The effect of exchange in autoionization processes

The effect of including distortion (with and without exchange) in the wavefunction for the continuum electron while calculating the probability of autoionization of 2s ^{2 1} S. 2s2p ^1,3 P, 2p ^{2 1} D and 2p ^{2 1} S states of He and Li⁺ has been studied.     

Equilibrium and pre-equilibrium emissions in proton-induced reactions on <Superscript>203,205</Superscript>Tl

In this study, the excitation functions for the reactions ²⁰³Tl(p, n)²⁰³Pb, ²⁰⁵Tl(p, 3n)²⁰³Pb, ²⁰³Tl(p, 2n)²⁰²Pb, ²⁰⁵Tl(p, 4n)²⁰²Pb, ²⁰³Tl(p, 3n)²⁰¹Pb, ²⁰⁵Tl(p, 5n)²⁰¹Pb, ²⁰³Tl(p, 4n)²⁰⁰Pb and ²⁰⁵Tl(p, 6n)²⁰⁰Pb have been calculated using pre-equilibrium and equilibrium reaction mechanisms. Calculated results based on hybrid model, geometry-dependent hybrid model and cascade-exciton model have been compared with the experimental data.      

Nuclear magnetic double resonance studies of the effect of deuterium substitution upon 1 J(31P-H) in dimethyl phosphite

A study of the absorption of light by pairs of exchange coupled manganese ions in the perovskite fluorides KMgF₃ and KZnF₃ has been made using the technique of high resolution phosphorescence excitation spectroscopy. Transitions to the following pair states have been observed: ⁶ A _1g ⁴ T _1g ^a ; ⁶ A _1g ⁴ E _g ^a ; ⁶ A _1g ⁴ A _1g ; ⁶ A _1g ⁴ E _g ^b ; ⁴ T _1g ^{a 4} T _1g ^a ; ⁴ E _g ^{a 4} T _1g ^a and ⁴ A _1g ⁴ T _1g ^a . Quantitative estimates of intensities have been made for some of these transitions as well as estimates of the effective exchange parameters. A detailed analysis of the transition ⁶ A _1g ⁶ A _1g → ⁶ A _1g ⁴ A _1g provides confirmation of the Tanabe mechanism of exchange induced absorption of light by pairs of transition metal ions. It is shown that absence of MCD in this pair absorption is predicted by the Tanabe mechanism.     

Finsler spaces with Riemannian geodesics

In Finsler spaces the intervalds=F(x ⁱ ,dx ⁱ ) is an arbitrary function of the coordinatesx ⁱ and coordinate incrementsdx ⁱ withF homogeneous of degree one in thedx ⁱ . It is shown that for Riemannian spacesds _R ²=g _ij dx ⁱ dx ⁱ which admit a non trivial covariantly constant tensorH _i .(x ^k ) there is an associated Finsler space with the same geodesic structure. The subset of such Finsler spaces withH _i .(x ^k ) a vector or second rank decomposable tensor is determined.     

Spectroscopic investigations on NO+(x1∑+,a3∑+,A1Ⅱ) ion using multi-reference configuration interaction method and correlation-consistent sextuple b

Three low-lying electronic states (x¹∑⁺,a³∑⁺,and A¹Ⅱ) of NO⁺ ion are studied using the complete active space self-consistent-field (CASSCF) method followed by highly accurate valence internally contracted multi-reference configuration interaction (MRCI) approach in combination of the correlation-consistent sextuple basis set augmented with diffuse functions, aug-cc-pV6Z. The potential energy curves (PECs) of the NO⁺(x¹∑⁺,a³∑⁺,A¹Ⅱ) are calculated. Based on the PECs, the spectroscopic parameters R_e, D_e, ω_e, ω_eχ_e, α _e, B_e, and D₀ are reproduced, which are in excellent agreement with the available measurements. By numerically solving the radial Schrödinger equation of nuclear motion using the Numerov method, the first 20 vibrational levels, inertial rotation and centrifugal distortion constants of NO⁺(x¹∑⁺,a³∑⁺,A¹Ⅱ) ion are derived when the rotational quantum number J is equal to zero (J = 0) for the first time, which accord well with the available measurements. Finally, the analytical potential energy functions of these states are fitted, which are used to accurately derive the first 20 classical turning points when J = 0. These results are compared in detail with those of previous investigations reported in the literature.     

