Yields of evaporation residues and average angular momentum in heavy ion induced fusion reactions leading to compound nucleus96Ru

Cross-sections for production of evaporation residues from the compound nucleus⁹⁶Ru* formed by fusion reactions²⁸Si+⁶⁸Zn,³²S+⁶⁴Ni,³⁷Cl+⁵⁹Co and⁴⁵Sc+⁵¹V have been obtained from the yields of their characteristicγ-rays. The measurements span an excitation energy range of 55 MeV to 70 MeV of the compound nucleus. The evaporation residue (ER) cross-sections have been analysed in terms of statistical model for the decay of the compound nucleus. A good agreement is found between statistical model calculation and the experimental evaporation residue cross-sections in all the four cases. It is shown that the average angular momentum of the compound nucleus can be deduced from a comparison of the experimentally measured and the statistical model predictions for the ER cross-sections. The validity of this method of deriving has been discussed for the case of¹⁶O+¹⁵⁴Sm system.     

Comparison of cross sections for C + O reactions in the second regime of complete fusion

Kinetic energy spectra, angular distributions, and elemental yield distributions have been measured for the ¹² C + ¹⁶ O, ¹² C + ¹⁸ O and ¹³ C + ¹⁷ O reaction products over an energy range from 2 to 7 times the Coulomb barrier energy. A careful kinematic analysis of the evaporation residues and comparisons with statistical-model calculations show that fusion proceeds with full momentum transfer followed by a statistical decay of the compound nucleus. The competition between complete fusion process and peripheral reactions in the ¹² C + ¹⁶ O system is less important than for the ¹² C + ¹⁸ O and ¹³ C + ¹⁷ O reactions. The unexpectedly high ¹² C + ¹⁶ O complete fusion cross sections are related to the possible occurrence of a superdeformation of the ²⁸ Si compound nucleus.     

Angular momentum transfer in incomplete fusion

Isomeric cross-section ratios of evaporation residues formed in¹²C+⁹³Nb and¹⁶O+⁸⁹Y reactions were measured by recoil catcher technique followed by off-line γ-ray spectrometry in the beam energy range of 55.7–77.5 MeV for¹²C and 68–81 MeV for¹⁶O. The isomeric cross-section ratios were resolved into that for complete and incomplete fusion reactions. The angular momentum of the intermediate nucleus formed in incomplete fusion was deduced from the isomeric cross-section ratio by considering the statistical deexcitation of the incompletely fused composite nucleus. The data show that incomplete fusion is associated with angular momenta slightly smaller than critical angular momentum for complete fusion, indicating the deeper interpenetration of projectile and target nuclei than that in peripheral collisions.     

Complete and incomplete fusion studies in7Li and16O induced reactions on51V by measurement of excitation functions and recoil ranges

Excitation function and mean projected recoil ranges of nuclei produced in the⁷Li and¹⁶O induced reactions on⁵¹V target were measured by conventional stacked foil and thick-target thick-recoil-catcher technique for bombarding energiesE ≤ 50.0 MeV for⁷Li ions andE ≃ 60.0-96.0 MeV for the¹⁶O ions. The measured recoil ranges are converted to momentum transfer. The momentum transfer information was used to get clues about some aspects of the interaction such as complete and incomplete fusion reaction mechanism which correspond to full and reduced momentum transfer respectively. The measured excitation functions are compared with the calculation based on the statistical model which describes only equilibrium decay of the compound nucleus using the CASCADE code. The comparison of the CASCADE code with the measured excitation functions for the residue radioisotopes⁵¹Cr and⁵⁴Mn for the⁷Li +⁵¹V system indicates the reaction mechanisms is complete fusion of⁷Li with the target nucleus⁵¹V. Similarly the comparison of the CASCADE code with the measured excitation functions of the residue radioisotopes for the system¹⁶O +⁵¹ V indicates that the four reaction mechanisms (i) complete fusion of¹⁶O, (ii) incomplete fusion of¹²C, (iii) incomplete fusion of⁸Be and (iv) incomplete fusion of⁴He respectively with the target might be contributing to reaction cross sections.     

