Microscopic description of diffractive deuteron breakup by <Superscript>3</Superscript>He nuclei

A microscopic formalism for describing observed cross sections for deuteron breakup by threenucleon nuclei was developed on the basis of the diffraction nuclear model. A general formula that describes the amplitude for the reaction ²H(³He, ³Hep)n and which involves only one adjustable parameter was obtained by using expansions of the integrands involved in terms of a Gaussian basis. This formula was used to analyze experimental data on the exclusive cross sections for deuteron breakup by ³He nuclei at the projectile energy of 89.4MeV. The importance of employing, in calculations, a deuteron wave function that has a correct asymptotic behavior at large nucleon–nucleon distances was demonstrated.     

Metastable helium cluster He<Stack><Subscript>4</Subscript><Superscript>*</Superscript></Stack>

The existence of a metastable cluster He ₄ ^* with total spin S = 2 is predicted. The cluster consists of two covalently bound excited spin-polarized triplet He ₂ ^* molecules and is rectangular in shape. The electron wavefunctions, the dependence of the energy He ₄ ^* system on the distance between the He ₂ ^* triplet molecules, the atomic spacing, the frequency spectrum of natural oscillations of the cluster, and other characteristics are calculated from first principles. It is shown that the metastable state is formed if one of the excited He ₂ ^* molecules is in the ³Σ _u ⁺ state, while the other is in the ³Π_g state. The radiation lifetime τ of the metastable cluster He ₄ ^* is calculated; it is found to range from 100 to 200 s, which is much longer than the lifetime τ ≈ 20 s of the triplet molecule He ₂ ^* (³Σ _u ⁺ ). The height U ≈ 0.5 eV of the potential barrier preventing the departure from the local energy minimum is determined. The energy E_acc ≈ 9 eV/atom accumulated in the He ₄ ^* cluster is calculated; this energy considerably exceeds the energy of known chemical energy carriers. It is shown that the accumulated energy is released virtually completely during decomposition of the He ₄ ^* cluster into individual helium atoms. This means that helium clusters are a promising material with a high accumulated energy density (HEDM).     

Partial-wave analysis of elastic <Superscript>4</Superscript>He<Superscript>4</Superscript>He scattering in the energy range 40–50 MeV

A partial-wave analysis of elastic ⁴He⁴He scattering is performed in the energy range 40–50 MeV.     

Three-body structure of low-lying <Superscript>18</Superscript>Ne states

We investigate to what extent ¹⁸Ne can be descibed as a three-body system made of an inert ¹⁶O core and two protons. We compare to experimental data and occasionally to shell model results. We obtain three-body wave functions with the hyperspherical adiabatic expansion method. We study the spectrum of ¹⁸Ne , the structure of the different states and the predominant transition strengths. Two 0⁺, two 2⁺, and one 4⁺ bound states are found where they are all known experimentally. Also one 3⁺ close to threshold is found and several negative-parity states, 1^-, 3^-, 0^-, 2^-, most of them bound with respect to the ¹⁶O excited 3^- state. The structures are extracted as partial-wave components, as spatial sizes of matter and charge, and as probability distributions. Electromagnetic decay rates are calculated for these states. The dominating decay mode for the bound states is E2 and occasionally also M1 .     

Structure of low-lying <Superscript>12</Superscript>C resonances

The hyperspherical adiabatic expansion is combined with complex scaling and used to calculate low-lying nuclear resonances of ¹²C in the 3α model. We use Ali-Bodmer potentials and compare results for other potentials α-α with similar ⁸Be properties. A three-body potential is used to adjust the ¹²C resonance positions to desired values extending the applicability of the method to many-body systems decaying into three α-particles. For natural choices of three-body potentials we find 14 resonances below the proton separation threshold, i.e. two 0⁺, three 2⁺, two 4⁺, one of each of 1^±, 2^-, 3^±, 4^-, and 6⁺. The partial-wave decomposition of each resonance is calculated as a function of the hyperradius. Strong variation is found from small to large distance. The connection to previous experimental and theoretical results is discussed and agreements as well as disagreements are emphasized.     

Theoretical study of charge-exchange and excitation processes in collisions of He<Superscript>+</Superscript> ions with C<Superscript>5+</Superscript>, N<Superscript>6+</Superscript>, and O<Superscript>7+</Superscript> hydrogen-like ions

Data on the cross sections for single-electron charge exchange and excitation in collisions of He⁺ ions with C⁵⁺, N⁶⁺, and O⁷⁺ ions in the He⁺ ion energy range of 0.2–3.0 MeV are obtained for the first time. The cross sections for the single-electron charge transfer into the singlet and triplet 1snl states of C⁴⁺, N⁵⁺, and O⁶⁺ (2≤n≤5) ions and for the 1s → 2p _{0, ±1} electronic excitation of He⁺(1s) ions are calculated. The calculations were performed by solving close-coupling equations on the basis of ten two-electron quasi-molecular states.     

