3) holds q`, by -q2 at the end q 0 =0, and for virtual, space-like pions, one must substitute of the calculations . For real pions where one cannot find the frame with q" = 0, the invariant vertex is given by the same eq. (3) with q the 7rN centre-of-mass momentum . We will write q2 in the formulae for simplicity, with the understanding that the corrections are taken care of at the end. For the coupling constants we take "') .f* , =0.36, .i,` =0.08, 4 rr 4 7r A,=A,+0 .000222[MeV

A ;=0.0075,

where s is the IVlandelstam variable for the rN system and

A,=0.0528,

(4)

the nucleon mass .

â

~aa~

~~¢ fi~7,~~~ q 4~~

~,~ ~

® _®(

aaa

~aaa~3

~~

ä a~~

~t ®~

®

__ ~

Q®

T

~ c un ®~~

Qtil~

i~

~

~

~

~

~~

Q

~

~a aT~

®

~~

.

~

q

Q

~

aa~~

A

P&

Coirdo'ho, F', Owe ? I-eunwevo

%, S P

Miectile .

i we nav the '"cit"an, we have p-wave coupli es. In such c xchange also plays some role, and the nuclear liminate t ction in the absence of form factor~ ~. We then substitute the -,,, exchange by ctive snin-iswnin interaction . Hence we chanee

t is me n form factor icat

f isospin coefficie (j) entering the calculati

S.

~~7ryt~~~rcl~~ c ~

~ir~~d~ c~, ~°.

c~t j

-~etcïlcetä~~®t

c) _2 3

_®

3 .

~. ~ee n

;~,p~ c~äagra

: f~r

ä~n

e~

f)

3

3

r~dnctia~n in the ~ ~, n ~ r~acti®~, ®n ~ar®t®n ®r neaatr®n targets, with

-eticätati~n pan the target and the ~r®^ectile.

t~'c

lot i i~g® ~? the set of iagra s ~~ is e ter t e ( p, n ) reaction on proton neutron t :trgets, together `~it t e isos in coe cients cotres o ing to each gra r~°e s uare t ese coe cie is ~~e o sante t at, in ter s o crons sections, -e~citati-ort in t e target `~it coton target ( ~. ~a ) is nine ti es bigger than -e~citatio~ in t e projectile ( ~. ). t e of er an , the target -excitation neutron target ( t~gs. c a e) has t e sa e strength as the projectile

e~citatio ~ i hgs®

i d an

i f~ .

e

feature ~~o

noting is t at t e target

-

cc anisn~ on t e r ton target has a st engt a factor o t ree larger ti~at tl~e ~:or es on ing ec anis o t e eutron target . l tl~e;e fe~~tures ti~ill sho®~~ ~~° en ~~e st y t e i ? e, t 1 an ~ ' e, ` ~e ) reactions. e~cit~ttion

`~9i~1an nee to e`9aluate ex ectatio ~~alues of , ~~~~ ~°e functions of ' e an t, or ' an ` e . ®r t is '

®~ °

o erators s~it in

ose ~re take for ' e or t function `~° ~° plate in co a alogti~ to t e uar ° o or t el t e aiw , ~~it e , di ercnce that the tiva~ e function in s in-isos i ~ ill no~~ e antis, etric rat er n s~~ etric as ~~-e ha~le in t e hark o et s z ~ . °T e S ( ? ~ x t~( ~ 1 antis~A et~;c ~~°a`°c funct as ur

~~`9e

axed sy. attic and antis° ~~a~°e ~t~ the attic isos i functions and

P. Fertidtide-- de C(;rdoba, F. ®se® / -1-e.xciiaiion

the corresponding ones for spin, in the nomenclat particular the wave function for 'He with spin I is %MS9 %MA

0(3

799 re of ref. 1-1 ) . In

Hel)=,/(',(-pnplll+npplll-ppnîll+ppnlll+pnplll-npplll), e(tl)=1/61- (-pnnlll+pnnlll+npnlll-npnlll+nnplll-nnplll) .

