In [1,2]the observed decrease in spectral peak energies of IMFs emitted from
hot nuclei was interpreted in terms of a breakup density that decreased with
increasing energy. Subsequently, Raduta et al. [3] performed MMM simulations
that showed decreasing spectral peaks could be obtained at constant density. In
this letter we examine this apparent inconsistency.Comment: 9 pages, 2 figures, 1 tabl

Beaulieu

Botvina

Bracken

Friedman

J.B. Natowitz

K. Kwiatkowski

Kwiatkowski

Lefort

Moretto

Poskanzer

Raduta

S.J. Yennello

Sobotka

V.E. Viola

Viola

Physics Letters B

English

arXiv

Crossref

Comment on breakup densities of hot nuclei

Viola, V.E.

Kwiatkowski, K.

Yennello, S.J.

Natowitz, J.B.

Texas A&amp;M Repository

arXiv:nucl-ex/0603007v1  6 Mar 2006Comment on Breakup Densities of Hot NucleiV.E. Violaa, K. Kwiatkowskib,S.J. Yennelloc and J.B. NatowitzcaIUCF and Department of Chemistry, Indiana University, Bloomington, IN 47405bLos Alamos National Laboratory, Los Alamos, NM 87545.cDepartment of Chemistry and Cyclotron Institute, Texas A & M University,College Station, TX 77843AbstractIn [1,2] the observed decrease in spectral peak energies of IMFs emitted from hotnuclei was interpreted in terms of a breakup density that decreased with increasingexcitation energy. Subsequently, Raduta et al. [3] performed MMM simulations thatshowed decreasing spectral peaks could be obtained at constant density. In this letterwe examine this apparent inconsistency.Key words: multifragmentation, breakup densitiesPACS: 25.70.Pq, 25.55,-e1 IntroductionIn a recent analysis of kinetic energy spectra for intermediate mass fragments(Z=2 < IMF < Z∼20) emitted in energetic light-ion-induced reactions, it wasshown that the centroids of the Coulomb peaks systematically shift to lowerenergies and the widths broaden as a function of increasing excitation energy,Preprint submitted to Elsevier Science 13 March 2018E*/A [1,2]. This result was interpreted as evidence for a decrease in the aver-age breakup density from normal nuclear density ρ0 at low excitation energiesto a constant value of ρ/ρ0 ∼ 0.3 for E*A ∼ 4 MeV and above. Subsequently,Raduta et al. [3] performed MMM (microcanonical multifragmentation model)calculations [4] that showed that the observed centroid shifts could qualita-tively be explained using a constant density of ρ/ρ0 ∼ 0.2. They concludedthat “ ... a decrease in the peak centroids for kinetic energy spectra can beobserved at low constant density, which is different than published results in[1]”. Here we examine this apparent conflict in interpretation.First, it is relevant to clarify the method used to fit the experimental spectrafrom which the experimental breakup densities were derived. The parameteri-zation of the spectral data was based on the model of Moretto [5], as adaptedby Kwiatkowski [6]. The model extends the fission transition state model ofNix and Swiatecki [7] to describe all mass divisions, accounting for the evo-lution of spectral shapes from Gaussian for fission to Maxwellian for nucleonemission. In addition to containing Coulomb barrier, slope(temperature) andkinematic parameters, the model has the important advantage of allowing fora broadening of the spectral widths with increasing excitation energy to ac-count for fluctuations that accompany higher E*/A values, as has long beenknown for fission [8].For present purposes the primary concern is the Coulomb parameter, whichdepends on the average charge separation distance between a given fragmentand the charge distribution of the remaining system. Using fission fragmentkinetic-energy systematics [9] as a reference point for the charge separationdistance at low excitation energies, the parameterization in [1,2] provides goodfits to IMF spectra at E*/A values below 2 MeV, for which ρ/ρ0 ∼ 1. For2higher excitation