Lithium elastic and inelastic scattering and lithium-induced single nucleon transfer reactions

Nuclear Physics A212 (1973) 573--599; (~) North-Holland Publishtng Co., Amsterdam Not to be reproduced by photoprint or microfilmwithout written permissionfrom the publisher

LITHIUM ELASTIC AND INELASTIC SCATTERING AND LITHIUM-INDUCED SINGLE NUCLEON TRANSFER REACTIONS P. SCHUMACHERt, N. UETA tt, H. H. DUHM, K.-I. KUBO ttt and W. J. KLAGES+*

Max-Planck-lnstitut flir Kernphysik, Heidelberg Received 12 April 1973 (Revised 25 June 1973)

Abstract: Absolute cross sections and angular distributions for lithium elastic and inelastic scattering as well as for lithium induced single nucleon transfer reactions have been measured at 34 and 36 MeV for several p and s-d shell nuclei. The elastic and inelastic scattering data have been analyzed in terms of the optical model assuming deformed targets and projectiles. Optical model potential parameters and deformation parameters have been deduced. The transfer data have been analyzed by finite range DWBA calculations using known spectroscopic factors. The sensitivity to the choice of potential parameter families is discussed. In some cases the best possible agreement with the transfer data has been obtained by selecting the distorting potentials for incident and exit channel corresponding to a potential sum rule for the real part of the potential. The elastic and inelastic scattering data are well described by the optical model. The transfer data are also reasonably well explained, although not in all cases as satisfactorily. NUCLEAR REACTIONS 12C, 13C, 160, 26Mg, 2aSi(6Li, eLi), (eLi, eli') (TLi, 7Li), (TLi, 7Li'), (eLi, 7Li), (7Li, 6Li), (7Li, erie), (7Li, SLi), E = 34 and 36 MeV; measured tr(0); deduced optical model parameters, FRDWBA analysis.

[

I

1. Introduction Single n u c l e o n transfer is one of the m o s t likely processes i n collisions o f atomic nuclei at sufficiently high b o m b a r d i n g energies. It has often been successfully described i n the f r a m e w o r k o f the D W B A f o r m a l i s m for the case o f light projectiles. It is expected that the D W B A formalism will also be applicable for reactions between complex nuclei provided the finite size o f the nuclei is t a k e n into account. L i t h i u m i n d u c e d single n u c l e o n transfer reactions which have n o t often b e e n investigated so far 3, 2) m a y be considered as the lightest heavy i o n reactions which are appropriate to test the reliability o f the finite range D W B A analysis ( F R D W B A ) . These reactions are still rather simple in c o m p a r i s o n to m u l t i - n u c l e o n transfer r e a c t i o n s . The corres p o n d i n g spectroscopic factors are k n o w n from the study o f s t a n d a r d single n u c l e o n t Now at II. Institut fiir Experimentalphysik, Universit~it Hamburg, on leave at CERN. tt On leave of absence from Universidade de S~.oPaulo, Brazil. Fellow of the Fundaq,ao de Amparo Pesquisa do Estado de SAo Paulo. ttt On leave of absence from Institute for Nuclear Study, University of Tokyo, Tanashi, Tokyo, Japan. ~; Now at the Erziehungswissenschaftliche Fakultiit der Universitiit Wiirzburg. 573

574

P. SCHUMACHER et al.

transfer reactions with light projectiles. Often shell model calculations are available as well 3). On the other hand, the lithium-induced reactions are complicated enough to require a more sophisticated analysis than a zero-range DWBA in particular because of the p-wave character of the valence nucleons in lithium. The 0p wave function vanishes in the very center of the projectile. In this paper we present a study of lithium-induced single nucleon transfer reactions for several target nuclei of the p and s-d shell. The F R D W B A analysis of the measured angular distributions is performed according to the formalism developed by Austern e t aL 4) using the F R D W B A code of Yoshida 5). The absolute cross sections are calculated with the introduction of no parameters other than the spectroscopic factors (which are known in our case), the distorting potentials and the geometry of the bound state potentials (BSP) for the transferred nucleon in the target nucleus and the projectile system, respectively. A standard Woods-Saxon potential well geometry (R = 1.25 A ~ fm, a = 0.65 fm) is used for the BSP. The distorting potential parameters are derived from elastic scattering data which are measured simultaneously with the transfer cross sections. The main ambiguity in the F R D W B A calculations results from the occurrence of several discrete sets for the real part of the distorting potentials. Our calculations show a varying degree of sensitivity to the choice of these potential parameter families. We obtain the most acceptable fits when selecting the potentials for incident and outgoing channel close to the potential sum ~ 1: bound rule, which e.g. for the (6Li, 7Li) reaction can be written as: 1, : 6LiT "n = VTLI. In sect. 2 we shall first describe the experiment. In sects. 3 and 4 we will present our results of the elastic and inelastic scattering data of 6Li and 7Li on various nuclei of the p and s-d shell. The inelastic scattering data are analyzed on the basis of the collective model. In sect. 5 the formulae for the F R D W B A calculations are given. In sect. 6 we present the single nucleon transfer data and their F R D W B A analysis.

2. Experimental procedure The angular distributions of the lithium-induced reactions should exhibit sufficient structure to provide a real test of the reliability of the F R D W B A calculations. Therefore the experiments were performed at the rather high energies of 34 and 36 MeV obtained from the Heidelberg MP Tandem Van de Graaff accelerator. The negative lithium ions were extracted from a Penning source with radial extraction 6). The maximum current at the entrance of the accelerator tube was about 150-300 hA, yielding approximately 500 nA Li 3+ on the target, but the average current on the target was not more than about 100 nA due to the instability of the beam. A scattering chamber was used with four movable A E - E detector telescopes which were mounted at 15 ° intervals at a distance of about 20 cm from the target. The 12C, 13C, 26Mg and 285i160 2 targets were made by conventional vacuum evaporation techniques. The size of the defining slits in front of the detectors and the aperture of the beam collimator (1 × 3 mm 2) were optimized to assure less than 100-150 keV kinematical

Li S C A T T E R I N G

575

Fig. l. Spectrum f r o m the particle identifier. The +He particles were cut by a lower threshold o f a single channel analyser.

I

100

I

'

I

i

~

i

I

13C(6Li, 6Li)13 C ~

8C

4 0 0 --

EaLi = 34 MeV ~ ' ~

~
22 °

~

. . . . . .

I

I 400

I

i

I I 6OO Channel Number

I

I

i

26Mg(6Li, 6Li)26Mg 36 MeV, 21" 0.8x3 mC

15oo

i

'

I

~o ~'0

~o

3 x 0.1 mC

~t

x :12s

8 2o0

o

I 500

i

I

g £

2ooo

~

12C(7Li ' 7Li)12C

~ 300

~:

--

I 5OO

I

ETLi = 36 MeV, 15"

u

~

§

o

+

i

I 600

I

i

I

I

700

I

i

I I 800 Channel Number

I

i v3

400

28Si02(7Li' 7Li128Si02

1~

~

ErLi =36 MeV, 375 ° 300

~_

3xO.6mC ,3

8

loool

M

i

5OO 0

200

'm'~"

+

I

55O

o° l tt

10C

650

750 Channel Number

C'

i

I

600

i

I

700

Fig. 2. Spectra from elastic and inelastic scattering o f 6Li and 7Li.

