Light-particle emission in the reactions of 16O with Ti

Nuclear Physics A411 (1983) 289-328 @ North-Holland Publishing Company

LIGHT-PARTICLE EMISSION IN THE REACTIONS OF I60 WITH Ti P. L. GONTHIER’,

H. HO++, M. N. NAMBOODIRI+++, J. B. NATOWITZ, S. SIMON, K. HAGEL, S. KNIFFEN and A. KHODAI**

Cyclolron Instituie,

Texas A & IU Universily,

College Station,

L. ADLER’,

Texas 77843-3366, USA

Received 14 June 1983 Abstract: Inclusive energy spectra and angular distributions for heavy ions (2 2 3) produced in the reactions of 227 MeV and 710 MeV I60 with Ti were measured. Also measured at the projectile energy of 310 MeV were energy and angular correlations between light charged particles (2 4 2) and heavy ions. From comparisons with statistical model calculations upper limits to the complete fusion cross sections of 647 mb and 265 mb were derived for projectile energies of 227 MeV and 310 MeV, respectively. At 310 MeV the cross section of incomplete fusion processes was estimated to be over 505 mb. Emission of fast, high-energy a-particles and protons was observed to be a characteristic feature of quasi-elastic, deep-inelastic and fusion-like reactions. Average multiplicities of fast light particles in coincidence with heavy ions at +20” and +40° were estimated to be of the order of 1. The prompt emission of light appears to be the principal mechanism which limits complete fusion. A second component of a-particles observed in coincidence with deep-inelastic projectile-like fragments and having an energy comparable to Coulomb energies of particles emitted from target-like and projectile-like fragments appears as an excess yield in the direction of the recoiling target-like fragments. This component cannot be accounted for in terms of sequential emission processes and may result from a mechanism other than the one which leads to fast particle emission.

E

NUCLEAR REACTIONS Ti(i60,X), E = 227 MeV, 310 MeV: measured a(fragment E), o(fragment 0); Ti(i60,X), E = 310 MeV; (particle) (particle) (0), energy correlations; deduced light-particle emission mechanism. Statistical, sequential decay models.

1. Introduction In the past few years many light-particle-heavy-ion correlation measurements have been performed in order to study the underlying mechanisms leading to fusion, quasi-elastic and deep-inelastic reactions 1-28). Some of the light-particle coincidence data 17-22) were shown to be in agreement with the assumption of sequential decay processes, i.e. in the first step formation of compound nuclei or ’ Present address: Hope College, Physics Department, Holland, MI 49423. ” NATO fellow. Present address: Max-Planck-Institut fir Kemphysik, Heidelberg, W. Germany. “’ Present address: Lawrence Livermore National Laboratory, Livermore, CA 94550, USA. * Present address: Department of Chemistry, Washington University, St. Louis, MO 63130, USA. ** Present address: Chemistry Department, National University of Iran, Tehran, Iran. 289

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deep-inelastic fragments and in the second step decay of the excited nuclei. On the other hand, other data ’ -i6) have shown deviations from sequential emission of light particles and have been interpreted in terms of nonequilibrium processes. Evidently, the observability of these processes depends crucially on the intensity of nonequilibrium light particles relative to particles emitted from equilibrated nuclei. This relative intensity for nonequilibrium light particles is expected to increase with bombarding energy: the higher the bombarding energy the larger the amount of kinetic energy transferred from the relative motion of heavy ions into internal excitation energy of the strongly interacting nuclei. This may lead ultimately to the situation that the lifetime for light-particle decay of the fragments is comparable with the interaction time, i.e. the time during which the fragments form a dinuclear system. Under these extreme conditions a large fraction of light-particle emission may take place during the interaction and give rise to dominant nonsequential features in the energy and angular correlations of the light particles. Indeed, extensive and detailed cr-HI correlation studies on light systems at low bombarding energies, e.g. 160 with 27Al at 4 MeV/u [ref. 12)] and I60 + 58Ni at 6 MeV/u [ref. “)I, show only multiplicities of < 0.02 for nonequilibrium a-emission, whereas similar studies at N 10 MeV/u [ref. “)I show an increase to values of about 0.10. This trend is confirmed by this study of the reactions of I60 with Ti at 20 MeV/u [refs. 9*‘“)I where the average multiplicity of nonequilibrium a-particles amounts to > 1.0. Further, as for the 160 + 238U system [ref. ‘“)I, we observe nonequilibrium processes for central collisions leading to fusion-like reactions as well as for peripheral collisions leading to quasi-elastic and deep-elastic reactions. This paper is divided into six sections. In sect. 2, we describe the experimental details. The total and differential yields, energy spectra and angular distributions of heavy ions (2 2 3) detected in the reactions of I60 with Ti at 227 MeV and 310 MeV are presented in sect. 3. In sect. 4, coincidence data for light particles and fusion-like residues are presented and discussed. Sect. 5 contains the data for coincidences between light particles and projectile-like fragments. A summary of our results and conclusions is given in the final sect. 6. Some of the present results obtained with 310 MeV projectile energy were published previously in the form of brief communications 9*lo).

2. Experimental details and data analysis Self-supporting natural titanium targets with thicknesses ranging from 0.3 to 1.6 mg/cm’ were bombarded with 227 MeV and 310 MeV 160 ions from the Variable Energy Cyclotron at Texas A & M University. At 310 MeV heavy ions (HI) with Z 1 3 and light charged particles (LP) with Z 5 2 were detected using AE-E techniques. The experiments consisted of inclusive measurements of heavy ions and light charged particles and of coincidence measurements of HI-LP and HI-HI correlations. Inclusive HI measurements were also performed with 227 MeV 160 ions.

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The heavy-ion inclusive measurements were performed using a single telescope to measure the energy spectra and angular distributions of all products with Z 2 3 at laboratory angles from 5O to 60°. This telescope consisted of a dE ionization chamber 29) (e q uivalent to 3 pm of Si) backed by a 1000 pm Si detector. In the HI-LP correlation experiments, two HI telescopes and two LP telescopes were used simultaneously to improve the efficiency of the data collection. The two HI telescopes consisted of ionization chamber AE detectors, one backed by a 50 pm-1000 pm silicon detector combination and the other by a single 1000 pm silicon detector. The HI telescopes were fixed at 20” and 40” with respect to the beam direction. The LP telescope used at forward angles included 23 pm, 100 pm and 5000 pm Si detectors. The telescope at back angles was composed of an 8.4 pm and 5000 pm pair. The LP telescopes were positioned at the in-plane angles of + lo”, -20°, +30”, -4O”, + 50”, f80”, - 130’ and + 140” where the negative sign is used to indicate angles on the opposite side of the beam from the HI telescopes. Out-of-plane measurements at angles ranging from 18” to 60° were made at inplane angles of - 15”, - 40.9”, - 56.5”, - 1lo”, + 120” and + 30”. The threshold for a-particles in the LP telescopes was about 4 MeV. Alpha particles energies up to 120 MeV could be measured by the telescopes. Protons of energies greater than 30 MeV passed through the telescopes producing a high-energy cut-off in the proton spectra. The solid angles of the various telescopes were in the range of 1 to 5 msr. Normalization of different runs to each other was accomplished using a beam integrator and two monitors placed at +5” with respect to the beam direction. Fluctuations in the beam direction were small as shown by the two monitors. Standard NIM electronic equipment was used to process the signals and a PDP15 computer was used for data acquisition. The results were recorded event by event on magnetic tape. During the coincidence experiments, the singles events in the different telescopes were also recorded at a scaled down rate. All events were tagged to distinguish the particular pair of telescopes which was in coincidence. For each event a time-to-amplitude converted output representing the time difference between the detection of the particles in the two telescopes was also recorded to enable corrections for accidental coincidences to be made. The singles data were analyzed using the code BINIT 30) which performed Zidentification for each event and constructed energy spectra for products of different atomic numbers. For HI’s detected in the gas ionization chamber telescope, Z-identification was done by a table-lookup procedure employing a table of AE expected for particles of each Z as a function of the total energy of the particles. The energy spectrum for each Z was constructed after corrections were applied for energy losses in the target and the detector window and for the usually small pulse-height defects in the detector. For the LP’s particle identification was performed using the algorithm of Butler et al. 31). Coincidence data were analyzed using the computer code TANTALUS which allowed Z-identification of the particles as described above and construction of the

