The low-energyD(α, γ)6Li and6Li+208Pb→D+α+208Pb cross sections

We have calculated theE1 andE2 contributions to the low-energyD(,)⁶Li fusion and to the⁶Li+²⁰⁸Pb D++²⁰⁸Pb Coulomb dissociation cross sections within a multichannel Resonating Group calculation based on many-body deuteron+ configurations and pseudo-states. For both reactions experimentally determined cross sections are reasonably well reproduced. We find that dipole capture contributes noticeably to the fusion cross sections atE500 keV, while it is negligible in the Coulomb dissociation data.     

Investigation of the isospin-forbidden reaction6Li(6Li,d 2)10 B 0+,1

Angular distributions of the isospin-forbidden reaction⁶Li(⁶Li, d₂)¹⁰ B _0+,1 were measured at six beam energies in the range from 3 to 8 MeV. The contribution of two-step transfer mechanism to the reaction under consideration was found to be negligible. Hauser-Feshbach model cross sections, obtained with parameters derived from a previous analysis of isospin-allowed reactions in the⁶Li +⁶Li system are consistent with the data, provided a 2% reduction factor reflecting isospin mixing of compound nucleus levels. From this factor an isospin-breaking matrix element of H _c ^{2 1/2}13 keV was deduced. The presence of one broad or several resonances with (J ^P ,T)=(1^–, 1) or (2^–,1) concentrated at an excitation energy of about 30.3 MeV in¹²C seems to be responsible for the observed shape of angular distributions and their energy dependence.This work was supported by Deutsche Forschungsgesellschaft under contact No. Fr575/2-1,2.     

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.     

Search for a transient electric field gradient in the system90Zr→148Nd with the crystal ball spectrometer

The particle- angular correlation of the 2⁺0⁺ transition in¹⁴⁸Nd, Coulomb excited by⁹⁰Zr projectiles, was investigated to search for a transient electric field gradient expected to be present during the stopping of the recoils in²⁰⁸Pb. An upper limit of V_zz <>¹⁹V/cm² was obtained for¹⁴⁸Nd recoiling with initial velocities of 0.05 c.     

Strong reaction channels at barrier energies in the system 6Li + 208Pb

Large cross-section reaction channels were measured in the systems ⁶Li( ⁷Li) + ²⁰⁸Pb with high statistical accuracy at 5(3) energies around the Coulomb barrier from 29 to 39 MeV. These channels were assigned (mainly) to the breakup of ⁶Li, very loosely bound, into α + d and to the breakup of ⁵Li, produced by n-transfer to the target, into α + p and to similar processes with ⁷Li beam. The cross-sections with ⁶Li, S _α = 1.475 MeV, are systematically larger than the ⁷Li ones. This reflects, most likely, the higher binding energy of ⁷Li, S _α = 2.468 MeV. Theoretical predictions for the ⁶Li + ²⁰⁸Pb system which include for ⁶Li breakup to continuum states within a continuum discretized coupled-channels approach (CDCC) and resonant breakup plus n-transfer with DWBA reproduce the angular distribution shapes but still underestimate the cross-sections by a factor ∼ 3. Received: 15 January 2001 / Accepted: 3 March 2001     

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.     

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.     

Pion production in heavy ion reactions induced by16O and84Kr beams at 60 MeV per nucleon

Low energy ⁺ and ^– production cross sections have been measured in¹⁶O at 65 MeV/u and⁸⁴Kr at 60 MeV/u induced reactions on⁷Li,¹²C,²⁷Al,¹⁰⁸Ag and¹⁹⁷Au. The results are compared with a previous measurement obtained with¹⁶O at 93 MeV/u. Large deviations are observed between light and heavy ion data. At variance with¹⁶O, the ratios ^–/ ⁺ are independent of the target in the Krypton case. A change in the regime of the projectile-target mass scaling of cross-sections is observed with the heaviest projectile.Experiments performed at GANIL facility, F-14032 Caen, France     

Analytic expressions for the partial waves of the off-shell two body coulomb T-matrix

Closed form expressions for all partial waves of the pure Coulomb off-shell T-matrix p¦ T_c,l.(k ²) ¦p are obtained. All singularities appear through simple special functions, which makes it possible to study the analytic properties of p¦ T_c,l(k²) ¦p as a function not only of one of the momentap, p but even of both of them. With use of the renormalization procedure found by Zorbas the transition to half-and on-shell values is performed reproducing known expressions. By the same method simple expressions for the partial waves of the Coulomb wave function in the momentum representation are found.     

