Cross sections for nuclear reactions in collisions of238U+238U and238U +197Au near and below the coulomb barrier

Cross sections for nuclear reactions at beam energies near and below the spherical Coulomb barrier V _c were measured in the very heavy collision systems²³⁸U +²³⁸U and²³⁸U +¹⁹⁷Au. The most probable reaction channel with mass transfer is the one-neutron transfer. Its excitation function is understood in terms of Rutherford trajectories together with the quantal process of neutron tunnelling over large distances. In addition, the exchange of up to 15 nucleons is observed down to 0.90 V _c . The excitation functions for the multi-nucleon transfer products have much steeper slopes than that for one-neutron transfer, and are steeper for²³⁸U +¹⁹⁷Au than for²³⁸U +²³⁸U, suggesting that nuclear contact is established in the associated collisions. The angular distribution for one selected multi-nucleon transfer product,²²⁷Th, shows that its formation occurs in more central collisions within contact times shorter than about 10^?21 s. There is no evidence for very longlived di-nuclear systems in the these reactions.     

Investigation of deep inelastic reactions in 238U + 238U at Coulomb barrier energies

We investigated deep inelastic reactions in ²³⁸U + ²³⁸U collisions at 6.09, 6.49, 6.91, 7.1 and 7.35×A MeV at the VAMOS spectrometer (GANIL). A large transfer of neutrons and protons was observed at all beam energies. For a transfer of more than 10 nucleons the total kinetic energy of the detected fragments becomes independent of the beam energy and reaches values far below the Coulomb barrier for spherical fragments. This points to the formation of a di-nuclear system in the entrance channel which develops an elongated shape and a strong neck. For such reactions we expect an enhanced lifetime of the di-nuclear system which is significantly longer than the time scale for elastic and quasi-elastic reactions. Different theoretical approaches predict delay times of more than 5×10^-21 s for a subset of our data.     

Quasielastic transfer reactions in 238U + 197Au and 197Au + 197Au collisions near the Coulomb barrier

Differential cross sections as a function of cm angle were measured for 1n- and 2n-transfer reactions in ²³⁸U + ¹⁹⁷ Au and¹⁹⁷ Au + ¹⁹⁷ Au collisions in the energy range from 0.881 V_c to 1.093 V_c and 0.825 V_c to 0.964 V_c, respectively. For ¹⁹⁸Au and ¹⁹⁹Au from the ²³⁸U + ¹⁹⁷Au collisions, for reduced distances of closest approach d _o 1.55 fm, the angular distributions at all bombarding energies are well described by the semiclassical theory. Equivalently, the transfer probabilities show the expected exponential decrease with increasing d _o over many orders of magnitude. For all other transfer products from ²³⁸U + ¹⁹⁷Au collisions, and for all transfer products from ¹⁹⁷Au + ¹⁹⁷Au collisions, markedly reduced cross sections relative to the semiclassical theory are observed for central collisions at all bombarding energies, even for values of d _o that are well outside the region where absorption is known to set in. Only for the more peripheral collisions, one observes agreement of the angular distributions (transfer probabilities) with the semiclassical expectations. The deviations for central collisions are absent for reactions with positive Q _gg values and scale roughly with increasingly negative values of Q _gg, i.e. with increasing Q-value mismatch. Channel coupling is proposed as the relevant mechanism.     

Fission of238U induced by136Xe for energies close to the Coulomb barrier

Excitation functions and angular distributions have been measured for fission of²³⁸U induced by¹³⁶Xe ions with bombarding energies between 4.5 and 5.9 MeV/N. Structures expected theoretically as characteristic for Coulomb fission have not been observed. The Q-value of ?(7.5±1.0) MeV measured for bombarding energies below 4.7MeV/N, however, appears to be compatible with inelastic scattering (e.g. Coulomb excitation) rather than subcoulomb transfer followed by fission. The total kinetic energy of deep inelastic events at 5.9 MeV/N is consistent with the current knowledge about mass diffusion, but also (for the highest excitation energies) with a fast fission process in the presence of the projectile.     

