Compact variational wave functions for bound states in three-electron atomic systems

The variational procedure to construct compact and accurate wave functions for three-electron atoms and ions is developed. The procedure is based on the use of six-dimensional Gaussoids written in the relative four-body coordinates r ₁₂, r ₁₃, r ₂₃, r ₁₄, r ₂₄, and r ₃₄. The nonlinear parameters in each basis function have been carefully optimized. Using these variational wave functions, we have determined the energies and other bound state properties for the ground 1² S-states in a number of three-electron atoms and ions. The three-electron atomic systems considered in this work include the neutral Li atom and nine positively charged lithiumlike ions: Be⁺, B²⁺, C³⁺, ..., Na⁸⁺, and Mg⁹⁺. Our variational wave functions are used to determine the hyperfine structure splitting and field shifts for some lithium-like ions. The explicit formulas of the Q ⁻¹ expansion are derived for the total energies of these three-electron systems. The article is published in the original.     

A Conjecture for the Superintegrable Chiral Potts Model

We adapt our previous results for the “partition function” of the superintegrable chiral Potts model with open boundaries to obtain the corresponding matrix elements of e^{−α H} , where H is the associated Hamiltonian. The spontaneous magnetization ℳ _r can be expressed in terms of particular matrix elements of e^{−α H} S ₁ ^r e^{−β H} , where S ₁ is a diagonal matrix. We present a conjecture for these matrix elements as an m by m determinant, where m is proportional to the width of the lattice. The author has previously derived the spontaneous magnetization of the chiral Potts model by analytic means, but hopes that this work will facilitate a more algebraic derivation, similar to that of Yang for the Ising model.     

Monte-Carlo optimization of correlated helium wave function

A new type of correlated wave function for the normal helium is proposed in the form:ψ(r₁, r₂)=Σc _mφ_m withφ _m=exp]−α(r ₁+r ₂)]/(br ₁₂+a) ^m wherea, b, α are non-linear variational parameters. Optimizing these parameters by the Monte-Carlo technique, an energy eigen-value of −2.903645(a.u.) is obtained withonly three terms in the basis expansion alongwith satisfactory cusp condition, compared to the essentially exact non-relativistic value of −2.903724 as given by Freundet al (Phys. Rev. A29, 980 (1984)).     

Quark-antiquark states and their radiative transitions in terms of the spectral integral equation: Charmonia

Earlier by the authors (Yad. Fiz. 70, 68 (2007)), the bƃ states were treated in the framework of the spectral integral equation, together with simultaneous calculations of radiative decays of the considered bottomonia. In the present paper, such a study is carried out for the charmonium states. We reconstruct the interaction in the c-c sector on the basis of the data for the charmonium levels with J _PC = 0⁻⁺, 1⁻⁻, 0⁺⁺, 1⁺⁺, 2⁺⁺, 1⁺⁻ and radiative transitions ψ(2S) → γχ _c0(1P), γχ _c1(1P), γχ _c2(1P), γχ _c(1S) and χ _c0(1P), χ _c1(1P), χ _c2(1P) → γJ/ψ. The c-c levels and their wave functions are calculated for the radial excitations with n ≤ 6. Also, we determine the c-c component of the photon wave function using the e ⁺ e ⁻-annihilation data: e ⁺ e ⁻ → J/ψ(3097), ψ(3686), ψ(3770), ψ(4040), ψ(4160), ψ(4415) and perform the calculations of the partial widths of the two-photon decays for the n = 1 states η _c0(1S), χ _c0(1P), χ _c2(1P) → γγ and n = 2 states η _c0(2S) → γγ, χ _c0(2P) → γγ. We discuss the status of the recently observed c-c states X(3872) and Y(3941): according to our results, the X(3872) can be either χ _c1(2P) or η _c2(1D), while Y(3941) is χ _c2(2P). The text was submitted by the authors in English.     

