document: nuclear multifragmentation is presently intensely studied both theoretically and experimentally . due to the similitude existent between the nucleon - nucleon interaction and the van der waals forces , signs of a liquid - gas phase transition in nuclear matter 
   are searched . while the theoretical calculations concerning this problem started at the beginning of 1980 @xcite , the first experimental evaluation of the nuclear caloric curve was reported in 1995 by the aladin group @xcite . a wide plateau situated at around 5 mev temperature lasting from 3 to 
   10 mev / nucleon excitation energy was identified . 
   the fact was obviously associated with the possible existence of a liquid - gas phase transition in nuclear matter and generated new motivations for further theoretical and experimental work . 
   similar experiments of eos @xcite and indra @xcite followed shortly . using different reactions they obtained slightly different caloric curves , the plateau - like region being absent in the majority of cases . 
   factors contributing to these discrepancies are both the precision of the experimental measurements and the finite - size effects of the caloric curve manifested through the dependency of the equilibrated sources [ @xmath5 sequence on the reaction type . 
   concerning the first point of view , recent reevaluations of the aladin group concerning the kinetic energies of the emitted neutrons brought corrections of about 10 @xmath6 ( in the case of the reaction @xmath1au+@xmath1au , 600 mev / nucleon ) . 
   more importantly however it was proven that the energies of the spectator parts are growing with approximately 30 @xmath6 in the bombarding energy interval 600 to 1000 mev / nucleon . on the other side , the universality of the quantity @xmath7 subject to 
   the bombarding energy variation ( which was theoretically proven @xcite to be a signature of statistical equilibrium ) suggests that for the above - mentioned reactions the equilibrated sources sequence [ @xmath5 should be the same . 
   consequently , we deal with an important nonequilibrium part included in the measured source excitation energies which may belong to both pre - equilibrium or pre - break - up stages @xcite . 
   the smm calculations suggest a significant quantity of nonequilibrium energy even in the case of the 600 mev / nucleon bombarding energy reaction @xcite . 
   thus , the necessity of accurate theoretical descriptions of the break - up stage and of the sequential secondary particle emission appears to be imperative in order to distinguish between the equilibrium and nonequilibrium parts of the measured excitation energies . 
   these approaches should strictly obey the constrains of the physical system which , in the case of nuclear multifragmentation , are purely microcanonic . 
   as we previously underlined @xcite , in spite of their success in reproducing some experimental data , the two widely used statistical multifragmentation models ( smm @xcite and mmmc @xcite ) are not strictly satisfying the microcanonical rules . 
   the present paper describes some refinements and improvements brought to the sharp microcanonical multifragmentation model proposed in @xcite and also the employment of the model in its new version in the interpretation of the recent experimental data of the aladin group @xcite . 
   the improvements brought to the model @xcite are presented in section ii . 
   section iii presents the new evaluations of temperature curves and the first evaluations ( performed with this model ) of heat capacities at constant volume ( @xmath8 ) represented as a function of system excitation energy and temperature and also the comparison between the model predictions and the recent experimental heli isotopic temperature curve [ @xmath9 @xcite . 
   conclusions are drawn in section iv . 
   the improvements brought to the microcanonical multifragmentation model concerns both the _ break - up _ stage and the _ secondary particle emission _ stage . 
   + ( i ) _ primary break - up refinements _ + comparing to the version of ref.@xcite the present model has the following new features : + ( a ) the experimental discrete energy levels are replacing the level density for fragments with @xmath10 ( in the previous version of the model a thomas fermi type level density formula was used for all particle excited states ) . in this respect , in the statistical weight of a configuration and the correction factor formulas @xcite the level density functions are replaced by the degeneracies of the discrete levels , @xmath11 ( here @xmath12 denotes the spin of the @xmath13th excited level ) . as a criterion for level selection ( i.e. the level life - time must be greater than the typical time of a fragmentation event ) we used @xmath14 1 mev , where @xmath15 is the width of the energy level . + ( b ) in the case of the fragments with @xmath16 the level density formula is modified as to take into account the strong decrease of the fragments excited states life - time ( reported to the standard duration of a fragmentation event ) with the increase of their excitation energy . to this aim the thomas fermi type formula @xcite is completed with the factor @xmath17 ( see ref.@xcite ) : @xmath18 where @xmath19 , @xmath20 and @xmath21 . 
