Directed and elliptic flow in 197Au+197Au at intermediate energies

Directed and elliptic flow for the ¹⁹⁷Au+¹⁹⁷Au system at incident energies between 40 and 150 MeV per nucleon has been measured using the INDRA 4π multi-detector. For semi-central collisions, the excitation function of elliptic flow shows a transition from in-plane to out-of-plane emission at around 100 MeV per nucleon. The directed flow changes sign at a bombarding energy between 50 and 60 MeV per nucleon and remains negative at lower energies. Molecular dynamics calculations (CHIMERA) indicate sensitivity of the global squeeze-out transition on the σ _NN and demonstrate the importance of angular momentum conservation in transport codes at low energies.     

Measurement of the 2H(p,n) Breakup Reaction at 170 MeV and the Three-Nucleon Force Effects

The effects of three nucleon force (3NF) have been actively studied via the nucleon–deuteron (Nd) scattering states. The differential cross sections and the vector analyzing powers A _y of the ²H(p, n) inclusive breakup reaction at 170 MeV were measured for the study of 3NF effects in the intermediate energy region. The polarized proton beam of 170 MeV was injected to the deuterated polyethylene (CD₂) target and the energy of scattered neutrons were measured by using TOF method. The data were compared with the Faddeev calculations based on modern nucleon–nucleon (NN) forces with and without the 3NF. Concerning the differential cross sections, we can see large discrepancies between the data and the calculations in the region of scattered neutron energies are low, which is similar to the results of the ²H(p, p) inclusive breakup reaction at 250 MeV.     

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.     

Time-dependent Hartree-Fock calculations for 16O + 16O reactions

Head-on collisions between ¹⁶O nuclei are treated in the Time-Dependent Hartree-Fock (TDHF) approximation. Reactions at center-of-mass bombarding energies of 2 and 8 MeV per nucleon result in fusion-fission processes with strong internal excitation of the fragments.     

The 12C(α, γ)16O reaction and stellar helium burning

The cross section for the reaction ¹²C(α, γ)¹⁶O has been measured for a range of c.m. energies extending from 1.41 MeV to 2.94 MeV, by using ¹²C targets of high isotopic purity, large NaI(T1) crystals, and the time-of-flight technique for the suppression of prompt neutron background and time-independent background. Gamma-ray angular distributions were measured at c.m. energies of 2.18, 2.42, 2.56 and 2.83 MeV. By means of theoretical fits, which include the coherent effects of the 1^? states of ¹⁶O at 7.12 MeV, 9.60 MeV, and those at higher energies, the electric-dipole portion of the cross section at astrophysically relevant energies has been determined. A three-level R-matrix parametrization of the data yields an S-factor at E_c.m. = 0.3 MeV, S(0.3 MeV) = 0.14^+0.14_?0.12 MeV · b. A “hybrid” R-matrix optical-m parameterization yields S(0.3 MeV) = 0.08^+0.05_?0.04 MeV · b. This S-factor is of crucial importance in determining the abundances of ¹²C and ¹⁶O at the end of helium burning in stars.     

Target fragmentation in proton-nucleus and16O-nucleus reactions at 60 and 200 GeV/nucleon

Target remnants withZ<3 from proton-nucleus and¹⁶O-nucleus reactions at 60 and 200 GeV/nucleon were measured in the angular range from 30° to 160° (?1.7<η<1.3) employing the Plastic Ball detector. The excitation energy of the target spectator matter in central oxygen-induced collisions is found to be high enough to allow for complete disintegration of the target nucleus into fragments withZ<3. The average longitudinal momentum transfer per proton to the target in central collisions is considerably higher in the case of¹⁶O-induced reactions (≈300 MeV/c) than in proton-induced reactions (≈130 MeV/c). The baryon rapidity distributions are roughly in agreement with one-fluid hydrodynamical calculations at 60 GeV/nucleon¹⁶O+Au but are in disagreement at 200 GeV/nucleon, indicating the higher degree of transparency at the higher bombarding energy. Both, the transverse momenta of target spectators and the entropy produced in the target fragmentation region are compared to those attained in head-on collisions of two heavy nuclei at Bevalac energies. They are found to be comparable or do even exceed the values for the participant matter at beam energies of about 1–2 GeV/nucleon.     

Study of the Three-Nucleon Force Effects in the 2H(p, n) Breakup Reaction at 170 MeV

For the study of three nucleon force (3NF) effects in the intermediate energy region, the differential cross sections and the vector analyzing power A _y were measured for the ²H(p, n) inclusive breakup reaction at 170 MeV. The polarized proton beam of 170 MeV was injected to the deuterated polyethylene (CD₂) target and the energy of scattered neutrons were deduce by TOF method. The data was compared with the results of the Faddeev calculations with and without 3NFs. Concerning about the differential cross sections, we can see large discrepancies between the data and the calculations in the region where the energies of scattered neutrons are low, which are similar to the results of the ²H(p, p) inclusive breakup reaction at 250 MeV.     

