Polarization in heavy-ion reactions

Hyperfine Interactions 21(1985)173 - 195 173

P O L A R I Z A T I O N IN H E A V Y - I O N R E A C T I O N S

Noriaki TAKAHASHI

College of General Education, Osaka University, Toyonaka 560, Japan

A series of experiments is descn'bed in which beta-ray asymmetry has been used to determine polarization of heavy-ion reaction products 12B and the present status of the studies of polarization phenomena in heavy-ion reactions is reviewed. A large amount of angular momentum sustained by the two colliding nuclei gives rise to polarization phenomena of reaction products. Coupling between the degrees of freedom accompanying the intrinsic and the relative motions is investigated from the systematic behaviour of polarization of reaction products disclosed by the experiments.

1. I n t r o d u c t i o n

Polarization phenomena are general features in nuclear reactions induced by light projectiles, i.e. protons, neutrons, deuterons, 3 He and, less frequently, tritons. They provide us with good probes to reveal coupling between the orbital and the intrinsic degrees of freedom in the reaction processes, irrespective of whether the incident beam is polarized or not'. A similar situation is expected for reactions induced by heavy ions, especially because of a large amount of orbital angular momentum sustained by the colliding nucleus-nucleus system. Various models of heavy-ion reactions have been proposed to explain the possible occurrence of polarization in reaction products. One of the arguments [1] is based on a phenomenological viscous force which acts between the touching surfaces of the two colliding nuclei, often referred to as nuclear friction. The model treats, by employing the concepts in classical mechanics, the reaction trajectories which have definite values of orbital angular momentum and relates them with the amount of energy transferred from relative motion to internal excitation, referred to as energy loss.

For a grazing collision taking place when energy loss is small, the reaction trajectory is deflected outwards owing to the repulsive Coulomb force between the two nuclei and is similar to that of Coulomb scattering. As the impact parameter pertinent to the trajectory decreases, the attractive nuclear force dominates over the Coulomb force. Now the trajectory is deflected inwards, thus towards smaller reaction angles than for the cases of smaller energy loss. Energy loss increases as the interaction

�9 J.C. Baltzer A.G., Scientific Publishing Company

174 N. Takahashi, Polarization in heavy-ion reactions

of the two colliding nuclei becomes more violent. As a result, two kinds of trajectories can be recognized; one deflected away from and the other deflected towards the centre of the target nucleus. Both extremes correspond to the two spectral peaks which have already been identified as quasi-elastic and deep-inelastic processes [2,3,4]. When the reaction products are observed at a given reaction angle the direction of the orbital angular momentum sustained by the colliding system is opposite for quasi-elastic and for deep-inelastic processes. If the spin of the product nuclei is governed by the coupling through the viscous (frictional) force, the direction of product spin is opposite for these two processes.

Such has been the situation when we intended to start a systematic study of polarization phenomena in heavy-ion reactions. The main incentives in our study are first the elucidation of reaction mechanisms and second the production df polarized beta-radioactive nuclei by means of heavy-ion reactions. We started by measuring polarization via the detection of asymmetry in beta decay of reaction products 12B in 14N induced reaction [5]. During the same period, polarization of residual nuclei was measured via the observation of circular polarization of gamma rays emitted from heavy and/or light reaction products [6].

There is a review of the heavy-ion polarization [7] and the article here is concentrated mainly on the polarization study via beta-ray asymmetry.

A brief history is outlined in sect. 2 and the experimental methods are described in sect. 3. The experimental results obtained are shown in sect. 4 and are discussed together with those obtained by other methods in sect. 5. Applications of polarized heavy ions can be considered in many ways and some of these will be mentioned in sect. 6.

2. A b r i e f h i s to ry

Retrospection brings us back to around the early sixties when I was involved in the measurements of proton polarization in (d,p) re)actions [8]. Kozi Nakai came one day to me and asked me an embarrassing question on the polarization of residual nuclei. What we knew about the polarization in (d,p) reactions was the Newns classical model [9] and its modified version [ 10]. Nobody knew exactly what degree of polarization the residual heavy nuclei would exhibit. It might be limited to some amount like the factor 1/3 or could rather reach unity.

Chase and Igo had tried to determine the nuclear polarization by observing the decay asymmetry of polarized beta emitters produced by (d,p) reactions with limited success [11]. Suglmoto and collaboratotors started to use the polari;~ed 17F from the 160(d,n)lTF reaction for their first trial to determine nuclear moments of short-lived beta emitters and successfully utilized the 2 MeV deuterons from the home- made static generator [12], adding to their menu with aligned fluorine and samarium a new flavour of polarization. Sugimoto has since then familiarized himself with polarized heavy ions, but their kinetic energy was less than approximately 1 MeV.

