Fragment emission from modestly excited nuclear systems

NUCLEAR PHYSICS A ELSEVIER

Nuclear Physics A 604 (1996) 219-244

Fragment emission from modestly excited nuclear systems Y. Lou a, R.T. de Souza a, S.L. Chen a, E.W. Cornell a, B. Davin a, D. Fox a,1, T.M. Hamilton a, K. Mcdonald a, M.B. Tsang b, T. Glasmacher h, J. Dinius h, C.K. Gelbke b, D.O. Handzy b'a, W.C. Hsi b'3, M. Huang b, W.G. Lynch b, C. Montoya h'4, C. Schwarz b'5, D. Prindle c, A.A. Sonzogni c, R. Vandenbosch c, J.L. Wile 0,6, M. Parker d, C.L. Coffing d a Department of Chemistry and Indiana University Cyclotron Facility, Indiana University, Bloomington, IN 47401, USA b National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824, USA c Nuclear Physics Laboratory, University of Washington, Seattle, WA 98195, USA d Department of Chemistry, Ball State University, Muncie, IN 47306, USA Received 8 December 1995; revised 6 February 1996

Abstract Fragment emission patterns occurring in nuclear systems of modest excitation are studied. Exclusive measurement of fragment emission in 14N+197Au reactions at E / A = 100, 130 and 156 MeV allows selection of central collisions where a single source dominates the decay. Low threshold measurement of 1MF emission for these events allows investigation of the influence of detector threshold effects. The time scale of fragment emission is deduced using fragmentfragment velocity correlations. Comparisons are made to the predictions of a statistical decay model. Keywords: NUCLEAR REACTIONS 197Au(14N,X), E = 100-156 MeV/nucleon; measured (fragment) (fragment) correlations, emission patterns; deduced emission time scale; statistical decay model

1 Present 2 Present 3 Present 4 Present 5 Present 6 Present

address: address: address: address: address: address:

AECL, Chalk River Laboratories, Chalk River, Ontario K0J I J0, Canada. Deloitte and Touche, LLP, Two World Financial Center, New York, NY 10281, USA. Indiana University Cyclotron Facility, Bloomington, IN 47408, USA. Merril Lynch, Two World Financial Center, New York, NY 10281, USA. GSI, D-64220, Darmstadt, Germany. Pathologists Associated, 2401 West University Ave., Muncie, IN 47306, USA.

0375-9474/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved PH S 0 3 7 5 - 9 4 7 4 ( 9 6 ) 0 0 1 0 6 - 6

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1. Introduction Low density nuclear matter at intermediate excitation might disassemble into a mixture of several intermediate mass fragments (IMF: 3 ~< Z ~< 20) and light charged particles (LCP: Z ~< 2) [ 1-4]. Such a decay mode, involving copious fragment production, might provide insight into the nuclear equation of state away from equilibrium density [5,6]. The experimental observation of such breakup configurations in intermediate energy heavy-ion collisions has stimulated considerable speculation as to the mechanism underlying this phenomenon [7-10]. In contrast, at relatively low excitation (E* ~< 300 MeV) where the probability of fragment emission is low, the emission of intermediate mass fragments is well understood in terms of a statistical emission process [ 11,12]. Light-ion and light heavy-ion induced multifragmentation are interesting as they allow one to prepare a highly excited system free of compressionally driven instabilities. Moreover, light heavy-ion induced reactions are not subject to the same transient shape instabilities as heavy-ion collisions at intermediate impact parameter [ 13]. However, bombardment of heavy nuclei with light heavy ions (A ~< 40) has suggested a saturation in the deposition of excitation energy into the composite system [ 14]. Such a saturation might limit the ability of light heavy-ions to induce multifragment decay at intermediate energies ( E / A <~ 200 MeV). In contrast, inclusive measurement of IMF cross sections for intermediate energy ( E / A = 20-100 MeV) 14N induced reactions on natAg and 197Au targets indicated that for a gold target nucleus multifragmentation might occur in the vicinity of E/A = 140 MeV. In order to resolve these ambiguities, as well as characterize the general features of light-ion induced multifragment decay with an exclusive measurement, we have investigated the reaction 14Nd-197Au at E/A = 100156 MeV. The present paper focuses on the transition from the low excitation regime to the regime where multiple fragment emission describes the average behavior of the excited system.

2. Experimental setup The experiment was performed using the K1200 cyclotron at the National Superconducting Cyclotron Laboratory at Michigan State University. Beams of 14N at E/A = 100, 130 and 156 MeV, with an intensity of approximately 1 × 108 particles per second impinged on a 197Au target with a surface density of 1 mg/cm 2. Charged particles emitted into the angular range 9 ° ~< 0lab ~ 160 ° were detected using the MSU Miniball array [ 15]. Each Miniball element consists of a 4 mg/cm 2 plastic scintillator foil backed by a 2 cm thick CsI(T1) crystal. Particles which punched through the plastic scintillator foils were identified by atomic number up to Z = 16 and by mass number for Z = 1 and 2. Particles which stopped in the scintillator foil were recorded, but could not be identified by atomic number. The approximate energy thresholds for particle identification were Eth/A ~ 2 MeV for Z = 3, Eth/A ~ 3 MeV for Z = 10, and Eth/A ~ 4 MeV for Z = 18. Energy calibrations, accurate to within 10%, were obtained for 9 ° ~< 0lab ~< 160 °, by

Y Lou et al./Nuclear PhysicsA 604 (1996) 219-244

221

combining the "punchthrough" points of light charged particles in the CsI(T1) crystal with detailed detector response functions measured at the NSCL K1200 cyclotron of Michigan State University. In this experiment, the Miniball 47r detector array was augmented by a set of 10 low threshold high resolution telescopes. These detectors consist of an axial ion chamberSi-CsI(T1) stack arranged in a compact geometry which allows each telescope to replace a single Miniball detector element [ 16]. The threshold for these detectors is 0.8 MeV/nucleon. Replacement of individual Miniball detectors at selected angles allowed sampling of the single particle distributions with low thresholds for comparison to the distributions measured by the Miniball. Two trigger conditions were used in this experiment. The first condition required that at least one ion chamber telescope was triggered in order to record the event. To suppress triggering on alpha particles in the forward ion chamber telescopes a fast veto logic circuit was employed. The second trigger condition involved a scaled down number of "inclusive" events which were also recorded. For these "inclusive" events, at least two detectors in the Miniball were triggered in order to record the event. The solid angle subtended in this experiment corresponded to 75% of 4~-.