292

P. L. Gonthier et al. 1 Light-particle emission

energy spectrum of each product with restrictions on the Z and energy of the coincident particle. Correction for accidental coincidences was made using the time spectrum. 3. Singles data Fig. 1 displays a two dimensional plot of the E versus AE for particles detected at 20” from the reactions produced with 310 MeV 160 projectiles and illustrates the Z-resolution obtained in the HI telescopes. Adequate resolution is obtained for the entire range of products observed in the ractions. For the Z-identified products the energy integrated differential cross sections d2a/dPdZ obtained at bombarding energies of 227 and 310 MeV are plotted in figs. 2a and 2b, respectively. The angle-integrated (from 5“ to 60”) yields of identified products are also shown in these figures. The identification requirement introduces energy thresholds which depend upon Z. As a result the distributions presented in these figures do not exactly reproduce the actual yield distributions; however, at forward angles the products are energetic enough so that threshold effects are small

310 MeV 160+Ti AE vs E

AE (MeV) Fig. 1. Energy loss in the silicon detector, E, as a function of the energy loss in the gas counter, AE, for products observed at 20“ from the reactions of 310 MeV I60 with Ti.

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0

227

MeV

5

IO

(a)

15

2u

25

30

0

ATOMIC

310

MeV

5

IO

(b)

I5

20

25

30

NUMBER

Fig. 2. Total and differential yield distributions of heavy products from the reactions of 227 MeV (a) and 310 MeV (b) I60 with Ti.

and the measured distributions are representative of the acutal ones. The yield distributions exhibit similar features at 227 and 310 MeV projectile energies. Three peaks corresponding to three qualitatively different groups of products are evident in these figures and will be discussed in more detail in this section. For 310 MeV projectile energy, fig. 3 contains energy spectra for some representative products with low and intermediate atomic numbers. The spectra for oxygen and carbon show structure which depends strongly on angle. We designate the group of products with low atomic number as “projectile-like fragments” (PLF). Products with intermediate atomic numbers have narrower energy spectra peaking at energies much lower than the incident projectile energy. These products which are nearly constant as is also have angular distributions (do/d@,, demonstrated in fig. 4. Such distributions are characteristic of composite systems having lifetimes of at least one rotation. The appearance of a peak in fig. 2 at atomic numbers near that which would result from symmetric fission of the 64Zn composite nucleus might be taken as

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emission

a

ENERGY

hleV)

Fig. 3. Singles energy spectra of carbon (a), oxygen (b) and aluminum (c) ,ions produced in the reactions of 310 MeV 160 with Ti observed at the indicated lab angles. The low-energy spike in (c) arises from misidentified, low-energy, heavy products.

suggestive of such a process ; however, symmetric fission would necessarily be accompanied by large excitation energies in the primary fragments and the final products would not appear near 2 = 15, but rather at much lower atomic numbers. In fact a fragment-fragment coincidence experiment in the reactions of 310 MeV I60 with Ti for three pairs of angle settings 32) shows that the most probable product associated with fragments of atomic number near 15 is carbon. This suggests that the group of products with intermediate atomic numbers are a result of the decay of target-like fragments (TLF) produced in deep-inelastic collisions. Calculations assuming two-body kinematics show that TLFs with sufficient kinetic

P. L. Gonthier et al. / Light-particle emission

25

50 75 8Cm (deg.)

100

295

I25

_..I

Fig. 4. Center-of-mass

singles angular distributions for deep-inelastic products from the reactions of 310 MeV I60 (dashed) and 227 MeV I60 (dotted) with Ti.

296

P. L. Gonthier et al. 1 Light-particle emission

energy to overcome the energy threshold in the TLF detector have to be produced in reactions with large negative Qz values (< - 190 MeV). Thus the observed yield of the target residues is much lower than the yield of the complementary PLF’s because only products of collisions in which large momenta are imparted to the TLF’s are detected and identified. As a result, the detection system provides a partial discrimination against the heavy partners of quasi-elastic collisions. In addition, collisions in which large momenta are imparted, i.e. deep-inelastic collisions, are those which lead to the highest excitation of the TLF’s and hence the greatest particle evaporation. Assuming that the available excitation energy is shared between I60 and 48Ti according to their masses, and that the angular momenta of the fragments correspond to values obtained for rigid rotation of the dinuclear system with a total angular momentum of 85 h, statistical model calculations using the code LILITA 33) indicate that carbon and sulfur are the most probable evaporation residues of the primary products of I60 and 48Ti. Products in the region of highest atomic numbers 16 5 Z s 30 account for a large fraction of the total reaction cross section and appear to be fusion-like residues (FLR). In addition to the identified products, the total yield for this range of atomic numbers includes low-energy products which are not identified correctly and those which are stopped in the AE detector. The high-energy losses of these unidentified products in the AE detector allows their separation from lighter products. Adding the three contributions together, the total cross sections for products with 16 s Z 5 30 are 1200 + 85 mb at 227 MeV and 1130 + 80 mb at 310 MeV. To explore the origin of this group of products in greater detail, we have used the code LILITA to calculate the differential yield distributions from the fusion of 227 MeV and 310 MeV I60 projectiles with 48Ti . These yields, shown in figs. Sa and 5b, were calculated under the assumption that the total cross sections for compound nucleus formation are the same as those observed for the products with 16 5 Z 5 30. The parameters used in the calculation were the same as in ref. I’) for a light system. Using the sharp cutoff approximation for the transmission coefficients these total cross sections correspond to critical angular momenta of 61 h at 227 MeV and 69 h at 310 MeV. As the figures demonstrate, the calculated yield distributions of the compound nucleus evaporation residues do indeed peak in the same region of atomic number and have similar widths as the observed distributions of products at both projectile energies. In spite of this similarity in yield distributions, the calculated angular distributions are much narrower than those observed. This can be seen in figs. 6a and 6b where the experimental angular distributions, do/da, for Z 2 16 are compared with the calculated distributions for projectile energies of 227 and 310 MeV, respectively. At the two different projectile energies, the calculated distributions are very similar indicating that the effect of increasing evaporation at

