Recoil study of transfer reactions: Evidence for α and 8Be transfers in 12C reactions with heavy nuclei (Au, Bi)

I

2.N

I

Nuclear Physics Al89 (1972) 193-219; Not

Publishing

Co., Amsterdam

to be reproduced by photoprint or microfilm without written permission from the publisher

RECOIL EVIDENCE

STUDY

OF TRANSFER

REACTIONS:

FOR a AND *Be TRANSFERS WITH HEAVY

NUCLEI

R. BIMBOT, D. GARDI% Laboratoire

@ North-Holland

de Chimie NaclPaire,

IN ‘*C REACTIONS

(Au, Bi)

and M. F. RIVET

Institut de Physique

NucMaire, BP no. 1, Orsay, France

Received 20 January 1972 Abstract: Transfer reactions induced with 12C ions in Au and Bi targets have been studied. The experimental technique involves the measurement of the cross sections, angular distributions, and recoil range at each recoil angle, of the heavy residual nuclei. The processes leading to the production of At isotopes in the case of a Bi target, and Tl and Bi isotopes in the case of an Au target, have been identified by means of a kinematic analysis of the experimental data. They appear to be 2p, c( and *Be transfers from the projectile to the target, followed by the evaporation of neutrons. The cross section for *Be transfer was derived from experimental data and is significant, of the order of 100 mb. The cross section for cc-transfer was estimated to 30 to 80 mb. All the observed characteristics of the residual nuclei produced through OLand *Be transfers (cross sections, ranges and angular distributions) are in good agreement with the cross sections and angular distributions of the direct u-particles which are the projectile residues of these transfers, and which were observed by other authors. E

NUCLEAR

REACTIONS 19’Au, 209Bi (“Caxn); lg7Au, 209Bi (I%, .!&I2 = 60-90 MeV; measured a(E), a(0), recoil ranges.

*Be, xn)

1. Introduction

Single and multinucleon transfer reactions between heavy ions and targets of different masses have been extensively studied (see the survey of ref. I)). The techniques used can be divided into two groups. In the first group are placed the methods which involve the observation of the projectile residues (light fragments) by counter **“) or radiochemical 4-6) tee h m‘ques. Angular and kinetic-energy distributions of the light nuclei are measured, and a kinematic analysis of the results can be made. This analysis allows an unambiguous interpretation of the experimental data when the mass and kinetic energy of the observed nucleus are close to those of the projectile ‘). But when the observation of the outgoing particle reveals a sizeable deficit of mass or kinetic energy, no definite conclusion can be drawn about the reaction mechanism. The second group of techniques consists of radiochemical and recoil studies of the target residues 7-11). Excitation functions, projected recoil ranges and angular distributions of recoil nuclei are measured. This method provides information about the majority of the involved nucleons, but generally it is not possible to proceed to a kinematic analysis because simultaneous measurements of angular distributions and recoil 193

194

R. BlMBOT et al.

energies for each angle are not performed. The main reason for this fact is the experimental difficulty of range measurements on low-energy heavy nuclei. However, such a study was performed by Croft et al. lo) in the case of ’ 6O induced transfer reactions on “‘Pb and “‘Bi , but the uncertainties in the experimental results, especially in range distributions at each angle did not allow precise conclusions about the mechanisms involved in the production of the observed nuclei. Following the same principle, the present work belongs to a more general study of single and multinucleon transfers induced with heavy ions in heavy targets, using precise determinations of the angular distributions and recoil ranges of the heavy residual nuclei at various angles in the lab system 12). Integrated cross sections and recoil-range straggling are also measured. This paper is mainly focused upon a and *Be transfers induced with 12C ions in “‘Bi and ’ 9‘AU targets, the observed radionucleides being At isotopes in the case of a Bi target, and Tl and Bi isotopes in the case of a Au target. 2. Experimental

procedure

2.1. IRRADIATIONS

The experimental set-up (fig. 1) consisted of three parts I, II and III, bombarded at the same time. The first chamber I was designed to measure angular distributions. The angle of the thin target (t,) could be varied relative to the beam direction by changing the target holder (h). The catcher-ring foils A covered the walls of the chamber over the angular range 0 = 5-90”, each of them corresponding to an aperture 46, = 5”.

Fig. 1. Experimental set-up. I: angular distribution chamber. II: chamber for range measurements. 111: Faraday cup. A and B: catcher rings; t, and tz: targets. h: target holder; c: collimator; S: stack of targets; F: towards beam integrator.

The second chamber II was used to collect recoil nuclei for range measurements as a function of 8. Its dimensions were reduced by a factor of 2 relative to the size of chamber I. The ring collectors B were placed over the angular range 15-90”, and each one covered A0 = lo”, except for the first one which corresponded to the angles 15-20”. In some experiments the ranges were measured over the angular interval O-90”. The energy loss in the target ti (50 pg/cm2 Bi or Au on 180 pg/crn’ Al backing)

TRANSFER

REACTIONS

195

was equal to about 0.2 MeV. The target ta was typically 100 pg/cm2 Bi on 180 pg/cm2 Al. The Faraday cup III was used for beam intensity measurements. Electron stripping by the targets tl and tz was taken into account in determining the charge of the ions reaching the Faraday cup 13). In some experiments a stack of targets was placed in the Faraday cup and the excitation functions of the products of interest were measured between the incident energy and the Coulomb barrier. Each target consisted of 1 mg/cm2 Bi or Au deposited on 1 mg/cm’ Al. The Al backing was placed downstream and was thick enough to stop the recoil nuclei. The energy loss of the “‘C beam was equal to 1-2 MeV in the Bi target and 24 MeV in the Al foil 14). In order to check that no appreciable error on beam intensity measurements was introduced by the fact that the Faraday cup was bombarded at the same time as chambers I and II, a special irradiation of the device III alone (Faraday cup+ targets) was made, and the cross sections were found to be in good agreement with the results of standard bombardments. The irradiations were performed with the external beam of the Orsay heavy-ion cyclotron. TypieaI intensities were 0.1 to 0.5 yA, and the bombardments lasted 4-9 h. By changing the acceleration conditions (magnetic field, frequency), the incident energy of 12C4+ ions could be varied between 60 and 90 MeV. This energy was calculated by extracting the radius R(m) and frequency I”(MHz) by means of the relation .E =

F2R2 222A (MeV),

in which A is the atomic mass of the accelerated ion. The validity of eq. (1) was checked by direct measurement of the beam energy for several acceleration conditions, with a solid-state detector, after scattering on a thin gold target. A general agreement to within + 1 % was found between measured and calculated values 1“1. 2.2. RADIOA~~V~TY

MEASUREMENTS

2.2.1. Angular d~~~rjb~tio~~. After irradiation, the seventeen catcher foils A from chamber I were separated from each other and their a- or y-radioactivity was measured as a function of time for several days. In the case of *09Bi target, the interesting nucleides were zog~210~z11Atand ‘l”Po; in the case of r9’Au target, the angular distributions of 201~202~203~204Bi and 198~1g9~200Tlwere measured, either directly, or on a radioactive daughter. Each isotope was identified by means of a specific tl- or y-ray, and the decay haif-life. The characteristics of the observed radionucleides are listed in table 1. The a-activities were measured in a double ionization chamber which is described in ref =24>. In this chamber, eight samples can be placed on a rotating plate and their radioactivity followed without opening the chamber, two of them being counted simuItaneously. The counting ethciency is 50 % and the resolution is about 100 keV

