Development of the Monte Carlo model CASCADE-2004 of high-energy nuclear interactions

The Monte Carlo code CASCADE for the calculation of inelastic hadron- and nucleus-nucleus interactions at energies from several tens of MeV up to several tens of GeV and for modelling of nuclear-physical processes accompanying the transport of particles and nuclei in matter is improved by considering a more detailed model of decay of highly excited residual (after-intranuclear-cascade) nuclei. Results of calculations are in good agreement with experiment. However, there are some deviations for light-isotope production, which prompt the necessity of developing more correct models of evaporation and strong asymmetric high-energy fission.     

Excitation functions of fusion reactions and neutron transfer in the interaction of 6He with 197Au and 206Pb

Excitation functions for evaporation residues in the reactions ¹⁹⁷Au(⁶He, xn)^203-xnTl, x = 2-7, and ²⁰⁶Pb(⁶He, 2n)²¹⁰Po, as well as for neutron transfer reactions for the production of ¹⁹⁶Au and ¹⁹⁸Au in the interaction of ⁶He with ¹⁹⁷Au were measured. The ⁶He beam was obtained from the accelerator complex for radioactive beams DRIBs (JINR). The maximum energy of the beam was about 10AMeV and the intensity reached 2×10⁷pps. The stacked-foil activation technique was used directly in the beam extracted from the cyclotron or in the focal plane of the magnetic spectrometer MSP-144. The identification of the reaction products was done by their radioactive γ- or α-decay. The fusion reaction with the evaporation of two neutrons was characterized by an increase in the cross-section compared to statistical model calculations. The analysis of the data in the framework of the statistical model for the decay of excited nuclei, which took into account the sequential fusion of ⁶He has shown good agreement between the experimental and the calculated values of the cross-sections in the case of sub-Coulomb-barrier fusion in the ²⁰⁶Pb + ⁶He reaction. An unusually large cross-section was observed below the Coulomb barrier for the production of ¹⁹⁸Au in the interaction of ⁶He with ¹⁹⁷Au. Possible mechanisms of formation and decay of transfer reaction products are discussed.     

Measurements of fusion reactions induced by radioactive 132Sn on 64Ni

Evaporation residue and fission cross sections of radioactive ¹³²Sn on ⁶⁴Ni were measured. Statistical model calculations using parameters simultaneously fitting stable Sn+⁶⁴Ni data reproduce the ¹³²Sn induced reaction very well. A large sub-barrier fusion enhancement was observed. The enhancement can be accounted for by coupled-channels calculations including inelastic excitation of the projectile and target, and neutron transfer.     

Fusion near the Coulomb barrier for the synthesis of heavy and superheavy elements: A theoretical approach

The compound nucleus formation is considered as a two-step process of touching and subsequent tunneling of the projectile into the target. The deep minima in the potential energy curve are due to shell effects in the experimental binding energies and give possible target-projectile combinations for the synthesis of heavy and superheavy elements. The asymmetric channels thus obtained are in remarkable agreement with the known experimental channels. In our model, the colliding partners are first shown to be captured in the pocket behind the outer (touching) barrier and the composite system so formed finally tunnels through the inner (fusion) barrier to form the resulting compound nucleus. These calculations reveal the importance of the fusion barrier, which occur only for the asymmetric target-projectile combinations. The calculated fusion cross-sections show a reasonable comparison with the observed one-neutron evaporation residue cross-sections. An estimate of the excitation energy carried by the compound nucleus is also obtained from our model calculations.     

Sub and near barrier fusion of neutron rich heavy nuclei – studies with radioactive ion beams

The availability of accelerated fission fragments at HRIBF allows us to study fusion reactions where one of the reactants is a short-lived exotic nucleus. Most interesting in this respect are entrance channels involving neutron-rich target and projectile – where enhanced survival probability of the compound system may allow the synthesis of heavier system. Much depends though on the dynamic evolution of the captured nuclei into a compound nucleus and the ensuing competition between fission and evaporation residue decay modes. Our studies of fusion between heavy neutron-rich nuclei are aimed at acquiring data that will lead to the understanding and eventually the ability to predict the probabilities for these different processes.     