(17)

Then we can show that Ecrz i iW

N=

J)j E 7':i:l$(

N=

PI

(18)

N = -I

where the sum runs over the nucleons . In general we can write these matrix elements ;n the base f states of total spin I j and isospin ! for - He and t. Indicating by 14 the states of either e or t, we have S- I J'l 1 u» = %= 1, M; ; S = !, 10.IT-'' (18a) 2 1 ;s= 29

M, ; S =', 2 M',ITA I T

(]~'l I -iA 0~) = (T

(18b) n

(18c)

With the help of these results or simply with direct calculation, as in eq. (18), we

can evaluate the J-propagator operators between states of 3 He and t, A , jf~j'I Y, (S~;Si+ TA _r+A -ir (7r P (7rA 1,11 1~7rA 1 1 'iejjkcrk.)jEMI

(19)

Thus we find the following results, which we need later +tl Y P 3 He 7r") 3 3 3

(7r"tl 1 Pj.,13 He 7r _~ 1 e

P

+ 3He) 12113

(r o 'Hel 1 %. OT -

el 1

;-~F2(M',1(2,biÉ 3 +3

P

ote that in the case of the

3

He) = (

, -3 'r He) (3

17 2 Sii _ 1 31 i Eiij,0.k

52ç

,133

1 ieii&Uk

3

lmâ

(20)

He, 0 transition, the matrix element is as in the (p, n)

case except that the spin-flip term has opposite sign . One can also see this in a different way by recalling that the T-operator is implicit in the transition (it comes from T" T" = j5,,

3 ie,

and hence the spin-independent term corresponds

~~x~ asr a~m ~~~ C`r~r°c~rah~, uu~~~

J ~ ®~t~irat~c~ra

.

s to e . ( . ®r ractical i e s, i ~ i ter s corres fact toc) e . ( ) inter ere ce et een i g ver ola izatio t e e is r oses, si ce ` en su treat t ~ (; e, t) transiti®n aS if ; t e S i ® o - i terliaS, e c t ~ 5 1 ® i ~~lever, n t t e case ln t ~ (; e, ; e~ ls 1S, ( , ~o . lve ~ ere e ling `~'~t t ver ~ e cle s e anges t e s i transition . s we can s e, the co e e t su uite i e e t t t e correof i, e lit es, ~~ ic are t e irs e en ent

s on ing ones in he i , ) tras~si i ns. . , re aci ave n ~r t e sa e i gra s as i n t e ( ' e~ t ) eaction ~, e ~vou! e -~rave , res ectively. an n to t e left of t e iagra s ~ ; e an t e -excitati® r ) an (1 ) for t e i ere t ter s is still i1~e - .atrix y e s. ( t e ro ectile tivit t e foll wi g ~ an es: t c t rget -excitation in the tar et, e . ( ): ~i3 ote c ange o -excitation (ii ) i the ro ~ctile, e . (1 ): ~û ~ ~ ~S ®~ ~ =i~®;,~ ~ . (

sign in t e ~-~ ter s get t e sa e iagra s as in fi . 2 'itl~ res ect io t e s-`vave ter s, we ~ atrix . e cont i u~tion s-wave scattering re h~ci g t e - ole by t e ~° ~ of t e iag a s is given y e s. ( ) a ( ) `vit t e c a ges : y (i) ~ ~ s-~vave excitati®n i t e tar et, e . ( ): ® ~ - ;. ây

o ~ ~ s-~vave excitati® in t e ro ectile, e . ( ) : e iately fro e . 1 i ~. is last rt~ . erty follo`vs i . 3. ee) i ere t ter . s for t e ( ~ e, ` are e icte in res on ing to these iagra ~s re ive a ai y e s. (

c a ges .

( ii )

r~~ectile excitation res ectively, wit

litueles -wave a ) a ) for target ( e

t e ollodvi g c an

s:

-excitati® in t e ro~ectile, e . l 1 ) : 1 r) ~ .e. o e . (? ). g. 3 `ve a`je ewritten helow eac iagra t e g~ig t o t e lo al isos i c cient i fros~t of tl~e s i -i e e ant ter a, i alogy° to t e coe cients i '~~® ~ . of t e iagra s i o e ~' analogy, for eac g . ` ~e ave t e com es on i wit the :~ -~ â.~ s-`~~ave a iit e re laci t e le. ~° ese ter s are calcu ate sing ~sgain t e for uias o e s. ( ) a D wit t e =~ _a g~s : 9

`~ dJ (

ii ~

°

s-`~4Îa~'~ e~~~tat~

'n t e tar et, e

s-wa~'e excitati n in the

~~oe ~cients t e i ~° ) ~~ith ?

