Finite size effects in the spin-1 XXZ and supersymmetric sine-Gordon models with Dirichlet boundary conditions

Starting from the Bethe Ansatz solution of the open integrable spin-1 XXZ quantum spin chain with diagonal boundary terms, we derive a set of nonlinear integral equations (NLIEs), which we propose to describe the boundary supersymmetric sine-Gordon model BSSG⁺ with Dirichlet boundary conditions on a finite interval. We compute the corresponding boundary S matrix, and find that it coincides with the one proposed by Bajnok, Palla and Takács for the Dirichlet BSSG⁺ model. We derive a relation between the (UV) parameters in the boundary conditions and the (IR) parameters in the boundary S matrix. By computing the boundary vacuum energy, we determine a previously unknown parameter in the scattering theory. We solve the NLIEs numerically for intermediate values of the interval length, and find agreement with our analytical result for the effective central charge in the UV limit and with boundary conformal perturbation theory.     

Isospin-forbidden β-decay of 28Mg

We have measured the branching ratio for the isospin-forbidden Fermi β-decay of ²⁸Mg to the 0.972 MeV 0⁺, T = 1 level in ²⁸Al. This decay occurs through an admixture of the 0⁺, t = 2 analog state at 5.992 MeV into the anti-analog level at 0.972 MeV. A charge-dependent matrix element of 17.0_?5.8^+4.3 keV is deduced from the observed (0.21 ± 0.12)% branch. Comparisons are made with matrix elements deduced in other nuclei. An analysis based on a simple shell model with fourfold degenerate Orbitals indicates the importance of the two-body Coulomb interaction in isospin mixing in nuclei with more than one valence proton.     

Bethe ansatz for the XXX-S chain with non-diagonal open boundaries

We consider the algebraic Bethe ansatz solution of the integrable and isotropic XXX-S Heisenberg chain with non-diagonal open boundaries. We show that the corresponding K-matrices are similar to diagonal matrices with the help of suitable transformations independent of the spectral parameter. When the boundary parameters satisfy certain constraints we are able to formulate the diagonalization of the associated double-row transfer matrix by means of the quantum inverse scattering method. This allows us to derive explicit expressions for the eigenvalues and the corresponding Bethe ansatz equations. We also present evidences that the eigenvectors can be build up in terms of multiparticle states for arbitrary S.     

Isospin impurity of 64Ga ground state

It is well known that the observation of a nonzero Fermi matrix element for a β-transition between states that differ in isospin can provide information about the relative isospin purity of the states involved. We have determined the log ft value for the 0⁺ → 0⁺ (ΔT ≠ 0) β-transition in ${}^{64}\text{Ga}\text{→}{}^{64}\text{Zn}$ decay as 6.516 ± 0.020. From this log ft value, we have deduced |M_F| = (43.4 ± 1.1) × 10^?3, |α| = (21.7 ± 0.6) × 10^?3 and |〈V_CD〉| = 41.7 ± 1.1 keV, where M_F,α² and 〈V_CD〉 represent the Fermi matrix element, isospin impurity and Coulomb matrix element, respectively. The Coulomb matrix element of 41.7 keV found for ⁶⁴Ga is one of the largest known from β-decay experiments. The experimental procedure involved a careful measurement of the intensity of the annihilation radiation relative to that of the other γ-rays from ⁶⁴Ga decay. As a by-product, we have obtained an improved ⁶⁴Ga decay scheme. We have also summarized the existing information on the isospin impurities of nuclear states as deduced from β-decay experiments.     

The decay of theT=1 isospin triplet inA=12 systems. III. Higher order effects in the evaluation of the asymmetry parameters α∓ for the electron emission from aligned12B and12N

Nuclear Structure: calculation of the asymmetry α_? ofβ rays emitted from polarized¹²B and¹²N nuclei including higher order contributions. Comparison with recent experimental values. The asymmetry parameters α_? and α₊ were evaluated including higher order corrections in the framework of the formulae derived in a previous paper. It was found that since α_? is affected by strong cancellation effects the corrective terms give in this case a very important contribution. The agreement between predicted theoretical values and very recent experimental data is excellent for bothβ ^? andβ ⁺ decays. The experimental results can be understood without invoking the existence of the induced pseudotensor interaction.     

