Tensor analyzing powers for Li7 breakup

PHYSICAL REVIEW CVOLUME 52, NUMBER 6 Tensor analyzing powers for Li breakup DECEMBER 1995 N. J. Davis, C. H. Shepherd-Themistocleous, *A. C. Shotter, T. Davinson, D. G. Ireland, ~K. Livingston, ~ E. W. Macdonald, ~R. D. Page, ~P. J. Sellin, and P. J. Woods Department ofPhysics and Astronomy, University ofEdinburgh, Mayfield Road, Edinburgh EH9 3JZ, Scotland N. M. Clarke, G. Tungate, J.A. R. Griffith, S. J. Hall, O. Karban, ~I. Martel-Bravo, **and J. M. Nelson School of Physics and Space Research, University ofBirmingham, Edgbaston, Birmingham B152TT, England K. Rusek Soltan Institute for Nuclear Studies, Zaklad I, Hoza 69, 00 68I Warsaw, Poland J. Gomez-Camacho Departmento de FAMN, Facultad de Fisicas, Universidad de Sevilla, Aptdo. 1065, 41080 Sevilla, Spain (Received 5July 1995) Differential cross sections and Tzo and T20 analyzing powers have been measured for 70 MeV Li breakup into the aparticle plus triton channel, on a'Sn target. Measurements were made for both continuum breakup and sequential breakup via the 4.63 MeV state in Li. The T20 data for the continuum breakup do not agree with asemiclassical Coulomb model, indicating that the breakup at small angles does not proceed solely via a Coulomb force. The data generally show asomewhat better agreement with continuum discretized coupled channels calculations, indicating the importance of the nuclear force and channel coupling in the reaction mechanism. PACS number(s): 25.70.Mn, 24.10.Eq, 24.70.+s I.INTRODUCTION The nplus triton cluster structure of Li results in alarge breakup yield to these fragments. Adetailed study of the breakup is of interest because two mechanisms have been observed [1— 3], sequential breakup following excitation of the Li, in particular to the 4.63MeV 7/2 state, and breakup into the aparticle plus triton energy continuum. In addition to the nuclear physics interest, breakup reactions may also be used to infer low energy photocapture cross sections necessary for an understanding of the creation of Li in the big bang standard model. It is difficult to obtain the photocapture data directly at the low relative energies which are most important because Coulomb repulsion between the uparticle and the triton results in very small cross sections. ACoulomb breakup reaction may be used instead, but it is essential to determine the importance of the nuclear force in the reaction mechanism, as any contribution from it may invalidate the inference of photocapture cross sections Present address: CERN, CH-1211, Geneva, Switzerland. ~Present address: Department of Physics, University of Glasgow, Glasgow, UK. ~Present address: General Accident Insurance, Perth, UK. ~Present address: Department of Physics, University of Liverpool, Liverpool, UK. Present address: Department of Physics, University of SheNeld, Sheffield, UK. ~Present address: Velice 26, 37351 Driten Czech Republic. Present address: Departmento de FAMN, Facultad de Fisicas, Universidad de Sevilla, Aptdo. 1065, 41080 Sevilla, Spain. The continuum breakup yield is strong at forward angles and falls off rapidly at larger angles [2]. The continuum breakup can be explained by the differential strong nuclear force between the target and fragments [5], in an nparticle plus triton cluster description of Li. However, the Coulomb force becomes important at extreme forward angles [6]. Differential cross sections for the Li continuum breakup on a'Sn target have previously been measured and found to agree at small angles with acalculation which assumes a pure Coulomb force [2,3,6,7]. The cross sections are calculated using asemiclassical approximation [8] in which the motion of the projectile along ahyperbolic trajectory is parametrized in the framework of first order perturbation theory by dimensionless orbital integrals. In order to determine the differential cross section the reduced transition probability as afunction of relative energy is required. This may be obtained [9]from data on the inverse fusion reaction [10].Thus the semiclassical Coulomb calculations of differential cross section require input based on other experimental data. Semiclassical calculations of analyzing powers, however, do not rely on additional experimental data. This is because the reduced transition probability is independent of spin substate and therefore cancels. Semiclassical Coulomb calculations have been successfully applied to Li elastic and quasielastic scattering Tzo analyzing powers [11].In the current work semiclassical Coulomb calcualtions are developed for breakup analyzing powers. The analyzing powers may be more sensitive to contributions from different forces than the differential cross section because they depend on interference terms between scattering amplitudes. Acomparison of calculations with the data therefore provides an additional test of the importance of the different forces. In particular, if the Coulomb force dominates, deviation of the continuum 0556-2813/95/52(6)/3201(11)/$06. 