Microscopic analysis of baryonic exchange mechanisms in the dd → n3He reaction at intermediate energy

Nuclear Physicx A370 (1981) 47995 © North-Holland Publishing Company

MICROSCOPIC ANALYSIS OF BARYONIC EXCHANGE MECHANISMS IN THE dd-" n3He REACTION AT INTERMEDIATE ENERGY J.M . LAGET

Département de Physique Nucléaire, CENSaclay, 91191, Gif-sur-Yvette Cedtx, France and

J.F. LECOLLEY and F. LEFEBVRES Laboratoire de Physique Corpusculaire LA34 associé à l'IN2P3 ISMRA, Université de Caen, France Received 9 February 1981 (Revised 13 May 1981) Abehact: The dd-n3 He reaction is analysed, at the microscopic level, in terms of the exchange of one nucleon or the exchange of one nucleon and one pion . Each mechanism dominates the cross section in well-separated kinematical regions. The sensitivity of the model to itsdifferentingredients (and especially to the two- or three-nucleon wave functions) is studied.

1. Introdaction In the study of the baryonic exchange mechanism between light nuclei, dd-> n3He is the simplest reaction besides the backward elastic scattering pd. At intermediate energy, these reactions imply high-momentum transfer and are sensitive to the high-momentum components of the nucleon wave functions inside light nuclei . The study of the energy dependence of the dd->n3He differential cross section') at a fixed t (squared four-momentum transfer between the incident deuteron and the outgoing 3He) gets rid of the t-dependence of the vertex functions and enables us to obtain some information on the relative importance of the different mechanisms involved in this reaction . Experimental data t), which have been obtained with the Saturne I deuteron beam, show the existence of a shoulder in the energy dependence of the total cross section rTT and the differential cross section drr/dt at fixed t. As in the pd-> dp reaction Z), this effect is observed in the energy region of the s-channel d(1236) formation. Moreover, the general trend of the differential cross sections is the same as in the p 4He ~ d3He reaction 3) - a steep forward slope at Tp = 156 MeV which vanishes at higher energy a .s) and a break in slope at t = 0.5 (GeV/c)2. This set of experimental results allows us to think that the reaction mechanisms are similar. The nucleon exchange in the t-channel (ONE: graph la), which is the most important contribution at lower energy, does not reproduce the experimental results in the intermediate energy region . Several explanations have been given to analyse 479

480

1.M. Laget et al . / dd -~ n3He

these deviations . The first one e) assumes the existence of N* in nuclei, and considers the exchange of this N* in the t-channel (graph lb). The second one' s) considers the ar-exchange and the d(1236) excitation by the ~rN interaction (ONPE: graph lc). One version of this model 1°) contracts the lower loop in fig. lc and links the A(p, d)A -1 reaction with the A(vr +, p)A -1 reaction which resonate in the d(1236) energy range. This method, which was successfully applied in the d(1236) excitation energy region (Tp > 600 MeV) for nuclei up to'ZC, needs the knowledge of the A(~r+, p)A -1 differential cross section. Moreover, it does not allow us to evaluate the contribution of other mechanisms (in particular the ONE) and to treat correctly interference effects.

P

A-~ icy Fig . 1 . The diagrams of the possible contributions in the A(p, d)A -1 reactions. (a) : one-nucleon exchange, (b) : exchange of N`, (c) : one-nucleon and pion exchange.

A better understanding of these mechanisms implies a microscopic calculation of the amplitudes corresponding to each possible contribution, using vertex functions directly linked to the wave function of the nucleons inside 3He and the deuteron. In this paper, we compute the non-relativistic limit, to order (p/m)Z, of the amplitudes corresponding to graphs 2a and 2c (ONE and ONPE). We obtain a simple analytic form for them, in which the term corresponding to each diagram can be singled out. This enables us to know the relative importance of each process, and for each amplitude to control the different components used to describe the vertex functions. Besides the direct term in the ONE process (fig . 2a), we have also considered a second order process (ODEB fig. 2b) where the inçoming neutron interacts with the deuteron cluster in 3He . Starting from the successful descripl'-i3) tion of the s-channel d(1236) formation mechanism, we have also computed the ONPE amplitude where the upper loop is contracted and the corresponding amplitude A d~,,,r is taken out the integral of the Fermi motion in the triangle diagram (fig . 2e). This amplitude is computed exactly in appendix A and good agreement with the experimental data is obtained . The success of the model in reproducing the or +d->pp reaction cross section gives us some confidence in the use of this formalism for deuteron stripping reactions at intermediate energy . However, since the exchanged pion (diagram 2e) is off-shell, the analytical continuation of the physical amplitude Ana~xrr needs kinematical choices which we shall discuss .

