Quantum registers based on single NV + <Emphasis Type="Italic">n</Emphasis><Superscript>13</Superscript>C centers in diamond: II. Spin characteristics of registers and spectra of optically detected magnetic resonance

The spin Hamiltonian method in combination with ab initio calculations of the spin characteristics of quantum registers that include an electron spin S = 1 of a single NV center in the ground electronic state and nuclear spins I = 1/2 of several atoms ¹³C located at different lattice sites near the vacancy of the NV center is applied to find eigenvalues and eigenfunctions of spin systems NV + n ¹³C for cases where the lattice sites nearest to the vacancy of the NV center contain one, two, or three ¹³C nuclear spins, as well as for cases where ¹³C atoms are located at sites more distant from the vacancy. For these single spin NV + n ¹³C systems, the spectra of optically detected magnetic resonance (ODMR) are calculated, which agree well with available experimental data.     

Electronic structure of the self-trapped exciton in rare gas solids

The Rydberg-like series of the self-trapped exciton R₂¹ in rare gas solids (Ar, Kr and Xe) are obtained by solving the effective mass equation which incorporates different corrections, including the central cell correction. The results are in good agreement with the recent transient optical absorption data in which the electron is excited into higher excited states. The origin of the luminescence bands is interpreted by analogy with a similar structure of the self-trapped excitons in alkali halides.     

The multiple hydrogen location near a α-Fe vacancy

The interaction between 10 hydrogen atoms and a α-Fe structure having a vacancy (V) has been studied using a cluster model and a semi-empirical theoretical method. The energy of the system was calculated by the atom superposition and electron delocalization molecular orbital method. The electronic structure was studied using the concept of density of states and crystal orbital overlap population curves.For the study of a sequential absorption, the hydrogen atoms were positioned in their energy minima configurations, near to the tetrahedral sites neighboring the vacancy, except the last H atom that was located far from the vacancy. The energy difference for H agglomeration was also computed. The vacancy-H_n complexes become less stable than VH species for more than three hydrogen's.The changes in the electronic structure of Fe atoms near the vacancy were also analyzed. The interactions mainly involve Fe 3d and 4s atomic orbitals. The contribution of Fe p orbitals is much less important. The Fe-Fe bond weakened as new Fe-H and H-H pairs were formed. The effect of H atoms is limited to its first Fe neighbors. The detrimental effect of H atoms on the Fe-Fe bonds can be related to the mechanism for embrittlement in α-Fe.     

B.c.c.-f.c.c. allotropy, F-bands,and metallization in xenon and krypton

APW-Xα calculations of a f.c.c.-b.c.c. phase transition in Xe prior to metallization give P ? 950 kbar, contrary to the 820 kbar result of Hama and Matsui; their use of non-touching APW spheres (f.c.c.) may be the crucial difference. Hartree-Fock plus correlation calculations in Kr indicate that f-bands play no role in rare gas crystal metallization.     

Über die Wechselwirkung zweier Heliumatome

The interaction energy between two helium atoms in the ground state is calculated by a variational principle. Besides the valence energy 387·exp(?4,42R) (R in Å, energy in eV) and the van der Waals energy ?0,58/R ^5,9 an additional energy term 366·exp(?7,15R) is obtained which is particularly important forR?3 Å. A potential minimum but no equilibrium exists because the zero point energy is too large. The results of other authors are discussed and compared.     

Influence of the relative magnitude of the Jahn-Teller effect and level splitting in a cubic crystal field on the properties of the ground state of vacancy defects in semiconductors

