Study of the 16O(16O, 12C)20Ne reaction mechanism by polarization measurements

2B : 2N

Nuclear

Phpsics A32î (1979) 481 - 509; © North-Holland Publlshiny Co., Anvttrdam

Not to be reproduced by photoprint or microfilm without written permtasion liom the publisher

STUDY OF THE ' 60(' 6 0,'X) 2 °Ne REACTION MECHANISM BY POLARIZATION MEASUREMENTS F. POUGHEON, P. ROUSSEL, M . BERNAS, F. DIAF, B. FABBRO, F. NAULIN, E. PLAGNOL and G. ROTBARD Institut de Ph~~.sique Nucléaire, BP no . 1, 91406 Orsay. France

Received 26 March 1979 Abstract : The ' `'O(' `'O, ' ZC) 2°Ne reaction has been studied at beam energies of 68 and 90 MeV. At these energies, this reaction is selective for populating high-spin states well known to have a large overlap with a+'°O. The angular distributions have been analyzed with an EFR-DWBA code . Good fits are obtained and the resulting relative a-particle spectroscopic factors for the =°Ne states are in good agreement with shell-model predictions, and with other results from different a-transfer reactions. The polarization of Z°Ne has been measured by angular correlations between ' 2C and '~O (product of the ~°Ne decay). As expected from a semidassical view of the transfer, a strong '°Ne polarization, on an axis perpendicular to the reaction plane, has been found. This polarization remains constant on a wide span of ' ZC angles. Different nuclear reaction models have been tested . With selected potentials, the DWBA predicts a strong polarization in this case of a heavy-ion transfer, but not as strong as the one observed in the experiment. Some possible reasons for this difference are indicated. E

NUCLEAR REACTIONS '60('60,'~C), E = 68-90 MeV ; measured o(0), O,,b = 5°-2l° ; correlation functions; 2°Ne levelsdeduced relative spectroscopic factors, polarization tensors, reaction mechanism EFR-DWBA analysis .

1 . Illtl'OdOCh011 In many nuclear reactions the final states are produced with a non-statistical spin distribution . Thus a measurement of the polarization of the nuclei involved in a reaction can yield important information regarding the reaction mechanism. Measurements of particle-y, y-y or particle-particle correlations can be employed to determine the nuclear polarization . In the past few years a large amount of experimental and theoretical works have been devoted to the study of heavy-ion induced transfer reactions . In most cases, the angular distributions of these reactions are non "L-dependent" and structureless for L > 2. Although a strong selectivity is observed in these reactions, little information about the spectroscopy and the reaction mechanism can be extracted from them. A deeper insight on the reaction mechanism can be reached by correlation measuromeats. The correlation depends on the amplitudes and phases of the transition amplitudes whereas the differential cross section depends only on the sum of the squared moduli of these transition amplitudes . 481

48 2

F. POUGHEON er al .

In the present paper, we report on polarization measurements, obtained by particle-particle correlations, in the four-nucleon transfer reaction

where the z°Ne* level is selected by the energy of the associated 12C . The spatial distribution of the coincident 160 yields the polarization state of the s°Ne*. This reaction was chosen for three main reasons : (i) All the spins of the nuclei involved in the reaction are equal to zero, with the exception of that of the residual nucleus . Hence the formalism of the correlation is simplified and all the components of the polarization tensor can be deduced from the correlation function . (ü) Several experimental and theoretical investigations have shown that in the (160, 1zC) reaction the four transferred nucleons are an a-like cluster in its Os ground state 1). (iii)Finally, since the 160('Li, t)2°Ne reaction has also been studied with correlation measurements Z ), it is interesting to compare these results to those obtained by the ( 160, 1zC) reaction . Some initial results of this work have already been published s ~ 4). In this paper, extensive measurements of the dependence of the z° Ne* polarization on the 1zC angle are presented. This has been made possible by the use of a new experimental setup for trajectory reconstitution . Sect . 2 of this paper gives the theoretical aspects of the problem and the influence of the reaction mechanism on the correlation function . The third part is devoted to the experimental setup. The angular distributions and their analysis are discussed in the fourth part. The results and analysis of the correlation functions and the deduced polarization of the residual nucleus are presented in sect . 5. Finally, we compare our results to the predictions of different reaction mechanisms . 2. Theoretical aspects In this study, one considers the following transfer reaction in which all the particles involved have spin zero with the exception of the residual nucleus which has a spin J: 160 + 160 -~ 1 iC ~., soNe* .

The geometry and the coordinate system used for the study of this reaction are shown in fig. 1 . 2.1 . CROSS SECTION AND POLARIZATION TENSOR

The cross section for populating a level of spin J, measured at an angle B~, can be

teat60 t :~:oNe

483

ITM IZ,

(1)

written as = E

where the T~'s are the reaction amplitudes . This expression can also be written as z (2) ~ITMI Z =EIp; ~I, where the pM are the components of the normalized tensor used to describe the state of polarization of the residual nucleus z °Ne. Both TM andp~ are complex numbers. The p~ are normalized to unity M

and Ip;'~ z is, by definition, the population of the magnetic substate M. The polarization P is defined as P = (1/J)~MM IP'; Iz . Thus the polarization will be equal to zero when the magnetic substate distribution is symmetric with respect toM=O. Assuming a standing wave description, the dependence on 9~ of the T~ is given in the following formula 6), the quantization axis being taken along the beam axis : TM(e~) _ ( -li`~ (- ~`lrf(1,U,1fMIJ11l)G,f .-arPi~M~(e~)Iiif,

where 1, and 1f are the angular momentum in the entrance and exit channels

I=

21+1,

C(l+ In1U ~~' and where the I~,f are proportional to the elements of the reaction matrix S. It is obvious that the measurement of the cross section at a given angle cannot alonegive any insight about the TA,` (neither about their relative phases nor about their amplitudes). Even measurements of a complete angular distribution will leave some ambiguities on the determination of the T~`. Most of these ambiguities can be removed by a correlation measurement. In the present case, when the residual nucleus (z°Ne) is formed in an excited state which decays through the emission of an a-particle, the spatial distribution of the emitted a-particle (or equivalently of the recoiling 160) will measure the polarization state of the z °Ne excited levels . The state of polarization depends on the 1zC angle. Hence we measure the angular distribution of the a (or 160) in coincidence with a 1zC at a given angle in the sequential reaction (see fig. 1) 16(160, 1zC)zoNe* -. a+ 16 0.