Light charged particle emission and fission in238U+238U collisions at 1,740 MeV

Inclusive⁴He and⁴H energy spectra and heavy fragment coincidence correlations have been measured for reactions of 7.31 MeV/u²³⁸U with²³⁸U and^?197Au targets. The H/He production cross sections are in the range 15–26 mb, and their emission spectra are very similar for the two systems. The observed strong kinematic shifts with angle are reproduced in shape and magnitude by Monte Carlo simulations of particle evaporation from projectile-like and target-like fragments, indicating competition between charged particle emission and sequential fission. No evidence is found for high energy charged particle emission associated with ultra-highZ composite systems. Heavy fragment measurements indicate an abundance of quasielastic and deeply inelastic reaction fragments, as well as sequential fission of target and projectile nuclei. For²³⁸U nuclei, the fission occurs predominantly in an asymmetric mode, reminiscent of fission at low excitation energy. For²³⁸+²³⁸U reactions in the vicinity of the grazing angle, the frequency of single sequential fission (with survival of the partner fragment) is twice as large as double sequential fission in which both the target and projectile undergo fission. In²³⁸U+¹⁹⁷Au reactions, the survival probability of the heavy fragments is even greater. The surprisingly high survival probabilities of high-Z fragments imply a preponderance of very soft collisions in these very-heavy-ion reactions, at least at energies not very far over the Coulomb barrier.     

Fusion of 60Ni + 100Mo near and below the Coulomb barrier

Various sub-barrier capture reactions with ^16,18O and ^40,48Ca are treated within the quantum diffusion approach. The role of neutron transfer in these capture reactions is discussed. The quasielastic and capture barrier distributions are analyzed and compared with the recent experimental data.     

Calculations for diabolic pair-transfer below the Coulomb barrier

Calculations of the probabilities for two-neutron transfer in the reaction²⁰⁸Pb +¹⁶²Dy at bombarding energies below the Coulomb barrier are presented. The reaction is dominated by the strong Coulomb excitation of the rotational bands in¹⁶²Dy and¹⁶⁴Dy, while the transfer process is a weak perturbation. The presence of a diabolic point in the interval [10⁺–12⁺] in the rotational sequence, above which the transfer matrix elements change sign, leads to a reduction in the total probability for transfer of up to 25%. The relative populations of the spin states above the diabolic point exhibit an even more pronounced variation.     

Total reaction cross section for 12C + 16O below the Coulomb barrier

The energy dependence of the total reaction cross section, σ(E), for ¹²C + ¹⁶O has been measured over the range E_c.m. = 4–12 MeV, by detecting γ-rays from the various possible residual nuclei with two large NaI(Tl) detectors placed close to the target. This technique for measuring total reaction cross sections was explored in some detail and shown to yield reliable values for σ(E). Although the principal emphasis of this work was placed on obtaining reliable cross sections, a preliminary study has been made of the suitability of various methods for extrapolating the cross section to still lower energies. The statistical model provides a good fit with a reasonable value for the strength function, 〈γ²〉/〈D〉 = 6.8 × 10^?2, over the range E_c.m. = 6.5–12 MeV, but predicts cross sections which are much too large for E_c.m. < 6.5 MeV. Optical model fits at low energies are especially sensitive to the radius and diffuseness of the imaginary component of the potential and, since these are still poorly known at present, such extrapolations may be wrong by orders of magnitude. A simple barrier penetration model gives a moderately good fit to the data and seems to provide the safest extrapolation to lower energies at the present time. It is clear, however, that our knowledge of the heavy-ion reaction mechanism at low energies is incomplete, and that cross-section measurements at still lower energies are needed to establish the correct procedure for extrapolating heavy-ion reaction cross sections to low energies.     

Fission product energies and anisotropies following complete fusion of16O+238U

Radioactive recoil techniques have been developed for measuring angular distributions and range distributions of individual fission products following heavy ion induced fission. From these measurements, values can be extracted for the recoil velocity of the fissioning nucleus, the velocity imparted by fission, and the fission anisotropy. These techniques were applied to reactions of 101 MeV¹⁶O on²³⁸U, and confirmed that the reaction mechanism is essentially entirely complete fusion-fission. Accepting this, the data determine the kinetic energy release in forming the various products to a precision of 1%; while the overall magnitude of the energy is in good agreement with previous results, the data suggest a systematic correlation between kinetic energy and the position of a product on the nuclear charge dispersion curve, not previously reported, which is similar to but significantly larger in magnitude than the effect expected from simple Coulomb repulsion. Significant variations in anisotropy are also observed between products, which appear to be partially correlated with the variations in kinetic energy.     

