Medium energy cluster knock-out reactions on 6Li and their interpretation in terms of distorted waves

The ⁶Li(d, 2d)⁴He and ⁶Li(d, dα)²H reactions were performed at 27 MeV. Analyses of these and the 42.8 and 55 MeV ⁶Li(α, 2α)²H reactions were performed using distorted wave and plane wave impulse approximations. The kinematic and potential coupling approximations to final state three-body Schrödinger equation and the post and prior form approximations to off-shell scattering cross section were studied for the three reactions. It was found that only the kinematic coupling and post form approximations could be used for the consistent analyses of the three reactions. The effects of distortions and localization of the reactions were investigated. Manifestations of deuteron cluster deformation were noticed in the analyses of the three reactions.     

The optical potential for 6Li-6Li elastic scattering at 156 MeV

Elastic scattering of ⁶Li from ⁶Li has been studied for a beam energy of 156 MeV. The experimental differential cross sections have been analysed on the basis of the optical model using various phenomenological forms. The spin-orbit interaction proves to be less significant. A semimicroscopic double-folding cluster model which generates the real part of the optical potential by an antisymmetrized dα cluster wave function of ⁶Li and αα, dd and dα interactions is well able to describe the experimental data.     

Neutron transfer reactions with very heavy ions

We have studied neutron transfer reactions induced by ¹³²Xe on three rare-earth targets at $\text{E}\text{V}{}_{\mathrm{C}}\text{～ 1.1}$. By using particle-particle-γ coincidence techniques we were able to identify final products and states populated in the one- and two-neutron reactions.The dependence of the transfer probabilities on the distance of closest approach is discussed in terms of effective penetration factors. The results seem to indicate the importance in two-neutron transfer of intermediate states with ? 6 MeV of excitation energy. The effect of excitation energy on the enhancement of the two-neutron transfer is discussed. A qualitative interpretation of the spin dependence of the one-neutron γ-ray yields in terms of the spatial localization of the wave functions involved is given.     

The γ-decay of two-particle states in 210Bi

The γ-decay of excited states in ²¹⁰Bi up to 3330 keV excitation energy has been studied using the ²⁰⁹Bi(d, pγ)²¹⁰Bi reaction. From the observed decay scheme, tentative J^π values are made for 25 states. The excitation energies, (d, p) strengths and decay branching ratios of these states are compared with those calculated using the two-particle shell-model wave functions of Kim and Rasmussen and Kuo and Herling.     

States of 74Ge via the (p,p') inelastic scattering at 22 MeV

The ⁷⁴Ge(p, p') inelastic scattering has been studied at 22 MeV with an overall resolution of 10 keV using a tandem Van de Graaff and a split-pole magnetic spectrometer. Angular distributions have been obtained for about 40 levels in ⁷⁴Ge and comparisons with DWBA and CCBA calculations have allowed spin and parity assignments. The presence of an important collective component in the wave functions of many levels is required in order to explain the data. Possible unnatural-parity levels are populated.     

Proton occupation numbers for Ca

The (d, ³He) proton pickup reaction on ⁴⁴Ca has been studied at a deuteron energy of Ed = 19.0 MeV using the Minnesota MP Tandem Van de Graaff. Differential cross sections were measured at forward angles and spectroscopic factors were extracted in the usual fashion for the transitions to five states of ⁴³K. The results are compared with previous proton pickup and stripping reactions on the even Ca isotopes. Only about half of the sd hole state excitation strength observed in the stripping reactions could be found in the pickup from the fp orbitals if the data are analyzed by standard distorted wave calculations. This discrepancy can be removed by using bound state potential radii which are slightly larger for sd orbitals than for fp orbitals.     

A study of the nucleus 107Ag in the core-excitation model with the (p,t) and (τ, d) reactions

The ¹⁰⁷Ag residual nucleus was studied in the core-excitation model using the (p, t) and (τ, d) reactions. The L, J, π of levels between 0.0 and 2.25 MeV was deduced from the combined reactions. The octupole state observed at 2.19 MeV in other experiments was resolved in (p, t) into a triplet of states at 2.182, 2.203 and 2.229 MeV; octupole strength was observed in (p, t) over a range from 1.144 to 2.229 MeV. Core-excitation wave functions for the quadrupole 2⁺ and 2'⁺ vibration doublets of ¹⁰⁷Ag were constructed using electromagnetic data. These wave functions, combined with data from the ¹⁰⁸Pd(p, t) core reaction, effectively reproduced the ¹⁰⁹Ag(p, t) differential cross sections to these states. The ground-state L = 0 transfer in (p, t) to ¹⁰⁷Ag was only 0.752±0.113 as strong as the corresponding transfer to ¹⁰⁶pd. this is an unexpectedly large blocking effect for an unpaired proton to exert upon a neutron-transfer reaction. An apparent dependence of the (p, t) angular distributions to states of ¹⁰⁷Ag built upon the same core excitation was observed, depending upon the J of the final state.     

