Asymmetry effects in fragment production

In this work we present the results for the investigation of\nintermediate-mass fragment (IMF) production with the proton-induced reaction at\n660 MeV on 238U and 237Np target. The data were obtained with the LNR Phasotron\nU-400M Cyclotron at Joint Institute for Nuclear Research (JINR), Dubna, Russia.\nA total of 93 isotopes, in the mass range of 30 < A < 200, were unambiguously\nidentified with high precision. The fragment production cross sections were\nobtained by means of the induced-activation method in an off-line analysis.\nMass-yield distributions were derived from the data and compared with the\nresults of the simulation code CRISP for multimodal fission. A discussion of\nthe super-asymmetric fragment production mechanism is also given.\n

The theoretical description of heavy-ion collisions at intermediate beam energies, 10 MeV ≲, E/A ≲ 150 MeV, is still in an unsatisfactory state. Different factors contribute to that situation. Thus, for one, the nucleon excitation energies are low and in that comparable to nucleon localization energies, indicating a likely importance of the quantal effects. With the change in the beam energy in the discussed range, the dynamics changes from that dominated by the mean field to that dominated by collisions (as evidenced in the appearance of the flow balance-energy). As excitation energies grow, they begin to exceed the average binding energies per nucleon and, within the mentioned range of E/A, a massive production of intermediate-mass fragments (IMF) takes place[1]. The production, in terms of IMF multiplicity or total mass that IMF carry, maximizes at E/A ~ 75 MeV. The description of the intermediate and light fragment production is beyond the capability of common single-particle models of collisions[2]. The single-particle models with fluctuating forces[3,4] can describe fragment production, but miss the shell effects and the discreteness of the mass and charge numbers. The involved limitation is recognized once one realizes that, in the very central Au + Au collisions at 100 MeV/nucleon, the probability for a proton to come out from the reaction as a constituent of an a particle is close[5] to 50%. Within the Boltzmann-Langevin model with the fluctuating forces[3,4], the α particle plays no distinguished role. Statistical models[6,7] account for the shell effects, but miss the reaction dynamics. The importance of the dynamics is seen, in particular, in the fact that the collective outward flow energy in the reactions is comparable to the thermal energy.

From the past few years, increasing experimental evidence has shown that clusters (multiple of $\ensuremath{\alpha}$ particles) of intermediate mass are emitted with quite large cross sections at forward angles in heavy-ion reactions. In the present work a theoretical investigation has been made to explore the role of $\ensuremath{\alpha}$-clustering in $^{13,12}\mathrm{C}+^{12}\mathrm{C}$ reactions populating $^{25,24}\mathrm{Mg}^{*}$ compound nuclei (CN), which results in the enhanced cross sections of intermediate mass fragments (IMFs) within the collective clusterization framework of the dynamical cluster decay model (DCM). With in the formalism the experimental cross sections are reproduced using the spherical as well as deformed configurations effects included up to quadruple deformations (${\ensuremath{\beta}}_{2i}$) for two nuclei having optimum orientations ${\ensuremath{\theta}}^{\mathrm{opt}}$. The ratio of the calculated (fission-like) yields of each isotopic fragment $^{6,7}\mathrm{Li}, ^{7,8,9}\mathrm{Be}$ obtained in the two reactions has been compared with the experimental and statistical model predictions also. The DCM calculated result is in little better comparison to the statistical models due to the inclusion of structure effects in the calculations. In the present calculations, the dynamical yields count for the preformation probability (${P}_{0}$) of the IMFs within the collective clusterization process of DCM, before penetrating the scattering potential barrier. Quite interestingly, the calculated ratio of ${P}_{0}$ of the corresponding IMFs ${P}_{0(\mathrm{IMFs})}^{^{25}\mathrm{Mg}^{*}}/{P}_{0(\mathrm{IMFs})}^{^{24}\mathrm{Mg}^{*}}$ for the CN $^{25,24}\mathrm{Mg}^{*}$ shows the trend of ratio of experimental cross sections, i.e., ${\ensuremath{\sigma}}_{\mathrm{IMFs}}^{^{25}\mathrm{Mg}^{*}}/{\ensuremath{\sigma}}_{\mathrm{IMFs}}^{^{24}\mathrm{Mg}^{*}}$. It is found that $\ensuremath{\alpha}$-cluster structure of complimentary fragments of the IMFs under investigation plays quite a significant role in their decays.

