Interpretation of rare-gas-induced broadening of Rydberg series lines

Approximate expressions have been derived for the cross-sections of rare-gas-induced broadening of the Rydberg series lines on the basis of the interatomic potential which is expressed as a combination of the van der Waals potential, the Fermi potential and the polarization potential. Only the effect of elastic scattering has been taken into account. Multichannel (two-channel) quantum defect theory has been combined with the broadening theory to include the effect of the mutual interaction of the Rydberg series. The resulting cross-sections are in reasonable agreement with the experimental values obtained for Na by Kachru et al. and for Ca and Ba by Ueda et al.     

Microscopic derivation of a complex heavy ion potential

The energy dependence of a complex heavy ion optical potential is derived in Brueckner Hartree Fock using a local density approximation and a selfconsistent single particle spectrum. The two ions are described by an antisymmetrized cluster model wavefunction. Both real and imaginary part are found to increase with energy. Results are given for the elastic scattering of ⁴⁰Ca+¹⁶O.     

Variable-phase method in positron-hydrogen elastic scattering

The elastic scattering of a positron by a hydrogen atom is studied by using the variable-phase approach to potential scattering. Values of the scattering length and the elastic scattering phase shifts obtained in the (i) static, (ii) polarization and (iii) extended polarization approximations for the e⁺?H interaction are found to be in close agreement with the results of earlier workers.     

Two-particle transfer contributions to elastic and inelastic heavy ion scattering

The contributions of two-particle transfer to elastic and inelastic scattering of heavy ions are treated simultaneously in the coupled channels framework using microscopic transfer form factors. As an example, the reaction ¹⁸O(¹⁶O, ¹⁶O)¹⁸O(g.s. and 2₁⁺) is investigated at three energies near the Coulomb barrier. The interference between scattering and transfer leads to a consistent interpretation of both elastic and inelastic data. Indirect transfer contributions give relatively small, but non-negligible corrections to the direct scattering plus transfer result, removing a previously reported energy dependence of the spectroscopic factor.     

Nucleus-nucleus scattering in the high-energy approximation and optical folding potential

A microscopic complex folding-model potential that reproduces the scattering amplitude of Glauber-Sitenko theory in its optical limit is obtained. The real and imaginary parts of this potential are dependent on energy and are determined by known data on the nuclear-density distributions and on the nucleon-nucleon scattering amplitude. For the real part, use is also made of a folding potential involing effective nucleon-nucleon forces and allowing for the nucleon-exchange term. Three forms of semimicroscopic optical potentials where the contributions of the template potentials—that is, the real and the imaginary folding-model potential—are controlled by adjusting two parameters are constructed on this basis. The efficiency of these microscopic and semimicroscopic potentials is tested by means of a comparison with the experimental differential cross sections for the elastic scattering of heavy ions ¹⁶O on nuclei at an energy of E ～ 100 MeV per nucleon.     

The effect of electron-spin uncoupling on differential scattering cross sections for excited alkalirare gas systems

We have measured differential cross sections for the scattering of laser-excited Na(3² P _3/2) by Ne. The rapid oscillations in the experimental scattering patterns measured at high angular resolution cannot be explained semi-classically on the basis of the elastic approximation. We therefore apply a collision model proposed by MasnouSeeuws et al. [1] which takes into account the partial uncoupling of the electron-spin from the orbital angular momentum. The results obtained with this model are — for the first time — compared quantitatively with the result of a fully quantummechanical close-coupling calculation and with our experimental data. In both cases good agreement is found. This proves that the observed oscillatory structure is strongly influenced byΠ-∑ interferences which — due to spin uncoupling — do not cancel even if the scattering signals are summed over all final fine-structure states. Our semi-classical analysis is also applied to the Na(3² P _1/2)-Ar and K(4² P _3/2)-Ar scattering experiments reported by Düren et al. [2, 3]. The agreement with regard to the frequency of the oscillatory structure indicates that here too spin uncoupling causes theΠ-∑ interferences to appear in the differential cross sections.     