;

iayin

e ole

a

`

~ .

Ql -® -~

° U® .

ro ecti e® e . ( ) : re lace f

coe vi h ~cient is not c ange i ue o e . (

6~n

t e roie of n i

a i a . ( 7 ). ( °T e

o -~

). )

ln a ~lition to t ese chacsg s `ve st o~~ i le e t t e n clear tra sitio ~ a °) factor ref. tat en fro ref. ~'l sii y o i e i

°he a sition . fact®r u

(

)

ti lies t e a

litu es

isc sse

or

ove

soi

Fernândez de Càrdéba, E. Oset / .1-e.ceitaiion 3 He

no

a) - .2

3

b)

C)

2

3He

3 He

C)

42--Z 3

Fig. 3. Feynman diagrams for pion production in the ( ; He, -"He) reaction, on proton and neutron targets, with .1-excitation on the target and the projectile .

It is now instructive to look at the weight of the diagrams with A-excitation i the target or the projectile . As we saw before, the weight for target to projectil excitation in (Te, t) on the proton is 9. By looking at the coefficients in fig. 3 for t e (3 He'3 He) (neglecting the fact that the spin-flip amplitudes are different, because they are small compared to the spin-independent part) we obtain a factor,&-17 for the sa e rati

P Amàndez de Cdrdoba, E. Oseî / 1-e.xeitatioti

802

Conversely the weight of the mechanism of A-excitation in the projectile has passed from being 4' of the target excitation mechanism in (3 He, t) on the p to being a factor about 22 in the (3 He, 3He) reaction on the proton. ith respect to the excitation on the neutron, the ratio of the projectile/target mechanisms passes from being I in the (3 He, t) reaction to 4'3 in the (3He , 3 He) reaction . We thus see that in both p and n cases the ( 3 He, 3 He) reaction is dominated by the 1-excitation in the projectile and, hence, both should have the same shape, and correspondingly also the ( 3 He, 3 e)) excitation on the deuteron . The other point worth noting is that due to the large weight of the projectile ;He, ;He) excitation mechanisms we expect a much larger cross sections in the ( (3 than in the He, 0 reaction . In addition to the diagrams which we have discussed we should consider the antisymmetric partners, but they are very small when using nuclear projectiles 14) since they involve exchange between bound and free particles and, hence, extra form Actors. This is obviously not the case in the (p, n) reaction with free particles for what some of the results obtained here in the (3 He, 0 reaction are not necessarily similar in the (p, n) reactions. The cross section for the (3 e, t) reaction is given by 10)

d

d2u

dE,

Pt (27r)5

A''

,(S,

He )

-1

YJ

Y_ I T1 2 8(E H ,+E(

) - Et - E ( p ') - w ( p,

(22)

where momentum conservation is assumed, PH,+P=A+P+P,,, with pp' the onomenta of the incoming and outgoing nucleon, and relativistic kinematics is used, ukh E( p) and w(p-) the total energy of nucleons and pions, respectively, the function A is the Kdllen function . For the ( - He, 'He) reaction we replace in ed. (22) the tritium variables by those of the outgoing 3 He and the matrix element as indicated before . he width of the .1 is taken as ' 5 ) : 1

6

p 2

p

2

,/-S VS_ +

-3 qN -1

(23)

with q, the c. m . nucleon momentum for the decay of the A with invariant mass Nfs into a pion and a nucleon .