l.M. Laget et al. / dd -~ R 3 HC

481

n m~ n' m;, Ibl m TM

P2

mZ

Ifl

Igl

Fig. 2. The diagrams discussed in this study. 2. Derivation of the results 2.1 . KINEMATICS AND NUCLEAR VERTEX FUNCTIONS Let P(p °, p), T(MT, 0), Dt (p°, p,) and Dz(pz°°, pz) be the four-moments in the lab frame of the incoming neutron and 3He and the two outgoing deuterons, respectively . The differential cross section of n3He->dd is, in the lab frame : %_ d~l

_

1 i xâ

mMâpi

~

m p 11i mtmZ

IT(Pmr~MnPtrni~Pzri+z)+T(PmP,MrPzrnz,Pimt)I

where m, M Md and mP , M, m,, mz are, respectively, the masses and the magnetic quantum numbers of the initial neutron and 3He and the final deuterons. ET is the total energy in the entrance channel (ET=p°+MT) . Taking into account the indiscernability of the outgoing deuterons, we add the two matrix elements T in which the two outgoing deuterons are exchanged. The differential cross section of the inverse reaction dd-~n3He is obtained using the detailed balance prescription . The non-relativistic limit of the deuteron vertex function dpn V+ is related to the deuteron wave function U; in the momentum space through : V+ (Pim~ . Pmr. nm ) ~ (n ° -E ) ~ Ui (IP -zP1I) x ~ (Im~, sm,Ilm~)('zrn~, imvlsm,,)Ym' m~ m,

(ri zPl) .

(2)

482

1.M. Laget et al, / dd -~ n3Ke

The off-shell energy of the internal nucleon is n° and is defined as p° + n ° =p,°. Its on-shell energy is Eo = "fin For Ua, we use a parametrization of the Reid soft-core wave functions is-is) with 1= 0 (S-state) and 1= 2 (D-state) :

m.

6

The parameters of this wave function are given in ref.'3). This choice is justified by its successful use in deuteron photodisintegration studies iz.is) . In the same way, the 3He vertex function (Tdp) V is related to the overlap integral U; between 3 He and the deuteron wave function in momentum space through V(OM nmo, Pzmz) - ~ (n ° -Eo) ~ Ui clnl ) x E (Imt,smsl2M)(zrn,1mzlsma)Yi`'(~), m,m,

nm

(4)

where n ° and E = are the off-shell and on-shell energy of the internal nucleon (MT = n ° + p °z) and s is the spin transfer (s = i for 1= 2, D-state and s = z for 1= 0, S-state). The structure of the three-nucleon systems, which has been the subject of many recent experimental and theoretical investigations is not known at the same level of accuracy as the deuteron system . Since in the intermediate energy region, the n3He->dd process implies high momentum transfers (0.2-0 .8 GeV/c), we cannot use 3He wave functions which do not reproduce the high-momentum part of the 3He charge form factor, in particular the dip observed at qz = 12 .5 fm-z. The sophisticated wave functions obtained by solving the Faddeev equations ie) or by using variational approaches l') are not very easy to use 18) and do not agree well with high transfer experimental data even though the important meson exchange effects are considered in the analysis of the charge form factor 19'zo) . ps a first step, the most simple method is to use a Tdp overlap function which is constrained to successfully reproduce the 3He charge form factors . We use the Eckart form parametrization of Lim zi) with Nz = 0.4970 GeVl ~z, ~ = 0.060 GeV and ß = 0.420 GeV, which is, in momentum space, related to a pole form : s

J.M. Laget et al. / dd -~ n 3 Ffe

483

2.2 . THE ONE AMPLITUDE The matrix element corresponding to the direct diagram 2a is : m + Ti(Pirrti, Pzmz) = -E V (Pima, Pma, nm~)E nm~, Pzmz) , (n ° -E ) v(ffM'