Validity of the equivalent-photon approximation for the production of massive spin-1 particles

We point out that the equivalent-photon approximation (EPA) for processes with massive spin-1 particles in the final state would have validity in a more restricted kinematic domain than for processes where it is commonly applied, viz., those with spin-1/2 or spin-0 particles in the final state. We obtain the criterion for the validity ofEPA for the two-photon production of a pair of charged, massive, point-like spin-1 particlesV ^±, each of massM and with a standard magnetic moment (κ=1). In a process in which one of the photons is real and the other virtual with four-momentumq, the condition for the validity ofEPA is |q ²|≪M ², in addition to the usual condition |q ²|≪W ²,W being theV ⁺ V ⁻ invariant mass. In a process in which both photons are virtual (with four-momentaq andq′), our condition is |q ²||q′²|W ⁴ ≪ 16M ⁸, in addition to |q ²| ≪M ², |q′²| ≪M ² and |q ²| ≪W ², |q′²| ≪W ². Even when these extra conditions permitting the use ofEPA are not fulfilled, convenient approximate expressions may still be obtained assuming merely |q ²| ≪W ² and |q′²| ≪W ². We also discuss how the extra conditions are altered when the vector bosons are incorporated in a spontaneously broken gauge theory. Examples ofW boson production in Weinberg-Salam model are considered for which the condition |q ²||q′²|W ⁴ ≪ 16M ⁸ is shown to be removed.     

Cross-section measurements of (n, 2n) and (n, p) reactions on 124,126,128,130,131,132Xe in the 14 MeV region and theoretical calculations of their excitation functions

The reaction cross-sections of ¹²⁴Xe(n, 2n)¹²³Xe, ¹²⁶Xe(n, 2n)¹²⁵Xe, ¹²⁸Xe(n, 2n)¹²⁷Xe, ¹³⁰Xe(n, 2n)^129mXe, ¹³²Xe(n, 2n)^131mXe, ¹³⁰Xe(n, p)¹³⁰I, ¹³¹Xe(n, p)¹³¹I, and ¹³²Xe(n, p)¹³²I were measured at the 13.5, 13.8, 14.1, 14.4, and 14.8 MeV neutron energies. The monoenergetic neutrons were generated via the ³H(d,n)⁴He reaction at the China Academy of Engineering Physics using the K-400 Neutron Generator with a solid ³H-Ti target. A high-purity germanium detector was employed to measure the activities of the product. The reactions ⁹³Nb(n, 2n)^92mNb and ²⁷Al(n, α)²⁴Na were adopted for neutron flux calibration. The cross sections of the (n, 2n) and (n, p) reactions of the xenon isotopes were obtained within the 13–15 MeV neutron energy range. These cross-sections were then compared with the IAEA-exchange format (EXFOR) database-derived experimental data, together with the evaluation results of the CENDL-3, ENDF/B-VIII.0, JENDL-4.0, RUSFOND, and JEFF-3.3 data libraries, as well as the theoretical excitation function obtained using the TALYS-1.95 code. The cross-sections of the reactions (except for the ¹²⁴Xe(n, 2n)¹²³Xe and ¹³²Xe(n, p)¹³²I) at 13.5, 13.8, and 14.1 MeV are reported for the first time in this study. The obtained results are beneficial in providing better cross-section constraints for the reactions in the 13–15 MeV region, thus improving the quality of the corresponding database. Meanwhile, these data can also be used for the verification of relevant nuclear reaction model parameters.     

Optical-Oscillator strengths for Ca X,Sc XI,Ti XII,Cu XIX,Zn XX,Br XXV and Kr XXVI

Summary We have applied the Tiwary approach to calculate the opticaloscillator strengths, of both the length and velocity forms, for the inner-shell excitation1s ² 2s ² 2p ⁶ 3s ² S ^e →1s ² 2s ² 2p ⁵ 3s ^{2 2} P ⁰ transition in Ca X, Sc XI, Ti XII, Cu XIX, Zn XX, Br XXV and Kr XXVI ions of the sodium isoelectronic sequence employing Hartree-Fock (HF) and configuration interaction (CI) wave functions of both the initial and final states involved in the transition. Our present calculated results demonstrate that the Tiwary approach is capable of yielding encouraging results. A part of this work was done while the author was Research Director and Professor, CNRS Laboratory, University of Paris-Sud and Observatoire de Paris, Meudon, Paris, France.     

Exact Solutions of the Two-Dimensional Schrödinger Equation with Certain Central Potentials

By applying an ansatz to the eigenfunction, an exact closed-form solution of theSchrödinger equation in two dimension is obtained with the potentials V(r) =ar ² + br ⁴ + cr ⁶,V(r) = ar + br² + cr ^–1,and V(r) = ar ² + br ^–2+ cr ^–4 + dr ^–6,respectively. The restrictions on the parameters of the given potential andthe angular momentum m are obtained.     