Elastic neutron transfer in the scattering of Si isotopes

Angular distributions of the elastic scattering of ²⁸Si on ²⁹Si and ³⁰Si have been measured for incident beam energies at E = 65 and 70 MeV with a time-of-flight spectrometer for heavy ions. At 70 MeV the neutron transfer ³⁰Si(²⁸Si, ²⁹Si)²⁹Si was observed in addition to the elastic channel. The pronounced oscillations in the elastic scattering distributions are interpreted as being due to an elastic transfer of neutrons between the colliding nuclei during the scattering process. This assumption is in accordance with some general features of the data and allows for the extraction of spectroscopic factors of the transferred neutrons.     

Generalized fresnel model for very heavy ion scattering: (III). Dynamic polarization effects

It is shown that the large deviations from the typical Fresnel shape of heavy ion angular distributions, observed recently in the elastic scattering from deformed nuclei, can be described quite adequately by a very simple modification of the closed formulae for the differential cross section ratio $\text{gs(θ)}\text{σ}{}_{\mathrm{R}}\text{(θ)}$ of the generalized Fresnel model presented in parts I and II of this work. Our treatment rests basically on the relatively long range of the dynamic polarization potential that describes the Coulomb excitation to which the large deviations from the normal Fresnel pattern are attributed. We also calculate the effects of nuclear coupling in an adiabatic approximation and show that these lead to another modification, this time of the damping function F(z), which is however much smaller than that for Coulomb excitation and hardly discernible in angular distributions for very heavy ion scattering.     

On the theory of elastic scattering of heavy ions with identical cores

Starting from a two-potential formula for the elastic scattering T-matrix of two heavy ions with identical cores, a DWBA treatment is obtained. This approach is compared with the LCNO theory; differences and similarities are discussed. An analysis of the ¹²C + ¹³C and ²⁸Si + ²⁹Si elastic scattering is given and shows good agreement with the data.     

Symmetry analysis in neutron diffraction studies of magnetic structures: 5. Polarization effects in the scattering of neutrons by magnetic structures

It is shown that both the cross section of elastic scattering by a magnetic structure and the polarization vector of the scattered neutrons beam are described by a set of complex axial vectors M^L. They depend on the vectors of atomic magnetic moments in a primitive cell of the crystal and the wave-vector star of the magnetic structure. Particularly, the intensity of a magnetic Bragg reflection and the polarization vector of the scattered beam of that reflection are determined only by a vector M^L connected with an arm star contribution of the magnetic structure and corresponding to the wave vector k_L of a star {k}. A single magnetic reflection allows one to determinean arm contribution of the magnetic structure if one uses polarization effects and an expansion of the magnetic structure over the basis functions of the irreducible representation of the crystal space group. In the general case minimal number of necessary reflections for the total determination of a magnetic crystal is equal to the arm number of the wave-vector star. All analyses here have been done for the single domain magnetic structure. The polarization phenomena will not be observed for many cases where there is a uniform distribution of domains.     

Fusion excitation function measurements for the 16O+58Ni and 16O+62Ni systems

High precision fusion excitation functions have been measured for the ¹⁶O+⁵⁸Ni and ¹⁶O+⁶²Ni systems from which fusion barrier distributions have been evaluated. Coupled-reaction-channels (CRC) calculations, which describe elastic and quasi-elastic scattering, also satisfactorily reproduce the fusion cross sections and barrier distributions. The small value of Z₁Z₂ in this case leads to barrier distributions with relatively little structure. However, in conjunction with the detailed elastic scattering data for these systems, this allows us to elucidate the role of previously ignored states in ¹⁶O in pushing the entire distribution to lower energies. These shifts are consistent with derived magnitudes of polarization potentials for both systems.     

Elastic scattering of an electron by the negative lithium ion

In the framework of the many-body theory, the differential and total cross sections of elastic scattering of slow electrons by the negative lithium ion Li⁻ are obtained. Calculations are performed both in the Hartree-Fock single-particle approximation and with regard to many-electron correlations, which take into account the dynamic polarization of the core. Features observed in the behavior of the phases and cross sections for p and d partial waves are associated with resonance scattering of electron waves. Considering the dynamic polarization of the core by an incident electron heightens the diffraction character of the scattering. The real process is compared with particle scattering in models with a repulsive potential.     