   + ( ii ) _ inclusion of the secondary decay stage _ + for the @xmath22 nuclei it was observed that the fragments excitation energies are sufficiently small such as the sequential evaporation scheme is perfectly applicable . according to weisskopf theory @xcite ( extended as to account for particles larger than @xmath23 ) , the probability of emitting a particle @xmath24 from an excited nucleus is proportional to the quantity : @xmath25 where @xmath26 are the stable excited states of the fragment @xmath24 subject to particle emission ( their upper limit is generally around 7 - 8 mev ) , @xmath27 is the kinetic energy of the formed pair in the center of mass ( c.m . ) 
   frame , @xmath28 is the degeneracy of the level @xmath13 , @xmath29 and @xmath30 are respectively the reduced mass of the pair and the separation energy of the particle @xmath24 and finally @xmath31 is the inverse reaction cross - section . due to the specificity of the multifragmentation calculations we considered the range of the emitted fragments @xmath24 up to the @xmath32 limit . for the inverse reaction cross - section we have used the optical model based parametrization from ref . 
   the sequential evaporation process is simulated by means of standard monte carlo ( see for example @xcite ) .    for nuclei with @xmath33 ( the only excited states of @xmath34 nuclei taken into consideration are few states higher than 20 mev belonging to the @xmath23 particle ) depending on their amount of excitation we consider _ secondary break - up _ for @xmath35 and weisskopf evaporation otherwise ( here @xmath36 is the excitation energy of the fragment @xmath37 and @xmath38 is its binding energy ) . 
   the microcanonical weight formulas have the usual form @xcite excepting the level density functions which are here replaced by the discrete levels degeneracies . due to the reduced dimensions of the @xmath39 systems , 
   the break - up channels are countable ( and a classical monte carlo simulation is appropriate ) when a mean field approach is used for the coulomb interaction energy . in this respect , 
   the wigner - seitz approach @xcite is employed for the coulomb interaction : @xmath40 where @xmath41 and @xmath42 denotes the mass and the charge of the source nucleus , the resulting fragments have the index @xmath13 , @xmath43^{1/3}$ ] and @xmath44 . here 
   @xmath45 denotes the break - up volume and @xmath46 the volume of the nucleus at normal density 
   . it should be added that @xmath47 is the radius of the source nucleus at break - up and @xmath48 is the radius of fragment @xmath13 at normal density .    for each event of the primary break - up simulation , 
   the entire chain of evaporation and secondary break - up events is monte carlo simulated . 
   using the improved version of the microcanonical multifragmentation model , the caloric curves corresponding to two freeze - out radii ( r=2.25 a@xmath49 and r=2.50 a@xmath49 fm ) are reevaluated for the case of the source nucleus ( 70 , 32 ) ( the microcanonical caloric curves evaluated with the initial version of the model are given in ref . 
   these are presented in fig . 
   1 ( a ) . one can observe that the main features of the caloric curve from refs . 
   @xcite are reobtained . 
   thus , one can recognize the liquid - like region at the beginning of the caloric curve , then a large plateau - like region and finally the linearly increasing gas - like region . 
   one may also notice that the caloric curve behavior at the freeze - out radius variation is maintained : the decrease of the freeze - out radius leads to a global lifting of the caloric curve . 
   as it is well known , the curves of the constant volume heat capacity ( @xmath8 ) as a function of system excitation energy ( @xmath50 ) and as a function of temperature ( @xmath51 ) may provide important information concerning the transition region and the transition order . 
   for this reason the curves @xmath52 and @xmath53 have been evaluated ( see fig . 