N. Takahashi, Polarization in heavy-ion reactions 175

After the installment of a 4 MV van de Graaff accelerator, the same method was successfully applied to the 12 B and 12 N cases. Besides the nuclear-moment deter- minations the method was extended also to probe into the nuclear-reaction mechanism. Via observation of beta-ray asymmetry with incorporation of NMR, Tanaka et al. disclosed the energy dependence of the substate population in the product nuclei 12Bgs(I = 1 § [13]. This is the first experiment which ever measured the complete population parameters of the final nuclear state produced in nuclear reactions. The existence of a sizable spin alignment together with the polarization of 12B was revealed in this measurement, thus showing that the treatment in the framework of plane-wave Born approximation was clearly insufficient. The distorted-wave Born approximation (DWBA) is usually better in fitting the angular distribution of (d,p) reactions. The experimental dependence of population parameters on the incident energy in the resonance region also showed that the DWBA could not correctly reproduce such behaviour. The incident energy was too low to allow comparison of the experimental results with that predicted by the DWBA, because of possible contribution of the resonances. The measurement of the alignment parameter enabled them to determine the configuration in the 1 § ground and 2 § first-excited states in 12 B.

There came a turning point around 1973 and then a new cyclotron was near completion at the Research Centre for Nuclear Physics, Osaka University. Heavy-ion beams were already expected to reach 10 MeV/u. Employing heavy-ion beams meant that a considerable amount of orbital angular momentum would be sustained by the colliding system. This would lead one immediately to the idea of producing polarized nuclei. Heavy-ion reactions can produce a variety of unstable nuclei, which are possibly spin-polarized and now they are energetic approximately up to the incident energy 10 MeV/u. What can be done bY using such polarized nuclei? Quite a lot! Not only would they be useful for nuclear moment and spectroscopic studies, but also for solid-state research.

Basic data which helped us to design heavy-ion polarization experiments at that time came mostly from Dubna. The Volkov diagram which revealed a simple relation between production cross section and reaction Q-value [14] was instructive. Dubna observed a variety of reaction products, among which sufficient yields were found for neutron-rich beta-radioactive species.

Once the reaction products are separated according to their charge and mass numbers by some means, e.g. electromagnetic separators, the decay of the nuclei can be studied utilizing their polarization: If the nuclei are beta-unstable, asymmetry of beta- ray emission can be observed by way of the then familiar method; beta-ray asymmetry detection for measuring polarization by incorporating the NMR technique for flipping spin directions [ 15 ]. In these circumstances the layout of such experiments is no longer impossible [ 16].

So we set off on an investigation of spin polarized unstable nuclei. The first step of the study was a general understanding of the polarization phenomena of


product nuclei in heavy-ion reactions; how they manifest themselves and what the responsible process is. The easiest beams of heavy ions to accelerate in the cyclotron were presumed to be those of nitrogen and neon. The beta-unstable nucleus 12B was one of the favourable cases and could be easily attained by the two-proton transfer reactions from 14N bombardment. The nucleus 12B is one of the auld-lang-syne friends of Sugimoto, to be found in the playing fields of physics.

The first experiment was started by using the cyclotron at the Institute for Physical and Chemical Research (Riken) at Wako-shi (for the new cyclotron was not yet ready at Osaka) and the results were published soon after [5]. The Munich group colleagues started their study of heavy-ion polarization via observation of gamma-ray circular polarization at approximately the same time. Their first result was announced at the International Conference on Nuclear Structure, Tokyo, 1977 [17]. To see the whole picture of the polarization phenomena compatible with results of these two methods, we had to await the observation of polarization in the deep-inelastic region [18] as well as the observation of circular polarization of gamma-rays from the light reaction products [19]. In relation to the study of direct regimes in the heavy-ion reactions, many-nucleon transfer reactions have been investigated up to a seven-nucleon transfer reaction 197Au(19 F, 12 B) and the polarization of 12B has been measured [20]. A systematic study of 12 B polarization in single-nucleon transfer reaction (13 C,12 B) has been carried out [21,22] and depict the contributions of direct and multi-step processes.

Polarization phenomena in heavy-ion reactions have also been studied in a number of ways. State-of-art descriptions of polarization studies in heavy-ion reactions were given in August, 1980 in the review talks at the Santa Fe International Conference [23]. An up-to-date compilation in this field will appear in a series of monographs [7]. Polarized heavy-ion beams had then been available from the first active Heidelberg polarized ion source [24], which was dismantled from the EN tandem there in Decem- ber, 1981, before the new PSI was installed on the MP tandem [25]. The physics carried out there to investigate the spin-dependent interactions is described in a review and in lecture notes [26]. Other methods to investigate polarization phenomena to be mentioned are the study of angular distributions of inelastically scattered ~60 nuclei from s6 Fe in coincidence with the de-excitation ~,-rays [27] and the correla- tion study of reaction products 2~ in the reaction 160(160,12C)2~ which undergo decay into 160" [28]. The asymmetry in the emission of protons from the reaction 93Nb + t4N -~ p has been studied by means of a double-target experiment [29]. All these experiments are specific and there were no established methods com- mon to all such polarization experiments. Still they have supplied insights ihto the reaction mechanisms related to angular momentum transfer.


