Orbital dispersion and wavefunction mapping in inclusive break-up experiments

Inclusive break-up cross sections of the reactions¹²C (⁶Li,a)X and²⁰⁸Pb (⁶Li,a)X at 26 MeV/amu, observed for the emission of break-up fragment into the forward hemisphere, are analysed in view of the information about the internal momentum distribution of the projectile. The longitudinal momentum distribution of the fragments in the projectile rest-frame is found to reflect the internal momentum distribution of the clusters whereas the transverse distribution is affected by the projectile-target interaction.     

Inclusive break-up reactions of 6Li at an incident energy of 26 MeV/nucleon

Inclusive charged particle spectra were measured from nuclear reactions induced by 156 MeV ⁶Li on ⁴⁰Ca. At forward angles the spectra exhibit broad break-up distributions centered around the energy corresponding to the beam velocity. The double differential cross sections together with previous results for a ²⁰⁸Pb target were analyzed in the framework of the DWBA approach to projectile break-up taking into account elastic and inelastic reactions of the break-up fragments. The high energy tails of the background due to preequilibrium emission of complex charged particles were estimated on the basis of the coalescence model.     

Angular correlations from 6Li break-up near the Coulomb barrier of 118Sn and 208Pb

Absolute coincidence cross sections for three-particle final states have been measured inplane in the ⁶Li + ¹¹⁸Sn and ⁶Li +²⁰⁸Pb reactions at incident energies of 22.2 and 23.0 MeV, respectively. Most strongly populated is the α + d branch, proceeding sequentially through the first excited state (E_x = 2.18 MeV, J^π = 3⁺) of ⁶Li. The angular distributions are fitted by DWBA calculations including Coulomb interaction in the excitation of the projectile. The main competing reaction channels above and at the Coulomb barrier (¹¹⁸Sn: E/E_c ≈ 1.3; ²⁰⁸Pb: E/E_c ≈ 0.9) are: neutron transfer (⁶Li, αp) and the non-sequential α + d break-up of ⁶Li. The latter spectra are consistent with a quasi-free break-up mechanism. No ³He or tritons have been found in the coincidence spectra, as well as no evidence for a three-particle dissociation of ⁶Li into α + p + n.     

Three-particle correlations from208Pb+6Li

Three-particle correlations in the reaction²⁰⁸Pb+⁶Li were studied near the Coulomb threshold between \(E_{6_{Li} } = 24\) and 30 MeV. Three reaction mechanisms contribute predominantly to the observed coincidences of the charged particles: 1. Coulomb excitation of the 2.184 MeV,J=3⁺ state of⁶Li, followed by the decay intoα+d, 2. Deuteron pick-up of the⁶Li to the ground state of⁸Be and sequential decay into twoα-particles and 3. Neutron-transfer to the ground state and the first excited states of²⁰⁹Pb:²⁰⁸Pb(⁶Li,αp). The last two reaction mechanisms explain the previously measured large contributions to theα-channel relative to thed-channel.     

Excitation functions of191+193Ir,197Au(6Li,xn+yp) compound nuclear reactions at ELi=48–156 MeV

Excitation functions of the compound nuclear reactions^191+193Ir,¹⁹⁷Au(⁶Li,xn+yp) forx =3–13 andy=0–2 have been investigated by means of in-beamγ-ray spectroscopy at the 156 MeV⁶Li beam of the Karlsruhe Isochronous Cyclotron. The beam energy has been varied in the range of 48 to 156 MeV in steps of about 10 MeV by Be-absorber foils in the external beam line. Absolute cross sections have been determined by normalizing the measuredγ-ray intensities to the production cross sections ofK- X-rays in the target. The experimental excitation functions are discussed on the basis of predictions of the preequilibrium (hybrid) model. While in most cases the theoretical calculations fairly well reproduce energy position and shapes of the curves, strong discrepancies in the absolute scale of the cross sections are observed. The theoretical predictions overestimate the (⁶Li,xn) cross sections by a factor of about 6. Conspicuous anomalies have been detected when comparing the (⁶Li, xn+1(2)p) reactions with (⁶Li,xn) reactions. The reactions with emission of one or two protons are considerably enhanced. The discrepancies and anomalies observed are tentatively explained by the influence of direct reaction channels as the⁶Li break-up, which experimentally proved to be the dominant contribution to the total reaction cross section. The enhancement of the reactions with emission of protons may be a consequence of transfer reactions into highly excited states combined with compound nucleus formation thus implying a cluster effect in preequilibrium emission process.     

