arX

iv:n

ucl-

ex/0

5010

22v1

24

Jan

2005

Comparison of mid-velocity fragment formation with projectile-like decay

S. Hudan, R. Alfaro, B. Davin, Y. Larochelle, H. Xu,∗ L. Beaulieu,† T. Lefort,‡ R. Yanez,§ and R.T. de SouzaDepartment of Chemistry and Indiana University Cyclotron Facility

Indiana University, Bloomington, IN 47405

R.J. Charity and L.G. SobotkaDepartment of Chemistry, Washington University, St. Louis, MO 63130

T.X. Liu, X.D. Liu, W.G. Lynch, R. Shomin, W.P. Tan, M.B. Tsang, A. Vander Molen, A. Wagner,¶ and H.F. XiNational Superconducting Cyclotron Laboratory and Department of Physics and Astronomy

Michigan State University, East Lansing, MI 48824

(Dated: February 8, 2008)

The characteristics of intermediate mass fragments (IMFs: 3≤Z≤20) produced in mid-peripheraland central collisions are compared. We compare IMFs detected at mid-velocity with those evap-orated from the excited projectile-like fragment (PLF∗). On average, the IMFs produced at mid-velocity are larger in atomic number, exhibit broader transverse velocity distributions, and aremore neutron-rich as compared to IMFs evaporated from the PLF∗. In contrast, comparison ofmid-velocity fragments associated with mid-peripheral and central collisions reveals that their char-acteristics are remarkably similar despite the difference in impact parameter. The characteristics ofmid-velocity fragments are consistent with low-density formation of the fragments. Neutron defi-cient isotopes of even Z elements manifest higher kinetic energies than heavier isotopes of the sameelement for both PLF∗ and mid-velocity emission. This result may be due to the decay of long-livedexcited states in the field of the emitting system.

PACS numbers: PACS number(s): 25.70.Mn

I. INTRODUCTION

Cluster emission from nuclear matter can arise from awide range of phenomena, such as statistical evaporationfrom normal density nuclear matter at modest excita-tion [1] or the multi-fragmentation of low-density nuclearmatter at high excitation induced by GeV hadronic pro-jectiles [2]. Collision of two heavy-ions at intermediateenergies (25 MeV ≤E/A≤100 MeV) also results in co-pious intermediate mass fragment (IMF : 3≤Z≤20) pro-duction [3, 4]. Considerable attention has been focusedon understanding the conditions governing the maximumfragment yield [5, 6] and the characteristics of the frag-ments produced [7, 8]. In peripheral collisions of twointermediate-energy (20≤E/A≤100 MeV) heavy nuclei(A∼100) a dissipative binary collision occurs resultingin the formation of an excited projectile-like fragment(PLF∗) and target-like fragment (TLF∗). The dominantIMF yield in such collisions is observed at velocities in-termediate between the de-excited PLF∗ and TLF∗, andis not-attributable to the standard statistical decay of ei-

∗Present address: Institute of Modern Physics, CAS, Lanzhou,China.†Present address: Universite Laval, Quebec, Canada.‡Present address: Universite de Caen, Caen, France.§Present address: Department of Nuclear Physics, The AustralianNational University, Canberra, Australia.¶Present address: Institute of Nuclear and Hadron Physics, Dres-den, Germany.

ther of the two reaction partners [9, 10]. The IMFs in thiskinematical region are referred to as mid-velocity IMFs.For more central collisions, the distinctive binary natureof the collision is no longer apparent, nevertheless mostof the IMF emission occurs in the same kinematical re-gion as in more peripheral collisions. While for more pe-ripheral collisions, the dynamical nature of mid-velocityfragments has been shown [11, 12, 13, 14], in the caseof central collisions, statistical approaches are generallyused to understand the fragment production [15, 16, 17].

On general grounds, the size, composition, and ki-netic energies of the observed clusters, apart from theiryield, can be related to the composition and excitationof the disintegrating system. For example, the compo-sition of fragments, namely their neutron-to-proton ra-tio, may provide information on the N/Z of the disinte-grating system [18, 19]. Several experiments have estab-lished the neutron enrichment of IMFs and light clusters(Z≤2) at mid-velocity [15, 16, 20, 21]. The observationof neutron-rich fragments in this kinematic region hasbeen interpreted as the N/Z fractionation of hot nuclearmaterial into a neutron-rich gas and a proton-rich liquid[15]. As with any claim of “enrichment” of a quantity, itis necessary to establish the appropriate reference withrespect to which the enrichment occurs. We propose thatthe most appropriate reference for investigating possibleenrichment of mid-rapidity fragments is the N/Z of theemitted fragments from near normal density nuclear mat-ter.

In this work, we examine the fragment characteristicslargely independent of the probability of their formation.

2

20 cm

MiniWall

11 (8)

MiniBall3 (15) 4 (12)

5 (17)6 (13)

7 (18) 8 (17)9 (14)

10 (12)

16 (11)15 (13)14 (15)

13 (13)

12 (11)

LASSARing

Detector

FIG. 1: Experimental setup used to study the reaction114Cd+92Mo at E/A=50 MeV. The number of detectors ineach azimuthal ring of the Miniball/Miniwall array is indi-cated in parentheses.

We show that, at mid-velocity, the fragment characteris-tics manifest significant differences as compared to thoseevaporated from near normal density nuclear matter. Incontrast, similar fragment characteristics at mid-velocityare observed both for mid-peripheral collisions and cen-tral collisions. In contrast to previous results [16], the sizeof the emitting system is shown to not be the determiningfactor in the composition of the emitted fragments.

To investigate the factors influencing fragment com-position, we measured IMF and light-charged-particle(LCP:1≤Z≤2) emission in the reaction 114Cd + 92Moat E/A=50 MeV. We examine mid-peripheral collisionsin which the survival of a well defined projectile-like frag-ment occurs. Emission from the PLF∗ (which presum-ably is at near normal density) provides a suitable refer-ence for understanding mid-velocity IMF emission in thesame collisions. We subsequently compare mid-velocityIMFs associated with mid-peripheral collisions and thoseassociated with central collisions.