00 3201 0& 1995 The American Physical Society 3202 N. J. DAVIS et al. 52 breakup data from the semiclassical Coulomb calculations could occur for even asmall contribution from the nuclear force in the breakup reaction mechanism. Continuum discretized coupled channels (CDCC) calculations, which include anuclear force, may also be performed to compare with the data. Such calculations have been found to provide avery good description of cross sections and analyzing powers for elastic and inelastic scattering of Li [12— 14].CDCC calculations, involving anuclear force only, have previously been compared with differential cross sections for Li continuum and sequential breakup on a'Sn target [12]. Reasonable agreement was obtained except at the forward angles. An investigation of the effect of the Coulomb force on the sequential breakup was performed by including a Coulomb interaction derived by folding the Coulomb potential between anucleon and the target with the transition densities between Li states. The Coulomb force was found to contribute significantly at forward angles. Asimilar investigation of the effect of the Coulomb force on the continuum breakup was not, however, performed. In the current work CDCC calculations are applied to breakup analyzing powers, providing avery important new test of the CDCC approach. Any breakup process resulting in two fragments is a three-body reaction with two reaction planes defined by the incident particle and the detected fragments. Consequently the choice of coordinate system is generally not obvious, although it is important for the theoretical interpretation of the data that it be as simple as possible, particularly when polarization effects are involved. Clearly the simplest situation corresponds to an experimental arrangement when the two reaction planes nearly coincide (see Sec. IV) and astandard two-body reaction coordinate system can be defined. It should be explained that in the semiclassical and CDCC calculations the underlying three-body reaction is interpreted by means of atwo-body reaction. In order to do this assumptions about the basic reaction mechanism have to be made. These are that the incident Li with spin s=3/2 and projection nis excited to acontinuum or resonant state characterised by spin s'and projection yand that this decays spatially into an nparticle and atriton with arelative angular momentum L, where L+1/2=s', and asubstate mz, where mz+m, =yand m, is the triton spin substate. Only in the case of J=0, when the breakup is isotropic, can the analyzing powers calculated by either inelastic scattering theory be compared directly with the experimental data. Generally, the measured analyzing powers have to be compared with predicted quantities involving polarization transfer coefficients and correlation functions (see Sec. III). The aim of the current work is ameasurement of the Tpp and Tzp analyzing powers for Li breakup, in order to determine the importance of the Coulomb and nuclear forces in the continuum breakup reaction mechanism and investigate the applicability of semiclassical and CDCC calculations. II.SEMICLASSICAL COULOMB CALCULATIONS Tkq (s s Xp~ssk( — 1)' ~.p,slF,sPI' F~P*F~'P y6 y6 where n' =u+ qand the usual notation k= /2k+ 1is used. For aspin zero target and residual nucleus, this expression is simplified because P= 8=0. If the motion and Coulomb interaction between the projectile and target can be described semiclassically, it may be parametrized in the framework of first order perturbation theory by dimensionless orbital integrals Rz (H, j) [8].The potential used in the time-dependent Schrodinger equation for the particle motion may be expanded in terms of components for different multipoles kwith projections p, .The orbital integrals are related to the coefficients of this expansion and depend only on the scattering angle 0and the dimensionless adiabaticity parameter j.The latter depends on the energy Fof the transition and the beam energy Ez if both are in units of MeV by ZZA F( A~ 1+— I, 12.7E~' (A, ]'(2) where Zis the atomic number, Ais the mass number, and the suffixes pand tindicate projectile and target, respectively. Using the semiclassical approach, the scattering amplitude for Coulomb excitation to astate with spin s', may be expressed in terms of the orbital integrals by [16] (sZs') F=— i(— 1)' kX, ,R„(~.C) (3) r( where y, ,is the strength parameter for multipole excitation of order kto afinal ejectile state of spin s'. The target remains in its ground state. Substituting