3. E x p e r i m e n t a l methods

Spin polarization of reaction products 12Bgs (I 7r = 1 § I"i/2 = 20.3 ms and Et~max = 13.37 MeV) was measured for reactions (a4N,12B), (13C,12B), (12C,12B), (11B,12B) and (l~ at several angles between 5 ~ and 35 ~ using incident beams with energies 60 ~ 200 MeV. In this section the experimental methods used mainly in a series of measurements on (14N,X2B) reactions are described in some detail. Al- though the experimental apparatus used has been continuously improved in the course of time, the principle and the basic method are essentially the same. The principle applied in the measurements of polarization [5] consists of the observation of asymmetric distribution of beta rays from the polarized nuclei 12 Bgs [30,31 ] for the determination of polarization and of the use of the range method for determining the kinetic-energy windows for reaction products 12 B.

Pulsed beams of unpolarized 14N were obtained from the cyclotrons of the Institute of Physical and Chemical Research and the Research Centre for Nuclear Physics, Osaka University. Energies of ~4N ions were 90, 130 and 210 MeV and the average intensity was 0.1 ~ 1 /aA. The thickness of the foil targets used corresponded to 10 "~ 20 MeV energy loss for the incoming beam. The irradiation was cyclic with an on-beam period of 20 ~ 30 ms, followed by an off-beam period of 30 ~ 80 ms. A schematic experimental setup is shown in fig. 1. Light reaction products, emerging from the target at a reaction angle 0 L near the grazing angle were passed through an energy degrader, which was aluminium foil with various thicknesses mounted on a wheel, lost a certain amount of their kinetic energy, and were then passed through a circular collimator. The soli d angle subtended was 3 msr and the angular spread was -+ 3 mrad. The reaction products ~2B were then implanted into a stopper, a platinum foil of thickness 5 ~ 25/am. Kinetic-energy windows for implanted reaction products 12B were thus determined from the thicknesses of the energy degrader and the stopper by using the range-energy relation [32].

Beta rays from the stopper foil were detected during the off-beam period by a pair of counter telescopes consisting of two AE (A, B in fig. 1), one E (E) and one anti-coincidence (C) plastic detectors. The anti-coincidence detectors created veto signals from beta rays that hit the bulky materials such as the magnet poles and the coils. Veto signals were also taken from each of the innermost AE detectors (A) and were fed to the other counter telescope to reject back-scattered beta rays. These telescopes were placed above and below the stopper with their axis parallel to the reaction normal n = kf X ki / Ik f • kil.* Beta rays with energy larger than 4 MeV were de-

*The sign of polarization parallel to the reaction normal n as above is taken as positive. Hero, kf and k i denote the outgoing and the incoming wave vectors, respectively. The direction of n corresponds to that of incident orbital angular momentum for the classical Coulomb grazing trajectory.


tected and the time spectra were consistent with the 12B lifetime of 20.3 ms. Possible background/~ emitters with similar beta-ray energy and lifetime were 12N and taB, but their yields were known to be insignificant [33].

AE

COLLIMATOR

WHEEL

COUNTER TELESCOPE

IDOWN)

COUNTER TELESCOPE

(UP) N~AGNE T COIL

~ r f COIL

)

Fig. 1. Schematic experimental setup.

Spin polarization P of nuclear states with spin I is defined by

I

P = ~.. m a r e / I , m = - I

where a m is the population of the substate with magnetic quantum number m and is normalized as


1

~ a m = l . m = - - I

The polarization of beta-emitting nuclei can be determined from the asymmetry in the beta decay. The angular distribution W(O) of beta rays with respect to the direction of polarization P is given as

I4/(0) = 1 + ~ . e

Here o/c is the ratio of the beta ray to light velocities. A' is the asymmetry parameter (see e.g. [34]). For the transition 12Bgs ( I ~ = 1 +) ~ 12Cg s (i~r= 0+), an allowed pure Gamow-Tel ler transition, A' = - 1 and o/c ~ 1 for the most part of the beta-ray spectrum.

In order to determine the beta-ray asymmetry free from spurious effects, the 12B spin direction was controlled by adopting the adiabatic-fast-passage method in NMR during the off-beam periods [12,35]. A static magnetic field IBol = 1.4 kG was impressed normal to the reaction plane around the stopper. The NMR was induced by an r.f. field at right angles to B o. The r.f. swept once across the resonance ~0 (= 1 MHz), thus the direction of the 12B spin was reversed immediately after every other on-beam period preceding the beta-ray counting period. After the end of the counting period, the r.f. field was again applied on resonance to restore the spin direction and the irradiation was continued. In the next period, the r.f. field was applied at off-resonance w (--- co o +, 100 kHz) and the spin direction was unaltered. The time sequence of the measurements is shown in fig. 2. From the up- and down-counting rates at on- and off-resonances we can determine the polarization as

R BEAM COUNT Nl NUMBER OF 12B

f ! FREQUENCYoF ~F~ " RF FIELD SPIN DIRECTION ] Tfl

i i ' 1

' i

, I I

J �9 I t

It i lTI I, Fig. 2. Time sequence for NMR measurements. The repetition time Tis 50 ~ 110 ms.


P = (~- 1)I(V~+ 1),

where R = (Nup/Ndown)off/(Nup/Ndown)o,. Total count runs and background runs were made with a thick and a thin stopper, respectively, and the differences in corresponding counting rates were used to deduce the polarization.