P. L. Gonthier et al. / Light-particle

emission

IO3

(b)

(a) 1

z

5 bN -0-o I

227

297

MeV

t

I5

20

25

I5

20

25

:31 0

ATOMIC NUMBER Fig. 5. Total and differential yield distributions for the compound-nucleus evaporation residues calculated using the code LILITA for the reactions of 227 MeV I60 (a) and 310 MeV 160 (b) with Ti.

higher is by increased velocity the compound In the distribution dramatically the energy from MeV 310 Similar have made Vigdor al. in system +40Ca projectile up 214 At projectile in present there large between calculated experimental distributions. differences also between calculated the energy of heavy In 7a 7b, compare energy for and with calculated LILITA. common factor extracted all spectra normalizing calculated to experimental of at The spectra in

P. L. Gonthier et al. / Light-particle emission

298

‘04F ?, (a)

227

MeV

I60 +Ti

$ Q,,,,(b)

310 l

0

100L 0

4 I I I :’ e IO 20304050607080

e

’

8,

0

MeV

I60 +Ti

EXPERIMENT CALCULATION

IO 20304050607080’

3

(DEG.)

Fig. 6. Comparisons of the experimental angular distributions for heavy products (Z 2 16) with the calculated distributions (LILITA) for the reactions of 227 MeV I60 (a) and 310 MeV I60 (b) with Ti. Critical angular momenta of 61h (a) and 69h (b) were assumed in the calculation.

their shapes with the higher portion of the experimental spectra, but the experimental spectra peak at lower energies than the calculated spectra. Reflecting the narrower angular distributions, the calculated spectra decrease more rapidly than do the experimental spectra. These differences between the model calculation and the experimental results may indicate contributions from deep-inelastic reactions or incomplete fusion processes to the experimentally observed heavy residue group. Indeed the fragment-fragment correlation experiment in the reactions of 310 MeV I60 with Ti has shown 32) that the atomic number distributions for TLFs in coincidence with PLFs are broad and extend to atomic numbers as large as Z = 22 thus contributing to the group of FLR’s. In order to obtain an estimate of this contribution from deep-inelastic collissions, we have normalized the singles angular distribution for Z = 13 to the angular distribution for FLR’s at backward angles and found an upper limit of 360 mb for FLR’s produced in deep-inelastic collisions. However, even after subtracting this contribution, the resulting angular distribution of FLR’s is still much broader than the one calculated by LILITA assuming complete fusion. Therefore we must conclude that there are other reaction mechanisms which lead to heavy residues with Z I 16 and that compound nucleus formation and TLFs from deep-inelastic collisions cannot account for the measured total cross section of FLR’s.

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et al. / fight-particle

299

emission

2@

35”

3s

5d

>j

g&!_dAu 0

)20’

E Fig. 7. Singles energy spectra of calcium (a) and vanadium (b) are compared to the calculated spectra (LILITA) for the indicated lab angles for the projectile energy of 310 MeV. The apparent structures in the calculated energy spectra (dotted lines) are a result of poor statistics in the Monte Carlo calculation.

300

P. L. Gonthier et al. / Light-particle

emission

Using the statistical model calculation, we can, however, derive an upper limit to the cross section of the compound nucleus evaporation residues. Assuming that the experimental yield observed at 5” can entirely be ascribed to the compound nucleus evaporation residues, normalization of the calculated angular distributions to this angle results in upper limits of 647 mb and 314 mb for 227 and 310 MeV bombarding energy, respectively. These smaller cross sections for compound nucleus evaporation residues are in agreement lo) with the friction model 35) and TDHF calculations 36). However, it will be shown in the following section that in case of 310 MeV projectile energy, the estimated total fusion cross section is indeed smaller than 314 mb. In the following section we will show that heavy-ion-light-particle correlation data indicate that incomplete fusion or massive transfer reactions are responsible for much of the total cross section. 4. LP-FLR coincidence results To explore the different processes leading to heavy products in the reactions of 310 MeV I60 with Ti, we have measured the light-particle emission from the products. For this purpose, we have performed coincidence experiments between HI’s (2 2 3) and LF”s (Z 6 2). The HI’s were observed at the fixed angles of +20° and +40” and LP’s were detected in and out of the reaction plane at the angles mentioned previously in sect. 2. The data for a-particles in coincidence with FLR’s are presented first. Experimental distributions can be observed in a comparison of the energy spectra of a-particles in coincidence with FLR’s detected at +20° on the opposite side and on the same side of the beam shown in figs. 8a and 8b, respectively. Fig. 9 shows the energy spectra of a-particles detected on the opposite side of the beam in coincidence with FLR’s at +40”. (Due to poor statistics a-energy spectra on the same side of the beam as the detected FLR’s are not shown for FLR’s at +40° in fig. 9.) The dashed curves indicate the predictions of the code LILITA. The calculation assumes a critical angular momentum of 69 h and includes the experimental energy thresholds for the FLR’s. The calculated spectra were normalized to the experimental ones at - 80” for both cases of FLR’s at + 20° and +40°. Comparisons of the observed and calculated spectra reveal that at forward angles the bump in the lower portion of the energy spectra seems to be approximately consistent with evaporation of the compound system. However, the experimental spectra show an additional large probability of a-particles with energies much greater than those predicted by the calculation. It appears then that the experimental spectra contain a high-energy, nonequilibrium component and a low-energy component. The most probable energies of the lower-energy component are smaller than those predicted by the calculation especially in the forward direction. At the most backward angle of - 130” in fig. 8a, the slope of the

P. L. Gonihier et al. / Light-particle emission

Fig. 8. Energy spectra of or-particle detected in coincidence with heavy products (2 2 16) observed at +200 in the reactions of 310 MeV 160 with Ti. Error bars represent the statistical errors. (a) Spectra on the opposite side of the beam from the detected heavy products, and (b) on the same side of the beam at the indicated lab angles. The calculated spectra are represented by dashed curves and have been normalized to the data at -800. The experimental energy thresholds of the heavy products have been taken into account in the caicufation. The apparent structures in the calculated spectra are a result of poor statistics in the Monte Carlo cakulation.

302

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-26

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60 80 lcxt I20 140 I60

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Fig. 9. Energy spectra of u-particles detected in coincidence with heavy products (2 2 16) observed at +W from the reactions of 310 MeV I60 with Ti. Details same as in fig. 8.