3. General properties In Fig. 1 the multiplicity distributions of charged particles emitted in 14Nq-197Au at Elab/A = 100, 130 and 156 MeV are shown. These multiplicity distributions are associated with the "inclusive" trigger condition used in the experiment. All these multiplicity distributions are typical of the distributions involving collisions of two heavy ions and can be characterized by a relatively fiat plateau over a broad range followed by an exponential tail at the highest multiplicities. The charged particle multiplicity can be qualitatively related to the excitation of the system. Increasing charged particle multiplicity corresponds to increasing excitation. Alternatively, the charged particle multiplicity can be related by a geometrical prescription [ 17] to the reduced impact parameter, b/bmax, where bmax represents the largest interaction radius for which two charged particles are emitted. Shown as arrows in Fig. 1 are the multiplicities corresponding to b/bmax = 0.4 and 0.2 at each incident energy. As the incident energy increases from E/A = 100 to 156 MeV, the multiplicity corresponding to b/bmax = 0.2 increases from Nc = 13 to Nc = 16. Selection of these high multiplicity events allows investigation of the most central collisions which presumably also correspond to systems of the highest excitation. An alternate means of examining the violence of the collision, is to investigate the extent to which a single residue survives. This survival probability can be deduced by examining the dependence of the total detected charge, Zsum (~--~Z ~< 20), on the charged particle multiplicity, N¢. A two-dimensional representation of this dependence is shown in Fig. 2. The shades of gray represent the relative probability of occurrence of events characterized by a specific Zsumand Nc. As the charged particle multiplicity,

222

Y Lou et al./Nuclear Physics A 604 (1996) 219-244 10 9

197Au

los

-

10 7

-- ~-~ .....

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E/A=I

6

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5

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15

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Nc Fig. 1. Charged particle multiplicitydistributions in 14N + 197Auat E/A = 100, 130 and 156 MeV. Arrows indicate the multiplicitycorrespondingto b/bmax <~0.2 and 0.4 at each incidentenergy. No, increases, the most probable value of Zsum also increases. For a given N o however, the distribution in Zsum is relatively broad. With increasing incident energy, the twodimensional distribution extends only slightly further into the Zsum-Nc plane. Even for the highest multiplicities at the highest incident energy only approximately 50% of the total charge of the system is detected. Since the efficiency for detection of light charged particles and IMFs is relatively high, this result is qualitatively consistent with the survival of a heavy residue. For high multiplicities, fission does not appear to be a significant decay channel as no angular correlation of two slow heavy fragments is observed. For more peripheral reactions fission is observed as a dominant exit channel by the strong back-to-back correlation of two slow heavy fragments. A more quantitative examination of these trends can be found in Fig. 3. The dependence of the first and second moments of the Zsum distribution on Nc is displayed in Fig. 3. At all three incident energies the (Zsum) increases linearly with Nc attaining (Zs,m) of ~ 40 for the highest multiplicity events. Thus, for the most central collisions approximately 50% of the total charge of the system is detected as light charged particles and IMFs at all three incident energies. This result, indicative of survival of a single evaporation residue following a fusion reaction, is qualitatively consistent with the direct measurement of the evaporation residue cross section [ 18] for this reaction. The standard deviation of the Zsum distribution, o-z~ also increases linearly with increasing N~ initially but saturates at a value of approximately 4-4.5 for the most central collisions. The solid and dashed lines shown in the figure depict the results of statistical model calculations (GEMINI) used to estimate the excitation of the system. These calculations are described more fully in Section 8. Shown in Fig. 4 is the dependence of the fragment multiplicity on the charged particle multiplicity, Nc. At each incident energy, the average fragment multiplicity increases as

Y. Lou et al./Nuclear Physics A 604 (1996) 219-244

223

8O 70 60

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Nc increases, reaching a maximum at the highest multiplicities. The maximum average fragment multiplicity, (NIMF), increases from 0.95 at E/A = 100 MeV to 1.35 at E/A = 156 MeV. These values of the fragment multiplicity are comparable to the fragment multiplicities measured for central 'collisions in 36mr + 197Au at E/A = 35 and 50 MeV ((NIMF) ~ 1 and 2, respectively). It is interesting to note that a previous inclusive measurement of IMF cross sections [ 19] for the systems 14N+natAg, 197Au at E/A = 20-100 MeV observed a dramatic increase in the IMF cross section for the Ag target at E/A ~ 70 MeV and suggested a similar increase might occur for the Au target at