The 18O(18O, 16O)20O reaction at 52 MeV

The structure of the ²⁰O nucleus was studied by the ¹⁸O(¹⁸O, ¹⁶O)²⁰O reaction at E_1ab = 52 MeV. Angular distributions for the transitions to the lowest four states in ²⁰O were obtained and analyzed with finite-range DWBA calculations. Optical potential sets were used which fit the experimental elastic scattering differential cross sections over almost the whole angular range. The two L = 0 transitions to the ground state and the 4.45 MeV state of ²⁰O populated by the ¹⁸O(¹⁸O, ¹⁶O) reaction were analyzed with exact finite-range DWBA calculations using microscopic form factors. These calculations underestimate the absolute cross sections by a factor of 11. The relative strength of the two L = 0 transitions is well reproduced in the ¹⁸O(¹⁸O, ¹⁶O) reaction. However, DWBA calculations for the ¹⁸O(t, p)²⁰O reaction overestimated the relative cross sections for the excited 0⁺ state by a factor of 6. Several model wave functions were tested for the ground-state transition. It was found that the absolute cross sections of the (¹⁸O, ¹⁶O) reaction are very sensitive to the mixing of shell-model configurations. The angular distribution shapes are also slightly dependent on the mixing.     

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.     

Dirac coupled-channels analysis of inelastic scattering of 800 MeV polarized protons from 16O, 24Mg and 26Mg

Coupled-channels calculations using the Dirac phenomenology have been performed to analyse cross sections and analyzing power data for inelastic scattering of 800 MeV protons from low-lying states in ¹⁶O, ²⁴Mg and ²⁶Mg. Large negative reals scalar potentials, large positive real vector potentials and large negative imaginary vector potentials were obtained. Considerable improvements were obtained using the Dirac equation compared to the classical Schrödinger calculations. These best fits have been found compatible with an imaginary scalar potential equal to zero (U_sⁱ=0) and therefore with less parameters (nine) than usually required in the classical calculations (twelve).     

Transparency effects in heavy-ion collisions over the energy range 100–300 MeV/nucleon

Direct measurements of total reaction cross sections between 100 and 300 MeV/nucleon indicate that σ_R reaches a minimum around 300 MeV/nucleon corresponding to the maximum of the (surface) transparency effects in heavy ion collisions. Data are well reproduced by simple microscopic calculations and are in agreement with the new parametrization we proposed earlier.     

Single-nucleon transfer reactions induced by16O on14C

Angular distributions of the proton and neutron transfer reactions¹⁴C(¹⁶O,¹⁵N)¹⁵N and¹⁴C(¹⁶O,¹⁷O)¹³C leading to the ground states of the final nuclei were measured atE _lab=20, 25 and 30 MeV. A DWBA analysis was performed using the no-recoil approximation of Buttle and Goldfarb. All angular distributions, including the pronounced structures of the proton transfer arising from the fact that the final nuclei are identical, are well reproduced. The spectroscopic factor for the neutron transfer is in agreement with shell model calculations whereas the proton transfer into aj _<-state yields a value which is too high. Exact finite-range calculations do not show this discrepancy, indicating that recoil effects are important even for light targets and lower energies. Contributions of the nonnormall-transfer, however, are small.     

Experimental determination of the total reaction cross section of the stellar nuclear reaction 16O + 16O

The total reaction cross section for ¹⁶O + ¹⁶O has been measured at six energies between E_c.m. = 6.8 and 11.9 MeV. Cross sections for the production of protons, alphas, neutrons, deuterons, ³¹S, ³⁰P, ¹²C(g.s.) + ²⁰Ne(g.s.) and the relative γ-yield were obtained with a variety of experimental methods. No ³H or ³He were found. All cross sections are normalized to ¹⁶O + ¹⁶O elastic scattering at θ_c.m. = 90°, which was measured separately with high precision between E_c.m. = 7.3 and 14.4 MeV. The elastic scattering and relative γ-yield of ¹²C + ¹²C were measured between E_c.m. = 3.9 and 7.5 MeV. The elastic scattering and neutron yield of ¹²C + ¹⁶O were measured between E_c.m. = 5.4 and 10.1 MeV.     