(6)

where n ° and E are the off-shell and the on-shell energy of the exchanged nucleon in the t-channel. The dpn and Tdp vertex functions are related by the expressions (2) and (4). To evaluate the second-order contribution (ODEB: diagram 2b), we factorize the matrix element T~ of the ONE elementary sub-reaction pd ~ dp (diagram 2d). Neglecting the Fermi motion, the matrix element becomes : Tz(P1m~,Pzrnz) =- ~ ('zrn~,irnPIlmzXzmP, 1m E~2M) m ;,mô mE

x Tva(PmT, ~mty Pimi, P~mv)

r

s d n , Uô (~R~~)Uô (~n' - zPz~) J (2or 4or

where the energy integration term in the loop has been replaced by the residue associated with the deuteron pole . The momenta and the magnetic quantum numbers of the exchanged particle in the loop are (~, mF), (p', mP) and (n', m~) for the deuteron and the two nucleons . Their on-shell energies are E~ = M, EP = ~and E;, = nJ~m, whereas the off-shell energies ~°, n'° and p'° p are related through MT = ~° + n' ° and n'° + ,°= pz . The form of the wave functions (3) and (5) allows us to compute analytically the integral in (7) : Tz(P1m1,Pzrnz) =- ~ (irn~,imvllmzXimô, 1mF~zM) m;,rlp mf

, , 21V,1Vz Pz x T~(PmP, ~m~ Pimi, P mr) E ~ C~i arctg ~ 2(rx, + yt)~ Pz

.

The matrix element T~ is similar to the expression (6) where the Tdp vertex function is replaced by the dpn vertex function including the S- and D-wave . This amplitude is estimated in the pd lab frame assuming that the incoming proton momentum, the outgoing deuteron momentum p, and the outgoing proton momentum (p' =pz) are on shell. 2 .3 . THE ONPE AMPLITUDE

In diagram 2c, where the s-channel d(1236) formation in the interaction orN appears, the isospin coupling at the vertex ordd is equal to zero and the intermediate

484

1.M. Laget et al. / dd -~ n3He

dinucleon must be in the isospin state T =1 . The ONPE amplitude is then calculated with the following simplified hypotheses : The wave function of the dinucleon NN is the same as the deuteron wave function . This is equivalent to assuming that the NN pair in the isospin state T = 1 is dominated by the threshold interaction and is similar to a bound np pair . The upper loop is contracted and the corresponding matrix element Tmt-.dam is taken out of the integral over the Fermi motion in the triangle diagram 2e . It is legitimated by the fact that the most important contribution to the integral comes from the low-momentum part of the rd overlap wave function . The matrix element Trrx~an is computed as described in appendix A. Of course, the nucleon exchange part (fig . 7a) has been removed. The energy integration loop puts the intermediate dinucleon on its energy shell. Ts(Pimi, Pzritz) _ -A,~Nrra(Pzmz, fime = 0)TNrr~a, .(PmP, nM.~ Pirni) x

d3~

Uô (~~~)

(2~r)3 ~qz-m~

.

Using the wave function (5), the integral is evaluated analytically : Ts(Pima, Pzmz) _ -A~Ntva(Pzmz~ ~mE - 0)TNN~a,. (PmP. ~. Pimi) x

mn D, arct g y` + ]. 4~pz ~ ~ Pz Nz

(10)

The matrix element A, .(1, ß is computed assuming that the Tr interacts with one nucleon. The integration on the loop (diagram 2g) is performed with the spectator nucleon on-shell : A,.xxa(Pzmz~OmF=O)=

28o ~ ~zmr~zm~~00)(zmr~z~tn~lmz) 2m m mv mo x~mv~Q' 4~ma)

Uô(~n~~)Uô(~n~-zPz~) . ~ d J (2a) 4a

(11)

The coefficient 2 comes from the fact that, in the isospin space, the np pair (T=1) is symmetrical. The integral is calculated analytically using the wave function (3) and neglecting its D-wave part : A,~rrrra(Pzrnz,UmE=O)=

8° m

~ ~imr,zm~~00)(zmP, m~~lmz)

mnmô mo

x (mpl Q

2

. 4l mp) 2N1 E pz 1

Pz } ~ ~; CrCi ~~B { 2(tx,+tx ;)