Measurement of excitation functions and mean projected recoil ranges of nuclei in12C-induced reactions on vanadium

Excitation function and mean projected recoil ranges of nuclei produced in the¹²C-induced reactions on⁵¹V target were measured by conventional stacked foil and thick-target thick-recoil-catcher technique for bombarding energiesE ≤ 84 MeV for¹²C ion beam. The measured recoil ranges are converted to momentum transfer. Information on momentum transfer was used to get clues about some aspects of the interaction such as complete fusion which corresponds to full momentum transfer and incomplete fusion reaction mechanism. The measured excitation functions are compared with the calculation based on the statistical model which describes only equilibrium decay of the compound nucleus using the Cascade code and the geometry dependent hybrid model which describes equilibrium as well as pre-equilibrium decay of the compound nucleus using the Alice/91 code. The measured excitation functions and average ranges of the radioisotope products of the reactions¹²C on⁵¹V indicate that the three separate reaction mechanisms could be attributable to complete fusion of¹²C, incomplete fusion of⁸Be and incomplete fusion of⁴He respectively with the target. The⁸Be and⁴He are the break-up component of¹²C into⁸Be +⁴He. The predictions of the codes, especially the Cascade, generally agree with the measured cross-sections which could be attributed to complete fusion of¹²C with the target⁵¹V.     

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.     

Formation and deexcitation of the 32S compound nucleus via the 20Ne+12C and 16O+16O entrance channels

Reaction-product cross sections following ²⁰Ne+¹²C and ¹⁶O + ¹⁶O collisions at several incident energies have been measured with a E-ΔE counter telescope. They are compared to statistical model predictions. Fair agreement is obtained for the high-Z evaporation residue cross sections, but a strong discrepancy is observed for the lower-Z reaction products. Possible explanations are discussed. It is shown that the compound nucleus formation does not depend on the structure of the colliding ions in the entrance channel and also that it is not limited by the ³²S yrast line.     

Fusion cross sections for 10,11B+12C at sub-Coulomb energies

Total fusion cross sections for the ¹⁰B + ¹²C and ¹¹B + ¹²C reactions have been determined over a 5 MeV (c.m.) energy range extending to ≈ 3 MeV below the Coulomb barrier. Absolute γ-ray yields for specific transitions in the de-excitation of the heavy products following compound nucleus decay were measured using a Ge(Li) detector. Statistical model calculations of the decay modes of the compound nucleus have been used to deduce, from the γ-ray data, cross sections for single proton, neutron and α-particle emission, and to determine total cross sections for compound nucleus formation. No evidence has been found for sub-Coulomb resonances in either reaction. The total reaction cross sections are compared with optical model calculations using different parameter sets and the observed trend in the very low energy cross sections is discussed relative to other reactions in the same mass region.     

Energy damping feature in light heavy-ion reactions

The energy damped reaction products from³⁷Cl+¹²C,²⁷Al,⁴⁸Ti and¹⁶O+⁴⁸Ti were measured over a wide range of angles (typically 18°<θ _lab<70°), incident energies (160 <E _lab(³⁷Cl)<200 MeV,E _lab(¹⁶O)=118 MeV) and charges Z, including two systems (³⁷Cl+³⁷Al and¹⁶O+⁴⁸Ti) which lead to the same compound nucleus⁶⁴Zn with the same excitation energy and comparable angular momenta. The angular dependences of total kinetic energy (TKE) and dσ/dθ were decomposed into two components (forward peaked and nearly constant at backward angles), and the elemental TKE and cross sections were derived. The backward components of³⁷Cl+²⁷Al and¹⁶O+⁴⁸Ti exhibit very different Z-distributions, indicating that the fragments do not originate from compound nucleus decay. The results can be understood in terms of an energy damping process.     

Incomplete fusion reactions in 16O+165Ho

Excitation functions for evaporation residues of the system ¹⁶O + ¹⁶⁵Ho have been measured up to 100 MeV. Recoil range distribution of long lived reaction products were measured at ¹⁶O beam energy of 100 MeV. Detailed Monte Carlo simulation of recoil range distributions of products were performed with the help of PACE2 code, in order to extract the contributions of incomplete fusion in the individual channels. The results clearly show the incomplete fusion contributions in the tantalum and thulium products. This is confirmed by the predictions of breakup fusion model of the incomplete fusion.     

