Effects of channel non-orthogonality in (d,p) reactions

Coupled channel calculations for (d, p) reactions were performed in which a strong coupling between the d and p channels was assumed. Reactions investigated were ¹⁶O(d, p) ¹⁷O(2s) and ⁴⁰Ca(d, p) ⁴¹Ca(2p) at E_d =10.5 MeV and the related (d, d) and (p, p) scattering processes. The nonorthogonality of the d- and p-channels were taken into account. The results of these calculations are presented and are compared with the coupled channel calculations neglecting the channel nonorthogonality and also compared with the DWBA and optical model calculations.     

Simulation of Neutron Reflection from the Surface of a Nanostructured Object in the Modified Kinematic Approximation

The applicability of the modified kinematic approximation for simulation of the specular reflection and the diffraction of a neutron beam from regularly ordered nanostructured objects on the surface and in the surface material layer is analyzed. The obtained results are compared with those of the real experiment and simulation of the distorted-wave Born approximation (DWBA). The influence of various factors on the obtained results is analyzed. These factors include the effect of neutron-wave refraction at the interfaces between media, the spectrometer-resolution function, and renormalization of the results for a nonspecular scattering signal based on data obtained for a specular channel. It is shown that, in many cases, it is possible to obtain rather good agreement with the experimental data and with the results of calculations using DWBA methods and of calculations using the Parratt algorithm.     

Study of (e, 2e) process on potassium at 6 eV—60 eV above threshold in second-order Born approximation

The standard distorted wave Born approximation (DWBA) method has been extended to second-order Born amplitude in order to describe the multiple interactions between the projectile and the atomic target. Second-order DWBA calculations have been preformed to investigate the triple differential cross sections (TDCS) of coplanar doubly symmetric (e, 2e) collisions for alkali target potassium at excess energies of 6 eV-60 eV. Comparing with the first-order DWBA calculations before, the present theoretical model improves the degree of agreement with experiments, especially for backward scattering angle region of TDCS. This indicates that the present second-order Born term is capable to give a reasonable correction to DWBA model in studying coplanar symmetric (e, 2e) problems in low and intermediate energy range.     

Spectroscopy of low-lying positive parity states in 30P from the study of the reaction (3He,d) at 14.0 MeV

The reaction ²⁹Si(³He, d)³⁰P was studied at an incident energy of 14.0 MeV. Spectroscopic strengths for 14 positive parity states up to an excitation of 4.50 MeV have been obtained using DWBA analysis. The incident channel optical-model parameters for the DWBA calculations were extracted from elastic scattering cross sections measured also at 14.0 MeV.     

Post collision interactions and polarization effect in (e, 2e) collisions of helium

A modified distorted-wave Born approximation (DWBA) method is used to calculate the triple differential cross sections (TDCSs) in a coplanar asymmetric geometry for the electron impact single ionization of a He (1s²) atom at intermediate and lower energies. The post-collision interaction and the polarization effect in (e, 2e) collisions of helium are considered in the calculations. The polarization potentials from the damping method and density functional theory (DFT) are compared. Theoretical results are compared with the recent experimental data.     

Non-orthogonality and overcompleteness in direct nuclear reactions

When rearrangement reactions are too strong to be treated by a one-step DWBA, they must be described by coupled reaction channel (CRC) equations or by a multistep DWBA derived from them. The derivation of these equations requires the use of projection operators on subspaces which are in general not orthogonal and which may be linearly dependent. We consider the case of many coupled two-cluster channels, and show how solving the non-orthogonality kernel to give an orthogonalized CRC formally simplifies the structure of the equation and clarifies the relations between different methods, including connected kernel approaches. We use the requirement that the distorted Faddeev (N = 3) or LBRS equations (general N) be satisfied in the two-cluster model space. We demonstrate that this determines the distortion potentials and that the resulting pole approximation yields the orthogonalized CRC equations. A modified one- and two-step DWBA is written in which non-orthogonality corrections are summed to all orders in each step. Methods of generating the non-orthogonality correction operator are discussed.     

Improved eikonal approach for charge exchange reactions at intermediate energies

In order to describe charge exchange reactions at intermediate energies,we implemented as a first step the formulation of the normal eikonal approach.The calculated differential cross-sections based on this approach deviated significantly from the conventional DWBA calculations for CE reactions at 140 MeV/nucleon.Thereafter,improvements were made in the application of the eikonal approximation so as to keep a strict three-dimensional form factor.The results obtained with the improved eikonal approach are in good agreement with the DWBA calculations and with the experimental data.Since the improved eikonal approach can be formulated in a microscopic way,it is easy to apply to CE reactions at higher energies,where the phenomenological DWBA is a priori difficult to use due to the lack,in most cases,of the required phenomenological potentials.     

Quantum mechanical treatment of electron-positron excitations in heavy ion collisions with nuclear contact

A general theory is formulated of electron-positron excitations in heavy ion collisions with nuclear contact, treating the nuclear relative motion quantum mechanically. A set of coupled channel equations for the electronic occupation amplitudes is derived, which is formally very similar to the semiclassical theory based on a classical nuclear trajectory, and reduces to the latter in the JWKB approximation. The new coupled equations contain all the quantum mechanical information on the details of the nuclear scattering during nuclear contact. The importantce of this formulation for a quantitative theory of spontaneous positron creation in supercritical systems with nuclear time delay is pointed out. The possibility of line structures in the positron spectrum, as predicted semiclassically and recently discovered experimentally, is discussed in the framework of the DWBA approximation. For light-particle scattering off a nuclear resonance, the Blair formula for vacancy production is recovered in the same approximation.     