484

F. POUGHEON et al.

2.2 . SYMMETRY PROPERTIES 2.2 .1 . Symmetries of the reaction amplitudes . It can be shown that the conservation laws in quantal mechanics lead to the following rules for the studied reaction A(a, b)B*, + + 0 0 + 0 Jx, ~ _ (-)`,

i f

l + i + E = even. Furthermore if the two particles are identical in the entrance channel this leads to

of

(1, = even, +e = even .

If the quantization axis is taken perpendicular to the reaction plane, the following properties are deduced (i) TM ~ 0 if n and M have the same parity, i.e . J-M even or odd for natural or as)) . unnatural parity states respectively (Bohr theorem (ü) T,ß(0) _ (-1f T~ M(0). (iü) TiM(x) _ (-1YT1 ~(n). TJ M(~-6 . T~`(0) ° ( - 1YT~(~) (iv) ~(e~) = )2.2 .2 . Symmetries of the correlation function . In the center of mass of the residual nucleus Z°Ne*, the decay particles, a and 16 0, have opposite directions . Thus the 1zC-a correlation can 1aC-160 correlation . be directly deduced from the The correlation function of the a emitted in the decay of the 2°Ne* state of spin J is equal to')

where the pi's are the components of the polarization tensor which describe the state of s°Ne*. The t~°(8) are the rotation reduced matrix elements . They are related to the Legendre polynomials by

B and r¢ define the emission angles of a in the 2°Ne* center of mass (fig . 1) . From the expressions (~ and (~, one sees that W is unchanged if all the are replaced by the imaginary conjugate ofp~ ~. This mama that the sign of the polariza-

pu

ie 0( ~s 0 ~zC)zoNe

485

Fig. 1 . The geometry and coordinate system used for the study of the sequential reaction 's0(`°O,'zC)z°Ne* ~ a+'6Q. The ' zC are detected in the focal plane region of the spxtrograph For a selected level of z°Ne', the correlations W(B = }n, ~) and W(B, ~ = 0°) are measured with the position-sensitive detector (PSD) in positions I and 2 respectively, detecting the `60 ions.

tion cannot be determined from such correlation measurements . Since the reaction plane is a symmetry plane for the primary reaction, the Bohr theorem 2') applies and W(B, ~) = W(B, ~+n) = W(-9, ~) = W(-B, ~+n). Because the p;' are only defined within an arbitrary phase factor and because they are normalized to unity, only 2J independent real parameters nced to be measured. 2.3 . REACTION MECHANISM AND POLARIZATION

It is interesting to see what would be expected for the correlation function in some cases corresponding to different descriptions of the reaction mechanism. (i) In the simple semiclassical description of the mechanism, one assumes that all (i.e. incident, exit and transferred) particles move in the common plane of their centers of mass which define the reaction plane (fig . 2). Then the transferred spin, which comes only from the orbital momentum is necessarily perpendicular to the reaction plane (z-axis) . If the incident particle .follows one of the classical trajectories corresponding to the positive or negative deflection angle, the population is then ~, ~Z = 1 for M = +J or M = -J and a complete polarization of Z°Ne* is ob-

486

F . POUGHEON et al.

Fig. 2 . Semiclassical description of the reaction mechanism . On the l .h.s . are shown the classical trajectories corresponding to positive deflection angles (1) and to negative deflxtion angles (2) . On the r .h .s . are shown the correlation patterns for a 3 - state in the reaction plane and in a plane perpendicualr to it, in the case where there is a coherent mixture of trajectories (1) and (2) with weights as 1 and 9 .

tamed. If there is a coherent mixture of trajectories with positive and negative deflection angles, both the M = +J and M = -J magnetic substetes would be populated resulting in a decreased polarization . With only one of the two values of M (complete polarization) the angular correlation function is isotropic in the reaction plane and it is a sin2'9 in the vertical plane. With the two values ofMthe correlation function keeps the same shape in the vertical plane while regular oscillations appear in the reaction plane. For an equal contribution from both trajectories, the modulation of the function is maximum that is to say the minima.are equal to zero . It appears that the correlation pattern is very sensitive to the admixture of a small amount of the other trajectory . In the example given in fig. 2, 10 ~ only . of ~P.r'~2 gives such a strong modulation . (ü) The second model can be called the "spectator ejectile model" . It is assumed that the ejectile b has no interaction with the target either in the incident channel (as a part ofthe projectile) or in the exit channel (fig. 3). The a-fragment is captured

16l60 iz~zoNe

487

along a direction which becomes the recoil direction. The spin of B, perpendicular to the recoil axis, is equally distributed around this axis and with a quantization along this recoil direction the population is then ~P; ~s = 1 . The correlation function is the same Legendre polynomial in any plane including the recoil direction (fig . 3).

Fig. 3 . The "spectator ejectile model" and the corresponding correlation functions in the reaction plane and in the plane perpendicular to it at the recoil dirxtion .

It must be noted that these predictions are not compatible with the classical one, since in the latter, only one vector M= = J is selected among those distributed around the recoil axis which are necessary to represent the case where MR = 0. The spectator ejectile model leads to the same predictions as the plane waves description of the mechanism. (iii) DWBA formalism. The transition amplitude TM can be calculated in the DWBA formalism and the tensor polarization and the correlation function can then be deduced. In fact, the TM's are calculated in DWBA before the cross sections are obtained . To perform the calculations we have used the code SATURN-MARS 1 [ref. t s)] . It is an exact finite-range code, including recoil effects and requiring the use of the cluster approximation for treating multinucleon transfer reactions. This code is based on a reformulation of the DWBA done by Tamura e) in a form which takes into account the pecularities of the heavy-ion induced reactions.