In the magnitude d 2u/df2 dE in the lab system the A-excitation in the target and in the projectile (DEP) give rise to diRerent distributions . Indeed we have for the -excitation in the target (DET) q,- = PHe - Pt,

no = Wnet,

(24)

P. Ferpuindez de Côrdoba, E Oses / 1-e.xciîation

803

while for the A-excitation in the projectile we have qpr

PH, - A - P,. 9

(25) The difference is apparent, in the DET mechanism for a fixed angle d eher of the t, both q,,, and s,, are fixed . The invariant mass of the delta is then fixe this mechanism. The p,, integration can be carried out and leads to the .1-wi allowing to cast the DET mechanism in a different way which is widely used i literature where d2 a/dfl dE is proportional to F d 'Q -

dfl dE 1 DET

oc

(%/ Stg

nSO) n)2 + (IF( So» 2 oc -lm op -

1

-

X + cy) .

(26)

However, the DEP mechanism does not allow this simplification because b t _ As a conseque ce ga r and sp, depend now explicitly on the variable of integration p_invariant mass Nfs p , which are covered in the there is a range of values of the delta DEP mechanism and this gives rise to a shape quite distinct to the one in the mechanism. In ref. '0) it was found that at Tie = 2 GeV the DEP mechanism peaks at much larger values of E, than the corresponding DET mechanism. The other noticeable difference is that, in the DET mechanism, the shape does not depend on the absolute value of EHe but only on the difference pie - pt, while in the mechanism it depends on the absolute value of E, and we obtain different sha at different energies . We carry out the calculation of the cross section by means of ed. (22) for all the mechanisms and take into account the interference, although small, of the DEP and DET mechanisms and the s-wave pieces, which are also rather small by themselves . 4.

esults and discussion

;He,t) ( reaction on the proton and the In fig. 4 we show the results for the neutron, as a function of Tt for 0=0'. We observe that on proton targets the contribution of the DEP mechanism is rather small but modifies the cross section 6 at higher t-energies and leads to a better agreement with the data ' ) . The effect of (3 the DEP mechanism is more apparent in the He, t) reaction on the n-target and lead-. to a substantial strength in the region of high T, The shapes of the reaction on the proton and on the neutron are rather different, as one can see in the figure. Neglecting screening effects and two step processes in the deuterium nucleus, which (3 should be small for the inclusive process He, t) on the d-target, we can obtain this cross section by adding the cross sections on the n and the p. The results are shown 17) in fig. 5 and compared with the experiment . The agreement is rather good but our peak is too sharp. By adding the p- and n-excitations we are shifting some strength toward higher T, energies and this is also apparent in the experiment .

804

Fertitiiidez de Ct;rdoba, E. Oset / -1-e.xcîlaîîtjtî

00 1500

1600

1700

1800

1900

2000

; (MW) Fig. 4. Double-differential cross section for O He, 0 on proton and neutron targets at fixed angle (0 =0°9 as a function of the t kinetic energy . Dotted line: DET on a proton target. Continuous line: DET+ DEP+ s-wave on a proton target . Experimental points for 01-le, 0 on a proton target from ref. "). Long-dashed line: DET on a neutron target. Short-dashed line: DET+ DEP+ +s-wane on a neutron target.

We should also mention t at, as noted in ref. "), the sum of our two distributions shifts the strength but not the pe k. In the experiment the peak is shifted a bit and has not the sharp features of r results, indicating that further corrections are e basic features am waver reproduced by the simple sum of the neutron istributions . These corrections and other many body corrections will ave to be accounted for when looking at the more apparent shift in heavy nuclei . we that the fact that the peak is not moved in our approach, which considers the emission channel is in agreement with present findings in ref. 4), where it is sh wn that the peak in the explicit -ffN channel in different nuclei appears at the s e place as for proton targets. The peak for 2N emission is however largely Is laced at higher t-energies when using nuclear targets and is mostly responsible f r the shift of the peak 4) . The shift of strength apparent in the deuteron is nicely i terprated here in terms of the contribution of the DEP mechanism for the neutron istribKon and is one element to consider in the study of ( 3 1-le, t) reactions in nuclei . he study done here is meant to give further support to the DEP mechanism. by selecting the analogous reaction to the ( 1 1-le, t), which however stresses the role of t Is ache his reaction is the Qe, 'He) reaction, as we discussed in sect. 3. I fig. 6 we s w the results for the (3 He, 3 He) reaction on the proton at THe = 2.0 eV as a functio of the outgoing He kinetic energy and for 0 = 0'. Two features a ear worth noti g. In t e first place the strength of the cross section is much igger tha for the cornea onding ('He, t) reaction . One can see there that the reaction is dominated by the mechanism, as we saw in the former section, and