12C + 7Li Reaction measurements and the 12C(7Li,t)16O reaction

A measurement of the residues from the ¹²C + ⁷Li reaction has been obtained for ⁷Li energies from 10 to 38 MeV. From these measurements the fusion cross sections and critical angular momenta for the ¹²C + ⁷Li system have been deduced. Cross sections for the ⁷Li(¹²C, t)¹⁶O reaction have been obtained for ¹²C energies from 54 to 62 MeV at θ_lab = 2.7°. The critical angular momenta obtained from the fusion cross sections have been used to perform Hauser-Feshbach calculations for the ¹²C(⁷Li, t)¹⁶O reaction. These calculations have been compared to measured angular distributions over a wide energy range. By comparing the fusion cross sections required by the Hauser-Feshbach calculations to fit the ¹²C(⁷Li, t)¹⁶O(8.87 MeV) reaction and the measured residue cross section it is estimated that at least 80 % of the measured residues are fusion products. The calculations also indicate that direct processes dominate the population of many ¹⁶O levels at forward angles and the 10.35 MeV state at backward angles. The necessity for using a critical angular momentum in Hauser-Feshbach calculations is discussed.     

Light charged particle decay in the reaction7Li+16O

Angular distributions and excitation functions for the emission of a large number of proton, deuteron, triton, and-particle groups in⁷Li+¹⁶O reactions have been measured in the vicinity of the Coulomb barrier. Within the framework of the statistical reaction model, two approaches are presented that can reproduce the only weakly anisotropic shape of the angular distributions and the absolute cross section for those groups of ejectiles where contributions from direct reaction modes are small. When a standard Woods-Saxon potential deduced from elastic scattering is used, the entrance channel angular momentum distribution must be limited to values below critical angular momental _cr which are smaller than the grazing angular momental _gr if fusion is to be described. A global proximity potential with a parameter set that has been adjusted to reproduce the fusion reactions of a variety of p- and sd-shell nuclei yields very similar results when applied to⁷Li+¹⁶O. The proximity potential effectively introduces a similar angular-momentum limitation. This analysis proves the existence of a fusion cross section limitation and the importance of strong direct reaction modes (transfer and possibly inelastic processes) in⁷Li+¹⁶O reactions at energies close to and even below the Coulomb barrier. Another aspect of⁷Li+¹⁶O is addressed briefly. The resonance-like structure observed in the heavy-ion radiative capture reaction⁷Li(¹⁶O, ₀₊₁)²³Na atE _x (²³Na)=25.4 MeV is not observed in the particle decay channels investigated in the present work.The authors would like to acknowledge the help received from B. Bellenberg, B. Dechant, H. Hemmert, T. Krischak, E. Kuhlmann, H. Putsch, and C. Scholz during the experiments.     

Angular anisotropy of the fusion-fission and quasifission fragments

The anisotropy in the angular distribution of the fusion-fission and quasifission fragments for the ¹⁶O + ²³⁸U , ¹⁹F + ²⁰⁸Pb and ³²S + ²⁰⁸Pb reactions is studied by analyzing the angular-momentum distributions of the dinuclear system and compound nucleus which are formed after capture and complete fusion, respectively. The orientation angles of the axial symmetry axes of the colliding nuclei relative to the beam direction are taken into account for the calculation of the variance of the projection of the total spin onto the fission axis. It is shown that there is a large contribution of the quasifission fragments in the ³²S + ²⁰⁸Pb reaction to the deviation of the experimental angular anisotropy from the statistical model results. Enhancement of anisotropy at low energies in the ¹⁶O + ²³⁸U reaction is connected with the quasifission of the dinuclear system having low temperature and relatively small effective moment of inertia.     

Energy dependence of fusion and reaction cross sections in the 9Be + 12C system

Angular distributions of protons, deuterons. tritons and α-particles were measured for the system ⁹Be + ¹²C at lab energies between 12 and 27 MeV. The compound nucleus model with level densities calculated according to the Gilbert-Cameron formula describes satisfactorily the measured proton, deuteron and triton data. In the α-particle spectra contributions from other processes seem to be present. In the analysis the fusion cut-off angular momentum was adjusted at each energy in order to reproduce correctly the proton, deuteron and triton channels. From this analysis the fusion cross section was determined as a function of the energy. The results were compared with fusion and total reaction cross section values calculated from a potential model with the real part of the interaction potential obtained from the double folding procedure of Satchler.     