energies, satisfactory fits can only be obtained with a reducedCoulomb barrier parameter, which implies a larger separation distance forthe breakup configuration and hence a lower density. In the excitation-energyregime where binary breakup is the dominant de-excitation mechanism, theparameterization of [1,2] should provide a satisfactory description of the IMF-heavy residue charge separation distance at breakup. For multifragmentationevents, it is assumed that this model provides a first-order approximation tothe average Coulomb field experienced by individual IMFs at breakup.The top frame of Fig. 1 shows the average Coulomb parameters derived fromthe moving source fits in [1,2]. The fits take into account the significant de-crease in source size with increasing E*/A, which coupled with the decreasingspectral peak centroids, leads to a near constant behavior at high excitationenergies. For example, at E*/A = 8 MeV the source is about 75% of thetarget mass due to fast cascade and preequilibrium processes. Shown in thebottom frame of Fig. 1 are the extracted experimental densities, which assumea spherical breakup geometry. Both the Coulomb parameter and the densi-ties are observed to decrease rapidly in the range E*/A = 1 - 4 MeV, afterwhich they become constant within experimental error. The upshot is thatup to E*/A ∼ 4 MeV the analysis shows a decreasing density as a functionof increasing excitation energy - which disagrees with the MMM calculations.However, above E*/A ∼ 4 MeV the decreasing Coulomb peak centroids leadto a nearly constant density, which is the same conclusion the Raduta et al.predict.In order to place the experimental results and the MMM simulations in per-spective, it is useful to compare the IMF multiplicity distributions, as shown inTable 1. The experimental distributions for specific multiplicities are shown inTable 1Comparison of IMF multiplicities and breakup densities between the experimentalvalues of [1,2] and MMM simulations [3].E*/A (MeV) 1.0 2.0 3.4 4.5 5.7 6.8 7.9 10.0MIMF 0.06 0.18 0.5 1.7 2.6 3.3 4.0 4.7MIMF (MMM) * * 2.8 4.5 6.0 7.6 8.9 10.1M(exp)/M(MMM) * * 5.6 2.6 2.3 2.3 2.3 2.1< ρ/ρ0 >(exp) 1.0 0.95 0.6 0.41 0.26 0.32 0.31 *ρ/ρ0(MMM) * * 0.2 0.2 0.2 0.2 0.2 0.2Fig. 2 , along with the probabilities for events with MIMF > 2. The multiplic-ity data show that below E*/A ∼ 4 MeV, IMF emission is primarily a binaryprocess. For higher excitation energies, the multiplicities increase rapidly, sig-naling the onset of multifragmentation as the dominant decay mechanism.With respect to the present discussion, the salient point is that multifragmen-tation does not become a significant decay process until the excitation energyhas exceeded this threshold and therefore comparison with statistical multi-fragmentation models such as MMM should be applied with caution at lowerenergies.The comparison of the absolute values and the multiplicity ratios in Table Ireveals significant discrepancies between the data and the MMM simulations.The IMF multiplicity and the charge distributions are basic observables thatone expects to be reproduced with any multifragmentation model. Two ob-servations are apparent in the table. First, for E*/A below 4 MeV, the MMMmodel increasingly overpredicts the multiplicities as the excitation energy de-4creases. Second, above this value the model/data ratio is a constant value ofabout 2.3. By increasing the breakup density in the model, this discrepancycould probably be resolved. Thus, it is useful to separate the analysis into twoexcitation energy regimes, above and below E*/A ∼= 4 MeV.First, we examine the higher E*/A results. In this regime, the experimentalresults of [1,2] lead to the same conclusion as the MMM model; i.e., the kineticenergy centroids shift systematically to lower energies with increasing excita-tion energy at constant