The 12C+24Mg elastic scattering: An example of anomalous transparency at coulomb barrier energies

Fifteen complete angular distributions of the elastic scattering of ¹²C+²⁴Mg were measured at energies around the Coulomb barrier (E_cm = 10.67–16 MeV). The angular distributions are strongly oscillating and could be well described by an optical potential family, whose real part was determined without continuous ambiguity. The imaginary part of this optical potential is very shallow. At four energies the inelastic scattering angular distributions leading to the 2⁺ state of the ²⁴Mg were also measured and analysed with coupled-channels calculations. The volume integrals of the optical potentials used in the coupled-channels calculations present the threshold anomaly in their energy dependence, with a clear Q-value dependence.     

Optical potential for 12C + 28Si scattering

¹²C + ²⁸Si elastic scattering angular distributions are smooth functions, relatively easily fit by optical potential predictions, at laboratory bombarding energies, E_1ab, within ≈ 10 MeV of the Coulomb barrier (i.e. up to E_1ab ≈ 27 MeV). Between E_1ab = 27 and 36 MeV the angular distributions show pronounced oscillatory structure which is not easily fit with an optical potential. No optical potential has been found to give a very good account of all the angular distributions simultaneously; the best simultaneous fit to all the data was achieved with a surface-transparent potential whose real and imaginary well depths are energy dependent.     

Antiproton-nucleus scattering with self-consistent model for medium corrections

The antiproton-nucleon t-matrix with propagation in the nuclear medium is calculated selfconsistently and applied to the construction of optical potentials for the elastic scattering of antiprotons from nuclei. We find that this treatment gives results that are sensitive to medium corrections even though the strong absorption acts to mask these corrections partially. The agreement with scattering experiments at 46.8 MeV on ¹²C is very good. We compare potentials containing medium corrections to those based on free $\text{p}\text{N}$ amplitudes for ¹²C and ⁴⁰Ca. The local approximation to the optical potential is found attractive at low energies, becoming shallower with increasing bombardment energy in the range considered here (up to about E_L = 120 MeV).     

The12C+12C reaction at subcoulomb energies (I)

The reaction¹²C+¹²C has been studied in the energy rangeE _cm=2.45–6.15 MeV byγ-ray spectroscopy. Gamma-ray transitions from a large number of excited states in²⁰Ne,²³Na and²³Mg were observed, which show strong and rapid yield variations. When the influence of the Coulomb barrier is removed, these structures appear superimposed on a flat reaction yield, which does not show a strong increase at low energies, in contrast to previous work. These results obviate the need for the hypothesis of absorption under the barrier at least down toE _cm=2.45 MeV. The nuclear and astrophysical aspects of the data are discussed.     

Fusion cross section for 13C + 13C at low energies

The energy dependence of the fusion cross section has been measured over the range E_c.m. = 3.05–6.88 MeV by detecting the γ-rays from residual nuclei in a 4π geometry. Analyzing the 1.37 MeV photopeak, originating from ${}^{24}\text{Mg}\text{1.37}\text{MeV}\text{→}\text{g.s. transition}$, the cross sections for ²⁴Mg+2n channel were also deduced. The measured fusion cross sections have been compared with those for ¹²C + ¹²C and ¹²C + ¹³C systems and found to be significantly different. For ¹³C+¹³C the fusion cross sections agree with the standard optical-model prediction down to the lowest measured energies, while for ¹²C + ¹²C and ¹²C + ¹³C they are, at the lowest energies, too low. It is suggested that the unpaired valence nucleons facilitate fusion at energies well below the Coulomb barrier.     

Accurate determination of the 13C-12C+n spectroscopic factor

We have measured ¹²C-¹³C elastic cross sections at 12 MeV between 40°–140° in 1° steps to ±1%. The observed oscillatory interference between Coulomb scattering and the neutron transfer process is analyzed using exact finite-range DWBA, and a model-independent value of C² = 2.55±0.10 for the asymptotic normalization of the $\text{1}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ neutron wave function in ¹³C is obtained. Using radial wave functions determined by elastic electron scattering the spectroscopic factor is found to be S = 0.81±0.04.     

Measurement of the 11B(11B, 10Be)12C proton transfer reaction at low energies

Differential cross sections for the ¹¹B(¹¹B,¹⁰Be)¹²C proton transfer reaction leading to the ¹⁰Be(g.sO+¹²C(4.43 MeV) $\text{(Q = 0.289}\text{MeV}\text{)}\text{and}{}^{10}\text{(3.37}\text{MeV}\text{) +}{}^{12}\text{C}\text{(g.s.) (Q = 1.36}\text{Me V}\text{)}$ final channels have been measured at E_c.m. = 5.5 MeV by coincident detection of the ¹⁰Be and ¹²C nuclei. The integrated cross sections for the ¹⁰Be + ¹²C(4.43 MeV) channel have been obtained for incident energies between E_c.m. = 2.66 and 3.64 MeV from the yields of the 4.43 MeV γ-ray emitted in the ¹²C 4.43 MeV → g.s. transition. The cross-section magnitudes compare well with the DWBA calculations. The sub-barrier transfer cross sections exhibit an unusual energy dependence: their ratio to the total reaction cross section is decreasing with decreasing incident energy.     

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).     

Detailed energy dependence of the elastic and inelastic12C +12C scattering between 5 and 10 MeV/nucleon

Excitation functions for¹²C+¹²C elastic and inelastic scattering to 2⁺ level have been measured over the energy range 30–60 MeV (cm) by 250 keV steps using the kinematical coincidence method. The intermediate structure resonances disappear aboveE _cm=35 MeV while the broad and irregular structure becomes a general feature of the interaction at higher energies.     