The characteristics of the <Superscript>8</Superscript>Be ground state in the effective-range approximation

We find the vertex constant for the synthesis α + α → ⁸Be and the corresponding asymptotic normalization coefficient of the Gamov wave function for ⁸Be in the ground state. We use modern data on the position and width of the narrow resonance of this state as well as the energy dependence of the αα scattering phase shift in the s-wave known from the literature. The effective-range theory was applied with the Coulomb interaction taken into account. The parameters of the standard effective-range function expansion up to the member with k ⁴ (k being the relative momentum) were found.     

H<Superscript>+</Superscript> and He<Superscript>2+</Superscript> impact charge transfer cross sections of magnesium

H⁺ impact single and He²⁺ impact single and double electron capture cross sections of magnesium atoms have been calculated in the modified binary encounter approximation (BEA). The accurate expressions of ion impact s_DE\sigma _{\Delta {E}} (cross section for energy transfer DE\Delta E) and Hartree-Fock momentum distributions of the target electrons have been used throughout the calculations. On the basis of the present work it is concluded that inner shell captures by H⁺ and He²⁺ ions incident on magnesium atoms contribute partly to single electron capture and partly to transfer ionization cross sections. The calculated He²⁺ impact double electron capture cross sections of magnesium are in reasonably good agreement with the experimental observations. This indicates the success of the present theoretical approach in study of charge transfer cross sections of atoms as indirect mechanisms do not interfere with double electron capture processes in this case.     

Electron Transitions during the Capture of an Electron by a He<Superscript>2+</Superscript> Ion at the Argon Atom

We have measured the absolute values of the total cross section of the one-electron capture by He²⁺ ions in the kinetic energy range 2–30 keV at the Ar atoms. The absolute values of the differential scattering cross sections of He⁺ ions formed during the one-electron capture and the electron capture with ionization at energies of 2.2, 5.4, and 30 keV have been determined. The electronic states of the formed ions have been determined using collision spectroscopy based on analysis of the change in the kinetic energy of He⁺ after the interaction. We have measured doubly differential (with respect to the kinetic energy and the scattering angle) cross sections of the formation of free electrons. The free electron formation channels (direct ionization and electron capture with ionization) have been analyzed by calculating the electron terms of the (HeAr)²⁺ system. The calculated cross section of capture with ionization is in conformity with the cross section measured using collision spectroscopy.     

Two-proton correlations in <Superscript>4</Superscript>He<Emphasis Type="Italic">p</Emphasis> interactions at a primary momentum of 5 GeV/<Emphasis Type="Italic">c</Emphasis>

Correlations of secondary protons in ⁴Hep interactions are investigated in an exclusive experiment with the aid of a 2-m liquid-hydrogen bubble chamber exposed to an alpha-particle beam of momentum 5 GeV/c the kinetic energy of primary protons in the rest frame of the nucleus is T_p=620 MeV). By using data obtained in 4π geometry for six basic channels of ⁴Hep interaction that lead to the production of two protons, the total correlation function for the pp system is determined, along with two-proton correlation functions for individual channels. Experimental results are compared with the predictions of the modified Lednicky-Lyuboshitz model. The value of R=1.6±0.3 fm is obtained for the root-meansquare spacetime radius of pp emission in ⁴Hep interactions. The dependence of the correlation function on the total momentum of two emitted protons and on the momentum-transfer direction is investigated.     

Interaction of <Superscript>3</Superscript>He<Superscript>2+</Superscript> and Ar<Superscript>6+</Superscript> ions with acetylene,ethylene, and ethane molecules

Time-of-flight mass spectroscopy methods are employed for studying processes occurring during capture of electrons by ³He²⁺ and Ar⁶⁺ multiply charged ions with energy 6z keV (z is the ion charge) from C₂H _n molecules (n = 2, 4, 6) with different multiplicities of C-C bonds. Fragmentation schemes of the molecular ions formed in such processes are established from analysis of correlations of recording times for all fragment ions. The absolute values of the cross sections of capture of an electron and capture with ionization are measured, as well as the cross sections of formation of fragment ions in these processes. The absolute values of total capture cross sections for several electrons are determined.     

Astrophysical <Emphasis Type="Italic">S</Emphasis> factor of the radiative <Superscript>4</Superscript>He<Superscript>12</Superscript>C-capture reaction at low energies

The possibility of describing new experimental data on the astrophysical S factor of radiative ⁴He¹²C-capture at energies ranging from0.9 to 4 MeV in the context of the potential cluster model is considered.     

Charge transfer in the collision system He<Superscript>2+</Superscript> + C<Stack><Subscript>60</Subscript><Superscript>+</Superscript></Stack>: Theory and experiment

Fullerenes are a direct link between atoms with discrete electronic energy levels and solids with a band structure and a well-defined surface. In this paper, we report on a quantum mechanical treatment of charge transfer and ionization in the ion-ion collision system ³He²⁺ + C ₆₀ ⁺ . This approach considers under- and over-barrier transitions through the one-dimensional barrier between the collision partners. The calculated cross sections for charge transfer compare favorably with experimental data measured in the center-of-mass energy range from 27 to 196 keV employing the crossed beams technique.     