224

Y. Lou et al./Nuclear Physics A 604 (1996) 219-244

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No Fig. 4. Dependenceof the averagefragmentmultiplicity,NIMF,on the total chargedparticle multiplicity,Nc. E / A ~ 125 MeV. The solid and dashed lines shown in Fig. 4 represent the results of the GEMINI calculations which are described in Section 8. In Fig. 5 we compare the dependence of the fragment multiplicity associated with central collisions (b/bmax <<. 0.2) on the center-of-mass energy (assuming full linear momentum transfer) for both the 14N and 36Ar induced reactions. While both the excitation functions exhibit a monotonic increase of fragment multiplicity with incident energy, the 36Ar induced reactions exhibit a significantly larger fragment multiplicity. Moreover, if the center-of-mass energy scale is corrected for the fraction of linear momentum transfer to the composite system (deduced from Viola systematics) then the apparent divergence for the two systems is reduced, suggesting a common underlying relationship between NIMF and the excitation of the system, E*. To examine more fully the characteristics of fragment emission for the 14N induced reactions we investigated the relative probabilities for fragment emission at the three incident energies selected on impact parameter. All the distributions shown in Fig. 6 are well described by Poisson distributions. This result has previously been observed for similar systems of modest excitation [20] and can be understood when the probability of emission of a single fragment is small. Higher fragment multiplicities which are observed simply correspond to the combinatoric probability associated with multiple single emission probabilities. Such a result is not too surprising considering the small average fragment multiplicities for these reactions.

225

Y Lou et aL/Nuclear Physics A 604 (1996)219-244

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NIMF Fig. 6. Relative fragment probability distributions selected on charged particle multiplicity. The solid lines correspond to Poisson functions. To examine the constraints imposed by previous inclusive studies of IMF emission, we have examined the preferential selection of collisions based on the IMF multiplicity (Fig. 7) or the detection angle o f a single IMF (Fig. 8). As can be seen in Fig. 7 selection o f at least one IMF preferentially selects higher multiplicity events. This preferential selection is observed at all three incident energies. Since multiplicity is correlated with the excitation o f the system, this bias can be understood since emission of at least one IMF requires a certain minimum excitation of the system. In contrast,

226

Y. Lou et al./Nuclear Physics A 604 (1996) 219-244

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0.06

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selection of two IMFs as opposed to one does correspond to only a small shift in the multiplicity distribution. The dependence of the multiplicity distribution on the angle of the detected IMF is explored in Fig. 8. Except for the most forward angle at E/A --- 100 MeV where the multiplicity distribution deviates strongly from a gaussian shape, detection of an IMF at any angle 0lab /> 10 ° seems to yield essentially the same multiplicity distribution. For the most forward angle (9 ° ~< 0lab <~ 16 °) at E/A = 100 MeV, the peaking of the

Y Lou et al./Nuclear Physics A 604 (1996) 219-244

227

multiplicity distribution at low multiplicities can be understood as sensitivity to more peripheral reactions. Nevertheless, these reactions comprise only a small fraction of the yield associated with fragment emission as can be seen in the figure.

4. Z distributions Element distributions associated with multifragment decay have stimulated considerable interest [21-23]. The element distributions associated with central collisions (b/bmax <~ 0.3) for this reaction at E / A = 156 MeV are depicted in Fig. 9. These distributions are constructed from the ionization chamber telescopes to avoid the distortions imposed by the Miniball thresholds. To investigate the effect of thresholds on the measured Z distributions, we have imposed the Miniball thresholds on the Z distributions measured by the ionization chamber telescopes. The result is displayed as the open diamonds in Fig. 9. The presence of thresholds has the overall effect of suppressing the measurement of large Z products. The effect is noticeable for 0lab ~> 35.5 ° and is severe at the backward angles, 0lab >/ 110 °. We have investigated the differences between fitting the measured distributions with a power law distribution ( Y ( Z ) c< Z - r ) and exponential distributions ( Y ( Z ) cx e-~Z). The fits were performed over the range Z = 3-14 to prevent threshold limitations at large Z from affecting the fit. The results of these fits are shown in the figure as the solid line (power law) and solid diamonds (exponential). As can be clearly seen, the suppression of the measured yield of large Z products yields an element distribution better characterized by an exponential than by a power law. In contrast, the Z distributions measured with low thresholds are better described by a power law ( Z - r ) than by an exponential. To examine any angular dependence of the element distributions, we have independently fitted the Z distributions at each of the angles measured. The results of these fits are shown in Fig. 10. At all three incident energies r exhibits a forward peaking, particularly for the inclusive measurement. Although selection of central collisions suppresses this forward peaking it does not totally eliminate it. Large values of 7- correspond to a steep Z distribution, indicating a relative enhancement of low Z IMFs in preference to high Z IMFs. This enhancement can be understood in terms of projectile-like fragments which contribute to the Z distribution particularly for peripheral collisions. The enhancement of r at forward angles for the central collisions is more difficult to interpret. Perhaps the forward-backward asymmetry is due to pre-equilibrium IMFs which are preferentially emitted in the forward direction. Systematic uncertainties in the extraction of 7- are depicted in the figure as representative error bars. The solid horizontal line and the dotted horizontal line shown in Fig. 10 correspond to the extracted value of 7- based on the angle-integrated Z distribution for the inclusive and centrally gated Z distributions, respectively. For peripheral reactions particularly at E / A = 100 MeV, the large values of 7- at forward angles clearly influence the angle-integrated value of 7- extracted. For central collisions, however, the angle-integrated value of 7" is in fair agreement with the values of 7- measured at backward angles. The value of 7- attains a

228

Y Lou et al./Nuclear Physics A 604 (1996) 219-244

lO 5 iO4 ~o 103 -~ 02 105 ~ ~

lO 4

3° 5

5 45 °

.~°.

lO 3

N 102 105 10 4 77 10 3

iO 2

0 5 lO15 0 5 lOi5 0 5 1015 Z Fig. 9. Element distributions measured with low thresholds (open circles) associated with b/brnax <~ 0.3 (scaled by a factor of 10 for clarity) for the reaction 14N+197Au at E/A = 156 MeV. Also shown are the element distributions (open diamonds) for particles above the Miniball thresholds. Power law and exponential fits to these latter distributions are shown as the solid lines and solid diamonds, respectively.