   1 ( a ) and fig . 1 ( b ) ) . 
   we remind that the constant volume heat capacity ( @xmath8 ) is calculable in the present model using the formula @xcite : @xmath54 ^ 2\right>+t^2\left<\left(\frac32 n_c- \frac52\right )      \frac1{k^2}\right>.\ ] ] it can be observed that the @xmath52 curve has a sharp maximum around 4.5 mev / nucleon excitation energy for both considered freeze - out radii . 
   this suggests that a phase transition exists in that region . 
   the transition temperatures can be very well distinguished by analyzing the @xmath53 . 
   one can observe two sharp - peaked maxima pointing the transition temperatures corresponding to the two considered freeze - out radii .    in order to make a direct comparison between the calculated heli isotopic temperature and the recent experimental results @xcite one has to deduce the sequence of excitation energy as a function of the system dimension [ @xmath5 . this is done as in refs . 
   @xcite using as matching criterion the simultaneously reproduction of the @xmath55 and @xmath56 curves . 
   this couple of curves can fairly well identify the dimension and the excitation of the equilibrated nuclear source @xcite . here 
   @xmath2 stands for the multiplicity of intermediate mass fragments and is defined as the number of fragments with @xmath57 from a fragmentation event while @xmath3 denotes the charge asymmetry of the two largest fragments and , for one fragmentation event is defined as @xmath58 with @xmath59 where @xmath60 is the maximum charge of a fragment and @xmath61 is the second largest charge of a fragment in the respective event . 
   @xmath4 represents the _ bound charge _ in one fragmentation event and is defined as the sum of the charges of all fragments with @xmath62 . 
   the simultaneous fit of the calculated curves @xmath55 and @xmath56 on the corresponding experimental data ( @xmath1au+@xmath1au at 1000 mev / nucleon ) is given in fig . 
   the agreement is very good . 
   the equilibrated source sequence [ @xmath5 we used for this purpose is given in fig . 
   3 together with the experimental evaluations of the excitation energies as a function of source dimension for the reaction @xmath1au+@xmath1au at 600 , 800 and 1000 mev / nucleon . 
   the theoretically obtained sequence is relatively close to the experimental line corresponding to 600 mev / nucleon bombarding energy . 
   the deviations between the calculated equilibrated source sequence and the three experimental lines suggest that the experimental evaluations contain a quantity of non - equilibrium energy which grows with increasing the bombarding energy . as suggested in ref . 
   @xcite , its origin may be situated in both the pre - equilibrium and pre - break - up stage . 
   these deviations are exclusively due to the neutron kinetic energies which , reevaluated @xcite from the 1995 data @xcite , are much larger . 
   it should also be pointed that apart from the smm predictions @xcite , the quantity of non - equilibrium energy predicted by the present model is smaller and thus the model predicted equilibrated source sequence is closer to the experimental line of the 600 mev / nucleon bombarding energy reaction .    after evaluating the sequence of the equilibrated sources a direct comparison the heli calculated isotopic temperature curve with the ones recently evaluated by the aladin group @xcite is performed . to this purpose the uncorrected albergo temperature is used : @xmath63 $ ] , the experimental predictions being divided by @xmath64 ( which is the factor used in the aladin evaluation of the heli caloric curve chosen as to average the qsm , gemini and mmmc models predictions ) . 
   the result is represented in fig . 
   4 as a function of @xmath4 . 
   it can be observed that the agreement between the calculated @xmath65 and the experimental data corresponding to the @xmath1au+@xmath1au reaction at 600 and 1000 mev / nucleon bombarding energy is excellent on the entire range of @xmath4 . in comparison 
   , the smm model predicts in the region @xmath66 a curve steeper than the experimental data . 
   sumarizing , the microcanonical multifragmentation model from ref . 