A comparative decay analysis of $^{80}\mathrm{Zr}^{*}$, $^{80}\mathrm{Sr}^{*}$, and $^{80}\mathrm{Kr}^{*}$ isobaric nuclear systems formed in $^{40}\mathrm{Ca}+^{40}\mathrm{Ca}$, $^{16}\mathrm{O}+^{64}\mathrm{Zn}$, and $^{32}\mathrm{S}+^{48}\mathrm{Ca}$ reactions, respectively, has been conducted to investigate the $N/Z$ dependence of different decay modes within a dynamical cluster-decay model based on the collective clusterization approach of quantum mechanical fragmentation theory. The comparative contributions of the emission of light particles (LPs), intermediate mass fragments (IMFs), and symmetric mass fragments (SMFs) in the total fusion cross-sections, ${\ensuremath{\sigma}}_{\mathrm{fusion}}$, have been calculated. The results show that LPs have a major contribution to ${\ensuremath{\sigma}}_{\mathrm{fusion}}$ in the decay of all three compound nuclei (CN). The percentage contribution of LPs is larger for CN with higher $N/Z$ ratio. The IMFs and SMFs cross-section are comparatively low in the total ${\ensuremath{\sigma}}_{\mathrm{fusion}}$ but their emissions are in competition in the decay process. The results show that the shape of mass distribution evolves from symmetric to asymmetric with increasing $N/Z$ ratio. The yield around SMFs is greater for the system having the lowest $N/Z$ ratio. This may be attributed to higher ${P}_{0}$ for the symmetric exit channel, particularly at higher $\ensuremath{\ell}$ values. The calculated fusion cross-sections for all three CN are in good agreement with the experimental data.

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The reaction systems, 64Zn + 58Ni, 64Zn + 92Mo, 64Zn + 197Au, at 26A, 35A and\n47A MeV, have been studied both in experiments with a 4$\\pi$ detector array,\nNIMROD, and with Antisymmetrized Molecular Dynamics model calculations\nemploying effective interactions corresponding to soft and stiff equations of\nstate (EOS). Direct experimental observables, such as multiplicity\ndistributions, charge distributions, energy spectra and velocity spectra, have\nbeen compared in detail with those of the calculations and a reasonable\nagreement is obtained. The velocity distributions of $\\alpha$ particles and\nfragments with Z >= 3 show distinct differences in calculations with the soft\nEOS and the stiff EOS. The velocity distributions of $\\alpha$ particle and\nIntermediate Mass Fragments (IMF's) are best described by the stiff EOS.\nNeither of the above direct observables nor the strength of the elliptic flow\nare sensitive to changes in the in-medium nucleon-nucleon (NN) cross sections.\nA detailed analysis of the central collision events calculated with the stiff\nEOS revealed that multifragmentation with cold fragment emission is a common\nfeature predicted for all reactions studied here. A possible multifragmentation\nscenario is presented; after the preequilibrium emission ceases in the\ncomposite system, cold light fragments are formed in a hotter gas of nucleons\nand stay cold until the composite system underdoes multifragmentation. For\nreaction with 197Au at 47A MeV a significant radial expansion takes place. For\nreactions with 58Ni and 92Mo at 47A MeV semi-transparency becomes prominent.\nThe differing reaction dynamics drastically change the kinematic\ncharacteristics of emitted fragments. This scenario gives consistent\nexplanations for many existing experimental results in the Fermi energy domain.\n Comment: 34 pages, 43 figures

The dynamical cluster-decay model (DCM) is developed further for the decay of hot and rotating compound nuclei (CN) formed in light heavy-ion reactions. The model is worked out in terms of only one parameter, namely the neck-length parameter, which is related to the total kinetic energy TKE($T$) or effective $Q$ value ${\mathit{Q}}_{\mathrm{eff}}(T)$ at temperature $T$ of the hot CN and is defined in terms of the CN binding energy and ground-state binding energies of the emitted fragments. The emission of both the light particles (LP), with $A\ensuremath{\le}4,Z\ensuremath{\le}2$, as well as the complex intermediate mass fragments (IMF), with $4lAl20,Zg2$, is considered as the dynamical collective mass motion of preformed clusters through the barrier. Within the same dynamical model treatment, the LPs are shown to have different characteristics compared to those of the IMFs. The systematic variations of the LP emission cross section ${\ensuremath{\sigma}}_{\mathrm{LP}}$ and IMF emission cross section ${\ensuremath{\sigma}}_{\text{IMF}}$ calculated from the present DCM match exactly the statistical fission model predictions. A nonstatistical dynamical description is developed for the first time for emission of light particles from hot and rotating CN. The model is applied to the decay of ${^{56}\mathrm{Ni}}^{\ensuremath{\ast}}$ formed in the $^{32}\mathrm{S}+^{24}\mathrm{Mg}$ reaction at two incident energies ${E}_{\mathrm{c}\mathrm{.}\mathrm{m}\mathrm{.}}=51.6$ and 60.5 MeV. Both the IMFs and average $\stackrel{\underline{}}{\mathit{TKE}}$ spectra are found to compare resonably well with the experimental data, favoring asymmetric mass distributions. The LPs' emission cross section is shown to depend strongly on the type of emitted particles and their multiplicities.