I

I

i

800 900 Channel Number

576

P. S C H U M A C H E R

et aL

broadening for the 1zC targets in the worst case. The thickness of the AE transmission counters (purchased from Ortec) ranged from 18 to 45/zm. The particle identification was provided by multiplication units with outputs proportional to M = AE(E+ aAE+bAE2). The variation of the adjustable parameters a and b allowed M to be energy independent for particles of neighbouring Z and A, e.g. for the He and Li isotopes (see fig. 1). The separation of the Li isotopes was satisfactory with the exception of the close vicinity of the elastic scattering peak. There, some leak-through i [ I l I l [ [ [ I [ I I I

:

IO~

l~c(TLi 7Li)12C

!oc

10" '~ 10 2

i)160

~

.

ld

10 ~

Li) 28SI

ld loC 10-' 10-21

V '

i(]--~ l [ ] I I ]I

0°

3(7

60 ° 90*

120' ecru.

0o

30 =

I I I I I i ~--

60 ° 90 =

12(3°

ecru.

Fig. 3. Elastic scattering cross sections a n d

the optical m o d e l

table 2, set III.

fits w i t h the potential p a r a m e t e r s

in

Li S C A T T E R I N G

577

to smaller mass signals was observed, which was partly due to insufficient charge collection. It could be reduced, but not completely eliminated, by applying higher voltages to the AE detector. The mass signals of the telescopes were fed into single channel analyzers providing the routing signals for four different types of particles, e.g. 6He, 6Li, 7Li and aLl. The adjustments of the multiplication circuit and single channel analyzers were controlled by polaroid photographs of the M x Etot display on an oscilloscope (Et.t = AE+ E). In the later period of the experiment adjustment and control were greatly facilitated by the use of the Sigma 2 on-line computer, providing a more convenient two-dimensional display. The routing signals were used to store the Et°t energy signals obtained from the four telescopes (4 ADC) into 4 x 4 subgroups of a Nuclear Data 16 K multichannel analyzer. The data were recorded on a magnetic tape and processed later on.

3. Elastic scattering Examples of the spectra obtained from the scattering of 6Li and 7Li on the various nuclei are shown in fig. 2. In the 7Li spectrum each line appears as a doublet corresponding to the 7Li, 3- ground state and the 7Li, ½- excited state at 0.48 MeV, which are both stable against particle emission.

Bound State and Scattering Potentials 3 0 0 ___--

f o r 6 Li

--

_ > 100

~.~y~_~

x 12C

60 -

• 160

40

o28~v~

-~56 Fe "8S" L26Mg "5S" ~'

12C "3S"

I

I

I

I

I

Q8

1.0

1.2

14

1.6

Fig. 4. Potential depths for scattering a n d b o u n d state potentials as a f u n c t i o n o f the radius p a r a m e t e r ro. T h e circles a n d crosses are t h e values f r o m t h e elastic scattering fits, a n d the d r a w n lines are the results f r o m b o u n d state calculations described in t h e text.

The measured differential cross sections for elastic scattering are shown in fig. 3. The absolute cross sections were obtained by normalizing to elastic scattering of 6 and 8 MeV Li particles measured at forward angles up to 40°, where the elastic scattering cross sections deviated at most by 30 % from pure Coulomb scattering. The optical model calculations were performed using the Woods-Saxon type potential:

U(r)=-V l+expr-Rrl-l-iW

[

ar

J

El + e x p r - R w 1 - ' +Vc, a w ..I

(1)

578

P. S C H U M A C H E R et al.

with R i = Fiatarget.

H e r e Vc is g i v e n b y t h e C o u l o m b i n t e r a c t i o n a r i s i n g f r o m a p o i n t c h a r g e d i s t r i b u t i o n incident on a uniform charge distribution: Vc = Z 1 Z 2 e

2

3-

2Rc)

=Z1Z2e2/r

for for

1"=< R c =

1.3A ~

r >Rc.

TABLE 1 Optical model Woods-Saxon potential parameters from a first parameter search

7Li 7Li 6Li 6Li 7Li 7Li

~ 12C -+ 13C -+ laC --~ 12C --~ 160 --~ 28Si

Energy (MeV)

V (MeV)

rr (fm)

at (fro)

W (MeV)

rw (fro)

aw (fm)

36 34 34 34 36 36

139.1 137.9 161.6 135.6 125.7 143.1

1.62 1.62 1.62 1.54 1.62 1.62

0.58 0.58 0.58 0.58 0.58 0.58

18.8 18.1 13.8 14.7 18.3 14.4

1.99 1.99 1.99 1.89 1.99 1.99

0.93 0.93 0.93 0.93 0.93 0.93

TABL~-2 Optical model Woods-Saxon potential parameters from an extended parameter search Energy (MeV)

Potential family

V (MeV)

rr (fro)

ar (fm)

W (MeV)

rw (fro)

6Li-t- 12C

34, 36

II III IV

121.3 173.2 243.8

1.20 1.208 1.210

0.888 0.802 0.770

9.6 8.9 10.6

2.17 2.17 2.17

0.946 0.945 0.945

6Liq- aaC

34

III IV

176.4 245.2

1.21 1.21

0.773 0.716

10.4 11.9

2.17 2.17

0.817 0.749

6Li+:60

36

III IV

164.3 222.3

1.21 1.21

0.826 0.800

10.6 11.8

2.017 2.017

1.064 1.035

6Li+26Mg

36

III IV

161.9 208.6

1.21 1.21

0.80 0.75

17.3 19.8

1.85 1.79

0.890 0.89

VLi÷12C

36

III IV

187.8 245.0

1.208 1.210

0.824 0.759

12.9 14.7

2.17 2.0

0.77 0.909

7Li+13C

34

11I IV

166.4 248.2

1.208 1.210

0.763 0.755

9.1 12.7

2.17 2.0

0.95 0.944

7Liq- 160

36

III IV

189.5 238.8

1.21 1.21

0.743 0.709

21.3 19.2

2.0 2.0

0.821 0.822

7Li+2sSi

36

III IV

177.3 214.6

1.21 1.21

0.775 0.83

9.4 14.4

2.10 2.10

0.848 0.73

The labelling of the parameter families corresponds to that given by Bassani et al. 9).

aw (fln)