48 8

F. POUGHEON et al.

In the DWBA framework, P. D. Bond has analyzed how the polarization of products of quasielastic heavy-ion reactions depends upon the bombarding energy, Q-value and specific reaction products') . The results obtained with DWBA calculations will be discussed in the last part of this paper. (iv) Single partial-wave model. It is well known that because heavy-ion transfer reactions are peripheral and localized in the "T' space, only a few values of L and if contribute to the cross section. Extending this idea to its limit, one can assume that only one value of l, and !f contributes to the cross section. The transition amplitude can be written as (the quantization axis being taken perpendicular to the reaction plane) ~(B~) ^' ~ ~liM~lfMfIJM)Y~'(~,0)Y,~f(~c,B~) . At,Arr

The transition amplitudes can be easily calculated and the populations of the magnetic substates deduced. It is found that both the shape of the cross section angular distribution and the polarization depend strongly and only on the value of L = Il,-lfl . Since in this model 7; M(B~) _ (-1)'~*(9~) and consequently IPA MIZ = IPMIZ, this model predicts no polarization at all. 3. Ezperim~tal set~p The optimisation of the efficiency is of major importance for correlation experiments. For this reason, we chose to detect the 160 resulting from the z°Ne decay instead of the a. The whole correlation can be obtained in one exposure as the 160 are emitted in a rather small solid angle . For the 1ZC particles, the setting of a system of trajectory reconstruction behind the spectrograph allowed a solid angle of 5 msr while maintaining an excellent determination of the 1 Z C angle. 3.1 . GENERAL ARRANGEMENT

The general arrangement of the experiment is shown in fig. 4. The beam from the Orsay MP tandem is focussed on self-supported Si0 targets (100 ~.g/cm2) and stopped in a Faraday cup. A collimated 80 pm thick silicom detector is set at a fixed angle (40°) to monitor the beam current and the target thickness. The energy and the direction of the decay products from the excited z °Ne* nucleus are obtained in a silicon position-sensitive detector (PSD), 5 cm long, placed in the target chamber 7 cm away from the target . This PSD can be set either m the reaction plane or perpendicular to it (fig. 1): The 1ZC particles are localized and identified in two position sensitive gas counters s) set in the focal space of the doubly focussing spectrometer .

ie

aie 0 ~zC~zoN e

489

PS.D

Fig. 4. General arrangement of the experimental setup.

3 .2 . TRAJECTORIES RECONSTRUCTION

A simple treatment of the two position measurements behind the spectrometer gives, on-line, the two parameters which characterize the trajectory coming from a point object : the angle B~ and the magnetic rigidity "Bp" . Moreover, it is possible to calculate the intercept of the trajectories with any plane and, hence, in particular, with the kinematically displaced focal plane for the studied reaction . The new experimental device built to perform this reconstruction is described in detail elsewhere 9). To summarize its performances one can say that two dE measurements are made, the first one with an accuracy of 10 to 12 ~, the second one with 5 to 6 ~. The angular measurement has a precision of 0.3° (FWHM) within a full aperture of 5 .2° corresponding to a solid angle of ~ 5 msr. The energy resolution is typically 150 keV mainly due to the target thickness . 3.3 . ELECTRONICS AND OFF-LINE TREATMENT OF THE DATA

t

Signals are processed through a T1600 computer which controls the writting of the data on tape, event by event and also provides on-line analysis and display. For each event, seven primary signals are generated, namely : St , SZ, S3, S4 from the two ends of the two gas counters, E and P'E' the energy and position signals from the PSD in the target chamber and the TAC which operates between timing signals coming from E' and the first gas counter. These signals are processed through a computer which provides for several on-line visualisations (inçluding a selected sample of the correlations). t

Ref. ' ~.

49 0

F. POUGHEON et al.

P'

2, 3

a,s

"

10,21

"

> 21

't

. .

.t . s. . .1 " I,

"t,

,`iV" ,RECOIL DIRECTION . ~7~j t " .t tt.. t.t.

1' "

,1 .

.. " t

t t

~

t

"

f ~.

"

-

~

.

"t

"t '

i

~ E'

Fig. 5. The distribution of the '60 and a-particles detected in the PSD and gated by the coincidence with ' ~C . P' is the position coordinate and E' the total energy of the particle in the PSD located in the reaction plane. In the upper part of the figure are shown the kinematical lines wrresponding to the doexcitation of ~°Ne'(8.45 MeV 5-) in the reaction '60('60,'=C)'°Ne' -+ a+'s0 for B~ = 17°5 . The blocks along the '60 line correspond to 5° steps in the 2°Ne center-of-mass system . In the lower part of the figure is shown the measured distribution of the detected particles for the same 2°Ne level . The groups of points in the middle of the figure correspond to the recoil nuclei'°Ne and "S which undergo y~ecay. The'2S is due to 2sSi in the target .

isais0" iz~zoNe

49l

To go further, off-line analysis is needed. A window is set on one of the z°Ne levels on the calculated excitation energy . Another window is set on the calculated 1 zC angle. The bidimensionnal E' x P' spectra gated with these two conditions are the basic data for the correlation. It is analyzed using the kinematical plot (fig . 5) deduced from the three-body kinematics . The final result is the correlation function W(~n, ~) ifthe 1?SD is set in the reaction plane or W(B, ~ _ ~«~°;,) if the PSD is set perpendicular to the~eaction plane (fig . 1). 4. Cross section.4 : results and analysis 4.1 . z°Ne SPECTRA: SPECTROSCOPY AND ANGULAR MOMENTUM MATCHING