Application of CR-39 detector to investigation of intermediate mass fragment production in reaction 40Ar+208Pb at E/A=19.6 MeV/u

Intermediate mass fragments of 4\ensuremath{\le}Z\ensuremath{\le}17 have been studied from the reaction 640 MeV $^{86}\mathrm{o}$/rKr${+}^{63}$Cu. Inclusive energy and angular distribution measurements have been made as well as coincidence measurements with fissionlike fragments of 18\ensuremath{\le}Z\ensuremath{\le}40. The coincidence configuration was such that two-body exit channels were excluded; nevertheless, heavy fragments were recorded both in plane and out of plane with respect to light fragments of 4\ensuremath{\le}Z\ensuremath{\le}10. Three mechanisms have been identified for intermediate mass fragment production. The dominant pathway for all intermediate mass fragments is two-body breakup of fission or evaporationlike character. A second pathway for Z\ensuremath{\le}10 is intermediate mass fragment ejection from the composite nucleus followed by sequential fission. The third path is simultaneous ternary breakup for 4\ensuremath{\le}Z\ensuremath{\le}9 that resembles ternary alpha-accompanied fission at low energies.

In this article, we investigate the dependence of nuclear temperature on emitting source neutron-proton () asymmetry with light charged particles (LCPs) and intermediate mass fragments (IMFs) generated from intermediate-velocity sources in thirteen reaction systems with different asymmetries, on , and , on , , , and at 40 MeV/nucleon. The apparent temperature values of LCPs and IMFs from different systems are deduced from the measured yields using two helium-related and eight carbon-related double isotope ratio thermometers, respectively. Then, the sequential decay effect on the experimental apparent temperature deduction with the double isotope ratio thermometers is quantitatively corrected explicitly with the aid of the quantum statistical model. The present treatment is an improvement compared to our previous studies in which an indirect method was adopted to qualitatively consider the sequential decay effect. A negligible asymmetry dependence of the real temperature after the correction is quantitatively addressed in heavy-ion reactions at the present intermediate energy, where a change of 0.1 units in source asymmetry corresponds to an absolute change in temperature of an order of 0.03 to 0.29 MeV on average for LCPs and IMFs. This conclusion is in close agreement with that inferred qualitatively via the indirect method in our previous studies.

In reference to the experimental data, the decay mechanism of 88Mo* compound system formed in 48Ti+40Ca reaction is investigated at three beam energies (Ebeam = 300, 450, and 600 MeV) using the collective clusterization approach of Dynamical Cluster decay Model (DCM). The calculations are done for spherical choice of fragmentation and with the inclusion of quadrupole (β2) deformations having “optimum” orientations. According to the experimental evidence 88Mo* decays via Fusion-Evaporation (FE) and Fusion-Fission (FF) processes, thus the decay cross-sections of this hot and rotating compound system are calculated for both channels. In FF decay mode, the explicit contribution of Intermediate Mass Fragments (IMF), Heavy Mass Fragments (HMF) and fission fragments (symmetric/asymmetric) is detected within DCM framework. The calculated FE and FF decay cross-sections find nice agreement with the available experimental data. Experimentally, it has been observed that the total contribution of FE and FF decay cross-sections is less than the total reaction cross-sections possibly due to the presence of some nCN component such as deep inelastic collisions (DIC), which generally contributes above critical angular momentum (ℓcr). The possibility of DIC contribution can be addressed as a future assignment in view of diminishing pocket of interaction potential above ℓcr.

Velocity correlations in the multifragmentation scenario

We made a descriptive theoretical analysis for the transverse momentum dependence of elliptic flow (ν2) of neutrons and protons within the framework of isospin-dependent quantum molecular dynamics (IQMD) model. Simulations are carried out for the symmetric reactions of 124Sn+124Sn and 197Au+197Au. We demonstrate the effect of momentum dependent interactions (MDI) as well as of nucleonic cross-sections (isospin-dependent & independent) on the elliptical flow. The MDI and different forms of cross-section are found to affect the elliptical flow of both protons and neutrons considerably.

Experimental results are presented on the charge, velocity, and angular distributions of intermediate mass fragments (IMFs) for the reaction Fe+Au at bombarding energies of 50 and 100 MeV/nucleon. Results are compared to the quantum molecular dynamics (QMD) model and a modified QMD which includes a Pauli potential and follows the subsequent statistical decay of excited reaction products. The more complete model gives a good representation of the data and suggests that the major source of IMFs at large angles is due to multifragmentation of the target residue.

Complex fragment emission sources characterized by linear momentum transfer measurements