196

R. BIMBOT

Characteristics Reaction product

Half-life

7.2 h 8.3 h

2osAt

5.4 h

TABLE 1 of the observed

Type of decay

9.4 h

201Pb

radionucleides

Ez or E,

a- or y-rays per disintegration

;c

5.868 MeV

0.409

16)

EC

245 1.180 5.65 545 780 790 1.448 5.30 315 422 219 167 368 455 412 412

0.79

16

Ref.

a

a

EC

0.52 s 138.4 d 11.4h 95 min 52 h 73 h 26.1 h 7.4 h 5.3 h 1.9 h

et al.

a

Lc EC EC EC EC EC EC EC IT EC

keV MeV MeV keV keV keV MeV MeV keV keV keV keV keV keV keV keV

330 keV

0.041 0.62 0.545 0.395

2’) 30 30 16

+10x 0.66 &IO% 0.795 f 5 % 0.0925* 5% 0.88 f 5% 0.14 *lo% 0.885 f 5 % 0.43 &lo% 0.90

1

‘,

1 17 1 30) 1s 19

;

20 21

;

21 22 ; 23 1

21 1

for 5.3 MeV a-particles. In our experiments, the resolution was much poorer, due to the fact that the radioactive atoms had penetrated the catcher foils to a substantial depth. Even in this case, however the resolution was sufficiently high to allow separation of the 7.45 MeV a-particle from ” rPo in equilibrium with ‘llAt from other a-rays. Measurements performed several weeks after irradiation revealed that ‘r”Po was the only a-emitter present in the catcher foils. The y-activities were measured with a resolution of 3.6 keV by means of 2 Ge(Li) detectors of 30 cm3 and 80 cm3 respectively. 2.2.2. Excitation functions. The a- and y-radioactivities from the targets were counted in the same way as in the case of the catcher foils. Due to the self-absorption of a-particles in the target, the a-counting efficiency was less than 50 ‘A and a correction was made to take this effect into account. This correction required a knowledge of the mean recoil range along the beam axis which was deduced from the range measurements and angular distribution. 2.3. DECAY

CURVE

ANALYSIS

Some of the decay curves were purely exponential and the extrapolated activity at the end of the bombardment was used to calculate the cross sections. In other cases, the variation of activity with elapsed time appeared more complex, because of accumulation of the observed nucleide from a parent. This situation was encountered for the following isotopes: The ‘OrBi and 203Bi cross sections were calculated from the “IT1 and ‘03Pb activities. The nucleus “‘Pb was the observed isotope for angular

TRANSFER

REACTIONS

197

distributions of “‘Bi , while ‘04Bi was accumulated from 3.5 h ‘04Po. The “‘Tl curve was sometimes a pure exponential, and sometimes (high energies) the sum of an exponential decay and an accumulation curve from *“Pb. Both contributions could be derived from the analysis of the curve. Direct production of 200T1 was attributed to transfer reactions, and accumulation from *“Pb to a (‘*C, 5n) reaction producing *04At, the radioactive chain being: 204~t

oL_

2OOBi

EC_

2OOpb

EC_*OOTi.

The cross section found for this reaction by *“Tl activity measurement is in good agreement with the results of ref. ‘“). A special problem was encountered for 19’T1 because of the existence of 19*“‘T1 (1.9 h). The relative production of the isomers is not known and the observation of the 412 keV y-ray was not sufficient to solve this problem, because this y-ray can be emitted following the decay of either isomer. However, the extrapolation of the 5.3 h asymptote of the decay curve could be used to calculate an approximate value of the total cross section o,,,+(T~ [ref. 27)]. The add it io na 1 uncertainty was equal to +8 %. 2.4. RANGE

MEASUREMENTS

Due to their initial velocity, the recoil atoms were stopped in the catcher foils at various distances from the surface, according to a distribution which could be defined by the mean distance d and the width Ad (FWHM of the distribution). The recoil range R and range straggling parameter p [defined in ref. ‘)I can be

Fig. 2. Comparison of the cc-spectrum from a catcher foil (CF) with the a-line (TS) from a thin sample of the same nucleide zllPo. AE is the energy shift and W the FWHM of the catcher-foil a-spectrum.

198

R. BIMBOT

et al.

deduced from d and Ad after some corrections to take into account the effects of target thickness and the angle of penetration in the catcher foil ’ “). The values of d and Ad were measured as functions of the recoil angle 8 by a method in which the penetration distance of the cc-emitter is revealed by the energy loss of the g-particle before leaving the catcher foil 1’s‘“). For this purpose, the catcher foils B from chamber II were separated from each other after irradiation, and a fraction of each (equal to 1 in the case of the smaller rings) was mounted in the standard shape of 2 x 2 cm2. The a-rays emitted by this sample were measured with a surface-barrier detector. The good resolution (20 keV) of the detector allowed precise analysis of the energies and shapes of the a-lines. A gain stabilizer was used to improve the stability of the electronics. The constancy of the energy response was checked from time to time with calibration samples of 211At-211Po and “‘PO. The comparison of the a-spectrum from the catcher foil with the a-line from a thin sample of the same nucleide ( 21‘PO) is shown in fig. 2. The energy shift AE was directly related to d and the FWHM W to Ad, thanks to experimental calibrations made previously with a thin radioactive sample and Al degraders of known thickness in the same counting geometry 12,’ “). This method was applied to the nucleides 209At, “‘PO and 211At, for which an M-ray could be isolated (see table 1). Because of the P-decay of ‘loBi and the EC decay of 210At, the range measurements made on ‘l”Po could correspond to the original residual nuclei 21‘Bi, ‘loAt or 210Po. However, the ‘loBi cross sections, measured in a separate experiment 12), were found to be only about 1 mb, a value that is negligibly small compared to the ‘l”Po and 21‘At cross sections. Furthermore, the angular distributions of “‘At (y,245 keV and 1.18 MeV) and 210At+2’oPo (a, 5.3 MeV) were individually measured and usually the peaks of ‘loAt and 210Po distributions did not occur at the same angle. Therefore no ambiguity was left in the assignment of the ranges. This was always the case for the peak at 17” in 21‘At angular distribution. For the peak around 40”, it was not always possible to isolate the contribution of ‘loAt and the result was an additional error in the range determination. 2.5. UNCERTAINTIES

2.5.1. Angular distributions. The uncertainties in the differential cross sections come from the activity measurements (variable), the catcher-foil widths (+ 10 %), and the integrated cross-section value which was used to normalize the angular distributions. This last uncertainty does not affect the shape of the angular distributions and is not quoted in the experimental results (figs. 4-6, 11, 12). 2.5.2. Excitation functions. The uncertainties in the integrated cross sections are equal to the quadratic sum of the uncertainties on counting efficiencies (5 % for y-rays, 1 ‘A for a-rays) branching ratios (see table l), target thickness (+ 5 ‘A), beam intensity ( f. 5 O/o)and activity measurements. For 19*T1 an uncertainty of (+ 8 %) has been added (see subsect. 2.3). 2.5.3. Range measurements and recoil energy determination. The uncertainty in

TRANSFER

199

REACTIONS

the range value is due to the error made in the AE determination

(variable),

and in

the’use of the calibration curves AE = f(d)( k 5 %). The transformation of R into a recoil-energy value implies the use of range-energy relationships which introduces an additional error of (& 10 o/,), the overall error on recoil energy being about 16 %. However if, in the same experiment, one can observe a nucleus 1 which is produced through a (compound nucleus, xn) reaction, and the nucleus 2 which is produced through another reaction, the ratio AE,IAE, of the energy shifts of the a-rays can be related to ERzIERI, the ratio of the recoil energies with a good precision. As ERI is known, ER, is thus determined with a higher precision (_tS”/o).

