Volume 189, number 3
PHYSICS LETTERS B
7 May 1987
T A R G E T M A S S D E P E N D E N C E O F T H E AVERAGE L I N E A R M O M E N T U M T R A N S F E R T. BATSCH a, j. B L A C H O T b, Q. C H E N c, j. C R A N ~ O N b, M. F A T Y G A c, A. G I Z O N d, j. JASTRZI~BSKI e, H. K A R W O W S K I ~,l, W. K U R C E W I C Z a, A. LLERES d, T. MR(~Z ~ 2, L. PIElqKOWSKI e, P.P. S I N G H c, S.E. V I G D O R c and I. Z Y C H O R " " Institute of Experimental Physics, Warsaw University, PL-00681 Warsaw, Poland b Centre d'Etudes Nuclkazres, F-38041 Grenoble, France Indiana Umverslty Cyclotron Facthty, Bloomington, IN 47405, USA d Instttut de Sciences Nucl~atres, F-38026 Grenoble, France Heavy Ion Laboratory, Warsaw Unwerszty, PL-O0681 Warsaw, Poland
Received 16 July 1986
The average transferred hnear momentum m nuclear reachons induced by 3He, 4He, 14N, and 2°Ne projectiles on Co, Cu and Ag targets was determined by thick-target-thick-catcher recoil range techmques for bombarding energies between 10 AMeV and 90 AMeV A comparison with results obtained from fission fragment angular correlations indicates a strong target mass dependence of the linear momentum transfer.
During the last few years considerable effort has been devoted to studies of the hnear m o m e n t u m transfer in light- and heavy-~on induced reactions (see refs. [ 1 - 3 ] for recent reviews of the experimental data). The work of Saint Laurent et al. [4] and Galin et al. [ 5 ] has indicated that the useful observables in linear m o m e n t u m studies are the average and max~m u m m o m e n t u m transfers from the projectile to heavy reacUon residues. These quantities have been extensively stu&ed using the method of angular correlation between fission fragments. At present a large body of systematic data on the average m o m e n t u m transfer for heavy fissionable nuclei is established [1-3,6] as a function of projectile mass and bombarding energy. The average linear m o m e n t u m transfer characterizes the global features of the projectile-target interaction. Its changes with the mass of the projectile and with bombarding energy may give some insight into the evolution of the reaction mechanism and perhaps reveal new phenomena expected to occur [7] Present address' Department of Physlcs, Umverslty of North Carohna, Chapel HIll, NC 27514, USA 2 On leave from the Institute for Nuclear Research, gw~erknear Warsaw, Poland. 0370-2693/87/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
m the energy range between 10 and 100 MeV per nucleon. The dependence of the average m o m e n t u m transfer on the target mass can give a d d m o n a l information about the projectde-target interaction. Recent calculations for central colhsions [ 8 ] indicate that, for example in 85 A MeV t2C induced reaction the linear m o m e n t u m transfer should increase by about a factor of two when the target mass changes from 60 to 238. Only a 6% increase is expected for this reaction from the "trivial" effect, due to the Coulomb barner difference. Expenmental data on the hnear m o m e n t u m transfer for light and intermediate-mass targets are much less abundant than for fissile elements. Investigations of the recoil velocities by the time of flight methods [ 9,10 ] are at present limited to the fusion like products. The method of the invariant cross section of evaporated particles [ 5 ] has not been applied systematically. In our previous work [ 11 ] we have employed the classical method of recoil range measurement for radioactive reaction products [ 12], m order to deduce the average hnear m o m e n t u m transfer m 4He + 59Co reacUons. The main assumption made was 287
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that the radioactive reaction products constitute a representative (statistical) sample of the whole population of heavy reaction residues, so that the average quantities determined for this sample are close to the average for the whole population. We refer to ref. [ 11 ] for more detailed discussion of this method. In the present letter we present the ensemble of average linear momentum transfer data gathered by us using the recoil range method. The systematics which emerge show a clear target mass dependence of the measured quantity. This dependence is further supported If the recoil range data for non-fissile targets are compared with results obtained for heav~y targets by the method of angular correlation between fission fragments. The experimental data were obtained using a hghtion beam from the Indiana University Cyclotron Facility and heavy-ion beam from accelerators in CERN (SC) and Grenoble (SARA). The main part of the experiment involves a determination of thicktarget recoil ranges [ 12 ] of the radioactive reaction products along with their production cross sections. Stacks of natural Co, Cu or Ag targets, together with aluminium, capton or carbon forward and backward catchers and beam energy degraders were irradiated for periods from 10 min up to a few hours. Up to seven targets (corresponding to seven different bombarding energies) were used in 3'4He bombardments and up to three targets were used in the irradiations with heavier ions. The counting of the samples started about 15 min after the end of bombardment and lasted for several months. The beam energy degradation along the stack was calculated from the rangeenergy tables of Hubert et al. [ 13 ]. The target thickness for the lowest bombarding energies of 14N and 2°Ne projectile corresponded to about 1.5 A MeV beam energy degradation in the target (Cu thickness of about 15 mg/cm2). The influence of the target thickness on the extracted average values of the transferred linear m o m e n t u m was estimated to be smaller than 5% for these ions. For light projectiles 5-6 mg/cm 2 thick targets were used with no appreciable beam energy degradation in the target. At 85 A MeV ~2C bombarding energy additionally thin-target-thin-catcher technique was used, employing natural Y and enriched ~2Sn targets. The details of this experiment were previously described [14]. 288