The polarization is essentially preserved during and after the process of implantation into the stopper, since the decoupling field B o is present [12] and the spin- lattice relaxation time is known to be much longer than the 12B lifetime in platinum at room temperature [36]. It is important to prepare against possible depolarization due to hyperfine interactions in the ions during their flight in vacuo. No appreciable depolarization is expected for 12B leaving the target because of the fully stripped state. After passing through the energy degrader, ions with energy less than ~ 11 MeV can capture electrons and depolarization becomes appreciable for ions with few- electron configurations. In subtracting the contribution of the background obtained by using a thinner (5 /am) stopper, contributions of such slow ions were eliminated at the same time.

One more parameter other than the spin polarization P = a 1 - a-1, designating an I = 1 ensemble is spin alignment A = 1 - 3a o .

Spin alignment can also be deterimed from the asymmetric angular distribution of beta rays from the oriented 12B nuclei with respect to the scattering plane. Since the alignment is primarily indifferent to the beta-ray asymmetry, alignment has to be converted to polarization by means of substate interchange using NMR [13,34]. The hyperfine spectra of 12 Bgs in magnesium single crystal, used as a stoppe r for alignment measurement, with the crystalline c-axis parallel to the static magnetic field is shown in fig. 3. Unequal Zeeman splittings between the magnetic substates are caused by the electric field gradient q in the presence of the static magnetic field B o. Corres- ponding to the three r.f. transitions adopted, selective interchanges of substate populations were feasible as shown in fig. 3. Beta-ray up-down asymmetry R is related to the resultant polarization PR, as

g _- w ( 0 -- 0 )

w ( 0 = '

W(O) = 1 -PRcosO.

Thus, the interchange of various substate populations enabled one to determine the original polarization P and alignment A in the following manner: The low-frequency transition, WL, exchanges m = - 1 and m = 0 states and the asymmetry measurement determines a 1 - a o = ~(P + A) ; the high-frequency transition, co H, m = 0 and m = 1, ao - a- i = ~ (P - A ); the double-quantum transition, 60 o, m = - 1 and m = i, a-a - a 1 = - P : At off resonance (not shown), co, a I - a- i = P. From the least squares fit, P and A can be determined.


I=1

m=- 1

o

+1

pH. pH.&eqQ

w.=pH. WH= Wo § I/4~ WL= tOo-31eqO 1/41 ~

Fig. 3. Splitting of the magnetic sublevels under influences of the magnetic dipole and electric quadrupole fields.

4. Experimental results

In this section, measured polarization of 12 B produced in (14 N,12 B) reactions is summarized.

Dependence of polarization on Q-value

The first result [5,37] was obtained for the reaction l~176 at 90 MeV and the 12B spectrum and polarization is shown in fig. 4(a) and (b). The upper part (a) is the energy spectrum of the reaction products 12B, measured by counting beta rays from the 12B implanted in the stopper. This spectrum agrees with the one obtained by using a solid-state detector telescope as shown by the dotted curve, proving that the method works. The lower part (b) is polarization versus the recoil kinetic energy of ' 2 B in the laboratory system. The abscissa scale corresponding to the reaction Q-value is also included with an indication of the ground-state to ground-state Q-value Q s : As mentioned earlier, the sign of the polarization in this article is taken opposite to the Basel convention.

A steep descent to large negative values of polarization at highest energies is the main result. Polarization tends to zero, crosses zero and remains positive as the kinetic energy of 12B decreases from the value corresponding to Qg:. It is interesting to note that the point of crossover is near the maximum of the energy spectrum. This tendency is often observed in the results. As will be shown later, this is connected with the kinematic matching conditions for transferred nucleons, often encountered in heavy-ion reactions.

The vertical bars on the experimental points indicate the uncertainty due to counting statistics and the horizontal bars show the energy windows corresponding to the thickness of the stopper.


"Mo( N. B)~"Ru E =901~ ,.=20 1.0 (a) . . --...~.

N'0'5 / ._~,........ ,~,- , , "~. . .~ ,

o., P 0 - (b)

-0.1 ~ SEMI.Ct~SS,C ~,@.

-50 -40 -30 -20 -1,iOa-ug(

30 4'o 5b 6b 7b 8'o so F-(r=B) in MeV

Fig. 4. taB energy spectrum measured by beta- ray countings (a) and polarization as a function of ~aB recoil energy (b). Curves shown are the results of calculations in terms of the classical kinematic matching and of the DWBA.

The present results on energy spectra, polarization and alignment of 12B in- volve the contributions from the ground state and the excited nuclear states in 12B with excitation energy up to E x = 3.35 MeV corresponding to the neutron separation energy. The partial yields for 12 B produced through particle emission of other re action products have been estimated from the exponential dependence of the cross section with Q-value and have been found to contribute less than 10%.

The dependence of polarization on incident energy has been investigated in successive studies [18,37]. The incident 14N energies were 125 MeV and 200 MeV. In fig. 5 the results of such studies are shown together with those at 90 MeV. The laboratory reaction angle 0 L is 20 ~ at 90 MeV and 200 MeV, while at 124 MeV e L is 25 ~ Measurements at 20 ~ have later been carried out at 125 MeV and the results at the two reaction angles are almost the same [38].