minimum value of r = 1.8-2.0 at backward angles. This value is also consistent with the value of r extracted from low threshold measurements of backward emission of IMFs in high energy induced 3He reactions on 197Au and natAg target [24]. In inclusive high energy ( 1 ~< Ep <~19 GeV) proton induced reactions on heavy nuclei a minimum in the r parameter was observed. The value of r measured in this work is only slightly higher than the value of rmin measured in those previous inclusive measurements. Perhaps r values in this range can be related directly to the onset of multifragment emission. Further systematic, exclusive low threshold measurements are needed investigate this possibility. In order to further illustrate the distortions caused by threshold effects on the extracted power law parameter, we have fitted the open diamonds in Fig. 9 with a power law. These extracted power law parameters decrease from a value of 3.2 at Blab = 16 ° to 2.2 at 0lab /> 50 °. For angles larger than 0lab = 50 ° the value of r rises purely as a consequence of the thresholds. Clearly, threshold effects are extremely important in the distortions they impose on measured Z distributions.

5. Angular distributions The angular distribution of fragments is shown in Fig. 11. These angular distributions were measured using the low threshold ion chamber telescopes. At forward angles

229

Y Lou et al./Nuclear Physics A 604 (1996) 219-244

~ - T ~ i4 N +

3.0

E/A-100

MeV-

....

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197Au

1 3 0 MeV

1 5 6 MeV

IC:crz~ z * Inclusive 2.5

*

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,%

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0

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]

, ,I .... J .... J . . . . . 1..... ~ l ~ 50 iO0 150 50 iO0 150

Olab (deg) Fig. 10. Dependence of the power law parameter, r, on laboratory angle as measured by the ionization chamber telescopes.

(0lab ~< 72 °) the angular distributions measured by the Miniball are essentially the same as the angular distributions measured by the ion chamber telescopes. At backward angles, however, the thresholds of the Miniball detectors result in a steeper angular distribution. Both the inclusive angular distributions as well as those selected on low multiplicity (peripheral collisions) and high multiplicity (central collisions) are shown. The similarity between the inclusive angular distributions and the angular distributions associated with central collisions is not surprising given the result of Figs. 7 and 8 which revealed that the detection of a single IMF preferentially selected high multiplicities. All the angular distributions shown are forward peaked, consistent with the decay of a moving source. All the angular distributions associated with peripheral collisions are more forward peaked than those associated with central collisions (most notably Z = 3 and 4), again demonstrating the suppression of forward IMFs by the multiplicity criterion. Such IMFs have been shown to originate from peripheral interactions (such as projectile breakup reactions) and complicate the interpretation of singles data [25].

6. Energy spectra Isolating the characteristics of a single source in heavy-ion induced reactions at intermediate energies requires complete phase space coverage over a broad angular range. Both energy spectra, as well as, angular distributions of emitted fragments are necessary to determine the extent to which a single source describes the fragment yield in a particular angular range. The energy spectra for various fragments 4 ~< Z ~< 9 are shown in Figs. 12-14. All the spectra shown can be approximately described as MaxwellBoltzmann distributions. As shown in Fig. 12, for a given Z with increasing laboratory

Y. Lou et al./Nuclear Physics A 604 (1996) 219-244

230

i0-i i0 2 i0 3 10-4

i0-i ._.10 -2

7

lo - 3


10-3 I0 4 i0-i 10-2 10-3 10-4

0

50

I00 150 0

50

i00 150

~lab(deg) Fig. 11. Angular distributions of intermediate mass fragments at E/A = 156 MeV measured by the ion chamber telescopes.

angle the spectra shift to lower energy. Moreover, the high energy component present in the tail of the spectra at forward angles (e.g. Z = 4, 0lab = 12.5 °) is significantly suppressed or absent at backward angles. This difference between the forward and backward energy spectra underscores the importance of measuring the backward angle fragment energy spectra for which dynamical, non-equilibrium processes play a lesser role than at forward angles. It is interesting to note that in the angular range measured, the heavier IMFs ( Z = 6, 7 and 8) do not exhibit a bump in the energy spectrum at large energy consistent with detection of a projectile-like fragment. Examples of the energy spectra measured at intermediate and backward angles are shown in Fig. 13. The inclusive energy spectra of fluorine fragments emitted at 0lab = 45 °, 72.5 ° and 110 ° in the present experiment at E/A = 100, 130, 156 MeV are compared. The general trends observed at all three angles are the same. The slope of the energy spectra at a given angle does not depend strongly on incident energy indicating a possible saturation in the temperature attained as a function of bombarding energy. For a given angle, the peak of maximum cross section decreases slightly in energy consistent with enhanced early light charged particle emission prior to IMF emission as the incident energy is increased. Since the spectra shown in Fig. 14 represent an average over all impact parameters we have investigated the details of the kinetic energy spectra of oxygen fragments associated with central collisions at E/A = 156 MeV.

