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     

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     

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     

Isotopic dependence of fusion cross-sections – linear relationships

A systematic study of isotopic dependence of fusion cross-section is carried out by adding neutrons gradually to N=Z colliding nuclei. We find that fusion barrier position increases and height decreases, both linearly with the increase of N/Z ratio of the compound system. The increase in barrier position is larger compared to decrease in barrier height. In terms of these linear relationships, a parameterized form of fusion cross-sections is given for the neutron-rich colliding nuclei. The fusion cross-sections are also enhanced linearly with the N/Z ratio, and this enhancement is larger for lower incident centre-of-mass energies and independent of the choice of reaction partners. Experimental data and other theoretical studies are called for to verify these results. Received: 27 February 1998 / Revised version: 22 May 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     

Complete and incomplete fusion in reactions of 7Li + 56Fe at E(7Li) = 50 and 68 MeV from analysis of recoil range and light-particle measurements

Excitation functions for the production of eight radioactive products of the reactions of ⁷Li on ⁵⁶Fe have been measured up to E(⁷ Li) = 89 MeV. Recoil range distributions for these products, together with inclusive proton, deuteron, triton and alpha spectra, have been measured at energies of 50 and 68 MeV. The α, t and d spectra show characteristic “break-up” components at forward angles, while the recoil distributions show evidence of complete fusion and incomplete-fusion process ⁵⁶Fe( ⁷Li,α) ⁵⁹Co ^* . A parallel study on ⁵⁵Mn shows some evidences of the ( ⁷Li,t) incomplete-fusion process, but the cross-section for this process is significantly less than for the triton fusion process. The recoil distributions can be reproduced on the assumption that essentially all the observed break-up fragments are in fact associated with incomplete fusion, but uncertainties in normalisation leave open the possibility of a significant contribution of pure break-up. A diffraction model of the ( ⁷Li,α) transfer process reproduces the observed break-up α spectra with some success. Received: 29 March 2001 / Accepted: 12 November 2001     

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     

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     

Fission fragment anisotropies for 19F +209Bi system

The fission fragment angular distributions have been measured for the system ¹⁹F +²⁰⁹Bi over a range of bombarding energies from 88.0 MeV to 125.6 MeV. The measured fission fragment anisotropies are in agreement with the saddle point statistical model calculations in the above energy range. Combining these data with those available for ¹¹B, ¹²C, ¹⁴N, ¹⁶O and ¹⁸O +²⁰⁹Bi, ²⁰⁸Pb systems, it is concluded that the spherical target plus projectile systems behave “normal” from near- to above – barrier energies. This observation is in contrast to the “anomalous” anisotropies exhibited by the deformed actinide target – projectile systems at near – barrier energies. Received: 5 May 1999 / Revised version: 25 July 1999     

Fusion around the barrier in 11,9Be +209Bi

The ⁹Be +²⁰⁹Bi fusion cross sections were measured in the range 37.5 MeV ≤ E _lab ≤ 45.0 MeV at the Munich Tandem via the observation of ground state α-decay of the evaporation residues. Fusion cross sections of ²⁰⁹Bi with the “halo”¹¹Be unstable projectile in the region around the Coulomb barrier were deduced from an experiment done with the same technique at the RIKEN Ring Cyclotron. Above the Coulomb barrier the ¹¹Be cross sections are larger than the ⁹Be ones in agreement with theoretical predictions based on the larger ¹¹Be halo radius. Also below the barrier these theories foresee the same behavior in disagreement with the experimental results, since the two cross sections are rather similar. Received: 2 April 1998     

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     

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.     

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     

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     

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     

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     

Search for dynamical effects in the fission decay in the 240 MeV 32S + 100Mo reaction

Light particles in coincidence with evaporation residues and heavy fragments have been measured by a 4π charged-particle detector at the INFN Laboratori Nazionali di Legnaro (Padua) for the 240 MeV ³²S + ¹⁰⁰Mo reaction leading to the ¹³²Ce composite system at 152 MeV of excitation energy. Energy spectra of the alpha-particles in coincidence with fission fragments were extracted for many correlation angles both in plane and out of plane. A prominent out-of-plane emission was observed, consistent with the pattern for the near-scission emission. From the fit to the spectra, the pre-scission alpha-particle multiplicity of 0.040±0.006 was obtained. This value is reproduced by the code PACE2 without the inclusion of a delay time for fission. The presence of fast fission, which could be responsible for this result, is discussed. Received: 6 August 2002 / Accepted: 9 October 2002 / Published online: 4 February 2003 RID="a" ID="a"e-mail: moro@na.infn.it Communicated by C. Signorini     

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.     

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     

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