The 1s~(1e~~ 1z~zoNe reaction has been studied at 68 MeV and 90 MeV incident energies . Typical spectra obtained for this reaction, at the two incident energies, shown in fig. 6, display the selectivity of this reaction . The most populated states are the members of the K = 0 + ground state band [0.00 MeV (0+ ), 1 .63 MeV (2 +), 4.25 MeV (4+), 8.78 MeV (6 +) and 11 .95 MeV (8 + )] and the K = 0 - band [5.79 MeV (1 -), 7.17 MeV (3- ) and 10.26 MeV (5 -)] . The population of the 5- state at 8.45 MeV is rather surprisingly important since this level has been attributed to the K = 2- band, the structure of which is Sp-lh. Such a configuration could only be populated via two-step processes involving lp-lh inelastic excitation in the 16 0 core. However, in the ('Li, t) reaction, this level has been already observed z) with a noticeable cross section and it is unlikely that the multistep process would favour this particular level in those two different reactions. Furthermore, the K = 2band has strong overlap with the K = 0 - band, which is strongly excited in atransfers. So this level should have at least a component of its configuration compatible with a direct a-transfer . This observed selectivity in the (160, 1zC) reaction is the same as that observed in the ('Li, t) [ref. 11)] and ( 13C, 9Be) [refs. 1z .1s)] reactions. So this confirms that the (160, 1zC) reaction is mâinly a direct a-transfer . The cross section for exciting a given level of z °Ne will then depend on two factors. First, the structure factor, which measures the overlap between the z°Ne wave function and an a-particle orbiting around an 160 core (where "a-particle" means four nucleons with all the symmetries of an a-particle). Second, the kinematical factor which reflects the angular momentum matching, and the Q-matching of the reaction . To give some insight into the kinematical factor we have used a semiclassical analysis 1a), considering the transfer of an a-cluster whose relative orbital momentum is zero in the incoming 160. Having chosen an interaction radius, the values of l and Q can be calculated 14) as a function of r° and directly compared to the Jand Q-values ofthe z °Ne levels to see which levels would be favoredbythe kinematical factor. One can see in fig. 7, that between 68 and 90 MeV incident energy the favored J-value increases only by one unit of fii but the favored Q-value increases by more

49 2

F. POUGHEON er al. Iso

T

~ 180, 12 C ~ 2~Ne ~

6+)

68 MeV Blpb " 19'

~, 300

4. 23 4+)

( a~ 200

(~I/2)

E

a4s I I

s-

7 .17 ( 3-)

10.28 (Sl

Z

t83 1 Y*1

100 0 (O+)

1

400

1

â00 Chpnnel

Chpn nel

Fig. 6. The

`ZC

energy spectra observed in the `60(`60,'X)=°Ne reaction at 68 MeV and 90 MeV incident energies . Spectra are obtained from two different exposures.

than 4 MeV . The shift in the Q-window is indeed clearly confirmed in the experimental spectra as well as the high spin (J ? 4) selectivity. 4.2 . ANGULAR DISTRIBUTIONS OF THE CROSS SECTIONS

Angular distributions for these levels have been measured in 1 ° intervals from 3° to 21° (lab) at 68 MeV and 90 MeV incident energies . Except for the angular distributions of the 0+(g.s.) which oscillates, the other angular distributions are rather

iba~e~ izC)zoNe

493

8 6 4

2 0

5

10

Ex (MeV)

15

Fig. 7. Angular momentum and energy matching for the `60(`60,'~C)Z°Ne reaction at two incident energies (68 and 90 MeV) . The enhanced regions of the spectra obtained by varying the interaction radius parameter r° are shown. The overlap with rotational band levels of ~°Ne' is also shown.

flat and structureless. They are slightly forward peaked and the overall slopes are about the same for all the levels at the two incident energies (fig . 8 and fig. 9). The analysis of the angular distributions, measured at 68 MeV incident energy, 16(160 12C) 20Ne