The compound nucleus reaction 12C(11B, 2α) 15N

Energy spectra and differential cross sections of nitrogen products formed in the reaction 28 MeV ¹¹B + ¹²C have been measured using a ΔE?E counter telescope. The energy spectra are smooth and therefore indicate that the nitrogen products were formed by a compound nucleus mechanism, via the formation and decay of the compound nucleus ²³Na. The experimental results are compared with statistical model calculations and good agreement is obtained. This result provides further evidence for the importance of the compound nucleus mechanism in heavy ion reactions with light nuclei and also gives added validity to the statistical model for light compound systems.     

Mass asymmetry dependence of fusion time-scales in11B+237Np and12C,16O,19F+232Th reactions in a dynamical trajectory model

Dynamical trajectory calculations were carried out for the reactions of¹¹B+²³⁷Np and¹²C,¹⁶O and¹⁹F+²³²Th, having mass asymmetries on either side of the Businaro-Gallone critical mass asymmetry α_BG, in order to examine the mass asymmetry dependence of fusion reactions in these systems. The compound nucleus formation times were calculated as a function of the partial wave of the reaction for all the systems. This study brings out that for systems with α<α_BG, the formation times are significantly larger than for α>α_BG, which is caused by the dynamical effects involved in the large scale shape changes taking place in the fusion process as well as due to the interplay between the thermal and the collective motion during the collision process. The calculated time scales are comparable to the experimental values derived from the pre-fission neutron multiplicity measurements.     

Fusion, resonances and scattering in12C+12C reaction

The variation of fusion cross-section (σJ_fus) with energy in the¹²C+¹²C collision is linked to the underlying resonance phenomenon through the behavior of reaction cross-section (σ) of which σ_fus is taken as a part. The calculation of σ_fus is done through an energy-dependent imaginary potential in the optical model potential (OMP). Through dispersion relation, such an imaginary potential gives rise to energy-dependent real potential which is incorporated in the OMP. In our calculation, a form of potential for the nuclear part which has a soft repulsive in-built core is introduced based on similar works done earlier. The calculated results of σ_fus are used to explain the oscillatory structure, astrophysical S-factor and the decreasing trend at higher energies of the experimental σ_fus data in the case of¹²C+¹²C system with remarkable success. The potential used for fusion calculation is tested for fitting elastic scattering data at some energies and is found good in forward angles. Further improvement of the fitting of these data is obtained by incorporating a coupling potential in the surface region. About twenty resonances are observed in our calculation in the specific partial waves and some of them are found close to the experimentally identified resonances in¹²C+¹²C reaction. Thus, we provide an integrated and comprehensive analysis of fusion, resonance and scattering data in the best studied case of¹²C+¹²C reaction within the framework of optical potential model.     

Spontaneous-fission decay properties and production cross-sections for the neutron-deficient nobelium isotopes formed in the 44, 48Ca + 204, 206, 208Pb reactions

Heavy-ion fusion reactions ⁴⁸Ca + ²⁰⁴Pb and ⁴⁴Ca + ²⁰⁸Pb leading to the same compound nucleus ²⁵²No^* were run in attempts to produce new neutron-deficient spontaneous-fission isotopes of ^249,250No using the electrostatic separator VASSILISSA. Production cross-sections for the spontaneous-fission activities with the half-lives 5.6 and 54 μs observed in these reactions are compared with the measured ones for the well-known isotopes of ^{251 - 255}No formed in the heavy-ion fusion reactions ⁴⁸Ca + ²⁰⁶Pb and ⁴⁸Ca + ²⁰⁸Pb. The obtained excitation functions for the reaction products formed after the evaporation of 1-4 neutrons from the corresponding compound No nuclei have been compared with similar data obtained earlier and results of statistical model calculations. Received: 26 July 2002 / Accepted: 5 November 2002 / Published online: 18 March 2003 RID="a" ID="a"e-mail: eremin@sunvas.jinr.ru Communicated by J. ?yst?     

Fragmentation of relativistic oxygen nuclei in interactions with a proton

The data on investigation of inelastic interactions of ¹⁶O nuclei in a hydrogen bubble chamber at an incident momentum of 3.25 A GeV/c are presented. Separate characteristics as fragments isotope composition and topological cross-sections of fragmentation channels are given. The processes of formation of light fragments and unstable nuclei, and the break-up of the ¹⁶O nucleus into multicharge fragments are investigated. A comparison between the experimental data and the calculations of the cascade fragmentation evaporation model (CFEM) is made. The observed singularities of the interactions point out the important role of the nucleus α-cluster structure in the formation of the final products. Received: 9 January 2001 / Accepted: 13 June 2001