Inclusive measurements of the break-up of 156 MeV6Li-ions at extreme forward angles

Inclusive alpha particle and deuteron spectra from collisions of 156 MeV⁶Li-ions with¹²C and²⁰⁸Pb were measured at extreme forward emission angles including zero degree. The measurements were performed with the Karlsruhe magnetic spectrograph ‘Little John’ and required an efficient reduction of the background from small-angle scattering. The observed double differential cross sections and angular distributions have been analysed on the basis of Serber's spectator break-up model. When going to angles smaller than grazing, where Coulomb effects are expected to be dominating, transitional features may appear. Corresponding effects probably associated with Coulomb break-up are observed with the²⁰⁸Pb-target and require a slight extension of the Serber approach. In the case of the¹²C-target the break-up cross sections in forward direction seem to reflect the shape of the internal momentum distribution of the alpha particle and deuteron cluster in the⁶Li-projectile and are in agreement with a 2S-type wave function. However, at larger angles the shape appears to be distorted, possibly by final state interactions.     

Electromagnetic and nuclear fission of238U in the reaction of 100, 500, and 1000 A·MeV208Pb with238U

The folding- and azimuthal-angle and velocity distributions for the²³⁸U fission fragments have been measured in reactions with 100, 500, and 1000 A·MeV²⁰⁸Pb. These distributions were used to decompose the fission cross section into its electromagnetic and nuclear components. The fraction of electromagnetic fission was found to be 0.16±0.07, 0.48±0.08, and 0.60±0.04, respectively. The electromagnetic fission cross section as a function of the²⁰⁸Pb nucleus energy is compared with theoretical predictions. The measured fission cross section from nuclear reactions (≈1.5 b) is approximately constant between 100 and 1000 A·MeV.     

Experimental and theoretical study of the elastic break-up of the alpha particle on58Ni nuclei atE α=172.5 MeV

The triton-proton angular correlation function has been measured for the⁵⁸Ni(α, t p)⁵⁸Ni reaction leading to the ground state of the target nucleus. The obtained experimental data have been interpreted in terms of the direct break-up (fragmentation) of the alpha particle on the target nucleus potential. It is shown that the main features of the measured double differential cross section are well predicted by the DWBA theory of the break-up. The dependence of the elastic and inclusive break-up cross sections upon the fragment-target interaction potentials is discussed.     

Asymptotic three-particle approach to the Coulomb breakup process <Superscript>6</Superscript>Li + <Superscript>208</Superscript>Pb → <Superscript>208</Superscript>Pb + α + <Emphasis Type="Italic">d</Emphasis>

On the basis of the distorted-wave method, experimental data on the triple-differential cross section for the Coulomb breakup reaction ²⁰⁸Pb(⁶Li, αd)²⁰⁸Pb are analyzed by employing a correct expression for the final-state ²⁰⁸Pb–α–d three-particle Coulomb wave function. It is shown that the effect of final-state three-particle Coulomb dynamics can be used to assess the kinematical condition of clean Coulomb breakup processes. New values of the astrophysical S factor for the direct-radiative-capture reaction d(α, γ)⁶Li at ultralow energies in the range of 70 ≤ E _dα ≤ 600 keV were extracted from experimental data. The value of S(0) = 1.60 ± 0.17 MeV nb was obtained.     

Reaction cross section measurements of the neutron-rich isotopes8,9,11Li at 80 MeV/nucleon

Total interaction cross sections have been measured for⁸Li on C and Pb targets, for⁹Li on C, Al, Cu, Sn and Pb targets as well as for¹¹Li on C, Sn and Pb targets. For each beam, we also used a plastic scintillator as target. The measurements with the scintillator targets are used to extract reduced nuclear radii of the lithium isotopes. These radii are then used for the calculation of the nuclear part of the total cross section for the other targets. The total electromagnetic-dissociation (EMD) cross sections have been deduced and are compared to different models. A strong target-charge-dependent EMD cross section is measured for¹¹Li reaching 2.96 _–0.82 ^+0.84 b for the Pb target. In the⁹Li case, a large EMD cross section for high-Z targets has been observed which amounts to 0.75 ± 0.45 b for the Pb target. The EMD cross sections of both,⁹Li and¹¹Li, may be understood by the giantdipole-resonance model.This work forms part of the PhD Thesis of B. Blank     

Fission and fragmentation of 208Pb nuclei in collisions with gold nuclei at an energy of 158 GeV per nucleon

The fission and fragmentation of ultrarelativistic ²⁰⁸Pb nuclei in collisionswith gold nuclei were studied by using a beam from the SPS accelerator at CERN at an energy of 158 GeV per nucleon. The detectors of the target area of the NA45/CERES spectrometer were used in respective measurements. The value obtained for the fission cross section is 301 ± 44 mb, where about 77% of events stem from the electromagnetic interaction of colliding nuclei, while the remaining part is the contribution of peripheral nuclear interactions. The spallation of lead nuclei that involves the formation of heavy fragments occurs only in collisions where the impact parameter satisfies the condition b > 10 fm. A complete disintegration of lead nuclei to intermediate-mass fragments and light particles is observed in some peripheral collisions.     

High energy structures in heavy ion collisions: A multi-phonon description

Energy spectra of fragments from the³⁶Ar+²⁰⁸Pb reaction at 11 MeV/n exhibit structures at high excitation energies. These structures are interpreted in terms of target multi-phonon excitations built from giant resonances. The importance of such processes for the kinetic energy dissipation in heavy ion collisions is emphasized.     