II. EXPERIMENTAL SETUP

Charged-particles produced in the reaction114Cd+92Mo at E/A=50 MeV were detected in theexclusive 4π setup depicted in Fig. 1. Peripheral colli-sions were selected by the detection of forward-movingprojectile-like fragments (PLFs). These PLFs weredetected in the angular range 2.1◦≤θlab≤4.2◦ andwere identified in an annular Si(IP)/CsI(Tl)/PD ringdetector (RD) by the ∆E-E technique. This telescopeprovided elemental identification with better thanunit Z resolution for Z≤48, as shown in Fig. 2. Thepeak at Z=48 corresponds to quasi-elastically scatteredprojectile nuclei associated with the most peripheralcollisions. The silicon ∆E element of this telescope was

segmented into 16 concentric rings on its junction sideand 16 pie-shaped sectors on its ohmic surface. Thering segmentation provided a good measurement of thepolar angle of the PLF, typically ∆θlab<0.2◦, while thepie-shaped sectors allowed a measure of the azimuthalangle [11]. Careful calibration of the CsI(Tl) crystalswith 70 fragmentation beams allowed determination ofthe light response of the CsI(Tl) crystals resulting in atypical energy resolution of 3%. From the measured Z,angle, and energy, the velocity of the PLF was calculatedby assigning the A for a given Z consistent with sys-tematics [22] adjusted near Zbeam to correspond to theN/Z of the projectile [23]. Intermediate mass fragmentswith Z≤9 and light-charged-particles were isotopicallyidentified in the angular range 7◦≤θlab≤58◦ with thehigh resolution silicon-strip array LASSA [24, 25]. Eachof the nine telescopes in this array consisted of a stackof three elements, two ion-implanted, passivated siliconstrip detectors (Si(IP)) backed by a 2 x 2 arrangementof CsI(Tl) crystals each with photo-diode readout. Thesecond silicon of each telescope was segmented into 16vertical strips and 16 horizontal strips, resulting in goodangular resolution (∆θlab≈0.43◦). The nine LASSAtelescopes were arranged in a 3 x 3 array, the center ofwhich was located at a polar angle θlab=32◦ with respectto the beam axis. The energy threshold of LASSA is2 and 4 MeV/A for α particles and carbon fragments,respectively. A typical example of the isotopic resolutionachieved by LASSA is shown in Fig. 3. Isotopes of Liand Be are clearly resolved with an energy resolutionof ≈2-5%. In order to augment the limited kinematicalcoverage of LASSA and the RD, the low-thresholdMiniball/Miniwall array [26] was used to identifycharged-particles emitted in the range 5◦≤θlab≤168◦.Using pulse-shape discrimination, particles detected inthe Miniball/Miniwall array were isotopically identifiedfor Z≤2. These particles were used to select the impactparameter of the collision and to globally characterizethe selected events.

III. GENERAL REACTION

CHARACTERISTICS AND EVENT SELECTION

We begin by examining mid-peripheral (MP) eventsdistinguished by the survival of a projectile-like fragmentat forward angles. In order to examine these peripheralcollisions we have selected events in which a heavy PLFwith 30≤Z≤46 is detected in the RD (2.1◦≤θlab≤4.2◦)coincident with at least three charged-particles in theMiniball/Miniwall array. This latter charged-particle re-quirement suppresses the most peripheral collisions andresults in the associated multiplicity distribution shownin Fig. 4a. These MP collisions are characterized byan average total charged-particle multiplicity, 〈NC〉, of10.2, with a second moment (µ2) of 3.6. Based on thecharged-particle multiplicity distribution [27], we esti-mate the impact-parameter ratio b/bmax ≈ 0.7 where

3

0 10 20 30 40 50ZRD

dN/d

ZR

D (

arb.

uni

ts)

FIG. 2: Element distribution measured by the ring detectorfor the angular range 2.1◦≤θ

lab≤4.2◦. The arrow indicatesthe atomic number of the beam.

350 400 450 500

Yie

ld (

arb.

uni

ts)

PID (arb. units)

102

103

104

105

6Li

7Li

8Li

9Li

a)

700 800 900

7Be

9Be 10Be

11Be

12Be

b)

FIG. 3: Isotopic resolution achieved in LASSA for isotopesof Li and Be. The spectra have been summed over all nineLASSA telescopes.

bmax represents the interaction for which at least threecharged-particles are detected in the Miniball/Miniwallarray. The center-of-mass velocity distribution of thePLF detected in the RD is shown in Fig. 4b with thebeam velocity indicated by an arrow for reference. Oneobserves that this distribution is a skewed gaussian witha tail toward lower velocities. The most probable value

10 20Nc

dN/d

Nc

(arb

. uni

ts)

⟨ Nc ⟩ = 10.2

a)

103

104

105

106

0

1

2

3

4

5

6

1 2 3 4 5VPLF (cm/ns)

dN/d

VPL

F (a

rb. u

nits

)

b)

2

2.5

3

3.5

4

4.5

30 35 40 45 50ZPLF

dN/d

ZPL

F (a

rb. u

nits

)

c)

FIG. 4: Panel a) Charged-particle multiplicity distributionassociated with the detection of a PLF with 30≤Z≤46 in theRD; Panel b) Velocity distribution for 30≤Z≤46 detected inRD; Panel c) Atomic number distribution of fragments de-tected in the RD.

of this velocity distribution is 3.7 cm/ns (〈VPLF 〉=3.57cm/ns), indicating an average velocity damping of 0.88cm/ns from the beam velocity. The atomic number dis-tribution of PLFs associated with these collisions is dis-played in Fig. 4c. The most probable value of ZPLF isZ=35 (〈ZPLF 〉=37) as compared to Zbeam=48, indicatedby the arrow. It should be realized that this most proba-ble (or average) ZPLF corresponds to the PLF followingthe de-excitation of the primary excited projectile-likefragment (PLF∗).

The general characteristic of this de-excitation of thePLF∗ is shown in Fig. 5a. Clearly evident in Fig. 5a is acircular ridge of yield centered at V‖ ≈ 3.5 cm/ns in thecenter-of-mass frame. This ridge can be understood asemission of 6Li fragments from the PLF∗, following theinteraction phase of the reaction. This distinctive emis-sion pattern indicates that for the collisions selected, abinary reaction has occured [28]. By utilizing the mea-sured multiplicities, kinetic energy spectra, and angu-lar distributions of particles detected in coincidence withthe PLF, we have reconstructed (under the assumptionof isotropic emission) the average atomic number of thePLF∗, 〈ZPLF∗〉 and its excitation [29]. For the collisionsstudied, we have determined that 〈ZPLF∗〉≈41. Alsoclearly evident in Fig. 5a, and well established by ear-lier work [9, 10], is that considerable fragment emissionoccurs at mid-velocity – emission not originating from theisotropic statistical decay of the PLF∗ or TLF∗ reactionpartners [12]. For the remainder of this work we define

4

0

1

2

3

4

5

6

7V

⊥ (

cm/n

s)114Cd+92Mo @ 50 A MeV

30 ≤ ZPLF ≤ 46

6Li

a)

0

1

2

3

4

5

6

7

-2 0 2 4 6V// (cm/ns)

V⊥ (

cm/n

s)

Nc ≥ 20

b)

FIG. 5: (Color online) Invariant cross-section plots of theemission of 6Li fragments in the center-of-mass frame. Panela) associated with 30≤ZPLF≤46. Panel b) associated withNC≥20. The dashed arrow indicates 〈VPLF

‖ 〉 while the solidarrow indicates VBEAM . The differential yield is presentedon a logarithmic scale.

mid-velocity fragments as those with 0≤V‖≤1cm/ns inthe center-of-mass frame.