The polarization observed at 125 MeV exhibits a steep descent at the highest t2B energies similar to that at 90 MeV. Scaling in terms of a model for direct reaction processes reproduces fairly well such behaviour in the region near Qgg. The reaction mechanism responsible for such large negative polarization which tends to zero to- ward the peak of the spectrum has been tentatively ascribed to the direct single-step process [5,37,39].

The polarization and spectrum obtained at 200 MeV is somewhat different from what has been seen above. The polarization at the highest energy region is not clear due to experimental difficulties. The polarization in the region far from Qgg is negative and tends to zero at both sides.


8 I~176 B) N'[3 a) ./"~

0 I I I I I ,

150 100 50

P l\ b) I ,I �9 O. 1 I" '~ f ? t", J \ /

_, -0.1 \. __4_, / -0.2 \ ./ -0-3 Ei (14~N)_.~ .2-O-0~eV o eL=2

12 5 M e V ,. 25 9 0 M e V �9 20 - 0-4 . . . . DWBA

- - - ~ TRANSPOI~T THEORY i ,

150 100 50 - Q in MeV "~

1'0

io Fig. 5. a~B spectra and polarization plotted as a function of the universal parameter - Q . The dotted and dot-dashed curves show the calculations from, the DWBA and the transport theory, respectively.

From the results at three incident energies combined by using the Q-value as the universal parameter, one can depict the dependence of polarization on the kinetic energy of the reaction products as follows.

(1) The polarization is large and the sign is negative at the region near Qgg. IPI tends to zero with a decrease of the reaction product kinetic energy, or in other words, with an increase of kinetic energy loss;

(2) Zero crossing of polarization takes place near the maximum in the energy spectrum;

(3) The polarization retains a small value but remains positive for a narrow kinetic energy range following the zero crossing;

(4) The polarization becomes negative again over a wide range of large kinetic energy loss and here the yields are large;

(5) In the region where the total kinetic energy of the reaction products correspond to the Coulomb energy between the two reaction products, the polarization tends to zero and the yield decreases also to zero.


Dependence o f polarization on target mass number

The general trends for the spectrum and polarization of t2B produced in (14 N,X2 B) reactions on various targets are described in the following.

The heavy target 232Th was used at 129 MeV and O L = 30 ~ The results are shown in fig. 6 [40]. The energy spectrum shows a double-peaked structure and the

t 1.5 1.0 0.5

P *02 .0.1

0 -0.1 -0.2

-0.3 -0.4

2aZTh~4N12B )

- e - .e .

150 1~3 50 ~ 0

E(14N)-= 200MeV * 129MeV �9

or. =- 3 0 *

~o 16o 5'o ~ o -Q in MeV "Qgg

Fig. 6. Same as fig. 4 but fora 23aTh target.

polarization shows the same sharp decrease in the region near Qgg. What appears specific here is the large positive polarization below zero crossing. The polarization shows the same trend (5) as for the case ofa l~176 target at 200 MeV. The large positive polarization observed within a wide energy region indicates the existence of a different reaction mechanism than that which caused the negative polarization (4) in the lO~ reaction. Various targets have been used to study the possibility of whether a systematic trend for polarization exists. These were 27A1, 4SSc, natTi, natFe, natCu, I~176 and 232Th. Figures 7 and 8 show experimental results with the (:*N, 12 B) reaction from some of these targets.

The two energy spectra obtained are similar to each other, as shown in fig.8; There is a wide bell-shaped peak with a slight dip in the middle. The polarization looks different for the reaction 27Al(14N,a2B), While the reaction natCu(14N,12B) shows a continuation in the behaviour of that for heavier targets, a large negative polarization near Qgg. For the 4s Sc target, the polarization is nearly zero and this target is at the crossover point for the sign change of polarization in the most energetic region, as


0.27 ~',. 27AI (~ N1, 2 B)

P O' 2,

- 0 . 2 '1' -*~-~'--

0.2' ~s ~ ~2 , ~ Sc(2N, B)

P 0 " ~ '

-0.2 ]" 0.2 r~,~ C u (lZ. N 1,2 B)

1 2 P 0 ~ -~--,~L-~--r

- 0.2 0.2

P 0

- 0,2 ~; ))'~F,--6--- eL=30 ~

o E(4N} _-" 200MeV I i '" 120MeV

A 90MeV I l J .

o 1%g_o2)/Vc

OL= 20~ I

eL-- 20 ~ 3 4

I

8L=20 ~ 3 ~

!

'OOMo(I~ N,)2B) ~- 8L=20~ 25~

..~p~-~...,t,.., 2 3 4 - 4 - --z--. 4-..' -9--_(:,_ t

2a2Th (14 N1,2 B) 0.2

0 P

-0.2

-0.4

4

Fig. 7. Polarization measured for (I*N,~2B) reactions on various targets. Note that the abscissa is reversed by using the ratio, energy loss to Coulomb energy, (Q~ - Q ) / V C.

shown in fig. 9. Negative polarization was observed in the region of large energy loss for almost all the targets except the heaviest 2a2Th. The disappearance of positive polarization between the two regimes of negative polarization will be discussed below.