3. Determination 3.1. SELECTION

BETWEEN

of the mechanisms THE

POSSIBLE

involved: kinematic study

MECHANISMS

can be considered as the The production of a given residual nucleus (i.e. “‘At) result of a two-step process. First, a nucleon or group of nucleons are transferred nucleus dissifrom the projectile “C to the target ” ‘Bi . Secondly, this intermediate pates its excitation energy by evaporating neutrons or emitting photons. The number of evaporated neutrons is closely related to the excitation energy of the intermediate nucleus (Ez). Therefore several mechanisms may lead to the formation of a given residual nucleus: for example, in the case of ‘11 At one has to consider 2p transfer and y-de-excitation (denoted 2p-y), 2pn transfer and one-neutron evaporation (3He-n), or a-transfer and two-neutron evaporation (c(-2n). In addition, because of the possibility of fast a-decay from ” 5Fr and ‘i ‘AC, transfers of ‘Be and even compound-nucleus formation should also be considered. The first step in the analysis of the results is to assign to each observed nucleus one or several production paths with, if possible, their relative probability. For this purpose, the various production paths for the observed nuclei are listed in table 2. Some of these paths can be excluded on several possible bases, and they are noted in parentheses in table 2, with the indices I, 2, 3 and 4 referring to the following: The index 1. The process is obviously energetically impossible, because it requires the evaporation of too many neutrons, e.g. (‘Be-7n)l in ’ “Tl production. The index 2. The half-life of the parent is such that the analysis of the decay curve is sufficient to reveal the non-existence of the parent-daughter relationship e.g. “lRn(15 h) + ‘l’At(7.4 h). No 15 h component was observed in the decay curve of ‘llAt, therefore the paths going through ‘llRn must be eliminated: (5Li-3n)2. The index 3. The comparison of the angular distribution of the corresponding isotopes produced with Au and Bi target may help eliminate some processes: e.g. as 5Li-3n is eliminated in ‘llAt production on the previous basis, the same process is eliminated in lggT1 production, the angular distribution of this last nucleide being identical to the case of “i At as far as large angles are concerned. The index 4. A kinematic test is performed on the mechanisms which were not

‘99TI lggPb 199Bi

[a-2n], 3He-n, [2p--y] (SLi-3n)2, (6Li-4n)2 ‘Be-n, [*Be-2n], (gBe-3n)4, (‘*C-a2n)* (lOB--4n)* (11B-5n)2 [12C-2n] ’

[‘Be -4n] 12C-a4n [‘*C-4n]

(a-3n)*, 3He-2n, [Zp-n] (5Li-4n)2, (6Li-5n)2 ‘Be-2n, [sBe-3n], (gBe-4n)4 (10B-5n)2, (“B--6n)* [12C -3n]

residual nucleus

mechanism

Bi target

TABLE 2

3He--y

a-3n, 3He-2n, [2p-n] (5Li-4n)3, (6Li-5n)3 (‘Be-6n)l, (8Be-7n)1, (10B-9n)‘, (llB-lOn)l (10B-5n)3, (‘1B-6n)3 (‘%I-7n)’

[a-2n1, 3He--n, [2p-yl (5Li-3n)3, (6Li-4n)3 (7Be-5n)1, (8Be--6n)i, etc, (‘*C-a6n)’ (ioB--8n)1 (1’B-9n)’ [12C-6n] ’

[a-n],

mechanism

*05At

202Bi

203~i

204Bi

residual nucIeus

Au target

of the observed isotopes, in the case of Au and Bi targets

[%-4n] i2C-a4n [‘*C-4n]

‘Be-2n, [*Be-3n], (gBe-4n)3, 12C-a3n (‘OB--Sn)j, (‘1B-6n)3 (i2C-7n)1

‘Be-n, ISBe-2n], (gBe-3n)3, (12C-a2n)3 (10B-4n)3, (11B-5n)3 [‘*C-6n] ‘*C-2n

‘Be--y, 6Be-n, etc 12C--an ‘*B-3n, I’B -4n [12C-5n]

mechanism

The underlined nucleide is the observed one. The mechanisms in parenthesis are excluded on a basis indicated by the index (see text). The mechanisms which play a significant role in the production of the observed nuclei are written in square brackets, i.e. [a-2n].

21’A~

_IIresidual nucleus

Possible mechanisms for the production

$ 2 %

E

P

TRANSFER

REACTIONS

201

excluded before and some mechanisms are energetically excluded after this test. The principle of the kinematic study is given in subsect. 3.2. For 20gAt and “‘Pb, only the mechanisms which were not excluded are given in table 2. 3.2. KINEMATIC

ANALYSIS

In the case of a Bi target, the experimental data (recoil angle and recoil range) could be used to proceed to a kinematic check of the possible ways of production. For each of these ways, the energy and momentum balance was made according to the equations E, = E,+E,+E*-Q, (2m, E,)+ = (2m,E3+

cos I??‘+(2m, ER)+ cos &,

(1)

(2mL EL)” sin f+, = (2m, I&)* sin OR,

where mi and Ei are the incident particle mass and energy, mL, EL and SL are the mass, kinetic energy and recoil angle in the lab system of the projectile residue after the transfer process, mR, ER and 8, the same quantities for the heavy intermediate nucleus, E* is the total excitation energy of light and intermediate nuclei, and Q is the mass balance in the first step of the reaction. The quantities Ei, mi, mL, mR and Q are known or result from the assumed mechanism, 8, is given by the angular distribution measurement and ER is given by the range value and range-energy conversion. The measured values ER and OR refer in fact to the residual nucleus, but the assumption is made that the evaporation of one to three neutrons does not affect significantly the recoil angle and energy of the heavy intermediate nucleus. For the range-energy conversion, data from refs. ‘, 14,28) were used. Good agreement was found with results obtained in the present work, whenever a compoundnucleus mechanism was obviously responsible for the formation of the observed nucleus. With the help of eqs. (l), the calculation of EL, 0, and E* could be performed and the calculated value of E*(E:) was compared to the minimum excitation energy (Ezin) of the intermediate nucleus giving a significant probability for the evaporation of the number x of neutrons consistent with the assumed mechanism. The empirical relation (2) was derived from experimental data ‘“) relative to 4HefBi reactions, and applied to every case.