H<Superscript>+</Superscript><Emphasis Type="Bold">and He</Emphasis><Superscript>2+</Superscript> impact single and double ionization of lead

H⁺ and He²⁺ impact single and double ionization cross sections of ground state lead atoms have been calculated in the binary encounter approximation. Calculations of direct double ionization cross sections have been performed in the modified double binary encounter model. The accurate expressions of σ_ΔE (cross-section for energy transfer ΔE) and Hartree-Fock velocity distributions for the target electrons have been used throughout the calculations. Contributions to double ionization from Auger effect following ionization of inner shells have been considered in the present work. Our H⁺ impact single and double ionization cross sections are in good agreement with the experimental observations. In calculations of He²⁺ impact cross sections, the present theoretical approach shows limited success in the experimentally investigated region (50–350 keV amu^-1).     

Surface composition modification of tungsten higher oxide under He<Superscript>+</Superscript> ion bombardment

The surface reduction of higher oxide WO₃ under irradiation by He⁺ ions with the energies 1 and 3 keV in a high vacuum is investigated by X-ray photoelectron spectroscopy. It is found that lower WO₂ and intermediate WO _x (2 < x < 3) oxides form first in WO₃ surface layers under He⁺ ion bombardment, and with an increase in the irradiation dose metallic tungsten forms. It is shown that the degree of irradiated oxide surface metallization increases with an increase in the energy of the bombarding He⁺ ions. A comparison of WO₃ oxide surface composition modification under He⁺ and Ar⁺ ion irradiation is presented.     

Structure of neutron-rich Isotopes <Superscript>8</Superscript>Li and <Superscript>9</Superscript>Li and allowance for it in elastic scattering

The differential cross sections for elastic proton scattering on the unstable neutron-rich nuclei ⁸Li and ⁹Li at E = 700 and 60 MeV per nucleon were considered. The ⁸Li nucleus was treated on the basis of the three-body α-t-n model, while the ⁹Li nucleus was considered within the α-t-n and ⁷Li-n-n models. The cross sections in question were calculated within Glauber diffraction theory. A comparison of the results with available experimental data made it possible to draw conclusions on the quality of the wave functions and potential used in the calculations.     

Parabolic sturmians approach to the three-body continuum Coulomb problem

The three-body continuum Coulomb problem is treated in terms of the generalized parabolic coordinates. Approximate solutions are expressed in the form of a Lippmann-Schwinger-type equation, where the Green’s function includes the leading term of the kinetic energy and the total potential energy, whereas the potential contains the non-orthogonal part of the kinetic energy operator. As a test of this approach, the integral equation for the (e ^?, e ^?, He⁺⁺) system has been solved numerically by using the parabolic Sturmian basis representation of the (approximate) potential. Convergence of the expansion coefficients of the solution has been obtained as the basis set used to describe the potential is enlarged.     

Three-body muon-transfer collisions from hydrogen isotope to He<Superscript>2+</Superscript> and Li<Superscript>3+</Superscript> ions

The muon transfer rates from hydrogen isotopes (p,d) to ^3,4He²⁺ and ^6,7Li³⁺ ions are calculated in the hyperspherical close coupling method. Well converged results are obtained. The present rates are comparable to those of existing calculations for He²⁺, but they are much larger for Li³⁺. The resonance parameters are also calculated for resonances near the (Hμ)_1s threshold.     

Three-body analysis of<Superscript>11</Superscript>Li and its<Emphasis Type="Italic">β</Emphasis>-decay to deuteron channel and to halo analog state<Superscript>11</Superscript>Be* (18.3 MeV)

The ground state wave function of¹¹Li obtained in a three-body model proposed earlier (S Kumar and V S Bhasin,Phys. Rev. C65, 034007 (2002)) has been employed to study the probability distributions, momentum distributions and n−n correlation. Complex scaling method has been used to find the energy positions and widths of the three resonant states of¹¹Li above the breakup threshold. The formalism is extended further to study the β-decay of¹¹Li to two channels. One is the β-transition of¹¹Li into a high lying excited state of¹¹Be at 18.3 MeV, i.e.,¹¹Be* and the second is the decay to deuteron +⁹Li channel. The¹¹Be* state has been considered as a halo analog state identified as a bound three-body (⁹Li + n + p) system. The n-⁹Li interaction incorporates both the virtual state and the p-wave resonance observed experimentally. For p-⁹Li interaction, a Coulomb corrected separable interaction is constructed using charge indepedendence for strong interaction part. The n-p interaction is operative only in³S₁ state corresponding to the isotopic spin T^h =0. As a result the¹¹Be* state has the same isotopic spin as that of⁹Li core, i.e.,T = 3/2. Using these realistic parameters as input and without invoking any other free parameter, the model has been used to predict the strength of the Gamow-Teller β-decay of¹¹Li to¹¹Be*, i.e.,Bgt = 1.5 and the value of the branching ratio to⁹Li + deuteron channel to be 1.3 × 10^-4. These results are found to be in rather good agreement with the recent experimental findings.