Y Lou et aL/Nuclear Physics A 604 (1996) 219-244

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Y Lou et al./Nuclear Physics A 604 (1996) 219-244

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Energy (MeV) Fig. 14. Energy spectra of oxygen fragmentsat E/A = 156 MeV. The different symbolsshown in each panel correspond to laboratory angles of 0lab = 72°, 110°, 130°, and 150° for both inclusive reactions as well as high multiplicity events. In Fig. 14 significant qualitative differences are noticed between the inclusive energy spectra and those associated with central collisions. The energy spectra associated with central collisions have smaller slopes indicating that they arise on average from a system of higher excitation. In addition, the Coulomb barrier portion of the spectrum is shifted towards lower energy as compared to the inclusive spectra. Lastly, the width of the Coulomb bump in the spectra is significantly widened. Similar trends have previously been observed in excitation functions involving 3He projectiles on Ag and Au targets [26] and interpreted as a reduced Coulomb field due to either substantial charge loss or an expanded nuclear system. For the more modest excitation studied in this work, we have investigated whether these changes in the low energy part of the spectrum are indeed consistent with sequential emission from a decaying source in which the Coulomb barrier at the time of IMF emission changes due to competing light charged particle emission. The open and closed arrows shown in the figure indicate the Coulomb barrier calculated for oxygen relative to a 139La and 197Au nucleus, respectively. The internuclear distance between the two touching spherical nuclei was assumed to be

233

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r J

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30

40

5O

Zsum Fig. 15. Dependence of the energy associated with maximum yield, Epeak, on the total detected charge, Zsum.

given by R = [ 1.2(A 1/3 + A~/3) + 2] fm, where Ap and At are the mass number of the projectile and target nuclei, respectively. The maximum yield associated with central collisions is in qualitative agreement with the Coulomb barrier calculated for the 139La nucleus. Since the total charge Zsum associated with these collisions is approximately 40, this result would indicate that low energy IMFs are emitted late in the de-excitation cascade. A more systematic investigation of the dependence between the energy associated with the peak of maximum yield (most probable energy) and Zsum is shown in Fig. 15. The backward angle energy spectra (Blab ~ 72 °) for Z = 4 at each of the three incident energies were fitted with a gaussian in the vicinity of the maximum yield peak. The center-of-mass velocity Vcm was varied between zero and the velocity corresponding to full linear momentum transfer so that the value of Epeak at all backward angles was the same. Thus, the value of Epeak corresponds to the most probable energy in the center-ofmass frame. With increasing Zsum the value of Epeak clearly decreases. For Zsum = 0 an extrapolated value of Epeak = 41 MeV is deduced. This value is in fair agreement with the Coulomb barrier of 39.4 MeV estimated for a touching spheres configuration. The general trend of decrease and, moreover, the same rate of decrease of Epeak with Zsum,

234

Y Lou et al./Nuclear Physics A 604 (1996) 219-244

is observed at all three incident energies. Given the correspondence shown in Fig. 3 between the charged particle multiplicity and Zsum, Zsum can also be viewed as either an excitation scale or a centrality scale for which larger values of Zsum correspond to more central collisions - composite systems of higher excitation. If the IMF was emitted first-independent of the excitation of the system-then no dependence of Epeak on Zsum would be expected. This is shown as a solid line in Fig. 15. Also shown in Fig. 15 is the Coulomb barrier assuming that the IMF is emitted last in the de-excitation cascade. The most probable energy for Be fragments predicted by GEMINI (E* = 350-1600 MeV) is also shown in the figure. The underprediction by the model of the most probable energy is most likely due to the use of fission-like configurations for the calculation of emission barriers.

7. Fragment velocity correlations While fragment-fragment velocity correlations have been used extensively in studying fragment emission time scales [27-37] for multifragmenting systems, limited knowledge exists regarding fragment emission in systems of more modest excitation (E* 1000 MeV). Qualitatively, one expects (based on statistical considerations) the fragment emission time to increase with decreasing excitation. We have examined fragmentfragment velocity correlations for the systems studied in this work in order to investigate this expected trend. The velocity correlation function, R(Vred), is constructed by relating the coincidence yield Y to the background yield yt: ZY(Vl,V2)

= Ct[1 + R(Vred) ] ~-~Y*(Vl,V2),

where vl and v2 are the laboratory velocities of the fragments,/)red is the reduced velocity given by Vreo = (vl - v 2 ) / ( Z 1 + Z2) U2 cm/ns [31], and C* is the normalization constant determined by the requirement that R(vred) ---* 0 at large reduced relative velocities where the Coulomb repulsion is small. The background yield was constructed by selecting fragments from different events [38]. Since residual collective motion can induce strong distortions on the correlation function [ 37 ], we have investigated the degree to which rotational motion is present for our centrally selected collisions. To this end we have constructed the azimuthal correlation function defined by [39] Y(A¢)/Y'(A¢)

= C[l + R(A¢)],

where Y(Aqb) is the coincidence yield of two (identical) particles emitted with relative azimuthal angle A¢, Y'(A¢) is the background yield constructed by mixing particle yields from different events which satisfy the same constraints as the coincidence events, and C is a normalization constant. The correlation functions were constructed for alpha particles and Be fragments as shown in Fig. 16 emitted in the polar angular range of 12.5 ° ~< 0lab ~< 160 °. The correlation function was normalized so that the average value

Y. Lou et at~Nuclear Physics A 604 (1996)219-244

235

oZ4 mZ=2

1.2 O

-G-

O

1.0

n

0

O

nn ~

0

-i

÷ 0.8 0

14N +

0.6

197Au

E/A=130 MeV -t L

0

,,,I

.....

50

I ....

