Formation of Stripes and Slabs Near the Ferromagnetic Transition

We consider Ising models in d = 2 and d = 3 dimensions with nearest neighbor ferromagnetic and long-range antiferromagnetic interactions, the latter decaying as (distance)^?p , p > 2d, at large distances. If the strength J of the ferromagnetic interaction is larger than a critical value J _c , then the ground state is homogeneous. It has been conjectured that when J is smaller than but close to J _c , the ground state is periodic and striped, with stripes of constant width h = h(J), and h → ∞ as \({J\to J_c^-}\) . (In d = 3 stripes mean slabs, not columns.) Here we rigorously prove that, if we normalize the energy in such a way that the energy of the homogeneous state is zero, then the ratio e ₀(J)/e _S(J) tends to 1 as \({J\to J_c^-}\) , with e _S(J) being the energy per site of the optimal periodic striped/slabbed state and e ₀(J) the actual ground state energy per site of the system. Our proof comes with explicit bounds on the difference e ₀(J)?e _S(J) at small but positive J _c ?J, and also shows that in this parameter range the ground state is striped/slabbed in a certain sense: namely, if one looks at a randomly chosen window, of suitable size ? (very large compared to the optimal stripe size h(J)), one finds a striped/slabbed state with high probability.     

Microscopic foundation of the interacting boson model in thes d-shell nuclei

Starting from an isospin invariant shell-model hamiltonian, we describe a method for deriving microscopically the IBM-hamiltonian appropriate to lights d-shell nuclei. The key ingredients of our approach are:a) the Belyaev-Zelevinsky-Marshalek (BZM) bosonization procedure;b) two successive unitary transformations that extract the “maximally decoupled” collective bosons with angular momentaJ=0(s _ππ ⁺ ,s _νν ⁺ ,s _πν ⁺ ) andJ =2(d _ππ ⁺ ,d _νν ⁺ ,d _πν ⁺ (T=0),d _πν ⁺ (T=1)). The method is applied to obtain the low-energy spectra and the electron scattering form factors for the 0 ₁ ⁺ →2 ₁ ⁺ transitions in²⁰Ne and²⁴Mg. Good agreement with the exact shell-model results is achieved. The inclusion of proton-neutron bosons (s _πν ⁺ ,d _πν ⁺ (T=1),d _πν ⁺ (T=0)), as well as the renormalization of boson parameters due to the non-collective degrees of freedom, are shown to play a crucial role.     

On some properties of the neutron in the statistical model

Using the statistical model to arrive at |ψ(r)|² the square modulus of theS state wavefunction of the neutron, the electric dipole moment |d _n ^e | of the neutron as well as its baryon number violating lifetime have been estimated. The baryon asymmetry of the universe depending on |d _n ^e | has also been studied in this context.     

Optische Untersuchung der Hyperfeinstruktur einiger La I-Linien und Interpretation der gemessenenA-Faktoren

Several La I transitions were investigated by means of optical interference spectroscopy. AllA-values of the levels of the configuration 5d 6s 6p withJ=9/2, 7/2, and 5/2 were measured. Applying sum rules, the one-electrona-valuea _6s (5d 6s 6p) was derived. It is shown that a promising interpretation of the measuredA-values cannot be done without properly considering core-polarization and configuration interaction with adjacent configurations.     

Hyperfine structure of the atomic osmium spectrum: Superposition of configurations and the effect of nucleus volume

The contributions of the superposition of configurations ns ²5d ⁷6s+ns5d ⁷6sn′s+ns5d ⁷6s ² (n=1–5, n′=7–10) to the parameters of the hyperfine structure a _5d ⁰¹ , a _5d ¹² , a _5d ¹⁰ , a _6s ¹⁰ in the spectrum of the osmium atom Os I are calculated. Nonzero contributions are shown to be made only to the parameters a _5d ¹⁰ and a _6s ¹⁰ . This fact justifies the inclusion of the parameter a _5d ¹⁰ in the semiempirical analysis of experimental values of magnetic dipole constants of the hyperfine structure of the 5d ⁷ s configuration in the spectrum of the osmium atom. The effect of nucleus volume on the parameters of the hyperfine structure in the spectra of osmium isotopes ¹⁸⁷Os and ¹⁸⁹Os is estimated.     