7 May 1987
Fig. 1 presents an example of the forward recoil ranges and observed cross sections of the radioactive products as a function of AA, the difference between target mass and the mass of a product for ~4N- and 2°Ne-induced reactions on a Cu target. A similar pattern of the recoil ranges was previously observed and discussed for t2C-induced reactions on Cu in ref. [15]. The backward recoils for t4N and 2°Ne reactions up to 50 A MeV bombarding energy were unmeasurable within the sensitivity of our experimental technique (forward to backward ratio, F/B>f 80). This is in agreement with the data of ref. [ 15 ] for ~2C projectile. For light projectiles the backward recoils were also small. In order to deduce the average linear momentum projected on the beam direction of heavy reaction residues, the forward recoil ranges measured were converted to velocities, vii, with the help of rangeenergy tables [ 16]. As was stated in ref. [ l l] this procedure involves an approximation in case of strongly side-peaking recoils because oil deduced from stopping distance projected on the beam direction (as measured in this work) is not precisely the same as oil deduced from the projection of the velocity of all recoils. The angular distributions of heavy recoils were measured for selected beam energies for 4 H e + C o reaction [11 ] and for some 12C induced reactions at 85 A MeV bombarding energy [ 14]. On the basis of these data it was estimated that the correction for angular distribution would decrease the average value of the transferred linear m o m e n t u m by about 15% at ~2C energy of 85 A MeV and less for lower heavy-ion energies. As we do not dispose of the angular distribution data for all target-projectilebombarding energy combinations, this correction (which always decreases the deduced values of ( o , ) ) was neglected in the results presented below. Fig. 2 presents, in the representation proposed in ref. [4], the ensemble of data on the average transferred linear m o m e n t u m deduced from our recoil range measurements for targets with mass number around 60. The systematics presented here essentially confirm the energy and projectile dependence of the linear momentum transfer obtained [ 1-6] from the angular correlation of the fission fragments for heavy targets. On a per nucleon basis the light projectiles (3He, 4He) are much more efficient momentum transfer agents than heavier ions. The
Volume 189, number 3
PHYSICS LETTERS B i
i
7 May 1987
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Fig 1. Example of the forward recollranges (FW) and observed cross section of the radloacuve products as a function ofAd =A,.,Bc,--Ap~od.ct for the '4N + Cu and 2°Ne + Cu reactions. The indicated bombarding energy ( m MeV/nucleon) corresponds to the m~ddle of the target.
present data seem to indicate also possible small differences in m o m e n t u m transfer between projectiles heavier than an alpha particle (e.g. 6Li versus 14N and 2°Ne); such differences have not been observed for fissible targets but are suggested by recent recoil time of flight measurement~ [ 18] a n d thin-target recoil range data [ 19 ]. The data for targets with mass n u m b e r A ~ 60 when compared with A ~ 240 targets suggest a rather strong
target mass dependence of the average transferred m o m e n t u m . However, different methods are used for the measurements in these two mass regions a n d a systematic difference arising from the different techniques cannot be ruled out a priori. Therefore the measurements of the linear m o m e n t u m transfer by the recoil range method were extended to the heavier target mass. The data for the reaction 4He + natAg shown in fig. 2 for large energy range confirm the target mass dependence for this projectile. Similarly, the target effect was observed by the rec011 range technique for heavier projectiles: ~4N at 30 A MeV and
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F~g. 2. The average transferred hnear momentum data obtained from the recoil range measurements (shown m the representation proposed m ref. [4]) for A~ 60 targets and for the 4He+ "tAg reaction. The 6Ll+Fe data are from ref. [ 17], 4He+Co and ~He+Co up to 50 A MeV from ref. [ 11 ]. Other data points are from the present work. The indicated vertical error bars for t4Nand -~°Ne-mducedreactions correspond to the assumption that the reco~hngmass ~sequal to the mass of the compound nucleus (upper hmlt) or the target mass (lower hmlt). This is eqmvalent to the assumption of the complete or incomplete fusion reaction mechamsm The horizontal error bars reflectthe target thickness 289
Volume 189, number 3
PHYSICS LETTERS B
highly fissile elements. The general character o f the m o m e n t u m transfer dependence on the b o m b a r d i n g energy and on the mass o f the projectile is similar to that observed for heavy targets, with a possible exception that the projectile d e p e n d e n c e m ay persist also for ions heavier than alpha particles. A strong d e p e n d e n c e o f the linear m o m e n t u m transfer on the target mass is observed.
