Charge exchange in He++Li collisions

A two-state model, based on atomic wave functions and allowing for momentum transfer factors, is employed to calculate cross sections for the formation of excited states of He⁺ in collisions of He⁺⁺ ions with Li in the ground state, for energies in the range 5–64 keV. It is shown that the selective capture into the n=3 levels of He⁺, predicted at low energies by Shipsey et al., persists up to energies of ≈30 keV.     

Investigation of the reaction D(<Superscript>4</Superscript>He, γ)<Superscript>6</Superscript>Li at ultralow energies

The cross section of the reaction D(⁴He, γ)⁶Li with titanium and zirconium deuterides as targets is measured for incident ⁴He⁺ ion energies of 30 and 36 keV, respectively. The ion beam is generated by a Hall pulsed plasma accelerator. For the first time, upper limits on the cross section of the reaction D(⁴He, γ)⁶Li at ultralow energies are imposed (at 90% confidence level): σ ≤ 1.2 × 10^?35 cm² for the TiD₂ target and E(⁴He⁺) = 30 keV, and σ ≤ 7 × 10^?36 cm² for the ZrD₂ target and E(⁴He⁺) = 36 keV     

The dependence of exchange and coulomb energies on wave functions of the interacting systems

First-order energies have been calculated for the He₂ system using a number of He wave functions. The convergence to the Hartree-Fock limit has been studied and a two-term expansion in Slater orbitals gives about 98 per cent of this limit. The effect of correlation has been examined by adding s′² and p ² configurations to the wave function and a change of approximately 10 per cent in the effective first-order energy has been noted.     

Exchange and nuclear symmetry interference in He+-He scattering

A method is described to determine the potential difference, V _g-V _u, that will accurately reproduce the exchange and nuclear symmetry oscillations observed by Aberth et al. in their experimental work on He⁺-He differential scattering. It is demonstrated that at higher energies and angles the experimental results for ⁴He⁺-⁴He, ⁴He⁺-³He and ³He⁺-³He appear incompatible with one another when investigated in terms of a two-state scattering theory. This is an indication that at these energies and angles the theory may require modification to include the effects of coupling to higher states.     

Theoretical Study of Triatomic Systems Involving Helium Atoms

The triatomic ⁴He system and its isotopic species ${^4{\rm He}_2^3{\rm He}}$ are theoretically investigated. By adopting the best empirical helium interaction potentials, we calculate the bound state energy levels as well as the rates for the three-body recombination processes: ⁴He + ⁴He + ⁴He → ⁴ He₂ + ⁴He and ⁴He + ⁴He + ³He → ⁴He₂ + ³He. We consider not only zero total angular momentum J = 0 states, but also J > 0 states. We also extend our study to mixed helium-alkali triatomic systems, that is ⁴He₂ X with X = ⁷Li, ²³Na, ³⁹K, ⁸⁵ Rb, and ¹³³Cs. The energy levels of all the J ≥ 0 bound states for these species are calculated as well as the rates for three-body recombination processes such as ⁴He + ⁴He + ⁷Li → ⁴ He₂ + ⁷Li and ⁴He + ⁴He + ⁷Li → ⁴ He⁷Li + ⁴He. In our calculations, the adiabatic hyperspherical representation is employed but we also obtain preliminary results using the Gaussian expansion method.     

Ultracold collisions in the system of three helium atoms

The Faddeev differential equations for a system of three particles with a hard-core interaction are described. Numerical results on the binding energies of the ⁴He₃ and ³He⁴He₂ trimers and on ultracold collisions of ^3,4He atoms with ⁴He₂ dimers obtained with the help of those differential equations are reviewed. The results obtained for the hard-core model using the Faddeev equations are compared with analogous results obtained by alternative methods.     

Comparison of the noncoplanar 6Li(p,pd)4He reactions at 120 and 200 MeV

The ⁶Li(p, pd)⁴He reaction was studied at 200.2 MeV, at the quasi-free angle pair (θ_p, θ_d) = (54°, ?48.9°), for noncoplanarity angles φ from 0° to 28°. ⁶Li αd spectroscopic factors of 0.84 and 0.76 are deduced from our coplanar data at this energy and 120 MeV, respectively, for ground-state 2S Woods-Saxon wave functions. A recent microscopic three-body calculation predicts spectroscopic factors from 0.70 to 0.75; using the ground-state wave functions from this study, we deduce a factor of 0.76 from the 200 MeV data. DWIA calculations fit the measured integrated cross sections versus φ for spectator momenta P_α ? 100 MeV/c at both bombarding energies, but underpredict them for larger P_α. Momentum form factors were better reproduced with 1S αd cluster wave functions for a soft-core bound-state potential than with the 2S Woods-Saxon wave functions, but the former wave functions generate unphysically large (～1.25) spectroscopic factors.     