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.     

Formation of covalent nuclear molecules in the 13C + 12C system

Angular distribution's of the elastic scattering of ¹³C on ¹²C and the inelastic scattering leading to the lowest-lying $\text{1}\text{2}{}^{\mathrm{+}}$ and $\text{5}\text{2}{}^{\mathrm{+}}$ states in ¹³C have been measured at energies close to the Coulomb barrier. Analyses carried out in the framework of a complete coupled-reaction-channel theory show that extremely polarized single-particle molecular orbits (hybridization) are formed during the scattering process which give rise to a multiple-step interaction of the valence nucleon, i.e. the formation of a covalent nuclear molecule.     

Coupled-channels analysis of energy-dependent isospin violation in the 12C(d, α)10B(1.74 MeV,T = 1) reaction

We have studied the isospin non-conserving ¹²C(d, α)¹⁰B(1.74 MeV, 0⁺, T= 1) reaction at several incident energies of 9 ≦ E_d ≦ 16 MeV in terms of a coupled-channels method. The reaction processes involved in the present analysis are the successive single-nucleon pick-up processes as well as the inelastic scattering of deuterons from ¹²C. It is assumed that the isospin violation should occur in the intermediate mirror cluster states of ³He + ¹¹B and t + ¹¹C, due to the Coulomb interaction. The calculation reproduces fairly well the observed features of the reaction, i.e. the decreasing cross section with increasing incident energy, and the variation of the angular distribution. We also note that the calculation shows the energy-dependent localization of isospin violation in the angular momentum space, i.e. a specifically narrow localization at the lower incident energies studied and its broadening at the higher energies. This fact is associated with the variation of the angular distribution from a forward-backward symmetry at the lower incident energies to a forward peak at the higher energies.     

High-resolution time-of-flight system for precise measurement of excitation energies and Q-values

A time-of-flight system has been installed for the measurement of accelerator beam energies with an absolute accuracy of 1.5 : 10⁵ as proved by determining excitation energies in ⁶⁰Ni. The first $\text{T=}\text{3}\text{2}$ resonance in ¹²C(p,p)¹²C was measured at E_p=14230.75±0. 20 keV.     

High-resolution proton scattering on 50Ti

Differential cross sections were measured for ⁵⁰Ti(p, p) at four angles for E_p = 1.83 to 2.97 MeV, with an overall energy resolution of about 350 eV. Spins, parities and total widths were extracted for 212 levels. An energy region near E_p = 1.37 MeV was also examined in order to study the analogue of the ground state of ⁵Ti. Coulomb energies and spectroscopic factors were determined for the analogues of the ground and first excited states of ⁵¹Ti. The latter analogue was highly fragmented. The s-wave spacing and width distributions were analyzed and the number of missing levels estimated. The $\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and $\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ proton strength functions were determined.     

A folded diagram microscopic calculation of nuclear Coulomb displacement energies

We have performed a rather extensive microscopic calculation of the ¹⁷F-¹⁷O Coulomb energy differences ΔE_C. Our main purpose has been to study the effects of (i) folded diagrams, (ii) core polarization and (iii) the effects due to different nucleon-nucleon potentials, different single-particle spectra and different radial wave functions. Using a proton-neutron representation we have included higher-order Coulomb corrections like e.g. the coupling of valence particles to collective vibrations of the core.The inclusion of folded diagrams is very important; it is equivalent to a self-consistent treatment of the Q-box starting energies. It causes a significant suppression of the effect due to core polarization, its contribution to ΔE_C becoming small, about 0.03 MeV. As a consequence of this “self-correcting” behavior our results for ΔE_C are quite stable with respect to the choice of different single-particle spectra. Two rather different nucleon-nucleon potentials, the Reid soft-core potential and a meson exchange potential of the Bonn-Jülich group also lead to quite similar results for ΔE_C. In the case of $\text{J =}\text{5}\text{2}{}^{\mathrm{+}}$, for example, Δ_C calculated with the Reid potential ranges, depending on other assumptions, from 3.36 to 3.43 MeV and from 3.36 to 3.40 MeV with the Bonn-Jülich potential: Both are significantly smaller than the experimental value of 3.54 MeV. Optimizing the radial wave functions in the spirit of a Brueckner-Hartree-Fock theory improves the calculated values of ΔE_C for the $\text{J =}\text{1}\text{2}{}^{\mathrm{+}}$ state but not for $\text{J =}\text{5}\text{2}{}^{\mathrm{+}}\text{or}\text{3}\text{2}{}^{\mathrm{+}}$.We feel that other processes such as the explicit inclusion of core deformation or mesonic degrees of freedom or both are needed to explain the Coulomb displacement energies.     

Multiple scattering features in neon ion scattering spectra (ISS) from polycrystalline materials

A systematic investigation of multiple scattering from polycrystalline materials in ion scattering spectrometry was carried out using Ne⁺ at a scattering angle of 90° over the energy range of 100 to 2500 eV. It was found that the intensity of multi scattering shoulders increased with ion beam energy. The intensity at a given energy could be predicted on the basis of interatomic distances of the target. The larger the interatomic distance, the more intense the multi scattering shoulder. The separation of the double scattering shoulder from the binary peak decreased linearly with increasing mass, and the maximum of the shoulder to higher energies from the binary peak could be calculated by the relationship $\text{ΔE}\text{E}{}_0\text{= 0.166 ?(0.00064)M}$, where M is the mass of the target atom.