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.     

Incomplete fusion reactions: Analysis of excitation functions and recoil range distributions in 16O + 51V

Incomplete fusion reactions were investigated by measuring the excitation functions of nine evaporation residues in ¹⁶O + ⁵¹V reaction in the beam energy 4-6 MeV/amu, using the well-known recoil catcher technique and gamma-ray spectrometry. The experimental data were compared with that obtained from Monte Carlo simulation calculations using the PACE2 code. The results indicate the presence of incomplete fusion process in the production of two alpha emission products. This was further confirmed by the measurement of recoil range distribution of these isotopes at 96 MeV beam energy. Calculations of the average angular momentum associated with these products revealed the peripheral nature of these ICF reactions. Received: 20 June 2001 / Accepted: 11 September 2001     

Energy spectra and angular distribution of projectile-like fragments in 84 MeV <Superscript>12</Superscript>C + <Superscript>169</Superscript>Tm

Kinetic-energy spectra and angular distribution of projectile-like fragments have been measured in the reaction of 84 MeV ¹²C on ¹⁶⁹Tm, using the surface barrier silicon-based ΔE-E telescopes. The fragments close to the projectile show typical spectra of quasi-elastic transfer reactions, which were found to be in agreement with the calculations based on the direct surface transfer reaction model. A significant cross-section of fast alpha-particles was found at forward angles, reminiscent of incomplete fusion reactions, which could be explained in terms of the direct surface transfer reaction model after taking into account the level density of continuum states in the heavy reaction product. The results have been explained in terms of the continuous evolution of the reaction mechanism as a function of the mass transfer. Received: 13 March 2002 / Accepted: 3 May 2002     

Evidence for a dissipative friction mechanism based on 8Be fragments from the interaction of 12C with 59Co

It is suggested that the spectra of the ⁸Be ground-state (gs) nuclei produced in the interaction of ¹²C with ⁵⁹Co at incident energies varying from 8.3 to 33.3 MeV/amu can be explained by introducing a dissipative friction interaction mechanism preceding projectile break-up. Received: 27 March 2000 / Accepted: 11 April 2000     

Dissipative dynamics of fission in the framework of asymptotic expansion of Fokker-Planck equation

The dynamics of fission has been formulated by generalising the asymptotic expansion of the Fokker-Planck equation in terms of the strength of the fluctuations where the diffusion coefficients depend on the stochastic variables explicitly. The prescission neutron multiplicities and mean kinetic energies of the evaporated neutrons have been calculated and compared with the respective experimental data over a wide range of excitation energy and compound nuclear mass. The mean and the variance of the total kinetic energies of the fission fragments have been calculated and compared with the experimental values. Received: 8 September 1999 / Revised version: 22 November 1999     

Alpha particle emission from the 198Pb compound nucleus: comparison between the fusion-evaporation and the pre-scission channels

The α-particle emission from the ²⁸Si+¹⁷⁰Er fusion-evaporation reaction at 165 and 185 MeV has been measured and compared with published data relative to the pre-scission emission in the same reaction. The spectra in the two channels exhibit nearly the same shape in the low energy region, whereas in the high energy region the spectrum for the fusion-evaporation case features a larger apparent temperature. The interpretation of the difference in shape between the two decay channels is based on statistical model calculations which account for the effects due to the different length of the decay chain. Statistical model calculations with standard parameters describe well the gross features of the alpha particle spectra in the fusion-evaporation channel and the proton spectra in the pre-scission channel. On the contrary, the model predictions seem to overestimate by ≃2 MeV the emission barrier for the alpha particles in the pre-fission channel. This effect is ascribed to the larger elongation of the nucleus during the fission process. An average axis ratio b/a∼ 2 for the emitter is suggested. Received 29 April 1997 / Revised version 10 September 1997     

Synthesis and decay properties of superheavy atoms in nuclear reactions induced by stable and radioactive ion beams

This talk consists of two parts. The first one presents the results of investigations performed in 1998-2000 in Dubna on the synthesis of superheavy nuclei in reactions induced by ⁴⁸Ca ions. The radioactive decay properties of the nuclei, indicating a considerable increase in the α-decay and spontaneous fission half-lives of the isotopes of elements 110-116 when approaching the closed neutron shell at N = 184, are given. In the second part the possible ways of advancing into the region of more neutron-rich nuclei, using stable and radioactive ion beams, are discussed. Since so far no intense radioactive ion beams are available, some experiments with stable beams are considered as a test for the suggested ideas. Received: 1 May 2001 / Accepted: 4 December 2001     