Comments about the stark effect on the energy levels of f9-electrons in cubic crystal fields

Effects of free ion wave functions and J-admixture, on the Stark split energy levels of f⁹ electron systems in cubic environments are studied. This is done by working out the example of Dy³⁺ ion in the CaF₂ matrix. It is shown that while the effect of free ion wave functions is rather small, the J-admixture has a larger effect on the Stark split levels.     

Experiment and theory for the 2H(e,p)e′n reaction

Differential cross sections and angular distributions of protons from the ²H(e, p)e′n reaction have been measured at four incident electron energies. The proton angular distributions were measured with the neutron-proton relative energy approximately constant, and an 85° differential cross section was measured as a function of the incident electron energy. The electrodisintegration cross section was calculated using the Hulthén wave function for the ground state with a plane wave for the final state. Reasonable agreement between experiment and theory is found.     

Sub-Coulomb transfer reactions on 208Pb with carbon and oxygen projectiles

Single-neutron transfers induced by ^{12, 13}C and ^{16, 17, 18}O projectiles on ²⁰⁸Pb and the ¹²C(¹⁷O, ¹⁶O)¹³C reaction have been studied at energies close to the Coulomb barrier. These processes are well described by the distorted-wave Born approximation. Coupled-channels effects are found to be small. Normalization factors have been determined for all projectile and target transitions, and also for the triton-deuteron overlap by comparison with previous measurements of the ²⁰⁸Pb(d, t)²⁰⁷Pb reaction. The root-mean-square (rms) radii of single-particle neutron wave functions in ²⁰⁸Pb and ²⁰⁹Pb were calculated using known spectroscopic factors. The distribution of the point neutron excess density in the surface region of ²⁰⁸Pb has been derived and its rms radius determined to be 5.93 ± 0.13 fm with a local potential model. This is in good agreement with theoretical predictions, but is considerably larger than estimates based on Coulomb energy differences. The phenomena of core polarisation by the odd particle or hole outside ²⁰⁸Pb is discussed using the single-particle orbitals determined in this work.     

Meson-exchange currents in thermal n-3He radiative capture

The cross section for radiative capture of thermal neutrons by ³He arising from 1π, 1ρ and 1ω meson-exchange processes is calculated using oscillator and exponential wave functions for ³He (including a D-wave component) and oscillator wave functions for ⁴He (also including a D-wave component). A correlation function with a range of 0.25 fm is incorporated in the wave function to describe the short-range behaviour. Results are sensitive to the assumed range of the correlation function and to the triplet scattering length in the neutron scattering wave function, which are not known accurately. For a reasonable set of parameter choices, a combination of one-body impulse approximation (between D-states) and two-body meson-exchange current processes can explain the entire experimental cross section.     

Retardation of E1 transitions and the neutron effective charge in 29Si

The effect of the giant dipole resonance on E1 transition rates is investigated, and an expression is derived which allows E1 effective charges to be calculated using the γ-absorption cross section of the neighbouring even-mass core. It is shown how this expression can be approximated using a sum rule in cases where the absorption cross section is not adequately known. Application is made to ²⁹Si; using wave functions from a particle-core model, calculated E1 transition rates are in excellent agreement with experiment.     

Wave packet splitting and zitterbewegung in two-dimensional semiconductor structures with spin-orbit coupling

Dynamics of electron wave packets in an asymmetric quantum well in the presence of Rashba spinorbit coupling was analytically and numerically studied. Electron Green’s functions were introduced and the evolution of 1D and 2D wave packets was studied. The effect of packet splitting caused by the presence of two branches with different chiralities in the Rashba Hamiltonian spectrum and zitterbewegung, i.e., packet center’s jitter, was studied. Spatial components of the spin density were calculated. It was shown that the component of the spin density S _y in split parts of the wave packet has opposite signs, and two other spin density components oscillate in space between scattering packets.     