Eq. (3) into Eq. (1) gives A. General formalism Analyzing powers may be expressed in terms of scattering amplitudes Fps where pand 6are the spin substates for the target and residual nucleus. The analyzing powers are given by [15] (s P. skX „(— 1)' (a+q k~( sZs' ~( s' sR~ R), a— qp, +q a— p) TENSOR ANALYZING POWERS FOR Li BREAKUP 3203 where p'=/L+q and the (O, j) dependence of the orbital integrals has been omitted for the sake of brevity. The strength parameter is independent of spin substate and therefore cancels in the expression for the analyzing powers. The analyzing powers for aCoulomb process consequently depend only on the initial and final spins, the multipole of the transition, and the orbital integrals. Coordinate System A: B.Application to Li continuum breakup For application of the calculations to the continuum breakup of Li into the uparticle plus triton channel, the relative motion of the fragments must be assumed to have a single angular momentum. The most significant Coulomb multipole term leading to breakup is an E1 transition, corresponding to L=O and leading to an nparticle plus triton final state which has spin parity 1/2+. Therefore s=3/2, s'=1/2, and X=1. Using Eq. (4) the second rank analyzing powers are calculated in terms of the orbital integrals as Coordinate System H: in in out IR»l'+ IRi-il' — 2IRiof' "2(IR»l'+IRi-tl'+IRiol') 'FIG. 1. Coordinate systems Aand Hused in the semiclassical Coulomb calculations of analyzing powers. +3(Rt~R to — Rt]R~p) 2(IRzzf +IR& —tl +IRiol )'(6) power in coordinate system Hmay be expressed in terms of the second rank analyzing powers in coordinate system Aas v3Rt)R) P~(IR»l'+ IR1—1I'+IR101 ) In order to proceed further with the analyzing power calculations, expressions must be found for the orbital integrals; these are coordinate system dependent. The helicity coordinate system [17],H, was used for the T2p measurements. However, orbital integrals are more readily calculated in a coordinate system [8],A, with the zaxis normal to the reaction plane and the xaxis bisecting incident, k;„, and outgoing, k,„„wave vectors. The coordinate systems Aand Hare shown in Fig. 1.Analyzing powers in Hmay be determined by first calculating them in Aand then rotating to H. The orbital integrals in Acan be expressed in terms of Coulomb excitation functions [8] Ix, which are real and coordinate system independent, such that Tk q=( — 1)~Tk*, (13) results in AA 2— 2220 (14) and consequently Eq. (12) becomes — [T2p+ +6T22cos( 8)] T20 2(15) where the rotation matrix elements Dto~ ((vr +8)/2, vr/2, 37r/2) are functions of the Euler angles [19]for the rotation. It should be noted that the general property of analyzing powers [15], +Ii=i R) 2+v ' Ri0— 0. (9) Substituting Eqs. (10) and (11)into Eq. (15) gives 6I),I) ) cos( 8)— I,t— It 22 To4(I2 +I2 )(16) Substituting Eqs. (8) and (9) into Eqs. (5) and (7) gives second rank analyzing powers in coordinate system A: A T20 2' (10) — +3I»Ii T22= +2(I (tI+, t) Analyzing powers are spherical tensors which transform in a simple manner [18]under rotations. Thus the T2p analyzing T20 is simply T20 referred to an axis normal to the reaction plane [20]. Consequently T2p= T2p, and so T2p is given by Eq. (10). In order to calculate angular distributions of T20 the Coulomb excitation functions must be calculated. This cannot be done analytically but may be done numerically [21].Values of the adiabaticity parameter, determined from Eq. (2), are used in the calculations. For 70MeV Li beam on a'Sn target, Z„=3,Z, =50, A~=7, A, =120, and E~=70 in Eq. (2). Emay take arange of values from 2.47, the breakup threshold in MeV, upwards, and so calculations may be performed using different adiabaticity parameters corresponding 3204 N. J. DAVIS et al. 52 TABLE I. Woods-Saxon optical potential parameters used in the CDCC calculations. rand aindicate radius and diffuseness parameters respectively and suNces r, i, and Cindicate real, imaginary, and Coulomb potentials, respectively. Vis the real potential depth and Wand Wd are imaginary and derivative imaginary potentials, respectively. +120S a t+ 120S b Li=t+ o. (MeV) 58.0 145.0 90' 1.46 1.25 1.39 a„ 0.708 0.690 0.700 W (MeV) 28.0 0.0 Wd (MeV) 0.0 27.5 (fm) 1.46 1~11 a; 0.708 0.920 (fm) 1.4 1.4 1.3 'C. M. Percy and F. G. Percy, At. Data Nucl. Data Tables 17, 1(1976). "R. P. Ward and P. R. Hayes, At. Data Nucl. Data Tables 49, 315 (1991). 