G.R. Satchler

On the “distribution of barriers” interpretation of heavy-ion fusion

Abstract The significance of the interpretation of heavy-ion fusion cross sections in terms of a distribution of potential barriers is discussed. The smoothing due to the quantal barrier penetration is shown to replace a set of discrete barriers by an effective continuous distribution. It is shown how this smoothed distribution may be obtained rather directly from the measured cross sections at near-and sub-barrier energies.

Causality and the threshold anomaly of the nucleus-nucleus potential

Abstract According to the causality principle, a scattered wave cannot be emitted before the arrival of the incident wave. This principle implies the existence of a dispersion relation between the real and the imaginary parts of the optical potential. We discuss the difference between the dispersion relations which hold for nucleus-nucleus scattering on the one hand and for nucleon-nucleus scattering on the other hand. In the case of nucleus-nucleus scattering, the dispersion relation predicts that the modulus of the real part of the optical potential has a bell-shaped maximum, as a function of energy, when the imaginary part approaches zero, i.e. for energies near the top of the Coulomb barrier. The shape of this apparent anomaly is investigated in the framework of several models. It is shown that there exists an algebraic model which is at the same time simple and sufficiently accurate in the sense that the difference between its outcome and that of more realistic models is smaller than the uncertainties introduced by the assumptions which have to be made. Various systems are discussed, in particular 16 O + 280 Pb and α + 40 Ca. Several implications of the anomaly are pointed out, including its effect on the sub-barrier fusion of two heavy ions.

Folding-model analysis of elastic and inelastic α-particle scattering using a density-dependent force

Abstract A folding model with a density-dependent form of the semi-realistic M3Y effective interaction is applied to α-particle scattering. A previous analysis of elastic scattering at 140 and 172 MeV is now applied to data at other energies from 25 to 120 MeV. The model is also extended to inelastic scattering, using both the collective model and a valence-plus-core-polarization model for the transition densities. The proton transition densities were normalized to measured B (E L ) values. When necessary, the neutron transition densities were rescaled to fit the (α, α′) data, providing a source of information on the neutron contributions. The neutron transition multipole moments thus obtained are compared to those derived from (p, p′) data at 800 MeV, as well as from other sources.

Folding model analysis of α-particle elastic scattering with a semirealistic density-dependent effective interaction

Abstract Differential cross sections for the elastic scattering of α-particles from 40Ca, 46,48,50Ti, 58Ni, 90Zr and 208Pb at 140 MeV and from 58,60,62,64Ni at 172 MeV are analysed using a double-folding model with a semirealistic density-dependent effective interaction based on the M3Y interaction for the real potential and various phenomenological imaginary potentials. Very good fits with consistent parameters of the model have been obtained. The application of the folding model analyses of α-particle elastic scattering to the determination of the nuclear matter density distribution is critically examined.

A density-dependent interaction in the folding model for heavy-ion potentials☆

Abstract The real parts of the optical potentials for heavy-ion scattering were calculated in a folding model using a density- and energy-dependent generalization of the M3Y interaction that was calibrated against a realistic reaction matrix. The resulting potentials must be reduced by factor of N D ≈ 0.8 to fit “low” -energy data, and N D ≈ 0.6 to fit 40 Ar data at 44 MeV per nucleon. This is inconsistent with the renormalization of N D = 1.3 required for the same interaction when applied to α-particle scattering over the same energy range. The effects of the density dependence on the shape of the potential are discussed.

Isospin and macroscopic models for the excitation of giant resonances and other collective states

Abstract Recently there has been some confusion over the excitation of “isovector” giant resonances by isoscalar probes. We present a unified theoretical description of macroscopic models that may be used to calculate the excitation of giant resonances by inelastic scattering so as to clarify this and related questions. Particular attention is given to the relative phase of the Coulombic and hadronic contributions. After describing models for the transition densities that are based upon certain sum rules, a folding model and a deformed optical potential model for the transition potentials are discussed. Applications are made to some examples of inelastic α-particle scattering and the two models are compared. Folding yields cross sections for the breathing-mode monopole resonance that are smaller than those from the potential model by almost a factor of two, so that the measured values appear to require more than 100% depletion of the sum rule. It is suggested that this might be due to neglect of density dependence in the effective interaction.

Nuclear rainbows and heavy-ion scattering

Abstract We discuss refractive effects on scattering in the presence of strong absorption, and conclude that a residuum of a true nuclear rainbow has been seen only for light ions. Such a rainbow seems to be unlikely for heavy ions because of their stronger absorption. Nonetheless, the structureless falloff in angular distribution that has been observed in some heavy-ion measurements to follow a “Fraunhofer crossover” region of diffraction oscillations indicates that the farside scattering amplitude has become dominant at these larger angles. This “farside tail” itself is a refractive effect and its observation already carries important information on the optical potential.

Radial and energy dependence of the dispersive contributions to the α + 16O and α + 40Ca potentials near the threshold anomaly

Abstract Previous work on the application of a dispersion relation to the energy dependence of the strength of the nucleus-nucleus potential near the threshold anomaly is extended to the radial shape, and the energy dependence, of the dispersive contribution to the real potential. The shape is studied both explicitly and in terms of radial integrals, including one with a gaussian weight factor. Detailed applications are made to the optical potentials for the scattering of α-particles by 16 O and 40 Ca.

Local potential model for pion-nucleus scattering and π+π− excitation ratios☆

Abstract Local potentials of Woods-Saxon shape are introduced to describe the elastic scattering of pions from the nuclei 40,48 Ca, 58 Ni, 90 Zr, 118 Sn and 208 Pb at energies in the 100–300 MeV range. Good fits to the measurements are easily obtained and potential ambiguities are discussed. The optical potentials are then applied, using the deformed-potential prescription and independent information on B (E2) and B (E3) values, to inelastic scattering exciting the lowest 2 + and 3 − collective states of these nuclei, as well as the giant quadrupole resonances. This procedure is parallel to that used in the analysis of scattering data for other hadrons. Sufficiently good agreement with experimental data is obtained to establish the validity of this approach for pions also. Remaining discrepancies are similar to those found when using a more microscopic and nonlocal approach. In particular, our semi-empirical method does not change the apparently anomalous M n M p ratios for the giant resonances deduced from comparisons of π + and π − scattering. These discrepancies are discussed in detail, and in relation to results obtained using other hadronic probes. We suggest that they arise from uncertainties in the data rather than in deficiencies in our understanding of the scattering.

Asymmetric deflection functions and the extinction of rainbows: A comparison of α-particle scattering from 40Ca and 44Ca

Abstract A decomposition of elastic scattering amplitudes into their nearside and farside components is employed to exhibit the presence of a striking farside (“nuclear”) rainbow in the angular distributions for α + 40 Ca scattering at energies from 36 to 61 MeV. The rainbow is identified by a deep “Airy minimum” which is present in the farside components of the angular distributions throughout this energy region. Over the same energy range, the angular distributions for the more absorptive α + 44 Ca scattering exhibit no Airy minima, and, in this sense, show no nuclear rainbow. However, a steepening of the slope of their smooth farside component, which appears at energies above that (∼60 MeV) for which the rainbow angle for α + 40 Ca becomes less than 180°, may serve to identify a residual rainbow effect, even in α + 44 Ca, at energies above 60 MeV. The manner in which the Airy minima of this and other nuclear rainbows are extinguished by absorption is examined in detail and is found to depend critically on the asymmetry in the shape of their deflection functions at low energies.