ES min

=jl

B,+ 1.7X,

where 3, is the binding energy of the nth neutron. If E,* < a??&, the mechanism is energetically excluded; if E,* > Ezi,, the mechanism is energetically possible, the available energy being shared between intermediate and light nuclei. In this case, it is interesting to compare E,* to E,&, which is the maximum excita-

202

R. BIMBOT

et al.

tion energy of the intermediate nucleus giving a significant probability for the evaporation of x neutrons (if E* > Ez,,, x+ 1 neutrons are evaporated) x+1

E*max

&#+1.7(x+l), =nT,

if Ezi, < E,* < E&, the mechanism is possible and the light partner has little excitation energy, if E,* > Ez,, the difference E8 -Ez,, is the minimum excitation energy of the light nucleus. If this difference is too large ( 2 20 MeV) the assumed mechanism is not probable, because it is difficult to imagine why the maximum probability of the transfer would correspond to such a high excitation of the light nucleus.

4. Experimental

results

4.1. Bi EXPERIMENTS

4.1 .l. Excitation

junctions.The

” rAt produced through “C+Bi

experimental cross sections for ‘09At, ‘loAt and reactions are given in table 3 and the excitation

functions are plotted in fig. 3. Some remarks can be made about these excitation functions: (i) The values found for ‘“At are in good agreement with the 1961 data from Alexander and Winsberg ‘) as far as the general shape of the curve is concerned, but there is a disagreement in the magnitude of the cross sections, the values from ref. ‘) being equal to about 100 mb at 90 MeV. The present results have been checked

TABLE 3 Experimental cross sections for At isotopes produced through 1*C+209Bi

.L

WW 88 88 87 85 83.5 82 80.5 79 78 76.5 76 75.5 74 73 71 68.5 65.5 62.5

211At 43.4 46 49

A9.0 &5 f10

44 47.3 39 46.5 39.2 41.7 40 39.4 42.0

zt9 -19.5 f8 h9.3 *8.0 A8.4 *4 +s.o +8.4

32.7 h6.6 26.0 55.2 19.3 k4.0 5.25zt1.00

reactions

=l”At

59.1&6.5 48.4+9.7 61.6f6.0

=09At

63 71 76.5

&5 &ll -+6.5

36.Oh7.2

188

&38

38.Ok7.6

222

135

51 AlO 47.1 f 5.2

220

*37

221

&12

89 118 96.2fll.O 111 +22 103 120 51.5flO.O 21 *4

137 &18 149 *11 64 &9.5 5.2 kO.9 2.7510.65

TRANSFER

203

REACTIONS

mrnb _ too =

/ i\’ I-

IO

,’

II

k%.

J

/I’

\

60

i

I

I

-I

70

80

90

Elab (MeV)

Fig. 3. Excitation functions for At isotopes produced through 1zC+z09Bi reactions. 1: Experimental cross section for total production of the isotope. Decomposition of the curves int: the excitation functions of the mechanisms involved in the production: compound-nucleus mechanism: reaction (I%, xn); - - - *Be transfer and neutron evaporation; - - - - 2p or a transfer and neutron evaporation.

several times, and, on the other hand, the excitation function of 211At produced through ’ 6O + ” 9Bi reactions which has been measured with the same technique 3 “) is in good agreement with the recent data of Croft et al. lo). Therefore it is possible that the discrepancy observed with ref. ‘) is due to the experimental difficulties which existed in 1961 in measuring the beam intensities.

R. BIMBOT et al.

204

I

-,

I

I

77.3MeV

IO

I

-

1: IO

30

30

of 209At produced through 12C+209Bi reactions for several incident energies.

Fig. 4. Angular distributions

1c

1 65.7 MN

7 -0

2 a

P

I

b D

77.3 MeV

l!!Yiil

0.1

Fig. 5. Angular distributions

IO

30

50

IO

30 @lab

50

of 210At produced through 1zC+209Bi reactions for several incident energies.

TRANSFER

205

REACTIONS

%b

IO

30

50

IO

70

30

50

70

%b Fig. 6. Angular distributions

of “‘At

produced through ‘2C-f-20pBi reactions for several incident energies.

(ii) The excitation function of ‘loAt exhibits a peak around 70 MeV which suggests a compound-nucleus mechanism, namely a contribution of the reaction “‘Bi (I%, 3n)‘l’Ac (see table 2). This wiii be confirmed by the range measurements and angular distributions. Beyond this peak, the cross sections remain significant, and another mechanism must be responsible for ‘loAt production. (iii) The *’ 9At excitation function is very similar to the low-energy part of the ” ‘At curveandsuggestsapredominantin~uenceofthe(’2C,4n)reactionin2ogAtproduction. This interpretation of the maxima by a (12C, xn) reaction is in good agreement with the results of several authors 31-33 > who measured the excitation functions of Ac or Fr isotopes produced through “C + 209Bi reactions with the help of fast detection techniques. 4.1.2. Angular distributions. The angular distributions of ‘09At, 210At, ‘“At are given in figs. 4, 5 and 6 for several incident energies in the lab system. For the energies which correspond to a peak in the excitation functions (“‘At at 66 and 73 MeV, ‘OgAt at 73 and 77 MeV), the distribution is peaked forward and

206

R. BIMBOT et of.

this is in good agreement with a compound-nucleus mechanism ‘Sag). The same shape is found for “i At at 60 MeV and reveals a (12C, 2n) mechanism at this energy. This observation is confirmed by range measurements (see later). For other energies, the angular distributions exhibit one or two maxima, one of them appearing sometimes as a shoulder. These maxima correspond either to an angle of about 17”, or to a much larger angle (about 40”). This fact suggests that, in addition to the (12C, xn) reactions, at least two mechanisms may be responsible for At formation. 4.1.3. Range measurements. The ranges have been measured at each angle 8 whenever the activity was sufficient. Otherwise, the measurement was made for the angles O,,, which correspond to the maxima of the angular distribution. Fig. 7 shows the curve R = f(O) obtained for 211At and an incident energy of 77 MeV. At this energy the angular distribution exhibits two peaks at 17” and 40” which are indicated by the arrows. It can be seen in the figure that the recoil ranges corresponding to these two peaks are significantly different.

II

0

IO

20

30

40

50

@lab Fig. 7. Range of “‘At versus recoil angle O,,, in the lab system. The nucleus *“At is produced through 12C+Z0gBi reactions. The incident energy is 77 MeV. The arrows indicate the position of the maxima in the angular distribution (fig. 6).

Table 4 presents the experimental range R and range straggling as a function of The last column gives the recoil incident energy and angle 8,,, for 209121 ‘* ‘“At. energy ER derived from R-values, for each isotope. 4.2. GOLD

4.2.1.

EXPERIMENTS

Excitation functions.

The excitation functions measured for the isotopes Bi are shown in figs. 8-10 and the experimental cross sections are given in table 5. The nuclei 20’, 203s 204Bi can be produced through a compound-nucleus process (see table 2) and the peaks observed in the excitation functions are in good agreement 198,199,20OTl

and

201.202.203.204

0 0 15 17.5 40 0 17.5 40 17.5 40

59.5 65.7

0.198it30.010 0.274f0.016 O.t82&0.008 0.216&0.024

0.284&0.017 0.3Q5Lt0.017

0.311fO.Of9

range fWcm21

0.418 0.375 0,462 0.432

0.343 0.417

0.306

0,218

P

2’1At

2.8810.21 3.5910.29 265 10.26 3.14fO.30

441.10.33 4.14&0.31 4.45 kO.44

0,184rtO.O17 0.198fO.020

0.278~0.017

0.211 f0.013 0.247&0.015

range Cm&m2 f

0.450 0.465

0.294

0.222 0.180

P

‘loAt

2.68f0.20 2JJ8 f Q,30

3.65 f0.30

3.l8&0.08* 3*51&O.O5*

0.30~~0.020

0.314f0.020

range (mglcm21 -

0.312

0.206

P

sogAt

4.4510.33

4.12LfO.08”


TABLE4 experimental values, for At isotopes, at several incident energies and for the angle S,,, which corresponds to the maxima of angular distributions

The uncertainties in p-v&es are not quoted in the table and correspond to (&lS %). The energies listed in the 3rd column for each isotope are calculated relatively to the energies indicated by an asterisk which correspond to a compound-nucleus mechanism kxe subsect. 2.5.3).

