Fusion-evaporation cross-sections for 48Ca + 154Sm near the Coulomb barrier

Measurements of fusion-evaporation cross-sections for the system ⁴⁸Ca + ¹⁵⁴Sm have been performed in the sub- and near-barrier energy range. Barrier-passing cross-sections have been obtained by adding recently measured capture-fission cross-sections at the same energies, and the barrier distribution for capture has been extracted. The data have been analyzed within a coupled-channel model, and a large subbarrier cross-section enhancement is observed, due to the ground-state prolate deformation of ¹⁵⁴Sm. The ⁴⁸Ca + ¹⁵⁴Sm capture cross-sections are compared to existing data on ¹⁶O + ¹⁸⁶W fusion, leading to the same CN, where a few higher-energy points have also been measured. The evaporation residue cross-sections for the two systems above the barrier indicate that complete fusion is inhibited for ⁴⁸Ca + ¹⁵⁴Sm by 40% in that energy region, with respect to ¹⁶O + ¹⁸⁶W.     

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     

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     

Evolution of the fusion cross-section for light systems at intermediate energies

Ar + Ni and Ni + Ni collisions are investigated between 32 and around 100A MeV incident energy with the 4π multidetector INDRA. Fusion cross-sections are found to decrease from ∼ 180mb at 32A MeV to zero above 50A MeV. Other experimental results, for light systems, are compared. Moreover, theoretical works are discussed and fusion cross-sections, calculated from two dynamical simulations based on nuclear Boltzmann equation (Boltzmann-Nordheim-Vlasov and Landau-Vlasov models), are also compared to experimental results.     

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     

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     

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     

Partial fusion of a weakly bound projectile with heavy target at energies above the Coulomb barrier

Partial-fusion cross-sections for the systems ⁶Li + ²⁰⁸Pb, ⁹Be + ²⁰⁹Bi have been determined. The effect of breakup on fusion for weakly bound projectiles ⁶Li and ⁹Be incident on ²⁰⁸Pb or ²⁰⁹Bi targets has been discussed comparing experimental fusion cross-section excitation functions to those evaluated with a semi-classical approach. It is shown that complete fusion of a weakly bound projectile with heavy target is reduced, whereas the breakup process has very little influence on the total-fusion cross-section for some of the studied systems at energies above the Coulomb barrier.     

Measurements of elastic scattering for 7Be, 7Li + 9Be systems and fusion cross sections for 7Li + 9Be system

Elastic scattering angular distributions have been measured for ⁷Be + ⁹Be system at E_lab = 17, 19 and 21 MeV in the angular range θ_cm=26^○–58°, and for ⁷Li + ⁹Be system at E_lab= 15.75, 24 and 30 MeV. An optical model (OM) analysis of these data have been carried out. For the ⁷Li + ⁹Be system fusion cross sections were obtained at E_lab = 15.75, 24 and 30 MeV by measuring the α-evaporation spectra from the compound nucleus at backward angles. The measured α-evaporation spectra were reproduced by the statistical model calculations and fusion cross sections were extracted therefrom. The ratios of the experimental fusion cross sections to the total reaction cross sections (obtained form OM analysis) were found to be rather small. This result suggests that break-up process has a strong influence on fusion process leading to a reduction in fusion cross section.     

Does break-up affect 9Be +209Bi fusion at the barrier?

The ⁹Be +²⁰⁹Bi fusion cross sections were measured in the 36.0 MeV ≤ E_lab≤ 50.0 MeV range, down to 0.6 mb, with high accuracy via in-beam detection of the ground state α-decay of the evaporation residues produced. The elastic scattering cross sections around 150° and 135° were also obtained with moderate angular resolution. The cross sections below the barrier are reproduced by coupled channel calculations which include only one break-up channel with a moderate strength and a phenomenological renormalization of the potential depth. These simple calculations overestimate the cross sections above the barrier most likely due to the fact that the ⁹Be break-up process becomes much stronger. The barrier distributions extracted do not have evident break-up signature since they show one-barrier structure. Received: 22 February 1999 / Revised version: 26 March 1999     

Production cross sections for the heaviest nuclei in complete fusion reactions induced by heavy ions