For central collisions (NC≥20 ; 〈NC〉=21.8; µ2=1.89)the ridge centered near the projectile velocity is no longerobserved, as shown in Fig. 5b. The observation that aclear Coulomb circle does not exist has traditionally beeninterpreted as evidence that the collision is no longera binary process. However, the observation of a largecharged particle multiplicity together with the absenceof a Coulomb circle does not preclude the existence of adissipative binary process. Rather, these observationscan be reconciled with the rapid de-excitation of thePLF∗ and TLF∗ on a timescale commensurate with theirre-separation. In contrast to the well defined Coulombcircle of Fig. 5a, the emission pattern for central col-lisions is broad and featureless with substantial emis-sion near the center-of-mass velocity. In these collisionswe deduce from the charged-particle multiplicity thatb/bmax= 0.26, from which we estimate Zsource ≈ 72 [30].The charged-particle multiplicity has often been used inthis manner to select central collisions. Examination ofthe Z distribution of the largest measured particle in the

Yie

ld (

arb.

uni

ts) Nc ≥ 20

a)102

103

104

105

106

0 5 10 15 20 25 30 35 40 45ZRD,max

ΣP(Z

RD

)

b)10-5

10-4

10-3

10-2

10-1

1

FIG. 6: Panel a) Z distribution of the largest fragment de-tected in the RD associated with events for which Nc≥20.Panel b) cumulative yield distribution of the largest fragmentin the RD associated with events for which Nc≥20.

RD associated with these events, however, is quite reveal-ing. As evident in Fig. 6a, while the largest probabilitiesare associated with either the detection of no fragment(Z=0) or a helium in the RD, there is a significant prob-ability of detecting a large fragment with Z ≥10 in theRD. (It should be noted that the triggering thresholdin the RD was set to not trigger on hydrogen nuclei re-sulting in a measured yield of zero for Z=1 in Fig. 6a.)This detection of a large fragment (Z≥10) occurs eventhough a large charged-particle multiplicity has been re-quired. This result is consistent with the physical pictureof a large overlap of projectile and target nuclei whichstill results in a binary exit channel with survival of aprojectile-like and target-like fragment. The cumulativeyield associated with such events, ΣP(ZRD), is shown inFig. 6b where

ΣP (ZRD) =

Zi∫

Z=45

dN

dZRD,maxdZ (1)

Evident in Fig. 6b is the result that ΣP(ZRD) ≈ 0.1for ZRD,max=10. This result reveals that ≈ 10 % ofthe central collisions selected simply by the requirementthat NC≥20 are in fact associated with binary colli-sions. Due to the limited angular acceptance of the RD,this“contamination” of true central collisions might besomewhat higher.

Further evidence that this “contamination” is asso-ciated with a binary exit channel and not simply ananisotropic emission pattern is provided in Fig. 7. In this

5

5

10

15

20

25

30

35

40

45

-2 -1 0 1 2 3 4 5 6 7VRD, max (cm/ns)

ZR

D, m

ax

Nc ≥ 20Most probable

FIG. 7: (Color online) Correlation between atomic numberand velocity (in the COM) of the largest fragment detectedin the RD. The most probable velocity for each Z is indicatedby a filled circle while the beam velocity is indicated by thearrow.

figure, we examine the correlation between the atomicnumber and the velocity of these fragments detected inthe RD. With the exception of the lightest fragments(Z≤3), the fragments detected in the RD have a mostprobable velocity (indicated by the points) that is slightlydamped from the beam velocity (indicated by the ar-row). For Z>9 the most probable velocity of the PLF is3.1 cm/ns, corresponding to a damping of ≈1.3 cm/nsof the beam velocity. This “contamination” of true cen-tral events with dissipative binary events does not signifi-cantly affect any of our subsequent analysis. However, toprovide the best isolation of true central events, we haveadditionally required in our selection of central eventsthat no fragment with Z≥5 is detected in the RD.

IV. ELEMENTAL YIELDS

The Z distribution for IMFs associated with mid-peripheral (MP) and central (Cent) collisions for bothPLF∗ emission and emission at mid-velocity is shown inFig. 8. The observed yields in each case have been nor-malized for the range 3≤Z≤ 8. To understand the Z dis-tribution at mid-velocity (0≤V‖≤1 cm/ns), we use PLF∗

emission (solid circles) as a reference. Fragments emittedfrom the PLF∗ were selected on the basis of their emis-sion angle, θPLF , in the PLF frame (85◦≤θPLF≤95◦).For these same MP collisions, the Z distribution at mid-velocity (open triangles) exhibits a suppression of yield

3 4 5 6 7 8Z

P(Z

)

0.05

0.1

0.2

0.5 MP, PLF*MP, Mid-velCent, Mid-velGEMINI

FIG. 8: Z distribution of fragments associated withmid-peripheral collisions emitted in the angular range85◦≤θ

PLF≤95◦ in the PLF frame (filled circles); mid-peripheral collisions and at mid-velocity (open triangles); andfragments associated with central collisions at mid-velocity(open squares). The lines depict the Z distribution predictedby the statistical model GEMINI (see text for details). Theyield for each case has been normalized to unity for the inter-val shown.

for Z=3 and Z=4 relative to the production of heavierIMFs (Z≥5) as compared to PLF∗ emission (solid cir-cles). This increase of the relative production of heavierIMFs at the expense of lighter IMFs is even larger for thecase of central collisions (open squares). We concludetherefore that at mid-velocity (both in mid-peripheraland central collisions), heavier fragments are produced atthe expense of lighter fragments, as compared to PLF∗

emission.