ECM=34 MeV

~ 10_ ~ 10 I

~f

~ ~ f ~~ ~

~~~

Of (p.s)

J0 1 2+

1.63 MeV

+~ .-+-~+

0

4+ 4.25 MeV *~y I

I

I

I "

10

IS '20

I

25

"~L ti~ I

35 e CM Fig. 8. A comparison of experimental angular distributions obtained at 68 MeV incident energy and EFR-DWBA calculations . The optical-model parameters used are given in table 1 (set A) . The form factors for the unbound states (right of the figure) have been calculated assuming a binding energy of 0.4 MeV (dashed curves). Predictions with a greater binding energy, I.5 MeV, are also shown (full lines) to indicate the influence on the form factor. A radius r° = 1 .35 fm and a difï'useness a = 0.65 fm have been used for the Woods-Saxon wells. 5

30

494

F . 1?OUGHEON et al. 100

+

Iso( IS~~IZ~ )

10 1

zo~

ECM-45MeV 1 f f

5

2+

+

f

1 .63 MeV

1

"

' " ~

" '

_ ' ~100 E

iso(IS~,IZ~) ~Ne E CM' 45MeV " "

" ' "

6+ 8.78 MeV

"

~ " ~ 100

' " " "

b

4+ 4.25 MeV

" + . ,

+ " "

~ I00

"5-

10 . 26 MeV

" " "

-1

l0

3 - 7.17 MeV

0

"

100

i 5

i 10

i 15

i 20

i 25

i 30

5

ecM

8+ 11 .99 MeV

I

I

I

I

10

15

20

25

~

30

eC .M .

Fig. 9. The measured cross section angular distributions of the ' 60(' 60, ' ~C)~°Ne reaction at 90 MeV incident energy .

was carried out within the framework of the EFR-DWBA . The computer program SATURN-MARS, written by Tamura and Low' s ), was used. It is an exact finiterange code, including recoSl effects . Two different sets of optical-model parameters were used. The set A (table 1) is a surface transparent potential Z°) and the set B is a strongly absorbing potential t9) . Calculations carried out with this code and using these two sets of optical-potential T~at.a 1 Optical-model parameters used in the DWBA analysis Set

Channel

V '(MeV)

rv (fm)

av (fm)

W (MeV)

r,r (fm)

a~. (fm)

r~ (fm)

7.2 5.8

1 .27 1 .27

0 .15 0 .15

1 .35 1 .35

1 .245 1 .245

0 .45 0 .45

1 .24 1 .24

A') A

` 6 0+` 6 0 ~ . `~C + =°Ne

17 17

1 .35 1 .35

0.49 0.49

B B

` 6 0+` 6 0 ~ `2C+~°Ne

50 SO

1 .245 1 .245

0.49 0.49

30 30

V, rv, av denote the real and W, r,r, a the imaginary Woods-Saxon parameters . The radii are defined R = r(Ai~3+A~~') for r = rv , r, r with A 1 (A=) the mass of projectile (target) nucleus . ') See ref. _~ .

16l60 iz~zoNe

495

parameters reproduce well the experimental angular distributions (see fig. 8). But with these rather flat angular distributions, it is likely that many sets can reproduce the data. Therefore, the choice of these optical potentials remain ambiguous if one only looks at the angular distributions. Table 2 lists the relative values of SQ derived from our analysis with set A and compared to other values derived from other reactions. In contrast with the (t Z C, 8 Be) results, the Sa values obtained in the present experiment are in excellent agreement with the shell-model results ") and they are quite similar to the ones obtained in ('Li, t) but using EFR-CCBA calculations tt) . Our results are also in agreement with t60( 1 3C, 9Be)zoNe [ref. ts)] . Thus, there is little doubt that the 16O(160~ t2C)zoNe reaction is a direct transfer of an a-particle. TAH~ 2

Relative a-cluster spectroscopic factors-in z°Ne E, (MeV)

~

0 1 .63 4.25 8.78

0* 2* 4+ 6+

`) Ref. ") .

present EFR CCAB experiment 38 MeV ") set A

x

1 .00 1 .40 1 .40 1 .10 b)

Ref. ' 8).

1 .00 1 .00 0.75

(' zC, 8 Be) 56 MeV b) 1 .00 0.61 0.26

`) Ref. ") .

9Be) 105 MeV °)

Cluster model °)

1 .00 1 .97 2.83 2.58

1 .00 1 .00 0.95

("C,

Shell model °) 1 .00 1 .00 1 .00 1 .00

°) Ref. ") .

Another analysis of the angular distributions has also been made in the framework of the single wave model. The 1; value has been taken as the incoming grazing angular

e

Fig. 10 . The measured cross suction angular distribution of the' 60('60, 'zC)z°Ne' reaction at 68 MeV incident energy leading to the 8.79 MeV (6+) state. Comparison with the predictions of the single pertialwave model (see text) with three dilFerent values of the angular momentum in the exit channel.

496

F. POUGHEON et al.

momentum (l, = 18>~) and the if values has been varied between l,-J and l;+J. It can be seen in fig. 10 that the shape of the angular distribution is roughly reproduced when !f = l, ± J. 5. Polarization : results and analysis 5.1 . ANGULAR CORRELATION FUNCTIONS

Correlation functions between 1zC and 160 (coming from the Z° Ne decay) have been measured for 1aC lab angles from 5° to 20° with an aperture of 0.9° (the choice of 0.9° is a compromise between the need of statistics and angular variation of the correlation pattern with the 1 ZC angle) . A sample of correlation functions obtained for some levels at several angles is displayed in figs . 11 and 12. From the shape of the correlation in thevertical plane it is seen that the correlation is strongly peaked in the reaction plane, and in this plane, rather regular oscillations are observed . Their number is equal to the spin of the level in the range of 0° to 180° . One can note that for 1 Z C angles smaller than 10° (lab) there is a change in the overall shape of the correlation functions. The position of the minima (or maxima) of the oscillations vary with the 1aC angles. The correlation function has a 1zC angular period of dB~ = 7° in the laboratory, that is the correlation measured at 9~ and B~+dB~ (1zC lab angle) is the same with regards to the position of the minima. This is illustrated in the fig. 13. This period is roughly independent of the spin J of the level as would be expected if diffraction were at the origin of the observed oscillations . 5.2 . POPULATION OF THE MAGNETIC SUBSTATES AND THEIR ANGULAR DISTRIBUTIONS

The population of the different magnetic substates can be extracted from the experimental correlation functions. Two different methods have been used. The first one gives the whole information, i.e., the population amplitudes, whereas the second one gives only an estimate of ~~~+~p~'~~ . 5.2.1. Least-square method. (i) Results. The population amplitudes were extracted from the experimental

angular correlations, using a least-square fit to eq . (5) as given in sect . 2. It is recalled that we chose the quantization axis perpendicular to the reaction plane and that with this axis, only the magnetic substates with J-M =even are populated. In the actual procedure, 2J+ 1 real parameters are deduced when the normalization of the correlation is left free . The angular distribution for the modulos of the population amplitudes, ~, ~, are shown in the fig. 14 for the three levels 3 - , 5 - and 6 + . One can observe a strong polarization of Z°Ne since the value of gyp'; ~ for M = J is by far the largest and this, for a large range of 1zC angles . The angular distributions of the sum ~pi~ 2 +pJ'I Z,