Compact variational wave functions for bound states in three-electron atomic systems

The variational procedure to construct compact and accurate wave functions for three-electron atoms and ions is developed. The procedure is based on the use of six-dimensional Gaussoids written in the relative four-body coordinates r ₁₂, r ₁₃, r ₂₃, r ₁₄, r ₂₄, and r ₃₄. The nonlinear parameters in each basis function have been carefully optimized. Using these variational wave functions, we have determined the energies and other bound state properties for the ground 1² S-states in a number of three-electron atoms and ions. The three-electron atomic systems considered in this work include the neutral Li atom and nine positively charged lithiumlike ions: Be⁺, B²⁺, C³⁺, ..., Na⁸⁺, and Mg⁹⁺. Our variational wave functions are used to determine the hyperfine structure splitting and field shifts for some lithium-like ions. The explicit formulas of the Q ⁻¹ expansion are derived for the total energies of these three-electron systems. The article is published in the original.     

A study of the 14C(6Li, 6He)14N reaction at 93 MeV

The reaction ¹⁴C(⁶Li, ⁶He)¹⁴N was investigated with 93 MeV ⁶Li ions in an angular interval of 7–26°. Angular distributions were analysed for the four most intense groups of ⁶He nuclei, corresponding to transitions to the ground (1₁⁺) and the excited (1₂⁺, 2₁^?, 4₁^?) states of ¹⁴N. In the theoretical analysis a mechanism of the spin-isospin excitation was suggested in the DWBA frame with the finite range of interaction and recoil in the light system (⁶Li⁶He) taken into account. In the calculations both shell-model wave functions and transition densities obtained in the theory of finite Fermi systems (FFS) were used. From the comparison between theory and experiment the Landau-Migdal force constant g′ is estimated in order to obtain some information on the degree of nuclear proximity to the threshold of pion condensation.     

Quasifree processes in the 2H + 3He interaction

Quasifree scattering and quasifree reaction processes have been examined in the ³He+ ²H → p+d+d, ³He + ²H → n+p+³He and ³He+²H → p+p+t reactions. Beam energies of E_d = 22.3 and 35 MeV and of E_3He = 30, 33.5, and 52.5 MeV were used. The experimental results are compared with PWIA calculations and Fourier transforms of the wave functions are extracted. The quasifree processes are described qualitatively by the PWIA, but some features cannot be described by either PWIA or DWIA.     

Variational Calculation of 4He Tetramer Ground and Excited States Using Realistic 4He–4He Potentials

We calculated binding energies and wave functions of the ⁴He tetramer ground and excited states employing various realistic ⁴He?⁴He potentials which includes the currently most accurate one with the adiabatic, relativistic, QED and residual retardation corrections. We used our Gaussian expansion method (GEM) for ab initio variational calculations of few-body systems. We found that precisely the same shape of the short-range correlation (r _ij < 4Å) in the dimer appear in the ground and excited states of trimer and tetramer. The four kinds of the binding energies of the trimer and tetramer ground and excited states, ${B_3^{(0)}, B_3^{(1)}, B_4^{(0)}}$ and ${B_4^{(1)}}$ , for the different potentials exhibit perfect linear correlations over the range of binding energies relevant for ⁴He atoms; namely, six types of the generalized atomic Tjon lines were observed.     

The binding of alkali atoms to the surfaces of liquid helium and hydrogen

Alkali atoms have been shown previously to have only unstable binding states inside liquid⁴He. We calculate the equilibrium configurations and binding energies of single alkali atoms near the liquid-vapor interface of⁴He and³He. A simple interface model is used to predict the surface deformation due to the presence of the atoms. A more realistic density functional model yields somewhat higher energies in the case of⁴He. For all alkali atoms, we find the surface binding energies to be around 10 to 20 K. A similar analysis with atom-H₂ interactions finds that alkali atoms tend to submerge into liquid H₂, with the exception of Li.     

双力程核子力的讨论

The binding energies of nuclei H³. He³, He⁴, the low energy n-p scattering length and effective range are calculated by using the standard variational methods. A two-range central Yukawa potential is considered in the first two sections. The longer range corresponds to the π meson mass. The smaller range corresponds either to the heavier meson or to the higher order field interactions. No repulsive core appears, when the force parameters are chosen to fit the low energy scattering and deuteron data. The calculated binding energies of nuclei H³, He³ and He⁴ are too high. This result is in agreement with most of the previous calculations. Tensor force of the Schwinger mixed type is considered in the third and fourth sections. The force parameters are chosen to fit the low energy two body data. They are not uniquely determined and are given for a set of possible D-percentage values. The adding of the tensor force reduces considerably the calculated binding energies of nuclei H³, He³, He⁴. But still, the calculated values increase too fast with the mass number. It does not fit the triton and helium binding energies simultaneously. The possibility of adding many body forces is discussed at the end of the paper.     