Entrance channel potentials in the synthesis of the heaviest nuclei

Entrance channel potentials in nucleus-nucleus collisions, relevant for the synthesis of superheavy elements, are systematically studied within a semi-microscopic approach, where microscopic nuclear densities of the colliding spherical or deformed nuclei are used in semi-classical expressions of the energy-density functional. From experimental data on fusion windows evidence is found that the existence of pockets in the entrance channel potentials is crucial for fusion. Criteria for the choice of the best collision systems for the synthesis of superheavy elements are discussed. Received: 14 May 2002 / Accepted: 6 June 2002 / Published online: 26 November 2002 RID="a" ID="a"e-mail: v.denisov@gsi.de, denisov@kinr.kiev.ua RID="b" ID="b"e-mail: w.nrnbrg@gsi.de Communicated by P. Schuck     

Modified Glauber model for the total reaction cross-section of 12C + 12C collisions

Glauber's theory has been adopted to calculate the total heavy-ion reaction cross-sections at high energies. At relatively low energies, Glauber's total reaction cross-section has been modified in order to take into account the Coulomb field effect and is called modified Glauber model I. In addition to the Coulomb field effect, the nuclear effect has also been taken into account in the Glauber model and is called modified Glauber model II. An analytical expression for the transparency function for heavy-ion reactions, involving the nuclear densities of the colliding ions and the nucleon-nucleon cross- section, has been obtained within the framework of the modified Glauber models I and II. The transparency and the total reaction cross-sections of the ¹²C + ¹²C collisions are calculated at different bombarding energies. The obtained results are in good agreement with the experimental data and with previous theoretical calculations. Received: 26 January 2001 / Accepted: 15 October 2001     

Possible Way to Synthesize Superheavy Element Z=117

Within the framework of the dinuclear system model, the production of superheavy element Z = 117 in possible projectile-target combinations is analysed systematically. The calculated results show that the production cross sections are strongly dependent on the reaction systems. Optimal combinations, corresponding excitation energies and evaporation channels are proposed, such as the isotopes^248.249 Bk in ^48 Ca induced reactions in 3n evaporation channels and the reactions ^45Sc＋246.248Cm in 3n and 4n channels, and the system ^51 V＋ 244pu in 3n channel.     

Measurement of fusion excitation functions of 27, 29, 31Al + 197Au

A systematic study of the sub-barrier fusion reactions with neutron-rich projectiles has been carried out for three isotopes ^27,29,31Al bombarding a ¹⁹⁷Au target. A target chamber equipped with a target stack and sets of MWPC was employed in order to enhance the efficiency of the radioactive beam experiment. Coupled-channel calculations including the quadrupole excitations do not well fit the measured fusion excitation functions, whereas flat barrier distributions to represent the coupling to the neutron transfer largely account for the observed enhancement of the sub-barrier fusion cross-sections. Received: 13 March 2001 / Accepted: 27 April 2001     

Isotopic dependence of fusion probabilities for neutron-deficient and -rich colliding nuclei

Isotopic dependence of the fusion dynamics is studied by analyzing the collision of a large number of isotopes of Ca and Ni with 0.6 N/Z 2. This study, which results from the Skyrme energy density formalism, reveals that the addition of neutrons favors fusion of reacting partners, whereas the reverse happens with the removal of neutrons. The fusion barrier heights and positions follow a non-linear second-order dependence on ( -1 ), whereas fusion cross-sections can be parameterized by a straight line.-1     

Neutron and Proton Diffusion in Fusion Reactions for the Synthesis of Superheavy Nuclei

The restriction of the one dimensional （1D） master equation （ME） with the mass number of the projectile-like fragment as a variable is studied, and a two-dimensional （2D） master equation with the neutron and proton numbers as independent variables is set up, and solved numerically. Our study showed that the 2D ME can describe the fusion process well in all projectile target combinations. Therefore the possible channels to synthesize super-heavy nuclei can be studied correctly in wider possibilities. The available condition for employing 1D ME is pointed out.     

Entrance channel mass asymmetry dependence of compound nucleus formation

The fusion reactions ⁴⁸Ca + ¹⁵⁴Sm and ¹⁶O + ¹⁸⁶W leading to the same compound nucleus ²⁰²Pb are studied within the framework of an improved isospin dependent quantum molecular dynamics model. The entrance channel mass asymmetry dependence of compound nucleus formation is found by analyzing the shell correction energies, Coulomb barriers and fusion cross sections. The calculated fusion cross sections agree quantitatively with the experimental data. We conclude that the compound nucleus formation is favorable for the system with larger mass asymmetry.     

Production of neutron-rich Ca isotopes in transfer-type reactions

The production cross sections of neutron-rich isotopes ^{52, 54, 56, 58, 60}Ca in the diffusive nucleon transfer reactions ⁴⁸Ca + ¹⁹⁷Au and ⁴⁸Ca + ²³⁸U at incident energies close to the Coulomb barrier are predicted. The global trend of production cross-section with respect to the charge (mass) number of target in reactions with ⁴⁸Ca beam is analysed for the future experiments.     