'For bound states the potential depth was adjusted in order to obtain the correct binding energy. to different fragment relative energies. The analyzing powers are then determined by using the calculated Coulomb excitation functions in Eq. (16). III. CONTINUUM DISCRETIXED COUPLED CHANNELS CALCULATIONS The CDCC calculations were performed using the computer code FREsco [22]. Cluster folding potentials were incorporated. The Coulomb as well as the nuclear interaction was included in the CDCC calculations. Both diagonal potentials and coupling interactions were taken into account. The nuclear and Coulomb potentials were obtained using the same method, by folding potentials between uparticle cluster and target and between triton cluster and target. The potentials for the channel coupling are derived from empirical optical model potentials for a'Sn target. These are Woods- Saxon in shape and are listed in Table I.Ideally the potentials should be for 40MeV nparticles [23], as is used, and 30MeV tritons, to correspond to beam velocity fragments from 70 MeV Li breakup. Ho~ever a20 MeV triton potential [24] was adopted because none was available at 30 MeV. The Li 3/2 ground state and 1/2 first excited state cluster wave functions were calculated in aWoods-Saxon potential well having geometry parameters as listed in Table I. These were chosen so as to reproduce the empirical value of the reduced transition probability B(E2;3/2 ~1/2 ) [25].The wave function of the 7/2 second excited state was calculated using aweak binding energy approximation [26], in which avery small binding energy is assumed for this state. The 5/2 third excited state was treated as an energy bin of 5MeV width. Test calculations were performed in order to establish the best discretization and truncation of the model space. The Li continuum was initially discretized as in aprevious CDCC study by Sakuragi et al. [12],with values of the relative orbital angular momentum Lfor the a+t clusters limited to L= 1,3. The test calculations were performed for the Li+ Pb system since experimental data for the elastic, inelastic, and breakup channels exist for this system [1,6]. Four channel calculations, including the ground state and the first three excited states, produced an angular distribution of the differential cross section for the 7/2 state similar in shape to the calculations performed by Sakuragi et al. [12], but of about 30% lower magnitude. This may be because the latter were performed with double folding potentials. The inclusion of the nonresonant continuum reduced this by less than 10%. The test calculations revealed that the influence of the wave number k=(0.75— 1.00) fm 'bin on the final results is very small and that the model space can in fact be limited to the range k=(0.25 — 0.75) fm '. The results for the lowest bin k=(0.00— 0.25) fm 'underestimated the experimental values [1] especially at the most forward angles. This energy range was dominated by the bin with L= 1and spin parity I=3/2 .Sakuragi et al. [12]argued that the coupling to the even Lbreakup states must be much weaker than to the odd Lstates and therefore the Lvalues can be restricted to L= 1,3. In order to investigate this further, the L=0bins were included in the calculations. It was found that, although the results for the elastic and inelastic scattering and for the 7/2 state were not affected by the inclusion of the L=O states, the cross section calcuIated for the lowest L=O, k=(0.00— 0.25) fm ', continuum bin was large at scattering angles ranging from 10' to 35'. It overestimated the measured [I]values. The large cross section for the L=0bin is in agreement with radiative capture studies [27] which revealed that F.1contributions dominate. The same was shown in an analysis of 63 MeV breakup data [28].It was therefore considered important to include even Lbreakup states in the CDCC calculations, especially because the forward angle data are of particular interest. The argument by Sakuragi et al. [12]for neglecting even Lrelies on athree-body model of nparticle, triton, and target in which the nparticle and triton potentials with respect to the target are similar. In the present study the uparticle and triton optical potentials used are very different, which may explain the large L=O cross section. CDCC calculations for 70MeV Li breakup on 'Sn were performed using the model space shown in Fig. 2. The width of the lowest bin was set to 0.38 fm 'to correspond to the continuum breakup data measured in the experiment. The model space was truncated to amaximum of 0.8fm 'and to L=0,1,2,3. For L=2, only the lowest k=(0.0— 0.38) fm bin was taken into account, in order to reduce the number of channels. This limitation is not expected to significantly affect the analysis, since calculated continuum cross sections were generally found to decrease with increasing relative energy. For acomparison with the continuum breakup data it was necessary to sum the contributions of the calculations 52 TENSOR ANALYZING POWERS FOR Li BREAKUP 3205 k(fm-& ) 0.8 0.75-- 6.08 6.08 Energy relative to 7Li~e+ tbreakup threshold (Mev) where the A~=(kcm. s'ylAlk s~) (18) 