This change in the Z distribution at mid-velocity whencompared to PLF∗ emission, can be understood within astatistical framework. Within such a framework, the Zdistribution is influenced by the excitation, density, andsize of the disintegrating system. Statistical emission of afragment is governed by an effective emission barrier rela-tive to the temperature of the emitting system. Increasedrelative probability for the emission of heavy fragments,can thus reflect either a reduction in this effective bar-rier and/or an increase in the temperature of the system.A reduction in the density of the emitting system natu-rally results in a reduction of the effective barrier. The Zdistribution of mid-velocity fragments in mid-peripheralcollisions is intermediate between that of PLF∗ emissionand emission associated with central collisions. From thisobservation one may conclude that within a statistical

6

a) MP, PLF*

10-3

10-2

10-1

7Be

10Be

b) MP, Mid-vel

P(V

⊥)

10-3

10-2

10-1

0 1 2 3 4 5 6 7

c) Cent, Mid-vel

V⊥ (cm/ns)10-3

10-2

10-1

FIG. 9: Distributions of V⊥, for 7Be and 10Be fragmentsin the center-of-mass frame. Panel a) mid-peripheral col-lisions and V‖≥V‖

PLF ; Panel b) mid-peripheral collisionsand 0≤V‖≤1 cm/ns; Panel c) central collisions and 0≤V‖≤1cm/ns. All distributions have been normalized to unity.

interpretation, the relative “energy cost” has already be-gun to change from that of the PLF*. At mid-velocity,the enhancement of yield for Z≥6 in the central case ascompared to MP collisions may be due to the influenceof finite source size. For MP collisions, the small sizeof the fragmenting system (Zsource≈21) at mid-velocitymay limit the production of heavy IMFs.

V. TRANSVERSE VELOCITY DISTRIBUTIONS

We present in Figs. 9 and 10 the transverse-velocitydistributions of 7,10Be and 6,9Li fragments. The differentdistributions correspond to fragments observed in differ-ent kinematical regions for mid-peripheral and centralcollisions. Depicted in Fig. 9a is the transverse-velocitydistribution of 7Be and 10Be fragments which have par-allel velocities larger than that of the PLF (in the PLFframe). Based on Fig. 5a we understand these frag-ments as being emitted from the PLF∗. In this case,peaked distributions are observed as is expected from theCoulomb ’ring’ observed in Fig. 5a, indicative of a well-defined Coulomb barrier characteristic of surface emis-sion. The relative probability of neutron-rich 10Be atlow V⊥ is larger than that of neutron-deficient 7Be. Itis important to note that the constraints of the exper-imental angular acceptance do not significantly impactthe observed most probable velocity, an expectation con-firmed by Coulomb trajectory calculations that will be

a) MP, PLF*

10-3

10-2

10-1

6Li

9Li

b) MP, Mid-vel

P(V

⊥)

10-3

10-2

10-1

0 1 2 3 4 5 6 7

c) Cent, Mid-vel

V⊥ (cm/ns)10-3

10-2

10-1

FIG. 10: Distributions of V⊥, for 9Li and 6Li fragments in thecenter-of-mass frame. Panel a) mid-peripheral collisions andV‖≥V‖

PLF ; Panel b) mid-peripheral collisions and 0≤V‖≤1cm/ns; Panel c) central collisions and 0≤V‖≤1 cm/ns. Alldistributions have been normalized to unity.

subsequently discussed. In contrast to the peaked distri-butions in Fig. 9a, the distributions associated with mid-velocity emission for mid-peripheral collisions (Fig. 9b)have broader peaks and extend to larger values of V⊥.For V⊥≤2.5 cm/ns, the V⊥ distribution for 10Be in par-ticular is essentially flat. The observation of large yieldfor low V⊥ indicates the absence of significant Coulombrepulsion in the transverse direction. Therefore, the ob-served V⊥ distributions reflect principally the initial V⊥

distributions. A broad and relatively flat initial V⊥ dis-tribution is compatible with a neck-fragmentation sce-nario [31] or a Goldhaber picture in which the mid-velocity zone results from abrasion/ablation of nucleonsbetween projectile and target nuclei followed by coales-cence [32, 33]. The difference in the tails of the V⊥ distri-bution between PLF∗ emission and mid-velocity emissionmay be interpreted as the mid-velocity source having ahigher initial temperature than the PLF∗ or possibly re-flect the Fermi motion of the ablated nucleons.

Displayed in Fig. 9c are the V⊥ distributions for frag-ments emitted at mid-velocity in central collisions. Thesedistributions also manifest broad peaks and high velocitytails similar to those observed in Fig. 9b. Close exam-ination however reveals that in this case the V⊥ distri-bution is more peaked than in Fig. 9b suggesting thatthe Coulomb repulsion is larger in magnitude. This hy-pothesis is qualitatively consistent with the larger size(atomic number) of the source at mid-velocity for centralcollisions in contrast to mid-peripheral collisions. On the

7

other hand, the peak for the central case is broader thanfor the case of PLF∗ emission shown in Fig. 9a possiblyindicating the volume breakup of a low-density source[34] or surface emission from a hot nucleus as it expands[35].

A semi-quantitative description of the V⊥ distribu-tions presented in Fig. 9 can be achieved by comparingthe experimental data with a N-body Coulomb trajec-tory model which simulates the superposition of multiplesource emission. In this model, all emission was assumedto be surface emission originating from either the PLF∗

or a mid-velocity source. The characteristics of the PLF∗

were taken from the Z and energy directly measured, as-suming the PLF∗ had the N/Z of the projectile. Event-by-event we assumed the Z of the mid-velocity sourceto be Zmid−velocity = Zsystem - ZPLF *(1+ZT /ZP ). Wedetermined 〈Zmid−velocity〉= 21. Each source also has anassociated temperature that is varied independently. Thetwo sources were separated by an initial distance of 30 fmand were allowed to emit isotropically. Our use of sur-face emission in the mid-velocity case for mid-peripheralcollisions simply provides an ansatz for performing thesimulation and should not be interpreted as a physicaldescription in this case. This particular choice of surfaceemission in the model notably affects the low-velocityregion of the transverse-velocity spectrum. While a vol-ume emission scenario results in a broader distribution,the shape of the spectrum in the high velocity region islargely unchanged.

This simple Coulomb model with TPLF∗=7 MeV pro-vides a reasonable description of the PLF∗ emission asshown in Fig. 9a by the lines. Under-prediction ofthe tail of the 7Be distribution by this simple modelis most likely due to pre-equilibrium fragment emissionprocesses, which are not included in the model. As ther-mal energy is the only source of initial kinetic energy inthe model, reproducing the spectra depicted in Fig. 9brequires Tmid−velocity=20 MeV. The physical origin ofsuch a high temperature is unclear. The simulation alsoindicates that the contribution of TLF∗ emission to themid-velocity region examined is insignificant. Analysis ofthe V⊥ distributions for Li isotopes reveals similar spec-tral shapes and slope parameters (TPLF∗=7 MeV andTmid−velocity=20 MeV) as shown in Fig. 10. Kinetic“temperatures” of similar magnitude have been previ-ously reported for mid-velocity IMF emissions [13, 36].

It is noteworthy that both the 7Be and 10Be, as wellas the 6,9Li, spectra associated with mid-velocity emis-sion, shown in Figs. 9 and 10, can be describedwith the same initial kinetic energy (Tmid−velocity=20MeV). The enhanced probability of low V⊥ emissionas compared to the surface emission model may reflecttemperature-dependent surface-entropy effects [37] or atransition from surface to volume emission [2].