P. L. Gonthier et al. / Lighr-particle

emission

303

experimental spectrum is steeper than the ones calculated. Integrating over the aenergy spectra, we obtain the angular correlations shown in fig. 10. The calculation (dashed curves) has the same normalization factors as in the energy spectra. The calculated yields at - 130” and + 140” for FLR’s at +20° are higher than the experimental ones since the a-energy thresholds were not included in the calculation. The excess yield in the experimental correlations in the forward direction results from the high-energy a-particles. In order to provide a global picture of the a-particles detected at various laboratory angles in coincidence with FLR’s detected at a fixed angle, we present the complete in-plane information in a velocity plot. Such a plot is a contour-polar plot of the a-particle coincidence cross section d3a/dvi, as a function of the laboratory velocity of the a-particles. The advantage of this cross section is its property of being galilean invariant. The procedure for the transformations of the cross section is described in detail in ref. 37). Fig. lla shows the experimental velocity plot for a-particles in coincidence with FLR’s at +20°. The velocity of the center of mass and the average velocity of the FLR’s are represented by the vectors Vc, and &, respectively. Due to the kinematic restriction imposed by demanding the observation of the FLR’s

8,

(deg.)

Fig. 10. Angular correlations of a-particles in coincidence with heavy products (Z 2 16) from the reactions of 310 MeV I60 with Ti observed at +20“ (a) and +40” (b). The calculated correlations assuming statistical equilibrium emission are shown as dashed curves. The same normalization factor was used in fig. 8.

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Fig. 11. Contour plots of the cross section, d”u/dva, as a function of the velocity of a-particles in coincidence with heavy residues (Z >=16) observed at +20”. The contours are expressed in units of 2 pb/(cm/ns)3. (a) Experimental results from the reactions of 310 MeV I60 with Ti. The straight lines indicate the angles at which data were obtained. The solid circle represents the energy threshold of the a-detectors. (b) Results of the calculation (LILITA).

at +20°, the major cross section occurs on the opposite side of the beam from the HI telescope. The peak of the cross section shown by a dashed line follows an approximately circular whose center lies between the velocity vectors, Vc, and I$,. A 4 MeV threshold (shown as a solid circle) in the a-particle telescope cuts off the ridge at backward angles ; however, the tail of the distribution indicates a smooth continuation of the circular ridge at backward angles. In fig. llb, we show a velocity plot calculated for evaporated @-particles leading to FLR’s at +20° using the computer code LILITA and assuming a critical angular momentum of 69h. The same energy thresholds as the experimental threshold for the FLR’s were incorporated in the calculation. The calculation

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305

reproduces the gross features of the experimental distribution. However, the peak in the calculated distribution exceeds the experimental peak by 50%. In addition to the a-particles emitted from equilibrated nuclei, the experimental velocity distribution shows a component with velocities close to that of the incident beam (V,,,,). Th is component is mainly concentrated in the forward direction, on the opposite side of the beam as the FLR’s and peaking at -20”. Such a high-velocity component is clearly not present in the calculated distribution of fig. 1lb. The experimental and calculated velocity plots for a-particles in coincidence with FLR’s at +40° are shown in figs. 12a and 12b, respectively. The experimental velocity distribution shows two approximately circular ridges of large intensity shown by dashed lines-one for high velocity and the other for low velocity tlparticles, each having a maximum at -20”. In contrast, the calculation shows only one circular ridge with a radius in between the radii of the two experimental ridges. The lower ridge suggests that the velocity of the emitting source is smaller than that of the compound nucleus and, therefore, the composite system has not received the full momentum from the projectile. Although the LP - HI coincidence experiments were primarily designed for the TV - HI correlations, protons were also detected in these measurements. The experimental and calculated energy spectra for protons in coincidence with FLR’s at +20° are presented in figs. 13a and 13b, respectively. (Poor statistics did not allow the comparison with the energy spectra of protons in coincidence with FLR’s at +400.) Due to the total thickness of 5.1 mm of the Si stack, protons with energies greater than 30 MeV pass’ through the telescope producing high-energy cutoffs in the spectra. The calculated energy spectra, shown as dashed curves, are normalized to the peak of the experimental energy spectrum at -80”. As in the case of the c+particles (figs. 8 and 9), the calculation gives most probable proton energies which are larger than the peak energies of the low energy component in the experimental spectra. The angular correlations for protons in coincidence with FLR’s detected at +20° and +40” are shown in figs. 14a and 14b, respectively. The LILITA calculations are shown as dashed curves with the same normalization factor as the energy spectra. Clearly there is a large excess in the experimental correlations which cannot be accounted for by the statistical decay of the compound nucleus. As in the case of high-velocity a-particles, most of these high-velocity protons appear to come from mechanisms other than compound nucleus decay. Out-of-plane correlations for a-particles and protons in coincidence with FLR’s measured at the angles indicated in sect. 2 were parameterized with smooth functions. Integrating over these functions, we estimate the average multiplicities of the low-energy, equilibrium component and the high-energy, nonequilibrium component of cr-particles and protons. These multiplicities are tabulated in table 1. The data indicate that there is a significant fraction of collisions producing

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(a) SCALE -

I

/

SCAL

Fig. 12. Contour plots of the cross section, d’u/dvf, as a function of the velocity of a-particles in coincidence with heavy residues (2 >= 16) observed at +40°. The contours are expressed in units of 2 pb/(cm/ns)‘. (a) Experimental results from the reactions of 310 MeV I60 with Ti. The lines indicate the angles at which data were obtained. The solid circle represents the energy thresholds of the a-detectors. (b) Results of the calculation (LILITA).

FLR’s in which high-energy a-particles and protons are emitted. Further, the comparison of the low-energy component in the coincidence energy spectra of a’s and protons with the calculated spectra indicates that the most probable energies in the experimental spectra are smaller than those calculated and that the experimental spectra are steeper than the calculated spectra at the most backward

P. L. Gonthier et al. / Light-particle

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307

!,. i,..,, Ii I D-30 20 ’ 40 ’ 60 ’ 60 d 100 ‘O-3o 20 40 60 60 100 I

EP

I

(MeV)

Fig. 13. Energy spectra of protons detected in coincidence with heavy products (2 >= 16) observed at +20° from the reactions of 310 MeV I60 with Ti. Details same as fig. 8.

Fast ejectiles emitted at the early stages of incomplete fusion processes would remove energy and angular momentum from the composite system and less linear momentum would be transferred than in complete fusion processes. The energy spectra of particles evaporated from the incompletely fused system would be angles.

P. L. Gonthier et al. / Light-particle emission

308

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Fig. 14. Angular correlations of protons in coincidence with heavy products (Z 2 16) from the reactions of 310 MeV I60 with Ti observed at +200 (a) and +40” (b). The calculated correlations assuming statistical equilibrium emission are shown as dashed curves. The same normalization factor was used. as in fig. 13.

steeper and would have smaller most probable enegies in the lab system. Thus the data suggest an incomplete fusion or massive transfer mechanism analogous to the type studied by several groups with different techniques 38-47). In order to study further the kinematic effects of such a mechanism, we have performed a calculation which allows the emission of fast particle and then follows the statistical decay of the residual composite system. The observed energy and angular distributions of the ejectiles were parameterized with simple functions. The parameters were adjusted to lit the high-energy’ portion of the a-particle spectra. The calculations were done for both 4He and *Be as fast ejectiles. For each calculation a multiplicity of one was assumed for the fast ejectile. The transfer of

TABLE

1

Average multiplicities of light particles in coincidence with heavy residues

eFLR

High E,

Low E,

High E,

+200 +400

0.4kO.l l.lkO.2

1.6kO.3 1.3kO.l

0.3 kO.1 0.2kO.l

Low E, 0.6kO.3 0.5 kO.3

P. L. Gonthier et al. / Light-particle emission

0

40

80

309

120 160 200

EFLR (MeV) Fig. 15. Singles energy spectra of heavy products (Z 2 16) from the reactions of 310 MeV I60 with Ti observed at the indicated angles. The solid curves are the predictions of the code LILITA for complete fusion. The dashed curves are the calculated spectra assuming that a fast 4He is ejected and that a r2C fuses with the Ti nucleus. The dotted curves are the calculated spectra assuming that a fast *Be is ejected and that a sBe fuses with the Ti nucleus. The apparent structures in the calculated spectra are a result of poor statistics in the Monte Carlo calculation. The calculated spectra were normalized to the data at 5O.