Critical behavior of the 3D Ising model on a poissonian random lattice

The single-cluster Monte Carlo algorithm and the reweighting technique are used to simulate the 3D ferromagnetic Ising model on 3D Voronoi-Delauney lattices. It is assumed that the coupling factor J varies with the distance r between the first neighbors as J(r)∝e^−ar, with a≥0. The critical exponents γ/ν, β/ν, and ν are calculated, and according to the present estimates for the critical exponents, we argue that this random system belongs to the same universality class of the pure 3D ferromagnetic Ising model.     

On the dynamic conductivity for an electron-impurity system

The correlation function formula for the dynamic conductivity of a system of non-interacting electrons in the field of impurities is analyzed in terms of proper connected diagrams. By selecting those diagrams appropriate in the region of weak coupling and low impurity concentration, a set of coupled equations for the energy broadening γ (ω, ε, n_s) and the energy shift Δ(ω, ε, n_s) is derived, where both γ and Δ depend on the frequency ω of a probing field, the energy ε of the electron, and the concentration, n_g, of impurities. With the assumption of a finite range potential, these equations are solved. It is found that γ (ω, n_s) is smaller than that extrapolated value which the conventional expression γ₀ for the low-concentration collision frequency would predict, in the entire region studied, that the difference γ₀-γ becomes appreciable when the ratio of the average time between scatterings, τ_c, to the average duration of a scattering, τ_d, is 100 or less, that γ (ω, n_s) decreases monotonically from its static value γ (0, n_s), and becomes vanishingly small in the region ω≈1/τ_d, and that in the static limit (ω=0), γ=γ₀[1?(2/π) (γ₀τ_d)+…], that the energy shift Δ is positive, and increases from 0 and reach a peak of magnitude γ₀ as ω is raised from 0. By using the γ and Δ obtained, the dynamic conductivity σ(ω, n_s) for degenerated electrons is calculated. The deviation, σ-σ₀, from the conventional expression σ₀=(?i) (n_ee²/M) [ω-iΓ₀]^?1, (n_e]=number density of electrons), for 0°K, is appreciable when the ratio τ_c/τ_d is 100 or less. The field-term correction, which arises from the modification of the scattering due to the probing field, is found to be negligible in the entire region studied.     

Effect of Wigner energy on the symmetry energy coefficient in nuclei

The nuclear symmetry energy coefficient(including the coefficient a_(sym)~((4)) of the I~4 term) of finite nuclei is extracted by using the differences of available experimental binding energies of isobaric nuclei.It is found that the extracted symmetry energy coefficient a_(sym)~*(A,I) decreases with increasing isospin asymmetry I,which is mainly caused by Wigner correction,since e_(sym)~* is the summation of the traditional symmetry energy e_(sym) and the Wigner energy ew.We obtain the optimal values J = 30.25±0.10 MeV,a_(ss)=56.18±1.25 MeV,a_(sym)~((4)) = 8.33±1.21 MeV and the Wigner parameter x= 2.38 ±0.12 through a polynomial fit to 2240 measured binding energies for nuclei with20 ≤ A ≤ 261 with an rms deviation of 23.42 keV.We also find that the volume symmetry coefficient J■ 30 MeV is insensitive to the value x,whereas the surface symmetry coefficient a_(ss) and the coefficient a_(sym)~((4)) are very sensitive to the value of x in the range 1≤x≤4.The contribution of the a_(sym)~((4)) term increases rapidly with increasing isospin asymmetry I.For very neutron-rich nuclei,the contribution of the a_(sym)~((4)) term will play an important role.     