Symmetry and boundness of four-particle coulomb systems

The problem of boundness of a ⁺ b ⁺ c ⁻ d ⁻ four-particle Coulomb systems (quadrions) is studied versus the masses of the particles involved. Inequalities that make it possible to deduce that, if some reference quadrions form a bound state, the same is true for a large number of quadrions formed by particles having various masses were derived. A compendium of calculations for energies of reference systems that possess various symmetries [positronium molecules (e ⁺ e ⁺ e ⁻ e ⁻) and quadrions of the a ⁺ b ⁺ b ⁻ b ⁻, a ⁺ b ⁺ a ⁻ b ⁻, and a ⁺ a ⁺ b ⁻ c ⁻ types] is given, and groups of bound asymmetric quadrions corresponding to them are determined. An inequality for kinetic energies of particles that makes it possible to find out, by using asymmetric reference systems, whether specific quadrions are bound is obtained. It is shown that the boundness of many quadrions is ensured by the boundness of respective three-particle systems. The entire body of the present results permits proving that, of the total number of 406 quadrions containing electrons, muons, pions, kaons, protons, deuterons, and tritons and their antiparticles, 227 quadrions are bound.     

Photoionization of Al IV (neon-type) from its ground 2s 22p 6 1 S e and excited 2s 22p 53p 3,1 P 0 3 S e states using the R-matrix method

The R-matrix method is used to calculate the total photoionization cross-sections from the ground 2s ²2p ^{6 1} S ^e and the first three excited 2s ²2p ⁵3p ^3,1 S ^e states of Al IV, for photon energies ranging from the first ionization threshold to just above the second threshold of the residual ion Al V. The two lowest LS terms of Al V − 2s ²2p ^{5 2} P ⁰, 2s2p ^{6 2} S ^e, 2s2p ^{6 2} S ^e, represented by sophisticated configuration interaction wavefunctions, are included in the R-matrix calculation. The resulting cross-sections are affected by Rydberg series of resonances converging to the 2s2p ^{6 2} S ^e excited threshold.     

The K<Emphasis Type="Italic">π</Emphasis> and <Emphasis Type="Italic">ππ</Emphasis> S-wave amplitude from D-meson decays

The issue of Kπ and ππ S-wave amplitude is addressed using decays of D-mesons. Model-independent measurements of the phases of the π ⁺ π ⁺ and K ^- π ⁺ S-wave amplitude from D ⁺→π ^- π ⁺ π ⁺ and D ⁺→K ^- π ⁺ π ⁺ decays are discussed. The result indicates a deviation from the phase of the K ^- π ⁺ S-wave amplitude obtained by scattering experiments. This could be interpreted as an indication of the presence of 3-body final-state interaction, or in other words, that the phases from production and scattering process cannot be directly compared.     

Chiral phenomenological relations between rates of rare radiative decays of kaon to pion and leptons and the meson form factors

In the framework of the chiral perturbation theory we obtain the phenomenological relations between decay branches of rare radiative kaon to pion and leptons K ⁺ → π⁺ l ⁺ l ⁻ and K _S ⁰ → π⁰ l ⁺ l ⁻ and meson form factors. The comparison of these results with the present-day experimental data shows us that the ChPT relations for a charge kaon can determine meson form factors from already measured decay rates at high precision level. However, in the case of the neutral kaon decays K ⁰ → π⁰ e ⁺ e ⁻(μ⁺μ⁻) the form factor data are known to a higher precision than data on the differential rates of radiative kaon decay K ⁰ π⁰ e ⁺ e ⁻(μ⁺μ⁻).     

Determination of hyperfine structures and Rydberg convergence limits of selected optical transitions in 93Nb using resonance ionization spectroscopy

Several two- and three-step schemes for resonance ionization of ⁹³Nb with field ionization of Rydberg levels were investigated in the context of feasibility studies of using ^93m Nb/⁹³Nb isomer ratio determination for fast neutron dosimetry. Hyperfine structures of the states 4d ⁴(a ⁵ D)5p ⁴ D ₁ ^2/0 , 4d ³5_s(a ⁵ P)5P ⁶ D ₁ ^2/0 , 4d ³5s(a ⁵ F)5p ⁶ F ₁ ^2/0 , and 4d ³5s(a ⁵ F)6s ⁶ F _1/2 of ⁹³Nb were measured. The Rydberg spectra of the excitation schemes were measured and corresponding ionization limits estimated.     

K+→π+π0e+e?: a novel short-distance probe

We study the decay K ⁺→π ⁺ π ⁰ e ⁺ e ⁻, currently under analysis by the NA62 Collaboration at CERN. In particular, we provide a detailed analysis of the Dalitz plot for the long-distance, γ ^∗-mediated, contributions (Bremsstrahlung, direct emission and its interference). We also examine a set of asymmetries to isolate genuine short-distance effects. While we show that charge asymmetries are not required to test short distances, they provide the best environment for its detection. This constitutes by itself a strong motivation for NA62 to study K ⁻ decays in the future. We therefore provide a detailed study of different charge asymmetries and the corresponding estimated signals. Whenever possible, we make contact with the related processes K ⁺→π ⁺ π ⁰ γ and K _L →π ⁺ π ⁻ e ⁺ e ⁻ and discuss the advantages of K ⁺→π ⁺ π ⁰ e ⁺ e ⁻ over them.     