0

1

2

3

4

5

R =

Y(10

Be)

/Y(7 B

e)

MP, PLF*

MP, Mid-vel

Cent, Mid-vel

⟨ R ⟩1.06

2.20

2.25

a)

0

0.1

0.2

0.3

0.4

0.5

1 1.5 2 2.5 3 3.5 4 4.5 5V⊥ (cm/ns)

R =

Y(9 L

i)/Y

(6 Li)

⟨ R ⟩0.110.210.26

b)

FIG. 11: Dependence of the ratios of 10Be to 7Be and 9Lito 6Li on V⊥ for different impact parameter and velocity se-lection criteria. Points displayed indicate the average valuefor 1≤V⊥<2, 2≤V⊥<3, 3≤V⊥<4, and V⊥≥4 cm/ns. Linescorrespond to the predictions of a two source emission model.The shaded region corresponds to different assumptions forthe neutron-enrichment of mid-velocity.

VI. ISOTOPIC COMPOSITION

The experimental observation that the transverse-velocity distributions for the neutron-rich (e.g. 10Be and9Li) isotopes are different from the neutron-deficient iso-topes (e.g. 7Be and 6Li) (Figs. 9 and 10) indicates thatthe ratio of these isotopes evolves as a function of V⊥.In order to examine this dependence in a more transpar-ent fashion, we examine the ratio of the yields of 10Be to7Be as a function of V⊥ in Fig. 11a. For all three casesshown one observes that this ratio decreases monotoni-cally with increasing V⊥. For the case of PLF∗ emission(solid circles) this decrease can be simply understood asa consequence of the Coulomb barrier. As the Coulombbarrier for both 10Be and 7Be emission is similar, the 7Be,on average, acquires a higher velocity than the 10Be. Theregion of low V⊥ is therefore preferentially populated bythe 10Be as compared to the 7Be as evident in Fig. 9a.

The most striking feature of Fig. 11a is that mid-velocity fragments associated with mid-peripheral colli-sions (open triangles) exhibit a significantly larger valueof Y(10Be)/Y(7Be) as compared to emission from thePLF∗ (solid circles). This enhancement is observed atall values of V⊥. Mid-velocity fragments associated withcentral collisions (open squares) also manifest large val-ues of Y(10Be)/Y(7Be), as compared to emission fromthe PLF∗. The yield ratios associated with central colli-

8

sions are even larger than those mid-velocity emission inthe mid-peripheral case (open triangles), however mostof this difference occurs for low V⊥ (V⊥ ≤2.5 cm/ns).This V⊥ dependence of Y(10Be)/Y(7Be) for both PLF∗

emission and mid-velocity emission can explain the angu-lar dependence of neutron-deficient fragments previouslyreported [38]. As different Coulomb repulsion in the dif-ferent cases leads to different behavior of the yield ratioas a function of V⊥, it is important to compare the yieldratios integrated over V⊥.

By integrating over the entire range of V⊥ observed,we find that 〈Y(10Be)/Y(7Be)〉 for PLF∗ emission is 1.06while at mid-rapidity it is considerably higher, 2.2 formid-peripheral collisions and 2.25 for central collisions.Based upon these integrated yields, one observes that forBe,

Rmid−velocity,mid−peripheral

RPLF,mid−peripheral=

2.2

1.06= 2.08 (2)

while

Rmid−velocity,central

RPLF,mid−peripheral=

2.25

1.06= 2.12 (3)

Thus, the integrated yield of 10Be/7Be at mid-velocity

for mid-peripheral and central collisions is comparable

and significantly different from PLF∗ emission. The be-havior exhibited by the Y(10Be)/Y(7Be) is also observedfor Y(9Li)/Y(6Li), as shown in the lower panel of Fig.11. It is remarkable that at mid-velocity not only are the

Z and transverse-velocity distributions similar for mid-

peripheral and central collisions, but the fragment com-

position is essentially the same – while markedly different

from PLF∗ emission.

It is important to consider the influence of the PLF∗

Coulomb field on the observed N/Z enrichment at mid-velocity. Radial repulsion of fragments from the PLF∗

results in 7Be fragments displaced more toward mid-velocity than 10Be fragments. Therefore the Coulombfield of the PLF∗ and TLF∗ lead to an increase inthe yield of neutron-deficient isotopes at mid-velocity.Hence, due to these qualitative arguments the primor-dial N/Z composition at mid-velocity is expected to behigher than that experimentally observed.

The N-body Coulomb trajectory model previouslydescribed can also be used to quantify this enhance-ment of Y(10Be)/Y(7Be) at mid-velocity as comparedto PLF∗ emission. The relative emission probability,Y(10Be)/Y(7Be), for the PLF∗ was taken from the ex-perimental data while for the mid-velocity source thisprobability was taken relative to the PLF∗ ratio asK*YPLF∗(10Be)/YPLF∗(7Be), where K was varied as afree parameter. For mid-peripheral collisions, the su-

perposition of PLF∗ emission and emission of the mid-velocity source with V‖>V‖

PLF in the model is indi-cated by the solid line in Fig. 11, while the correspond-ing yield at mid-velocity is represented by the dashedline. Reproducing the V⊥ dependence of the relative

yield, requires consideration of both the Coulomb re-pulsion from the emitting source, and the initial ve-locities of the fragments. Accounting for the initialvelocities in a realistic manner is accomplished by at-tributing a temperature to the emitting source. In thecase of emission from the PLF∗ we use, consistent withthe V⊥ of Fig. 9a, a temperature of TPLF∗=7 MeVto model the PLF∗ decay. The solid line presented inFig. 11 reflects predominantly the emission from thePLF∗. Reproducing the mid-velocity data necessitatesthat Ymid−velocity(10Be/7Be)=2* YPLF∗(10Be/7Be) and

that Tmid−velocity=20 MeV. These latter temperaturesare also consistent with those deduced from the V⊥ dis-tributions shown in Figs. 9 and 10. Shown as theshaded region in Fig. 11 is the sensitivity of the yieldratio to the parameter K. The bottom of the shaded re-gion corresponds to K=1.5 while the top corresponds toK=2.5. While the dashed line represents the superposi-tion of mid-velocity and PLF∗ emission, the dotted linedepicts the contribution of only the mid-velocity source.While the dotted line is only slightly higher than thedashed line, this difference is sensitive to the assumptionof isotropic emission from the PLF∗. Enhanced backwardemission from the PLF∗, as has recently been reported[39], would correspondingly result in a larger difference.All the trends described for Y(10Be)/Y(7Be) are also ob-served for Y(9Li)/Y(6Li), as shown in Fig. 11b, support-ing the conclusion that the Y(10Be)/Y(7Be) ratio is notan isolated case but is representative of other fragments.To extract more quantitative information on the rela-tive yield enhancement at mid-velocity, it is necessary tomore accurately account for the “distortion” introducedby the presence of the PLF∗ and TLF∗. The distortion,particularly important for low V⊥, depends on the IMFemission rates relative to the PLF∗-TLF∗ re-separationand is beyond the scope of the present analysis.