Interpretation of electronic spectra by configuration analysis: Absorption spectra of monosubstituted naphthalenes

The electronic absorption spectra of four monosubstituted naphthalenes, α-, β-naphthols, and α-, β-naphthylamines have been investigated by means of configuration analysis with particular attention to the dependence of spectra on the position of substitution and on the electron-donating power of the substituent. The results of molecular orbital calculations based on the Pariser-Parr-Pople method are analyzed in terms of locally excited states and intramolecular charge-transfer configurations. The characteristic changes in location and polarization of the L_b, L_a, and B_b bands caused by substitution at the α- or β-position are adequately explained by the analysis. Two strong absorption bands of α-substituted naphthalenes, which appear in place of the B_b band of naphthalene, are shown to result from a mixing of the $\text{B}{}_{\mathrm{3u}}{}^{\mathrm{+}}\text{(B}{}_{\mathrm{b}}\text{)}$ and $\text{A}{}_{\mathrm{g}}{}^{\mathrm{?}}$ states. The amino group exerts a great influence on the electronic structure of the parent molecule, so that the B_b band cannot be identified in the spectrum of β-naphthylamine.     

The adsorption and desorption of oxygen on the Pt(110) surface; A thermal desorption and LEED/AES study

The interaction of oxygen with a Pt(110) crystal surface has been investigated by thermal desorption mass spectroscopy, LEED and AES. Adsorption at room temperature produces a β-state which desorbs at ~800 K. Complete isotopic mixing occurs in desorption from this state and it populates with a sticking probability which varies as (1 ? θ)², both observations consistent with dissociative adsorption. The desorption is second order at low coverage but becomes first order at high coverage. The saturationcoverage is 3.5 × 10¹⁴ mol cm^?2. The spectra have been computer analysed to determine the fraction desorbing by first (β₁) and second (β₂) order kinetics as a function of total fractional coverage θ using this fraction as the only adjustable parameter. The β₁ desorption commences at θ ～ 0.25 and β₁ and β₂ contribute equally to the desorption at saturation. The kinetic parameters for β₁ desorption were calculated from the variation of peak temperature with heating rate as ν₁ = 1.7 × 10⁹ s^?1 and E^≠₁ = 32 kcal mole^?1 whereas two different methods of analysis gave consistent parameters ν₂ = 6.5 × 10^?7 cm² mol^?1 s^?1 and E^≠₂ = 29 and 30 kcal mole^?1 for β₂ desorption. The kinetics of desorptior are discussed in terms of the statistics for occupation of near neighbour sites. While many fea tures of the results are consistent with this picture, it is concluded that simple models considering either completely mobile or immobile adlayers with either strong or zero adatom repulsion are not completely satisfactory. The thermal desorption surface coverage has been correlated with the AES measurements and it has been possible to use the AES data for PtO as an internal standard for calibration of the AES oxygen coverage determination. At low temperature (170 K) oxygen populates an additional molecular α-state. Adsorption into the α- and β-states is competitive for the same sites and pre-saturation of the β-state at 300 K excludes the α-state. This, together with the AES observation that the adsorption is enhanced and faster at 450 than 325 K suggests a low activation energy for adsorption into the β-state.     