Li SCATTERING

579

The optical model parameter search was performed with the code Jib 3 [ref. 7)]. With the input parameter values obtained by Bethge et al. s) for 20 MeV we obtained potentials with rather large real radii, which, however, could not fit very well the larger angles of the elastic scattering distributions (see table 1). In the continuation of the parameter search we finally arrived at 6Li parameters given in table 2 with much smaller real radii which agree quite well with the parameter families obtained by Bassani et al. 9) for 28 MeV scattering. (We used somewhat larger radii for the imaginary potential.) In order to judge which potential family might be the most appropriate one, we performed bound state calculations similar to those of ref. 10). For example, the potential depth for 6Li scattering on 12C was calculated for a mass-6 particle moving in the field of a 12C core with a binding energy equal to the experimental separation energy of 6Li from the lSF 1 + ground state. The angular momentum of the center of mass motion of 6Li was assumed to be l -- 0, and the number of nodes of the wave function was obtained from the oscillator model yielding a 3S wave function for the center of mass motion of 6Li for the 12C target. For the 160, 26Mg and 28Si target nuclei one gets a 5S wave function, and for s 6Fe ' e.g., lying in the middle of the f, p shell one obtains an 8S function. The corresponding bound state potentials, plotted as a function of the radius, are shown in fig. 4. The potentials approximately obey the relation Vr o = const, rather than Vr2o = const. [ref. 11)]. The calculated bound state potential depths, although differing for the different target nuclei, are clearly below the upper estimate of six times the single nucleon potential. This is interpreted to result from the partial saturation of nuclear forces within the projectile. It is possible to select a potential parameter family for 6Li very close to the calculated potentials. The selected potential family is the potential set III from table 2 with a depth of about 170-180 MeV and a radius of R = 1.21 A~fm. This rather shallow 6Li potential is not in contradiction with the results from the '°superposition model" 12) in which the real part of the 6Li potential V6Liis obtained by a superposition of V~ and Vd. Since the saturation effect of nuclear forces is most important within the ~-particle, the 0t-particle potential itself will be considerably weaker than four times the nucleon potential, as has been shown by high energy ~scattering results lo, 13). The folding of the comparatively shallow ~-potential [V~(r o = 1.2 f m ) ~ 120 MeV, energy dependent] with the deuteron potential [Vd(r0 = 1.2 fm) ,,~ 70 MeV] yields a quite comparable potential depth with the parameter family III obtained from the present 6Li data. The 7Li potentials are only slightly deeper.

4. Inelastic scattering We now confine the analysis of the inelastic scattering data to the collective model, assuming that both the target nuclei (carbon, oxygen, magnesium) and the projectile 7Li are deformed. One might hesitate to apply the collective model to a few-nucleon

580

P. SCI-{UMACHER et aL

system like 7Li, in particular since the M1/E2 ratio for the ½- ~ { - transition is rather large ~4). The deformed model type calculation, therefore, should be considered with sutticient caution. For the present calculation it is assumed that the 7Li ground state and first excited state belong to the K = ½- band with reversed level order for the ½- and ~- states due to the decoupling parameter ts). The departure from sphericity of the nuclei is contained in the radius parameter R of the optical model potential U(R), which for axially symmetric quadrupole deI

I

lO1 ~ ' i

\-

l

I

I

I

I

I

i

i

I

i

i

12C (6Li6Li)12C4 43 34 MeV /%, £ =2, J3 = 0.28 ~p.. 13Rw=142

lo°

lo-1 "'~

12C 36(6Li6Li)12C443 MeV

lc

.,r"~ ~-~.

£=2, 13 =0.32 13Rw= 1.58

lo ° ¢,,

,,.o°

lo-1 102

I

I

I

I

I

I% 101 J ~

r~l

I

I

inelastic

I

I

I

I

I

I

~

ii ~'

I~

"

r

\

E loO~

13C (6Li6Li)13C 3 090 ~qre,~ 34 MeV

scattering

36 MeV

10 °

,% c~ v

,,, ~=~

~ ~ ?/"", ~7 $ ;4~,- \

i

lo-1

~",,e-/e---~ o o.~o "I~'~D

~ - R , . ~ ~.,v~.,

11 i

#

ij V

102 '/~

PRw'3'5

V

10-1

12C (7Li,7Lig.,.)12C443"

# = 0.32 PRw= 1.73

10°

E=2

•

,

£=2

#

PRw=1,52

lO-"

12C('Li,7Lio~8~2C4.43

• •

M,

10-,! t

0o

I

I

30 °

I

: _

0.o.=

--

ee°

,

26Mg (6Li,6Li)26~Mg 1.806 36 MeV LeI ~

t; ~ / ~

= 0.51

,=1

p =0.71

ld .~b 100

..

" i%,",

I

I

60 °

I

I

I

I

I

I

I

9 0 ° _ 120 ° (.gc.rn.

Fig. 5. Angular distributions from 7Li inelastic scattering on ~ C . The dotted curves are the collective type D W B A calculations using the optical potential family III in table 2.

*

0o

1

I

30 °

I

I

I

60 °

I

I

I

I

90 °

I

I

I

120° ecru

Fig. 6. Angular distributions from 6Li inelastic scattering on various nuclei. The dotted curves represent the collective type D W B A calculations using the optical potential family III in table 2.

Li SCATTERING

581

formation may be written approximately: R ~ RtJ)[1

+fl~21)Y20(01)-I+R~02)[1 +flt22)Y20(02)]

= R 0 + 6R ° ) + tSRt2).

(2)

Here 01 and 02 refer to the body fixed axes of the colliding fragments which may have any orientation to each other. The first term of the Taylor expansion of the potential about R = R 0 leads to the DWBA amplitude for single excitation of either the target nucleus or the projectile: TDwaA(1, 2) - (Z~-)I6R (~' 2) d__U_UIz~+)>" dr

(3)

The mutual excitation of both the target and the projectile must be calculated in second-order pelturbation theory, including a direct term with the second derivative of the potential and a two-step excitation term. This requires a coupled channel analysis which has not been performed here. Figs. 5 and 6 show the inelastic scattering angular distribution. Experimentally, the mutual excitation is reduced by a factor of 100 in comparison to the single excitation. The calculations for the single excitation were performed with the code D W U C K 16). According to the rotational model one obtains the relation Oexp =

(Ii LKOIIf K)2B2a(DWUCK),

where (IiLKOIIrK) is the Clebsch-Gordan coefficient for the angular momentum coupling between the initial and final state of the excited nucleus, K is the quantum number of the rotational band and flL is the deformation parameter. A complex derivative type form factor was used, the imaginary part of which almost yields the total amount of the cross section. This is due to the much larger radius Rw of the imaginary potential in comparison to the radius of the real potential. Consequently R w was used in order to determine the deformation lengths 17) given in figs. 5 and 6. In order to transform the fl-values to the corresponding electromagnetic transition probabilities B ( E L ) we make use of the fact that the fir values are rather constant for different potential radii 17). Thus, we transform our deformation parameter to the equivalent fl~e) for the electromagnetic transition by

fl °) = flL Rw/Ro, where R, = 1.2 A ~ fm. The reduced transition probability will be obtained from the equation ~272D2LR(e)2

B(EL)J,-

9 ~ "~ "', vz. 16rr 2 2L+l _ _

(4)

where the downward arrow indicates the de-excitation probability from the higher to the lower spin state *. Introducing the "single particle" unit or "Weisskopf unit" * For further information the reader is referred to the work of Dehnhard and Hintz 18) and references therein.