89.4

77.3

72.8

f3mm

(degree)

E lab

@ieV)

Range and rage-stragg~jn~

2 ?X

$

E

g

2 2 FA

R. BIMBOT et al.

208

z

L

100

IO

I

30

I

70

80

Ebb (MeV)

I 90

Fig. 8. Excitation functions for Tl isotopes produced through 12Cf197A~ reactions. # : 200TI; 1g9T1; i : 1g8T1.The vertical arrows indicate 0: that the exierimental value is an upper limit. The solid lines are drawn through the experimental points to guide the eye. The dotted line is the sum of the cross sections of TI isotopes.

60

70

60

70

80

I

Fig. 9. Excitation functions for 301*202*203Bi produced through izC + r 97A~ reactions. 0: ZOlBi; : 202Bi; : *03Bi. The dotted lines + i represent the contribution of a compound-nucleus process. The solid lines represent the contribution of a transfer mechanism.

80 Elnh 0&z

Fig. 10. Excitation function for 204Bi produced through 12C+197A~ reaction. The data from the present work (i) are compared to the cross sections from Bimbot et al. 2h), (0) for the reaction i2C+ 19’Au + 204At.

TABLE 5

Experimental

cross sections for Tl and Bi isotopes produced through ‘2C+197A~ reactions o (mb)

E,,, WeV) 87.8 85.3 82.7 80 77 74.4 71.6 68.8 66 62.6

198g.l98mT]

16.2*2.6 17.8k2.6 12.7*2.5 10.5f2.5 8 f1.7

lOlBi

l99Tl

zooTl

52 +14 52 ill 48.0+8.5 35.5k7.0 < 19&5

13.lf2.6 18.5f2.4 25.41t3.8 31.8f4.8 35.6h5.3 29.4+5.0 27 +4 21.5*3.9 17.6k2.7 ll.Okl.8

5.8*1.4 t3 < 2.3

IO

33

50 %b

202Bi

89.5zt13.5 86.5f13.5 69.5kl2.0 132 zt25 54 zt10 109 *19 42.6f12.5 114 &25 41.5+10.0 93 *15 50.0+10.5 53.5f9.7 47.0*10.8 39.5* 6.7 33.3 16.3 20.6+ 5.3 15.9h2.9

203Bi

204Bi

152 117 74.5kll.O 29.2k4.0 10.5*1.1 7.25&1.10 9.8kl.4 13.7k2.2 15.4k2.3 12.8k2.4

320 +50 384 &57 413 160 375 &60 255 140 131 *21 41.6b6.5 < 31

70

0.1 elab

Fig. 11. Angular distributions of Tl isotopes produced through r2C+Au reactions. The solid lines refer to the incident energy of 89 MeV, the dotted lines to the energy of 69 MeV. For r’s Tl and r 99T1,only the places of the maxima were determined at this last energy.

@lob Fig. 12. Angular distributions of Bi isotopes produced through ‘%+Au reactions. The solid lines refer to the incident energy of 89 MeV, the dotted lines to 69 MeV. For *03Bi and 204Bi at 89 MeV, cross sections have been divided by 10.

210

R. BIMBOT et al.

with the results of Bimbot et al. 2”) on 19’Au (r2C, xn)At reactions. For 204Bi cross sections, this agreement is obtained if the adopted branching ratio of the 375 keV y-ray is equal to 0.90. This value results from our determination 30), and differs from a previous measurement ‘*). 4.2.2. Angular di~trib~t~on~. The angular distributions of the Tl and Bi isotopes are shown in figs. 11 and 12 for the incident energies of 69 and 89 MeV. The distributions are peaked forward for Bi isotopes at the energies for which they are produced through a (“C, xn) reaction. Otherwise the maximum always occurs at 0 = 17”. In the case of Tl isotopes, the angular distributions exhibit a single maximum which occurs at 30°-4W at 69 MeV and at 45” at 89 MeV.

5. Interpretation

The peaks observed in the angular distributions can be divided into three groups, according to the value of emaX. 5.1. THE GROUP i3,,,,, < IO”; COMPOUND-NUCLEUS

REACTIONS

The angle O,,, < 10” corresponds to a compound-nucleus mechanism, namely to a reaction (r2C, xn). The range measurements for IQ= 0” (table 4) and the shape of excitation functions confirm this interpretation. 5.2. THE GROUP

@,,, = 30” to 50”: TWO-CHARGE

TRANSFER

The observation of maxima at large angles (0,,, = 30” to 50”) is associated with non-compound-nucleus reactions in which two charges are transferred from the projectile to the target. This conclusion is supported by the large values of O,,, in the Tl angular distributions, and by the kinematic study in the case of At isotopes produced in a 2ogBi target. This study shows that, among the mechanism listed in table 2, only those which correspond to Zp, ‘He or g-transfer are energetically possible for the peaks at 40” in 210P211At distributions. A typical example of the results obtained is given in table 6 in the case of 211At for 89 MeV “C ions. In this table, the calculated value Ez is compared to E$,, and E,& for each mechanism, and the result of the comparison appears in column 5 which gives the limits for Ez, the excitation energy of the light partner. These limits are equal to E,* - E~in and Ez -E,*,, respectively. One can see that a *Be transfer is energetically excluded, and that 2p, 3He and a transfers are possible. However the Zp-y mechanism would lead to a light nucleus (loBe) with 18 to 28 MeV of excitation energy, and this high value is difficult to admit because one cannot unders~nd why the transfer probability would be largest for such a high excitation energy of the projectile residue. Therefore the results of the kinematic analysis suggest that a-2n or 3He-n mechanisms are responsible for this peak.

TRANSFER

Summary of the kinematic Mechanism

E*,I.

