Spin lattice coupling coefficients of Co2+ ion in cubic ZnS Crystal

Summary From a uniform and simple method suitable to alld ⁿ ions for the calculation of the spin-lattice coupling coefficientsG ₁₁ andG ₄₄ inT _d symmetry, the analytic expressions ofG ₁₁ andG ₄₄ ford ⁷ ions in this symmetry have been obtained from the high-order perturbation formulae of zero-field splitting in low symmetries based on the weak-field approximation. By using these expressions, the coefficientsG ₁₁ andG ₄₄ for Co²⁺ ion in ZnS crystal have been calculated and the signs of these coefficients are also given. The absolute values of the calculated results show good agreement with the observed values and the signs of these coefficients remain to be verified experimentally. The author of this paper has agreed to not receive the proofs for correction. The project was supported by National Natural Science Foundation of China.     

Spin-phonon coupling of Al2O3:V3+ by quantitative spectroscopy with phonons

Superconducting tunnel junctions were used as tunable monochromatic phonon sources by selecting a narrow band of bremsstrahlung phonons by modulation. For quantitative spectroscopy, the line shape of the modulated band was calculated. Using this, the experimental results on Al₂O₃: V³⁺ were analyzed in terms of the spinphonon Hamiltonian including rotational coupling. In contrast with the theory, the coupling with theL mode along the trigonal axis was not forbidden and, furthermore, exhibited an unexplained narrowing. The analysis of the other modes yieldedG ₄₄=+0.4 cm^?1 andG ₄₁=? 8.1 cm^?1. The observation of “resonance fluorescence” is also reported.     

Application of symmetry coupling coefficients in zero-field splitting of d5 ion complexes

Symmetry coupling coefficients and symmetry reduced matrix elements are used in calculating the minimum required matrix elements required to determine the analytical expressions for the three ⁶ A ₁ ground-state energy levels for a d⁵ ion in a weak crystal field of tetragonal symmetry. Expressions for the spin hamiltonian parameters a, D, F and G are derived, from which the effect of spin-orbit coupling and the tetragonal component of the crystal field are examined. The parameters describe the form of the hamiltonian and consequently the spin eigenfunctions and eigenvalues of the ground state where a is a measure of the isotropic component whereas D, F and G measure the tetragonal component of the interaction giving rise to the zero-field splitting. Some experimental results are examined.     

Quark-pion coupling constant in a chiral quark model

Incorporating chiral-symmetry to the potential model of quarks with confining potentialU(r)=1/2 (1 +γ°)ar ² with m _q =10 MeV anda=2.273 fm⁻³ that gives a reasonable quark-core contribution to μ _p , 〈r ² 〉 _p ^1/2 andg _A , the quark-pion coupling constant for quarks in a nucleon is estimated.G _qqπ ² /4π obtained between 0.4 and 0.5 is consistent with those extracted from experimental vector meson decay-width ratios by Suzuki and Bhaduri. The nucleon-pion coupling constantG _NNπ ² /4π comes out to be of the order of 13.1 in reasonable agreement with the experimental value.     

(2,0) Heterotic superstring with Wess-Zumino coupling

By means of the identity operator and vertex operator technique, reparametrization invariance and BRST symmetry are proven for the heterotic string with Wess-Zumino term coupling the fiber bundle. The motion space of the string is assumed to be a direct productM _d G of a Minkowski spaceM _d of dimensiond with an intrinsic group manifoldG of dimensiond _G , and turns out to give the critical dimension.     

Static and dynamical elastic behaviour of squaric acid around its phase transition

Ultrasonic velocity measurements could be performed on a good quality single crystal of squaric acid close to its transition temperature around 373 K. The behaviour of the stiffness componentsc ₃₃ andc ₄₄ clearly demonstrates a first-order transition. The temperature variation ofc ₁₁ andc ₆₆ can be fitted to a formula obtained from the Landau theory and assuming a strictive-type coupling between order parameter and strain. From attenuation measurements characteristic times for the order-parameter dynamics can be estimated, ranging from 10^?11 to several 10^?10s in a temperature range of about 12 K on either side of the transition.     