Site-specific ϕ- and ψ-torsion angle determination in a uniformly/extensively 13C- and 15N-labeled peptide

A solid-state rotational-echo double resonance (REDOR) NMR method was introduced to identify the ?- and ψ-torsion angle from a ¹H–¹⁵N or ¹H–¹³C′ spin system of alanine-like residues in a selectively, uniformly, or extensively ¹⁵N-/¹³C-labeled peptide. When a C_α(i) or a ¹⁵N peak is site-specifically obtainable in the NMR spectrum of a uniformly ¹⁵N/¹³C-labeled sample system, the ψ- or ?-torsion angle specified by the conformational structure of peptide geometry involving ¹⁵N(i)–¹H_αi–¹⁵N(i + 1) or ¹³C′(i − 1)–¹H^Ni–¹³C′(i) spin system can be identified based on ¹³C_α- or ¹⁵N-detected ¹H_α–¹⁵N or ¹H_N–¹³C REDOR experiment. This method will conveniently be utilized to identify major secondary motifs, such as α-helix, β-sheet, and β-turn, from a uniformly ¹⁵N-/¹³C-labled peptide sample system. When tested on a ¹³C-/¹⁵N-labeled model system of a three amino acid peptide Gly–[U–¹³C, ¹⁵N]Ala–[U–¹³C, ¹⁵N]Leu, the ψ-angle of alanine obtained experimentally, ψ = −40 ± 30°, agreed reasonably well with the X-ray determined angle, ψ = −39°.     

Z 3-Graded exterior differential calculus and gauge theories of higher order

We present a possible generalization of the exterior differential calculus, based on the operator d such that d³=0, but d²0. The entities dx ⁱ and d² x ^k generate an associative algebra; we shall suppose that the products dx ⁱ dx ^k are independent of dx ^k dx ⁱ , while theternary products will satisfy the relation: dx ⁱ dx ^k dx ^m =jdx ^k dx ^m dx ⁱ =j ²dx ^m dx ^m dx ⁱ dx ^k , complemented by the relation dx ⁱ d² x ^k =jd² x ^k dx ⁱ , withj:=e^2i/3.We shall attribute grade 1 to the differentials dx ⁱ and grade 2 to the second differentials d² x ^k ; under the associative multiplication law the grades add up modulo 3.We show how the notion ofcovariant derivation can be generalized with a 1-formA so thatD:=d+A, and we give the expression in local coordinates of thecurvature 3-form defined as :=d² A+d(A ²)+AdA+A ³.Finally, the introduction of notions of a scalar product and integration of theZ ₃-graded exterior forms enables us to define the variational principle and to derive the differential equations satisfied by the 3-form . The Lagrangian obtained in this way contains the invariants of the ordinary gauge field tensorF _ik and its covariant derivativesD _i F _km .     

Energy Levels of the Single Excited States in the Boron Isoelectronic Sequences

Energy levels of the single excited 1s²2s²ns (²S), 1s²2s²np (²P), 1s²2s²nd (²D) and 1s²2s²nf (²F), n = 3-8 states for the boron isoelectronic sequence are calculated using the simple configuration Hartree-Fock method. Good agreement is obtained between our results and previous experimental and theoretical data.     

Porous piezoelectric composites with extremely high reception parameters

The reception parameters Q ₃₃ ^* and Q _h ^* of modified fiber composites based on high-e ₃₃ ^FC /c ₃₃ ^{FC, E} ferroelectric piezoceramics (e ₃₃ ^FC is the piezoelectric constant, c ₃₃ ^{FC, E} is the elastic modulus) are considered as functions of the electromechanical properties and the porosity of the components. Pore configurations at which the values (Q ₃₃ ^* )²≈(Q _h ^* )²≈7×10⁻⁹ Pa⁻¹ for the polymer matrices of 1-0-3 composites are much higher than for conventional ternary composites are analyzed.     

Collisional — Radiative Model of Helium Plasma. II. Global Population Coefficients

We present results of our calculation of global population coefficients based on a collisional — radiative model of the helium plasma. The results are given for 2³P, 2¹P, 3³S, 3¹S, 3³P, 3¹D, 3³D, 3¹P, 4³ and 4¹ states of helium atoms. We consider electron densities from 10⁷ to 10¹⁸ cm^?3 and electron temperature from 1 to 10 eV. The electron distribution function is considered to be Maxwellian and the plasma to be radiatively thin.