582

P. SCHUMACHER et al.

of the electromagnetic transition strength as B(EL)~.p.$ = ~

e ~

,

one obtains B(EL)~ _ 1 ( 3 + L ) 2 Z2fl~)2 ' B(EL)~.p.$ 4n ( 2 L + 1)

(5)

which yields for 7Li the B(E2) strength of B(E2)~-_,~- = 8.26 W.u. = 6.6 e 2 • fm 4, which is close to the accepted value of about 7 e 2 • fm 4 [ref. t9)]. The f i r values for the excitation of ~2Co +-,2 + and 26Mg o +--,2+ given in figs. 5 and 6 agree reasonably well with the numbers (fl = 0.57, R = 2.86, f i r = 1.63 for deuteron scattering on ~2C; fl = 0.33, R w = 4.46, f i r w = 1.47 for 3He scattering and f i r = 1.40 for e scattering on 26Mg) which were taken from the literature 20-22). The calculation for the x3C~ --'~* transition to the 3.09 MeV state which is shown in fig. 6 has been performed to demonstrate the sensitivity of the shape of the angular distribution to the transferred angular m o m e n t u m / . The use of the collective (derivative) type form factor in the present calculation may be justified in view of the fact that the shape of the angular distribution does not very sensitively depend on the form factor. Nevertheless, a more realistic calculation would be desirable which takes into account the p~ ~ s~ single nucleon excitation process and yields a more meaningful strength parameter than the value given in fig. 6. [Such microscopic calculations of inelastic scattering of complex projectiles are in progress 30)]. 5. Theoretical background for the F R D W B A calculations In the following we will consider the stripping reaction A + (b + x)~ --, (A + x)B + b. The D W B A cross section can be written 4): do" dr2

#~/~b kb 2 J n + l (2fib2) 2 k a 2JA+ l

~

[

~

ANtLtN2L21:iN1L1N2L2[I~'~I 2

lJiJ2m N1LIN2L2 rzlJIJ2

Ulm

kV]l'

(6)

where we neglect spin-orbit coupling in the distorted waves Z. The partial amplitude is given by ~ __ ( -- i)t BN1LIN2L2[A" lm \~1

ff

, a'b]Jlm

with the Jacobian aB

La ~,n'a,

~3

and the form factor ftN~LIN2L2(Ra, Rb) defined by the expansion * ~IN1L1MI(I'Ax)V(rbx)~/N2L2M2(rbx)

=

liar I I ~ ' ~ f 3M21NtL1N2LzfD Rb) , ~(L1L2M1, --1"21 .... . I t , - - 1 J i m ~,L"a,

l, nl

(8)

Li SCATTERING

583

where ~N~L~M,, I~IN2L2M2a r e the wave functions of the relative motion of the transferred particle x in the final nucleus and in the projectile, respectively; V(rb~) is the Woods-Saxon type interaction potential between b and x, the depth V°~ of which will be obtained to give the proper binding energy for ~S~L2M~(rb~). The coordinates are defined in fig. 7.

X

_

a

A Fig. 7. Radius vector diagram for the FRDWBA calculations.

The spectroscopic coefficient in eq. (6) can be written: ANtLIN2L2

,s~s2

= (-)L'+z2+sx-s2itW(Ll J1LzJ2, Sxl)

× c(rAtx,

rB)C(tbtx, ta) --

SI,(B -"

(b) N2÷'L2

a+x)Sl2(a --, b+x).

(9)

Here C(T) and C(t) are the isospin Clebsch-Gordan coefficients for the target nucleus and the projectile, respectively; S~ is the spectroscopic amplitude, the square of which yields the spectroscopic factor, which for our case of single nucleon transfer can be expressed by a coefficient of fractional parentage a) S:I = n(JBTB{IJATA, Jltx)2; n is the number of particles available in a given shell; J1 = LI+S~ and J2 = / - 2 + Sx are the transferred total spins between the initial and final state of the target nucleus and of the projectile, respectively (see table 3). E.g. for the (7Li, 6Li) TABLE 3 Selection rules for spin and angular momentum transfer in the FRDWBA calculations

Jt = Ll+~; J1 = JA÷Ja target system J 2 = Lz+~; Jz = J~-}-Jb projectile system 1 = Llq-Lz;

1 = JtWJz

reaction J2 equals ~ or ½. The factors (B/A) u1+½zl and (a/b) N'+½L2are the so-called recoil terms arising from the proper transformation of t.h,.e center of mass motions for the separation of B -~ A + x and a ~ b + x . .... ' By making use of the finite range code of Yoshida we can factorise the cross section

584

P. S C H U M A C H E R et al.

I

J

I

I

I

I

I

I

60

50

12C ( 7Li,6He)13N

1/20.00

36MeV, 12.5°, 3 x O . O 3 3 m C

5C 4 0

Oo =- 8 . 0 3 6 MeV

0

5/2°(3/2 -) 3 . 5 6 (3.51)

~ 3o

~2o 10 0

800

• .°

1'2

1'4

. ~

°

lk

]. t q- "... -L

° .°,

°°

1~

°°

2b

i

22

2~4

i

26 ELAB [MeV]

t

i

I

12C(TLi,eLi )~3C 5_*

600

36MeV, 12.5 °, 3xO.lmC

2

385

Q o =- 2.306 MeV

{/)

~ 400 o "6

-- 1 1 0 k e Y

L

I"

.13

0000

E c-

~lc~

200 -i~

.o ~. . .

T~=~l~

8~

0 20

25

o~

~Q"%.=. t2 7 7 12 C ( L i , L i ) C4,43

i

E LA. E M e V ]

Fig. 8. The 126(7Li, 6Li)laC and 12C(7Li, 6He)taN spectra.

Li S C A T T E R I N G

585

into a D W B A cross section aU.,L2 calculated by the code and a normalization factor Nz: "exp =

El N,,,,L,L2,

(10)

with

2Ja-t-1 1 (~4)2N'+L'(b)2'v2+L2

N,(stripping) = - -

2 J A + l 5093 -

J2(V°)2

x C(T)2C(t)2(21+ 1) ~" S a S, 2 W2(L~ J~ L2 J2; ½1), Nz(pick-up) = 2J~ + 1 2JA + 1 N~(stripping). 2,/b + 1 2J s + 1

(11) (12)

The selection rules for angular momentum transfer are given in table 3. In particular the triangle condition I = g , + 1 2 has an interesting consequence if both Jt = L x - ½ and J2 = L 2 - ½. Then the maximum angular momentum transfer will be given by lm~x = Lt +L2 -- 1, where (-)t,,.~ ~ ( _ ) L I ( _ f2. Consequently/max is "parity forFINITE R A N G E D W B A C A L C U L A T I O N 12C(7Li,6Li)13C

E = 36MeV "

•

12C(7Li,6He)13N I

I

I

I

I

I

"~ Qo =-8.036

I

I

I

-

MeV

10 °

"./ 10-1

=,

loo

10 -1

~q,,,. ,(,

10 -2

10-3 0o

30 o

60oA 90 ° ~c.m.