Production of the heaviest nuclei in complete fusion reactions induced by heavy ions has been considered in a systematic way in the framework of the conventional barrier passing model coupled with the statistical model. Available data on excitation functions for fission and production of evaporation residues (ER) in very asymmetric combinations induced by ions lighter than Ne on actinide target nuclei are described rather well in the framework of these models. The data allow one to adjust model parameters and to reveal the quasi-fission effect caused by the interaction with deformed target nuclei, which is manifested in the suppression of the ER production at sub-barrier energies. For reactions induced by Mg and heavier projectiles, quasi-fission is starting to suppress fusion (ER production) at energies above the Coulomb barrier. One has to introduce empirically the quantity of the fusion probability P_fus to reproduce the ER excitation functions in the framework of the conventional approach. The exponential dependence of P_fus on the combined fissility parameter (a similar parameter that was introduced for the extra-push energy scaling) was found in search for scaling for the P_fus values resulting from the data analysis.     

Potential energy surfaces and penetrabilities for sub-barrier synthesis of Z = 118 isotopes

A specialized macroscopic-microscopic method is applied to calculate binary configuration deformation energy for fusion processes. The deformed two-center shell model is utilized to obtain the transition of the two independent level schemes for target and projectile, going through overlapping configuration up to the final compound nucleus. The macroscopic part is obtained with the usual Yuakawa-plus-exponential method applied to fusion-like configuration. The tensor of inertia is obtained within the Werner-Wheeler approach and dynamics is treated using the multidimensional WKB penetrability method. Calculations are applied to the sub-barrier synthesis of ^{294,290,286,280}118 isotopes.     

Fusion cross-section of the 7Li + 11B reaction

The ⁷Li + ¹¹B reaction has been investigated in the energy range 5.5 MeV < E _lab < 19MeV, by detecting γ-ray resulting from the de-excitation of evaporation residues. Statistical compound-nucleus calculations have been performed in order to extract both the cross-sections of individual exit channels and the fusion cross-section of the system. The total angular momentum that the compoundn ucleus ¹⁸O can support has been deduced and is seen to exhibit saturation for a limiting value of 8.5ħ at the high-energy extreme. The results are discussed in terms of the entrance channel and statistical yrast line limitations.     

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     

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     

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     

Mass distribution studies in the <Superscript>19</Superscript>F + <Superscript>197</Superscript>Au reaction

Mass distribution and evaporation residue measurements have been carried out in the reaction ¹⁹F + ¹⁹⁷Au using the recoil catcher technique followed by off-line γ-ray spectrometry. The random neck rupture model (RNRM) has been used to compute the variance of the mass distribution ( σ²_A) and the average kinetic energy ( ˉ) of the fission fragments for the present system. The results of model calculations have been found to be in good agreement with the experimental observations. Measured evaporation residue cross-sections have been compared with the statistical model calculations.     

Decay Analysis of Ge Isotopes Formed in Reactions Induced by Tightly and Loosely Bound Projectiles

The dynamical cluster-decay model (DCM) is employed to investigate the decay of ^68,70Ge^* compound nuclei formed respectively via tightly (⁴He) and loosely (⁶He) bound projectiles, using ⁶⁴Zn target. The study is carried out over a wide energy range (E_c.m.~5 MeV to 16 MeV) by including the quadrupole deformations (β2i) and optimum orientations (θ_i^opt) of the decaying fragments. The fusion cross-sections, obtained by adding various evaporation channels show nice agreement with the experimental data for ⁴He+⁶⁴Zn reaction. The contribution from competing compound inelastic scattering channel is also analyzed particularly for ⁶⁸Ge^* nucleus at above barrier energies. On the other hand, the decrement in the fusion cross-sections of ⁷⁰Ge^* nuclear system is addressed by presuming that ⁶⁵Zn ER is formed via two different modes:(i) the αn evaporation of ⁷⁰Ge^* nucleus, and (ii) 1n-evaporation of ⁶⁶Zn^* nuclear system, formed via breakup and 2n-transfer channels due to halo structure of the ⁶He projectile. Besides this, the suppression in 2np evaporation cross-sections suggests the contribution of another breakup and transfer process of ⁶He i.e. ⁴He+⁶⁴Zn. The contribution of breakup+transfer channels for ⁶He+⁶⁴Zn reaction is duly addressed by applying relevant energy corrections due to the breakup of " ⁶He" projectile into 2n and ⁴He. In addition to this, the barrier lowering, angular momentum and energy dependence effects are also explored in view of the dynamics of chosen reactions.