   @xcite is improved by refining the primary break - up part and by including the secondary particle emission . 
   the caloric curve rededuced with the new version of the model preserves its general aspect @xcite manifesting an important plateau - like region . 
   the transition regions are clearly indicated by the sharp maxima of the @xmath52 and @xmath53 curves . 
   the model proves the ability of simultaneously fitting the `` definitory '' characteristics of the nuclear multifragmentation phenomenon @xmath55 and @xmath56 . evaluating the equilibrated source sequence @xmath67 [ by using the criterion of reproducing both @xmath68 and @xmath69 versus @xmath70 , a nonequilibrium part of the experimentally evaluated excitation energy growing with the increase of the bombarding energy 
   is identified . 
   the direct comparison of the calculated heli caloric curve shows an excellent agreement with the experimental heli curves recently evaluated by the aladin group . 
   g. fai and j. randrup , nucl . 
   a * 404 * , 551 ( 1983 ) ; comp . 
   phys . comm . * 
   42 * , 385 ( 1986 ) ; l. p. csernai , g. fai and j. randrup , phys . 
   b * 140 * , 149 ( 1984 ) ; g. fai , l. p. csernai , j. randrup and h. stocker , phys . 
   b * 164 * , 265 ( 1985 ) . 
   j. pochodzalla _ 
   et al . _ , 
   lett . * 75 * , 1040 ( 1995 ) . 
   j. a. hauger _ 
   et al . _ , 
   lett . * 77 * , 235 ( 1996 ) . 
   y. g. ma _ et al . 
   b * 390 * , 41 ( 1997 ) . 
   a. schuttauf _ 
   _ , nucl . phys . 
   * a607 * , 457 ( 1996 ) . 
   j. pochodzalla , progr . 
   . phys . * 39 * , 443 ( 1997 ) . 
   w. trautmann _ 
   et al . _ , gsi - preprint 98 - 20 , march 1998 . 
   hongfei xi _ 
   et al . _ , 
   a * 359 * , 397 ( 1997 ) . 
   w. f. j. mueller , proceedings of the workshop on multifragmentation , hirschegg ( austria ) ( 1999 ) , gsi . 
   al . h. raduta and ad . 
   r. raduta , phys . 
   c * 59 * , 323 ( 1999 ) . 
   al . h. raduta and ad . 
   r. raduta , nucl . phys . * 
   a647 * , 12 ( 1999 ) . 
   j. p. bondorf , a. s. botvina , a. s. iljinov , i. n. mishustin and k. sneppen , phys . rep . * 257 * , 133 ( 1995 ) . 
   d. h. e. gross , rep . 
   . phys . * 53 * , 605 ( 1990 ) . 
   al . h. raduta and ad . 
   r. raduta , phys . 
   c * 55 * , 1344 ( 1997 ) . 
   h. raduta and ad . 
   r. raduta , phys . 
   c * 56 * , 2059 ( 1997 ) . j. randrup and s. koonin , nucl . 
   a471 * , 355c ( 1987 ) . 
   v. weisskopf , phys . rev . * 
   52 * , 295 ( 1937 ) . 
   a. s. botvina , a. s. iljinov , i. n. mishustin , j. p. bondorf , r. donangelo and k. sneppen , nucl . phys . 
   a475 * , 663 ( 1987 ) . i. dostrovsky , z. fraenkel and g. friedlander , phys . rev . * 116 * , 683 ( 1959 ) . 
   al . h. raduta and ad . 
   r. raduta , phys . 
   c * 59 * , r1855 ( 1999 ) .
summary: the microcanonical multifragmentation model from [ al . 
   h. raduta and ad . 
   r. raduta , phys . 
   rev . 
   c * 55 * , 1344 ( 1997 ) ; * 56 * , 2059 ( 1997 ) ; * 59 * , 323 ( 1999 ) ] is refined and improved by taking into account the experimental discrete levels for fragments with @xmath0 and by including the stage of sequential decay of the primary excited fragments . the caloric curve is reevaluated and the heat capacity at constant volume curve is represented as a function of excitation energy and temperature . 
   the sequence of equilibrated sources formed in the reactions studied by the aladin group ( @xmath1au+@xmath1au at 600 , 800 and 1000 mev / nucleon bombarding energy ) is deduced by fitting simultaneously the model predicted mean multiplicity of intermediate mass fragments ( @xmath2 ) and charge asymmetry of the two largest fragments ( @xmath3 ) versus bound charge ( @xmath4 ) on the corresponding experimental data . 
   calculated heli isotopic temperature curves as a function of the bound charge are compared with the experimentally deduced ones .