VII. GEMINI CALCULATIONS

To understand the PLF∗ decay better, we performedcalculations with the statistical-model code GEMINI[40], which describes surface emission from an excitednucleus including emission from excited states and theirsequential decay. We examined the isotopic yields as afunction of the excitation and spin of a parent nucleus.At each excitation energy we roughly reproduce the av-erage atomic number of the measured PLF. In Table I,for a fixed J one observes that the Y(10Be)/Y(7Be) de-creases with increasing E*/A, while for fixed E*/A, itincreases with increasing J. For J = 0~ to reproduce themeasured value of 1.06 associated with PLF∗ emission,we deduce an excitation of E*/A ≈ 3-4 MeV. As the leveldensity is taken to be a=A/9 MeV−1 in the model, thisexcitation corresponds to a temperature of T≈6 MeV,in reasonable agreement with the tails of the transverse-velocity distribution. If the PLF∗ has significant spin(≈20~), the temperature of the source must be some-

9

E∗/A(MeV) J=0~ J=20~ J=40~

2 1.50 >1.8 4.67

3 1.29 1.14 2.11

4 0.78 1.17 1.42

TABLE I: Results of GEMINI calculations indicating the de-pendence of Y(10Be)/Y(7Be) on excitation energy, E∗/A, andspin, J, for emission from the PLF∗ (Z≈ 40-48, N/Z ≈ 1.375).

what higher. Thus, within a surface emission picturethe Y(10Be)/Y(7Be) and the transverse-velocity distri-butions constrain the excitation and spin of the emittingsource. Correctly accounting for the interplay of both ofthese quantities is necessary to describe the conditions ofthe emitting source. For these conditions (Z=48, A=114,E∗/A=3.5 MeV, J=0~), we have compared the yield dis-tribution of fragments predicted by GEMINI with thatobserved for PLF∗ emission. The solid line shown inFig. 8 is the GEMINI yield distribution normalized tothe range 3≤Z≤8. While in general the agreement be-tween the GEMINI calculations and emission from thePLF∗ is reasonable, GEMINI overpredicts the relativeyield of Z=3 while under-predicting the relative yield forZ≥4. An improved description of PLF∗ emission couldbe done with a meta-stable mononuclear model which ac-counts for its expansion [41]. While this may affect theoverall emission probabilities, such a treatment is un-likely to affect the ratios presently discussed.

VIII. Z AND A DEPENDENCE OF 〈E⊥〉

The average transverse energies of 2≤Z≤6 fragmentsare displayed in Fig. 12 for different impact parame-ter and velocity selection criteria. To examine emis-sion from the PLF∗ without being biased by the min-imum angular acceptance of LASSA, we have selectedemission for 85◦≤ θPLF ≤95◦ in the PLF frame. Thevalues of 〈E⊥〉 for these different selections can be un-derstood in the context of a simple physical picture inwhich fragments acquire their transverse kinetic energyas a result of Coulomb repulsion, thermal motion, andpossibly energy associated with collective expansion [42].As the thermal component is mass (Z) independent, anobserved Z dependence can be attributed to Coulombrepulsion of fragments from the emitting PLF∗ or thepresence of collective motion [42]. Distinguishing be-tween the Z and A dependence of the 〈E⊥〉 can differen-tiate between the Coulomb and collective contributionsto the transverse energy. In the case of emission from thePLF∗ (solid circles), the measured average transverse ki-netic energies in the PLF frame generally increase withZ. The magnitude of 〈E⊥〉 for Z=2 is roughly consis-tent with values previously reported for a similar sys-tem [43]. These measured magnitudes of 〈E⊥〉 can beunderstood within a surface emission picture in which

0

5

10

15

20

25

30

35

0 1 2 3 4 5 6 7Z

⟨ E

⊥ ⟩

(MeV

)

MP, PLF*

MP, Mid-vel

Cent, Mid-vel

FIG. 12: Average transverse energies for 2≤Z≤6 selected un-der different criteria. For the PLF∗, fragments were selectedin the angular range 85◦≤θ

PLF≤95◦ while mid-velocity frag-ments have 0≤V‖≤1cm/ns in the center-of-mass frame.

fragments are emitted from the surface of a hot nucleus.The 〈E⊥〉 in such a picture is given by 〈ECM 〉 = 〈VC〉+ 2 〈T〉 where the Coulomb energy VC= 1.44 (Zsource-Zfragment)*Zfragment/R with R, the center-to-centerseparation distance between the fragment and source,taken as R=1.2*((Asource-Afragment)

1/3+Afragment1/3)

+ 2 fm. The average Coulomb energy has been calcu-lated within this simple picture. The corresponding 〈E⊥〉(〈E⊥〉 = 2

3〈ECM 〉) for a temperature of T=7 MeV is in-

dicated by the solid line in Fig. 12 while T=9 MeV isrepresented by the dotted line. The magnitude of theobserved 〈E⊥〉 and the dependence on Z is qualitativelydescribed by this simple model, bolstering the view thatthis emission is standard statistical emission from a nearnormal density PLF∗.

In Fig. 12, a marked contrast between emissionfrom the PLF∗ and fragments at mid-velocity associ-ated with mid-peripheral collisions (open triangles) is ob-served. Mid-velocity fragments in MP collisions manifestsignificantly lower 〈E⊥〉 in the PLF frame and for 3≤Z≤6essentially no dependence of 〈E⊥〉 on Z exists. The 〈E⊥〉for helium is approximately 25-30% lower than for IMFs.The magnitude of 〈E⊥〉 for 3≤Z≤6 is ≈22 MeV, essen-tially 2/3 of the Fermi energy. The magnitude of 〈E⊥〉for Z=2 is ≈16 MeV. 〈E⊥〉 values of similar magnitude atmid-velocity have previously been reported for IMFs, in-tegrated over Z, and neutron-rich light-charged-particlesfor a significantly lighter system [44]. This independenceon Z, together with the fact that the 〈E⊥〉 is approx-imately 2/3 the Fermi energy suggests that the trans-

10

verse energy of these fragments does not contain any sig-nificant Coulomb contribution, as was previously conjec-tured based upon the V⊥ distribution shown in Figs. 9and 10. This result is consistent with a physical picturein which fragments aggregate in a dilute nuclear medium– compatible with a Goldhaber scenario as has been pre-viously suggested [36]. Both the Z independence of 〈E⊥〉and the reported magnitudes in the present work are con-sistent with those previously reported [36]. Alternatively,this behavior can be viewed as the volume breakup of alow-density source or as emission from a distended config-uration. On the basis of transverse energies, it has beenproposed [13, 36] that fragments intermediate betweenthe PLF∗ and TLF∗ are dynamical in nature, maintain-ing early-stage correlations of the collision [45].