4He to the ta r get nucleus with 12C as a fast ejectile is not expected to contribute to the observed FLR’s, since for these collisions there would be insufficient momentum transfer for the FLR’s to be detected above the energy threshold of our HI detector. We have compared the singles energy spectra of the FLR’s to the calculated spectra in fig. 15. The solid curves represent the calculated energy spectra for the case of complete fusion. The dashed curves are a result for the case in which 4He is emitted and the remaining i2C fuses with the target nucleus. The dotted curves are for the case in which sBe is emitted and the remaining *Be fuses with the target

310

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nucleus. The calculated curves are normalized to the data at 5”. As the transferred mass decreases the energy spectra shift downward. The discrepancy between the data and the calculation for the complete fusion (solid curves) is always in the lower portion of the energy spectra. The comparisons reinforce the conclusion that both fusion and incomplete fusion are contributing to the production of FLR’s. From the normalization of the calculated energy spectrum assuming complete fusion, we derive a new upper limit to the total fusion cross section of 265 mb. At 310 MeV this upper limit corresponds to 12% of the total reaction cross section. Note that this value is smaller than the one estimated previously in sect. 3. The kinematic effects of the emission of high-energy particles cause the angular distribution of the FLR’s to broaden as shown in fig. 16 in which the experimental singles angular distribution of FLR’s is compared to the calculated angular distributions resulting from complete and incomplete fusion processes. The solid curve represents the calculation for complete fusion. The dashed curve is the calculation for the massive transfer of “C and a fast 4He ejected. The dotted curve is the calculation for the massive transfer of ‘Be and a fast *Be ejected. To estimate

Fig. 16. Singles angular distributions of heavy products (Z 2 16) from the reactions of 310 MeV I60 with Ti. The solid curve is the prediction of the code LILITA for complete fusion. The dashed curve is the calculated distribution assuming that a fast 4He is ejected and that a “C fuses with the Ti nucleus. The dotted curve is the calculated distribution assuming that a fast sBe is ejected and a “Be fuses with the Ti nucleus. The dot-dashed curve is the singles angular distribution of aluminium normalized to the distribution of heavy products at 500.

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the maximum contribution of heavy products resulting from deep-inelastic collisions, we have normalized the singles angular distribution of 2 = 13 (shown as a dot-dashed curve) to the singles angular distribution of FLR’s at 50”. As we mentioned previously in sect. 3, products of atomic number 13 are representative of the group of target-like fragments which result from deep-inelastic collisions. Although at the most backward angles target-like fragments from deep-inelastic collisions may dominate, their contribution cannot be greater than 360 mb or 30% of the total cross section of FLR’s. With this upper limit together with the upper limit of the total fusion cross section, we extract a lower limit of 505 mb for the cross section of incomplete fusion processes. The shape of the calculated angular distribution resulting from a *Be ejected (dotted curve) is similar to the shape of the experimental distribution. The total multip~city of 1 assumed for the fast *Be would produce 2 fast oc-particles per collision. This multiplicity is consistent with the measured average multiplicities of 1 for high-energy ds and protons. On the basis of these studies, we can conclude that a major fraction of the total cross section of fusion-like residues results from incomplete fusion or massive transfer reactions indicating that the complete fusion cross section is very small at 20 MeV/u for this light system.

5. LP-PLF coincidence results In this section we present the data for light charged particles (LP) in coincidence with projectile-like fragments (PLF). We begin by considering the data for CIparticles in coincidence with carbon ions. Recalling fig. 3, it can be seen that the energy spectrum for carbon at 20° consists of almost equal contributions of deep-inelastic and quasi-elastic carbon. The a-particle energy spectra in coincidence with quasi-elastic carbon ions (Q, ’ - 170 MeV or E, z=-120 MeV) at + 20” are presented in figs. 17a and 17b. Figs. 17~ and 17d show the a-particle energy spectra in coincidence with deepinelastic carbon ions (- 170 > Q2 > -230 MeV or 20 < EC < 120 MeV) at +20°. The spectra on the opposite side of the beam from the detected carbon ions (negative angles), figs. 17a and 17c, have very similar shapes. There are some differences in the spectra on the same side of the beam, figs. 17b and 17d, in the most forward angles of + lo* and +30°. In the case of the quasi-elastic carbon, fig. 17b, two distinct components are observed. The high-energy component peaks around 80 MeV at + loo. These a’s appear to come from the decay of PLF’s. In the case of deep-inelastic carbon shown in fig. 17d, due to the slower moving source, the higher-energy component in the spectrum at +lO” peaks around 60 MeV and is no longer distinct from the lower-energy component. Fig. 18a shows the velocity plot for a-particles in coincidence with carbon ions resulting from quasi-elastic collisions. The distribution is characterized by two

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*-g--

ZE-

p

9+

%*

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Fig. 18. Contour plots of the cross section, d30/dvi, as a function of the velocity of a-particles in coincidence with carbon ions detected at +20°. The contours are in units of 2/rb/(cm/ns)3. The velocity vectors are indicated for the primary beam, the center of mass, the mean velocity and its variance for the detected carbon ions and for the target-like fragment : (a) for quasi-elastic carbon ions, and (b) for deep-inelastic carbon ions. Solid circles represent the energy thresholds of the or-detectors. The dashed circles indicate the ridges resulting from the most probable emission from the target-like and projectilelike fragments.

circular ridges (shown as dashed circles) of high intensity. One ridge centered about the average velocity of the carbon ions (Vc) arises from the decay of PLFs and has an intense region in the beam direction with beam velocity. The other ridge centered about the velocity of the recoiling TLFs arises from the decay of these TLFs. This ridge is broad and symmetric with respect to the direction of motion of the TLFs. If the spin of the TLFs is aligned perpendicular to the reaction plane, one expects an isotropic circular ridge in-plane 37). This, however, is not observed; instead there is an enhancement in the direction of the TLFs. An isotropic spin distribution in the plane perpendicular to the motion of the emitting TLFs would give rise to such an enhancement in the direction of the TLFs; however, there would also be an equal enhancement in the direction opposite to

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the motion of the TLFs. We would expect to see this enhancement in the higherenergy portion of the spectra in spite of the detector thresholds ; instead the cross section is seen to decrease rapidly. Therefore, the excess yield in the direction of the TLFs appears to be a result of nonequilibrium processes. In fig. 18b, we present the velocity plot for a-particles in coincidence with deepinelastic carbon at +20”. The a-particle distribution exhibits two maxima separated by a minimum in the direction of the carbon ions (Vc). The two maxima appear to result from the overlap of the two circular ridges (shown as dashed circles) which arise from the decay of TLFs and PLFs. The energy spectra of a-particles in coincidence with other PLF’s are essentially identical to those in coincidence with carbon ions. Integrating over the cc-energy spectra, we show the a-correlations in coincidence with PLFs of atomic number from 4 to 10 for quasi-elastic PLFs at +20”, deep-inelastic PLFs at +20°, and deep-inelastic PLFs at +40°, in figs. 19a, 19b, and 19c, respectively. The dashed lines are drawn to connect the points as a guide for the eye. The correlations are all quite similar peaking in most cases at - 10” on the opposite side of the beam.