Hyperfine structure measurements in the4 I 9/2 ground state of141Pr

Using the atomic beam magnetic resonance method, the five hyperfine structure separations in the 4f ³ 6s ^{2 4}I_9/2 ground state of ₅₉ ¹⁴¹ Pr have been measured. The results are:F F′ E _FF′ ^* /h (MHz) 7 6 6477.913423(17) 6 5 5556.359848 (6) 5 4 4633.023306 (2) 4 3 3708.201146 (5) 3 2 2782.190601(15) From these quantities, the multipole interaction constantsA _k,k=1, 2, 3, 4 between the nucleus and the electron shell have been calculated.A ₄ especially then served to give the following limit for the intrinsic hexadecapole moment: ¦Q ₄₀¦<0.4eb ². Furthermore, theg _J -factors of the⁴ I multiplet have been measured at magnetic fields of 300 Oe. The results are:g _J(⁴ I _9/2)=0.7310371(15)g _J(⁴ I _11/2)=0.9651476(20)g _J(⁴ I _13/2)=1.1063197(40)g _J(⁴ I _15/2)=1.197963 (30) Small corrections due to perturbations by neighbouring fine structure levels are included.     

Analyticity properties and a convergent expansion for the inverse correlation length of the high-temperatured-dimensional Ising model

We show that the inverse correlation lengthm(β) (= mass of the fundamental particle of the associated lattice quantum field theory) of the spin-spin correlation function 〈s _x s _y 〉,x, y εZ ^d , of thed-dimensional Ising model admits the representation $$m(\beta ) = - ln\beta + r(\beta )$$ for small inverse temperaturesβ > 0.r(β) is ad-dependent function, analytic atβ = 0.c _n , the nth β = 0 Taylor series coefficient of r(β) can be computed explicitly from the Z^d limit of a finite number of finite lattice A spin-spin correlation functions 〈s₀s_x〉t>Afor a finite number ofx = (x ₁,x₂, ..., x_d), ¦x¦ = ∑ _i ^d 1¦x_i¦< R(n), where R(n) increases withn. Furthermore, there exists aβ' > 0, such that for eachβ ε (0,β')m(β) is analytic. Similar results are also obtained for the dispersion curve ω(p), ω(p)=ω(0)=m, pε(-π, π]^d?1, of the fundamental particle of the associated lattice quantum field theory.     

Laser-rf double-resonance hyperfine structure measurements of the metastable 3d 4s 1 D 2 state of43Ca

The hyperfine structure of the (3(d 4s)¹ D ₂metastable state of⁴³Ca has been measured using theABMR-LIRF method (atomic beam magnetic resonance, detected by laser induced resonance fluorescence). The measurements yielded for the magnetic dipole and electric quadrupole constantsA=?17.650(2) MHz andB=?4.642(12) MHz, respectively. From the measuredB factor the spectroscopic electric quadrupole moment (uncorrected for shielding effects) has been calculated to beQ(⁴³Ca)=?0.062(12) barn. In addition, isotope shifts in the lines (3d 4s)¹ D ₂(3d 4p)¹ F ₃ ⁰ and (3d 4s)¹ D ₂(4s 5p)¹ p ₁ ⁰ for the stable calcium isotopes have been obtained by high resolution laser spectroscopy.     

Production of a pion system in exclusive B c → V (P)+n π decays

Exclusive Bc-meson decays accompanied by the production of vector or pseudoscalar heavy quarkonia (η _c , η _c (2S), J/φ, φ(2S), and B _s ^(*) ) and an nπ light-meson system, where 1 ≤ n ≤ 5, are considered.     

