Elastic and inelastic scattering of carbon ions at intermediate energies

Elastic and inelastic scattering have been measured at E_lab = 360 MeV and 1016 MeV for the ¹²C + ¹²C system, as well as elastic scattering for ¹³C + ²⁰⁸Pb at 390 MeV. An optical-model analysis is reported and nuclear surface transparency effects are discussed, together with the energy dependence of the nuclear potential. A DWBA analysis of data on the 2⁺, 4.4 MeV state of ¹²C is reported and trends in the energy dependence of mean-field excitations are deduced.     

The impact parameter dependence of the K MO X-ray emission in208Pb +208Pb collisions

The emission probabilities for quasimolecular K-x-radiation (K-MOR) have been measured in²⁰⁸Pb +²⁰⁸Pb collisions at 4.3 MeV/u and 4.8 MeV/u as a function of the scattering angle using the particle-photon-coincidence technique. The probabilities exhibit a superposition of two exponential slopes with different fall-off constants. We identify the sharp fall off at very small impact parameters (<60 fm) with the K-MOR contribution from the decay of 1sσ-vacancies. The flatter slope for impact parameters larger than 60 fm is attributed to the radiative decay of holes in 2p _1/2 σ molecular states. In this way, experimental “1sσ-MOR-emission probabilities” could be extracted and compared with theory. For 4.3 MeV/u the1sσ- and 2p _1/2 σ-excitation probabilities could also be determined and have been compared to coupled-channel calculations and to a scaling law for 1sσ excitation.     

Coulomb dissociation of 8B and solar neutrino problem

We measured the cross section for Coulomb dissociation of ⁸B using a radioactive ⁸B beam of 46.5 MeV/u energy with a ²⁰⁸Pb target. The corss section for the ⁷Be(p,γ)⁸B capture reaction was deduced at E_cm = 0.6 – 1.7 MeV. The extracted astrophysical S₁₇ factors were consistent with the values measured by Vaughn et al. and Filippone et al. Possible corrections due to ⁷Be excited state population, E1 and M2 contribution, nuclear contribution and post acceleration effects are considered.     

Elastic scattering of polarised deuterons from 16O at 200, 400 and 700 MeV

Angular distributions of cross section, and A_y and A_yy analysing powers were measured for polarised deuteron elastic scattering from ¹⁶O at 200, 400 and 700 MeV. The data at 200 MeV bear evidence of the nuclear rainbow phenomenon while those at 400 and 700 MeV are reminiscent of the proton scattering results at equivalent energies. The data were analysed in terms of the optical model. The real central potential shape changes from an attractive Woods-Saxon form at 200 MeV to a wine-bottle-bottom form with a repulsive interior at 700 MeV. The total reaction cross sections deduced display a clear nuclear transparency effect in the present energy domain in agreement with predictions from the Glauber theory optical limit. Comparison with previous results for ⁴⁰Ca and ⁵⁸Ni targets is made.     

12C1 and 8Be production in 12C + 208Pb collisions

The mechanisms involved in the production of fast α-particles in ¹²C-induced reactions have been studied for the ¹²C + ²⁰⁸Pb system at the bombarding energies of E_12c = 132, 187 and 230 MeV. Absolute cross sections for the reactions ²⁰⁸Pb(¹²C. ¹²C¹→α + ⁸Be), ²⁰⁸Pb(¹²C, ⁸Be(g.s.)) and ²⁰⁸Pb(¹²C, ⁸Be(2.94 MeV)) have been determined by coincidence measurement of two or three correlated α-particles. Inclusive α-particle production cross sections were also measured at E_12c = 187 MeV. It is found that the inelastic process (¹²C, ¹²C¹→α + ⁸Be) does not contribute significantly to fast α-particle production but that the production of ⁸Be by projectile fragmentation is an important source of α-particles. At the highest bombarding energy (230 MeV) it appears that the ¹²C → 3α fragmentation reaction becomes more prominent at the expense of the ¹²C→α + ⁸Be fragmentation channel.     

The (p,t) reaction on 12C, 54Fe and 208Pb at 80 MeV

Angular distributions have been measured for the low-lying levels of the residual nuclei for the ¹²C, ⁵⁴Fe and ²⁰⁸Pb(p, t) reactions at E_p = 80 MeV. The shapes of these angular distributions are generally well reproduced by the zero-range distorted-wave Born approximation (DWBA). Enhancement factors extracted from the data show that the DWBA predicts relative strengths consistent with those observed at lower bombarding energies. However, the overall empirical DWBA normalization at E_p = 80 MeV is observed to be $\text{1}\text{12}$ ($\text{1}\text{4}$) of that required at 40 MeV for ²⁰⁸Pb (⁵⁴Fe).     

Alpha-nucleus elastic scattering at intermediate energies

Elastic scattering of 288,340,480 and 699 MeV Alpha-particles was measured on ²⁰⁸Pb, ¹¹⁶Sn and ⁵⁸Ni. The data were analysed in terms of a phenomenological optical model. The optical potentials obtained were found to vary consistently with the target nucleus and the incident energy. The radial zone where the potentials are well determined was studied in detail. The data for ²⁰⁸Pb were also analysed with a folding model. The energy dependence of the strong-absorption radius and of the reaction cross section shows that the nuclear surface becomes slightly transparent for incident energies above 150 MeV per nucleon.     