Quark-Antiquark states and their radiative transitions in terms of the spectral integral equation: Bottomonia

In the framework of the spectral integral equation, we consider the states and their radiative transitions. We reconstruct the interaction on the basis of data for the levels of the bottomonium states with J ^PC = 0⁻⁺, 1⁻⁻, 0⁺⁺, 1⁺⁺, 2⁺⁺ as well as the data for the radiative transitions γ (3S) → _γχbJ(2P) and γ(2S) → _γχbJ(1P) with J = 0, 1, 2. We calculate bottomonium levels with the radial quantum numbers n ≤ 6, their wave functions, and corresponding radiative transitions. The ratios Br[_χbJ(2P) → _γγ(2S)]/Br[_χbJ(2P) → _γγ(1S)] for J = 0, 1, 2 are found to be in agreement with data. We determine the component of the photon wave function using the data for the e ⁺ e ⁻ annihilation, e ⁺ e ⁻ → γ(9460), γ(10 023), γ(10 036), γ(10 580), γ(10 865), γ(11 019), and predict partial widths of the two-photon decays ηb0 → γγ, χb0 → γγ, χb2 → γγ for the radial excitation states below the threshold (n ≤ 3). The text was submitted by the authors in English.     

Surfing and generation of cosmic rays in relativistic shock waves

We consider the problem of cosmic-ray generation through the surfing acceleration of charged particles in relativistic magnetosonic shock waves (the branch of fast magnetic sound) propagating in magnetized space plasmas. The dependence of the particle surfing acceleration efficiency on the angle θ _Bn between the normal to the shock front plane and the magnetic field vector in the plasma upstream of the shock is analyzed in detail. We show that for angles satisfying the condition χ = βΓ tan θ _Bn ⩾ 1, where β = U/c, Γ = (1 − β)^{2 −1/2}, U is the shock velocity, and c is the speed of light, the particles can theoretically be accelerated through surfing for an unlimited time and can gain an unlimited energy. For angles satisfying the condition χ < 1, the kinetic energy ℰ of the particles is limited by ℰ = 2mc ²χ²/(1 − χ²) (m is the particle rest mass). Our main conclusion is that the generation of cosmic rays through the surfing acceleration of particles in the front of a relativistic shock wave for Γ ≫ 1 is also efficient when the angle θ _Bn is very small, i.e., it differs significantly from a right angle. Estimates for the energies of particles accelerated through surfing in relativistic jets are provided.     

Bound states and critical behavior of the Yukawa potential

We investigate the bound states of the Yukawa potential V (r)=−λexp(−αr)/r, using different algorithms: solving the Schr?dinger equation numerically and our Monte Carlo Hamiltonian approach. There is a critical α = α_C, above which no bound state exists. We study the relation between α_C and λ for various angular momentum quantum number l, and find in atomic units, α_C(l) = λ[A ₁ exp(−l/B ₁) + A ₂ exp(−l/B ₂)], with A ₁ = 1.020(18), B ₁ = 0.443(14), A ₂ = 0.170(17), and B ₂ = 2.490(180).     

Spin state and exchange in the quasi-one-dimensional antiferromagnet KFeS2

We report the optical spectra and single crystal magnetic susceptibility of the one-dimensional antiferromagnet KFeS₂. Measurements have been carried out to ascertain the spin state of Fe³⁺ and the nature of the magnetic interactions in this compound. The optical spectra and magnetic susceptibility could be consistently interpreted using aS=1/2 spin ground state for the Fe³⁺ ion. The features in the optical spectra have been assigned to transitions within thed-electron manifold of the Fe³⁺ ion, and analysed in the strong field limit of the ligand field theory. The high temperature isotropic magnetic susceptibility is typical of a low-dimensional system and exhibits a broad maximum at ∼565K. The susceptibility shows a well defined transition to a three dimensionally ordered antiferromagnetic state atT _N=250 K. The intra and interchain exchange constants,J andJ′, have been evaluated from the experimental susceptibilities using the relationship between these quantities, andχ _max,T _max, andT _N for a spin 1/2 one-dimensional chain. The values areJ=−440.71 K, andJ′=53.94 K. Using these values ofJ andJ′, the susceptibility of a spin 1/2 Heisenberg chain was calculated. A non-interacting spin wave model was used belowT _N. The susceptibility in the paramagnetic region was calculated from the theoretical curves for an infiniteS=1/2 chain. The calculated susceptibility compares well with the experimental data of KFeS₂. Further support for a one-dimensional spin 1/2 model comes from the fact that the calculated perpendicular susceptibility at 0K (2.75×10⁻⁴ emu/mol) evaluated considering the zero point reduction in magnetization from spin wave theory is close to the projected value (2.7×10⁻⁴ emu/mol) obtained from the experimental data.     