Analysis of the lattice,strong coupling series for g0φ4 field theory in d dimensions

We analyze the renormalized strong coupling series for lattice g₀φ⁴ field theory which is a double series in x = M⁴a⁴/g₀a_4?dandy = 1/M²a², where M is the renormalized mass, a the lattice spacing, g₀ the bare coupling constant and d the dimension of space-time. We extrapolate to large y for fixed x by using a Padé-like extrapolation technique. We study the dimensionless renormalized coupling constant G/M^4?d and find that as we approach the continuum(x → 0, y → ∞) the entire spectrum of g₀ from zero to infinity can be studied. Our results for d = 1,2,3,4 based on a series in y up to y⁵ and in x up to x³ show that for fixed lattice spacing a, G/M^4?d is a monotonic function of g₀ ranging from zero at g₀ = 0 to a maximum at g₀ = ∞. Using the high temperature expansion results, we have also derived 9 terms in y on 8 lattices of dimension 1,2,3 and 4 for the linear term in x, and studied this series to see if one can see a breakdown in this monotonic behavior of G for large y. The analysis of this latter series is inconclusive.     

Pulsed-laser photolysis of chromium and molybdenum hexacarbonyls at 308 nm: Simultaneous monitoring of optical and acoustic emissions

An acoustic technique developed earlier was applied to measure the molar number of fragments produced in the XeCl-laser-induced gas-phase photolysis of Cr(CO)₆ and Mo(CO)₆. The bluish-green Cr and Mo emissions were also monitored and correlated with the acoustic signal. For laser fluence ranging up to about 25 mJ/cm² (38 mJ/cm²), the Cr (Mo) optical signal varied with laser fluence asy =dx ³, in agreement with the model that highly excited metal atoms were produced by direct three-photon processes. The acoustic signal varied with fluence asy = ax + bx ², consistent with the model that most fragments were formed via sequential and direct two-photon processes. Quite expectedly, all coefficientsa,b andd vary linearly with carbonyl partial pressure. Both optical and acoustic signals showed onset of saturation at 25 mJ/cm² (38 mJ/cm²) for the case of chromium (molybdenum) hexacarbonyl, suggesting that all photolysis channels were equally affected by the depletion of parent molecules. By assuming a common depletion mechanism, upper limits on the branching ratios of the various photolysis channels were estimated.     

Study of the three-dimensional Ising model on film geometry with the cluster Monte Carlo method

Topological properties of clusters are used to extract critical parameters. This method is tested for the bulk properties ofd=2 percolation and thed=2, 3 Ising model. For the latter we obtain an accurate value of the critical temperatureJ/k _B T _c=0.221617(18). In the case of thed=3 Ising model with film geometry the critical value of the surface coupling at the special transitions is determined as J_1c/J=1.5004(20) together with the critical exponents ₁ ^m =0.237(5) and=0.461(15).     

Two-proton neutron-hole yrast excitations in 66 147 Dy81

The level structure of theN=81 nucleus¹⁴⁷Dy has been studied byγ-ray spectroscopy following reactions of 230–250 MeV^58,60Ni beams on⁸⁹Y and^90,92Zr targets. Yrast and near-yrast levels in¹⁴⁷Dy above the known 59-s 11/2^? state are established up to ～3.7 MeV; they include isomeric levels at 2,681, 3,407 and 3,650 keV. Guided by the results of shell model calculations, we interpret most of the observed level as senioritythree states arising from the coupling ofs _1/2,d _3/2, andh _11/2 neutron holes withπh _11/2 ².     

The distribution of205Tl proton hole states and estimation of the root mean square radii of206Pb and208Pb from their charge distributions

The fragmentations of the 3s _1/2, 2d _3/2, 2d _5/2 and 1.h _11/2 proton states were deduced using the hole-core coupling model calculation and compared with recent²⁰⁶Pb ( \(\vec d\) ,³He) reaction data. The energies of the proton fragments carrying the main shell-model strengths were used to deduce the radial wave functions of²⁰⁵T1 and²⁰⁷Tl that give rise to charge distributions of these nuclei. From their respective charge distributions, root mean square radii of²⁰⁶Pb and²⁰⁸Pb were extracted.     