Inversion-rotation spectrum and spectroscopic parameters of 14ND3 in the ground state

The far-infrared spectrum of ¹⁴ND₃ has been recorded in the region between 30 and 220 cm^?1 at a resolution, before deconvolution, of approximately 0.004 cm^?1. ΔJ = +1, ΔK = 0, a ← s and s ← a inversion-rotation transitions have been measured and assigned up to J″ = 19. These transitions, the pure inversion-microwave transitions and ground-state combination differences from the analysis of the ν₂ and ν₄ bands have been fitted simultaneously to an inversion-rotational Hamiltonian which includes Δk = ±3 and Δk = ±6 interaction terms. The ground-state spectroscopic parameters obtained in this way reproduce the transition frequencies within the accuracy of the measurements.     

Polarisierte Anregung der metastabilen 6s 5d-Terme im Ba I-Spektrum und Messung derg J-Faktoren

In an atomic beam experiment Ba-atoms were excited in the metastable levels of the 6s 5d-configuration by optical pumping and electron impact. The three states 6s 5d ¹ D ₂ and³ D _1,2 were populated by optical excitation of the 6s 6p ¹ P ₁- and³ P ₁-level resp., which decay partly into the metastable states. The¹ D ₂- and³ D ₃-level could be excited and aligned by impact of 50 eV-electrons. Radiofrequency transitions between Zeemansublevels were detected by resonance scattering of light and theg _J-values of the four 6s 5d-levels were measured:g _J(^1D ₂)=1.0032 (2),g _J(^3D ₁)=0.4986 (2),g _J(^3D ₂)=1.1638 (2) andg _J(^3D ₃)=1.3341 (2).     

Hyperfine anomaly in the spectrum of the osmium atom. effect of the spatial distribution of nuclear charge

Contributions of the superposition of configurations ns ²5d ⁸+ns5d ⁸ n′s (n=1–5, n′=6–10) and ns ²5d ⁶+ns5d ⁶ n′s (n=1–6, n′=7–10) to parameters a _5d ⁰¹ , a _5d ¹² , and a _5d ¹⁰ of the hyperfine structure in the spectrum of the osmium atom OsI are calculated. It is shown that the nonzero contribution is made only to a _5d ¹⁰ . The effect of the spatial distribution of nuclear charge on the parameters of the hyperfine structure in the spectra of ¹⁸⁷Os and ¹⁸⁹Os isotopes and on the hyperfine anomaly for the 5d ⁷6s levels in the spectrum of these isotopes is estimated.     

Determination of the ππ scattering lengths from data on πN → ππN reactions by the method of Roy equations

Fitted phase-shift curves from the threshold to the dipion mass, which is equal to 1 GeV, are constructed on the basis of all available experimental values of the S-and P-wave phase shifts for five charged channels of pion-pion scattering. The resulting phase-shift curves are introduced in the Roy equations in order to obtain the subtraction constants λ _l ^I (s). By using these subtraction-constant values as functions of the dipion mass, the S ₀-and S ₂-wave pion-pion scattering lengths are found to be a ₀ ⁰ = (0.240 ± 0.023)m _π ^?1 and a ₀ ² = (?0.034 ± 0.013)m _π ^?1 . A strong correlation of the S-wave scattering lengths is demonstrated.     

Photoluminescence in germanium with a quasi-equilibrium dislocation structure

The dislocation-related photoluminescence of n-Ge single crystals with a quasi-equilibrium structure of 60° dislocations is investigated at a temperature of 4.2 K. It is shown that the dislocation-related photoluminescence spectra are described by a set involving from 8 to 13 Gaussian lines with a width of less than 15 meV. With due regard for the data available in the literature, the Gaussian lines with maxima at energies in the range 0.47 < E _m ≤ 0.55 eV are assigned to the emission of 90° Shockley partial dislocations involved in quasiequilibrium segments of 60° dislocations with different values of the stacking fault width Δ (Δ = Δ₀, Δ < Δ₀, and Δ > Δ₀). It is revealed that the d8 line at the energy E _m = 0.513 eV, which corresponds to the emission of straight segments with the equilibrium stacking fault width Δ₀, dominates in the photoluminescence spectra only at dislocation densities N _D < 10⁶ cm^?2. As the dislocation density N _D increases, the intensity of the d8 line decreases with the d7 line (E _m ≈ 0.507 eV) initially and the d7 and d6 lines (E _m ≈ 0.501 eV) then becoming dominant in the photoluminescence spectrum. The d7 and d6 lines are attributed to the emission of segments with stacking fault widths Δ < Δ₀. Possible factors responsible for the formation of stacking faults with particular widths Δ ≠ Δ₀ for quasi-equilibrium dislocations are discussed.     