8. (OEG) Fig. 19. Angular correlations of a-particles in coincidence with quasi-elastic products (a), with deepinelastic products (b) observed at + 20°, and with deep-inelastic products observed at +W (c). Atomic numbers of these projectile-like products are indicated.

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There is an appearance of a shoulder in the correlations around + 10” to + 30” especially evident in figs. 19a and 19b. As a result of these similarities, we have combined the data to improve the statistics by adding the data for PLF’s ranging in atomic number from 4 to 10. Figs. 20a and 20b show the resulting velocity plots for deep-inelastic PLF’s at + 20” and +40°, respectively. The two maxima at - 20° and +40° and the minimum at + loo in fig. 20a shift with the detection angle of the PLF’s. In fig. 20b,

(b) SCALE

\ \

\

“01

1

Fig. 20. Contour plots of the cross section, d%/dv& as a function of the velocity of or-particles in coincidence with deep-inelastic products (Z = 4-10) observed at +200 (a) and at +4& (b). The contours are in units of 2 rb/(cm/ns)3. The dashed circles represent the energy threshold of the a-detectors.

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the maxima are at - 10” and + 80° and the minimum is at + 50°. This behavior might be consistent with the sequential decay (defined as the statistical decay of fully accelerated fragments) of PLF’s and TLFs. The two maxima could result from the overlap of the circular ridges one from the decay of the TLF’s and the other from the decay of the PLFs. As the detection angle of the PLF’s moves from + 20” to +40°, so might the maxima and the minimum move by about 20”. The energy spectra of a-particles in coincidence with quasi-elastic PLF’s (QEPLF’s) at +20” are shown in figs. 21a and 21b and in coincidence with deepinelastic PLF’s (DI-PLF’s) at +20” are shown in figs. 21c and 21d. Note that these spectra are very similar to the energy spectra of a-particles in coincidence with carbon ions presented previously in fig. 17. In order to estimate how much of the a-particle cross section can in fact be explained in terms of the sequential decay of both PLF’s and TLF’s, we have performed simple schematic calculations. The a-decay energies are parameterized with Boltzmann distributions and the primary energy and angular distributions in the laboratory frame of the decaying PLF’s are parameterized with gaussians and exponentials whose means and widths vary smoothly with the laboratory angle of the primary PLF’s. Because of the two-body intermediate state, the primary distributions of the PLF’s determine the spatial distribution of the TLF’s prior to their decay. The emission of the light particles is assumed to be isotropic in the reaction plane defined by the HI-detector and the beam direction. The two cases considered are (9

16Q+48Ti + 16Q*+4*Ti + ‘2C+a+4*Ti,

(ii)

‘60+48Ti

-+ 1zC+52Cr* + ‘2C+48Ti+a.

A simple analytical expression for the cross section can be obtained because of the assumption of the three-body final state. Case (i) provides the contribution to the a-distributions from the decay of the 160 and case 2 from the decay of the 52Cr. It is clear that in reality with 200 MeV excitation energy there will be many particles in the final state. The effect of multiple particle emission leads to broader angular correlations and broader a-spectra and PLF spectra. The parameters are adjusted to fit the data at selected angles in which sequential decay processes are expected to dominate. After the shapes of the calculated energy spectra of both a-particles and PLF’s reproduce the experimental spectra, then the calculated spectra are normalized to the data. Although many particles might be emitted in these collisions, with this procedure we are able on the average to account for the effects of multiple-particle emission. In what follows we will be comparing the calculated energy spectra from this model for the above two cases to the a-particle and PLF energy spectra obtained by adding together the spectra for the PLFs of atomic numbers from 4 to 10. The experimental light-particle energy thresholds have not been included in the calculation.

Fig, 21. Energy spectra of a-particles in coincidence with quasi-elastic products (2 = 4-10) (a) and (b), and with deep-inelastic products (2 = 4-10) (c) and (d) observed at +2Oa. The dashed curves are the calculated spectra for the decay of the PLFs, the dotted curves for the decay of the TLFs, and the sum of both contributions is represented by solid curves.

*I$

(d)

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The dashed curves in fig. 21 are the cc-energy spectra arising from the decay of the PLF’s (case (i)) and the dotted curves are the result of the decay of the TLF’s (case (ii)). The solid curves are the sum of the two contributions. The energy spectra of the PLF’s in coincidence with the a-particles are presented in figs. 22a and 22b together with the calculated curves. The dashed curves are the “C energy spectra arising from the decay of the I60 (case (i)) and the dotted curves are the r2C energy spectra from case (ii) in which “C appears as a primary fragment and does not decay. The shapes of these spectra hardly change with angle. The solid curves are the sum of the two contributions. The parameters for the decay of the TLF’s are adjusted to best describe the spectra at the backward angles of -80” and - 130” where the decay of the PLF’s is not expected to contribute due to the kinematic restrictions and also where nonequilibrium effects are minimal. The decay energy distributions are adjusted to reproduce the shape of the a-spectra at -80” and - 130° in figs. 21a and 21~. The contribution to the energy spectra from the decay of the TLF’s isi a djusted to the

70

I40 210 280 350

EK~ (MeV) Fig. 22. Energy spectra of projectile-like fragments (Z = 4-10) observed at +200 in coincidence with u-particles at the indicated angles. The dashed curves are the calculated spectra for the decay of the PLFs, the dotted curves for the decay of the TLFs, and the sum of both contributions is represented by solid curves.