3.56 (3.51) 5•2 + (312-) i

0o

i

i i 30 o

i

i i i i 60°@ 90 ° c.m.

Fig. 9. The 12C(TLi, 6gi)laC and 12C(7L1, 6I-[e)XaN angular distributions. The curves are the F R D W B A calculations, which have been performed with the potential parameters set III o f table 2, the b o u n d state potential parameters ro = 1.25 fro, a = 0.65 fin, the spectroscopic factors o f table 4, the integration radius o f 15 f m with a step size o f 0.16 fm, and 28 partial waves. F o r 6He the same parameters were used as for 6Li.

586

P. S C H U M A C H E R et al.

bidden" for any zero range type DWBA calculation, and an FRDWBA analysis may become particularly necessary, since otherwise one does not get sufficient damping for the structure of the angular distribution in the high bombarding energy case 23).

6. The lithium-induced single nucleon stripping and pick-up transitions 6.1. THE REACTIONS 12C(7Li, 6Li)13C A N D 12C(7Li, 6He)13N

Fig. 8 shows the spectra for the mirror nuclei 13N and ~3C. The states in x3C are more strongly populated than the 13N levels and the relative intensities for the 13C levels differ quite significantly from those for 13N. These differences result from the different spins for 6Li and 6He in the exit channel and from the Q-value dependence of the cross section. The peak corresponding to t h e 12C(7Li, 6Li0+, r=l)13Cg.s. --==="l

101

l

I

~}d

I

I

I

I

ETu 36 MoV 2

L...

t I

LeO

10.. -

i:2 ','-,

',

_ ,

.=.~4o'~ I!

I

t/

L,

;;I

I~-1

.

\ Ii ~,

10"

Ii

{:0 'I I; 'I II II II li II

'

"~ !

O*

I~. I # t 3 I ! t ~1 II I 1 |1 I / i| i I l! V

li

lo <

I

I

30*

t

No-;TS I

I

I

I"1

60* ec.rll.

Fig. 10. The calculated F R D W B A cross section for the 12C(7Li, 6Li)IaC ground state transition and its fragmentation into the different components of angular momentum transfer. The full curves in the top, the middle and the bottom of the figure are the total differential cross section. The dotted curves are the different/-value contributions with weighting factors N~ defined in eq. (11).

Li SCATTERING

587

transition which is the analog of the (7Li, 6He) ground state transition is covered by the strong 3.85 MeV, {+ state in taC. Above the ~aC neutron threshold at 4.95 MeV there is no significant increase in the background due to three-body reactions. In this respect the taC spectrum is quite comparable to the 13N spectrum in which only 13Ng.s" is proton stable and nevertheless not much background can be observed at higher excitation energies. Underneath the 13C, 7.68 MeV state a broad background peak is visible which may be attributed to the 12C(TLi' 6Li ° +, r= 1)13C3.85, ~t+ transition which is broadened by the v-recoil from the de-excitation of the 6Li, T = 1 state. Fig. 9 shows the tZC(TLi, 6Li)t3C and 12C(7Li, 6He)taN angular distributions together with the F R D W B A calculations. The F R D W B A calculations were performed with the potential parameters set III of table 2, the bound state potential parameters ro = 1.25 fm and a = 0.65 fm, the spectroscopic factors of table 4, the integration radius of 15 fm with a step size of 0.16 fm and 28 partial waves. For 6He the same potential parameters were used as for 6Li. From the selection rules mentioned above we obtain for the (TLi, 6Li) ground state transition three/-value contributions, namely l = 0, 1, 2, whereas for the (TLi, 6He)reaction we get only the values l = 1, 2. Fig. 10 shows the different strengths for the different momentum transfers and indicates that the largest/-value yields the largest contribution to the cross section. This is true for all our investigated transitions. In our case of lithium-induced single nucleon transfer reactions the largest /-value is always "parity allowed", since the transitions 7Lig.s. ---} 6Lig.s. and 7Lig.s. - - + 6I-Ieg.s. are dominantly J2 = P~-(J2 = L2 + +½) transitions (see sect. 5). The "parity forbidden" l = 1 contribution is weak, but it does reduce the oscillatory structure of the angular distribution, since it is out of 1:hase with the l = 0 and l = 2 parts of the differential cross section. One problem which always has to be taken into account is the dependence of the

I

1

I

I

I

I

r

I

12C (7Li ' 6Li ) 13Cg s Q =-2.306 IVieV ~ = 2, E = 36 MeV

10' "\~

optical potential

Ill

,L,6.

::!,1 ':,

lO0

-

10-1

10-0o2

~

I

I I 20 °

~

I I 40 °

/

I I 60 °

] 80 °

Ocrn. Fig. 11. F R D W B A results for different combinations of potential parameter families from table 2.

588

P. S C H U M A C H E R et al.

DWBA calculations on the choice of the distorting potentials. Fig. 11 shows the 1 = 2 contributions calculated for various combinations of potential parameters from table 2 for the ~2C(TLi, 6Li)~aCg.,. transition. This reaction has only a slightly negative Q-value, and consequently the reaction is very well surface localized. We do not find any significant dependence on the choice of the potential parameters in this case (see subsect. 6.5). 100

i

i

i

I

~-.5.~ 3%5.83

i

I

i

i

i

13C(TLi,6He)14 N 0LA B = 20 ° ELA B = 34 MeV 1.5 m C

8O 0

o 60 "6

1ooo

o-.49~ Qo = - 2 . 4 3 M e V 2-.5.16

~ 4o i-

20 0

36.44

/.,,.-,,.,..j I

I

20

300

~l

i

22

' I

I

24

26

28

i

I

I

30 ELA B [MeV]

13C(7Li. 6Li)14C eLAB = 2 0 ° ELA B = 34 MeV 15 m C

25o

~, x.'~J3 ,t i.• 14C .~ 2-. 734 li ~3c 5t2% 385

Q0 = 0 , 9 2 4 MeV

2OO

6L O'T=1 :3 ~,6 MeV

q

13C gs [~

0

14p (1)%80,_

"5 1 5 0

~4C ~ 14Q1(1'21" 104

JCI E

0-, 690 ", 7 01 ~4C I I 14C 112)*. 832 I I [14C3-' 673

T.I / {

~oo 5/2-, 75 •

I,,ct 6 86

I

512"

I1111,, 1% 60g

t'l

gs.

50

I 20

I 22

I 24

I 26

I 28

I 30

I 32 ELAB[ Mev ]

Fig. 12. The (7Li, 6Li) and (7Li, 6He) s p e c t r a o n tsC.