Measurement of the spindependent relative conversion coefficients in α-Fe and α-Fe2O3

The relative differences δ _ns (n=1, 2, 3) of the spindependent conversion coefficients were measured for α-Fe and α=Fe₂O₃. In contrast to theoretical predictions of δ_1s≃−10⁻⁵ we found δ_1s≃−1.0(4)x10⁻² for both α-Fe and α-Fe₂O₃. As a possible source for this difference we consider a dynamic coupling with the atomic spin during the conversion process.     

Spin-dependent correction to the relativistic-electron mass in QED in the presence of an external electric field

A new expression is found for the spin-dependent contribution Δm _s to the self-energy of an electron moving with a transverse momentum p⊥ in an electric field. The structure of an asymptotic expansion of Δm _s (r, χ) as a function of two dynamical invariants r = γ _⊥⁻² and χ = γ _⊥|ɛ|/ɛ _c (γ _⊥² ≡ 1 + p _⊥²/m ² c ² and ɛ _c ≡ m ² c ³/|e|ℏ) is clarified with the aid of this expression. The expansion of Δm _s (r, χ) can be represented in the form of a Taylor series in r, the coefficients in this series, F ₀(χ), F ₁(χ), etc., being integrals of the Mellin type. The major coefficient F ₀(χ) is universal and, in the case of an appropriate interpretation of χ, describes well-known spin-dependent corrections to the mass in three different cases of a constant external field (for r → 0). The asymptotic properties of the function F ₁(χ) are studied in detail, but only order-of-magnitude estimates are obtained for F ₂(χ) and F ₃(χ). A comparison of these contributions revealed that, in the semiclassical region χ ≪ 1, r is indeed the parameter of the aforementioned expansion, while, for χ ≫ 1, the true parameter is rχ ² ≡ β ². In particular, the anomalous magnetic moment develops, owing to F ₁(χ), a term that grows logarithmically for χ ≫ 1, but which does not violate the hierarchy of terms in the Taylor series being considered, provided that β remains smaller than unity.     

Quantum-chemical modeling of structural,electronic, and spin characteristics of NV centers in nanostructured diamond: Surface effect

The effect of the surface of diamond on atomic, electronic, and spin properties of diamond nanocrystals containing single nitrogen-vacancy defects ([NV]⁻ centers) is studied. The surface was modeled with clusters C₃₃H₃₀[NV]⁻, C₆₆H₇₂[NV]⁻, which were constructed based on bulk clusters C₃₃H₃₆[NV]⁻ and C₆₉H₈₄[NV]⁻, respectively. In all cases, clusters in the triplet state S = 1 are considered with the cluster charge being −1. The geometric structure of clusters is optimized using the principle of minimization of the total energy of the system; then, the electronic and spin characteristics of clusters are calculated by the density functional theory. The isotropic and anisotropic hyperfine interaction constants of the electron spin of the NV center with the nuclear spin of the nitrogen atom and ¹³C atoms located at different sites in the cluster are calculated. It is found that, in contrast to bulk clusters with [NV]-centers in which the spin density is mainly localized at the three carbon atoms that are the nearest neighbors of the vacancy of the center, upon arrangement of the NV center in the immediate proximity to the surface, the spin density is redistributed such that it is mainly localized at the three carbon atoms that are the nearest neighbors of the nitrogen atom of the center and at C atoms that form the first atomic layer of the (111) surface of the nanocrystal.     