The half-infinite XXZ chain in Onsagerʼs approach

The half-infinite XXZ open spin chain with general integrable boundary conditions is considered within the recently developed ‘Onsager?s approach’. Inspired by the finite size case, for any type of integrable boundary conditions it is shown that the transfer matrix is simply expressed in terms of the elements of a new type of current algebra recently introduced. In the massive regime −1<q<0$-1<q<0$, level one infinite dimensional representation (q-vertex operators) of the new current algebra are constructed in order to diagonalize the transfer matrix. For diagonal boundary conditions, known results of Jimbo et al. are recovered. For upper (or lower) non-diagonal boundary conditions, a solution is proposed. Vacuum and excited states are formulated within the representation theory of the current algebra using q-bosons, opening the way for the calculation of integral representations of correlation functions for a non-diagonal boundary. Finally, for q generic the long standing question of the hidden non-Abelian symmetry of the Hamiltonian is solved: it is either associated with the q-Onsager algebra (generic non-diagonal case) or the augmented q-Onsager algebra (generic diagonal case).     

The decays of 21.55 min 162gTm and 24.3 s 162Tm (a new isomer)

The decay of the 21.55 min ground state and of the 24.3 s isomeric state of ¹⁶²Tm was investigated with semiconductor detectors. The γ-ray spectrum was investigated with a Compton-suppression Ge(Li)-NaI(Tl) arrangement. A Si (Li) detector, mounted in an electron transport solenoid, was used to investigate the conversion electron spectrum. Three-dimensional coincidence measurements were performed with large-volume Ge(Li) detectors. The ¹⁶²Tm ground state has spin-parity 1^? and Nilsson assignment p[411]↓?n[521]↑. An allowed β-transition (log ft ≈ 6.4) was observed to a 2^?, 2 octupole vibrational level at 1572.84 keV. The Q-value determined from positon-gamma coincidence measurements is 4705 ± 70keV. The discrepancy of the experimental K /β⁺ ratio with theoretical predictions might possibly be explained by a large number of unobserved weak γ-rays besides the total of 315 stronger ones observed in this study. The average β-strength function was calculated to be 1.2 × 10^?5. Among the 50 levels observed in the decay, the 2⁺, 4⁺ and 6⁺ members of the ground-state band, the 2⁺, 3⁺ and 4⁺ members of the γ-band, several 0⁺ and 2⁺ members of the K = 0 β-bands and 1^?, 2^? and 3^? octupole vibrational levels were identified. Parameter values Z_γ(0) and Z_γ(2) determining the mixing between the γ-band and the ground-state band, allow no conclusive evidence about unequalness of the intrinsic quadrupole moments of the ground states and the γ-band. The Z(0) parameters, determining the mixing between the β-bands and the ground-state band, and X parameters determining the ratio of E0 to E2 transition probabilities, were deduced. A previously unreported 24.3 sec isomer in ¹⁶²Tm was observed to decay in 10% of the cases by an allowed unhindered (log ft = 4.7) β-ray transition to a level at 1712.20 keV in ¹⁶²Er. The Nilsson configurations assigned to the isomeric and 1712.20 keV levels are p[523]↑ + n[521]↑₅₊ and n[523]↓ + n[521]↑₄₊ respectively. The isomeric level decays in 90% of the cases by an E3 transition (E_IT < 125 keV) to a p[404]↓ ?n[521]↑_2? level at 66.90 keV in ¹⁶²Tm, which decays by an (M1+ < 40 % E2) to the 21.55 min ¹⁶²Tm 1^? ground state.     

Quark mass effects toO(α s ) ine + e −→hadrons asymmetries and precision tests of electroweak physics

We estimate, to first order in α _s , quark mass effects on a number of fully integrated and “two-jet” asymmetries for the processe ⁺ e ^?→ \(q\bar q \to q\bar qg\) . We find that the effects of strong interactions are appreciably decreased, especially in the case of theb quark, with respect to the massless case. For the fully integrated asymmetries these effects are sizeable. Concentrating on the “two-jet” asymmetries, we find that for small values of the parameters ε and δ defining a ”two-jet” event all the asymmetries are α _s independent. For larger values of these parameters this is no longer true. However it is still possible to define regions in the (ε, δ) plane where the strong interaction effects can be made arbitrarily small. These important features enhance the role of “two-jet” asymmetries as specially convenient candidates for high precision tests of Electroweak Physics.     