Energy dependence of the optical model parameters for 3He ions scattered from 40Ca and 58Ni

The differential cross sections for the elastic scattering of ³He ions on targets of ⁴⁰Ca and ⁵⁸Ni have been measured at incident energies of 27.7, 51.4, 73.2 and 83.5 MeV. The results of optical model analyses showed that only one unique potential (J_R ≈ 330 MeV · fm³) with a surface absorptive term can provide acceptable fits to the large angle elastic scattering cross sections at 83.5 MeV. The particular geometrical set found at 83.5 MeV could not, however, give an adequate fit to the data with energy less than 40 MeV. Subsequent analyses indicated that a break in the energy dependence of the real potential is observed for the low energy data. Explicit energy dependent terms were obtained by fitting all the data simultaneously. These phenomenological potentials were also compared with the folded nucleon-nucleus potential. The influence of the α-particle channels on the elastic scattering of ³He ions at 83.5 MeV was also examined.     

Microscopic optical model analysis of elastic scattering cross sections for nucleon-40Ca systems at low energy

Neutron and proton-⁴⁰Ca elastic scattering angular distributions and total reaction cross sections are calculated between 10 and 40 MeV using the microscopic optical potential derived by Bouyssy et al. within the nuclear structure approach. Direct comparison with experiment confirms that our calculation reproduces the imaginary potential at low energy for protons, but it gives insufficient absorption above the deuteron pick-up threshold. A renormalization of both the real and the imaginary parts of the potential leads to good agreement with the data. For both parts of the potential this renormalization is compatible with the renormalization factors obtained by Bouyssy et al. from a comparison of calculated and phenomenological volume integrals.     

Semiclassical treatment of heavy ion elastic scattering

A generalized semiclassical treatment for the elastic scattering of heavy ions is developed in the presence of a complex optical potential. The scattering phase shift and its derivatives with respect to the impact parameter are calculated after extending the JWKBL approximation. The results are compared with experimental data for the elastic scattering of¹⁶O from medium and heavy target nuclei and relation between the present treatment and that of the optical model and Regge pole analysis is established     

Elastic and inelastic scattering of 79.5 MeV 11B and 87.5 MeV 10B ions

The elastic scattering of 79.5 MeV ¹¹B ions has been studied for seven targets ranging in mass from ²⁴Mg to ¹⁹⁷Au and of 87.5 MeV ¹⁰B ions for three of these targets (^{24, 25}Mg, ⁶⁰Ni). Angular distributions were measured from ~10° c.m. in steps of 0.5°, to angles beyond 40° c.m. where the elastic cross sections are ? 10^?3 of the Rutherford values (except for ¹⁹⁷Au). Inelastic data for exciting the lowest 2⁺ states of ^24,26Mg and ⁶⁰Ni were also obtained. Important odd-A-even-A differences are observed in the ¹¹B elastic angular distributions for the Mg and Al targets; for ¹⁰B scattering these are obscured by projectile quadrupole moment effects on the elastic scattering. The elastic data were analyzed using the optical model with potentials of both Woods-Saxon and double-folding form. The data for both ¹⁰B and ¹¹B are consistent with the potential obtained in the folding model with the M3Y interaction without renormalization. The inelastic data were analyzed by the distorted-waves method.     

On semi-quantal approximations to heavy-ion scattering

The coupled-channel equations for heavy-ion scattering are approximately solved in a closed form, in the context of semi-quantal approach. Our solutions are shown to contain dynamic polarization potentials (arising from two and/or multi-step processes) in a natural way. A closed form treatment, of the effects of dynamic polarization by Coulomb excitation, on the elastic scattering of deformed heavy-ions is also presented. As an example, we compare our results for quadrupole Coulomb excitation of¹⁸⁴W ions by¹⁸O ions at 90 MeV, with those obtained from optical model treatments.     

The contribution of nuclear inelastic excitation to the optical potential for heavy ions

Using the plane-wave approximation we derive analytical expressions for both the real and imaginary parts of the polarization potential arising from nuclear inelastic scattering. These potentials and the resulting elastic and inelastic cross sections are compared with exact coupledchannel calculations for ¹³C on ⁴⁰Ca at 68 MeV. The agreement, for the most part, is good. We also briefly discuss the numerical non-local potentials for this system and the imaginary polarization potential for ¹⁶O on ²⁰⁸Pb at 104 MeV.