The deuteron breakup reaction induced by protons of 65, 85 and 100 MeV

Coplanar energy sharing spectra for p + d breakup at 65, 85 and 100 MeV proton bombarding energies were measured using the University of Maryland sectored isochronous cyclotron, by measuring the energies of either two protons or one proton and one neutron in coincidence. The detector angles were chosen to enhance either the p-p or p-n quasifree scattering, or the p-n final state interaction. The energy dependence of the peak cross section at equal symmetric quasifree scattering angle pairs was extracted for the ²H(p, 2p)n and ²H(p, pn)p reactions. Quasifree angular distributions were obtained for the reaction ²H(p, 2p)n at 65 MeV and for the reaction ²H(p, pn)p at 65, 85 and 100 MeV. The plane wave impulse approximation theory can only qualitatively reproduce the shape of the quasifree scattering peak in the energy sharing spectra and the shape of the p-p quasifree angular distribution. The discrepancies observed between the plane wave impulse approximation theory and the experimental data imply that the presence of the spectator particle (i.e., the multiple scattering effects) has a strong influence on the magnitude and the shape of the experimental results. Multiple scattering calculations were carried out in the three-body model of Aaron, Amado and Yam except that the S-wave separable two-body amplitudes were modified to fit two-nucleon elastic scattering data at higher energies. Comparisons of the results of these multiple scattering calculations to the experimental data show excellent quantitative agreement throughout the energy range and the angular region of this experiment, except for a few cases in which this model is inherently insufficient; namely, regions in which the Coulomb interaction is important, or regions for which a Hulthén wave function is inaccurate and the off-shell effects are not properly taken into account.     

The pd → tπ+ reaction in an isobar model: Angular distributions

Various wave function effects are studied in the differential cross section for the pd → tπ⁺ reaction. These include both S- and D-waves for the deuteron and the triton as well as the production of p-wave and d-wave pions. For the triton a parametrized Faddeev wave function is employed and for the deuteron a wave function of Hulthén or McGee type. The two-body correlations considered are NΔ(⁵S₂, ^5D₂, ⁵P₃) and NN(¹D₂) which are found to be the most important partial waves in the pp → dπ⁺ reaction.     

Fabrication of pellicle beam splitters for optical bus application

The optical bus architecture for on-board applications requires a number of optical splitters with precise split ratios to route part of the input signal. Since hollow metal waveguide provides well collimated beams with very small gap loss, it opens the possibility of inserting discrete optical beam splitters (taps). The optical tap requires low excess loss, polarization insensitivity, temperature stability, minimized walk-off of the propagating beam, and cost effective manufacturing. By benefiting from the mature interference coating technology for polarization insensitivity and temperature stability, we design a pellicle beam splitter based on a static microelec tro-mechanical system (MEMS) and develop processes to fabricate pellicle splitters using wafer level bonding of silicon and glass substrates, with subsequent thinning to 20 μm. With the approaches described in this paper, we have demonstrated optical beam splitters with excess loss of less than 0.17 dB that operate at a data rate of 10 Gb/s showing a clean eye diagram while providing controlled split ratio and polarization insensitivity. We have demonstrated a high yielding MEMS based silicon processing platform which has the potential to provide a cost effective manufacturing solution for optical beam splitters.     

Oscillator strengths for singly ionized oxygen

The electric dipole oscillator strengths for multiplet and individual lines between some doublet and quartet levels have been calculated using the weakest bound electron potential model theory (WBEPMT) in singly ionized oxygen. We employed both numerical Coulomb approximation (NCA) wave functions and numerical non-relativistic Hartree-Fock (NRHF) wave functions for expectation values of radii in determination of parameters. The calculated oscillator strengths have been compared with available theoretical and experimental results. A good agreement with results in literature has been obtained. Moreover, oscillator strengths not existing in the literature for some highly excited levels have been obtained using this method. Electronic supplementary material  Supplementary Online Material     

Mechanisms in d + 6Li three-body reactions at low bombarding energies

The three-body reactions induced by low energy deuterons on ⁶Li have been studied. The contributions from the sequential processes through the excited states of the intermediate ⁴He, ⁵Li, ⁶Li and ⁷Li nuclei dominate the coincidence spectra. The quasi-free d + d → d + d, d + α → d + α, and d + d → p + t reactions have been observed and compared with plane wave impulse approximation (PWIA) calculations.     

Impurity states of electrons in quantum dots in external magnetic fields

The influence of isolated impurity atoms on the electron energy spectrum in a parabolic quantum dot in quantizing magnetic field is studied. The impurity potential is approximated by a Gaussian separable operator which allows one to obtain the exact solution of the problem. We demonstrate that in the electron energy spectrum there is a set of local levels which are split from the Landau zone boundaries in the upward or downward direction depending on the impurity type. We have calculated the local level positions, the wave functions of electrons in bound states, and the residues of the electron scattering amplitudes by impurity atoms at the poles.     

Differential cross sections for np and nd elastic scattering near 130 MeV

We have measured the np (nd) elastic scattering cross sections at 25(17) angles in the interval 30°–168° (c.m.), using a neutron beam with a broad spectrum peaked near 130 MeV. At backward angles the outgoing charged particles from a liquid hydrogen (deuterium) target were detected; at forward angles we detected neutrons scattered from a hydrogenated (deuterated) scintillating target. Cross sections have been normalized to the energy dependent solution of the Livermore nucleon-nucleon partial wave analysis, evaluated at 130 MeV. The np measurements represent a marginal improvement on previous work; the nd cross sections show some differences from pd measurements, in agreement with earlier indications at an energy of 152 MeV.