Average g-factors for high-spin states in 78Kr

Inverse reactions of ^{63, 65}Cu beams on ^{18, 16}O targets have been used to populate states of ⁷⁸Kr by fusion-evaporation reactions. The excited nuclei recoiled at high velocity v/c ≈ 7 % through a polarized iron (⁵⁴Fe) layer and were stopped in a copper layer. During the period in iron, 0.05–0.65 ps, the nuclei were subjected to the intense transient magnetic field (initially ～ 3500 T). The resulting precession of the high-spin nuclear states populated during this time was determined by measuring the time integral rotation angle of the discrete γ-ray transitions at low spin.The average g-factor at low spin 2 ≦ J ≦ 8 compared to that at higher spin 8 ≦ J ≦ 12 in ⁷⁸Kr was found to be identical within the experimental uncertainties of ～ 15 %. This result implies that either there are no rotational alignment effects at the backbend in ⁷⁸Kr or more plausibly, proton (g ≈ 1) and neutron (g ≈ 0) aligned bands are equally competitive and both populated in the reaction. It is then likely that the resulting g-factor represents an average over many populated proton and neutron aligned bands.     

g-factors of high-spin isomeric states in 216Ra

The g-factors of two isomeric states at E_x = 3763 and 5170 keV in ²¹⁶Ra have been measured to be 0.51 ± 0.03 and 0.63 ± 0.06, respectively, with a TDPAD method. Spin and parity assignments of 19^? for the 3763 keV state and 25^? or 24⁺ for the 5170 keV state are consistent with the measured g-factors. Proposed configurations for the 19^? and 25^? assignments are of the same type as those predicted by a deformed independent-particle model for ²¹⁴Rn, which is an isotone of ²¹⁶Ra.     

Theoretical studies of the g factors and local structure for the rhombic Fe center in NaF

The anisotropic g factors and local structure for the rhombic Fe⁺ center in NaF are theoretically studied using the perturbation formulas of the g factors for a rhombically distorted octahedral 3d⁷ cluster. The impurity Fe⁺ is found not to occupy exactly the host Na⁺ site in NaF but to experience the off-center displacement of about 0.28 Å along [1 1 0] axis due to size mismatch substitution. The calculated g factors based on the above impurity displacement show reasonable agreement with the experimental data. The local structure of the Fe⁺ center is discussed.     

Evidence for high-l rydberg states in atomic lithium excited by electron impact

By a time-of-flight technique we have studied the radiative decay of lithium atoms excited to high Rydberg levels by electron impact. The observed decay rates are consistent with large values for the orbital angular momentum quantum number l.     

Studies of the crystal field energy levels and g factors for Ce in LiYF4 crystal

The five observed crystal field energy levels and EPR g factors g_//and g_⊥ for Ce³⁺-doped LiYF₄ crystal are calculated together from a complete diagonalization (of energy matrix) method. In the method, the contributions to g factors of ground Kramers doublet from all the rest doublets within the ground and excited manifolds ²F_5/2 and ²F_7/2 are included. The calculated results show reasonable agreement with the experimental values. The calculations suggest that the crystal field parameter B₂₀ > 0 in LiYF₄: Ce³⁺ crystal. The opinion of the parameter B₂₀ < 0 in the previous paper is not correct. Since this opinion is based on the calculation of g factors using a very simple method where only the contributions to g factors from the doublets within the ground manifold ²F_5/2 are considered, it is suggested that this simple method is not effective in the calculation of g factors for 4f¹ ions in crystals.     

Theoretical explanation of g factors for Ti ions in LiNbO3 and LiTaO3 crystals

The EPR g factors g_// and g_⊥ for Ti³⁺ ions at the trigonal octahedral Li⁺ sites of LiNbO₃ and LiTaO₃ crystals are calculated from the third-order perturbation formulas of g factors for 3d¹ ion in trigonal symmetry. In the calculations, the crystal-field parameters are obtained from the structural data by using the superposition model. The calculated values are in reasonable agreement with the observed values. The results are discussed.     

Callan—symanzik β(g) function in different topological sectors

Using the formalism developed by Amati and the present author for constructing a perturbation theory around an instanton in gauge theories, it is proved that the Callan—Symanzik β(g) function is the same as in the perturbation theory developed around zero.     