0.6 0.5-- 3.16 -—3.16 -—3.16 0.4 0.38 4.94 2.16 4.21 are amplitudes calculated by the FRESCO code, st and m, are the spin and projection for the triton, k, k, ,and k; are the uparticle, triton, and incident momenta, respectively, Ais an appropriate form factor, and 0.86 0.86 0.86 0.86 0.86 0.86 0.86 c.m. ka+ ~t- (19) Equation (17) may be written in terms of asum over spherical harmonics of the breakup angular momentum L=3, projection mz.' (k,k, ,s,m, iA ik, ;su) L: 1+ 2 -2.47 3 2 -1.99 I 2 5+ 2 3+ 2 5 2where =g Ag(s,m,Lmiis'y)YI (k„), ym~ 4k, — 3k k„= (20) (21) FIG. 2. The discretization of the Li=a+t breakup continuum used in the coupled channels calculations. for different spin parity values to obtain totals for the differential cross section and analyzing powers. An incoherent summation over the contributions was taken and analyzing power contributions were weighted by the corresponding differential cross sections. In order to investigate the roles of the nuclear and Coulomb forces in the CDCC calculations, additional calculations were performed with anuclear interaction only. It was found that, subject to limitations on the numerical integrations of the coupled equations to 40 fm and on the partial waves to 150A,,the results were very similar, indicating adominant effect of the nuclear interaction. To achieve aCDCC result for consistent comparison with the measured analyzing powers, some consideration has to be made of the phase space detected in the experiment. For the continuum breakup, the large contribution from L=O results in the phase space having little effect on the calculations; hence, results direct from the FRESCO code are compared with the data. For the L=3sequential breakup, phase space is far more important. In order to take account of this, consider the scattering amplitude (k,k, ,s,m, iAik;;su) =g(k,k, ,s,m, ik, ,s' y)A (17) This relative momentum taken as triton relative to cv particle could equally well be taken as aparticle relative to triton. In order to calculate appropriate analyzing powers from the scattering amplitudes, the coincidence detection probability f(0„,$„) for fragments with relative momentum direction given by spherical polar coordinates (0„,@„)in the helicity coordinate system Hneeds to be incorporated. This probability function was calculated using aMonte Carlo simulation code [29]in which the collimator positions for the coincidence detection were defined. Li nuclei were excited to the 4.63 MeV state with aLorentzian distribution and were scattered isotropically over asolid angle large enough to include the collimators. The probability function f(8„,P„) was extracted from the Monte Carlo calculation in the form of atwo-dimensional spectrum of number of counts versus O„and P„, for which the aparticle and triton were detected in coincidence. For this spectrum the O„range was divided into 5' bins and the P„range was divided into 10' bins. f(0„,$„) is an even function of @„because of the symmetry of the coincidence detection system above and below the plane in which the scattering angle is defined. The double differential cross section do.(k, ,k„)/ dA, md'„and analyZing POWerS Tkq COrreSPOnding tO haV- ing the center of mass momentum of the uparticle plus triton in asolid angle 0, and the relative momentum in a solid angle A„are given by dcr(k, ,k„) 1Lk' (2s+ 1)TI,q+XI,qqiqis L dQ, dA„4, ,q' qI00 L) 0) W(LLs's';k's, )Yg q(k„), (22) where the polarization transfer coefficients are given by Xlq ~q=g (s~&qis~')&(s'y&'q'is'y')&'AP (23) 3206 N. J. DAVIS et al. However, the experiment does not resolve in detail the double differential cross section. Instead, those relevant events where an uparticle and atriton are detected in coincidence are counted as sequential breakup (SBU), which happens with the probability f(8„,P„).Thus (2s+ 1)T c.m. 2do.(k, ,k„) f(9„,@„)(2s+1)Tk 'sing„d g„d@„ 0@~=0J8„=0 c.m. r 1.,I. gXlq ks'L W(LLs's';k's, )Ik (24) where (2m fm cording to Eq. (23). The analyzing powers are then calculated from Eq. (24), normalizing such that Tpp= 1. I„= Yl,«(9„,@„) f(8„,P„)sing„d O„d@„. qb„=0 39„=p (25) 1.0 0.5 0.0 -0 5" /j' /:/ /:/ 'J' 20 1.0 05" 0.0- — 0.5 — 3.0IIIII 030 60 90 120 150 180 8„(degrees) FIG. 3. CDCC calculated analyzing powers as afunction of center of mass relative momentum direction, for 15 laboratory scattering angle. The solid, dashed, dot dashed, and dotted curves are for P„= 0, 30', 60', and 90', respectively. This integral is necessary because of the sensitivity of the calculated analyzing powers to the angles O„and P„.This is illustrated in Fig. 3, which shows analyzing powers calculated assuming single H„and P„values for alaboratory scattering angle of 15'. Iki ~reduces to areal number since f(8„,$„) is even in P„and the integration is taken