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     

Influence of entrance channel properties on heavy-ion reaction dynamics

In the fusion of heavy nuclei, there is a distribution of fusion barrier energies resulting from coupling between intrinsic motion and internal degrees of freedom. Precise experimental measurements of excitation functions have allowed the extraction of the distributions by taking the second derivative using a point-difference method. In the case of statically deformed nuclei, experimental data shows that the different fusion barrier energies correspond to different physical configurations of the colliding nuclei, the latter affecting the subsequent dynamical trajectories over the potential energy surface, influencing the ultimate reaction products, as for example in quasi-fission. The fusion barrier distribution is also valuable in understanding the fusion of weakly bound nuclei, enabling a reliable prediction of the expected fusion cross-sections, and thus the determination of fusion suppression factors at above-barrier energies. Received: 1 May 2001 / Accepted: 4 December 2001     

Synthesis of superheavy nuclei in the reactions of 244Pu and 248Cm with 48Ca

This paper presents results of the experiments aimed at producing long-lived superheavy elements located near the spherical-shell closures with Z ⩾ 114 and N ⩾ 172 in the ²⁴⁴Pu + ⁴⁸Ca and ²⁴⁸Cm + ⁴⁸Ca reactions. The large measured α-particle energies of the newly observed nuclei, together with the long decay times and spontaneous fission terminating the chains, offer evidence of the decay of nuclei with high atomic numbers. The decay properties of the synthesized nuclei are consistent with the consecutive α-decays originating from the parent nuclides ^{288, 289}114 and ²⁹²116, produced in the 3n and 4n evaporation channels with cross-sections of about a picobarn. The present observations can be considered as experimental evidence of the existence of the “island of stability” of superheavy elements. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: utyonkov@sungns.jinr.ru     

New results on elements 111 and 112

Experiments on the synthesis and identification of the nuclei ²⁷²111 and ²⁷⁷112 were performed in order to confirm previous results. Three additional decay chains were measured in the reaction ⁶⁴Ni + ²⁰⁹Bi →²⁷³111^*. The study revealed considerably improved data on the decay chain originating from ²⁷²111. One additional chain was measured in the reaction ⁷⁰Zn + ²⁰⁸Pb →²⁷⁸112^*. The decay properties of the chain starting at ²⁷⁷112 are in excellent agreement with the second chain of the first experiment down to ²⁶⁵Sg, where the new chain ends by a previously unknown spontaneous-fission branch. A re-analysis of all the data on elements 110, 111, and 112 measured at GSI since 1994 (a total of 34 decay chains was investigated) revealed that for 2 chains (the second chain of ²⁶⁹110 measured in 1994 and the first chain of ²⁷⁷112 measured in 1996) the results of the new analysis differed from the previous one. In all other cases the earlier data are exactly reproduced. Received: 21 December 2001 / Accepted: 15 January 2002     

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.     

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     

Transfer reactions and sub-barrier fusion in 40Ca + 90, 96Zr

The two systems ⁴⁰Ca + ^90,96Zr have been studied by measuring nucleon transfer reactions at two energies near the Coulomb barrier, thus complementing the available sub-barrier fusion cross-sections. Angular distributions for various transfer channels have been determined. Significantly larger neutron transfer cross-sections are found for the target ⁹⁶Zr that exhibits the larger enhancement in the sub-barrier fusion cross-sections. All data have been analyzed with a new model for heavy-ion collisions that calculates simultaneously transfer cross-sections, fusion excitation functions and barrier distributions. The model gives a good account of both transfer and fusion data. Received: 2 May 2002 / Accepted: 4 June 2002 / Published online: 26 November 2002 RID="a" ID="a"e-mail: montagnoli@pd.infn.it, Fax +39049 8277102, Tel. +39049 8277117. RID="b" ID="b"On leave from the China Institute for Atomic Energy, 102413 Beijing, China. Communicated by C. Signorini     

Study of the fusion-fission process in the 35Cl +24Mg reaction

Fusion-fission and fully energy-damped binary processes of the ³⁵Cl+²⁴Mg reaction were investigated using particle-particle coincidence techniques at a ³⁵Cl bombarding energy of E_lab≈ 8 MeV/nucleon. Inclusive data were also taken in order to determine the partial wave distribution of the fusion process. The fragment-fragment correlation data show that the majority of events arises from a binary-decay process with a relatively large multiplicity of secondary light-charged particles emitted by the two primary excited fragments in the exit channel. No evidence is observed for ternary-breakup processes, as expected from the systematics recently established for incident energies below 15 MeV/nucleon and for a large number of reactions. The binary-process results are compared with predictions of statistical-model calculations. The calculations were performed using the Hauser-Feshbach method, based on the available phase space at the scission point of the compound nucleus. This new method uses temperature-dependent level densities and its predictions are in good agreement with the presented experimental data, thus consistent with the fusion-fission origin of the binary fully-damped yields. Received: 12 March 1998     