2P--Y 3He-n u-2n *Be-211

Conclusions

72.8 77.3 89.4

211

TABLE6 study for the peak at 37” in the case of 211At for 89 MeV W (see text)

(MeV) 0 7 15 15

REACTIONS

E*,,,

(MeV) 10 16 25 24

ions

Elc (MeV)

E*, (MeV)

Conclusion

28 22 21 -36

18-28 6-15 O-6 to

? possible possible impossible

TABLE7 of the kinematic analysis for the peaks around 40”, for Z1oAt and 211At

mechanism

E*,_(MeV)

mechanism

2P-Y 2P--Y 2P--Y 3He-n or-2n

o-3 2-12 IS-28 6-15 o-5

2p-n

E*‘ (MeV)

O-8.5

The conclusions of the kinematic analysis for the peaks around 40” are given in table 7. It should be noted that the peak at 40” in ‘r ‘At distribution is due to a 2p transfer (followed by the evaporation of one neutron), and that the situation is the same for 211At at low energies. This does not mean that a-transfer does not occur at low energies, but that the excitation energy of 213At is not sufficient to evaporate two neutrons. If one neutron only is emitted after a-transfer, the residual nucleus is “‘At which cannot be observed by our technique because of its short half-life. But the production of this isotope in C+Bi reactions has been detected by the heliumjet technique 31,32). Furthermore, in the case of a gold target, the corresponding isotope “‘Tl is observed with a significant cross section, its ways of production being u-n or 3He-y mechanisms. Because of the structure of the 12C nucleus, the cl-n mechanism seems to be more probable. 5.3. THE GROUP

&,,,. = 17”: ‘Be TRANSFER

The peaks observed at the angle emax = 17” correspond to reactions in which the charge of the nucleus is increased by four units. This fact is clearly shown by the angular distributions of Bi isotopes from a gold target (fig. 12). Therefore, in the case of a Bi target, the peaks at 17” in angular distributions must be attributed to a mechanism which leads to the production of a Fr isotope which decays rapidly into an At isotope. This conclusion is in agreement with the shape of excitation functions and

212

R. BIMBOT

et al.

magnitude of cross sections observed for Fr isotopes in “C-t- 2*‘Bi reactions 31- 33). Therefore, two processes have to be considered (table 2): (a) The transfer of a Be fragment from projectile to target, followed by the evaporation of neutrons (i.e. ‘Be-n, ‘Be-2n, sBe-3n for ” ‘Fr production), or (b) a compound-nucleus formation followed by the evaporation of an a-particle and two or three neutrons which would lead to the same nucleus. The angular distribution resulting from this last mechanism would present a peak at an angle ernBx> 10” because of the impulse given to the recoiling compound nucleus by the a-evaporation. An estimation of 8,,, can be made by using the relation (02> = 2( Vi)/3V& adapted from ref. 34) in which 0 is the recoil angle of the nucleus after a-evaporation relatively to the beam direction, in the lab system, (tJ2) is the average value of 0*, (J(0*) must be close to e,,,), V,, is the recoil velocity of the compound nucleus before emitting the a-particle, V, is the recoil velocity communicated to the recoiling nucleus by the a-evaporation. This equation corresponds to an isotropic evaporation of the a-particle, and the effects of neutron evaporation are neglected. If one assumes an a-energy equal to 20 MeV, and a recoil energy of 4 MeV for the compound nucleus, the value found for J(e*> is 15”. This value is close to the experimental angle e,,, = 17”, and the corresponding mechanism cannot be excluded on this basis. The distinction between the two possible processes (a) and (b) is made by means of the recoil range values which have been determined for the angle @,,, = 17”. If the involved mechanism is (b), the mean recoil energy of the residual nucleus EcN(Omax) can be calculated, and is equal to

ECN(emax) = Ei

mi mncos*e,,,. ("ifmJ2

In this equation, Ei and mi are the incident projectile energy and mass, and m, and ~1, are the masses of the target and residual nucleus after evaporation, respectively. This calculated value ECN(tJmax)can be compared to the recoil energy ER(@max) determined from the experimental ranges at the angle 0,,, (table 4). The result of this comparison is shown in fig. 13 where the ratio ER(O,,,)/Ec,(O,,,) is plotted against incident energy in the lab system for 21‘At and ‘“At and for 8,,, x 17”. The uncertainties on these ratios are shown on the figure, and the good precision obtained comes from the fact that it was possible to compare the range of the At nucleus to the range of another isotope produced through a compound-nucleus process. Both being measured with the same technique, the unce~ainty in the ratio is reduced. If the involved process were (b) the ratio would be constant and equal to I. The observed ratio is a decreasing function of incident energy and such a curve is a characteristic feature of transfer reactions, observed by several authors ‘, lo* “* 35) for the ratio of the ex~riment~ projected range to the calculated value corresponding to a total momentum transfer. The observation of a ratio higher than unity, at low inci-

TRANSFER

REACTIONS

213

dent energies, is typical and related to the backward emission of the projectile residue after transfer. Therefore, the results of range measurements show unambiguously that the peaks observed at 17” in angular distributions correspond to the transfer, from the projectile “C to the target (l”Au, “‘Bi) of a Be nucleus. The kinematic analysis

o*56u 70

Fig. 13. Variation

80

of ‘ER/ECN(Omax) for 211At and ‘loAt incident energy (see text). 0

El& ( MeV) produced

: ‘llAt;

4

90

through

‘*C+Bi

reactions

versus

: * 1“At.

was applied to this mechanism, for different Be isotopes and showed that, for each case, the ‘Be transfer followed by the evaporation of two or three neutrons was in good agreement with the experimental data. The calculated excitation energies E,* varied from 19 &-5 to 24 + 5 MeV in the case of 211At, the energy needed to evaporate two neutrons from the intermediate 21‘Fr isotope being between E&, = 15 MeV and E:,, = 24 MeV. In the case of 21‘At, for which E,$,, = 24 MeV and Ez,, = 32 MeV the values found for EE for incident energies of 89 and 77 MeV were equal to 25+ 5 MeV and 34+ 5 MeV respectively. The ‘Be -(3 or 4n) mechanism were excluded, a deficit of about 10f5 MeV appearing in the energy balance, but the ‘Be - (n or 2n) mechanisms could not be excluded on this basis. Nevertheless, the particular structure of the “C nucleus makes it very probable that the involved mechanism is a *Be transfer. 5.4. INFLUENCE FUNCTIONS

OF INCIDENT ENERGY: OF At ISOTOPES

DECOMPOSITION

OF

EXCITATION

With the help of the angular distributions, the cross section measured at each incident energy in the case of a Bi target can be divided into several components corresponding to the different mechanisms involved. Therefore, the excitation functions of At isotopes can be decomposed into the excitation functions of each particular mechanism. This decomposition has already been done for Bi excitation functions in the case of a gold target, and is not necessary for Tl isotopes. The result of this decomposition for the reactions “C+ 2ogBi + At is shown in fig. 3. The situation is about the same for the three At isotopes: the first mechanism

R. BIMBOT et al.

214

responsible for the production of a given isotope is the (CN, xn) process, followed by the ‘Be-xn ~ont~bution which becomes pr~ominant when the CN process becomes small. At a higher energy the contributions of 2p transfer and a-transfer appear which have been summed in the case of 211At. It is interesting to note that the apparently smooth excitation function of ‘llAt is in fact due to the sum of several contributions. 6. Excitation functions for CL and *Be transfers 6.1 a THE ‘Be TRANSFER

The transfer of a ‘Be nucleus can be followed by the evaporation of a certain number of neutrons. To obtain the total *Be transfer cross section, one has to sum the *Be-n 8Be-2n ‘Be-3n, etc., contributions. The angular distributions observed for 204Bi’in the case of a gold target show that the ‘Be-n mechanism is negligible, the excitation energy given to the “‘Bi nucleus resulting from the transfer of a ‘Be nucleus being sufhcient to evaporate two neutrons. If one makes the assumption that the situation is the same in the case of a Bi target, the 8Be transfer cross section is the sum of the 8Be-2n, 3n and 4n contributions, as shown in fig. 14A. The resulting cross section increases with incident energy, the value of 90 + 20 mb corresponding to 89 MeV. This high value of the cross section for *Be transfer is a very surprising fact, and seems

u

60

Eiab (MeV)

Fig. 14. Excitation functions for sBe transfer. (A) In the case of a Bi target, the cross section of *Be transfer is obtained by summing the cross sections for the mechanisms ‘Be-2n, aBe-3n and *Be-4n. (B) In the case of a Au target the cross sections for production of Bi isotopes are summed, when the (‘%, xn) mechanism is excluded. The resulting curve includes the possibility of (W, axn> reactions, the a-particle being evaporated.