For mid-velocity fragments associated with central col-lisions (open squares), examination of the dependence of〈E⊥〉 on Z, and in particular the magnitudes of the mea-sured 〈E⊥〉 is particularly revealing. For this case, 〈E⊥〉increases monotonically with Z, indicating a Coulomb in-fluence. For Z=2, the value measured in this work is con-sistent with values previously reported [43]. The magni-tude of 〈E⊥〉, however, is only slightly larger than in thecase of emission from the PLF∗ (solid circles). These twocases, however, involve significantly different charge as-sociated with the emitting system. For central collisionsthe initial atomic number of the mid-velocity source isalmost double that of the PLF∗ (ZS=72 as comparedto ZPLF∗=41). Hence, the similarity of the values of〈E⊥〉 for central collisions with those for emission fromthe PLF∗ suggests that for central collisions, fragmentsoriginate either from a dilute nuclear system (either vol-ume breakup or surface emission during expansion), orafter considerable charge has been removed from the sys-tem, by fast, light-charged-particle emission. The largeCoulomb barrier for IMF emission favors early emissionof IMFs making IMF emission following light-charged-particle de-excitation, on average, less likely.

To disentangle the contribution of Coulomb energy andany possible collective flow [42] to the 〈E⊥〉, we exam-ine the dependence of 〈E⊥〉 on A for individual elementsin Fig. 13. Significant collective expansion effects havebeen previously asserted [17, 46], particularly for thecase of central collisions. Evident in panel a) for thecase of central collisions is that for IMFs, in the case ofN≥Z, the observed 〈E⊥〉 does not increase with increas-ing A for a given Z but is either constant or decreasesslightly. This observation contradicts the expectation ofa mass-dependent collective flow, at least in the trans-verse direction. The most striking feature of Fig. 13ais that neutron-deficient isotopes, particularly 3He, 7Be,and 11C, exhibit larger 〈E⊥〉 than other isotopes of thesame element. For 6Li essentially no enhancement is ob-served while for 10B only a modest enhancement is ob-served. One possible reason for this difference betweenodd and even Z is that only for even-Z are nuclides withN<Z observed with significant yield. This enhancementin the kinetic energy of neutron-deficient fragments in

15

20

25

30

35

40

45

5 10 15

⟨ E⊥ ⟩

(MeV

)

Cent, Mid-vel

a)

5 10 15A

MP, Mid-vel

b)

He

Li

Be

B

C

5 10 15

MP, PLF*

c)

FIG. 13: Average transverse energies as a function of massnumber for 2≤Z≤6 for mid-peripheral and central collisionswith different selection criteria. For the PLF∗, fragmentswere selected in the angular range 85◦≤θ

PLF≤95◦ while mid-velocity fragments have 0≤V‖≤1cm/ns in the center-of-massframe.

comparison to other isotopes of the same element hasbeen previously reported for central collisions in the sys-tem 112Sn + 112Sn at E/A=50 MeV and has been in-terpreted as evidence for surface emission from a hot,expanding nuclear system [47]. It has been hypothesizedthat the larger kinetic energy observed for the neutron-deficient isotopes originates because they are emitted onaverage earlier than other isotopes of the same element[47].

In contrast to the previous work which focused solelyon central collisions [47], we also present the dependenceof 〈E⊥〉 associated with mid-peripheral collisions for bothemission from the PLF∗ and the mid-velocity regime. Inthe case of mid-velocity we observe the same effect as forcentral collisions, although the magnitude of the enhance-ment is somewhat less. As the physical picture of a hot,source which emits as it expands is not compatible withthe case of mid-velocity emission for mid-peripheral colli-sions, the observed trend must have an alternate explana-tion. In the case of emission from the PLF∗, 11C does not

show an enhancement in contrast to the two mid-velocitycases, emphasizing the difference between mid-velocityfragment production and emission from the PLF∗. Asignificant enhancement of the average kinetic energy isstill observed for 3He and 7Be emitted from the PLF∗.Thus, this kinetic enhancement of neutron-deficient iso-topes is not associated simply with central collisions inwhich a low density, expanded source is formed but also

11

15

20

25

30

35

40

0 2 4 6 8 10A

⟨ EC

M ⟩

(M

eV)

64Ni + 100Mo @ 11 A.MeV

HeLiBe

FIG. 14: Average center-of-mass energies for 2≤Z≤4 as afunction of mass selected by element following incomplete fu-sion in the reaction 64Ni + 100Mo at E/A=11 MeV [40].

occurs in the standard statistical decay of a near normaldensity PLF∗.

If the observed effect is related to a displacement in theemission time distributions of neutron-deficient isotopeswith respect to heavier isotopes of the same element [47],one would expect the effect to decrease with increasingexcitation energy as the system moves toward instanta-neous breakup [2]. As a baseline for a nuclear system atrelatively low excitation, we have examined helium iso-topes and IMFs emitted in the reaction 64Ni +100Mo atE/A=11 MeV [40]. Following incomplete fusion of theprojectile Ni nuclei with the Mo target nuclei, evapora-tion residues were measured in coincidence with emittedneutrons, charged particles, and IMFs detected at se-lected angles. The kinetic energy spectra of these emittedparticles is clearly evaporative. On the basis of its veloc-ity, the excitation of the evaporation residue is estimatedto be E∗=319±27 MeV [48]. Thus, this system providesan important low-excitation reference point in a systemof comparable Z and A to the central collision data of thepresent work. The dependence of 〈ECM 〉 on A is shownin Fig. 14. Clearly evident in this figure is the fact thatstandard statistical emission at low excitation does not

result in a large enhancement of the kinetic energies ofthe neutron-deficient isotopes 3He and 7Be. A differenceof ≈2 MeV is observed between the 3He and 4He aver-age kinetic energies. Due to the low excitation energy ofthis system, sequential feeding of 3He is expected to benegligible. Consequently, the observed energy differencebetween 3He and 4He can be largely attributed to theearlier average emission time of 3He. This difference pro-

vides a reference point for the increase in cluster kineticenergy due to differences in the average emission time.The large difference observed in average kinetic energiesof neutron-deficient isotopes in the 114Cd + 92Mo sys-tem is therefore not principally due to differences in theaverage emission time of fragments.