(12)

The exchanged pion being far from its mass shell, it is necessary to introduce at the zr-baryon vertex a monopole form factor and to consider also the p-exchange

J.M. Lager et al. / dd -" n'He

485

zz) contribution, as in the analysis of the ar + d-> pp reaction or the analysis of the zs) z3) yd-> pn reaction . It is completely equivalent to simulate both effects by a single form factor : z z z A,ra - m~ . h.o(9 )= AnP-qz

with a cut-off mass Ap = 600 MeV. The final expression of the matrix element is then : Ts(Pirni, P~zmz) =

3Nz 4,~ar Pz

A,~xxa(Pzrnz, UmE = 0)T"P-.d,~° (Pmv~ nm", Pima)

where the isospin coefficient 3 takes into account the two sub-processes np-r dar° and nn ~ dar - . The amplitude T~~a-.vP is calculated (see appendix A) in the lab frame, where the deuteron is at rest . This amplitude is evaluated with the incoming and outgoing particles on-shell with well-defined kinematics . Then, the analytical continuation T° " ~ T°a implies a kinematical choice of the frame which allows us to fix the energy of the pion and the transfer variable of the sub-process. The total energy in the entrance channel np ~ dar° is : S~ = WPP =(P+3T)z =2m z +2mp ° ,

(14)

where p ° is the energy of the incident proton in the lab frame. The off-shell mass of the virtual pion is computed assuming that the pion is absorbed by one nucleon : N- z = ('zDz-3T)z = 6(t - m z) .

(15)

Taking into account that the vertex functions are related through the relative momentum of the nucleon, the amplitude T°~ is evaluated using the off-shell K°ff(E°n components of the pion four-momenta , p°a ) with : Ea - (SPP - Mâ - fi z)l2Ma

(16)

There are two obvious choices for the variable transfer : t and cos 8 * . Since the first choice leads to a kinematical cut-off at large angle' ° ), we have used the fixed cos B* prescription : B.* d = Baâ. 3. Comparison with experiment and discussion The prediction of the model is compared to the available experimental data 1 ) . In the intermediate energy region, a set of eight differential cross sections of the reaction dd ~ n 3 He and dd -> 3 Hp in the 0~0° c.m . angular range, has been measured

486

Fig. 3. The ONE and ODEB contributions with the D-wave of the TDN overlap integral . Dot~ashed line : S-part of the dpn and rdn vertices, dashed-line : respectively, D- and S-parts of the dpn and rdn vertices, dotted-line : ODEB contributions, full line : coherent sum ONE+ODEB . for incident deuteron moments between 1 .1 and 2.5 GeV/c (3 .97 .39 GeV total energy in the c.m .s . In fig. 3, we show the ONE differential cross section (diagram 2a) ; the wave functions used are these of Reid (RSC including the S- and D-part) for the dpn vertex, and Lim (S-part for the Tdp vertex). The dot-dashed line (SS) and dashed line (DS) represent, respectively, the S- and D-parts of the deuteron

1.M. Laget et al. / dd -> n'He

487

wave function. It is worthwhile noting the importance of the deuteron D-wave in this high-momentum transfer reaction . In the forward direction the contribution of the ONE mechanism rapidly decreases with increasing energy, but at large angles this contribution is important in the whole energy region and the change of slope

d+d iH+p

I

p, . ~ n GeV/c

W

103 .

m C7

102

.

:., . v '. `,,

' b v

;, y ~

v

Q75

.

__

,

~

s\

103

.

,

ONE .ODE9

"

/.: y

0

10~

.

3 895 GeV

" 7~ 00

v ~~

.1

065

055

Q4b maa

d + d .~~He + n p, . t992 Ge~c

t ,.

W:lisv GeV

-

d+d~~Fle+n

I

pi . 2 492 GeV~c

..

W 1328 GeV

.

10

v b v

_ n n

10~

:i ;,.' :o O6

04

02

2

t ~GeV~c~

0

_

'\

065

" \ 035

U15

\ .2

. -006

t ~GeV~~

Fig. 4. The ONE and ODEB contributions with the S- and D-waves of the rdp overlap integral . Dotted-line : S-part of the dpn and rdn vertices, dashed-line: respectively D- and S-parts of the dpn and rdp vertices, dot~ashed line : respectively S- and D-parts of the dpn and rdn vertices, cross-dashed line : D-part of the dpn and rdp vertices, full line : rnherent sum of ONE+ODEB .