is0( ie0 i:C)~oN e

497

8.79 MeV (6 + ) Ai2c . 5°50

A, ZC = 8°

A,~c . 9°50

AiZ

0.40 0.20

N F

3 0.40

n

0.20

3o

so

c

= 12°

ru

90 1zo 15o,f

3o

so

90 120 150 ~

8 .79MeV (6+) A,2~ -_

13°75

I

I

Ap~ = 15°

Fig. 11 . The ' 2C-' 6 0 angular correlations measured in the sequential reaction ' 6 0(' 6 0, 'ZC)2 °Ne' -" a+' 6 0 at 68 MeV incident energy for the 6 + state (8 .78 MeV) . The correlations are observed in the reaction plane (B = }rz) for d~tï'erent 'ZC lab angles.

which we have called the "alignment", is shown in the fig. 15: This alignment is, indeed, very large (? 90 ~) and quite constant from 20° to 40°. It is only at very small iZC angles that it decreases towards its limiting value at 0°, indicated as LF (Litherland and Ferguson) in fig. 15, and which is independent of the mechanism . The phases of the different population amplitudes are also deduced from the least-

498

F. POUGHEON et al .

0.40 0. 20 N F

3

0.40 0.20

Fig. 12 . The ' 2 C-' 60 angular correlations measured in the sequential reaction '60(' 60, '2C)2 °Ne' -. a+' 60 at 68 MeV incident energy from the 3 - (7 .17 MeV) state. Thecorrelations observed in the reaction plane (B = }n) are shown on the Lh .s . of the figure while the correlations observed in the perpendicular plane including the recoil direction (~ = n) are shown on the r.h .s. The dotted lines correspond to the least-square fit from which the values of the populations are extracted. 20 15 a _°10 V

=' 5 m 20 15 10 5 20 15 10 5 0

100

150 ~~o Fig. 13 . The position of the minima (full circles) in the correlation function for dil%rent values of the '=C lab angles .

isais0 iz~zoNe

499

-

0. 5 p' 0.50

'e

"

" *J .*/ +-/ ° _J

7.17 MeV (3- ) *

0 .25

° 0

"

*

8

10

ô

. *~ .*a

a 0.50

~ +_~ ° _6

I

"° ~ I I I

° +

° ;

30

I I I I

40 90 "

8 .79MeV (6 + ) rt n +

0

40

"

0 o -?

0.25

"

20

" *s

0.75

+

30

+ o°

0

° *

~*

8.45MeV (5 - )

° _a

0.25 E

~ +°

+

20 "

f tJ " f/ o -/ a" + -s

0 50

v

10

_ " *s

0.75

"

10

20

°

° 30

40 91z~(C.M)

I

Fig. 14. The angular diatributions for the amplitude ~p~ of the elements of the polarization tensor with the quantization axis perpendicular to the reaction plane. The points plotted at 0° indicate the calculated limiting values which at this angle are independent of the mechanism.

square method as seen before . They are shown as a function of t Z C angle, for the 3 - level, in fig. 16. The phases are relative to the substete M = +J. They exhibit a linear dependence on 1ZC angles . The phase ofp~' is directly related to the position of the minima of the correlation as indicated in fig. 13. (ü) Sensitivity ofthe method. The sensitivity of thecorrelation to a small change in the admixture of M = J and M = - J is dramatically dif%rent depending on whether the populations ~P,', ~~ or ~P - ' ~ 2 are close to 0.5 (no polarization) or to 1 .0 (complete

500

F. 1?OUGHEON et al.

N 77

0.75

Plans waws

LF

7.17MeV (3 - ) 0,25

0

10

20

30

40 A, ZC (C .M )

N

~~ 075 o. Planq waves

L.F

i

8 .45MeV (5 - )

0.25

0

10

20

30

i

40 ~ 90 6,x c (C.M )

N

-» 075 o. Plms rava

l..F

8.79 MeV (6+)

025

0

10

20

30

40 9, zc lCM 1

Fig. 15 . The angular distributions of the alignment (i .e. the sum of the populations for the magnetic substetes M = +J and M = -J). The quantizetion axis is taken perpendicular to the reaction plane. The points plotted at 0° indicate the calculated limiting value which at this angle is independent of the mechanism. For a plane wave description the same value would hold for all angles.

16lV 160

~ : C)~o Ne

501

polarization). This is due to the structure of formula (5) and to the observed strong alignment (I P,', I Z + I P,' I Z x 1). This is shown in the following for the simple situation where only the magnetic substates M = J and M = J contribute. The correlation in the reaction plane (8 =fin) takes the following form W(~p) = 1 + 2 ~P cos 2j~p, with P = IP.'rl i.

f

Hence the derivative of W with respect to P is 1-2P p(1 _ P) cos~cp .

d W(~p) dP

It appears that dW(~)/dP = 0 if P = 0.5 whereas dW/dP tends to infinity if P tends to 1 .0 (or to 0). The shape ofthe correlation is then very sensitive to a small change of the polarization for large polarization whereas it is rather insensitive to even large changes when I Pi I x IP,' I . The same conclusion applies in a plane perpendicular to the reaction plane. In a more realistic situation where other populations contribute, the same conclusion is again found and this is displayed in fig. 17 where M = J = 6 and M = - 6 have been differently mixed with a constant contribution of 9 ~ of M = 4 and 4 ~ of M = -4. The quantitative determination of the errors is difficult. In particular, any isotropic component in the correlation tends to increase the deduced polarization . However, given the low background obtained with the detection methods used (see fig. 5), we estimate the error to be 15 ~ in the polarization and 10 ~ in the alignment. 5.2 .2. Results obtained from the average value of the correlation function . The correlation function, in the reaction plane W(~n, ~P), averaged over ~P can be related oc~,

200 0 -200

10

20

30

6,k(CM ) Fig. 16 . The angular distributions of the phases of the elements of the polarization tensor, relative to the magnetic substate M = +J for the 3- state of 2 °Ne at 7 .17 MeV.

F. POUGHEON er al.

502

w le 3

.25

0

20

40

60

80

100

120

1r.0

180

Cx

3 ~

.25

Fig. 17 . The angular correlation functions calculated for different values of the magnetic substate populations. The values of the populations ~pé~~ and ßp6 ads ere kept constant and oqual to 9 ~ and 4 respectively . The phases relative to ~ are respectively x, x and 0 for M = 4, -4 and -6.

to the populations of the magnetic substetes as follows :

2J+ 1 = 4n E h;`I ZR~~~ x

te 0(te0~ , :~2uNe

503

with (J-~M~)!!(J+~M~)!!

For a level with a given spin J, the numerical factor ß~ depends only on the value of ~M~, so :

where ( Wa) is the contribution, with weight (gyp'; 2 p~~~Z), of the two magnetic substetes M and - M to the average value of the correlation function (for M = 0, p,°r is counted only once). In fig. 18, the horizontal lines are the different partial average values < W,,M), that is to say the average value of the correlation function if only the two magnetic ~

a2

_

n

3

o.t

+~~

IMI=3

_________________IMI_t

7.17

MeV

(3') ~M~~5

n 3 V

0.2

o .t

_.

_ ._._._._._ ._._._ ._._ ._ 8.45 MeV

(5')

~M~= 3

~Ml~i =B

a2

n 3 v

o.t

=c

-__-___-_-_--_-_ --__ -. -.__~~=ö 8.79 MeV to

(6t) 20

3o g,=a

~c.~.)