ESR of V4+ in α-RbTiOPO4 single crystals

We have recorded and investigated the ESR spectrum of vanadium-doped α-RbTiOPO₄ single crystals in the temperature interval 77–300 K. Two types of structurally distinct centers, V1 and V2, with a 4:1 ratio of the peak intensities were observed. The angular dependences of the resonance magnetic fields are described by a spin Hamiltonian corresponding to axial symmetry with the parameters g _∥1=1.9305, g _⊥1=1.9565, A _∥1=−168.2×10⁻⁴cm⁻¹, and A _⊥1=−54.3×10⁻⁴cm⁻¹ for V1 centers and g _∥2=1.9340, g _⊥2=1.9523, A _∥2=−169.0×10⁻⁴cm⁻¹, and A _⊥2=−55.2×10⁻⁴cm⁻¹ for V2 centers. A model of a paramagnetic center is proposed: The vanadium ions replace titanium ions in two structurally distinct positions Ti1 and Ti2 (V1 and V2 centers, respectively). The possibility that a VO²⁺ ion forms when α-RbTiOPO₄ crystals and crystals of the KTP group (KTiOPO₄, NaTiOPO₄, α-and β-LiTiOPO₄), studied earlier, are doped with vanadium is discussed. Fiz. Tverd. Tela (St. Petersburg) 40, 534–536 (March 1998)     

Spectral theory of elliptic operators in exterior domains

Diverse closed (and selfadjoint) realizations of elliptic differential expressions A = Σ_{0⩽|α|,|β|⩽m} (−1) ^α D ^α a _α,β (x)D ^β , a _α,β (·) ∈ C ^∞($ \bar \Omega $ \bar \Omega ) on smooth (bounded or unbounded) domains Ω in ℝ ⁿ with compact boundary ∂Ω are considered. Trace-ideal properties of powers of resolvent differences for these closed realizations of A are proved by using the concept of boundary triples and operator-valued Weyl-Titchmarsh functions, and estimates for negative eigenvalues of certain selfadjoint extensions of the nonnegative minimal operator are derived. Our results extend classical theorems due to Vishik, Povzner, Birman, and Grubb.     

Compact and accurate variational wave functions of three-electron atomic systems constructed from semi-exponential radial basis functions

The semi-exponential basis set of radial functions [A.M. Frolov, Phys. Lett. A 374, 2361 (2010)] is used for variational computations of bound states in three-electron atomic systems. It appears that the semi-exponential basis set has a substantially greater potential for accurate variational computations of bound states in three-electron atomic systems than was originally anticipated. In particular, the 40-term Larson’s wave function improved with the use of semi-exponential radial basis functions now produces the total energy –7.4780581457 a.u. for the ground 1²S-state in the ^￥Li^\infty{\rm Li} atom (only one spin function c₁\chi_1 = aba\alpha\beta\alpha - baa\beta\alpha\alpha was used in these calculations). This variational energy is very close to the exact ground state energy of the ^￥Li^\infty{\rm Li} atom and is substantially lower than the total energy obtained with the original Larson’s 40-term wave function (–7.477944869 a.u.).     

A μSR Study of Er Spin Dynamics in (Y1−x Er x )Ni2B2C Superconductors

Zero field μSR has been used to probe rare earth spin dynamics in the magnetic superconductors, Y_1−x Er _x Ni₂B₂C. The muon spin relaxation function is stretched exponential, exp (−(λt)^β), in form, as usually found for spin glass systems above the glass temperature. However, the Y_1−x Er _x Ni₂B₂C compounds show no evidence of coexisting superconducting and static spin glass ground states even at concentrations below the critical value (x=0.6) for long range antiferromagnetic order. The temperature dependence of both the muon spin relaxation rate λ and the exponent β suggests that Er spin dynamics change significantly at the superconducting transition temperature. This revised version was published online in September 2006 with corrections to the Cover Date.     

Low-frequency fluctuations in stochastic processes with a 1/<Emphasis Type="Italic">f</Emphasis><Superscript>α</Superscript> spectrum

The results of numerical analysis of the Brownian movement of a particle in the force field of the potential corresponding to interacting subcritical and supercritical phase transitions are considered. If the white noise intensity corresponds to the critical intensity of the noise-induced transition, the system of stochastic differential equations describes random steady-state processes with fluctuation power spectra inversely proportional to frequency f, S(f) ∼ 1/f ^α, where exponent α varies in the interval 0.8 ≤ α ≤ 1.8. Exponent β of distribution function P(τ) ∼ τ^−β for the duration of low-frequency extremal fluctuations, which are analogous to avalanches considered in the models of self-organized criticality in many respects, varies between the same limits. It is shown that exponents α and β are connected through the relation α + β = 2.     

