Reply on the "Comment on "Investigating the phase diagram of finite extensive and nonextensive systems" by Al. H. Raduta and Ad. R. Raduta" by A. S. Botvina and I. N. Mishustin

2 Pages·0.06 MB·English

by  Al. H. Raduta

Reply on the “Comment on “Investigating the phase diagram of finite extensive and
nonextensive systems” by Al. H. Raduta and Ad. R. Raduta” by A. S. Botvina and I.
N. Mishustin”
Al. H. Raduta1,2, Ad. R. Raduta1,2
1GSI, D-64220 Darmstadt, Germany
2NIPNE, RO-76900 Bucharest, Romania
PACSnumbers: 24.10.Pa;25.70.Pq;21.65.+f
TheBotvinaandMishustin’scommentaddressesade- the nuclear phase diagrams from Ref. [8]). This very
tail (minor subject to the aim and topic of the paper, simple reasoning shows that the conclusions of Botvina
3 i.e. the Coulomb effects on the liquid-gas phase transi- and Mishustin are actually in disagreement with what
0 tion) of the recent paper [1], namely a free volume ap- one would expect from a real nuclear system.
0
proachaimedto allowsomequalitativeestimationofthe But let us now discuss the free volume approach we
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system’scriticalpoint. Intheirviewthis distortsthebe- used Ref. [1]. This approach was employed in Ref. [1]

n haviourofthepressure(P)versusvolume(V)curvesdue with the intention of reaching densities ρ → ρ0 unaf-
a
to the “non-conservation of the center of mass (c.m.) of fordable with a spherical fragment scenario. Within this
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the system” implied by the employed parametrization. scenario it is assumed that each fragment is blocking for
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1 While we agree with the evident idea that, apartfrom itself and the rest of the fragments its own volume. Ob-
thecaseofthelargesystems,thecenterofmassofasmall viously, at ρ → ρ0 such a formula can only be justified

1 systemshouldbe conservedinthermodynamicalcalcula- by a deformed fragment scenario. And this differs a lot
v
tions in order to obtain accurate results, one should re- from what Botvina and Mishustin claim to understand
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markthatthe BotvinaandMishustin’s argumentationis from our paper: the removal of the physical assumption
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0 based on a specific view on freeze-out: non-overlapping that fragments don’t overlap. The latter assumption is
1 spherical fragments placed in a spherical “recipient” of indeed unphysical while the deformed fragment scenario
0 volume V. The shape of the fragments is therefore fixed (actually used in our calculations) is not.
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for each fragmentation event. This is, indeed, a sce- Of course, the deformed fragment scenario deserves a
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nariowidelyusedinstatisticalmodelsfromthebeginning more refined treatment than our calculations from Ref.
/
h of the nuclear multifragmentation studies. Within such [1]: a proper account for the fragments’ deformation de-
t
- a scenario, the Botvina and Mishustin’s comments are gree of freedom, a sharp conservation of the center of
l
c surely correct and they apply to most of the statistical mass,anaccuratetreatmentofthe binding energies,etc.
u calculationsperformedsofar(MMMCmodel[2],Koonin Definitely, these aspects haveto be addressedin the sta-
n
and Randrup model [3], Das Gupta and Mekjian calcu- tistical models for a better description of the real multi-
:
v lations [4], and even recent calculations performed with fragmentation.
i the SMM model [5], etc.). Following this hypothesis, at Summarizing, the Botvina and Mishustin’s P(V)
X T
a given temperature, P will converge to a finite value curves correspond to a simplified scenario for the freeze-
r
a when V will approach the volume of the source nucleus out: nonoverlapping spherical fragments inside a spher-
at normal density (V0) (see e.g. [6]). ical freeze-out recipient, which, as explained before dif-
However, dynamical calculations clearly show that fers from the scenario corresponding to our free volume
fragments are not at all spherical at break-up but have parametrization: non-overlapping fragments with vari-
variousshapesvariatingfromeventtoevent(seee.g. [7]). ous shapes at freeze-out. The latter scenario is the re-
It means that the spherical fragment hypothesis is actu- alistic one, being in agreement with the results of the
ally away from reality and this has to be reflected in all various dynamical simulations of nuclear multifragmen-
thermodynamical observables. In this case, the system’s tationand,moreover,atρ→ρ0 thefragmentshavetobe
positioncoordinates(enteringtheintegrationwhichleads deformed in order to fit the recipient. As explained be-
tothe freevolumeterminthe partitionfunction)willbe fore,withinthisscenariothepressurehastodivergewhile
sharedbetweenthepositionsofeachfragment’sc.m. and V approachesV0 (fact in agreementwith ourresults and
the additional coordinates corresponding to each frag- in disagreement with Botvina and Mishustin ones) since
ment deformation. (In other words there are more than the power of V will necessarily be greater than N −1.
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N −1 contributing degrees of freedom.) Obviously, this More refined treatments than ours are surely necessary
detailwillraisethepowerofV toavaluelargerthanthe for obtaining very accurate results, but the qualitative
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N−1responsibleforthe finite valueofP whenV →V0, character of our evaluation was already stated in Ref.
and therefore P will diverge near this limit leading to [1]. Itresultsthat, inspite ofthe roughness(commented
the well known van der Waals behavior (see for example above) of our approximation, the Botvina and Mishus-
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tin’sresult[ontheP(V)T curves]isinfactthe “mislead- (1987).
ing”onesince itdiffersessentiallyfromwhatisexpected [4] S. Das Gupta and A. Z. Mekjian, Phys. Rev. C 57, 1361
from real systems. (1998).
[5] J. B. Elliott and A. S. Hirsch, Phys. Rev. C 61, 054605
(2000).
[6] A.S.BotvinaandI.N.Mishustin,nucl-th/0203059(2002).
[7] P. B. Gossiaux and J. Aichelin, Phys. Rev. C 56, 2109
(1997).
[1] Al. H. Raduta and Ad. R. Raduta, Phys. Rev. Lett. 87,
[8] J. N.De, B.K. Agrawal and S.K. Samaddar,Phys. Rev.
202701 (2001). C 59, R1 (1999).
[2] D. H.E. Gross, Rep.Prog. Phys. 53, 605 (1990).
[3] S. E. Koonin and J. Randrup, Nucl. Phys. A474, 173