The reaction 2~Al(14N,*2B)exhibits negative polarization similar to that obtained with natCu and *~176 targets in the region of large energy loss. In the region near Q~ , large positive polarization is observed [28,41]. This positive polarization persists in the range of incident energy E i = 90 ~ 200 MeV and in the angular range 0 L = 6 ~ ~ 20 ~ Observation a t e i ~ 120 MeV O L ~ 1 5 ~ ~ revealed that the polarization near Q~ is negative for target nuclei heavier than 4s Sc.


natcu(14 N~ZB) Ei~120 MeV 3 eL= 2(/'

Np 2

1

0

0 P

- 0.1

- 0 . 2

- 0.3 0

' - - t l - - 4 ' - -qp~

I I

27A1(74 NIz B} Ei-120MeV

0 . 5 I ~ ~=20"

0 ' '

0.1 P

0

f 4-+ - 0.1

O in MeV ++ - 0.2 Q in t'q eV -75 -so - 2 ~ ? 03 -75 -so -2so lo

25 ,,o50 7~i 160 0 2'5 vc'~o 7'5 160 E(IZB) in MeV E~2B) in MeV

Fig. 8. Same as in fig. 4 but for natcu and 27A1 targets.

0.4

0.3

0.2

0.1

po

-0.1

-0.2

-0.3

- 0 . t ,

- 0 . 5

-0.6

P(Q-Ogg)

't e 8L < Ogr. �9 e L - @g~.

o OL > Ogr.

200

Target moss numb e r

Fig. 9. Dependence of polarization on target mass number observed in the region near Qgg.


5. Discussion

Polarization of nuclei produced in heavy-ion reactions can be envisaged in the following way under considerations of angular-momentum conservation. The colliding two-nucleus system sustains a large amount of orbital angular momentum of relative motion. This angular momentum can be carried off largely by the reaction products as their orbital angular momentum of relative motion. There is a coupling between the orbital and intrinsic angular momenta such as spin-orbit coupling for nucleons transferred during the reaction process. Because of large initial orbital angular momentum of relative motion, the reaction products have intrinsic angular momentum with respect to a specific direction of orbital angular momentum in space, i.e. these product nuclei are polarized. Let us assume such a coupling can be expressed in terms of a viscous force acting between the two touching surfaces of the colliding nuclei. The two nuclei are given parts of the orbital angular momentum of the relative motion when they are in close touch and the nuclei are polarized in the direction of the reaction normal.

Overall view

Two reaction regimes have been recognized from the two broad separate peaks encountered in the energy spectra of heavy-ion reaction products: One of the peaks is concentrated around the quasi-elastic event and the other near the product kinetic energy corresponding to the Coulomb energy. The nomenclature for these processes is tentatively quasi-elastic and deep-inelastic, respectively. The product nuclei in the former are more energetic than those in the latter. In understanding heavy-ion reactions qualitatively, the classical concept of orbits is a good approximation, as the wave length for each reaction'partner is shorter than the nuclear radii. The orbits in these processes pass the different sides of the target nucleus; the near side and the far side, respectively. It is apparent that the sign of polarization changes for these two processes from each other, i.e. in going from the reaction products of larger kinetic energy to smaller kinetic energy. The ansatz can be assayed by looking at the experimental results obtained.

Polarization observed in the region of large energy loss for the reactions (14N,12B) on the targets 27A1 through l~176 clearly indicates the negative sign. This polarization presumably corresponds to that accompanying the negative deflection angle. The positive polarization observed for the reaction 232Th(14N,12B) in the corresponding region supports this assumption. For such a heavy target the Coulomb force between the two nuclei is strong and pushes the trajectory as a.whole to a positive deflection angle. Such is also the case with polarization observed by the circular polarization of 3,-rays emitted from the residual nuclei [6,19,42]. The reaction 160 + Ni shows polarization with signs opposite to each other in the energetic quasi-


elastic region and in the deep-inelastic region. In the reaction Kr + Au, the sign of polarization remains unchanged in going from the quasi-elastic to the deep-inelastic regions. Except for the negative polarization observed in the (~4N,12B) reactions at the most energetic part of the spectra, the qualitative agreement is good.

To visualize the situation, plots of polarization and alignment in terms of the ratio of energy loss (Qgg - Q) to Coulomb energy 7 c is shown in fig. 10. The wide region of negative polarization observed for the reaction l~176 at (Qgg - Q ) / V c = 2 ~ 3 has no correspondence for the reaction 232Th(I*N,12B), where V c is larger. Negative polarization in the region of large energy loss is expected for the latter reaction, when the incident energy is raised.

- - 0 . 3

- - 0 .4

- -0. !

0..~

p 0 .2

0.1

lo --0.1

--0"2 i - 0 .3 - 0 . 4

0

-o2 # - * - lOOM O{ 14 N. 12 B)

232Th(14 N!2 B)

t

o Ei(14N) ~ 200MeV. E~L~-20 ~

�9 1 2 5 MeV. 25 ~

A 9 0 MeV, 2 0 ~

| I I

1 2 3 4 ( Qgg -- O) / 'Vc

Fig. lO. Polarization and alignment a~ functions of the ratio (Q~ - Q)/Yc" See caption to fig. 7.