Properties of the πη,$ \eta{^\prime}$,σ, f0(980) and a0(980) mesons and their relevance for the polarizabilities of the nucleon

The signs and values of the two-photon couplings F _Mγγ of mesons (M) and their couplings g_MNN to the nucleon as entering into the t -channel parts of the difference of the electromagnetic polarizabilities (α - β) and the backward angle spin polarizabilities γ_π are determined. The excellent agreement achieved with the experimental polarizabilities of the proton makes it possible to make reliable predictions for the neutron. The results obtained are α_n = 13.4±1.0 , β_n = 1.8±1.0 (10^-4fm^3), and γ⁽ⁿ⁾ _π = 57.6±1.8 (10^-4fm^4). New empirical information on the flavor wave functions of the f ₀(980) - and the a ₀(980) -meson is obtained.     

The phase diagram of (NH4I)x(KI)1−x

The χ,T phase diagram of (NH₄I)_x(KI)_1−x has been determined using neutron diffraction experiments and dielectric spectroscopy. At low temperatures and with decreasing χ, the sequence γ, β, ε and glass phase has been detected. The critical concentration χ_c≈0.55 separates the glassy phase with frozen-in orientational disorder from the ε phase which reveals long-range orientational order. Close to χ_c our experiments reveal evidence for two subsequent glass transitions.     

Uncertainties on <Emphasis Type="Italic">α</Emphasis><Subscript><Emphasis Type="Italic">S</Emphasis></Subscript> in global PDF analyses and implications for predicted hadronic cross sections

We determine the uncertainty on the strong coupling α _S due to the experimental errors on the data fitted in global analysis of hard-scattering data, within the standard framework of leading-twist fixed-order collinear factorisation in the [`(MS)]\overline{\mathrm{MS}} scheme, finding that α _S (M _Z ²)=0.1202_−0.0015^+0.0012 at next-to-leading order (NLO) and α _S (M _Z ²)=0.1171_−0.0014^+0.0014 at next-to-next-to-leading order (NNLO). We do not address in detail the issue of the additional theory uncertainty on α _S (M _Z ²), but an estimate is ±0.003 at NLO and at most ±0.002 at NNLO. We investigate the interplay between uncertainties on α _S and uncertainties on parton distribution functions (PDFs). We show, for the first time, how both these sources of uncertainty can be accounted for simultaneously in calculations of cross sections, and we provide eigenvector PDF sets with different fixed α _S values to allow further studies by the general user. We illustrate the application of these PDF sets by calculating cross sections for W, Z, Higgs boson and inclusive jet production at the Tevatron and LHC.     

The potts glass in uniform and random fields: a monte carlo investigation

As a simple model of an anisotropic orientational glass with short range forces, the 3-state Potts model on the simple cubic lattice with nearest neighbor interactions drawn from a Gaussian distribution is considered. With Monte Carlo methods we study the response of the system to a uniform “field” which favors one of the states. This is motivated by experiments which apply stress that favors one molecular orientation of the quadrupolar glass. The responsem to that fieldh=H/k _BT is analyzed in terms of an expansionm= χ₁ h+χ₁ h ²+χ₁ h ³+..., where χ₁ is the linear susceptibility, and χ₂,χ₁₃ are nonlinear susceptibilities. Unlike the case of spin glasses, where the spin inversion symmetry of the system in the absence of fields implies χ₂≡0,χ₂ is nonzero here and diverges to −∞ at the zero temperature transition of the model, while χ₃ diverges to +∞ as in spin glasses. At inifinite temperature, however, χ₁=1/3, χ₂=1/18 and χ₃=-1/54, i.e. the nonlinear susceptibilities have a different sign as at low temperature. In contrast, a random field does not induce a uniform order parameterm but only a glass order parameterq. The temperature dependence of this glass order parameterq(T) shows for intermediate field strength order parameterq(T) shows for intermediate field strength a maximum of the slopedq(T)/dT very similar to corresponding experiments.