~`er~raâaac~er c~e C`~~r~®ba, ~`. ®set /

-~~a°ït~rïr~ra

OS

0.8

0 .6

0 .4

0 .2

0 .0

1400

1500

1600

1700 ~, ~

1800

1900

2000

evj

1=ig . 5 . Double-difi~erential cross section for d ; He, t) on deuteron target at fixed angle as a function of the t kinetic energy . Dotted curve : DET mechanism done . Solid curve : DET+ DEPT s-vrave . 1-listogram : experimental results from ref. °' ) .

that the cross section with the I~ET mechanism alone is a negligible fraction of the total . On the other hand, the other apparent feature is that the peak ofthe distribution is displaced at higher outgoing ~Ie kinetic energies than the corresponding t-energies in the ( ; e, t) reaction. As we mentioned, the strength and shape of the I~EI' mec anis depends on the abso®utr value of the incoming Iie energy . Thus we have calculated the results at THe = 10.0 GeV. In fig. 7 we show the results for the ( ; e, t) reaction at T~,e = 10 eV. The strength has increased as a consequence of the fact that g' = 0 ere and the nuclear form factor close to unity, but the shape and widths of the distribution is I' ec anis much like in fig. 4. V~/e can also see in the figure that the role of the is .ow negligible. On the other hand, in fig. ~ we plot the results for the (~ e, ; e) reaction at THe = 10 Gel/ and we see that the shape is still dii~erent to the one in the (; e, t) reaction. On the other hand, while the strength of the (~ e, t) reaction

1

È?i~

P. Fertitäartîem de it)'radnf)ca, L.

O.ced / .l-e.\eiaaaîit)ta

f

T----F---l

7 M > q 3

1

G) C)

31 y .s c

c

">

/-0-,

1,

:.,

o

U +

t n. " . LU oo G]

O

t C ~

`.

O E

COD

,O

3

c

Ô ."I

1

(AaYj/ .is/qtu)

i

~,

3PlIP/vo p

I

1

1

I

I..,

~w u

v v 3 C Ç Q

P Ferncindez- de C®rdoba,

1

'He p __> 'He

E. Osec / .1-exei'ation

807

n

9=0'

6

TH.= 10 GeV

W b G ICY b

N

--~

J7

8600

1~

8800

1

9000

9200 9400 Txe(MeV)

9600

9800 10000

Fig. 8. As in fig. 7 but for the ('He, 'He) reaction .

cross section has increased, the one for the (; He, 'He) reaction has decreased with respect to the values at T,,, = 2 GeV. The decrease of the ('He,'He) cross section is a consequence of the fact that the DEP mechanism plays now a smaller role, because the phase space does not favour placing the .1 on-shell in the DEP mechanism . The DET mechanism plays now a more important role than at 2 GeV, but the DEP mechanism is still important and leads to a different shape than the one in the (`He, t) reaction . Finally, in figs. 9-11 we show the results for the excitation on the neutron : In fig . 9 for the (- He, 'He) reaction at 2 GeV, in fig. 10 for the ('He, t) at 10 GeV and in fig. 11 for the ('He, 'He) reaction at 10 GeV. Our absolute values for 10 GeV should in principle be less accurate, since one is extrapolating the effective interaction of eq. (15) to a much higher energy regime than the one where this interaction is tested. The qualitative features about the relative strength of the different mechanisms should, however, be quite firm .

808

P. Fernandez de Côrdoba, E. Oset / A-excitation 0

r-

r

ô

ô

_~o0

Cr L m

0 0 v i~.

(AgNI/ .is/qtu)

ZpUp/DZ p

u

v a

c. C O v. C u C C O C O u ar v

v v

s

ar C4

(1l-In/as/qua)

3püp/Dop

f? Fernandez de C®rdoba, E. Oset / 41-excitation

9

W

w

8600

8800

Fig. 11 . Results for the

9000

9200 9400 TH®(MeV)

(3 He, 3 He) reaction on

9600

9800

10000

a neutron target at 10 GeV.