over 2qr in P„. In order to calculate the analyzing powers, the integrals Ik qare calculated according to Eq. (25) using the probability function f(0„,P„) obtained from the Monte Carlo calculation and the polarization transfer coefficients Xkq prq&are calculated from the FREsm amplitudes Ayac- IV. EXPERIMENT The experiment was performed using 70 MeV polarized 7Li beams from the polarized heavy ion source [30] and accelerated by the tandem Van de Graaf accelerator, at the Nuclear Structure Facility at Daresbury Laboratory in the UK. FOI the T2o measurements polarization of the beam was achieved using rf transitions between the 2-8 and 4-6 hyperfine atomic levels [31]in amagnetic field, resulting in states with equal magnitude but opposite signs of the tensor polarization and equal odd rank polarizations. This equality was verified by comparison with an unpolarized beam. The T20 measurements were made at alater date when optical pumping [32] was available for polarization of the beam, doubling the theoretical maximum polarization obtainable. Ions with each of the four spin substates were selected in turn, using ahigh frequency transition in amagnetic field to switch between substates. For both T20 and T20 measurements, the polarization states were switched every few seconds, after aspecified integrated beam current was measured, to minimize systematic errors due to beam drift or polarization fluctuations. AWien filter was used to orient the polarization symmetry axis along the beam direction at the target for the T2O measurements and normal to aplane bisecting fragment coincidence detector centers for the T2o measurements. The beam polarization was determined from the 'H( Li,n) He reaction [16] using apurpose built downstream polarimeter [33].The measured magnitudes of second rank beam polarizations were typically t2o= 0.4for the T20 measurements and t20=0.6for the T20 measurements. Measurements of first and third rank polarizations in the optically pumped beam resulted in magnitudes no larger than 0.05 each. For the breakup reactions a2mg cm 'Sn target was used. The yield for continuum breakup of Li into an n particle and atriton is large for small relative energies of the fragments [2].For this reason fragments with asmall opening angle must be detected. The detection system consisted of two pairs of AF. Edetector telescopes placed symmetrically, one pair either side of the beam, as shown in Fig. 4. The symmetric arrangement was used so that data from both sides of the beam could be summed, thus eliminating systematic errors arising from any shift in position of the beam on target and the effects of odd rank polarization components in the beam. The telescopes comprised of 230 p,mthick p-n TENSOR ANALYZING POWERS FOR Li BREAKUP 3207 Plan view 120 S target 7Li beam Side view fragments e' 6 fragments AE Veto Pair of detector telescopes Pair of detector telescopes Veto Ti(H) polarimeter target Polarimeter ~detector telescope I I AE E Ta beam stop Counts 40 30" 20" 0 0.00.51.01.52.02.53.0 Relative energy (MeV) l20 S target 7Li beam EVeto FIG. 4. Detector system. FIG. 6. Fragment relative energy spectrum for the 'Sn(7Li, nt) 'oSng, reaction at alaboratory angle of 15'. breakup via the 4.63 MeV state in Li and the data between the peaks arise from continuum breakup [2]. The relative energy ebetween the triton and nparticle may be calculated according to V. RESULTS The fast coincidence data were gated on the ground state of 'Sn by summing triton and nparticle energies. An energy resolution of 0.4MeV was achieved. Acoincidence spectrum of triton energy is shown in Fig. 5. The sharp peaks correspond to the two kinematic solutions for sequential Counts 50 40" 30" 20" 10" ~tgatatI L. . 10 20 30 40 Energy (MeV} FIG. 5. Energy spectrum of triton sfrom the Sn( Li,trt) 'Sng, reaction at alaboratory angle of 15'. junction silicon AE detectors and 4mm thick lithium drifted silicon Edetectors. Similar detectors placed behind the E detectors acted as vetos to eliminate high energy charge 1 particles which pass through the Edetectors. The detector collimators were 8mm wide and 6mm high with the centers for agiven pair 12 mm apart. The detectors in each pair of telescopes were mounted symmetrically above and below the beam axis and 150mm from the target. The detectors were energy calibrated using 5.486MeV nparticles from 'Am sources mounted close to the detectors. Particle identification was achieved using the AE and E signals. Fast timing was achieved by signals generated from the AE preamplifiers, used to start and stop atime to amplitude converter for each pair of telescopes. Data were transmitted from analogue to digital converters to aGEC 4190 computer and recorded event by event on tape. T2p and "T2p data were obtained for arange of angles to the beam direction, 8, shown in Fig. 4, from 9to 25 in the laboratory frame. 