Electronic absorption spectrum of CO+ in an ion beam

The He+He⁺¹ interactions have been studied, as a function of the internuclear separation R, in terms of the electronic forces acting on the nuclei and the change in the charge distribution. The analysis reveals that at large R the atomic densities are polarized inwards, causing an attractive force on each nucleus, while at small R the difference in the nature of the interactions in the ²Σ_u and ²Σ_g systems is noted. It is seen that the He+He⁺¹ (²Σ_u) interaction is less attractive than the He⁺¹+He⁺¹ interaction at lower values of R.     

Exit angle dependence of charge-state distribution of backscattered He ions

Exit angle and energy dependences of the charge-state distribution of backscattered He ions were investigated when 500 keV He⁺ ions were incident on SiO₂. The energy dependence of the He⁺ fraction was estimated by comparing the measured He⁺ spectra with the simulated spectra of He ions in all charge states at the exit angles of 5-25° with respect to the SiO₂ surface. We found that the He⁺ fraction is almost independent of the exit angle at energies higher than 250 keV and the observed energy dependence of the He⁺ fraction is in good agreement with that for the carbon-foil-transmission experiment. In the low energy region (<250 keV), however, the He⁺ fraction decreases as the exit angle decreases.     

Neutron-induced charged-particle reactions in 6Li and 9Be

Angular distributions of tritons from the ⁶Li(n, t)⁴He reaction were measured at E_n = 7.25, 6.77, 6.57, 5.24 and 4.71 MeV. Angular distributions of douterons from respectively, the ⁶Li(n, d)⁵He two-body breakup reaction were measured at E_n = 6.77 and 6.57 MeV, and of protons from the ⁶Li(n, p)⁶He reaction at E_n = 6.77, 5.24 and 4.71 MeV. All these reactions in ⁶Li were analyzed as direct interaction in the formalism of the distorted wave Born approximation. The optical model for the nuclear interaction was found to apply reasonably well to nuclei as light as ⁴He, ⁵He, ⁶He and ⁶Li. In addition, ⁶Li as an alpha-deuteron cluster gives the best bound-state wave function to describe the experimental angular distribution of tritons. The excitation functions at forward angles of the ⁶Li(n, t)⁴He, ⁶Li(n, d)⁵He and ⁶Li(n, p)⁶He reactions were measured for incident neutron energies between 4.4 and 7.3 MeV. It is found that the ⁶Li(n, d)⁵He two-body breakup reaction has a threshold at about E_n = 5.3 MeV. Angular distributions at E_n = 18.3 MeV for tritons and protons from the ⁹Be(n, t)⁷Li and ⁹Be(n, p)⁹Li, respectively, were also measured.     

Tensor analyzing power T 20 of the dd → 3Hen and dd → 3Hp reactions at zero angle for energies 140, 200, and 270 MeV

RIKEN Accelerator Research Facility data on the tensor analyzing power T ₂₀ of the dd → ³Hen and dd → ³Hp reactions at zero angle for deuteron kinetic energies of 140, 200, and 270 MeV are reported. The observed positive sign of T ₂₀ clearly demonstrates the sensitivity to the D/S-wave ratio in the ³He and ³H wave functions in the energy range of the experiment. Data on T ₂₀ for the ³Hen channel are in agreement with those for the ³Hp channel within the experimental errors.     

Proton momentum distributions in the 7Li nucleus in a potential cluster model

Distributions of the proton momentum in the ⁷Li{αt} → p + ⁶He{αnp} fragmentation channel were, along with the corresponding widths and spectroscopic factors, calculated in the αnn model representation of wave functions of the ⁶He nucleus in the (0⁺,1) ground and (2⁺,1) excited states. The results are compared to the available theoretical calculations and experimental NIKHEF data on the ⁷Li(e,e′p)⁶He electron-induced proton knock-out process.     

Ab initio study of formation, migration and binding properties of helium-vacancy clusters in aluminum

Ab initio calculations based on density functional theory have been performed to study the dissolution and migration of helium, and the stability of small helium-vacancy clusters He_nV_m (n, m=0-4) in aluminum. The results indicate that the octahedral configuration is more stable than the tetrahedral. Interstitial helium atoms are predicted to have attractive interactions and jump between two octahedral sites via an intermediate tetrahedral site with low migration energy. The binding energies of an interstitial He atom and an isolated vacancy to a He_nV_m cluster are also obtained from the calculated formation energies of the clusters. We find that the di- and tri-vacancy clusters are not stable, but He atoms can increase the stability of vacancy clusters.     

Binding energies and scattering observables in the 4He3 atomic system

The ⁴He₃ system is investigated using a hard-core version of the Faddeev differential equations. Realistic ⁴He-⁴He interactions are employed, among them the LM2M2 potential by Aziz and Slaman and the recent TTY potential by Tang, Toennies and Yiu. We calculate the binding energies of the ⁴He trimer, but concentrate in particular on scattering observables. The scattering lengths and the atom-diatom phase shifts are calculated for center of mass energies up to 2.45 mK. It is found that the LM2M2 and TTY potentials, although of quite different structure, give practically the same bound-state and scattering results. Received 19 June 2000