Model-independent analysis of the differential cross section for the reaction n+d→π0+t at medium energies

Experimental values of the differential cross section for the reactionn+d→π ⁰+t at large angles (θ?50°) in the neutron energy range 460–560 MeV and the known values of the coupling constants \(G_{nn\pi ^O }^2 \) andG _tdn ² are used to predictdσ/dΩ at smaller angles. The method is based on the use of general analytic properties of the differential cross section in the cosgq-plane.     

High precision hyperfine structure measurements in185Re and187Re

The hyperfine structure of the atomic levels 5d ⁵ 6s ^{2 6} S _5/2 and⁴ P _5/2 in¹⁸⁵Re and¹⁸⁷Re has been studied with high precision by atomic-beam magnetic-resonance. Additional measurements were performed in the 5d ⁵ 6s ^{2 4} G _5/2 and 5d ⁶ 6s ⁶ D _9/2 states of¹⁸⁷Re. For the interpretation of the results eigenvectors in intermediate coupling have been derived by a least squares fit of all known levels of the configurations (5d+6s)⁷. The ratioB(¹⁸⁵Re)/B(¹⁸⁷Re) is the same for the⁶ S _5/2 and the⁴ P _5/2 state within the error limits of 6 parts in 10⁵. Combining the present results with the known hyperfine structure data of¹⁸⁶Re and¹⁸⁸Re we find the magnetic-dipole hyperfine anomalies for the isotopic series^185?188Re.     

Elastic constants in RbI,determined by inelastic neutron scattering

Long-wavelength acoustic phonons have been studied in the whole (100)-plane of RbI at 295 K by means of inelastic neutron scattering. The raw data have been corrected for resolution effects taking into account the curvature of the dispersion surface and variations of the mode eigenvectors. The shifts of the neutron groups due to these resolution effects are discussed in detail. The analysis of the experimental results gives for the zero sound elastic constantsc ₁₁=28.15±0.5,c ₁₂=3.7±0.5 andc ₄₄=2.85±0.1 10¹⁰ dyn/cm². A comparison with first sound elastic constants taken from ultrasonic measurements yields significant differences between the high and low frequency elastic constantsc ₁₁ andc=(c ₁₁–c ₁₂)/2. The differences calculated from recent theories are in agreement with the experimental results for the elastic constantsc ₁₁,c ₄₄ andc, but not forc ₁₂. The dispersion surface in the (100)-plane is also shown for some out-of-symmetry data and compared with ultrasonic data as well as with theoretical results.Research supported by BMFT     

Representations ofSO(p+q) andO(p) with an application to the shapes of8,9Li

It is easy to show that the symmetry groups governing a system ofZ protons andN neutrons areSO(p+q) andO(p), wherep, q are related toZ, N and the symmetry groups are transitive on a Grassmann manifoldG _p,q. In this paper the general representations ofSO(p+q) andO(p) are found and used to describe the geodesics onG _p,q for the nuclear manifolds of the neutron rich-elements^8,9Li.     

Elastic constants of sodium chlorate from 77 K to 350 K

The elastic constantsC ₁₁,C ₁₂ andC ₄₄ of sodium chlorate single crystal have been evaluated using 10 MHz ultrasonic pulse echo superposition technique. The values areC ₁₁=4.90,C ₁₂=1.39,C ₄₄=1.17 (× 10¹⁰ N/m ²) at 298 K and 6.15, 2.16, 1.32 (×10¹⁰ N/m ²) at 77 K. The data agree well with the values measured earlier up to 223 K. Brief mention is also made of the low temperature bonding problems in these soft crystals.     

Cosmology withG and Λ coupling scalars

Cosmology with the gravitational and cosmological constants generalized as coupling scalars in Einstein's theory is considered. A general method of solving the field equations is given. Fifteen exact solutions for zero pressure models satisfyingG=G ₀(R/R ₀) ⁿ are given in the Appendix; they are briefly discussed.     