Observation of the nuclear rainbow scattering for12C+12C atE Lab =300 MeV

The elastic and inelastic scattering of¹²C on¹²C has been measured in the angular range between 2.8° and 70.4° in the c.m. system atE _Lab =300 MeV. Optical model calculations have been performed with Woods-Saxon and folded potentials, the ground state and the first 2⁺-state were coupled in the calculations. The large cross sections of the elastic scattering at large angles is related to the nuclear rainbow scattering, which is centered at about 56°. This requires a potential depth of 100 MeV at a distance of 3 fm, the fit to the data is sensitive down to this region. The calculations with the folded potential show a better agreement with the data than those with the Woods-Saxon shape. The total reaction cross section of 1,420 mb, obtained from the optical model analysis, corresponds to the geometrical value; no transparency is observed.     

Analysis of proton-induced reactions on 208Pb with incident energy 590 MeV and 322 MeV

The double differential cross section of emitting particles, the mass and charge distribution of the residual nuclei from proton-induced reaction on ²⁰⁸Pb with incident energy 590 MeV and 322 MeV have been analyzed by the quantum molecular dynamics (QMD). The time scale of the change of reaction mechanism in the process of reaction is investigated. The reaction process can be divided into three stages i.e., the direct, the cascade and the evaporation stage with the corresponding time scale of about <30 fm/c, 30–100 fm/c and >100 fm/c, respectively. Received: 16 January 1998 / Revised version: 17 September 1998     

Relativistic effects in heavy-ion collisions at SIS energies

The covariant and non-covariant Quantum Molecular Dynamics models are applied to investigate possible relativistic effects in heavy ion collisions at SIS energies. These relativistic effects which arise due to the full covariant treatment of the dynamics are studied at bombarding energiesE _lab=50, 250, 500, 750, 1000, 1250, 1500, 1750 and 2000 MeV/nucl. A wide range of the impact parameter fromb=0 fm tob=10 fm is also considsered. In the present study, five systems¹²C-¹²C,¹⁶O-¹⁶O,²⁰Ne-²⁰Ne,²⁸Si-²⁸Si and⁴⁰Ca-⁴⁰Ca are investigated. The full covariant treatment at low energies shows quite good agreement with the corresponding non-covariant whereas at higher energies it shows less stopping and hence less thermal equilibrium as compared to the non-covariant approach. The collisions dynamics is less affected. The density using RQMD rises and drops faster than with QMD. The relativistic effects show some influence on the resonance matter production. Overall, the relativistic effects at SIS energies (≦2000 MeV/nucl.) are less significant.     

Phase shift analysis of heavy-ion elastic scattering measured at intermediate energies

An elastic scattering phase shift analysis based on McIntyre parametrization is presented. It has been applied to¹²C+¹²C system at 360- and 1,016 MeV incident energies as well as to¹⁶O scattering on¹²C,⁴⁰Ca,⁹⁰Zr and²⁰⁸Pb targets at 1,503 MeV. The success of this model allows the interplay between diffraction and refraction to be pinned down: a presence of a nuclear rainbow is clearly evidenced in several cases.     

Elastic and inelastic scattering of 1.03 GeV 12C projectiles

Elastic scattering cross sections of 86 MeV/N ¹²C ions on ¹²C, ^NATCa, ⁸⁹Y and ²⁰⁸Pb targets has been measured together with inelastic scattering to the 4.4 MeV state of ¹²C. There is some indication for giant (quadrupole) resonance excitation in ⁴⁰Ca. Optical model and DWBA analyses are reported. Nuclear transparency effect is discussed.     

The PbPb collision

The reaction ²⁰⁸Pb on ²⁰⁸Pb was studied at bombarding energies of 7.0 and 7.57 MeV/u. One-particle inclusive measurements using a large-area position-sensitive ionisation chamber delivered the kinetic energy, charge and scattering angle of the reaction products. A precise calibration of the stopping power for very heavy ions in the detector gas was performed. The measured Wilczynski diagrams show, for increasing loss of kinetic energy, an increase of the mean scattering angle. It is attributed to the dominance of the repulsive Coulomb forces with respect to the attractive nuclear forces. The element distribution for the ²⁰⁸Pb on ²³⁸U reaction at 7.5 MeV/u was also measured and compared to the PbPb and UU reactions. Fission probabilities are derived as a function of charge and total kinetic energy loss. The most striking result is seen in the σ_z² versus TKEL correlation: the average rate of energy loss per nucleon exchange is abnormally large. It is shown that this behaviour is associated with the double magic closed shell character of the colliding nuclei. Nuclear structure information is extracted through a simple parametrisation.     