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tails in the spectra at - 130” in figs. 21a and 21~. This provides the normalization factor to be applied to other a-angles for both cc-energy spectra and PLF energy spectra. The parameters for the primary energy distributions are adjusted to fit the PLF energy spectrum at -80° in fig. 22. The parameters for the contribution to the a-distributions from the decay of the PLF’s are adjusted to reproduce the data at +50° together with the contribution from the decay of the TLF’s. At this angle the contribution of the PLF’s is normalized to the tails of the a-energy spectra at +50° in figs. 21b and 21d. This factor for the PLF’s contribution is common to all other angles for both cc-spectra and PLF spectra. The assumption then is that at + 50° the a-energy spectra can be explained entirely in terms of sequential emission processes. Therefore, the calculation gives an upper limit for the contribution of sequential emision processes. For the decay of the QE-PLF’s, one can observe that the forward emission is distinctly separated from the backwards emission in the calculated z-energy spectra at + 10” and 30° in fig. 21b. Comparing these spectra to the same spectra for DIPLFs in fig. 21d, we note that the separation is not as great since the emitting PLFs are not moving as fast. This effect is manifested in the data at both + 10” and +30”. However, the experimental spectra are not exhausted by the calculated spectra presumably because at these forward angles sources of nonequilibrium aparticles contribute to the spectra. Comparing the calculation to the a-energy spectra on the opposite side of the beam, we find that the decay of the QE-PLF)‘s can contribute significantly to the higher-energy portion of the spectra at forward angles (- 10” in fig. 21a) whereas the decay of the DI-PLFs contribute to the lower portion of the spectra (- loo fig. 21~). This also is the effect of different source velocities. From these comparisons, most of the high-energy a-particles from -loo to -40° are not accounted for in terms of the sequential decay of both PLF’s and TLF’s. It is also interesting to note that the lower portion of the energy spectra from - 10“ to -80” is also not all accounted for by the calculation, especially notable in fig. 21a. It would seem that after subtracting the calculated spectra for the sequential decay of both fragments from the experimental spectra, a broad high-energy component would remain and extend to low energy. This would indicate that the excess yield in the lower portion of the energy spectra might arise from a mechanism similar to the one which leads to the emission of high-energy aparticles. However, if this is the case, then one would also expect a similar excess yieid in the lower portion of the energy spectra for a-particles in coincidence with FLR’s (figs. 8 and 9). The absence of the excess in case of FLR’s suggests that these lower energy a-particles are a result of some mechanism other than the one that leads to high-energy a-particles. In a similar manner, the calculation was performed for the cx-particles in coincidence with PLF’s at +40°. At this angle the contribution from the quasi-

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320

‘” 0

40

80

120 I60

206 0 Ea

40

80

120 I60

200

(MeV)

Fig. 23. Energy spectra of a-particles in coincidence with deep-inelastic products (2 = 4-10) observed at +400. The dashed curves are the calculated spectra for the decay of the PLF’s, the dotted curves for the decay of the TLFs, and the sum of both contributions is represented by solid curves.

elastic component is gone. Figs. 23a and 23b show the a-energy spectra on the opposite side of the beam and on the same side of the beam as the detected PLFs, respectively. As before the calculation cannot explain the high-energy portion of the spectra in the forward direction from -loo to -40” on the opposite side of the beam in fig. 23a. The calculation is in much better agreement on the same side of the beam in fig. 23b with the exception of + lo0 where the caicuiation overestimates the data. In figs. 24a and 24b, the energy spectra of the PLF’s at +40” in coincidence with cr-particles are presented together with the calculated spectra. It is interesting to note that the excess high-energy tr-particles at - lOa to -30” shown in fig. 23a appear to come primarily from lower energy PLFs, as the calculation agrees better

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E~LF (MeV) Fig. 24. Energy spectra of projectile-like fragments (2 = 4-10) observed at +W in coincidence with a-particles at the indicated angles. The dashed curves are the calculated spectra for the decay of the PLFs, the dotted curves for the decay of the TLFs, and the sum of both contributions is represented by solid curves,

with the higher portion of the PLF spectra shown in fig. 24. A sharp change in the shape of the experimental PLF spectra occurs between - 40° and - 30”. At - 40” the peak occurs at 60 MeV, whereas at -30” the distribution becomes broader and the peak shifts to 35 MeV. This occurs also at just the angle where the high-energy component in the a-spectra begins to dominate (fig. 23a). Figs. 25a, 25b and 25c show the evolution of the angular correlations from lowto high-velocity a-particles in coincidence with QE-PLFs at +20”, with DI-PLFs at +20° and with DI-PLFs at +40°, respectively. Windows have been placed on the laboratory velocity of the cl-particles, and the average velocities are indicated. At the bottom of these figures are the angular correlations integrated over the whole energy spectrum of the cc-particles. The calculated contributions from the sequential decay of the PLFs, from the decay of the TLFs and the total

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Fig. 25. Angular correlations of c+particles in coincidence with quasielastic products (2 = 4-10) observed at 20” (a), with deep-inelastic products (2 = 4-10) observed at +20° (b), and with deep-inelastic products (2 = 4-10) observed at +W (c). The correlations are plotted for different velocity windows in the laboratory velocity of the a-particles. The average velocity for each window is indicated in units of cm/ns. At the bottom of the figures, the total correlations integrated over the entire velocity spectra of the a-particle are shown.

contributions are indicated as dashed, dotted and solid curves, respectively. Since the experimental energy thresholds for a-particles have not been included in the calculation, the experimental points at - 130° and + 140” fall below the calculated correlations.

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The correlations with an average velocity of 6 cm/m are representative of CG particles with beam velocity. In the case of the QE-PLFs this angular correlation is symmetric with respect to the beam direction, whereas in the case of DI-PLFs at both +20° and +40° the correlations are asymmetric peaking at - 10” regardless of the detection angle of the PLFs. This indicates that these high-velocity aparticles are emitted during the early stages of the collision before the two nuclei have interacted strongly. The component of the lower velocity n-particles is represented by the correlations with an average velocity of 3 cm/ns. In these correlations there is good agreement on the same side of the beam as the detected PLFs. However, on the opposite side the of the beam between - 10” and -40° the calculation underestimates experimental points. In case of the PLFs at +40”, the peak of the contribution from the decay of the PLFs has moved from - 10” (b) for PLFs at +20” to + loo (c). The shape of the experimental correlation on the opposite side of the beam becomes skewed in (c) as compared to (b). This dependence on detection angle of PLFs might suggest that these lower velocity a-particles are emitted during the interaction time but prior to the full acceleration of the two heavy fragments. The emission of protons in coincidence with PLFs is similar to the emission of a-particles. The angular correlations integrated over the proton energy spectra for QE-PLFs at + 20°, for DI-PLFs at + 20° and for DI-PLFs at + 40° are shown in figs. 26a, 26b and 26c, respectively. In the case of QE-PLFs, the largest excess over the predictions for sequential decay is on the same side of the beam as the detected PLFs, whereas, in the case of DI-PLFs, the largest excess is on the opposite side of the beam. For DI-PLFs at +40°, the calculated correlation agrees with the experimental one except at + 10” where the calculation overestimates the data. Due to the higher velocity of the protons, the calculated correlations for the sequential emission of protons are broader and exhibit less structure than the calculated correlations for a-particles seen at the bottom of fig. 25. This is in contrast to the experimental angular correlation which exhibit more structure in the case of protons than of a-particles. This same contrast is observed in the comparison of the correlations of a-particles (fig. 10) and protons (fig. 14) in coincidence with fusion-like residues. Integrating over the out-of-plane correlations measured at the angles indicated in sect. 2 and over the in-plane correlations, we have estimated the average multiplicities of a-particles and protons in coincidence with PLFs. The average multiplicities of the low-energy component and the high-energy, nonequilibrium component of a-particles and protons are tabulated in table 2. Also listed in this table are the average multiplicities accounted for in terms of the sequential model calculations and those which are not accounted for by sequential emission processes. It should be noted, that the portion of the average multiplicities explained by sequential emission processes is an upper limit.