48 8

1.M. Laget ct al. / dd -~ n3He

observed in the experimental results is related to the rise of the dT overlap function which was constrained to successfully reproduce the 3He charge form factor . The ODEB differential cross section (dotted line : fig. 3) is significantly lower than the ONE differential cross section and can be considered as a second order correction . In view of the importance of the deuteron D-wave, it is interesting to introduce, in the same way, the D-part of the dT overlap function . Recently, some dT overlap ia .za zs ' ), but integrals using different triton wave functions have been calculated 26) their differences are still important and it is difficult to draw definite conclusions about the relative amounts of the S- and D-component in the dr overlap integral . However, we have used an approximative D-wave functions similar to that of Za), ref'. conserving the Lim S-wave normalized at 0.85. Fig. 4 shows the different contributions of the ONE differential cross section. The introduction of the D-part in the dT overlap function fills up the dip. This effect comes from the DD term (cross~ashed line, fig. 4) which corresponds to the D-part of the Tdp and dpn vertex function . The relative contribution of the ONE and ONPE mechanisms is represented in figs . 5 and 6 and compared with the experimental results. The influence of the Fermi motion, which is very strong in the energy region where elementary processes are resonating, is taken into account by a shift of the total energy W* (40 MeV) . This situation is reminiscent of the case of the 3He(y, ar +)t reaction . When the Fermi motion effects on the yp->n~r+ elementary reaction are neglected, the d-peak should be shifted 29 '3° ) (20-30 MeV) . But if the Fermi motion effects are fully taken into account, the agreement between theory and 30~ .

experiment becomes perfect 1 It is worthwhile pointing out that two mechanisms dominate the cross section in very well separated kinematical domains, making it possible to check each of them separately . In the d(1236) energy region (around W* = 4.05 GeV), the ONPE mechanism is dominant in the forward direction and the slope of the differential cross section is well reproduced. In this angular region, the ONE contribution is significantly lower than the ONPE contribution which is not sensitive to the high-momentum component of the Tdp overlap integral. The use of several Tdp functions which was constrained to reproduce the dip of the 3He charge form factor does not change the results in the forward direction . In spite of some simplifications in the computation of the diagram and of an analytical continuation of the amplitude Tna~, r,, this model gives a good description of the excitation function . At large angles, the influence of this mechanism vanishes and the QNE becomes predominant. The break in the slope observed in the experimental results is related to the rise of the Td overlap function . This angular range appears as a privileged region to test the high momentum components of the 3He wave function . t Its parameters are given in appendix B .

1.M. Laget et al. / dd -~ n 3 He

48 9

Fig. 5. The relative contribution of the ONE and ONPE as compared to the experimental cross section. Short-dashed line : ONE, long-dashed line : ONPE, full line : coherent sum ONE+ONPE . Outside the 4(1236) energy region, an obvious improvement in the model would be to introduce the other waves of the ~rN scattering amplitudes in the T,.a~xrt amplitude calculation, and also to take into account other rescattering mechanisms (dd or n3He scattering in the initial or final state) which might be important at the lower energies.

Fig. 6. See fig. 5 .

This model provides us with a reasonable description of the A(d, p)A+ 1 reaction in the kinematical region in which the s-channel d-formation is allowed. Contrary to previous attempts, the spin and isospin degrees of freedom are fully taken into account and the coherent sum of the dominant ONE and ONPE amplitudes has been computed : this is the only way to predict the polarizations and asymmetries, which are a by-product of the calculation, and which should be systematically