Direct evidence that the excitation of the emittingsource is primarily responsible for the enhancement ofthe neutron deficient isotopes is presented in Fig. 15 foremission from the PLF∗. In panel a) the 〈E⊥〉 for isotopesof helium are shown as a function of the PLF velocity.For this portion of the analysis we expand our definitionof the PLF to include 15≤ZPLF≤46 [29]. It has previ-ously been demonstrated that the velocity damping ofthe PLF∗ is associated with the excitation incurred inthe PLF∗ following the interaction phase of the collision[29]. The deduced excitation energy scale is indicated atthe top of the figure while the beam velocity is repre-sented by an arrow. As 〈VPLF 〉 decreases from the beamvelocity (excitation energy increases) the 〈E⊥〉 for 3He,4He, and 6He all increase monotonically. To explore thedifferences between the increase in kinetic energy for thedifferent helium isotopes in a more sensitive manner, weexamined the increase in the 〈E⊥〉 for 3He and 6He rela-tive to 4He. These results are presented in the lower panelof Fig. 15. The difference in transverse energy between3He and 4He increases with increasing excitation from5.7 MeV at 〈E*/A〉≈2 MeV to 9.3 MeV at 〈E*/A〉≈5.8MeV. On the other hand, aside from an initial decrease,the transverse energy difference between 6He and 4He rel-ative remains approximately constant over the measuredrange. We emphasize that the average kinetic energy en-hancement for neutron-deficient isotopes increases withincreasing excitation energy (solid stars), opposing theexpected behavior based upon an emission time displace-ment argument.

These observations may be qualitatively understood byconsidering the growing importance of charged-particledecay channels with increasing excitation energy. A frag-ment emitted from a hot source with an initial thermalenergy accelerates in the Coulomb field of the emittingsystem and acquires its asymptotic kinetic energy. Ifthis fragment decays by neutron emission, the velocityof the secondary fragment is on average the same as theprimary fragment at the moment of decay, thus its ob-served kinetic energy is only impacted by the change inmass. However, should the fragment undergo charged-particle decay, then the kinetic energy observed for thesecondary fragment reflects the Coulomb energy acquiredby its parent up to the moment of decay, which is largerdue to the larger parent atomic number. Only if thelifetime of the parent is sufficiently long for it to trans-form a significant fraction of its initial Coulomb energyinto kinetic energy will the kinetic energy of the daugh-ter fragment be appreciably increased. Instantaneous de-cay of the parent fragment will not result in an increasein the kinetic energy of the daughter fragments. Thisphysical picture suggests that the neutron-deficient iso-

12

16182022242628303234

⟨ E⊥ ⟩

(MeV

)

3He4He6He

a)5.83 4.6 3.52 2.78 2.35 2.02

⟨ E*/A ⟩ (MeV)

0

2

4

6

8

10

6.5 7 7.5 8 8.5 9 9.5

⟨ VPLF ⟩ (cm/ns)

∆⟨ E

⊥ ⟩

(MeV

)

3He - 4He6He - 4He

b)

FIG. 15: Panel a) 〈E⊥〉 for helium isotopes as a functionof 〈VPLF 〉 and deduced excitation energy (upper axis). 3He(solid circles), 4He (open circles), and 6He (solid squares).Panel b) Average transverse energy of 3He and 6He with ref-erence to 4He.

topes manifest a secondary decay contribution from rel-atively long-lived charged-particle channels, i.e narrowresonances at relatively low excitation in the parent frag-ment. It is therefore clear from the evidence presentedthat the fragments are not created relatively cold as pre-dicted in some multi-fragmentation models [49]. More-over, these hot fragments do not decay instantaneously.Measurement of the yield associated with multi-particleresonant decay would provide quantitative informationabout this scenario. Unfortunately, the present experi-mental data does not allow examination of these resonantdecays. With increasing excitation, the secondary decayfeeding to 3He and 4He changes, presumably affects theyield ratios of the two isotopes a reference benchmark forisotope thermometry [50, 51]. It should be realized thatindependent of the underlying origin of the kinetic en-ergy difference, there is an inherent danger of examiningdouble ratios such as (Y(3He)/Y(4He))/(Y(6Li)/Y(7Li))involving only one isotope with N<Z that manifests aconsiderably different kinetic energy. Our results mayalso suggest that extracting the primordial N/Z to inves-tigate the possible isospin fractionation of a dilute nuclearmedium requires detailed measurement of both neutronand charged-particle resonant decays.

IX. CONCLUSIONS

In summary, it is revealing to compare the charac-teristics of mid-velocity fragments and those emittedin the de-excitation of a hot, near-normal density nu-cleus, namely the PLF∗. The Z distributions and thetransverse-velocity distributions, for mid-velocity emis-sion are different from those associated with PLF∗ emis-sion. On the other hand, fragments observed at mid-velocity are rather similar independent of whether theyare associated with mid-peripheral or central collisions.The integrated yield ratios of 10Be/7Be and 9Li/6Li re-veal that mid-velocity and PLF∗ emission are also sub-stantially different in N/Z. For central collisions and mid-peripheral collisions, these observed yield ratios are en-hanced by a factor of approximately two with respect toPLF∗ emission. In the case of emission from the PLF∗,the Z dependence of 〈E⊥〉 shows that fragment emissionis consistent with standard evaporation from near normaldensity nuclear matter. In central collisions the Z depen-dence and magnitude of 〈E⊥〉 for mid-velocity fragmentsare inconsistent with normal density formation. For mid-velocity fragments formed in mid-peripheral collisions,the Z independence of 〈E⊥〉 and a magnitude of approx-imately two-thirds of the Fermi energy, suggest clusterformation through coalescence of ablated nucleons. Allthese facts are consistent with the low-density formationof fragments at mid-velocity for both mid-peripheral andcentral collisions, indicating that the conditions for frag-ment formation at mid-velocity are significantly differ-

ent from those of PLF∗ emission. Examination of 〈E⊥〉for isotopically identified fragments shows that neutron-deficient isotopes, particularly those with N<Z, exhibitlarger kinetic energies than heavier isotopes of the sameelement. This enhancement of the kinetic energies forneutron-deficient isotopes increases with increasing exci-tation energy. This result suggests that fragments areproduced hot and that long-lived charged-particle decaymay be important for N<Z clusters, motivating the fu-ture study of resonant decay.

Acknowledgments

We would like to acknowledge the valuable assistanceof the staff at MSU-NSCL for providing the high qualitybeams which made this experiment possible. This workwas supported by the U.S. Department of Energy underDE-FG02-92ER40714 (IU), DE-FG02-87ER-40316 (WU)and the National Science Foundation under Grant No.PHY-95-28844 (MSU).

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