Li SCATTERING

589

6.2. THE REACTIONS 13C(7Li, 6Li)l'~C AND laC(TLi, 6He)t4N

Fig. 12 shows the spectra for 14C and ~4N which were obtained from a ~aC target which contained an amount of 25 % ~2C. But the low-lying states in l'tN can easily be detected because of the more positive Q-value of the (TLi, 6He) reaction for laC than for the 12C contaminant (AQ = 5.6 MeV). The t4N s~p{ and d{p~r doublets at FINITE RANGE DWBA CALCULATIONS E = 3 4 MeV 101

.\,"CC'L,,%)'%.o'., r.,

IX,

I

I

f

i

I

Q • 092 MeV t =0,1.2 -:-

lOc

lO-2 E

loof 152~"

I 1 I I I ~3C{TLiflHel14Nal J" • Q =-2.43 MeV e l e ~= 0,1,2 ~

i,÷

1

"O

b "O

_

10°

]

00

I

I

I

I

÷ I

I

73C(TLi,eHe)14N3~,1o ~ ~.-637MeV = 0,1,2

~-i

I l I I l I

:30*

°iiI '~-

I

I

I

I

I

I

I

60 ° ,~ 0 o 30 ° 60 ° ecru ec.m Fig. 13. The IaC(7Li, 6Li)14C and xaC(TLi, 6He)14N angular distributions. See caption of fig. 9. Somewhat better fits could be expected if the potentials were chosen according to the "potential sum rule" as in fig. 20. However, because of the large amount of computer time required for the FRDWBA calculation and the uncertainty in obtaining the 6i.[e potentials, we did not repeat the calculations with the IV/III parameter combination. 0o

5 and 5.8 MeV could not be resolved. From the taC(TLi, 6Li)14C spectrum only the ground state transition was evaluated. The (TLi, 6Lio÷,r=~) transition was covered by the 12C ~ lSC ground state transition. Fig. 13 shows the angular distributions for the three low-lying states in ~4N and 14Cg.~.. The spectroscopic factors are given in table 4. 6.3. THE REACTIONS (TLi, 6Li) AND (TLi, 6He) ON 160 AND 2sSi T h e (TLi, 6Li) a n d (7Li, 6He) reactions have been m e a s u r e d on a 2sSi1602 target. Fig. 14 shows the c o m b i n e d spectra for 2 op a n d 17 F a n d for 2 9Si a n d x 70, respectively. A n g u l a r d i s t r i b u t i o n s have b e e n extracted for the g r o u n d state t r a n s i t i o n s only (see fig. 15). The spectroscopic factors which have been used in the calculation are given in table 4.

590

P. SCHUMACHER et al.

TABLE4 Spectroscopic factors used in the present FRDWBA calculations. The p-shell spectroscopic factors are taken from Cohen and Kurath a) Nucleus

Ex (MeV)

(J~, T)

Fragmentation

Spectroscopic factor p~.: 0.888 Pk: 0.431 p½:0.289 p~: 0.855 p½:0.039 p~: 0.98 p½:0.056 p~: 0.321 p$: 0.124 p½:5 699 p.~: 0.613 p~.: 1.122 s~r: 0.9 a) dl: 1.0") p$: 0.613 p~: 1.734 pk: 0.008 p~: 1.376 p$: 1.734 Pk: 0.326 p~: 0.0703 p~: 4.0 a) d.~: 1.0 a) d~: 1.0 a) d.]_: 3.5 b) s½ : 0.8 b) szk: 0.8 b)

7Li

g.s.

~-' ½

16Heg.s.+p [6Li~.s.+n

7Li

0.48

½-, ½

6Lil.s.+n

SLi

g.s.

2 +, I

7Lis.~.+n

SLi

0.97

1+, 1

7Li+n

12C aaC laC laC xaC a3N 14C 14N

g.s. g s. g.s. 3.09 3.85 g.s. g.s. g.s.

0 +, 0 ½-, ~ ½-, ~ ½+, ½

~+, ½

12Cz.s.-~n

½-, ½ 0 +, 1 1+, 0

:2Cs.~.+ p

lgN 14N

2.31 3.95

0 +, 1 1+, 0

laC+p laC+p

160 170 17F

g.s. g.s. g.s.

298i 29p

g.s. g.s.

0 +, 0 ~+, ½ ~+, ½ 0 +, 1 ½+, ~ ½+, ½

1S o + n 160+n 160+p 2SMg+n 2aSi+n 2aSi-}-p

26Mg

11C+n 12Cs.s.+n 12C 4.43+n 12Cs.s.+n

13C--~-n 13C+p

a) Assumed spectroscopic factors which, however, e.g. for the positive parity levels in xaC, are close to the calculated values of Barker 24) and to the experimental results of Glover and Jones 2n). b) Taken from ref. 26). In fig. 15 the n e u t r o n a n d p r o t o n transfer cross sections are collected for several t r a n s i t i o n s in o r d e r to give an overall impression a b o u t the quality o f the F R D W B A calculations. I n the calculation p a r t i c u l a r care m u s t be given to the i n t e g r a t i o n p r o c e dure. The n u m b e r o f p a r t i a l waves a n d the integration radius m u s t be big e n o u g h a n d the integration step small e n o u g h to yield reliable numerical results. The integration radius R = 10 fm is definitely t o o small for the A = 28 target region, b u t it is a p p r o p r i a t e for lighter target nuclei. This has been n o t e d in an early analysis {.see fig. 16) o f the same transitions as presented in fig. 15. 6.4. THE REACTIONS 13C(6Li, 7Li)12C AND i3C(TLi, 8Li)12C The energy spectra o f b o t h the (6Li, 7Li) a n d (7Li, 8Li) reactions o n 13 C are shown in fig. 17. The 0 +, g r o u n d state a n d the 2 +, 4.43 M e V level in 12C are d o m i n a n t l y p o p u l a t e d . They a p p e a r as doublets in the spectra which c o r r e s p o n d to the ~ - ,

Li S C A T T E R I N G I

200

t3 0

L)

150

[

591 I

I

(TLi, 6He) on 28Si 1602

I

36 MeV, 10", 3xO.lmC

I

i

t

Qo =-z24 MeV Q° =-9.38MeV

100

fi

":"• 4 " . . . .

50

,

"

"

° o

.

I

20 I

I

I

I

I

22

I

I

24

26 28 ELab (MeV)

I

I

I

I

2500 (7Li, 6Li) on 28Si 1602 2000"

36 MeV, 20* 3 x 0.6 mC

m 1.500u

~ r

Q o = 1.22 M e V

t

Q, =-311 MeV

i•

1

1(](]0 o

0

I

22

I

24

I

26

I

I

28

30

~~ ~~ ~0

o~

~7

o~o

o

~

I

I

32

I

34 36 ELab (MeV)

Fig. 14. The (TLi, 6He) and (7Li, 6Li) spectra on a 2ssix602 target. The dark peaks correspond to 17F and t 70 states, respectively.

ground state and ½-, 0.48 MeV level in 7Li and the 2 +, ground state and 1 +, 0.97 MeV state in SLi which are stable against particle decay. The intensity ratios a(Lig s.) TABLE

5

Cross section ratios cr(Lig.s.)/cr(Lilst) = ¢7(0)fi7(1) integrated from 15 ° to 35 ° for the ground state and first excited state in 7Li and SLi Reaction

(7(0)/o'(1) exp.

