Atomic beam magnetic resonance investigations in the3 F 2 Ground State of177Hf,179Hf and180Hf

The 5d ²6s ^{2 3} F ₂ ground state of¹⁷⁷Hf,¹⁷⁹Hf and¹⁸⁰Hf has been studied using the atomic beam magnetic resonance method. The atomic beam was produced by an universal evaporation technique described in a previous paper. The results are¹⁸⁰Hfg _j (³ F ₂)=0.695812 (10)¹⁷⁷Hf Δv(³ F ₂;F=11/2?F=9/2)=991.7917 (10) MHz Δv(³ F ₂;F=9/2?F=7/2)=477.0081 (10) MHz Δv(³ F ₂;F=7/2?F=5/2)=162.8890 (10) MHz¹⁷⁹HfΔv(³ F ₂;F=13/2?F=11/2)=82.1320 (10) MHz Δv(³ F ₂;F=11/2?F=9/2)=392.8498 (10) MHz. The magnetic dipole and electric quadrupole moments of the¹⁷⁷Hf and¹⁷⁹Hf nuclear ground states as calculated from these hyperfine structure measurements are the following: μ(177)=0.75(8)μ _k , Q(177)=4.34 (65) barns μ(179)=?0.61 (6)μ _k , Q(179)=4.90 (75) barns.     

The Δk = ±2 perturbation-allowed ν4 band and inversion-rotation energy levels of 15NH3

More than 800 Δk = ±2 and 60 Δk = ±3 forbidden transitions to the ν₄ and 2ν₂ vibrational levels, respectively, have been assigned in the Fourier transform spectra of ¹⁵NH₃, recorded with a pathlength of 96 m. Combination differences derived from these transitions provide information on the spacing between the ground state energy levels with different rotational quantum numbers K in the interval from 0 to 16. These data along with wavenumbers of all the available allowed transitions pertaining to the ground and ν₂ states have been subjected to a simultaneous least-squares analysis using two different parametrization models to obtain precise values of the inversion-rotation energy levels.     

On the separation of initial and final state effects in photoelectron spectroscopy using an extension of the auger-parameter concept

First, we show that the quantity Δβ(i) = ΔE_A(kii) + 2ΔE_B(i) — ΔE_B(k) is directly related to the final state relaxation contribution ΔE_R(i) of the binding energy shift ΔE_B(i). ΔE_A(kii) is the kinetic energy shift of the Auger transition which corresponds to the decay of a hole state with a hole in level k into a final state with two holes in level i. The shift parameter Δβ(i), which is based on information on two binding energies, is conceptually similar to Wagner's Auger parameter. To establish the relation between Δβ(i) and ΔR(i) one needs, however, less drastic approximations than in the case of Auger parameter shifts. The only approximation necessary is the assumption that ΔR(i) is determined by coulomb contributions.Secondly, we use Δβ (i) to analyse the experimental data of eighteen gaseous phosphorus-containing compounds obtained by Sodhi and Cavell¹. It is shown that ΔR(P_2p) is strongly related to changes in the polarizability of the ligands. The initial state effects derived from our study deviate from those expected on the basis of simple electronegativity considerations.     

Asymptotic correlation functions and FFLO signature for the one-dimensional attractive spin-1/2 Fermi gas

We investigate the long distance asymptotics of various correlation functions for the one-dimensional spin-1/2 Fermi gas with attractive interactions using the dressed charge formalism. In the spin polarized phase, these correlation functions exhibit spatial oscillations with a power-law decay whereby their critical exponents are found through conformal field theory. We show that spatial oscillations of the leading terms in the pair correlation function and the spin correlation function solely depend on ΔkF and 2ΔkF, respectively. Here ΔkF=π(n_↑−n_↓) denotes the mismatch between the Fermi surfaces of spin-up and spin-down fermions. Such spatial modulations are characteristics of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. Our key observation is that backscattering among the Fermi points of bound pairs and unpaired fermions results in a one-dimensional analog of the FFLO state and displays a microscopic origin of the FFLO nature. Furthermore, we show that the pair correlation function in momentum space has a peak at the point of mismatch between both Fermi surfaces k=ΔkF, which has recently been observed in numerous numerical studies.     

Pairing in one-dimensional antiferromagnetic superconductors in the presence of a homogeneous magnetic field

Assuming a one-dimensional like electron band and considering the free energy difference δF(= F_s?F_N) near the second order phase transition temperature, it is shown that for an antiferromagnetic superconductor in a homogeneous magnetic field (howsoever weak) the minimum of δF occurs when the state with spatially varying order parameter (having same period as the antiferromagnetic ordering) coexists with the usual BCS state.     

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.     