Shell model isomers near Z = 64, N = 82: g-factors of Yrast states in 146Gd and 147Gd

Nuclear g-factors have been measured for the 7^? isomer in ¹⁴⁶Gd and for the $\text{27}\text{2}{}^{\mathrm{?}}$ isometer in ¹⁴⁷Gd. For ¹⁴⁷Gd the results is consistent with the expectation for a pure shell model configuration.     

Studies of the g factors and the local structure of the orthorhombic Ni center in KTaO3 crystal

The local structure and the g factor (g_x, g_y, and g_z) of the Ni⁺ center in KTaO₃ are theoretically studied using the perturbation formulas of the g factors for a 3d⁹ ion in orthorhombically elongated octahedra. The orthorhombic field parameters are determined from the superposition model and the local geometry of the system. In view of the covalency, the contributions from the ligand orbital and spin–orbit coupling interactions are taken into account from the cluster approach. In the calculations, the orthorhombic center is attributed to Ni⁺ occupying the host Ta⁵⁺ site, associated with the nearest-neighboring oxygen vacancy V_O along the c-axis. Furthermore, the planar Ni⁺–O²⁻ bonds are found to experience the relative variation ΔR (≈0.076 Å) along the a- and b-axis, respectively, due to the Jahn–Teller effect and the size mismatching substitution of Ta⁵⁺ by Ni⁺. Meanwhile, the effectively positive V_O can make the central Ni⁺ displace away from V_O along the c-axis by about 0.20 Å. The calculated g factors based on the above local distortions show good agreement with the experimental data.     

New measurement of (g−2) of the Muon

The g-factor anomaly, a≡(g?2)/2, has been measured for μ⁺ in the new Muon Storage Ring at CERN. The result is a = (1 165 895 ± 27) × 10^?9. This is (13 ± 29) × 10^?9 below the theoretical value which includes sixth-order QED terms and a hadronic contribution of (73 ± 10) × 10^?9.     

Magnetism of Zr atomic wires

By using the full-potential linearized augmented plane wave method to perform ab initio total energy calculations, we have explored magnetic ordering in one-dimensional Zr wires. The result shows that Zr can form linear, or dimerized, or zigzag wires, and the magnetic properties strongly depend on their geometric structures. The linear and zigzag wires exhibit ferromagnetic ground states at the equilibrium bonding distance, while the dimerized wire, despite its higher stability than that of the linear one, exhibits nonmagnetic ground states. The most stable geometry is shown to be the zigzag wire with a magnetic moment of 0.26μB per atom.     

Series representation of the Percus-Yevick pair correlation function g(r) of a hard-sphere fluid

An explicit expression for g(r) is derived using contour integration in K space: poles, occurring at complex K values as a result of disordering in the fluid state, give rise to damped oscillations whose asymptotic form accords with experiment.     

EPR g factors and tetragonal distortion for the isoelectronic Ni and Cu centers in the CuGaSe2 crystal

The EPR g factors, g_|| and g_⊥, for the isoelectronic 3d⁹ ions Ni⁺ and Cu²⁺ at the tetragonal Cu⁺ site of the CuGaSe₂ crystal are calculated from the high-order perturbation formulas based on a two-spin-orbit-parameter model. In the model, both the contributions to g factors from the spin-orbit parameter of central 3d⁹ ion and that of ligand ion are contained. The calculated results appear to be consistent with the experimental values. The tetragonal distortions (characterized by θ−θ₀, where θ is the angle between the metal-ligand bond and C₄ axis, and θ₀≈54.74° is the same angle in cubic symmetry) of Ni⁺ and Cu²⁺ centers, which are different from the corresponding angle in the host CuGaSe₂ crystal and from impurity to impurity, are obtained from the calculations. The difference of the sign of g_||−g_⊥ between the isoelectronic Ni⁺ and Cu²⁺ centers is found to be due to the different tetragonal distortions of both centers in the CuGaSe₂ crystal.     