Variation of total kinetic energy and mass distributions in the fusion-fission reaction of 16O,19F + 209Bi at near barrier energies

Fission fragment mass and energy distributions and their correlations have been measured for the ¹⁶O and ¹⁹F + ²⁰⁹Bi reactions over a wide range of excitation energies ( E ^* = 30-50 MeV). It is observed that in the case of ¹⁶O + ²⁰⁹Bi reaction, the average total fragment kinetic energy, <TKE> is nearly independent of the bombarding energy. However, in the case of ¹⁹F + ²⁰⁹Bi reaction, the average total kinetic energy of the fission fragments shows a peaking behaviour near the barrier. The variation in <TKE> at near barrier energies in the ¹⁹F + ²⁰⁹Bi system seems to be correlated with corresponding strong variation in the variance of the fragment mass distribution. The present results may imply certain dynamical effects leading to compact scission configurations in the fission of ¹⁹F + ²⁰⁹Bi system at near barrier bombarding energies. Received: 9 April 2001 / Accepted: 26 May 2001     

The role of the entrance channel in the fusion of massive nuclei

The role of the entrance channel in the fusion-fission reactions leading to nearly the same superheavy compound nucleus is studied in the framework of dynamic model. The calculations are done for ⁴⁸Ca +²⁴⁴Pu and ^74,76Ge +²⁰⁸Pb reactions which could lead to formation of superheavy element Z = 114. It is shown that for these reactions there is an energy window for the values of the bombarding energy at which a capture probability is sufficiently large. Together with the restriction coming from the intrinsic barrier for fusion, it helps to find an optimal value of the bombarding energy for a given projectile--target combination. Received: 15 July 1998     

Analytical calculation of fusion cross-sections

We analyse the fusion cross-sections, calculated by using two different analytical parameterisations and compare them with the experimental data. Both the parameterisations are based on ion-ion potentials calculated within the framework of Skyrme energy density formalism. In the first case, the ion-ion potential (including the spin-density term) was parameterised and then, by adding the Coulomb potential, one could compute the fusion barrier analytically. In the second case, the calculated fusion barrier heights and positions were parameterised directly. Both of these (previously) reported parameterisations are used here to calculate the fusion barriers and fusion excitation functions for more than 50 reactions belonging to the s-d and f-shell nuclei. A detailed comparison of these parametrisations with the experimental and several other theoretical results shows that both of these parameterisations are able to reproduce the experimental data equally well. As the (second) direct parameterisation depends only on the charges and masses of colliding nuclei, it is very useful for predicting/ understanding the fusion process in low energy heavy-ion reactions. Received: 24 February 1999 / Accepted: 16 March 2000     

Interaction at the barrier in the systems 9, 10, 11Be + 209Bi: Well-established facts and open questions

The experimental data relative to the interaction for the systems ^{9, 10, 11}Be + ²⁰⁹Bi at the Coulomb barrier are critically discussed and compared also with present theories. The break-up (BU) of the two loosely bound projectiles, ^{9, 11}Be, seems to influence the fusion process by “hindering” the fusion cross-sections; but, contrary to expectations, the ¹¹Be halo structure has no influence, since no “enhancement” is evident from the existing data. Attempt to describe simultaneously all the ⁹Be + ²⁰⁹Bi system data: fusion, elastic scattering and BU, within a coupled-channel (CC) approach is only partly successful. It is important, from a theoretical viewpoint, to include in the CC formalism as well as possible the BU process both to continuum states as well as to unbound resonances. More accurate and well-focused experiments are also necessary to pin down this problem. Received: 1 May 2001 / Accepted: 4 December 2001     

Fast fission mechanism and duality of the diffusion process

The reaction of ²³⁸U with ¹²C was studied radiochemically with the purpose of elucidating fast fission characteristics. From the difference in the mass distribution below and above the critical energy where fast fission is predicted to set in, fast fission component was extracted in far-asymmetric mass region and interpreted as the mass diffusion following the Fokker-Planck equation. Anomalous charge dispersion widths in the corresponding mass region and a sudden increase of the whole mass distribution width at the critical energy were also observed to support the above result. The reaction time of fast fission deduced from the width and position of the mass distribution was 5×10⁻²¹s as well by taking into account the effect of neutron emission during the diffusion process, which turned out to be more than one order of magnitude longer than the corresponding life time of typical deep inelastic scattering but substantially short compared to ordinary fusion-fission life time. Evaluation of the driving potential for mass drift required dinuclear configuration be of an elongated or deformed form for fast fission in contrast to a more compact form for the deep-inelastic process. Received: 11 November 1997