Fig . 18 . The angular distributions of the average values of the wrrelation ftmetions in the reaction plane. The experimental values (full circles) and the values calculated from the populations given by the least square fit (hollow circles) arc drawn. The horizontal lines are the values of < W,) calculated with the contribution of only one ~M~ value (see text).

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F . POUGHEON et al.

substetes M and -M are populated. One can note that the value
6.1 .1. Spectator ejectile model. As seen before (sect. 2) the "spectator ejectile model" as well as the plane-wave model leads to the population of a magnetic substate M = 0 on a quantization axis along the recoil axis . With a quantization axis perpendicular to the reaction plane, this leads to a broad distribution over the different magnetic substetes, symmetrical around M = 0, with a larger weight on M = f J, but which by far does not correspond to the observed alignment. The same result would be obtained with plane waves as shown in fig. 15 for the magnetic substetes M = fJ. These models are in complete disagreement with the experimental values . 6.1 .2. Semi-classical model. The semi-classical model predicts a complete alignment ofthe Z°Ne spin along the axis perpendicular to the reaction plane (see sect . 2) in agreement with the large experimental value. The strong experimental polarization shows that among the two trajectories contributing in this model, one is strongly dominant and, due to the strong absorption, it is likely to be the one corresponding to a positive deflection angle. 6.1.3. Single partial-wave model. Since this model predicts no polarization at all I!'! X12 = I~~I Z), o~Y the predicted alignment can be compared to the experimental one. The calculations have been done with the entrance grazing angular momentum li = 18h and three ditï'erent values of lr, namely k = l ~ = 1,-J and 1~ = l,+J. The results obtained for the 6 + level are shown in the 1-îg.19. Good fits are obtained

~60(~60~ izC)zoNe

505

9î2 c (GM.)

Fig. 19 . A comparison of the angular distribution predicted by the single partiahwave model (see text) with the experimental one for the alignment of the z° Ne 6+ state.

for If = I,±J. On the contrary, for If = 1,, there is a strong disagreement between the predictions and the experiment . This result indicates that the strong experimental alignment found in this reaction comes from the fact that the grazing angular momentum in the exit channel If is close to the value 1,-J, and that the width in the "l" space is sufficiently narrow_ 6 .1 .4 . DWBA analysis. The DWBA codes have been modified to allow the extraotion ofthe transition amplitudes which are given in all the codes with the quantization axis along the beam direction. A rotation is then made to set the quantization axis perpendicular to the reaction plane. Finally the correlation functions are calculated. The correlation function calculated for the 6+ at 17.5° with set A (see table 1) is shown and compared to experiment in fig. 20 . One sees that the fit with this set is not good at all. The fits obtained with set B are better, but there is a phase shift between the experimental and the calculated correlations . The improvement of the fit obtained with set B comes from its stronger surface absorption . This is well illustrated in table 3 where the polarization and the alignment are calculated using

N

3 0.40 C

0.20

Fig. 20. Measured and calculated' zG' 60 angular correlations in the reaction plane for the sequential reaction '60('60,"C)z°Ne" ~ a+'60 at 68 MeV. fihe EFR-DWBÂ calculation iâ done using the optical parameters of set A.

F. POUGHEON et aJ.

506

Tesr.e 3 Variation of the polarization and alignment as a function of the imaginary diffusitivity a,r for the 6 + state (8 .78 MeV) of 2 °Ne at B~ = 23~.m . [ref. '~] andcomparison with the experimental values Calculated values (~)

aa. (fm) 0.25 0.35 0.45 0.60

IY61 2

IY6 6I2

40 5062 71

41 33 21 12

Experimental values (~)

Il'6I2 + W6

6I2

U'6~ 2

81 83 83 83

IY6

5

85

612

IY61 2 + ~6

612

90

The other-optical potential parameters are V = 50 MeV, W = 30 MeV, r,. = 1 .24 fm, a,, = 0.49 fm, rw = 1.24 fm, r~ = 1 .24 fm .

set B but with dit~erent absorption dif~usivities. One can also see in table 3 that the stronger the absorption, the stronger the polarization, although the alignment remains roughly constant. The predicted alignments nearly reach the experimental value, but the strongest calculated polarization remains well below the experimental value. This situation holds for the whole t2C angular range and is illustrated in fig. 21

0.30 0.25

PJOM 11dY"f

i~

0)

0

10

20

40

8ac (C.M)

.- -~-~cw.aa

0.75 0.50

30

~.c____.____._ .. .______._ ._ .._________ .. ... ..__._. ._.__.

0.25

8.79MaW (6+)

b)

40 30 ` (C .M) suc Fig. 21 . A comparison of the experimmtRl and 1?WBA predictions for the angu1ar distributions of (a) the magnetic substete populations I P,',12 and (b) the alignment I Pj l2 + I Pr' 12. The EFIt-DWBA calcinations are those of Bond's using set B optical parameters. 0

10

20

ia 0( ia0 i~~zoNe

SU7

where the predicted angular distributions (set B) for the polarization and for the alignment are compared to experiment . In summary, the DWBA is able to reproduce the observed strong alignment of s°Ne if selected optical-potential parameters are used. But even the best predictions for the polarization are smaller than the observations . Actually, if one looks at the populations ~Pi~2 and ~p.r'~2 separately, the disagreement is even more apparent . So it appears that to obtain a quantitative agreement with the data, it is necessary to introduce in the reaction mechanisms some phenomena not taken into account in the DWBA formalism. Different hypothesis can be suggested : (i) The orbit polarization phenomenon as studied by Delic 22) . (ü) The Coulomb excitation or reoricntation in the exit channel as suggested by Frahn zs). (iii) The necessity to treat the full three-body aspect (16 0+ 1a C+a) of the problem za) or resonant phenomenon at some step in the mechanism. 6 .1 S . Conclusions . It can be concluded from this analysis with different reaction models that : (i) The origin of the alignment is the 1-matching and the localization in the 1-space of the reaction . This is well ill"~strated by the good fit obtained for the angular distribution of the alignment with the single partial wave model if h is set equal to one of its extreme allowed values, l,±J. A similar conclusion has also been reached by Bond'), but for the polarization, with a parametrization of the radial integrals in the framework of the DWBA . (ü) The origin of thepolarization, once the alignment is obtained, seems to be the strong surface absorption of this reaction . This is obvious with the semiclassical model where one trajectory must be strongly damped to explain the observed polarization. This is also indicated by the DWBA calculations where the calculated polarization increases with the imaginary diffusivity. (iii) None of the tested models have given a good agreement with the observed polarization. 6 .2 . COMPARISON WITH THE ('Li, t) REACTION