--0.1 I

0.1 A

01 -0.1


Spin alignment A = 1 - 3a o of 12B, measured for the l~176 and 232 Th(14 N,~ 2 B) reactions at an incident energy of 200 MeV behaves alike within the experimental error. In a classical picture, the alignment is expected to be large (A ~ 1), for I >> 1, since the angular momentum is aligned perpendicular to the reaction plane. The smaller the spin value, the poorer is the classical approximation. The quantal nature of the I = 1 12B spin exhibits itself; the spin angular momentum precesses around the reaction normal. This obscures the preferential direction otherwise exist- ing. As a result, the alignment becomes smaller than unity. The results that alignment is actually small and approximately zero indicates a large fraction of a o prevailing in the reaction products. A close look at fig. 10 reveals that A for the reaction l~176 tends slightly to the negative side, while A for the reaction 232Th(~4N,~2B) tends to the positive side. This may indicate the existence of a depolarization process and the difference of its degree being revealed by the two different reactions.

Direct transfer o f nucleons

The large negative polarization observed in the most energetic region has been interpreted as due to direct transfer of a two-proton pair [5,37,39]. A steep decrease of P at the zero crossing at approximately the peak in the energy spectrum is observed. Kinematic matching conditions as proposed by Brink [43] reproduces the gross feature of the Q-value dependence of polarization to around 20 ~ 30 MeV below Qgg. Such a curve is included in fig. 4. Our notation includes: R 1 and R 2 for radii of the two nuclei, ?q, ~'2 for angular momentum components perpendicular to the reaction plane of the transferred two-proton pair in the incoming and the residual nuclei, m and Po for the mass of the two-proton pair and the momentum due to relative motion, respectively. Matching of momenta

Ap = Po - X I h / R I - L2h /R2 ~ 0

and matching of angular momenta

A L = L z - h I + ~ P o ( R l - R 2 ) / h + Qeff m(R1 + R2)/Po ~ 0

lead to the polarization as a function of the reaction Q-value corrected for Coulomb energies, aeff Q - f e _ i i 2 where Z~, f and Zil i = (Z 1Z 2 Z I Z 2 ) e / (R 1 + R2) , Z 2 , Z 2 are the proton numbers of nuclei in the final and initial states, respectively. More sophisticated computation has been done in the framework of DWBA by Udagawa and Tamura [44]. The fit to the energy spectrum and polarization has the same tendency as that of the kinematic matching conditions but the fit is better, as seen in fig. 4. Here a single-step transfer process is considered and the continuum final states are composed of states


in a harmonic oscillator potential. Another application of the kinematic matching conditions is the dependence of the analyzing power for the reaction sa Ni(7 L~,6 Li)S 9 Ni on the Q-value [45]. The agreement between the experimental result and calculation was good.

The two approaches in terms of the single-step direct process do not reproduce polarization for the larger energy loss properly. Udagawa and Tamura tried to calcu- late polarization below the zero crossing down to the region where the small positive polarization is observed. They simply assumed that the difference between the measured and the calculated spectra is due to the multi-step interaction where polarization is presumed to be vanishingly small and they conform with small polarization. The effectiveness of the direct one-step process down to energy loss of more than 30 MeV is somewhat dubious and polarization due to multi-step processes has to be seri- ously considered.

Polarization observed in the region near Qgg is plotted against the mass number of the target nucleus A in fig. 9. Systematic change in 12 B polarization in the high-energy region suggests a coexistence of two different reaction mechanisms whose importance changes with target mass number. One is a process giving rise to the positive polarization and the other is to the negative polarization. A crossover of the sign of polarization takes place at A -~ 45.

The negative polarization which has been proven characteristic for direct two-proton transfer tends to decrease in lighter target nuclei The contribution of direct processes is considered to be responsible for this change, since the direct processes occur along a grazing trajectory in the region of small energy loss. However, the strength of the direct process distributes the outgoing nuclei at more forward scattering angles as the mass number of the target decreases. The value of the grazing impact parameter is relatively small for the 2 ~A1(14 N,Z 2 B) reaction and the target and the projectile nuclei overlap considerably. Attractive force is dominating over the repulsive Coulomb force. This is one of the explanations why the Q-value dependence of polarization is different for the reaction 27Al(Z4N,X2B) than that of the (14N,12B) reactions on other targets. The case of 4s Sc(X4 N,12 B), in which zero polarization was observed, lies intermediately between the two cases discussed above.

Friction model

An altemative idea came from the calculation in terms of transport theory, in which Reif and Schmidt [46] assumed positive and negative deflection angles for the quasi-elastic and deep-inelastic regimes, respectively. The heaviest 232Th target indicates only a positive deflection angle even for a deep-inelastic process, as mentioned before. The results are reasonable, especially since the calculation can properly reproduce the zero crossing, as seen from fig. 5.

The friction model is applied to (14N,12 B) reactions to reproduce the systematic variation of the z 2 B polarization with a change of Q-value and mass number of


the targets. It proves that the gross behaviour of 12B polarization can be explained in the framework of the classical friction model qualitatively as a function of Q-value. However, this model is inadequate in reproducing the negative polarization observed for heavy targets, in the region for small energy loss where the direct two-proton transfer process plays a major role.