1.M. Laget et al. / dd -. n'Ffe

491

measured to check it in details. We have demonstrated that a good description of the nuclear vertex function and a precise treatment of the d-formation sub-process are very important to get quantitative agreement with the data : we have used realistic two- .and three-body vertex functions which are constrained to fit the corresponding electromagnetic form factors, and we have been able to get an excellent fit to the ~rd->NN reaction cross section, with the same model which accounts also for the yd->pn reaction'3). In that energy range, no need appears for a contribution coming from other "exotic mechanisms" (such as N* exchange), which should be looked at and studied elsewhere: they might be important at higher sub-process energies and/or higher s momentum transfer for the vertex [see for instance ref. ')], where our model begins to fail to reproduce the data . Appendix A THE PIONIC DISINTEGRATION OF THE DEUTERON Let K(k°, k), D(Md, 0), Pl(p°, P1), Pz(p °z, pz) be the four-moments of the incoming pion, the deuteron at rest in the laboratory and the two outgoing protons. The differential cross section in the c.m .s . of the Tr +d -'pp reaction is : dQ _

d,fl*

1

(2vr

m zMd p* 1_ 2Wz k*3

E 1 IT(M,Pirni~Pzrnz) - T(M,Pzmz,Pirni)~ z ~

(A .1)

mZ

where p * and k* are, respectively, the momentum in the c.m .s . of the outgoing and incoming channel. W is the total energy in the entrance channel (W z = mn + Mâ +2Md k°), m,, mz are the magnetic quantum numbers of the outgoing protons. The amplitude T"à~PV corresponding to the diagram 7a and 7b has been z3) computed using the same method as in the case of yd ~ pn reaction : The amplitude T, ." a~rr corresponding to the diagrams 7a and 7b has been

To(P1rnl,Pzrnz) = -~

0 go ~ (mi~Q . (e+pi))~m~) 2m ,n  \k-2

i Uô (~Pz~) x { (im~, ~mz~1M) + ~ (2m,,lm,I1Mi(irn~,zmzllm=)~(IPz~)Yi~`(~z)} . mim,

(A .2)

where Uô (~pz~) and Uz (~Pz~) are the S- and D-parts of the deuteron wave function .

492

J.M. Laget et al. / dd -~ n3He

160 E~

200 (MsV)

Fig. 7 . The deuteron pionic disintegration total cross section. Experimental points are taken from ref. a~).

The matrix element corresponding to the s-channel d(1236) formation (diagram 7b) is: ds n Bo Tn ° ~ 3 E Ua (~n I)~mn, imPllm.*Xfmt, smsllM) m  2m J (2~r) my

x

m~n,,

ym~

(n ) ~

0

Ta*p y T a*n~a°PCIi12l r Q` 4 (A .,r-pln -Zhl 4 nn

-~

I

1 , p2) / mnl

(A.3)

The one-loop diagram is computed exactly (numerical integration) by taking into account the Fermi motion . The elementary matrix element Ttv~ty 1S given in ref. tz) with the same values of the mass M and the width T of the d(1236) . As

l.M. Laget et al. / dd ~ n'He

493

in the analysis of the yd-> pn reaction'3) and the yr +d ~ pp reaction z'), we introduce a form factor at each pion baryon vertex and we consider also the p-exchange mechanism. A cut-off mass 11  = 1 GeV is used for the monopole form factor associated to the ~-baryon vertex and A,~ = 2m for the pNN. The coupling constant of the dvrN vertex is gs = 2.005/mTr. Fig. 7 shows the total cross section ~T versus the kinematic energy of the incident pion . Good agreement with the data z') is obtained except near the threshold . The reason is that we used only the P-wave -trN scattering amplitude . In fig. 8, we show four differential cross sections versus B*. Here also, a good agreement with the za) data is obtained in the d(1236) excitation region .

n P

r~ ~azs

C Z

_~

d TT

Mev

/8

Hl~

/Ô

ba 60 40 20 0

4o

eo

120

160

e~M

0

a

4o

TP ~ 463 MeV

so

eCM

1zo

1so

TP ~ 662 MeV

C

C~ v w

.2 ee "

p .15 v

b v

/ e $9~ee

q

1

.1

50

.OS 0

40

rt0

120 eCM

160

0

40

li0

120

160

eCM

Fig . 8 . The angular distribution of the np ~ dpi reaction . Experimental points are taken from ref. ~) .

1.M. Laget et al. / dd ~ n3He

494

Appendix B rdp OVERLAP FUNCTION

For the S- and D-part of the Td overlap function, we have used the same parametrization as the deuteron wave function : Dr Uô~~P~)=4vrNzt~ipz+yi ' Uz~~P~)=-4~rN3Pz

s

zF t~i P rJt ~p

The parameters are : NZ =178.8 MeV ,

S-part,

+n '

N3 = 9.12 GeV ,

D-part .

pz = 0.0288 .