density. This result has been shown previously withthe simultaneous SMM [10] model in [11,12], a calculation that also repro-duces the experimental charge distributions and the multiplicities. Thus, inthe regime where multifragmentation is the dominant decay mode, the simu-lations presented by Raduta et al, which use a more sophisticated Coulombcalculation for multifragment events, reinforce previous conclusions. In orderfor the MMM model to yield more quantitative agreement in this region, itsparameters need to be modified to reduce the multiplicities by a factor of twoand to reproduce the charge distributions. In addition, the calculation needsto include the significant decrease in source size at higher excitation energy.Irrespective of any parameterization, the observed centroid decrease with in-creasing E*/A must logically be explained at least in part by a decrease in thedensity, as originally pointed out by Poskanzer [13]. The sequential EES model[14] and the metastable mononucleus model [15] have been shown to describethe density evolution in this low energy regime. Raduta et al do not addressthis necessary evolution in the breakup density from ρ/ρ0 = 0.2 assumed intheir model to ρ/ρ0 = 1.0 at low excitation energy.In conclusion, for excitation energies where multifragmentation is the domi-5nant breakup mechanism, i.e. E*/A > 4 MeV, the MMM simulations of [3] andthe experimental results [1,2] both show a decrease in the IMF spectral peakswith increasing E*/A at constant density. Thus, in this regime, the experi-mental results and the calculations are qualitatively self-consistent. For lowerexcitation energies, binary breakup is the dominant decay mode and analysisof the spectra with a multifragmentation mechanism cannot account for thedata.Acknowledgements: This work was supported by the U.S. Department of En-ergy.References[1] V.E. Viola et al., Phys. Rev. Lett.93 (2004) 132701.[2] D.S. Bracken et al., Phys. Rev. C 69 (2004) 034612.[3] Ad. Raduta et al., Phys Lett. B 623 (2005) 43.[4] Al. Raduta et al., Phys. Rev. C 65 (2002) 054610.[5] L.G. Moretto, Nucl. Phys. A 247 (1975) 211.[6] K. Kwiatkowski et al., Phys. Lett. B 171 (1986) 41.[7] J.R. Nix and W.J. Swiatecki, Nucl. Phys. 71 (1965) 1.[8] V.E. Viola and T. Sikkeland, Phys. Rev. 130 (1963) 2044.[9] V.E. Viola, K. Kwiatkowski and M. Walker, Phys. Rev. C 31 (1985) 1550.[10] A. Botvina et al., Nucl. Phys. A 507 (1990) 649.[11] L. Beaulieu et al. Phys. Rev. C 64 (2001) 064604.6[12] T. Lefort et al. Phys. Rev. C 62 (2000) 031604(R).[13] A.M. Poskanzer et al., Phys. Rev. C 3 (1971) 882; Phys. Rev. C 4 (2001) 1759).[14] W.A. Friedman, Phys. Rev. C 42 (1990) 667.[15] L.G. Sobotka et al. Phys. Rev. Lett 93 (2004) 132702.7Fig. 1. Top: Dependence of the average moving-source Coulomb parameter < kc >as a function of excitation energy. Symbols are as follows: 200 MeV 4He (); E/A= 20-100 MeV 14N (△); 4.8 GeV 3He (). Bottom: Average density < ρ/ρ0 > as afunction of E*/A derived from the kc values in the top panel.80246ExperimentalCorrection ICorrection II10-210-1100.250.50.7510 1 2 3 4 5 6 7 8 9 10 11P(Mimf = 0,1,2)P(Mimf ≥ 3)E*/A (MeV)< N imf >P(N imf)P(Mimf)Fig. 2. Top: Average number of IMFs as a function of excitation energy for the 8GeV/c pi− + 197Au reaction: observed Nimf (circles), corrected for geometry (solidtriangles) and corrected for both geometry and fragment energy thresholds Mimf(open triangles. Middle: probability for a given number of observed IMFs. Bottom:Probability for corrected IMF multiplicity Mimf > 2 (circles) and Mimf < 3 (solidcircles).9

Comment on Breakup Densities of Hot Nuclei

Comment on Breakup Densities of Hot Nuclei

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Comment on Breakup Densities of Hot Nuclei

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Texas A&amp;M Repository

Texas A&M Repository