Hyperfine structure in the atomic spectrum of niobium

A parametric analysis of the fine and the hyperfine structure for the three even configurations 4d^45s, 4d ⁴5s ² and 4d⁵ has been performed. Effective one-electron parameters a _nl ^kskl(k _s k _l = 01, 12 and 10) and b _nl ⁰² were determined for these three configurations. Extremely large ratios a _4d ¹⁰/a _4d ⁰¹ were found. Theoretical predictions for the hyperfine structure constants A and B for all levels of the configurations 4d^45s, 4d ⁴5s ² and 4d⁵ have been determined from experimental data. Additionally, the fine and hyperfine structure for the two energetically high lying even configurations 4d^46s and 4d^35s6s are discussed. The results presented here call into doubt the existence of the fine structure levels 4d ³5s6s ⁶ F _11/2 at an energy of 39 408.88 cm^-1 and 4d ³5s5p ⁶ G _13/2 at 18 876.46 cm^-1 given in the Moore tables.     

立方对称晶场中6S(3d5)态离子的磁相互作用及其自旋哈密顿参量的微观起源

基于完全对角化方法(complete diagonalization method, CDM), 研究了⁶S(3d⁵)态离子在立方对称晶场中的磁相互作用,分析了自旋哈密顿参量(a, g,Δg)的微观起源.研究中除了考虑研究者通常考虑的SO(spin-orbit)磁相互作用外,同时考虑了SS(spin-spin),SOO(spin-other-orbit),OO(orbit-orbit)磁相互作用.研究表明：⁶S(3d⁵)态离子在立方对称晶场中的自旋哈密顿参量起源于五种机理,即SO机理,SS机理,SOO机理,OO机理以及SO-SS-SOO-OO联合作用机理.文中研究了五种机理的相对重要性,结果表明：SO机理与SO-SS-SOO-OO联合作用机理在五种机理中最为重要.尽管SS,SOO,OO磁相互作用单独作用时对自旋哈密顿参量的贡献很小,但它们的联合作用SO-SS-SOO-OO机理对自旋哈密顿参量的贡献非常可观.此外研究表明：零场分裂参量a主要来自纯自旋四重态及自旋二重态与自旋四重态联合作用的贡献,而Zeemang(或者Δg)因子主要来自纯自旋四重态的贡献.纯自旋二重态对自旋哈密顿参量a与g(或者Δg)的贡献为零.在我们所选择的晶场区域,发现下列关系始终成立：a>0,a(-|Dq|)<a(|Dq|),g(-Dq)=g(Dq),a(-Dq,-ξ_d,B,C)=a(Dq,ξ_d, B,C),Δg(-Dq,-ξ_d, B, C)=Δg(Dq,ξ_d, B, C).作为本文理论的应用,研究了四种典型的Mn²⁺掺杂晶体材料,即Mn²⁺:KZnF₃,Mn²⁺: RbCdF₃,Mn²⁺: MgO,Mn²⁺: CaO,理论与实验测量符合很好. 关键词： 自旋哈密顿参量 6S(3d⁵)态离子')" href="#">⁶S(3d⁵)态离子 磁相互作用 完全对角化方法(CDM)     

Structural phase transitions in Pd0.8 Si0.2 and Pd0.75 Si0.20 Ag0.05 alloys observed by pac

The phase transition in the alloys Pd_0.8 Si_0.2 and Pd_0.75 Si_0.20 Ag_0.05 have been investigated through the quadrupole interaction of¹¹¹Cd impurities. The quadrupole interactions were measured by means of the TDPAC technique from room temperature up to about 870 K. The variation of the quadrupole interaction with temperature in the alloy PdSiAg shows aT ^3/2 dependence below and above 629 K, with coefficientsB=5.43(25)·10⁻⁵ K^−3/2 andB=3.70(15)·10⁻⁵ K^−3/2, respectively. This demonstrates that the alloy undergoes a phase transition around 629 K. The existence of two electric field gradients observed in the alloy PdSi,V _zz (1)=3.47(54)·10¹⁷ V/cm² andV _zz (2)=2.29(36)·10¹⁷ V/cm², indicates that there are two different¹¹¹Cd sites. The corresponding fractionsf ₁ andf ₂ strongly depend on temperature. Below 520 K, most¹¹¹Cd nuclei are subject to the higher EFGV _zz (1) (f ₁≈70%), whereas above 520 Kf ₁ falls rapidly to zero andV _zz (2) becomes dominant. The temperature dependences of thef ₁ andf ₂ reveal a picture of the phase transition between the two crystal structures.