The spatial structure of a vacancy and the properties of its electronic energy levels in a semiconductor with a lattice possessing point symmetry T _d are considered for an arbitrary relationship between the Jahn-Teller stabilization energy (associated with the F ₂ vibrational mode) and the t ₂-a ₁ splitting (Δ) caused by the cubic crystal field. The position of the minimum of the adiabatic potential and the distortion of the electronic density are calculated for the vacancy ground state for different relative values of Δ and coupling constants of the vacancy to the F ₂ vibrational mode. It is shown that, if the ground state of a carrier bound to a vacancy is a t ₂ state, the trigonal symmetry of the environment of the vacancy persists for any values of Δ, but the amount of displacements of atoms near the vacancy and the localization of the wave function of the bound carrier on the broken bond earmarked by the Jahn-Teller effect can depend heavily on Δ and are maximal at Δ → 0. This is also the case when the ground state of the vacancy is the a ₁ state, but the magnitude of Δ does not exceed a certain value, which is determined by the coupling constants and the elastic constant. The relation between Δ and the coupling constants is also shown to affect the properties of trigonal vacancy-shallow-donor complexes. For these complexes, calculations are performed of the dependence of the dipole direction determining the optical properties of the vacancy defect on the distortion of vacancy orbitals caused by the donor entering into the complex.     

Diffusion and correlation effects in nonstoichiometric crystals

The correlated diffusive motion of atoms in the presence of a large concentration of point defects (for example, in nonstoichiometric materials such as some transition metal oxides, fast-ion conductors, and transition metal hydrides) is investigated in terms of the encounter model. Within the framework of this theory the correlation factor f is defined as the ratio of the mean square displacement, 〈R²〉_enc, of a tracer atom in an encounter with a point defect (in units of the nearest-neighbor distance) and the mean number of correlated tracer jumps per encounter, Z_enc. In the limit in which the energy of interaction between different point defects is much smaller than the thermal energy kT, the parameters 〈R²〉_enc and Z_enc (and thus f) are determined as functions of the concentration of point defects by means of a Monte Carlo-type computer simulation technique. Our results for the monovacancy mechanism of self-diffusion in f.c.c., b.c.c., and s.c. crystals are discussed in relationship to the results presented recently by Koiwa, Benoist et al., Sanke et al., DeBruin et al. and Murch et al. The validity of a simple analytical expression for f as a function of the vacancy concentration is investigated.     

Scattering of slow electrons by inert gas atoms. Effective polarization potential method

The problem of selecting the polarization-correlation potential V _pol for describing the interaction of electrons with atomic targets is examined. Based on the differential cross section for electron scattering by the hydrogen atom calculated using the partial wave method and the exact exchange operator, the optimal form of this potential is determined. It is demonstrated that the parameters of the potential V _pol can be determined from the condition of equality of the calculated and experimental values of the electron affinity of the hydrogen atom. For the interaction of slow electrons with inert gas atoms, the polarization parameter R _p is proposed to be determined from the known position of the Ramsauer minimum in the total elastic scattering cross section. In particular, calculations are performed for krypton and argon atoms. The results agree well with numerous experimental and theoretical published data.     

Semiempirical calculation of the fine-structure parameters for np 5 n′p configurations

The fine-structure parameters are calculated semiempirically in the intermediate coupling scheme for the np ⁵ n′p configurations of rare gas atoms and a number of ions. The calculation is based on the two-electron matrix of the energy operator, which takes into account, along with the electrostatic interaction, all magnetic interactions. Diagonalizing the energy matrix with the calculated values of the fine-structure parameters yields energy values exactly coinciding with the experimental data, as well as the coupling coefficients and the gyromagnetic ratios. The results obtained are compared with the available literature data.     

Point-defect properties of and sputtering events in the {001} surfaces of Ni3Al I. Surface and point-defect properties

Constant-area and fully relaxed molecular dynamics methods are employed to study the properties of the surface and point defects at and near {001} surfaces of bulk and thin-film Ni, Al and Ni₃Al respectively. The surface tension is larger than the surface energy for all {001} surfaces considered in the sequence: Al (1005?mJ?m^?2)<?Ni₃Al (mixed Ni–Al plane outermost, 1725?mJ?m^?2)<?Ni₃Al (all-Ni-atoms plane outermost, 1969?mJ?m^?2)<?Ni (1993?mJ?m^?2). For a surface of bulk Ni₃Al crystal with a Ni–Al mixed plane outermost, Al atoms stand out by 0.0679?Å compared with the surface Ni atoms and, for the all-Ni-atoms surface, Al atoms in the second layer stand out by 0.0205?Å compared with Ni atoms in the same layer. Vacancy formation energies are about half the bulk values in the first layer and reach a maximum in the second layer where the atomic energy is close to the bulk value but the change in embedding energy of neighbouring atoms before and after vacancy formation is greater than that in the bulk. Both the vacancy formation energy and the surface tension suggest that the fourth layer is in a bulk state for all the surfaces. The formation energy of adatoms, antisite defects and point-defect pairs at and near {001} surfaces of Ni₃Al are also given.     