~r(0)/(r(1) spin multiplicity

(7(0)/cr(1) FRDWBA

13C(6Li, 7Li)12C~.s. 13C(7Li, SLi)12Cg.s.

1.4 3.7

2 5/3

1.2 5.0

592

P. S C H U M A C H E R e t al.

p -transfer

n - transfer 102

i J J i

i i

10 2

i

I u i

I I I I

12C(7Li,6Ho)I3No.s.

12C(TLi,eLi)13Co s.

lol

Q =-9.04 MoV

101

10 °

~ % =

~6 ~,v

z.1.2

100 ee e

10-1

~

10-2

I I I I I I I

101

I\l

I I il

10-I

* ".

10-2

I I I I J I J

i i i i J i i:

101

I

136 (TLi,(SLi)14C 0 s. ( ° = O.92 MeV

10 °

13C(7Li ,6He)I4N2 31 ,Tot Q.-474 MoV -

MeV

"

10-1

10_1

10-2

lO-2 I

10-3 10 2

j

113

I

I

i

i i

I

el

f-:

10-3

I I I I I I I

102

I I I i I I L160(7Li, 6He)17Fg.s Q =-9.38MeV

~=1,2,3 E.36 MeV

13 b 10 ° "(3

ff

I

I

160(7Li,6Li)1700 $

101

~

i I i

I

o.-311M~v ,E,

t. 1.2 _

10 °

:.o.1.2.

E=34

101

~,1,2.3

•

E = 36 MeV

It I

100

10-1

10-1 o~

10-2 101

I

I

V

I

i

i

i

i

10-2 101

I I I I I 28Si(7Li,6 Li) 29Sio.s. ~ •

10 °

i

Q=1.22 MeV r=l

J i

i i

Q • -724 MeV

10 0

10-1

10-2 --

10-2 I I I I I I I

i i i

285i(Tli,6H•) 29Pg s.

10-1

10-3

I I I I I I I

10-3

0 o 20 ° 40 ° 60 ° 80 ° Oc.m.

z.1

I

I

I

I

I

I

Oo 2 0 o 4 0 ° 6 0 ° 8 0 ° E)c.m.

Fig. 15. Compilation o f several angular distributions in the p and s-d shells. For the parameters in the F R D W B A calculations see caption o f fig. 9.

593

Li SCATTERING n

10 2

!

p - transfer

transfer

-

I I I I"I I~ / 12C('tLi'eLl) 13C$ .•. ]

•

Q --2.31MeV

101

102

= I

10-1

10-2

101 10 °

I

I

i

I I I I I I 13C(TLi'6Ll)14C ¢ I. Q , 0 92MeV

~

I

I

I

m V~ ~

= 34

I

r/

101

I

¢ • I. 2

10-2

i

101~]

I

I

I

= I I

I

=

=

I

=

i:

13C(1Li,6He)I4N ~ 31,T,1 Q°-4.74 MIV -

.

E.3','"~

1o ° L ~ .

-

~V

I0-I I ~ ' ~

10-1

10-2 I

10-3 10 2

I

I

I

I

I

10-3L

I

102

I I I I I"'1 I ---~t ~QO(7Li,S Li¿1~011 •

i I

101

~

e•

V

I

I

I

i

I

I

i

I

r

i-1' i

teO(TLi, 6HI )l/Fg i. O . - 9 3EIMeV

O'--311MrOV

~

= =-I

K"t ,o-,'°°

lO °

r.0

I

12C(TLi'eHe)13Ng s, Q ,-8.O4 MeV

101

f -1,2.3

=.1,=.3 e E " 36 I~N

b "D

10°

100 ~

10-1

10q t I I I I I I I

10-2 101

V

=

~n lO °

=

I

10-2 f

I

-

o.122,,v ~

~.ln

~ r

I

I

I I

t

I

a

J

2:

o.-~24~v

I

I

I

17

t-'

: ~°I~A

E=36M~V

1 0 -1 .-

:--I

I-

zsSi(TLi,6He) 29pg s

-"~

E'36M~v'~

~

w I

1

~ " ~ ,nO - I n

V~

10-3

101--'T

28Si(7Li ISLi)29SiO $"~

1 0 -1 :-

,o-

I-~

I

10-3_

0 o 20 ° 40 ° 60 ° 80 o

0o

I

'%', \ ) I

I

I

i

I

20 ° 40 ° 60 °

I

I0 o

@c.m. Oc.m. Fig. 16. Compilation of the same angular distributions as in fig. 15, but using for the calculations the optical model potential parameters of table 1 and an integration radius of 10 fro, which yields in particular for 28Si rather serious disagreement between the calculated DWBA curves and the experimental data. For the carbon isotopes and 160, however, the fits are of the same quality as in fig. 15.

594

P. SCHUMACHER 300

--r

i

T

T

T

e t al.

r

--r'----

1

13C(7Li. eLio.oo)12C

250

0.97 e L A a = 125 °

03

ELAs = 34 MeV

200

0,9 mC Qo = -2914 MeV

0 o

"8

150

E

100

L(1) ..Q E

443

ooo

50 9.64

I 18

16

t

7.66

I 20

I

22

i

200

I 28

26

]_

E eLi = 3 6 MeV, 12 ° •

® ~

~

3xO.32mC

I 30 32 ELAB [MeV]

I ~"

I

I

13C(6Li, 7Li)12C

O ¢J

E C

I 24

)

1~]

b

- 400

~ o

"

,oo

lo

Ioo

IO0

I

300

I

400

I

t

500

600 Channel

Fig. 17.

Spectra from the pick-up reactions

Number

13C(6Li, 7Li)12C and 13C(7Li, SLi)12C.

/tr(Lil, ) of the doublet states are comparatively far from the values given by the pure spin multiplicity 2 J + 1 (see table 5). This deviation can be understood as a combined effect of the spectroscopic factors and the Q-value dependence of the reaction cross section. The trend of this deviation from the spin multiplicity is reproduced by the FRDWBA, but there is no precise agreement in particular for the (TLi, 8Li) reaction. This discrepancy has to be attributed to the insufficient quality of the DWBA calculations - e.g. to the choice of potentials for 8Li which were taken to be identical with the 7Li potentials. The spectroscopic factors for (SLi{I 7Li x n) (given in table 4) should be correct, since they have been checked by the (d, p) measurements by Schiffer et al. 27). The ~6Li, 7Li) and (TLi, 8Li) angular distributions on t3C are

Li SCATTERING

595

13C(6Li 7Li)12C 13C(TLi, aLi)~ C E = 34 MeV

E = 34 MeV

1011 '\ . . . . . . . . . . QO=2306 MeV 10 0 13C(6Li7Li000)12C000" , 10 -1

101

I I ~/ I I I I I I I

•

100

,'t~,, ,~%,,~{+ 104

:

-

~(~4aLiccxg~Z Co.oo

-

~C6L~_iog~=Co.oo

,÷

101

10°

Qo" -2.914 MeV

10°

~,/'~ ,~

104

,~~48)'*Cooo.