The width of the 5.11 MeV state in 10B and isovector parity mixing

We review estimates for effects of parity mixing on the α-capture of vector polarized ⁶Li to the 5.16 MeV, 2⁺, T = 1 state in ¹⁰B. The cross section depends on the ⁶Li polarization direction because of isovector parity mixing with the 5.11 MeV, 2^?, T = 0 state. The effect is enhanced due to isospin conservation. The α-width of the 5.11 MeV state, an important parameter for calculating the enhancement, has been measured to be 0.98 ± 0.07 keV. The consequences of parity mixing are reevaluated using best available values for the relevant parameters.     

Partial molar adiabatic compressibilities of transfer of some amino acids from water to aqueous lactose solutions at different temperatures

Apparent molar adiabatic compressibilities (K_{?, s}) of glycine, L-alanine, L-valine, and L-leucine have been determined in aqueous and mixed aqueous solutions of lactose (2 to 6 mass%) at T = (293.15, 298.15, 303.15, and 308.15) K. From these data partial molar adiabatic compressibilities at infinite dilution (K_{?, s}⁰) have been evaluated to calculate corresponding transfer function. The transfer partial molar adiabatic compressibilities at infinite dilution (ΔK_{?, s}⁰) are found to be positive. The decrease in the magnitude of transfer partial molar adiabatic compressibilities from glycine to L-leucine indicates the dominance of hydrophobic-hydrophobic interactions between the increasing side chains of amino acids. Also, the contributions of NH₃⁺COO⁻ , and CH₂ groups have been calculated by the linear correlation of K_{?, s}⁰ with number of carbon atoms in the alkyl chain of amino acids.     

Difference equations in spin chains with a boundary

Correlation functions and form factors in vertex models or spin chains are known to satisfy certain difference equations called the quantum Knizhnik-Zamolodchikov equations. We find similar difference equations for the case of semi-infinite spin chain systems with integrable boundary conditions. We derive these equations using the properties of the vertex operators and the boundary vacuum state, or alternatively through corner transfer matrix arguments for the eight-vertex model with a boundary. The spontaneous boundary magnetization is found by solving such difference equations. The boundary S-matrix is also proposed and compared, in the sine-Gordon limit, with Ghoshal-Zamolodchikov's result. The axioms satisfied by the form factors in the boundary theory are formulated.     

Model calculation of amplitudes for FT-ICR ion detection in a cylindrical Penning trap

A Green’s function strategy first proposed by Grosshans et al. is used to calculate the electric charges induced by trapped ions on the 4-fold or 8-fold segmented ring electrode of a cylindrical Penning trap. The ions are assumed to move in the central region of the trap where the harmonic approximation holds. The electric charges induced on each detection segment of the ring electrode are obtained in the form of a triple Fourier series with coefficients that describe the contribution of each frequency combination m ₊ ν ₊+m _? ν _?+m _z ν _z as a function of R ₊, R _?, Z, where ν ₊, ν _?, ν _z are the characteristic frequencies and?R ₊, R _?, Z the corresponding amplitudes of the ion motion. The sideband structure is analyzed and the origin of the sidebands is tracked. Finally, single-electrode, differential, and additive detection are discussed.     

Adsorption of nitrogen on platinum

The adsorption and desorption of nitrogen on a platinum filament have been studied by thermal desorption techniques. Nitrogen adsorption becomes significant only after any carbon contamination is removed from the surface by heating the platinum filament in oxygen, and after the CO content in the background gas is reduced substantially. At room temperature nitrogen populates an atomic tightly bound β-state, E^≠ = 19 kcal mole^?1. The saturation coverage of the (3-state is 4.5 × 10¹⁴ atoms cm^?2. Formation of the (β-state is a zero order process in the pressure range studied. At 90 K two additional α₁- and α₂-desorption peaks are observed. The activation energy for desorption for the α₂-state is 7.4 kcal mole^?1 at low coverage decreasing to 3 kcal mole^?1 at saturation of this state, 6 × 10 molecules cm^?2. The maximum total coverage in the α-states was 1.2 × 10¹⁵ molecules cm^?2. A replacement process between the β- and α-states has been observed where each atom in the (β-state excludes two molecules from the α-state.     