Far infrared spectrum and spectroscopic constants of AsH3 in the ground state

The far ir spectrum of arsine, AsH₃, was recorded in the range 25–100 cm^?1 with a resolution of approximately 0.004 cm^?1. ΔJ = +1, ΔK = 0 rotational transitions were measured and assigned up to J″ = 12. These transitions, together with the presently available microwave and submillimeter-wave data and ground state combination differences, were analyzed on the basis of a rotational Hamiltonian which includes Δk = ±3 and Δk = ±6 interaction terms. The derived ground state molecular parameters reproduced the transition frequencies of both allowed and “perturbation allowed” transitions within the accuracy of the measurements. The equilibrium structure was determined for the AsH₃ molecule.     

Ground state energy of spin polarized hard core neutron matter

The expansion of the ground state energy of spin polarized hard core neutron matter in powers of x =k_Fc (k_F = Fermi momentum, c = hardcoreradius) is calculated up to terms ≈x⁸.     

Cooper pair and electron-hole pair instabilities in a quasi-one dimensional system

We calculate for an almost half-filled tight-binding band, the mean field ground state energy differences between the charge-density-wave (CDW) and BCS paired states for a truncated model Hamiltonian with zero-range instantaneous electron-electron interactions. The CDW pairing is found to be always unstable vis-à-vis BCS for a static lattice distortion of wave vector Q = (2k_F, π, π).     

Nuclear hyperfine structure in the XΣ state of ZrC

Electronic band systems of zirconium monocarbide, ZrC, in the 16 000-19 000 cm⁻¹ region have been observed following the reaction of laser-ablated Zr atoms with methane under supersonic free-jet conditions. Rotational analyses of high-resolution spectra have shown that the ground state of ZrC is a ³Σ state, with r₀=1.8066 Å and an unexpectedly small spin-spin parameter, λ=0.5139 cm⁻¹. The spectra are dense because of the five naturally occurring isotopes of Zr. Four of these, with mass numbers 90, 92, 94, and 96, have I=0, but the fifth, ⁹¹Zr, present in 11.22% abundance, has I=5/2. Lines of ⁹¹ZrC can be assigned in some of the strongest bands, and are found to display sizeable hyperfine splittings, with widths of up to 0.2 cm⁻¹. Analysis shows that the largest hyperfine effects are in the ground state, where b=−0.03133±0.00015 cm⁻¹ and c=−0.00123±0.00037 cm⁻¹ (3σ error limits). The large Fermi contact parameter, b, indicates that an unpaired Zr 5sσ electron is present, which, taken together with the small value of λ, means that the ground state must be a ³Σ⁺ state, from the electron configuration (Zr 5sσ)¹ (C 2pσ)¹. Internal hyperfine perturbations occur between the F₁ and F₃ electron spin components of the ground state in the range N=2-4, producing extra lines in some of the branches; the perturbations are of the type ΔN=0, ΔJ=±2, and are a second-order effect arising because the F₁ (J=N+1) and F₃ (J=N−1) spin components both interact with the F₂ (J=N) component through ΔN=0, ΔJ=±1 matrix elements of the Fermi contact operator. Second-order perturbations of this type can only occur in states that are very close to case (b) coupling.     

On the three body contributions to the ground state energy of nuclear matter

The theory of nuclear matter is investigated by means of the method of unitary transformations in the special case of point transformations. The induced three body forces are constructed, their contributions to the ground state energy of nuclear matter are given in first order perturbation theory, and the connexion with Jastrow's procedure is shown. A first numerical estimate of the three body contributions to the energy per particle gives approximately 1 MeV in the physical density range. For higher values of the Fermi momentum (k _F ≈2 fm^?1) the contributions increase rapidly. Generally the induced three body forces cannot be neglected if one wants to calculate the correct saturation data.     

Size-dependent energy scales in the ideal fermi gas

Abstract

The simplest model for the electronic properties of small metal particles is an ideal Fermi gas confined to a finite volume. When the confining region of size L has a regular shape such as a sphere or a cube, there are two distinct scales of energy which characterize the spectrum of eigenvalues near the Fermi energy E_F ≡ ?² k ² _f/2m. The inner scale δ ～ E_F /(k_FL)² is the mean spacing between successive energy levels, while the outer energy scale Δ ～ E_F /(k_FL) describes clustering of several levels, or shell structure. Consequences for the behaviour of thermodynamic properties are investigated. There are three regimes of temperature T: normal metallic (T > Δ), shell-metallic (δ < T < Δ) and semiconductor-like (T < δ). Finally, if the shape of a hard-walled container is allowed to vary so as to minimize the energy, it is argued that the optimal shape fluctuates between spherical and distorted as L is changed.     

Activation volumes for formation and motion of defects in crystalline solids

By consideration of the factors that affect the activation volume for formation, ΔV_F, and for motion, ΔV_M, of a diffusing species, it is suggested that the sign dependence of the activation volume for self-diffusion, ΔV_D, can be predicted. Our predictions are based on the assumption that (1) interstitial diffusion is associated with an abnormally low activation energy for diffusion, (2) vacancy diffusion is present where normal activation energies are observed, and (3) a disordered, liquid-like region is produced when the diffusing species moves into the activated state. Several examples are presented to illustrate our proposed model.     

