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     

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     

Fusion-fission reactions induced by 6He-ions

The experimentally measured excitation functions for the fission and 4n evaporation channels are presented for the ⁶He + ²⁰⁹Bi reaction. The secondary ⁶He beam was produced using the special beam line (Q4DQ-spectrometer) of the U400M accelerator at FLNR, JINR. The comparison of the obtained experimental data with similar results for the ⁴He + ²⁰⁹Bi reaction shows that in the case of the ⁶He + ²⁰⁹Bi reaction a significant enhancement of the cross-section is observed for energies above the barrier. In order to get an agreement between the experimental data and the theoretical calculations it is necessary to reduce the Coulomb barrier by 15-20% , which corresponds to an increase of the parameter r₀ of the nuclear potential up to 1.5-1.6 fm. Received: 1 May 2001 / Accepted: 4 December 2001     

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     

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     

Dynamical effects on the way to fusion of very heavy nuclei

The central collision of ⁴⁰Ar and ²⁰⁸Pb is studied considering the ellipsoidal deformations and isovector dipole mode of motion in the approaching phase. The collective energy dissipation is suggested to originate from the Fermi surface deformation which is treated as a kinematically independent mode of motion within the canonical Lagrange-Rayleigh dynamics. The possible extensions of the approach are discussed. The potential energy surface, calculated using the generalized (folded) surface potential, is studied. The saddle point in the potential energy surface lying at the border of strongly deformed compact configurations is located. The potential energy at this point is about 10MeV smaller than that of the ions touching each other in the spherical shape. The examination of trajectories followed by the system in its evolution shows that the inertia forces strongly hinder the motion of ions along the potential energy valley. The collective energy dissipated during the approach is found to be smaller than the difference in the potential energies at saddle point and at the touching configuration of unpolarized ions.     

Discrete structures in fusion-barrier distributions for vibrational nuclei

We obtain a closed-form expression for the distribution of fusion barriers for vibrational nuclei using a generalization of Dasso, Landowne, and Winther's model, which represents the nuclear surface vibrations as a number of harmonic oscillators, and allows the excitation of an arbitrary number of phonons in the target and/or projectile. We find that this expression is in reasonable agreement with the average trends of the empirical distributions for the fusion of ¹⁶O with ⁹²Zr, ¹⁴⁴Sm and ²⁰⁸Pb, but fails to reproduce the double peaking of the distribution for the ¹⁴⁴Sm target. Only when we restrict the number of excited phonons to a limited number, we are able to reproduce such discrete structures. We show that limiting the number of coupled channels, particularly in the case of strong coupling, increases the spacings between the channel eigenvalues that determine the positions of the peaks of the barrier distribution and modifies their heights. Received: 6 March 2000 / Accepted: 31 January 2001     

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.     

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     

Dynamical effects on the quasiprojectile temperature in the Ar + Al reaction

The temperature of the quasiprojectile (QP) emerging from binary collisions of the light Ar + Al system at 65 MeV/nucleon is studied theoretically in the framework of the Landau-Vlasov dynamical model. The slope parameter of a charged-particle kinetic-energy spectrum, calculated in the forward-hemisphere of the QP reference frame, is taken as the apparent temperature. The apparent temperature associated to the true QP emission displays a weak dependence on the impact parameter and the hottest primary QPs are formed at intermediate values of b. Received: 28 April 2000 / Accepted: 27 October 2000     

Elastic, inelastic scattering and fusion of the 14N +59Co system at energies close to the coulomb barrier

Elastic and inelastic scattering differential cross sections were measured in the energy range 30 MeV ≤ E _lab ≤ 55 MeV, for the ¹⁴N +⁵⁹Co system. Ambiguities of the optical potential derived from the analysis of the elastic scattering data were removed by performing calculations at the radius of sensitivity and by comparison with the available fusion cross section data. A simultaneous analysis of the three mechanisms was performed by coupled channel calculations, and a unique energy independent nuclear potential was found to be able to fit the data. Discussions and comparisons concerning the optical model, the threshold anomaly, full and approximated coupled channel calculations are presented. Received: 6 February 1997 / Revised version: 1 August 1997     

Isospin dependence of the isotopic distributions from 36Ar and 40Ar fragmentation at about 60 MeV/nucleon

Fragments produced in the reactions of 69 MeV/nucleon ³⁶Ar and 55 MeV/nucleon ⁴⁰Ar on a Be target have been measured experimentally. The isotopic distributions from fragmentation reaction for both projectiles are compared with modified statistical abrasion-ablation model calculations. A strong isospin effect exhibits in the fragment distributions produced in ³⁶Ar and ⁴⁰Ar fragmentation. Experimental evidence for the disappearance of the isospin effect in the isotopic distributions produced by projectile fragmentation is observed with the increase of the violence of nuclear reaction. Received: 15 November 2000 / Accepted: 11 April 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     

Enhanced neutron pair transfer and collective excitations in the system 206Pb + 118Sn at barrier energies

At energies below the Coulomb barrier, neutron transfer and Coulomb excitation have been measured in a very heavy asymmetric nuclear system, in ²⁰⁶Pb + ¹¹⁸Sn. These are semi-magic nuclei showing super-fluid properties. Particle-γ coincidence techniques using 5 Euroball Cluster detectors (EB), combined in a set-up with the Heidelberg-Darmstadt NaI Crystal Ball (CB), have been used. Position-sensitive detectors allowed the observation of scattering processes covering angles from 110 up to 150 degrees. The fragments are identified via the known γ-decays of the lowest excited states using the high resolution of EB. Using the unique feature of the set-up with the CB, transfer to well-defined final channels with known quantum numbers is selected using the high-efficiency multiplicity filter of the CB with no second γ-ray, i.e. without feeding. The data are analysed using the semi-classical approach and transfer probabilities are obtained. Coulomb excitation has been analysed using known transition probabilities. The enhancement is deduced for the two-neutron transfer populating the low-lying super-fluid 2⁺ states in ¹²⁰Sn and ¹¹⁶Sn, while the 2n transition remains in the ground state for the ^20NPb nuclei. Large enhancements up to EF ≃ 10³ are observed. This is the first observation of neutron pair transfer enhancement for a heavy nuclear binary system with super-fluid properties with experimentally separated levels. The calculations with microscopic 2-neutron wave functions, with configuration mixing over six shell model configurations and using the coupled reaction channels approach, reproduce well the observed probabilities and the enhancement. Received: 27 August 2002 / Accepted: 9 December 2002 / Published online: 25 March 2003 RID="a" ID="a"e-mail: oertzen@hmi.de Communicated by D. Schwalm     

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     

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     

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