5. Conclusions

We have studied the ( ; He, t) and (; He, IHe) reaction on the proton and the neutron at THe = 2 and 10 GeV. We have made emphasis in the mechanisms of A-excitaiivn on the target and the projectile and have found that while the DEP is rather small for the (; He, t) reaction on the proton, it is quite important for the reaction on the neratron . This leads to a shift of strength towards higher t-energies of the differential cross section on the deuteron with respect to the one on the proton target . However, the most spectacular effects of the DEP mechanism are found in the ( He, 3 He) reaction, where we find that the DEP mechanism is mostly responsible for the reaction at THe = 2 GeV, giving rise to a cross section quite different in shape and magnitude to the (3 He, t) one .

S 10

f'. h`~raaa,ad~~

c ,~(irair~ha,

. (~sct /

- ~`c°itatiraaa

eco es less i port~nt and e , t e ec anis t i energies, ~, t ~ ts egligi le in t e ( ~ e, t) reactio , ut it still as so e a precia le strengt in the . e, ~ e ) reaction . ( t e ( ~ e, t ) an ( S e, ~ e) reactl®nS t is clear that the si altere s stu y t e reaction ec anis s o f e nucleon excitation 0 ers n interestin innig t i char exc a e reactio s. ile t e (; e, t) reaction in t e alfa re ion and t e e as receive uch ex eri entai acte fion, t e ( ~ e, = e ) reaction as not yet been icates t at a si ultaneous study of the st ie ex eri entally . he resent wrork i uc ric er source of i for ation on the reaction mechanisms t`vo reactions is a than the (z e, t) reaction alone, an vwe urge t e ex eri entalist to carry out this reaction.

his `vor is partially sup o ed

y C C `I' roject no.

90-0049 . l'. Fern~ndez

e Cordoba `vishes to ac nowle ge t e ellov++s i from the Consejo Superior de Investigaciones Cient~ cas. he co potations are done in part in the Centro Infor~tico de la L~niversidad de ~lale cia . e e e ces 11 (' . Gaarde, Nucl . Phys. A47 119881 475c 21 E.A. Garee`~, Yu .L. Ratis, E .A . Strokovsky, ®. Melkinova and J .S . Vaagen, talk at I-Iirschegg Meeting 1 Austria 1 January 1991 3 ) F.A. Gareev, Yu .L . Ratis, E .A . Strokovsky and J .S . Vaag°n, talk at Varenna Meeting ( Italy ),June 1991 4) G . Gaarde, talk at the Int. Workshop on pions in nuclei, ed . E . ®set, M .J . Vicente-Varas and C . Garcia-Recio, Peaàiscola, June 1991 1 World Scientific, Singaporel p . 375 5 ) ß .1C . Jain, ihid, p . 40b b) E .A . Strokovsky, E .A . Gareev and Yu L . Ratis, ihid, p .395 i ) V .G . Ahleev et al , Sov . Phys . J E7- P Lett . 4® 11984 ) 763 ; Phys . Lett . 264 11 y911 264 S ) ~ . Ellegaard et al., Phvs . Rev . Left . X 119831 1745 99 J . elorme and P .A .M . Guichon, Phys . Lett . 13263 119911 157 li)) E . ®set, E . S üno and . Toki, Phys . Lett . 224 (19891 249 i 11 R . ~ achleidt, 1C . olinde and Ch . Elster, Phys . Reports 149 119811 1 1 _' 1 J .I) . Eljorken and S .D. [)rail, Relativistic quantum fields l McGraw-Hill, New York, 19651 i , 9 F . E . ( lose, An introduction to quarks and partons l Academic Press, New York, 19791 1-19 V . l~imitriev, ® . Suchkov and C . Gaarde, Nucl . Phys . A 59 ~ 19861 503 159 E . ¬)set and V~' . `Weise, Nucl . Phys . A319 119791 477 1f~9 (' . Ellegaard ea al., Phys . Lett . 154 (19h51 110 17 9 (' . Gaarde, Nuci . Phvs . A47g 119881 475c