Anisotropic contribution of magnetostriction to the elastic compliance constants in hexagonal materials: The Δs-effect

In this paper, we consider the single crystal analogue of the ΔE-effect in hexagonal materials with uniaxial magnetic anisotropy. We define Δs_ijld as the fractional change in the elastic compliance tensor s_ijkl in the demagnetized state relative to its value in the saturated state. The Δs-effect depends in general on the direction of the applied stress and the resulting magnetostrictive strain. We can show, however, that Δs_ijkl is always nonnegative when i=k and j=l. We then consider the measurements of the elastic constants in magnetic materials which have large magnetocrystalline anisotropy. The stresses applied in these measurements are not sufficient to rotate the magnetization away from the magnetically preferred direction, and hence cause no magnetostriction, and no Δs-effect. Therefore, it is not necessary to apply a saturating magnetic field along the easy axis in order to measure the true elastic constants in these materials.     

Superconductivity in W5SiB2 with the T2-phase structure studied by the specific heat measurement and band structure calculation

The superconducting state of W₅SiB₂ with the T₂-phase structure has been investigated by a specific heat measurement and a density of state calculation. The estimated ΔC_p/γT_c and 2Δ(0)/k_BT_c values are 1.49 and 3.32, which are close to 1.43 and 3.53 within the weak coupling regime. The electronic specific heat data clearly indicates the absence of gap nodes in the superconducting order parameter, suggesting an isotropic s-wave superconductor. From the density of state calculations, we found that W d-orbital plays an important role for the superconductivity in W₅SiB₂.     

The ground state well depth position Rm of Van der Waals molecules and the spectral line shapes

As the ground state potential curve is strongly related to spectral line shapes, the minumum position of the ground state potential is obtained from the experiemental absorption profile k(Δν, T) at high density of the radiating atoms. The temperature dependence of the absorption processes of Hg and Cd lines 253.65 and 326.1 nm, respectively perturbed by inert gases (Xe, Kr, Ar and Ne) had been carefully studied over a wide spectral range. Using the point of the maximum temperature dependence Δν_m in each case, we are able to calculate the position of the ground state potential R_m using a simple formula.     

Single particle energies of nuclear matter and the reference spectrum method

The single particle energies and the ground state energy of a superfluid system of nuclear matter are investigated. There are two difficulties in calculating these quantitites in the t-matrix approximation: (1) On account of the structure of thet-matrix equation the single particle energy is a very complicated expression, which cannot be evaluated explicitly in general. (2) Due to the superfluidity of nuclear matter, there are singularities in thet-matrix. — To overcome these difficulties we apply the reference spectrum method, recently proposed byBethe, et al. The most important properties of a superfluid medium, the shift of the ground state energy and the gap in the single particle spectrum can then be very well described qualitatively. The quantitative results, however, are not satisfying. Furthermore, the estimation of the single particle potential is very much simplified. However, this is useful only for hole states. For particle statesk>k _F , the single particle energy cannot be calculated with sufficient accuracy on account of new complications coming from the rearrangement energy.     

Exact results of a mixed spin-1/2 and spin-1 Ising chain with both longitude and transverse single-ion anisotropies

The mixed spin-1/2 and spin-1 Ising chain with both longitude and transverse single-ion anisotropies Dz and Dx is solved exactly by means of a mapping to the spin-1/2 Ising chain with the alternating transverse fields and the Jordan-Wigner transformation. The analytical expressions of the quasi-particles' spectra Λk, the minimal energy gap Δ₀ for exciting a fermion quasi-particle, the minimal energy gap Δh for exciting a hole, and the ground state energy are obtained. The phase diagram of the ground state is also given. The results show that when Dz?0 for any finite value of Dx, there is no quantum critical point and the ground state is always in a spin ordered phase disregard of the boundary condition in the present system.     

On perturbation theory for the gr2N anharmonic oscillator

Perturbation series (PS) in powers of the coupling constant g for the D-dimensional anharmonic oscillator with power anharmonicity gr^2N is considered. The high order PS coefficients ?_k for the ground state energy are calculated explicitly with the help of recurrence relations among intergers. The rate of approach ?_k to their asymptotics $\text{?}{}_{\mathrm{k}}$ as a function of space dimension D is discussed.     

Neutron scattering study of the metal-semiconductor phase transition in K2Pt(CN)4Br0.3 ·3D2O under pressure

The elastic scattering associated with the 2k_F instability in the one-dimensional (1-d) conductor K₂Pt(CN)₄Br_0.3 · 3D₂O (KCP) has been studied at the low temperature super lattice point (0.5, 0.5, 3.7) as a function of temperature for different pressures. Within the investigated region between 0 and 11 kbar, we find that the value of 2k_F remains constant at $\text{1.703 c}{}^1$, although the absolute value of 2k_F changes by 1.5%. At the same time the Peierls gap Δ(0) and the interchain correlation length ξ_⊥ (0) decrease. We conclude that the 1-d character of KCP is enhanced under pressure.