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7 May 1987
o4 Stimulating discussions with J. Alchehn, C. Gregoire, H. Oeschler and V. Viola are gratefully acknowledged.
I
5
Co Cu
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Y Ag Sn I 5
I 6
U
A I/3 target
Fig 3 Average hnear momentum transfer (in beam momentum units) as a function of target mass The 4He+U point is from refs. [3,20], 14N+U from ref [6] and ~2C+U from ref [21] The ~2C+Cu point is the average value from the present work and ref [22]. The sohd hnes are to grade the eye ~2C at 85 A MeV. In fig. 3 the target mass dependence o f the average linear m o m e n t u m transfer is shown for selected projectiles and b e a m energies. To our best knowledge there is at present no m o d e l calculation o f the target d e p e n d e n c e o f the average (i.e., integrated o v e r all impact p a r a m e t e r s ) linear m o m e n t u m transfer for ions heavier than an a - p a r ucle. Th e calculation [23] based on one- and twobody dissipation for 4He ions o f 35 A M e V b o m barding energy predicts 20% increase between Co and U targets in good agreement with the experimental data. F o r heavier ions m o d e l calculations [ 8 ] based on the B o l t z m a n n - U e h l i g - U h l e n b e c k ( B U U ) approach show a strong target mass d e p e n d e n c e o f the transferred linear m o m e n t u m but are at present h m i t e d to small impact parameters, i.e., central collisions. In summary, the data presented in this letter extend to lighter target masses the systemaUc o f average linear m o m e n t u m transfer, previously known only for
290
[ 1] V E. Viola Jr, lectures presented at XVth Masunan Summer School on Nuclear physics (Mlkolajkl, Poland, 1983) [2] B Tamam, lectures presented at XVlth Masunan Summer School on Nuclear physics (MlkoIajkl, Poland, 1984) [3] K. Kwlatkowskl et al., Proc. III Workshop on Nuclear dynamics, ed V. Viola (Copper Mountain, CO, 1984) [4l F. Saint Laurent et al, Phys Lett B 110 (1982) 372 [5] J Galan et al ,Phys Rev. Lett 48 (1982)1787 [6] M. Fatyga et al, Phys. Rev. Lett. 55 (1985) 1376. [7] D K Scott, Nucl Phys A354 (1981)375 [8] J Aichehn, Phys. Rev C 33 (1986) 537. [9] Y. Chan et al, Phys Rev C 27 (1983) 447. [10] H Morgenstern et al, Phys Lett B I13 (1982)463 [ 11 ] J Jastrzgbskl et al, Phys Lett B 136 (1984) 153, Phys. Rev C 34 (1986) 60. [12] J.M Alexander, m. Nuclear chemistry, Vol 1, ed L Yaffe (Academic Press, New York, 1968) p. 273 [13] F Hubert et al., Ann Phys (Pans) 5 (1980) S 1-214 [ 14] A Lleres et al ,Z Phys A 312 (1983) 177 [15] L. Kowalsklet al, Phys Rev Lett 51 (1983) 642; J. Cummmg, private communication [16] L C. Northchffe and R F Schilling, Nucl Data Tabl. 7 (1970) 233 [ 17 ] J Jastrzgbska et al, Phys Rev. C 19 (1979) 724. [18] G.S.F Stephansetal, Phys Lett B 161 (1985) 60 [ 19] J Blachot et al, Z. Phys A 321 (1985) 645. [20] V.E Viola Jr, private communlcatxon. [21]F J Mhller, PhD thesis, Ruprecht-Karls-Umversxtat, Heidelberg (1981), unpubhshed, U Lynen et al, Nucl Phys A 387 (1982) 129c [22] T. Lund et al, Z Phys A 306 (1982) 43. [23] C Gregolre and F Scheuter, Phys Lett. B 146 (1984) 21