The reaction Q-value corresponding to the zero crossing between the positive polarization for the quasi-elastic and the negative polarization for the deep-inelastic process is shown as a function of target mass numberA in fig. 11 [38]. The experimental

> 0

I

100

50

EL= 120 MeV

e L - Grazing Angle

f

J

o 27 63 l o o zoo z

TARGET MASS NUMBER A

Fig. 11. Q-value corresponding to the point of crossover for the sign of polarization between positive and negative deflections.

zero crossings are obtained from measurements near grazing angles. The reaction Q- value corresponding to the second zero crossing is fitted by a straight line. This relation can be reproduced by the friction model. The zero crossing is expected to be a good indicator for the kinetic energy loss of projectile-like fragments which come from negative angle deflections. We follow the argument in ref. [38].

It is assumed that the viscous force is proportional to the relative velocity u between the colliding nuclei. The kinetic energy loss due to such a viscous force is written as a function of the interaction time r as

Eloss = Ei(1 - exp(2kr//a)).


The interaction time T is determined from the angle of observation and the angular velocity of the double-nucleus system. The latter is the ratio of the moment of inertia of the double-nucleus system and total momentum of the system. The moment of inertia I can be written as

I = p R 2 ,

where R is the distance between the centres of the projectile and target nuclei and is determined from a proximity potential [47] as

R = 1.15 (A~ la + A~/3) - 1.37,

where A 1 and A 2 are the mass numbers of the projectile and the target. The tz is the reduced mass of the system.

The rotational angular velocity w is therefore

r = %/2(Ecr n - VCi)/#/R ,

where Vci is the Coulomb energy of an incoming channel. The rotation angle 0 is taken as twice the grazing angle 0~r to fit the experimental data taken near the grazing angle

D = 4D 0 = 2 X 0g r = 4 sin -x 2 R - D 2R-----'D'

where D = Z 1 X Z2/Eem = VCi X R/gem. The energy loss by the nuclear frictional forces is obtained by using r = 0/60

and taking the leading term,

Eloss = 2 kr (Eem - Vci)[#

= (A x + A 2 ) k A I / 2 E L

= 6.9 • 1021k(A1 + A 2 ) A x / 2 E 1 (MeV).

The friction constant (2.5 +0.5)• 10 -22 MeV. s/fm 2 reproduces well the systematic dependence of the zero crossing as a function ofA.

Huizenga et al. have reported the friction constant for the Xe + Bi reaction as 3 X 10 -22 MeV.s/fm 2 [48] by applying the transport model to the atomic number distribution of projectile-hke fragments. Our value in any case is in good order of mag- nitude agreement with their value.


6. Conclusion and scope

From the results of experiments described here, a consistent picture of polarization phenomena in heavy-ion reactions has been obtained, i.e. an effective approximate description of the processes involved in the collisions between nuclei has been made by use of classical concepts, such as viscous forces acting on the nuclear surfaces of two colliding nuclei.

Systematic behaviour has been found for the polarization and the degree of polarization in many cases is sizable. Especially in the region of the highest kinetic energy of the outgoing nuclei the degree of polarization is largest and the direct reaction regime is predominant in this region. The deep-inelastic region is another promising field where the reaction products exhibit large polarization and the macro- scopic features are effective in describing the reaction process. Microscopic description of the whole process which allows understanding in terms of a whole consistent picture is still to be awaited. One is tempted to extend reaction studies from the point of view of polarization of reaction products, not only for low-energy heavy ions but also for high-energy heavy ions. Study of unstable nuclei produced in rich abundance in high- energy heavy-ion reactions will be interesting, especially if they are polarized.

The field of heavy-ion polarization is still in its early stage. The experimental methods involved are diverse and new ones are expected to conform to specific aspects of experimental problems, as they unfold.

Now that appreciable polarization has been proven to exist in general for many heavy-ion reactions, utilization of such nuclear properties will be highly profit- able for physics research tO many fields. To name some, by using these reaction products, solid-state research could be conducted in which implantation of atoms with nuclear polarization can be a good indicator of the interactions involved. The use of polarized nuclei for the test of various symmetry properties will also be benefited by such heavy-ion reactions as a means of producing polarized nuclei. Reaction products in heavy-ion nuclear reactions are energetic and have a long range in matter. This is a good complement to the polarization of slow ions produced by the hyperfine interactions in ions passing through tilted foils [49,50]. These ions are of short range in matter.

Acknowledgemen t s

The experimental data as given here have been taken in cooperative efforts of the group consisting ofK. Sugimoto, A. Mizobuchi, T. Minamisono, Y. Nojiri, Y. Miake, K.-H. Tanaka and the author. The first experiment carried out at the IPCR is the cooperative work of the above group and K. Asahi (Tanaka), M. Ishihara and H. Kamit- subo. The author expresses his sincere appreciation for the cooperation and the dis- cussions. The willingness of the crews of both cyclotrons at IPCR and RCNP is highly


appreciated. This work is supported in part by the Toray Science and Technology Grants and the Grants in Aid of Scientific Research.

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