TRANSFER

REACTIONS

215

to be difficult to explain with the present theories of transfer reactions. One can remark that this result is obtained under the assumption that the shoulder in the angular distribution of “‘At is due to a 8Be-4n mechanism. The range value for 89 MeV and 17” corresponds to 4.45 MeV and is difficult to interpret. However the total a-evaporation from 20gBi+ i2C reactions is only 15 mb (see table S), and this effect cannot change significantly the magnitude of the 8Be transfer cross section (90 mb). In the case of a ’ g7A~ target, the cross section for 8Be transfer is given by summing the cross section of Bi isotopes whenever a (“C, xn) mechanism is excluded (see fig. 8). The resulting curve is shown in fig. 14B and has the same shape as the one in fig. 14A, the magnitude of the cross section being now equal to 160& 30 mb at 89 MeV. However, this value includes the contribution of ~-evaporation from a compound nucleus. The corresponding cross section was determined by the measurement of cr-particles 36), and is equal to 30 mb. Therefore, the cross section for 8Be transfer amounts to 130 + 30 mb, a value which seems higher than in the case of a Bi target, although the uncertainties are large. This can be explained in two ways: (i) The transfer of 8Be in gold must be favoured by the Q-value which is equal to -25 MeV in the case of the reaction r2C+20gBi -+ ‘r7Fr+ 01and -12.5 MeV for the reaction 12C+‘97A~ -+ “‘Bi+ a. The Coulomb energy balance being about the same for both targets, the Q-effect must be predominant, the less endoergic transfer being favoured 37S3” ). (ii) The measured cross section corresponds to a transfer reaction followed by the evaporation ofneutro~~s. If another de-excitation mode takes place (i.e. fission of the intermediate nucleus) the residual At or Bi isotope will not be observed. This de-excitation by a fission process could take place for a 2t ‘Fr intermediate nucleus, and would be less probable for a 205Bi intermediate nucleus. This effect, which is not a difference in the transfer process itself, would explain as well a higher cross section in the case of an Au target. 6.2. ALPHA TRANSFER

The situation is less clear as far as a-transfer is concerned. 6.2.1. Au target. In the case of a gold target, an upper limit can be set for atransfers by summing the cross sections of Tl isotopes (see fig. 8). The value obtained is certainly too high because part of the production of 199Tl and ’ 98Tl must occur through a 2p transfer as in the case of a Bi target. Nevertheless, it is interesting to observe that the magnitude of the cross section is equal to 85 mb at 89 MeV, that is to say smaller than the cross section for 8Be transfer. 6.2.2. Bi target. In the case of a Bi target, the a-n process cannot be observed, and the main result of the study is a relatively strong indication that the a-2n mechanism is responsible for the peak at 40” at an incident energy of 89 MeV (the 3He-n mechanism being neglected for structure reasons), and that the a-3n mechanism has a negligible cross section. The comparison with the case of a gold target shows that the a-n mechanism has a low cross section at 89 MeV, so that the value of 36 mb found

216

R. BIMBOT et al.

for the u-2n cross section is a good estimate of the a-transfer cross section at this energy. 7. Comparison with direct a-particle measurements In the previous sections it was assumed that, when the kinematic analysis could not decide between 3He and 4He transfer on the one hand and ‘Be and *Be transfer on the other hand, the transfer of 4He or *Be was chosen because of the 3u structure of the “C nucleus. This assumption will be justified in this section. When a *Be is transferred from the projectile to the target, the projectile residue is an a-particle, and reciprocally when an 4He substructure is transferred, the residue is a *Be nucleus. Because of its instability, this last nucleus decays very rapidly into two a-particles. The lifetime of 8Be (2 x 10-l 6 s) is long enough to allow the application of the two-body kinematics (sect. 3) but too short to allow the measurement of *Be as an entity with the usual techniques. Therefore, the projectile residues after 01 or *Be transfers will be a-particles. The measurement of the angular distribution of the a-particles emitted in “C + Au and “C + Bi reactions have been performed 36, 3“) and a-particles produced through a non-compound-nucleus mechanism have been observed with a high cross section for incident energies of 80 to 120 MeV. The results are summarized in table 8. TABLE 8 Cross

sections for evaporated

Reaction

Cl-B1

C+Au

Comparison

and direct a-particles in 12C+Z09Bi and 1*C+197A~ reactions

Lb (MeV)

a,_ cypp(mb)

126 105 85 126 86

73 30 15 120 29

between the measured direct a-particles

%I

(mb)

850*150 410*100 180* 50 830&150 200f 50

oDLDl our results (mb)

160525 260&50

and the values derived from this work.

The origin of such a-particles was not explained until now, and it is of interest to compare the cross sections and angular distributions with the present results. 7.1. CROSS SECTIONS

The cross section for direct a-particles at 89 MeV was deduced from our experimental results in the following way: the cross section for ‘Be transfer was added to twice the value of the cross section for a-transfer (each of the residual *Be decaying into two a-particles). The resulting values are: 0R(209Bi) =

90+2x36

= 160+30 mb,

a,(19’Au) < 130+2x 83 = 296k60 mb.

TRANSFER

REACTIONS

217

If it is assumed that the production of ’ 98T1is due to a 2p-n mechanism, as in the case of 21‘At from a Bi target the cross section for a gold target is: a,(i9’Au)

= 130+2x 65 = 260+_50 mb.

These values are listed in table 8 and one can see that the agreement is good with the direct measurements. 7.2. ANGULAR

DISTRIBUTIONS

The knowledge of the angular distributions and range distributions of 210-211At isotopes for each recoil angle makes it possible to calculate the angular distributions of the a-particles correlated with a and ‘Be transfers, for the reactions “C+ Bi. (i) The reactions ‘Be-2n and ‘Be-3n lead to a Fr nucleus and an a-particle. The angular distribution of the a-particle is directly deduced from the Fr distributions which are the same as the observed 2lo* ” 'At distributions (peaks at 17”). (ii) At the energy of 89 MeV, the a-transfer leads mainly to 211At (mechanism a-2n) as was mentioned earlier (subsect. 6.2.2) and the angular and range distribution of ‘llAt can be converted into 8Be angular distribution. The angular distribution of the a-particles from ‘Be decay is supposed to be similar to the ‘Be angular distribution, the angle between two a-particles being equal to 1” if the decay occurs from the ground state of ‘Be and to 15” if it occurs from the first excited level. The magnitude of the differential cross section is only multiplied by 2. The experimental distributions of At were therefore converted into the cm. system 12) and the derivation of aangular distributions in the c.m. system was then straightforward. The angular distribution of the a-particles in the lab system is about the same as in the c.m. system, and no correction was made to account for the low velocity of the c.m. The results are presented in fig. 15 where the angular distribution (da/dS2(8)) of the a-particles resulting from (i) a *Be transfer, and (ii) an a-transfer are added to give the points with error flags, which are compared to the experimental data from Britt and Quinton 39). 0 ne can see that the agreement is very good at all angles, the shape of the curve and the magnitude of the differential cross sections being the same. This very good agreement confirms the fact that a-particles and ‘Be nuclei are transferred from 12C to Bi with a large cross section. The fact that the total cross section observed for direct a-particles can be explained by transfer reactions indicates that the break-up of “C into three a-particles, none of them being absorbed by the nucleus, represents a small contribution, if any, in the production of these a-particles at 89 MeV. At higher energies for which the direct a-particle cross section is much larger (800 mb at 120 MeV), the question is still open. The probability of a and ‘Be transfer probably increases, but it would be interesting to repeat the present experiments to see if the production of a-particles can still be explained with transfer reactions alone.