Probing the equation of state for cold nuclear matter in fusion reactions

To probe the nuclear equation of state, several fusion cross-sections have been analyzed using microscopic nucleus-nucleus potentials calculated in the framework of the Hamiltonian energy density approach through the well-known Skyrme nucleon-nucleon effective interaction with eighteen different parameterizations which express various equations of state. Three density-dependent M3Y-Paris effective forces are examined also within the double-folding model. The various effective forces give incompressibility modulus values which vary over a rather wide range between 188MeV and 372MeV. The extracted fusion barrier distributions are examined too with the same aim. The most successfully investigated interactions in deriving satisfactory fusion excitation functions as well as barrier distributions are those giving equations of state with nuclear incompressibility values in the range of 230-241MeV, according to the isospin asymmetry of the interacting nuclei.     

Entrance-Channel Dependence of Isospin Effects on Double n/p Ratio in HIC

Within the hadronic transport model IBUU04, we investigate the effect of density-dependent symmetry energy on double neutron/proton (n/p) ratio of free nucleons in heavy ion collisions by taking four isotopic Sn+Sn reaction systems. Especially the entrance-channel asymmetry and impact-parameter dependence of the effect of symmetry energy are discussed. It is found that in both central and semi-central collisions the sensitivity of the double n/p ratio to the density-dependent symmetry energy is more pronounced in neutron-richer systems. Our results also indicate clearly that the effect of symmetry energy is stronger in central collisions than that in semi-central collisions.     

Effect of the entrance channel on the synthesis of superheavy elements

Cross-sections for the synthesis of superheavy elements were analyzed using the concept of a dinuclear system. Experimental values for the production of elements Z = 104, 108, 110, 111 and 112 by cold fusion reactions with targets of ²⁰⁸Pb and ²⁰⁹Bi were reproduced. The model reveals the importance of entrance channel dynamics and competition between quasi-fission and complete fusion processes. Energy windows were observed which allow capture of the reacting nuclei and formation of the compound nucleus. The quantities were studied which are significant for the interaction dynamics of massive nuclei in the entrance channel.     

GSI experiments on synthesis and nuclear structure investigations of the heaviest nuclei

Isotopes of elements up to Z = 113 have been synthesized using medium heavy projectiles and target nuclei around doubly magic ²⁰⁸Pb. Synthesis of still heavier elements in reactions of ⁴⁸Ca projectiles with actinide target nuclei has been reported. To obtain more information about production mechanism of transfermium isotopes nuclear reaction studies including investigations of massive transfer were resumed at SHIP, GSI. Nuclear structure investigations at SHIP have been concentrated so far mainly on systematic investigations of low lying Nilsson levels in odd-mass nuclei. Recently this field has been extended to decay studies of isomeric states in nobelium nuclei at E^* > 1 MeV.     

Fission and ternary cluster decay of hyper-deformed 56Ni

Coincidences between two heavy fragments have been measured from the fission of ⁵⁶Ni compound nuclei formed in the ³²S + ²⁴Mg reaction at E _lab( ^32S ) = 165.4 MeV. A unique experimental set-up consisting of two large-area position-sensitive (x, y) gas detector telescopes has been used allowing the complete determination of the observed fragments and their momentum vectors. In addition to binary fission events with subsequent particle evaporation, narrow out-of-plane correlations are observed for two fragments emitted in purely binary events and in events with a missing charge consisting of 2α - and 3α -particles (¹²C). These events are interpreted as ternary cluster decay from ⁵⁶Ni nuclei at high angular momenta through hyper-deformed shapes.     

Isotopic dependence of neutron emission from dinuclear system

Using the statistical approach, we study the isotopic dependence of the de-excitation of dinuclear systems formed in the entrance channel of heavy-ion reactions. The probabilities of neutron emission from the dinuclear systems ^62-73Ni + ²⁰⁸Pb are estimated and a possible experiment for the observation of this emission is discussed.     

Validation of CASCADE code using the monitor reactions

Production cross-sections of monitor reaction ²⁷Al(x, y)²⁴Na for proton, neutron and deuteron projectiles have been estimated from the CASCADE code from tens of MeV/n to tens of GeV/n energy and compared them with the available experimental data. It has also been shown that using the CASCADE code production cross-section of ²⁷Al(d, y₂)²⁴Na reaction can be obtained from the proton and neutron projectiles. Implicitly, this provides an alternative way of knowing production cross-section of ²⁷Al(n, y ₁)²⁴Na reaction which may be used to monitor the neutron flux in a wide range of energy. However, in the paper need of experimental determination of cross-sections for neutron projectile has been stressed. Similarly, cross-section of other monitor reactions like ²⁷Al(p, y ^′)²²Na and ²⁷Al(n, y ^′ ₁)²²Na are also calibrated as function of energy up to several GeV.