Variational calculations of asymmetric nuclear matter

We report on variational calculations of the energy E(ρ, β) of asymmetric nuclear matter having ? = ?_n + ?_p = 0.05 to 0.35 fm^?3, and β = (?_n ? ?_p/g9 = 0 to 1. The nuclear h used in this work consists of a realistic two-nucleon interaction, called v₁₄, that fits the available nucleon-nucleon scattering data up to 425 MeV, and a phenomenological three nucleon interaction adjusted to reproduce the empirical properties of symmetric nuclear matter. The variational many-body theory of symmetric nuclear matter is extended to treat matter with neutron excess. Numerical and analytic studies of the β-dependence of various contributions to the nuclear matter energy show that at ? < 0.35 fm^?3 the β⁴ terms are very small, and that the interaction energy EI(ρ, β) defined as E(ρ, β) ? T_F(ρ, β), where T_F is the Fermi-gas energy, is well approximated by EI₀(?) + β²EI₂(ρ). The calculated symmetry energy at equilibrium density is 30 MeV and it increases from 15 to 38 MeV as ? increases from 0.05 to 0.35 fm^?3.     

On the applicability of finite order perturbative QCD calculations of jet rates ine + e − annihilation

We have studied the measurement of α _s using exact second order QCD matrix element calculations of jet rates ine ⁺ e ^?→hadrons. We investigate the dependence of α _s (M _Z ² ), measured by experiments at theZ ⁰ resonance, on the choice of renormalisation scale in terms of the functional form of the three-jet matrix element. We find that only a restricted domain of the jet resolution parametery _c , $\Lambda _{\overline {MS} } $ , and scale gives a perturbation series which is well-behaved to second order, and that this domain is different for the various jet algorithms in current use.     

Thermopower in the region of hopping conduction in TlNiS<Subscript>2</Subscript>

Samples of the composition TlNiS₂ in the hexagonal system with the unit cell parameters a=12.28 Å, c=19.32 Å, and ρ=6.90 g/cm³ are synthesized. The results of the investigation into the electrical and thermoelectrical properties of TlNiS₂ samples in the temperature range 80–300 K indicate that TlNiS₂ is a p-type semiconductor. It is found that, at temperatures ranging from 110 to 240 K, TlNiS₂ samples in a dc electric field possess variable-range-hopping conduction at the states localized in the vicinity of the Fermi level. The density of localized states near the Fermi level is determined to be N_F=9×10²⁰ eV^?1 cm^?3, and the scatter of the states is estimated as J≈2×10^?2 eV. In the temperature range 80–110 K, TlNiS₂ exhibits activationless hopping conduction. At low temperatures (80–240 K), the thermopower of TlNiS₂ is adequately described by the relationship α(T)=A+BT, which is characteristic of the hopping mechanism of charge transfer. In the case when the temperature increases to the temperature of the onset of intrinsic conduction with the activation energy ΔE=1.0 eV, there arise majority intrinsic charge carriers of both signs. This leads to an increase in the electrical conductivity σ and, at the same time, to a drastic decrease in the thermopower α; in this case, the thermopower is virtually independent of the temperature.     

Gell-Mann-Low function in QCD

The Gell-Mann—Low function in QCD β(g)(g=?²/16π², where ? is the coupling constant in the Lagrangian) is shown to behave in the strong-coupling region as β_∞ g ^α, where α≈?13 and β_∞～10⁵.