Polymers and g|φ|4 theory in four dimensions

We investigate the approach to the critical point and the scaling limit of a variety of models on a four-dimensional lattice, including g|φ|₄⁴ theory and the self-avoiding random walk. Our results, both theoretical and numerical, provide strong evidence for the triviality of the scaling limit and for logarithmic corrections to mean field scaling laws, as predicted by the perturbative renormalization group. We relate logarithmic corrections to scaling to the triviality of the scaling limit. Our numerical analysis is based on a novel, high-precision Monte Carlo technique.     

An interpretation of the g factors for the tetragonally-compressed Cr centers in YVO4 and YPO4 crystals

The g factors g_∥ and g_⊥ for the tetragonally-compressed (CrO₄)³⁻ clusters in YMO₄ (M=V, P) crystals are calculated from the high-order perturbation formulas based on the two-mechanism model for the compressed d¹ tetrahedra with the ground state |d_z²〉. From the calculated values and by considering a small admixture of the first excited state |d_x²−y²〉 to the ground state |d_z²〉 due to the vibrational motion of ligands (which leads a twinkling compressed tetrahedron to become an elongated one), the observed g_∥ and g_⊥ for Cr⁵⁺ centers in YMO₄ crystals are explained reasonably. The difficulty of the large deviations of g_∥ from g_e (≈2.0023) in the two systems is therefore removed and the above dynamic effect may be the cause which results in the large deviation of g_∥ from g_e for some (CrO₄)³⁻ clusters in crystals.     

Investigation of the EPR g factors and defect structure for the Cu-VNa center in the X-irradiated NaCl: Cu crystal

The g factors of a tetragonally-compressed Cu²⁺ center in NaCl: Cu⁺ crystal X-irradiated at room temperature are calculated from the high-order perturbation formulas based on the two-mechanism model. In the model, the contribution to g factors from both crystal-field (CF) and charge-transfer (CT) mechanisms are included. The calculations are based on the defect model that the tetragonally-compressed Cu²⁺center is assigned to the Cu²⁺ ion (which is caused by Cu⁺ ion (at the Na⁺ site) irradiated by X-ray) associated with a nearest Na⁺ ion vacancy V_Na along C₄ axis due to charge compensation. From the calculations, the g factors g_|| and g_⊥ are explained and the defect structure (charactering by the displacement ΔZ of the Cl⁻ ion intervening in Cu²⁺ and V_Na) of the Cu²⁺ (or Cu²⁺-V_Na) center is obtained. The results are discussed.     

On the g factor for electrons in n-type silicon surface inversion layers

Self-consistent calculations for energy levels are performed for n-type inversion layers of silicon with magnetic field perpendicular to the (100) surface. ‘Apparent’ g factor g¹, obtained from the period of oscillation of states density at Fermi level for varying magnetic field, is plotted as a function of the $\text{Γ}\text{2βH}$, where Γ is the width of Landau levels. The results show that $\text{g}{}^1\text{～ g}\text{for Γ ? 2β}\text{H,}\text{and}\text{g}{}^1\text{～}\text{5 for Γ < 2β}\text{H}$. This means that we should be very careful when interpret the g shift of electrons in inversion layers for small surface electron density.     

Studies of EPR g factors of the isoelectronic 3d series Cr, Mn and Fe in SrTiO3 crystals

The g-shifts Δg(=g−g_s, where g_s≈2.0023 is the free-ion value) of the isoelectronic 3d³ series Cr³⁺, Mn⁴⁺ and Fe⁵⁺ in SrTiO₃ crystals are calculated from the high-order perturbation formula based on the cluster approach for 3d³ ion in cubic octahedral site. The formula includes not only the contribution from the crystal-field (CF) mechanism, but also that from the charge-transfer (CT) mechanism (which is omitted in the CF theory). From the calculations, it is found that the contribution Δg_CT from the CT mechanism in sign is contrary to the corresponding Δg_CF from the CF mechanism and the relative importance of CT mechanism (characterized by |Δg_CT/Δg_CF|) increases with the increasing valence state (and hence the atomic number) of 3d³ ion. The positive g-shift Δg of SrTiO₃:Fe⁵⁺ is due mainly to the contribution of CT mechanism. So, for the explanations of g factors of the high valence state 3dⁿ ions (e.g. Mn⁴⁺ and Fe⁵⁺) in crystals, the contributions from both CF and CT mechanisms should be taken into account.