Investigation of the sequential break-up mode6Li→6Li*(31 +)→α+d of 156 MeV6Li projectiles on208Pb in the very forward angular hemisphere

The sequential break-up of 156 MeV⁶Li projectiles colliding with²⁰⁸Pb has been investigated in the very forward angular hemisphere in order to explore the role of the Coulomb and nuclear interaction in inducing projectile break-up processes. The experiments use the Karlsruhe spectrograph Little John with a newly developed technique to detect efficiently break-up pairs of-particles and deuterons emitted with small relative energies and within a small opening angle. The observed differential cross section for the projectile excitation⁶Li⁶Li^* (I=3_i ⁺) has been analysed (together with forward elastic scattering) by a coupled channel approach, and various sensitivities to the nuclear potential and other ingredients have been studied. We conclude, that in the angular region below half the grazing angle the excitation is completely due to the Coulomb force. This feature is a basis for an application of the disintegration approach for studies of radiative capture cross section of astrophysical interest.On leave from Institute of Atomic Physics Bucharest, Romania     

Refractive scattering and reactions,comparison of two systems:16O+16O and20Ne+12C

Elastic, inelastic scattering as well as one-neutron transfer channels have been measured over a wide angular range for systems¹⁶O+¹⁶O at the incident energy of 350 MeV and²⁰Ne+¹²C at 390 MeV, respectively, using the Q3D magnetic spectrometer. In both cases differential cross sections have been measured down to about 50 nb/sr (or d/d _R10^–4) at large angles. For the¹⁶O+¹⁶O system refractive contributions are found at the level of these cross sections, whereas in the²⁰Ne+¹²C case a steeper decrease of the differential cross section with the angle is observed and the refractive contribution can not be determined. The elastic scattering data have been analyzed using standard Woods-Saxon potentials and potentials calculated in different versions of the double-folding model. Some properties of these potentials are tested in the calculations for inelastic scattering and one-neutron transfer within the DWBA. With the refractive pattern observed for the¹⁶O+¹⁶O system, the scattering and transfer data are found to be sensitive to the interaction potential at small internuclear distances down to about 2.5 fm.It should be acknowledged that part of the folding analysis reported here was done while one of the authors (D.T.K.) was staying at the Institute for Theoretical Physics, University of Tübingen. We also thank Prof. H. Clement and H. Abele for numerous discussions and contributions and Prof. G.R. Satchler for helpful comments on the use of the DWBA code PTOLEMY.     

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.     

Complete and incomplete fusion in12C+93Nb and16O+89Y reactions

Excitation functions for the evaporation residues for the reactions¹²C+⁹³Nb and¹⁶O+⁸⁹Y in the projectile energy range of 4 to 6.5 MeV/amu have been measured using off-line gamma spectrometry. The excitation functions for neutron(xn), proton(pxn) and one alpha(xn) emission channels are practically similar for both the reactions. However the products formed by two alpha(2xn) emission show much higher cross sections in the¹²C+⁹³Nb than the¹⁶O+⁸⁹Y system. This has been explained in terms of the incomplete fusion process involving transfer of an alpha particle from the projectile to the target in the former case.Authors thank Shri D.C. Ephraim for making the rolled metal foils and the operation crew of PELLETRON facility for their help in carrying out the irradiations. Authors are grateful to Dr. P.R. Natarajan, Head Radiochemistry Division for his keen interest in this work.     

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.     