Fragmentation of the total cross section in the reaction16O+208Pb

The fragmentation of the total reaction cross section was investigated for¹⁶O +²⁰⁸Pb atE _c.m.=84 MeV andE _c.m.=92 MeV. Total cross sections for the inelastic, transfer and fission channels were measured. The sum of the inelastic and transfer channels accounts for 30% of the total reaction cross section; the residual strength is found in a compoundfission process.     

Two-neutron pickup strengths on the even lead isotopes the transition from single-particle to “collective”

The (p, t) reaction on ²⁰⁸Pb, ²⁰⁶Pb, and ²⁰⁴Pb has been studied with 35 MeV protons. It is observed that the L = 0 ground-state cross section rapidly increases as one changes targets from ²⁰⁸Pb to ²⁰⁶Pb to ²⁰⁴Pb while the cross section for other natural-parity transitions decreases. The observed cross sections are compared with predictions of the shell model and the pairing-vibration model. Both models are seen to describe some features of the data.     

An experimental study of He elastic,inelastic and charge-exchange scattering from Li

A target of ⁶Li was bombarded with the ³He beam from the University of Illinois cyclotron. Differential cross sections for the elastic scattering, the inelastic scattering to the first two excited states of ⁶Li, and the (³He, t) charge-exchange reaction to the ground state of ⁶Be were determined over angular ranges of approximately 20° to 115° (c.m.) at ³He energies of 24.6 MeV and 27.0 MeV. (The weak inelastic transition to the 3.56 MeV state of ⁶Li, ordinarily obscured by a background of three-body break-up, was observed by requiring a coincidence at most angles between the scattered ³He and the ⁶Li recoil.) The ratio of the integrated charge-exchange cross section between 55° and 115° to the integrated inelastic cross section for this transition (both with ΔT = 1) is somewhat less than expected from isospin considerations (i.e., about 1.6 instead of 2.0).     

Analysis of proton transfer in polarized 7Li scattering by 208Pb at 33 MeV

Angular distributions of the differential cross section and the second-rank tensor analysing power T₂₀ have been measured for the one-proton transfer reaction induced by polarized ⁷Li on ²⁰⁸Pb at 33 MeV leading to several states in ²⁰⁹Bi. The experimental data were analysed simultaneously with data for elastic and inelastic scattering of ⁷Li by means of CCBA and CRC calculations. The spectroscopic factors for ²⁰⁹Bi states are obtained.     

Forward-backward asymmetries in the direct breakup of6Li

The (α+d) breakup of 60 MeV⁶Li scattered from²⁰⁸Pb has been measured inside the grazing angle for c.m. energies of the fragments between 100 keV and 1.5 MeV. The distinctly different anisotropies of the sequential and direct breakup components show that Coulomb dissociation cannot be related in a straightforward manner to the astrophysically relevant⁴He(d, γ)⁶ Li capture reaction.     

Nucleon transfer reactions to rotational states induced by206, 208Pb projectiles

In a systematic study of nucleon transfer reactions accompanied by Coulomb excitation we have bombarded¹⁵²Sm,¹⁶⁰Gd and²³²Th with^{206, 208}pb beams at incident energies close to the Coulomb barrier. Particle-gamma coincidence techniques were used to identify excited states of reaction products populated through inelastic scattering and in nucleon transfer reactions. One-neutron stripping and pick-up reactions on¹⁵²Sm were observed leading to known states of the rotation alignedi _13/2-bands in¹⁵³Sm and¹⁵¹Sm. In the¹⁶⁰Gd+^{206, 208}Pb systems no significant population of low lying states of product nuclei was found in the nucleon-transfer channels. Large cross sections were observed for one- and two-neutron pick-up from²³²Th at an incident energy of 6.4 MeV/u. Around the grazing angle they are of the same order of magnitude as the cross section measured for inelastic scattering. The results are analyzed in the framework of semiclassical models.     

Role of anharmonicities and nonlinearities in heavy ion collisions A microscopic approach

Using a microscopic approach beyond RPA to treat anharmonicities, we mix two-phonon states among themselves and with one-phonon states. We also introduce nonlinear terms in the external field. These nonlinear terms and the anharmonicities are not taken into account in the “standard” multiphonon picture. Within this framework we calculate Coulomb excitation of ²⁰⁸Pb and ⁴⁰Ca by a ²⁰⁸Pb nucleus at 641 and 1000 MeV/A. We show with different examples the importance of the nonlinearities and anharmonicities for the excitation cross section. We find an increase of 10% for ²⁰⁸Pb and 20% for ⁴⁰Ca of the excitation cross section corresponding to the energy region of the double giant dipole resonance with respect to the “standard” calculation. We also find important effects in the low-energy region. The predicted cross section in the DGDR region is found to be rather close to the experimental observation.     

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.