100 Aq5 ( d e e )

I,,

150

Fig. 16. Azimuthal correlation functions for Z = 2 and Z = 4 particles emitted in central collisions at E/A --- 130 MeV.

is 1. Emission from a rotating source yields a characteristic V-shape, i.e. suppression in the correlation function at ,dO = 90 °. This feature is noticeably absent in Fig. 16. The only salient feature of Fig. 16 is the suppression of yield at small A~b particularly for the Be fragments. This suppression has been previously observed for other systems [40] and is the result of Coulomb repulsion between the fragments and the remainder of the charged particles in the event. With the exception of the Coulomb suppression feature, the azimuthal correlation functions are relatively fiat for the central collisions selected. This result suggests that minimal angular momentum is present for the centrally selected collisions. All the correlation functions shown in this work were integrated over a narrow range in Z (4 ~< Zl, Z2 ~< 6). Recent evidence [41] suggests that different Z IMFs might sample different stages in the de-excitation cascade. If different mass IMFs do sample different emission times, then the restricted range in Z suppresses this additional effect. In Fig. 17 the dependence of the inclusive correlation function on increasing incident energy is depicted. The fragments used in constructing the correlation function were emitted in the angular range 16° ~< Olab ~ 80 °. The normalization constant was determined in the region 0.025c to 0.08c where the correlation function is relatively flat. At low relative velocity, the mutual Coulomb repulsion between the fragments results in strong suppression in the probability of observing fragments of similar velocity for all the correlation functions shown. As the incident energy is increased from E/A = 100 MeV to E/A = 156 MeV the correlation function does not exhibit any significant changes in shape. This result is in agreement with the results from another projectile-target system [33]. To examine the fragment interaction between pairs not subject to the additional complications of near/sub-barrier emission, we have constructed the correlation functions for fragments with E/A ~> 6 MeV. As can clearly be seen in Fig. 17, the selection of high velocity pairs results in a significantly wider Coulomb well indicative of a

236

Y. Lou et al./Nuclear Physics A 604 (1996) 219-244

i 9 7 A u ( 1 4 N , Z 1Z2)

¢)

4=
b/brn.xZi0.3

1.0

o

oe?

>

o O o 0 o

t

0 ©

0.5 0 O

4>

o.o

O /A)

• •

0

0

0 o

0 •

•

0 o •

•

I

10

20

30

o

lO0 MeV

o

156 MeV

•

156 MeV (E/A k 6 MeV)

40

50

Vr d (10 -:3 c) Fig. 17. Inclusivecorrelation functions integrated over 16° ~
Y. Lou et al./Nuclear Physics A 604 (1996)219-244

i

b/bm,~x 5 0.3,

1.0~0.5

..

" )-

.-

T=50 f m / c 3 body --7.=100 fm/c c a l c u l a t i o n : - - 7 . = 2 0 0 fm/,c , 17" 0 f m / c

/~

/

.~- ~e " ~ Y / I

.

r

r

i

i

I

[

130MeV ~ .-

0.5 ,° I

•/

0.0

i

•

•

.~-

"U ©

+

E//A _~ 6 MeV

,/A=loo Mev

r ~P--q

0.0

237

i

i

r

4 [

r

[

I ~

[

r

~

L'."

/ ~

I

J

[

[

[

I

r

]

i

[

I [

r

[

1 0

0

lO

20 Vre d

30 ( 10-3

40

50

C

Fig. 18. IMF velocity correlation functions associated with central collisions (b/bmax ~ 0.3) and EIMF/A ) 6 MeV. The solid lines depict the results of 3-body Coulomb trajectory calculations. matter density. Calculations were performed for characteristic times of 7- = 50, 100, 200 and 300 f m / c . In the trajectory calculations, the same energy restrictions (EIMF/A >~ 6 MeV) were used as were used for the data. The results of the trajectory calculations are compared in Fig. 18 to the experimental correlation functions. At all three incident energies the experimental data is intermediate between r = 50 f m / c and r = 100 f m / c . This short emission time scale is contrary to the expectation of a long emission time scale for a system of modest excitation. These deduced emission times are, however, comparable to the emission time scales extracted for other multifragmenting systems [42,40]. The short fragment emission time scales measured could be understood in terms of a limited "window of opportunity" for fragment emission. In considering the statistical decay of an excited nuclear system, the fragment emission probability depends on the excitation and density of the emitting system. If after the emission of the first fragment the system de-excites substantially via light charged particle emission, the probability of emission of a second IMF is significantly reduced. Therefore, the emission of two IMFs would occur from a narrow window in time when the source is still relatively excited. In essence, two-fragment emission might by its nature select an

238

Y Lou et al./Nuclear PhysicsA 604 (1996)219-244

early time in the de-excitation cascade of a modestly excited system. In order to examine the range of R-r values which describe the fragment-fragment interaction strength we have performed 3-body calculations in which the radius of the source R and the emission time r were treated as free parameters [42] within physical limits. The lower limit on the radius of 5 fm is approximately equal to the sum of the radii for 2 IMFs. The upper limit of 12 fm corresponds to a source density of P/po = 0.1. The range of R-r values which describe the experimental data is shown in Fig. 19. The solid diamonds in this figure represent best fits to the data at E/A = 100 MeV, respectively (Zs = 79,As = 197). For the range of assumed source radii, r ~< 60 fm/c for the data at E/A = 100 MeV. This value represents the maximum mean emission time deduced at this bombarding energy. We have examined the sensitivity of our extracted time scale to our assumption regarding the size of the source by assuming the source to be a 139La nucleus. The effect of changing this assumption is shown in Fig. 19. The 139La nucleus was chosen to represent the extreme case in which virtually all the light charged particle emission preceded the fragment emission. As can be seen in Fig. 19, the change in the source size results in only a minor change in the deduced time scale. In addition, assuming a source of smaller radius would result in a stronger Coulomb interaction and consequently a longer deduced emission time. On the other hand, shorter emission times would be extracted if a larger source radius were assumed. Since the emission time is already so short, we consider significantly larger radii as unphysical. Also shown in Fig. 19 for reference is the deduced spatial-temporal extent for the system 36Ar+197Au [42] at E/A = 50 and 110 MeV and 84Kr-l-197Au at E/A = 35 and 70 MeV. The 50 MeV and 110 MeV data are represented by the solid and dashed lines, respectively. Because the trajectory model does not treat sub-barrier emission, the correlation functions were constructed for fragments with a velocity above the trajectory model Coulomb barrier (v >1 4 cm/ns). In the Ar induced reactions, a source charge of Zs = 40 was assumed for the simulations to represent the limiting case where the light charged particles are emitted early in the de-excitation process, followed by the fragments. For the Kr induced reactions, at E/A = 35 and 70 MeV, the source charge was assumed to be 57 and 32, respectively. This assumption was based upon the total measured charge (corrected for detector acceptance) and assuming the fragments are emitted last in the de-excitation cascade. Thus, this assumption represents an estimated lower limit for the source charge. The source velocities were determined from moving source fits to be 2.4 and 3 cm/ns at E/A = 35 and 70 MeV, respectively. The spatialtemporal extent for the 36mr -k- 197Au data at E/A = 110 is very similar to that of the 84Kr --}- 197Au data at E/A = 35 MeV, while the Ar data at E/A = 50 MeV has a larger spatial-temporal extent.