Coulomb forces in the three-body problem with application to direct nuclear reactions

Faddeev equations are considered in the case of three charged particles interacting with both separable nuclear two-body interactions and also including Coulomb forces. Modified Faddeev equations with Coulomb Green's functions are introduced. The three-body amplitudes are given into pure Coulomb and distorted-Coulomb amplitudes. Introducing a decomposition in the angular momentum states, a set of three-body integral equations is obtained. The effect of pure coulomb amplitudes is studied in direct nuclear reactions and found to give a large contribution to the cross sections. The three-body integral equations obtained are applied for direct nuclear reactions. The angular distributions for¹²C(⁶Li,d)¹⁶O,¹⁶O(⁶Li,d)²⁰Ne, and¹²C(⁶Li,α)¹⁴N transfer reactions are calculated as well as for the⁶Li elastic scattering on¹²C. From the good agreement between the theoretically calculated and experimental data, better spectroscopic factors are extracted. The effect of including Coulomb forces in the three-body problem is found to improve the results by about 16.26%.     

The competition between fusion-fission and deeply inelastic reactions in the medium mass systems

The competition between fusion-fission and deeply inelastic reactions in the Cl + Ni system has been studied by investigating the exit channelQ-value dependence of theZ-distributions of fission-like fragments. TheZ-, kinetic energy- and angular distributions of the fission-like fragments produced in the³⁷Cl +⁶⁴Ni system atE _lab=170, 186 MeV and in the²⁸Si +⁷⁴Ge system atE _lab=176 MeV have been measured by counter telescopes. TheZ-distribution of the³⁷Cl +⁶⁴Ni system was found to be essentially the same as that of the³⁵Cl +⁶²Ni system at the same bombarding energy. It is shown that this result can not be explained by the statistical fusion fission model but is consistent with a deeply inelastic model. A systematic study of the fission-like phenomenon in this mass region indicates that the maximum angular momenta for fusion reactions as well as the minimum angular momenta for DIC can be reproduced by the Bass model in the sliding limit (f=1.0) while the maximum angular momenta for fully energy-damped deeply inelastic reactions are governed by the strong interaction radius as predicted by the successive critical distance fusion model. The significance of these results are discussed.Communicated by V. Metag     

Isotopic dependence of electron screening in fusion reactions

The fusion reactions⁶Li(p, )³He,⁶Li(d, )⁴He, and⁷Li(p, )⁴He have been studied over the c.m. energy rangeE=10 to 1450 keV. Each reaction involved the use of hydrogen projectiles and LiF solid targets as well as Li projectiles and hydrogen molecular gas targets. In all cases the effects of electron screening on the low-energy fusion cross sections (exponential enhancement) have been observed; the effects are somewhat stronger in the case of atomicp ord projectiles compared to the case of molecularH ₂ orD ₂ gas targets. If isotopic effects on electron screening are negligible, all three reactions should exhibit the same enhancements for each set of experimental techniques. The measurements confirmed this expectation to a large extent.Supported in part by the Landesamt Nordrhein-Westfalen (IVA5-10600387), the Deutsche Forschungsgemeinschaft (Ro429/ 18-2 and Ro429/21-1), and the Comision Interministerial de Ciencia y Tecnologia (AEN90-0932)     

On the information value of angular distributions in elastic scattering of heavy ions

A method is developed for computing the total cross section σ_F of complete and incomplete fusion, quasifission, and deep-inelastic collisions, as well as the total cross section σ_D of peripheral reactions, on the basis of analysis of angular distributions for elastic scattering of heavy ions. The method makes it possible, on a unified basis, to explain the mechanism of formation of σ_F and σ_D both for strongly and for weakly bound ions. The method permits the calculation of quantitative characteristics of fusion enhancement (and, accordingly, suppression of peripheral reactions) for strongly bound ions and, conversely, the suppression of fusion (and, accordingly, enhancement of peripheral reactions) for weakly bound ions. The potential of the method is demonstrated for two systems, ¹⁶O+²⁰⁸Pb and ⁹Be+²⁸Si, the projectile ion being strongly bound in the former system and weakly bound in the latter one.