F1 = 0.73402 ,

~It = 75 .422 MeV ,

yz = 480 MeV ,

Fz = -6.40173 ,

rlz = 168.565 MeV ,

D3 = +6 ,

ys = 900 MeV ,

F3 = 4.89929 ,

~ls = 222 .76 MeV ,

D 4 = -4 ,

ya =1320 MeV ,

F4 = 7.19040 ,

r1a = 915 .88 MeV ,

DS =1 ,

ys =1740 MeV ,

FS = -6 .42198 ,

'fs = 975 .248 MeV .

D1 =+1 ,

y1= 60

Dz = -4 ,

MeV ,

References G. Bizard et al., J. Phys . Soc. Japan 44 (1978) suppl . 478; Phys . Rev. C22 (1980) 1632 B.E . Bonner et al., Phys . Rev. Lett. 39 (1977) 1253 M. Bernas et al., Nucl. Phys . A156 (1970) 289 J. Berger et al., Nuovo Cim. Lett. 19 (1977) 287 T. Bauer et al., Phys . Lett . 67B (1977) 265 A.K. Karman and L.S . Kisslinger, Phys . Rev. 180 (1969) 1483 G. Barry, Ann. of Phys. 73 (1972) 482 N.S . Craigie and C. Wilkin, Nucl. Phys . B14 (1969) 477 V.M. Kolybasov and N. Ya . Smorodinskaya, Yad. Fiz. 17 (1973) 1211 [Sov. J. Nucl. Phys. 17 (1973)630] 10) C. Wilkin, J. of Phys . G6 (1980) 69 11) J. Blomgvist and J.M. Laget, Nucl. Phys . A280 (1977) 405 12) P. Bosted and J.M . Laget, Nucl . Phys . A296 (1978) 413 13) J.M . Laget, Nucl. Phys . A296 (1978) 388; A312 (1978) 265 14) R.D . Raid, Ann. of Phys . 50 (1968) 411 15) I. MacGee, Phys . Rev. 151 (1966) 772 16) A. Laverge and C. Gignoux, Nucl . Phys . A203 (1973) 597 ; R.A . Brandeburg, Y.E . Kim and A. Tubis, Phys. Rev. C12 (1975) 1368 ; F.P . Harper, Y.E . Kim and A. Tubis, Phys . Rev. C2 (1970) 877 17) M.R. Strayer and P .U. Sauer, Nucl . Phys. A231 (1974) 1 18) Ch. Hajduk, A.M. Green and M.E . Sainio, Preprint HU-TFT 79-32, Research Institute for Theoretical Physics, University of Helsinki 19) D.O . Riska and M. Radomski, Phys. Rev. 16 (1977) 2005 1) 2) 3) 4) 5) 6) 7) 8) 9)

J.M. Laget et al. / dd -.n 3 He 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) 31)

C.H . Hajduck and P.U . Sauer, Nucl . Phys . A322 (1979) 329 T.K. Lim, Phys . Lett . 42B (1973) 349 M. Brack et al., Nucl . Phys . A287 (1977) 425 J.M . Laget, Nucl . Phys . A312 (1978) 265 F.D . Santos, A.M. Eiro and A. Barroso, Phys. Rev. C19 (1978) 238 A.D . Jackson, A. Lande and P.U . Sauer, Phys . Lett . 35B (1971) 365 ; L.M. Delves and J.M . Blatt, Nucl . Phys . A98 (1967) 503 ; Y. Akaishi, M. Sakai, J. Hiura and M. Tanaka, Prog . Theor, Phys . Suppl. 56, 8, 6 (1974) L.D . Knutson and S.N . Yang, Phys . Rev. C20 (1979) 1631 C. Richard-Serre et al., Nucl . Phys . B20 (1970) 413 S.S . Wilson et al ., Phys . Lett . 35B (1971) 83 C. Lazard, R.J. Lombard, Z. Maric, Nucl . Phys . A271 (1976) 317 L. Tiator, A.K. Rej and D. Drehsed, Nucl . Phys. A333 (1980) 343 S. Jena, Z. Phys . 296 (1980) 323

495