10 '-1

10-2

++'*t*tt

101 .,.(3 E

"o

10 °

lO° 10.-1

Io o 10_1

10°

1011 104

100~ " " ~ L

,,:c'"

lo-21°4_ ir~-3

~0

10"2

J . . . . .

30 °

10-3

". . . . .

60 °

90 ° ecm.

i I

o"

t

i

30 °

i

i

i

60-

i

i

i 9o=

Oc.m

Fig. 18. Angular distributions for the (6Li, 7Li) and (TLi, aLi) reactions on 13C. The DWBA calculations use the optical model parameters of table 1 and an integration radius of 10 fm. For 6Li the same parameters as for 7Li have been used.

596

P. S C H U M A C H E R

et al.

given in fig. 18. The measured cross sections for the 13C(6Li, 7Li)12C ground state transition are in good agreement with the experimental data from the reverse reaction 12C(7Li, 6Li)~aC given in fig. 9. The FRDWBA curves were calculated using the potential parameters in table 1. 6.5. T H E G R O U N D

STATE T R A N S I T I O N S

(6Li, 7Li) O N ;2C, 160 A N D 26Mg

The (6Li, 7Li) pick-up reactions have also been studied for a 26Mg target on carbon backing which was slightly oxidized. A typical spectrum is shown in fig. 19. For I

t

I

1

I

I

x ^ 1/4 2000 26Mg(6Li. 7Li)25Mg 36 MeV, 9 °, 3 x O 6 3 m C

0

1500

J

g

÷ to c0

o

L)

1000

O

o5~

o

5

500

eq 6~ xl" ed

o~o I

500

I

I

600

I

~" ¢d

I

700

to t-.

P

800 Channel Number

Fig. 19. The (6Li, 7Li) spectrum from 26Mg on carbon backing which was slightly oxidized. The Pthole state is strongly suppressed by the Q-value dependence of the cross section.

26Mg, only the ground state transition has been evaluated which is by far the dominant transition. From the oxygen contamination in the target only the p~"1 ground state in *50 can be detected. The p~_ hole state at 6.16 MeV is completely suppressed by the strong Q-value dependence. Fig. 20 shows the angular distributions. The FRDWBA calculations have been performed with the potential parameters III/III from table 2 which gave quite satisfactory fits for the 12C(7Li, 6Li)13C reaction. But in the present case we obtain rather bad agreement with the data which is most significant for the 12C(6Li, 7Li)11C reaction which has the most negative Q-value. In view of the momentum mismatch conditions for this reaction we used different potential parameter families for the DWBA calculations. In contrast to the momentum matching case presented in fig. 11, the calculated cross section turned out to be much more parameter dependent. The DWBA results for the potential III for the incoming 6Li and potential IV for the outgoing 7Li gives somewhat better although

Li SCATTERING

597

not satisfactory fits. The latter potential c o m b i n a t i o n fulfills rather closely the relation V i . + Vbouna = Vout for the real part o f the potential (V~o.. a = 61 M e V at r o = 1.25 fm). This potential sum rule is k n o w n to be a useful criterion for a proper choice o f potentials for zero range calculations in the case o f m o m e n t u m mismatch conditions i o. 28). i

I

i

I

I

I

I

I

i

i

i

_

12C(6Li,TLigs)11Cgs _ .#~.fGQ---11A67 MeV

10C

t; '~G

10£ - - ~ 12C(6Li7Lio.48)llcgs, " ; ~ \ \ Q =- 1~945 MeV

i(~I~- ¢~ 1~ '!

_~/E

-

lO-3

I~3

'~ 160(6U,71i048)150g s -* ~ Q = - 8.893 MeV --

10-2

_

4%( ~,~

101 ;~26Mg~LJ~ig.s) 251v~jg.s i0° -'~Q =- 3.824 MeV 10-1 1Ey2

10-3

O°

"! ~ p" ~,~,=~/ N i i i i [~ll~'l~i i i i 30° 60° 90° @cm

Fig. 20. Angular distributions for various (6Li, 7Li) pick-up reactions. In contrast to the results for the x2C(TLi, 6Li)13C reaction in fig. 1 l, we observe a larger sensitivity to the choice of potential families which might be due to the momentum mismatch conditions imposed by the negative Q-values. The potential combination III/IV for 6Li and 7Li respectively fulfills rather closely the relation V6u + V . b°u°a = VTu for the real part of the potential.

598

P. SCHUMACHER

e t al.

7. Conclusion

The elastic scattering of lithium ions can be successfully described in the framework of the standard optical model 8, 9, 11, 12,32). The observed discrete ambiguities of potential parameter families cannot experimentally be reduced unless data at higher bombarding energies become available similarly as in the case of ~-scattering 10, 13). Guided by the investigation of the bound state potentials and of the superposition of the ~ and deuteron potentials, however, one may select parameter family III from table 2 with V = 170 MeV, r 0 = 1.21 fm as the most reasonable potential for 6Li scattering. The 7Li potential should only be slightly deeper. The inelastic scattering angular distributions are well described by the collective type DWBA analysis. However, we have not yet investigated the double excitation process of both the target nucleus and the projectile. For the case that this double excitation proceeds in a single scattering event between the target and projectile nucleons, a full microscopic analysis of inelastic scattering with complex projectiles would be desirable in particular in view of the analysis of the (rLi, 6He) reaction 29). Such microscopic calculations are in progress 30). The lithium-induced single nucleon transfer reactions show no significant deviations from the transfer reactions with light projectiles, The F R D W B A analysis uses known spectroscopic factors and gives a rather reasonable overall agreement with experiment for the absolute cross section as well as for the shape of the angular distributions. The choice of potentials according to the potential sum rule seems to provide the best fits. But nevertheless, the fits are not completely satisfactory. The sensitivity to the choice of potential parameters seems to increase with increasingly negative Q-values. The Q-value dependence of the absolute cross section is rather drastic. E.g. the p~ 1 hole state in a 50 could not be observed in the 160(6Li, 7Li)lsO reaction, although this state has a very large spectroscopic factor. The "parity forbidden" /-value contributions of the finite range calculations fill up the minima of the calculated angular distributions, but their contribution to the absolute cross section is rather small. This allows the application of zero range type DWBA-calculations using the heavy ion approximation just in the spirit of the Buttle and Goldfarb assumptions 3t). Those recoilless DWBA-calculations which are useful in view of the reduced computing time will be presented in a subsequent paper 2). We thank A. Pilt for a critical reading of the manuscript.

References

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