New Neutron-Rich Isotope 208Hg

The new neutron-rich isotope ²⁰⁸Hg has been identified for the first time from the reaction products in fully-stopping thick ^nat.Pb target bombarded by 30MeV/u ¹²C beam provided by the Heavy Ion Research Facility in Lanzhou.Assignment of the nuclide ²⁰⁸Hg was based on the measurements of the deacy γ energy and halflife of its daughter ²⁰⁸Ti,which was grown up with ²⁰⁸Hg β-deacy.The half-life of ²⁰⁸Hg β-deacy was determined to be 42+23－12 min.The average production cross section of ²⁰⁸Hg over the incident energy region from Coulomb barrier to 30MeV/u is found to be 1.1±0.5μb.     

Charge and mass transfer in the reaction136Xe+208Pb at energies close to the coulomb barrier

Mass and charge transfer was investigated for the system¹³⁶Xe+²⁰⁸Pb at 5.9 MeV/nucleon incident energy with aΔE —E-time of flight telescope. The angle and energy integrated cross section for the strongly damped events was found to be 510 mb, very close to the total reaction cross section. The width of the mass distribution as function of the total kinetic energy loss was measured and is compared to the width of the corresponding charge distribution. An upper limit of 1 μb has been found for processes with very large mass transfer.     

Nuclear compression moduli and density-dependent forces

Density-dependent zero-range forces of the form of the modified delta interaction (MDI) are generalized (MDI3, MDI4) in order to yield reasonable values of the compression modulus in nuclear matter (K_N = 200 MeV). This low value can be fitted by introducing two terms with different density dependence in the force. The four free parameters of MDI3 are adjusted to reproduce the nuclear matter values of the binding energy, density and compression modulus, and to fulfil the condition that the total energy of ¹⁶O in harmonic oscillator wave functions has a minimum at the oscillator length b = 1.75 fm, corresponding to the correct rms radius. MDI4 contains in addition a two-body spin-orbit interaction. The five parameters of MDI4 are fitted to the above three nuclear matter data and by requiring that Hartree-Fock (HF) calculations in ²⁰⁸Pb yield the experimental charge rms radius and reasonable values of certain single-particle spin-orbit splittings. The quality of MDI4 is checked by comparing calculated rms radii, binding energies, and elastic electron scattering cross sections with available experimental data for doubly closed shell nuclei. As a test the energy levels and the nuclear monopole polarization of muonic ²⁰⁸Pb are calculated self-consistently yielding impressive agreement with experiment.     

The heavy-ion reaction channels of the system 16O + 16O

The reaction channels of the system ¹⁶O + ¹⁶O with outgoing heavy particles from lithium to magnesium have been measured using a ΔE-E telescope. Excitation functions from 49 to 65 MeV at θ_Lab = 30° and angular distributions from θ_Lab = 10° (20°) to 50° at E_Lab = 51.5 MeV are presented for the strong transitions. The excitation function of the ¹²C-²⁰Ne (4.25 MeV) channel shows a pronounced regular cross structure with peaks at 52 and 60 MeV. A selective excitation of certain states in the inelastic scattering and the ¹²C-²⁰Ne channel is observed; the yields of the other heavy-ion channels being weaker by at least one order of magnitude. An explanation of this phenomenon is given by considering the angular momentum matching between entrance and exit channels. Furthermore it is shown that no strong dependence of the cross sections on the transferred angular momentum or on the nuclear structure of the final states is observed. Possible implications of these results on the reaction mechanism are discussed.     

Momentum transfer in 30–200 MeV 4H induced reaction with 59Co

Thick-target recoil ranges of radioactive nuclei produced in 30–200 MeV alpha-particle bombardment of ⁵⁹Co have been used to deduce the longitudinal momentum transfer per projectile nucleon (p₆/A) as a function of residue mass and bombarding energy. The average value of p₆/A increases monotonically with bombarding energy and reaches a maximum value of ≈ 160 MeV/c at ≈ 23 MeV/u, and decreases thereafter. The maximum value of p₆/A is equal to the incident momentum up to ≈ 23 MeV/u and saturates at a value of ≈ 220 MeV/c beyond this energy.     

Total reaction cross sections measurement for <Superscript>6,8</Superscript>He and <Superscript>8,9</Superscript>Li nuclei with energies of (25–45)/<Emphasis Type="Italic">A</Emphasis> MeV on <Superscript>nat</Superscript>Al and <Superscript>nat</Superscript>Pb

Preliminary results of measurements of the total reaction cross sections σ_R for weakly-bound ^6,8He and ^8,9Li nuclei at energy range (25–45)/A MeV on ²⁷Al and ²⁰⁸Pb targets are presented. The secondary beams of ^6,8He and ^8,9Li were produced by bombardment of the ¹¹B (33 A MeV) primary beam on Be (89 mg cm^–2) target and separated by COMBAS fragment-separator. In dispersive focal plane a horizontal slit defined the momentum acceptance as 1% and a wedge degrader of 200 μm Al was installed. The B_ρ of the second section of the fragment-separator was adjusted for measurements in energy range (25–45)/A MeV. The secondary products were detected by a telescope consisting of two Si ΔE detectors 300, 1000 μm and E-detector, which consisted of nine CsI/Tl granules.