Positron spectra from internal pair conversion observed in 238U + 181Ta collisions

We present new results from measurements and simulations of positron spectra, originating from ²³⁸U + ¹⁸¹Ta collisions at beam energies close to the Coulomb barrier. The measurements were performed using an improved experimental setup at the double-Orange spectrometer of GSI. Particular emphasis is put on the signature of positrons from Internal-Pair-Conversion (IPC) processes in the measured e⁺-energy spectra, following the de-excitation of electromagnetic transitions in the moving Ta-like nucleus. It is shown by Monte Carlo simulations that, for the chosen current sweeping procedure used in the present experiments, positron emission from discrete IPC transitions can lead to rather narrow line structures in the measured energy spectra. The measured positron spectra do not show evidence for line structures within the statistical accuracy achieved, although expected from the intensities of the observed γ-transitions ( E _γ∼ 1250-1600 keV) and theoretical conversion coefficients. This is due to the reduced detection efficiency for IPC positrons, caused by the limited spatial and momentum acceptance of the spectrometer. A comparison with previous results, in which lines have been observed, is presented and the implications are discussed. Received: 27 April 2000 / Accepted: 14 September 2000     

Fusion reactions around the barrier for Be+~(238)U

Fusion-evaporation cross sections of ~(238)U (~9Be,5n)~(242)Cm are measured over a wide energy range around the Coulomb barrier.These measured cross sections are compared with model calculations using two codes,namely HIVAP2 and KEWPIE2.HIVAP2 calculations overestimate the measured fusion-evaporation cross sections by a factor of approximately 3.In KEWPIE2 calculations,two approaches,namely the Wentzel-Kramers-Brillouin(WKB) approximation and the empirical barrier-distribution (EBD) method,are used for the capture probability;both of them properly describe the measured cross sections.Additionally,fusion cross sections of ~(7,9)Be+~(238)U measured in two experiments are applied to constrain model calculations further through three codes,i.e.,HIVAP2,KEWPIE2,and CCFULL.Parameters in these codes are also examined by comparison with measured fusion cross sections.All the comparisons indicate that the KEWPIE2 calculations using the WKB approximation agree well with the measured cross sections of both fusion reactions ~(7,9)Be+~(238)U and the fusion-evaporation reaction ~(238)U (~9Be,5n)~(242)Cm.Calculations using the fusion code CCFULL are also in good agreement with the measured fusion cross sections of ~(7,9)Be+~(238)U.     

Fission and gamma-ray decay of the238U shape isomer

The decay of the²³⁸U superdeformed shape isomer has been reinvestigated by detecting for the first time simultaneously the fission and the gamma-back decay. An electrostatic deflection system has been used to transport the^238mU recoils, produced in a²³⁸U(d, pn) reaction with a pulsed beam of 18 MeV deuterons, in front of a detector set-up consisting of three ion-implanted solidstate detectors and a Ge(Li) gamma-detector. The gamma-back decay has been measured in coincidence with conversion electrons of the 2⁺ 0⁺ transition deexciting the first rotational state in²³⁸U. Two gamma-transitions of 2.513 MeV and 1.878 MeV have been observed with half-lives consistent with the result obtained for the decay by delayed fissionT _1/2=(298±18) ns.Dedicated to Prof. Dr. P. Kienle on the occasion of his 60th birthday     

Study of the heavy products from84Kr+238U collisions at 522 MeV

Angular distributions and integral cross sections for heavy reaction products from⁸⁴Kr +²³⁸U collisions at 522 MeV were measured using catcher foil techniques and off-line X-ray identification of individual reaction product isotopes. There is no evidence for a fission-fusion mechanism being responsible for the formation of the “gold finger”. The data show that usual deep inelastic collisions account for the formation of all products with 70≦Z≦86. Compared to existing data atE≦605 MeV, the deduced mass distribution indicates reduced fission probabilities forZ≧80 fragments at 522 MeV. This is consistent with the expected dependence of fission probability on excitation energy and especially on angular momentum.     