The polarization of the z°Ne has been studied by angular correlations in the 16~('Li, t)Z°Ne* -. a+ 160 reaction 2). This is also an a-transfer but induced by a lighter projectile . So the comparison of the two results obtained is interesting for the point of view of the reaction mechanism. The results obtained in the ('Li, t) reaction are quite dif%rent from the ones obtained in the present work. The correlation pattern looks like a Legendre polynomial centered near the recoil direction. The population parameters deduced from a XZ analysis are on average ~ - ° ~s = 90 ~ with a quantization axis set at the maximum of the correlation peak (i.e. close to the recoil direction) . It must be noted that this result, close to the plane-wave one, is incompatible with the (160, 1ZC)

508

F. POUGHEON et al.

results, since a large population of the magnetic substete M = 0 implies that there is no strong polarization on any axis . The ('Li, t) results can bewell explained by the a+t structure of'Li which lends itself to the use of the spectator ejectile model. It implies that the distortion coming from the triton is small in both channels and hence that the distortion in the entrance channel comes mainly from the a. The data have been analyzed in the framework of the DWBA [ref. zl )] . Good fits to the angular correlations have been obtained and the calculated populations are close to the experimental ones . On the contrary, the 1zC cannot be regarded as a spectator in the transfer of an a-particle from 160. But the process is more relevant to a semiclassical treatment. This can explain why the results obtained in (160, 1zC) `-'l are very dif%rent from the ('Li, t) results . Note that here too, the DWBA calculations reproduce in part the observed difference between the two reactions but again the predicted difference is not as strong as the experimental one. 7. Conclusion

The aim of the present work was to study the 160(160, 1zC)zoNe reaction mechanism. The energy spectra of the z°Ne exhibit a strong selectivity. The angular distributions of the cross sections are structureless (with the exception of that of the ground state) . Good fits have been obtained with an EFR-DWBA code and the deduced relative a-spectroscopic factors confirm that this reaction is mainly an a-direct transfer. To better understand the mechanism, the polarization of the z °Ne residual nucleus has been studied by angular correlation measurements . Owing to a new experimental setup the angular distribution of the magnetic substete population amplitudes have been obtained over a wide span of 1zC angles . All the studied z°Ne levels are found strongly aligned and polarized along an axis perpendicular to the reaction plane. It is only at very small 1zC angles that the polarization and the alignment decrease towards their expected values for 0° which are then independent of the mechanism. The experimental results have been compared to the predictions of different reaction models. It is concluded that the origin of the alignment is, for this reaction, the 1-matching and the localisation in the 1-space and that the origin of the strong observed polarization comes from strong surface absorption . Nevertheless, it appears that to obtain a better quantitative agreement between the data and the reaction models it is necessary to include new effects not taken into account until now in the formalisms. This study has shown the possibility to obtain a nucleus in a state of strong polarization by transfer reactions induced by heavy ions. It has also shown that polarization measurements represent a stringent test of the reaction models and yield new insights into the reaction mechanism.

~s0( ib0 mC)zoN e

509

The authors want to thank Dr. M. Roy-Stephan for her assistance with some of experiments and C. Stamm for his help in the analysis of the data . We are grateful to Dr. A. Panagiotou for his participation to the lust part of the experiments and for many usefull discussions all along this work. We would also like to acknowledge Pr . P. Benoist-Gueutal and Dr. C. Marty for many discussions regarding this work. We are also indebted to Dr. P. D. Bond for his contribution to the DWBA analysis and for several helpful suggestions and to Professor E. Kashy for his critical reading of the manuscript. References 1) M . C. Mallet-Lemaire, A1P Conf. Pros . N .47, Clustering aspects of nuclear structure and nuclear reactions, Winnipeg 1978, p. 271 and refs . therein 2) A. D. Panagiotou, J. C. Cornell, N. Anyas-Weiss, P. N. Hudson, A. Menchaca Rocha, D. K. Scott and B. E. F. Macefield, J. of Phys . A7 (1974) 1748 3) F. Pougheon, P. Roussel, M. Bernas, F. Diaf, B. Fabbro, F. Naulin, A. D. Panagiotou, E. Plagnol and G. Rotbard, in Proc. Int. Conf. on nuclear structure, Tokyo 1977, ed . Organizing Committee (lnternational Academic Printing, Tokyo, 1977) p. 627 4) F. Pougheon, P. Roussel, M . Bernas, B. Fabbro, F. Naulin, A. D. Panagiotou, E. Plagnol and G. Rotbard, J. de Phys. 21 (1977) 417 5) J. G. Cramer and W. W. Eidson, Nucl. Phys . 55 (1964) 1 6) T. Tamura, Phys. Reports 14 (1974) 59 7) P. D. Bond, Phys . Rev. Lett . 40 (1978) 501 8) B. Saghai and P. Roussel, Nucl . Insu. 141 (1977) 93 9) P. Roussel, M . Bernas, F. Diaf, F. Naulin, F. Pougheon, G. Rotbard and M . Roy-Stephan, Nucl . Insu . 153 (1978) 1 ! 1 10) F. Dial, thesis, Paris Xl University (1978) (unpublished) 11) M. E. Cobern, D. J. Pisano and P. D. Parker, Phys . Rev. C14 (1976) 491 12) A. A. Pilt et al., Nucl . Phys. A273 (1976) 189 13) P. S. Fisher et al., Annual report, Nuclear Physics, Laboratory, Oxford University (1977-1978) 14) F. Pougheon and P. Roussel, Phys. Rev. Lett. 30 (1973) 1223 15) T. Tamura and K. S. Low, Comp. Phys . Comm . 8 (1974) 349 16) T. Matsuse and M . Kamimura, Prog . Theor. Phys . 49 (1973) 1764 17) J. P. Draayer, Nucl . Phys. A237 (1975) 157 18) E. Mathiak, K. A. Eberhard, l. G. Cramer, H. H. Rossner, J. Stettmeier andA. Weidinger, Nucl . Phys . A259 (1976) 129 19) P. D. Bond, private communication 20) A. Gobbi, R. Wieland, L. Chua, D. Schapira and D. A. Bromley, Phys. Rev. C7 (1973) 30 21) E. F. Da Silveira, Ph .D. thesis, Paris Xl University (1977) (unpublished) 22) G. Delis, K. Pruess, L. A. Charlton and N. K. Glendenning, Phys . Lett . 69B (1977) 20 23) W. E. Frahn, private communication 24) J. L. Quebert, private communication 25) A. Bohr, Nucl . Phys . 10 (1959) 486