218

R. BIMBOT et al.

Fig. IS. Angular distribution of direct tc-particles emitted in 12C+zogBi reactions at 85 MeV. l : from Britt and Quinton measurements 3g); A: deduced from the At angular and range dist~butions (present work). The solid line represents the ~ntribution of the a-particles resulting from a 8Be transfer, and the dotted line is the contribution of cc-particles from an a-transfer. The sum of these two contributions is represented by the triangles with error bars.

8. Conclusion

The main result of this work is the discovery of a large cross section for *Be transfer in reactions of “C with heavy nuclei (Au, Bi). This transfer, followed by the evaporation of two, three and four neutrons is the mechanism responsible for the production of ‘03*2o2z201Bi in the case of a gold target, and of 21‘*2’ 4, 213Fr in the case of a bismuth target, the Fr isotopes decaying into 2111‘lo, “‘At which are the observed nucleides. When several processes are involved in the production of a given residual nucleus, the 8Be transfer can be isolated thanks to the angular distribution, the corresponding peak being situated at the angle 8,,, = 17” in the lab system. Careful measurements of the recoil range showed clearly that this peak must be att~buted to non-compound-nucleus reactions, the variation of the recoil energy with projectile energy being typical of a transfer reaction. The sum of the cross sections corresponding to the mechanisms 8Be-2n, *Be-3n, 8Be-4n is the total cross section for ‘Be transfer. A large value is obtained for both targets (90 mb for Bi; 130 mb for Au, at 89 MeV). Furthermore a significant cross section was found for a-transfer reactions although it was not possible to determine precisely the corresponding cross section. The approximate value in the case of a Bi target is 30 mb at 89 MeV. For a gold target an upper limit of 85 mb was found. These two types of transfer (a and ‘Be transfer) are associated with the emission of cl-particles which are the residues of the projectile. (In the case of an a-transfer, the residue is *Be which decays into two a-particles.) These direct cl-particles have been observed by several authors ’ 6*3“) wit’ h 1ar ge cross sections. From the angular distributions and range measurements of residual nuclei obtained in this work, the

TRANSFER

REACTIONS

219

angular ~stribution of the complementary a-particles was evaluated and compared to the experimen~l results for an incident energy of 89 MeV. The good agreement obtained for the shape of the angular distributions and the magnitude of the cross section constitutes additional evidence for the assumed mechanisms. Moreover the present work gives the explanation of the origin of these direct c+particles, which was not clear up to now. We thank the cyclotron operating crew for their cooperation. We are particularly grateful to C. Cabot, C. Deprun and J. L. Reyss who helped in the experiments, to J. M. Alexander and M. Lefort for many interesting discussions, and to N. T. Porile for careful reading of the manuscript. References 1) J. M. Aiexander, in Nuclear chemistry, ed. L. Yaff6 (Academic Press, New York) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) 31) 32) 33) 34) 35) 36) 37) 38) 39)

J. Galin, B. Gatty, M. Lefort, J. PBter, X. Tarrago and R. Basile, Phys. Rev. 182 (1969) 1267 V. V. Volkov, G. F. Gridinev, G. N. Zorin and L. P. Chelnokov, Nucl. Phys. Al26 (1969) 1 J. A. McIntyre, T. L. Watts and F. C. Jobes, Phys. Rev. 119 (1960) 1331 R. Kaufmann and R. Wolfgang, Phys. Rev. 121 (1961) 192 E. Lozynski, Nucl. Phys. 64 (1965) 321 J. M. Alexander and L. Winsberg, Phys. Rev. 121 (1961) 529 H. Kumpf and E. D. Done& JETP (Sov. Phys.) 17 (1963) 539 R. 1. Morse and I. L. Preiss, Phys. Lett. 20 (1966) 509 P. D. Croft, J. M. Alexander and K. Street, Phys. Rev. 165 (1968) 1380 R. Bimbot, D. Gardes and M. F. Rivet, Phys. Rev. C4 (1971) 2180 D. Gardes, These de 3eme Cycle, Orsay, 1970 L. C. Nortbcljffe, Phys. Rev. 120 (1960~ 1744 L. C. Northcliffe and R. F. Schilling, Nucl. Data Tables A7 (1970) 233 R Bimbot, D. Gardes and M. F. Rivet, rapport interne IPNO RC 71-02 (1971) R. W. Hoff, UCRL 2325 (1953) A. Rytz, Helv. Phys. Acta 34 (1961) 240 Y. Le Beyec, These, Orsay, 1966 W. L. Croft, B. G. Petterson and J. H. Hamilton, Nucl. Phys. 48 (1963) 267 R. Bimbot, These, Orsay, 1966 C. M. Lederer, J. M. Hollander and I. Perlman, Table of isotopes 6th ed. 1967 R. E. van de Vijver, Physica 29 (1963) 1 B. Jung and G. Anderson, Nucl. Phys. 15 (1960) IO8 R. Bimbot, C. Deprun, D. Gardes and Y. Le Beyec, to be published R. Bimbot and D. Gardes, to be published R. Bimbot, M. Lefort and A. Simon, J. Phys. 29 (1968) 563 M. F. Rivet, These de 3iime Cycle, Orsay, 1971 P. D. Croft and K. Street, Phys. Rev. 165 (1968) 1375 J. M. Alexander, unpublished data R. Bimbot, D. Gardes and M. F. Rivet, to be published Y. Le Beyec, M. Lefort and M. Sarda, preprint; Nucl. Phys., to be submitted R. A. Cough, Ph.D. thesis, McMaster University, 1970 J. C. Bell, I. S. Grant, K. Gregory and R. J. Williams, Int. Conf. on statistical properties of nucIei, Albany. Ed. J. B. Garg (Plenum Press, New York, 1972) G. N. Simonoff and J. M. Alexander, Phys. Rev. 133 (1964) B104 H. Delagrange, A. Fleury, F. Hubert and G. N. Simonoff, Phys. Lett. 37B (1971) 355 B. Gatty, M. Lefort, X. Tarrago and C. Brun, unpublished data J. Galin, These de Doctorat d’Etat, Orsay, 1971 R. M. Diamond, A. M. Poskanzer, F. S. Stephens, W. J. Swiatecki and D. Ward, Phys. Rev. Lett. 20 (1968) 802 H. C. Britt and A. R. Quinton, Phys. Rev. 124 (1961) 877