Antiproton-proton cross sections at 200 and 900 GeV c.m. energy

Data on antiproton-proton cross sections at the c.m. energies 200 and 900 GeV are presented. The data were obtained at the CERN antiproton-proton Collider operated in a new pulsed mode in which the same beams were accelerated and decelerated between beam energies of 450 and 100 GeV. The properties of the machine determine the ratio of the luminosities at the two energies to about 1% and thus an accurate measurement of the ratioR of the inelastic cross sections could be made. We findR (=σ ⁹⁰⁰/σ ²⁰⁰)=1.20±0.01±0.02, where the first error is statistical and the second systematic. Interpolating existing data to estimateσ _ine1(200 GeV) this measurement ofR leads toσ _ine1(900 GeV)=50.3+0.4+1.0 mb. Using an extrapolated value ofσ _e1/σ _tot we estimate the total cross section at 900 GeV to be 65.3±0.7±1.5 mb. Both the inelastic and total cross sections are compatible with a ln² s dependence. Comparisons are made with different fits to the total cross section energy dependence.     

Ionization potential of a metal cluster containing vacancies

A consistent procedure for determining the ionization potential of a large metal cluster of radius R _{N, v} , consisting of N atoms and N _v vacancies, is proposed. The perturbation theory in small parameters R _v /R _{N, v} and L _v /R _v (Rv and L _v are average distance between vacancies and the length of electron scattering on vacancies, respectively) is constructed in the effective-medium approximation for the electron ground state energy. The effective vacancy potential profile, the electron scattering phase and length are calculated by the Kohn–Sham method for a macroscopic metal in the stable jelly model. The obtained analytical dependences can be useful to analyze the results of photoionization experiments and to determine the size dependence of the vacancy concentration, including that near the melting temperature.     

Reactions of excited atoms and molecules with atoms and molecules

Ionizing collisions of long lived excited particles with atoms and molecules are studied by a cross beam technique. For the first time reactions of atoms in high Rydberg states are included in the investigation. In this paper we report relative cross sections for the production of the ions RH⁺, RH ₂ ⁺ , and H ₂ ⁺ by collisions of excited rare gas atoms R^* with H₂. With HD as the target molecule the isotope effect for the production of RD⁺ and RH⁺ has been determined. In the case of argon and krypton, ions are produced only by the high Rydberg states, whereas in the case of helium and neon only the metastable states contribute to a measurable extent. The data indicate, that the reaction mechanism is different in principle for metastable and highly excited atoms. Simple models are proposed to explain the experimental results.     

Excitons in rare gas atoms and solids

Excitons in rare gas are described using the integral equation approach and an appropriate semi-empirical simplification of the short-range terms. In the solids, polarization effects are taken into account using a semi-continuum model in analogy with F-centre problem. Reasonable agreement with experiments is obtained for exciton binding energy shifts passing from atoms to crystals.     

Hall effect studies in ytterbium through the f.c.c.-h.c.p. transformation

The Hall coefficient (R_H) of polycrystalline Yb showing the f.c.c.-h.c.p. transformation has been determined at 20 koe in the range 1.8–420°K. Both the structural and the associated magnetic transformation would separately be expected to modify R_H, but the evidence suggests that the observed behaviour through the transition arises primarily from the effects of the change in structure. A more detailed interpretation is presently not possible, however, because of the lack of knowledge of the band structure of h.c.p. Yb.     