4E,+3E 4$3E— rE cos(@) 7(26) where E, and Eare the triton and nparticle energies respectively and @is the angle between them. Figure 6shows arelative energy spectrum, where Phas been taken to be the angle between the detector collimator centres. The peak is from the sequential breakup and the data at lower relative energies are from continuum breakup. Yields were obtained for each polarization state of the beam. This enabled data for the continuum breakup to be obtained from athreshold of 100keV to 1.7MeV in relative energy. The measured analyzing powers for the 'oSn( Li,nt) 'Sng, continuum breakup are compared with semiclassical Coulomb and CDCC calculations in Fig. 7.The small relative energy dependence of the semiclassical Coulomb calculations of T2p is shown by the dashed curve which corresponds to zero relative energy and the dotted curve which corresponds to arelative energy of 2.16 MeV, equivalent to the value for sequential breakup via the 4.63 MeV state in Li. The corresponding calculation of T2p is not relative energy dependent and is shown by the dashed curve. The "T2p data agree well with the semiclassical calculation at small angles but deviate from it at the larger angles. The T2p data clearly do not agree with these calculations. The angular trend of the data opposes that of the calculations and large magnitude T2p values are measured, in disagreement with the small magnitudes predicted by the calculations. This result is in contrast with the results of differential cross section [2,3,6] measurements which indicated that the Coulomb force is responsible for the continuum breakup at small angles. Analyzing powers are more sensitive than differential cross sections to the contributions of different forces in the reaction mechanism and thus will be affected by anuclear force present in the reaction mechanism even if the Coulomb force also plays alarge role. The extent of the disagreement between the T2p data and the calculations indicates, however, that the nuclear contribution to the continuum breakup is significant. The T2p measurement provides amore rigorous test of the semiclassical Coulomb model than the T2p measurement. This is because the calculation of T2p depends di- 3208 N. J. DAVIS et al. 52 20 1.0 0.5 T~ Q4 20 0.2 0.00.0 20 1.0 05" — 0.5" 20 — 0.2" 0.2 01I~ L=O, I=1/2 L=2, I=3/2 L=2, I=5/2 — 0.5'— 0.1" 0510 15 20 25 30 Center of mass angle (degrees) 20 — 0.2 0.4510 15 20 25 30 FIG. 7. Tzo and Tqo for 'Sn( Li,nt) 'Sns, continuum breakup for e~ 1.7MeV. The dashed curves show semiclassical calculations for Tzp and for Tpp with a=0 MeV and the dotted curve shows the semiclassical calculation for Tzp with e=2.16MeV. The solid curves show the CDCC calculations with all Lvalues from 0 to 3included. rectly on the Coulomb excitation functions whereas the calculation of Tzp does not. The semiclassical calculation of Tpp only depends on the assumption of multipolarity 1, which is good for aCoulomb force but is not necessarily so for anuclear force. Nevertheless, Tpp can not distinguish the multipolarity 1component of anuclear force from aCoulomb force. The Tzp data thus expose the disagreement with the semiclassical Coulomb model better than the "Tzp data. If aCoulomb force were responsible for the continuum breakup asmall deviation of the data from the calculations might be expected due to the approximations used in the semiclassical model. However, the extent of the deviation for Tpp indicates that the disagreement is more fundamental and asignificant nuclear force contribution to the continuum breakup reaction mechanism is therefore expected to be present. The poor agreement of the Tzp data with the semiclassical Coulomb calculations, observed together with the good agreement of the Tpp data with the calculations at small angles suggests that the nuclear force contribution to the continuum breakup reaction mechanism is not only significant, but also has alarge multipolarity 1component. CDCC calculations for t~oSn(7Li, nt) 'oSn, continuum breakup analyzing powers are shown for the different Lcontributions in Fig. 8. The L=O contributions are the most important, because of the large associated differential cross section, with the L=2and L=3contributions insignificant. The L=0 component of the CDCC calculation of Tpp takes values between 0.4and 0.6over an angular range of 0'— 25, and so is very similar to the semiclassical calculation which gives avalue of 0.5. The L=1contributions have — 0.2" 0.2 20 0.1' L=1, I=1/2 L=1, I=3/2 L=3, I=5/2 L=3, I=7/2 0.0 — 0.1" R 0 5 10 15 20 25 30 Center of mass angle (degrees) FIG. 8. CDCC calculations of Tzp and T~p for Sn( Li,nt) 'Sns, continuum breakup, for