Sequential calculations for heavy-ion induced two-nucleon transfer on 14N, 15N and 16O

¹¹B and ¹³C induced two-nucleon transfer data on ¹⁴N, ¹⁵N and ¹⁶O are compared with exact finite-range sequential transfer calculations. The data appear to be consistent with this reaction model and the assumed shell-model structure of the states populated. Single-nucleon transfer data on these targets is also analyzed using the DWBA. Modifications to the exit channel optical potential are required to obtain agreement with shell-model spectroscopic factors.     

Magnetic sub-state population cross sections in inelastic alpha-nucleus scattering

Properties of the sub-state population cross sections σ_M for inelastic α-nucleus scattering are explored within the deformed collective nuclear model. The interference between the nuclear and Coulomb parts of the inelastic transition potential is calculated with the DWBA. The effect on the M = ?2 sub-state cross section is substantially more pronounced than that for the usual inelastic differential cross section Σ_mσ_m. The effect of re-orientation terms is calculated by means of a coupled channel formalism for small values of the quadrupole deformation parameter β₂. It is found to shift the angular position of the minima of the σ_M relative to the DWBA result, in a way which depends on the sign of β₂. A spin orbit potential has only a small effect on the σ_M. The calculations refer to 15 MeV α-particles incident on a nucleus of the size and charge of Ca.     

Elastic and inelastic scattering of 16O and 12C by 24Mg near the Coulomb barrier

Angular distributions for ¹⁶O + ²⁴Mg and ¹²C + ²⁴Mg elastic and inelastic (2⁺, 1.37 MeV state in ²⁴Mg) scattering have been measured at energies spanning the Coulomb barrier. Apart from the structure typical of strong destructive Coulomb-nuclear interference, the data exhibit some additional specific features. Coupled channel calculations were performed, along with DWBA calculations to analyse the data using fixed coupling strengths deduced from the results of Coulomb excitation work. The importance of higher-order effects such as reorientation, is demonstrated.     

Microscopic (p,p′) calculations and polarization charges with large basis shell-model wave functions

Techniques have been developed for performing microscopic model DWBA calculations of inelastic nucleon-nucleus scattering using large basis shell-model wave functions to describe the nuclear states involved. For the case of ¹³⁸Ba at a bombarding energy of 30 MeV, we obtain good fits to the data by including the exchange amplitude in the DWBA and assuming a state and multipole independent polarization charge.     

Proton spin flip at 12 MeV for nuclei near the neutron shell closure, N = 28

Spin-flip angular distributions for the nuclear pairs ^{48, 50}Ti and ^{54, 56}Fe have been measured using the (p, p'γ) correlation method. These data are compared to collective model DWBA calculations using a distorted spin-orbit potential of the full Thomas form. The spinflip angular distribution data for ⁵⁴Fe exhibit two peaks of nearly equal magnitude while the data for ⁵⁶Fe and ^{48, 50}Ti more closely resemble the usual single large peak at back angles predicted by DWBA calculations.     

Study of （e, 2e） process on potassium at 6 eV-60 eV above threshold in a second-order Born approximation

The standard distorted wave Born approximation(DWBA) method has been extended to second-order Born amplitude in order to describe the multiple interactions between the projectile and the atomic target.Second-order DWBA calculations have been preformed to investigate the triple differential cross sections(TDCS) of coplanar doubly symmetric(e,2e) collisions for the alkali target potassium at excess energies of 6 eV-60 eV.Compared with the previous first-order DWBA calculations,the present theoretical model improves the degree of agreement with experiments,especially for the backward scattering angle region of TDCS.This indicates that the present second-order Born term is capable of giving a reasonable correction to the DWBA model in studying coplanar symmetric(e,2e) problems in low and intermediate energy ranges.     

M_(αβ) X-ray production cross sections of Pb and B iby 9–40 keV electron impact

The experimental data of Mαβ X-ray production cross sections for Pb and Bi by 9–40 keV electron impact have been given. Thin films with thick carbon substrates are used in the experiment. The effects of target structure on the Mαβ X-ray production cross sections are corrected by using the Monte Carlo method. The corrected experimental data are compared with calculated cross sections in terms of the distorted-wave Born approximation(DWBA) theory. The measured Mαβ X-ray production cross sections for Pb and Bi are lower than the DWBA calculations. The atomic relaxation parameters used in comparing the DWBA values with experimental results affect the degree of difference.     

Large-angle 6Li + 28Si elastic and inelastic scattering at 27 and 34 MeV

Elastic and inelastic scattering data extending to θ_c.m ≈ 175° are reported for ⁶Li + ²⁸Si at 27 and 34 MeV. Optical model analyses of the elastic data were made using a variety of real potential forms. The large-angle data cannot be fitted with a Woods-Saxon real potential, but are well described by Woods-Saxon squared, double-folded or Fourier-Bessel potentials. The real potential is the same at both energies, but the imaginary potential is weaker at 27 MeV. The inelastic data were analyzed using the DWBA and coupled channels techniques with folded real form factors and deformed Woods-Saxon imaginary potentials, with the deformations taken from electron scattering. The 2⁺ state was fitted well at both energies with the DWBA, while the prediction decreased too rapidly at large angles for the 4⁺ state. The large-angle 4⁺ data were better described when two-step excitations were included in the coupled-channels calculations. The forward-angle 2⁺ data are sensitive to the interference between Coulomb and nuclear scattering and show that the nuclear and Coulomb deformation parameters β₂ are equal for this transition.