Y. Lou et al./Nuclear Physics A 604 (1996) 219-244

200

t

'

'

I

I

. . . .

. . . .

I

'

197Au(X,Z~Zz)

I

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150 --

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©

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35

o

~

70

~

50

Ar

110

N

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,

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100

239

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e

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50

\o \

•

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\

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•

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15

R s (fin) Fig. 19. Range of R-l" in the 3-body calculation which describe the experimental correlation function. The source was assumed to be a 197Au nucleus with R = 7 fm. For the 14N data 4 ~< Z1, Z2 ~< 6; for all other data 4 ~< Zl, Z2 ~< 9.

8. S t a t i s t i c a l m o d e l c o m p a r i s o n s

Previous semi-exclusive measurements of heavy-ion induced reactions indicated that the IMF cross sections are well correlated with the deposited excitation energy [43]. To better understand the observed characteristics of the decaying system, we have performed statistical model calculations using the code GEMINI [44] and compared the model predictions to the results of our exclusive measurement. This code calculates the deexcitation of an excited compound nucleus via a sequential binary decay mechanism. We investigated the dependence of several experimental observables (neutron multiplicity, charged particle multiplicity, total detected charge, and fragment multiplicity) on the excitation energy for a 197Au nucleus. The results of the calculations are summarized in Fig. 20. With increasing excitation energy the neutron multiplicity increases monotonically. At high excitation (E* ~> 1000 MeV) a saturation of the neutron multiplicity with increasing excitation energy is evident. For E* /> 300 MeV charged particle emission also becomes an important mode of de-excitation. Beyond this initial threshold for charged particle emission, the dependence of Nc on E* is approximately linear reaching

Y Lou et al./Nuclear Physics A 604 (1996) 219-244

240 Table 1 Initial GEMINI predictions

E*

1

Nc

Nn

Np

Na

NIMF

350 600 850 1000 350 600 850 1000 350 600 850 1000 350 600 850 1000

0 0 0 0 20 20 20 20 40 40 40 40 60 60 60 60

4.0 9.4 14.7 17.7 4.3 9.2 14.9 17.9 4.3 9.1 14.8 18.2 3.8 9.1 14.6 17.2

20.0 25.9 30.4 32.9 19.3 26.3 29.7 32.8 19.6 25.3 30.1 32.8 20.0 26.4 30.8 33.4

1.58 3.83 5.89 7.21 1.51 3.80 5.83 7.00 1.23 3.00 5.40 7.62 1.00 3.63 5.38 6.97

1.17 2.17 2.86 3.16 1.27 1.83 3.43 3.36 1.55 1.85 3.20 2.77 0.67 2.00 3.00 3.04

0.155 0.429 0.724 0.841 0.268 0.600 1.130 0.960 0.273 0.846 0.933 1.154 0.833 1.000 0.875 1.191

a value of approximately 30 for E* = 1600 MeV. The fragment multiplicity, NIMF also increases with increasing E* attaining a value of approximately 2 for E* = 1600 MeV. Shown by the solid arrows in the figure are the observed charged particle and fragment multiplicities associated with central collisions. Zero order corrections for the solid angle coverage to the experimental multiplicities are indicated by the open arrow. While the observed fragment multiplicity suggests an excitation of approximately 900 MeV for the composite system the charged particle multiplicity is consistent with an excitation of approximately 1300 MeV. For these calculations, the angular momentum of the compound nucleus was assumed to be zero. The influence of angular momentum on the quantities investigated is summarized in Tables 1 and 2. As can be seen in Table 1, at low excitation the fragment multiplicity is quite sensitive to the angular momentum. For E* = 350 MeV, the unfiltered fragment multiplicity increases by 70% as the angular momentum increases from £ = 0 to £ = 20. However, at high excitation ( 1000 MeV) a change of 20h only results in an increase in the fragment multiplicity of 14%. The Z distribution of reaction products predicted by GEMINI for a Au nucleus as a function of excitation is depicted in Fig. 21. As clearly visible in Fig. 21a, at low excitation the yield distribution manifests three distinct regions. At large atomic number the cross section attributable to the survival of an evaporation residue is recognizable. At intermediate atomic number (10 <~ Z ~< 65) the yield distribution can be understood as arising from the binary fission of the initially excited nucleus into two relatively massive nuclei. At low atomic number (Z ~< 10) a steep distribution is observed in which the yield decreases dramatically with increasing Z. This region of the spectrum is populated by statistical emission of light charged particles and IMFs from the excited nucleus. With increasing excitation as seen in Figs. 21b-d, the portion of the spectrum associated with the survival of an evaporation residue shift to lower Z and decreases in

241

E Lou et al./Nuclear Physics A 604 (1996) 219-244

50~_

1

40 I30 F

Z

, •

"

40 Z

-

-

c

•

"

!

3O o

•

....

>

[

i

....