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-’ -100

102

-180

-20 20 100 8,~ (DEG)

Fig. 26. Angular correlations of protons in coincidence with deep-inelastic products at +20” (b), and with deep-inelastic are the calculated spectra for the PLF’s, the dotted curves of both contributions is represented

6.

180

quasi-inelastic products at +20° (a), with products at +40° (c). The dashed curves for the decay of the TLF’s, and the sum by solid curves.

Conclusions

We have performed inclusive experiments and have measured the energy spectra and angular distributions of heavy ions (Z 1 3) produced in the reactions of 227 MeV and 310 MeV 160 with Ti. Comparisons with statistical model calculations allowed us to derive upper limits to the complete fusion cross sections of 647 mb and 265 mb for projectile energies of 227 MeV and 310 MeV, respectively; these cross sections are about 54% and 24% of the total cross sections for the group of fusion-like residues (Z >= 16). For the case of 310 MeV projectile energy, an upper limit of 360 mb was estimated for the cross section of target-like fragments from binary reactions which could contribute to the group of fusion-like residues. We extracted a lower limit of 505 mb for the cross section of incomplete fusion processes.

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TABLE2 Average multiplicities of light-particles in coincidence with projectile-like fragments e PLF

High E,

Low E,

+2O=‘QE”)

0.17*0.03

1.4kO.5

+20’= DI b,

0.28 + 0.05 0.31*0.06

1.9kO.5 2.1 f0.6

Seq. a

Nonseq. a

+4O=‘DI 9PLF + 20° QE + 20” DI +40° DI ‘) “) ‘) d,

0.63 TLF “) 0.44 TLF 0.80 TLF

0.35 PLF ‘) 0.26 PLF 0.19 PLF

0.60 1.5 1.4

High E, x0.2

zo.4

0.51 kO.08 0.19+0.03 Seq. p 0.35 TLF 0.70 TLF 0.74 TLF

Low E,

Q.16 PLF 0.26 PLF 0.34 PLF

1.0 _+O.l 0.78 k 0.09 Nonseq. p 0.1 0.55 0

Quasi-elastic products Z = 410. Deep-inelastic products Z = 410. Sequentially emitted from target-like fragments. Sequentially emitted from projectile-like fragments.

We have further studied the a-particle and proton decay of excited nuclei produced in the reactions of 310 MeV I60 with Ti and we have found emission process of light particles which do not result from simple statistical evaporation. Emission of high-energy a-particles and protons is observed to be a characteristic feature of quasi-elastic, deep-inelastic and fusion-like reactions. Average multiplicities of the order of 1 for these fast, high-energy a-particles and protons in coincidence with any HI at + 20° or +40° were estimated. The energy spectra of these fast particles are broad and extend to the lower portion of the spectra where sequential processes contribute. The angular correlations of high-energy light particles are narrow and asymmetric with respect to the beam direction peaking on the opposite side of the beam at - 10” or 20°. (In the case of proton correlations there is also a peak at +30”.) These correlations are also independent of the identity of the coincident heavy ion and the heavy-ion detection angle indicating that these fast particles are emitted during the early stages of the collision. According to Dtinnweber and Hartmann 48) the deflection function of the heavyion collision is reflected in the asymmetry of the correlation of fast light particles emitted in binary collisions. In this picture, the correlations of fast particles in coincidence with projectile-like fragments would be consistent with negative-angle scattering. The fast particles are emitted during the early phases of the interaction and remove energy and angular momentum, and the two fragments will either fuse resulting in incomplete fusion processes or undergo inelastic scattering resulting in incomplete deep-inelastic processes. The process responsible for the prompt emission of light particles appears to be the principles mechanism which limits complete fusion and leads to the observation of fusion-like residues. This is in contrast to the predictions of dynamic-model calculations 35) which predict the

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increase of deep-inelastic processes as the mechanism reducing the compound nuclear cross section. A second component of a-particles observed in coincidence with deep-inelastic and quasi-elastic projectile-like fragments and having an intermediate velocity between the velocities of the beam and the center of mass appears as an excess yield in the direction of the recoiling target-like fragments and cannot be accounted for in terms of the sequential decay of both primary fragments. The lower velocities of these light particles (as compared to the high-velocity component) and their angular correlations indicate that these particles result from stronger interactions than those producing the fast particles and are emitted during the interaction but prior to the full acceleration of the two outgoing fragments. These particles would not necessarily have to be characterized as pre-equilibrium or nonequilibrium as in the case of the high-velocity component. During the interaction a large amount of the relative kinetic energy may be converted into excitation energy and may be even fully dissipated due to short internal equilibrated time. As a result the lifetime for light-particle emission becomes of the order of the interaction time. The detection angle of the PLF’s appears to play an important role in the observation of nonequilibrium processes. If the angle is small and close to the grazing angle, contributions of nonequilibrium processes at forward angles are hidden under a large amount of light particles sequentially emitted from the projectile-like fragments. This problem is especially severe if ones considers quasielastic reactions l’). The detection angle of the heavy ions in the present study were chosen far behind the grazing angle of 5”, so that the contribution of nonequilibrium light particles was enhanced. We wish to thank the operations crew of the Texas A & M cyclotron for their assistance. We also appreciate the effort of Chris Landphair for the many hours of data processing. This work was supported by the United States Department of Energy and the Robert A. Welch Foundation. References 1) J. Galin, B. Gatty, D. Guerreau, C. Rousset, U. C. Schlotthauer-Voos and X. Tarrago, Phys. Rev. C9 (1974) 1126 2) J. W. Harris, T. M. Cormier, D. F. Geesaman, L. L. Lee, Jr., R. L. McGrath and J. P. Wurm, Phys. Rev. Lett. 38 (1977) 1460 3) H. Ho, R. Albrecht, W. Diinnweber, G. Graw, S. G. Steadman, J. P. Wurm, D. Disdier, V. Rauch and F. Scheibling,Z. Phys. A283 (1977) 235 4) H. Ho, P. L. Gonthier, G.-Y. Fan, W. Kuhn, A. Pfoh, L. Schad, R. Wolski, J. P. Wurm, J. C. Adloff, D. Disdier, A. Kamili, V. Rauch, G. Rudolf, F. Scheibling and A. Straazeri, Phys. Rev. C27 (1983) 584 5) G.-Y. Fan, H. Ho, P. L. Gonthier, W. Kuhn, A. Pfoh, L. Schad, R. Wolski, J. P. Wurm, J. C. Adloff, D. Disdier, V. Rauch and F. Scheibling, Z. Phys. A310 (1983) 269 6) C. K. Gelbke, M. Bini, C. Olmer, D. L. Hendrie, J. L. Laville, J. Mahoney, M. C. Mermaa, D. K. Scott and H. H. Wieman, Phys. Lett. 71B (1977) 83

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