18O(p,p)18O and18O(p,p′)18O1for E = 6.1−16.6 MeV

Angular distributions of cross sections and analyzing powers have been measured for ¹⁸O(p, p)¹⁸O and ¹⁸O(p, p₁)¹⁸O¹(1.98 MeV) for proton energies between 6.1 and 16.6 MeV. The measurement were crarried out in 25 keV intervals between 6.1 and 8.0 MeV, and in 100 keV intervals between 8.0 and 16.6 MeV. Although the general appearance of the angular distributions changes quite smoothly with energy above about 8 MeV, structure is evident in the backangle excitation functions up to 14 MeV. A phase-shift analysis of the elastic scattering data yielded resonance parameters for 25 levels in ¹⁹F in the excitation enrgy region 13.8?21.4 MeV. A large fraction of these levels have odd parity, and the energies of the $\text{1}\text{2}{}^{\mathrm{?}}$ and $\text{3}\text{2}{}^{\mathrm{?}}$ levels coincide closely with peaks seen in the ¹⁹F photonuclear yield curves. A simple model involving proton single-particle states coupled to the 2₁^+; and 3₁^? levels of ¹⁸O is able to account for some features of the observed structure. The energy-averaged elastic and inelastic scattering data for E_p > 12 MeV agree reasonably well with the spherical optical model and the DWBA, respectively, as well as with coupled-channels calculations.     

Comparison of the fusion reactions12C+20Ne and16O+16O near the Coulomb barrier

The partial cross sections of heavy residual nuclei produced in the heavy ion fusion of¹²C+²⁰Ne have been measured atE _c.m.=6–15 MeV viaγ-ray spectroscopy with a Ge(Li) detector. Windowless and recirculating gas target systems have been used. The dominant residual nuclei are²⁴Mg,²⁷Al,²⁸Si,³⁰Si,³⁰P and³¹P, which arise from two- and three-body breakups in the exit channels. The observed excitation functions are smooth in their energy dependence and give no indications for the existence of pronounced resonance structures, in contrast to theoretical predictions. The Coulomb excitation of²⁰Ne served as an intrinsic calibration standard in the determination of absolute partial and total fusion cross sections. The same experimental set-up was also used in the reaction studies of¹⁶O+¹⁶O atE _c.m.=7–14 MeV, going through the same compound nucleus³²S at similar excitation energies. The observed energy dependence in the excitation functions is in good agreement with previous work. The total fusion cross section agrees fairly well with two sets of values reported previously, but deviates significantly from other reported absolute cross section values. The relative evaporation distributions of the residual nuclei are similar for both heavy ion reactions. However, the ratio of their total fusion cross sections deviates from model predictions and suggests that compound nucleus formation does depend on the microscopic structure of the colliding nuclei in the entrance channel. From the observed energy dependence of the above ratio, particularly at subcoulomb energies, geometrical effects in the entrance channel (due to deformed and spherical nuclei) appear to be weak. The astrophysical aspects of the data in the context of late stellar nucleosynthesis are discussed.     

9Be + 12C, 9Be + 16O,9Be + 19F reactions at energies below the barrier

The ¹⁶O + ⁹Be reactions have been studied from E_c.m. = 2.0 MeV to 5.1 MeV, an energy near the top of the Coulomb barrier. The cross section for the neutron transfer reaction ⁹Be(¹⁶O,¹⁷O¹ (0.87 MeV))⁸Be has been measured over this range by detecting the prompt 0.87 MeV γ-rays. The total fusion cross section has been determined from E_c.m. = 2.8 to 5.1 MeV by observing individual γ-ray transitions in the evaporation residues with a Ge(Li) detector, and then summing the separate yields. Direct processes are found to dominate the reaction yield below E_c.m. = 4 MeV. A comparison of the energy dependence of the fusion cross section for this reaction and the ¹²C + ¹³C reaction, which proceeds via the formation of the same compound nucleus, ²⁵Mg, reveals differences at sub-barrier energies. Optical model and incoming-wave boundary condition calculations are presented. Data have also been obtained for the near optimum Q-value neutron-transfer reactions ⁹Be(¹²C, ¹³C¹)⁸Be and ⁹Be(¹⁹F, ²⁰F)⁸Be, and these are discussed in terms of a simple model of sub-barrier direct reactions.     

Cross sections for 6Li production in the reactions 10B + 16O and 12C + 14N at low energies

Absolute cross sections have been measured for the reactions ¹⁰B(¹⁶O, ⁶Li)²⁰Ne and ¹²C(¹⁴N, ⁶Li)²⁰Ne at several energies in the range E_c.m. = 7.5–16.2 MeV, and 13.8–16.6 MeV, respectively. The predictions of Hauser-Feshbach calculations show generally good agreement with the experimental data without parameter variation. The consequences of an angular momentum cutoff in the entrance channel and in the compound nucleus are discussed.     

Monopole excitation of 4He in α-particle scattering from 12C, 13C,and 16O

The excitation of the O⁺ state in ⁴He at 20.1 MeV has been studied in α-scattering from ¹²C, ¹³C, and ¹⁶O at E_α=65MeV by measuring the decay $\text{α}{}^1\text{→}\text{p}\text{+}\text{t}$ with a coincidence method. DWBA calculations of this monopole transition using both microscopic and collective model transition densities are presented.