Hadronic contributions to (g−2) of the leptons and to the effective fine structure constant α(M Z 2 )

The new experiment planned at Brookhaven to measure the anomalous magnetic moment of the muona _μ≡(g _μ?2)/2 will improve the present accuracy of 7 ppm by about a factor of 20. This requires a careful reconsideration of the theoretical uncertainties of theg?2 predictions, which are dominated by the error of the contribution from the light quarks to the photon vacuum polarization. This issue is cruicial also for the precise determination of the running fine structure constant at theZ-peak as LEP/SLC experiments continue to increase their precision. In this paper we present an updated analysis of the hadronic vacuum polarization using all presently availablee ⁺e^? data. This seems to be justified because previous work on the subject was based to some extent on preliminary or incomplete experimental data. Contributions from different energy ranges are presented separately forg?2 of the muon and the τ-lepton and for α(M _Z ² ). We obtain the resultsa _μ ^had* =(725±16)×10^?10 anda _τ ^had* =(351±10)×10^?8, where the asterisk indicates the dressed (renormalization group improved) value. For the effective fine structure constant atM _Z=91.1888 GeV we obtainΔα _had ⁽⁵⁾ =0.0280±0.0007 and α(M _Z ² )^?1=128.896±0.090. Further improvement in the accuracy of theoretical predictions which depend on the hadronic vacuum polarization requires more precise measurements ofe ⁺e^? cross-sections at energies below about 12 GeV in future experiments.     

Study of the lowest electronic states of Xe2, XeKr, and XeAr molecules by the method of multiphoton resonance ionization

The spectra of Xe₂, XeKr, and XeAr molecules in the range 66 500–68 800 cm^?1 are obtained by the methods of (2 + n) and (3 + n) (n = 1, 2, 3) resonance multiphoton ionization during the registration of molecular and atomic ions. The combining of two-and three-photon resonance excitations of Xe₂ molecules makes it possible to obtain the spectra caused by transitions from the ground state X0 _g ⁺ to the excited states of Xe*6s[3/2] _1,2 ^o Xe¹ S ₀ molecules both of the even (0 _g ⁺ , 1 _g ) and of the odd (B0 _u ⁺ , B′1 _u , 2 _u ) symmetries. The data on the Ω = 2 _u state of the Xe₂ molecule with the dissociation limit Xe*6s[3/2] ₂ ^o + Xe¹ S ₀ and on the Ω = 1 state of the XeAr molecule with the dissociation limit Xe*6s[3/2] ₁ ^o + Ar¹ S ₀ are obtained for the first time. The potential curve of the excited 2 _u state of the Xe*6s[3/2] ₂ ^o Xe¹ S ₀ molecule is repulsive and intersects the potential curve of the B0 _u ⁺ state of the Xe*6s[3/2] ₁ ^o Xe¹ S ₀ molecule. In the case of the three-photon excitation, it is observed that all the bands in the spectra of XeKr and XeAr molecules are broadened and are shifted, which indicates that, in an intense light field, the influence of the dynamic Stark effect is significant.     

Theoretical studies of energy-energy correlation ine + e− annihilation

We calculate theO(α _s ² ) correction to the energy-energy corelation cross section ine ⁺ e^? annihilation using different resolution criteria in the limit of vanishing resolution cuts. We compare this in the back-to-back angular region with results of the logarithm approximation (LA) and deduce higher order corrections (beyondO(α _s ² )) from the LA formula. The final results are compared with recent TASSO data.