Potential pockets in the238U+238U system and their possible consequences

Within the double-folding model the separation, shape, and orientation dependence of the interaction potential is studied for two heavy ions. An effective nucleon-nucleon interaction (M3Y) derived fromG-matrix elements and based upon the Reid soft-core potential is used. Deformed Fermi-type matter densities with static quadrupole and hexadecapole deformations were utilized. The model is applied to the²³⁸U+²³⁸U system and shows dramatic dependence on the deformations and orientations.     

Study on the formation of the composite system of 238U+238U

Strongly damped reactions of 238U+238U, at Ecm = 680-1880 MeV have been studied based on the improved quantum molecular dynamics model. We find that at a certain energy region the entrance channel potential is weakly repulsive and the dissipation is very strong after touching configuration, these two effects make the time delay of re-separation for colliding system. The single particle potential well of the transiently formed composite system has Coulomb barrier about 15-20 MeV high at the surface, which makes the excited unbound protons being still embedded in the potential well and moving in a common mono-single particle potential for a period of time and thus restrains from quick decay of the composite system.     

The reaction238U +238U at 7.42MeV/u

One-particle-inclusive measurements have been performed for the charge, kinetic energy and angular distributions of reaction products from²³⁸U +²³⁸U at 1 766MeV (7.42MeV/u) incident energy. The deep inelastic products exhibit features similar to those seen in reactions induced by medium heavy nuclei: increasing particle transfer is observed with increasing energy damping, the angular distributions are peaked near the grazing angle, they broaden significantly with increasing energy loss and/or charge transfer. The dominant reaction mechanism, however, is found to be sequential fission of one or both primary reaction products. The reconstructed primaryZ- andQ-value distributions show more particle transfer at a given energy loss than in other systems, i.e. the diffusion process seems to proceed colder in this system. This is confirmed by relatively large cross sections for surviving deep inelastic reaction products belowZ=92. A direct search forα-decay or fission of superheavy nuclei being produced in a deep inelastic reaction and being implanted in a surface barrier detector resulted in an upper cross section limit of 2 ×10^?32cm².     

Systematic studies of positron production in heavy-ion collisions near the Coulomb barrier

We present the results obtained from systematic studies of positron creation for a series of heavy-collision systems, with united chargeZ _u =Z ₁ +Z ₂ ranging fromZ _u =164 (Pb + Pb) toZ _u =184 (U+U) at bombarding energies close to the Coulomb barrier, using the Orangeβ-spectrometer at GSI. For each collision system studied, the dominating continuous distributions due to quasiatomic and nuclear positron emission are determined accurately. This is essential in obtaining the characteristics of the still unexplained monoenergetic positron lines which appear in the energy range between 200 keV and 400 keV. Our results are compared with coupled-channels calculations for quasi-atomic positron creation. The latter describe quite well the global features of the measured spectra, but overestimate systematically their absolute values. From the comparison, a common normalization factor of about 0.75 can be established for the calculated spectra. In particular, the dependence onZ _u of the measured emission probabilities was found to follow a power law (∝Z _u ^195±1), in fair agreement with the theoretical prediction.     

Heavy-ion fusion below the Coulomb barrier: The systems 28,30Si + 58,62,64Ni and 32,34,36S + 58,64Ni

Fusion cross-sections for the 12 systems ^28,30Si + ^58,62,64Ni and ^32,34,36S + ^58,64Ni were measured at many energies from well below up to about 1.5 times the Coluomb barriers. The data show large sub-barrier fusion probabilities with strong isotopic dependences. The results of coupled-channel calculations involving the lowest 2⁺ and 3⁻ levels of both colliding nuclei and the 2-neutron transfer channel are compared with the measured excitation functions. Indications for the importance of the transfer channels are found. Signatures of system-dependent effects of the positive Q-value transfer channels are evidenced, also from a systematic intercomparison of the data.