•

20 10 3.0 2.5 2.0

Z

1.0 15 i 0.5

°

0

500

~-° ° " "

i

1000 ] 5 0 0 2 0 0 0

Excif~afAon E n e r g y

(Iv~eV)

Fig. 20. Predicted dependence of neutron multiplicity, alpha multiplicity, and IMF multiplicity on the excitation energy for a 197Au nucleus. Table 2 GEMINI predictions filtered E*

l

Nc

Nn

Np

Na

NIMF

350 600 850 1000 350 600 850 1000 350 600 850

0 0 0 0 20 20 20 20 40 40 40 40 60 60 60 60

3.8 8.8 13.7 16.5 4.0 8.6 14.3 17.0 4.2 8.2 14.3

20.0 25.9 30.4 32.9 19.3 26.3 29.7 32.8 19.6 25.3 30.1 32.8 20.0 26.4 30.8 33.4

1.50 3.65 5.59 6.84 1.46 3.67 5.65 6.76 1.14 2.77 5.33 7.31 1.00 3.38 5.25 6.60

1.11 2.04 2.66 2.92 1.20 1.67 3.30 3.08 1.55 1.69 3.13

0.126 0.337 0.552 0.633 0.244 0.500 0.913 0.760 0.227 0.538 0.800 0.615 0.333 0.750 0.625 0.788

1000

350 600 850 1000

16.6

3.3 8.4 13.4 15.8

2.62

0.67 1.75 2.75 2.76

relative probability. W h i l e this trend is qualitatively in a g r e e m e n t with the experimental data, m o r e detailed c o m p a r i s o n s have yet to be made. In order to c o m p a r e the G E M I N I p r e d i c t i o n s to our e x p e r i m e n t a l data w e have selected those decays consistent with the survival o f a heavy residue. Our criteria for the atomic n u m b e r o f this residue are shown as the arrows in Fig. 20. T h e s e arrows correspond to Zres ~> 63, 58, 52 and 49 at

242

Y. Lou et al./Nuclear Physics A 604 (1996) 219-244

10 4

~

1

-

~

?

~- ;

60

80 100

i0 3 I0 E J

i01 i0 0 10 3 i0 E i0 l I0 0

0

E0

40

60

80

0

20

40

A t o m i c N u m b e r (Z) Fig. 21. Z distributions predicted by GEMINI for the decay of a 197Au nucleus with E* = 350, 600, 850 and 1000 MeV. Arrows shown correspond to the minimum Z associated with survival of an evaporation residue.

E* = 350, 600, 850 and 1000, respectively. For higher excitation calculations Zres/> 44, 40 and 36 were used at E* = 1200, 1400 and 1600. To account for the center-of-mass motion the charged particles predicted by the GEMINI calculations were transformed to the laboratory frame assuming a source velocity of 1.0 cm/ns. The source velocity was estimated based upon source fits to the energyangular distributions for central collisions. The transformed model predictions were then filtered for the detector acceptance (solid angle, energy threshold, and detector granularity) and are compared to the experimental data in Figs. 3 and 4. In Fig. 3, the solid line corresponds to the total detected charge (Z ~< 15) predicted at excitation energies of 350, 600, 800, 1000, 1200 and 1600 MeV prior to filtering. The dependence of (Zsum) and o'z~m on Nc after correcting for the detector acceptance is depicted by the dashed line. As can be seen, GEMINI reproduces the total measured Zsu m rather well. In addition, with the exception of low Nc the width of the Zsum distribution (as described by t r z ~ ) is reasonably described except for the lowest multiplicities. These results are perhaps not surprising since most of the detected charge consists of light charged particles. The dependence of fragment emission in GEMINI on the excitation of the system is demonstrated in Fig. 4. For the same excitation energies mentioned above the relationship between fragment multiplicity, NmlF and Nc in the model is shown as lines in Fig. 4. The solid line represents the unfiltered model predictions for the excitation energy range described in the previous figure, while the dashed line depicts model predictions filtered for the detector acceptance. The filtered theoretical predictions suggest that the largest experimental fragment multiplicities correspond to the decay of a Au nucleus with an excitation energy of approximately 1600 MeV.

Y. Lou et al./Nuclear Physics A 604 (1996) 219-244

243

9. Summary The fragment emission patterns for central collisions in the reactions 14N-/-197Au at E / A = 100, 130 and 156 MeV appear consistent with the decay of a modestly excited nuclear system in which a heavy residue survives. In this energy range for this system fragment emission becomes the average behavior for the highest multiplicity events. Fragment-fragment velocity correlations indicate a very short mean time between emissions r ~< 60 f m / c . This extracted time scale is significantly shorter than the expectation for statistical emission from a modestly excited nuclear system. However, the extracted time scale is comparable to the fragment emission time scale extracted for multifragmenting systems and may imply that the fragment emission occurs on a time scale concurrent with the energy deposition. Comparison with a statistical model suggests an excitation of approximately 1300 MeV for central collisions based on the charged particle multiplicity. However, the fragment multiplicity indicates a significantly lower excitation of approximately 900 MeV. This discrepancy might signal the greater sensitivity o f IMFs to the level density, angular momentum effects, etc. particularly for nuclear systems o f modest excitation.

Acknowledgements We would like to acknowledge the valuable assistance of the operating personnel of the K1200 cyclotron at the National Superconducting Cyclotron Laboratory for providing the high quality beams which made this experiment possible. This work was supported by the U.S. Department of Energy under DE-FG02-92ER40714 (Indiana University) and the National Science Foundation under Grant Nos. PHY-89-13815, PHY-90-15957, and PHY-90-9010I (Ball State), One o f the authors (R.D.) would like to acknowledge the support o f the Alfred E Sloan Foundation through the Alfred P. Sloan Fellowship program.

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