A DFT + U description of oxygen vacancies at the TiO2 rutile (1 1 0) surface

Experimental observations indicate that removing bridging oxygen atoms from the TiO₂ rutile (1 1 0) surface produces a localised state approximately 0.7 eV below the conduction band. The corresponding excess electron density is thought to localise on the pair of Ti atoms neighbouring the vacancy; formally giving two Ti³⁺ sites. We consider the electronic structure and geometry of the oxygen deficient TiO₂ rutile (1 1 0) surface using both gradient-corrected density functional theory (GGA DFT) and DFT corrected for on-site Coulomb interactions (GGA + U) to allow a direct comparison of the two methods. We show that GGA fails to predict the experimentally observed electronic structure, in agreement with previous uncorrected DFT calculations on this system. Introducing the +U term encourages localisation of the excess electronic charge, with the qualitative distribution depending on the value of U. For low values of U (?4.0 eV) the charge localises in the sub-surface layers occupied in the GGA solution at arbitrary Ti sites, whereas higher values of U (?4.2 eV) predict strong localisation with the excess electronic charge mainly on the two Ti atoms neighbouring the vacancy. The precise charge distribution for these larger U values is found to differ from that predicted by previous hybrid-DFT calculations.     

Collision of Rydberg atom A** with atom B in the ground electronic state. Optical potential

A method for calculating the complex optical potential of slowly colliding Rydberg atom A^** and neutral atom B in the ground electronic state is suggested. The method is based on the asymptotic approach and the theory of multichannel quantum defects, which uses the formalism of renormalized Lippmann-Schwinger equations. The potential is introduced as the 〈q|V _opt|q〉 matrix element of the optical interaction operator, for which the integral equation is derived, and is calculated in the basis set of free particle wave functions |q〉. Fairly simple equations for the shift and broadening of the ionic term are obtained, and the principal characteristics of these equations are analyzed. By way of illustration, the optical potential of the Na^**(nl)+B systems, where B is a rare gas atom, is calculated.     

Two-sphere hydrodynamic interactions and mobilities in a porous medium

The translational mobility tensor of an arbitrary number of spheres immersed in a viscous fluid enclosed in a porous medium is formally calculated in a power serie expansion in R⁻¹, where R is the inter-particle distance. This calculation is realized by solving the screened Navier-Stokes oquation with the recent formalism of Mazur and van Saarloos. Explicit expressions are derived for the pair mobility tensor up to order R₋₇.     

Temperature dependence of the establishment time of the vacancy equilibrium in simple crystals

Establishment times of vacancy equilibrium t* in spherical samples of simple crystals of radius R due to thermal motion of atoms during the process maximally approached to the equilibrium upon lowering the temperature from the melting point to the current value T have been calculated. It has been found that (i) with a decrease in T, the equilibrium time t* exponentially increases, and (ii) with a decrease in the sample radius R, the time t* exponentially decreases. The general tendency toward increase in the time t* due to lowering the temperature overlaps the effect of decreasing sample size R; therefore, for any small samples, the temperature range T < T*, for which the diffusion process is almost frozen, always exists.     

One-body dissipation and nuclear dynamics

We discuss recent developments in the “one-body” dissipation theory described in B?ocki et al. [Ann. Phys. (N.Y.)113 (1978), 330]. The principal new result is the derivation of the functional form of the dissipation expression (the Rayleigh Dissipation Function) for a finite idealized nucleus with a diffuse surface, in the form of an expansion in powers of the dimensionless ratio of the surface diffuseness to the size, R, of the system. The leading term in such an expansion is a surface contribution, of relative order R², in the form of the “Wall Formula” of B?ocki et al. The next is a curvature correction of order R. At the next level (R⁰) there are two higher order curvature corrections and a correction for the presence of gradients in the normal velocity field specifying the motion of the surface. For simple models of the nuclear surface profile we work out analytically the coefficients in the curvature and velocity-gradient correction terms. We compare the one-body dissipation theory formulated in this way with recent linear-response and Time-Dependent Hartree-Fock treatments of the nuclear problem. The principal theme that emerges from this study is the close analogy between the problem of the nuclear macroscopic dissipation function and the problem of the nuclear macroscopic potential energy.