different Lvalues. most effect for the larger angles, 20' — 30 .The result of incoherently combining all components of the CDCC calculation gives the solid curves shown in Fig. 7.Agood description of the Tzp data is obtained over the angular range measured, with the significant contribution from the L=1 components at larger angles enhancing agreement with the data. The CDCC and semiclassical calculations of Tzp are quite similar, with the CDCC generally alittle lower than the semiclassical result of 0.5. However, the oscillations in the CDCC calculation, which are not present in the semiclassical calculation, improve the agreement with the data. The CDCC calculation is within error bars of three of the five data points while the semiclassical calculation only exhibits this quality 52 TENSOR ANALYZING POWERS FOR Li BREAKUP 3209 3 10 „ 10 (mbsr )10'. 10 ' 20 1.0 05 0.0 Q,o. (mbsr )10'; 10. 10 '" '— —— Sum over L= 0to 3 Normalised by 0.187 L=O, l=1/2 —-—-L=2, l=3/2 20 1.0 05" 0.0-- — 0.5" 10' — 0.5 10', dQ, 10'... {mbsr )10'. 10; 10'; l=1/2 l=3/2 l=5/2 l'=7/2 -1.00 5 10 15 20 25 30 Center of mass angle (degrees) FIG. 10. T20 and T2O for 'Sn( Li,at) 'Sns, sequential breakup via the Li 4.63 MeV state. The dotted curves show the CDCC calculations obtained directly from FREsCo and the solid curves have phase space effects included. 10 0510 15 20 25 30 Center of mass angle (degrees) FIG. 9. Differential cross sections for 'Sn( Li,at) 'Sns, continuum breakup for m~1.7MeV. The curves show CDCC calculations for different Lvalues. of agreement for the smallest angle data point. The total CDCC calculation of T2p shown in Fig. 7reproduces the data at the smaller angles, largely from the L=0contribution. At the larger angles where the L= 1, I"=3I2 component has a significant effect and is of opposite sign to the data, the agreement is poor. Detection phase space effects would be more important at the larger angles but are impractical to incorporate into the continuum breakup calculations. The CDCC calculation does, however, give better agreement with the small angle T2p data than the semiclassical Coulomb calculation does. The CDCC calculation reproduces within errors the trend between the two smallest angle data points, while the semiclassical calculation merely crosses this trend at about 12'. It was not the aim of the experiment to measure absolute differential cross sections for the breakup and normalization difficulties prevent areliable result. However, angular distributions of differential cross sections, for which the trend is accurate, were obtained and it is interesting to compare these with CDCC predictions. Differential cross section data for Sn( Li,at) 'Sns, continuum breakup are compared with the results of CDCC calculations in Fig. 9.It is interesting to note that L=0gives the dominant contribution to the calculated differential cross section for 7— 19 .Beyond 19' the L=1, I=3)2 contribution dominates. The total CDCC calculation exhibits very good agreement with the data if normalized by afactor of 0.187. There are several explanations for why this normalization is necessary. The data may have systematic uncertainties due to inaccuracies in the target thickness and in the solid angle which had to be determined by aMonte Carlo calculation [29]into which some assumption of the continuum breakup yield variation with relative energy had to be incorporated, the result of asemiclassical Coulomb calculation being used. Acalculation using the FRESCO code could not reasonably be performed because of the small energy bins which would be required. Some data were also lost due to detector dead regions and electronic thresholds. The CDCC calculations may not give the correct absolute magnitude of the differential cross sections because of their cluster model basis. The agreement of the angular distribution of the CDCC calculations with the differential cross section data is, however, excellent. Analyzing power data for 'Sn( Li,nt) 'Sns, sequential breakup via the 4.63 MeV state in Li are compared with CDCC calculations in Fig. 10. The results obtained directly from the FRESCO code, shown by the dotted curves, are not sufficient to reproduce the data. However, when the phase space effects are included, as shown by the solid curves, the calculations exhibit excellent agreement with the data, with the exception of the predicted 13 maximum in T2p which is not seen in the data. This is most probably because the data are smeared alittle over arange of angles because of finite detector sizes. The predicted maximum in T2p corresponds to aminimum in the differential cross section, as shown in Fig. 11.This means such smearing will have alarge effect in this case, bringing the measured T2p towards values for nearby angles.