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.     

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.     

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.     

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.     

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.     

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.     

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.     

Two-electron excitation in helium-like ions by electron impact

Calculation of cross-sections for the two-electron excitation in helium-like ions by electron impact employing Coulomb-Born-Oppenheimer (CBO) approximation is presented. Analytical expressions for the differential and total scattering cross-sections without using partial wave expansion of the wavefunction reported earlier have been used. The total and differential scattering cross-sections for each of the excitations 1s ^{2 1} S* → 2s ^{2 1} S ^e , 2s2p ^1.3 P ⁰, 2p ^{2 1} S ^e ,³ P ^e,¹ D ^e in Be²⁺ and B³⁺ are computed. Results for Li⁺ reported earlier are also included for comparison.     

Three-Body Spectrum of 18C and its Relevance to r-Process Nucleosynthesis

The ¹⁸C spectrum has been studied in a three body n + n +¹⁶C model that includes deformation and the 2⁺ excitation of the ¹⁶C core as well as Pauli projection of forbidden states. The ¹⁶C – n interaction employed in this study has been fitted to reproduce the experimental spectrum of ¹⁷C. The calculations show that two neutron separation energy in ¹⁸C in consistent with three-body structure of this nucleus and predict more states bound with respect to three-body decay. The comparison of their position to known excited states in ¹⁸C is discussed. These calculations suggest also that a few states may exist in astrophysically relevant region between the ¹⁷C+n and ¹⁶C + 2n decay thresholds. The most important of them is 1⁻ as it can give a large E1 resonant contribution to ¹⁷C(n, γ)¹⁸C neutron capture. The calculations also suggest that a virtual s-wave state may exist above the ¹⁷C + n threshold that can give rise to non-negligible M1 contributions to the ¹⁷C(n, γ)¹⁸C reaction rate. The presence of these states in the ¹⁸C spectrum can lead to an increased ¹⁷C(n, γ)¹⁸C reaction rate, which can significantly influence the abundances of uranium and thorium synthesized in the r-process in the supernovae explosions.     

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.     

Fine-structure energy levels, oscillator strengths and lifetimes in Co XV

Excitation energies from ground state for 97 fine-structure levels as well as oscillator strengths and radiative decay rates for all electric-dipole-allowed and intercombination transitions among the fine-structure levels of the terms belonging to the (1s ²2s ²2p ⁶)3s ²3p, 3s ³ p ², 3s ²3d, 3p ³, 3s3p3d, 3p ²3d, 3s3d ², 3s ²4s, 3s ²4p, 3s ²4d, 3s ²4f, and 3s3p4s configurations of Co XV are calculated, using extensive configuration-interaction (CI) wave functions, obtained with the CIV3 computer code of Hibbert. The important relativistic effects in intermediate coupling are included through the Breit-Pauli approximation via spin-orbit, spin-other-orbit, spin-spin, Darwin and mass correction terms. Small adjustments to the diagonal elements of the Hamiltonian matrices have been made. Our calculated excitation energies, including their ordering, are in excellent agreement with the experimental results and the experimentally compiled energy values of the National Institute for Standards and Technology (NIST) wherever available. The mixing among several fine-structure levels is found to be very strong, with most of the strongly mixed levels belonging to the (1s ²2s ²2p ⁶)3p ²3d and 3s3d ² configurations. The strong mixing among several fine-structure levels makes it very difficult to identify them uniquely. Perhaps, that may be the reason for the lack of both experimental and theoretical results for these levels. We believe that our extensive calculated values can guide experimentalists in identifying the fine-structure levels in their future work. From our radiative decay rates we have also calculated radiative lifetimes of some fine-structure levels. In this calculation we also predict new data for several fine-structure levels where no other theoretical and/or experimental results are available.     

MCD spectroscopy of transition metal ions in fluoride crystals

Absorption spectra of crystals of KZn _x Fe_1-x F₃ (0·006 < 1 - x < 0·07) have been measured in order to obtain information about Fe²⁺-F^--Fe²⁺ pairs. However, by means of high resolution MCD spectroscopy, it has been established that very small amounts of Fe³⁺ are present in the crystals. The absorption spectra then show features which are due to (a) Fe²⁺, (b) Fe³⁺ and (c) Fe²⁺, Fe³⁺ pairs. In addition to the characteristic Jahn-Teller split ⁵ T _2g → ⁵ E_g band of Fe²⁺, there is a weak, spin-allowed, vibronically assisted transition near 40 000 cm^-1, which is assigned to ⁵ T _2g (d⁶) → ⁵ A _1g (d⁵s). The MCD of this band is consistent with this assignment. The remainder of the visible and near ultra-violet absorption intensity is associated with Fe²⁺/Fe³⁺ pairs. Most of the bands are due to excitations localized on the Fe²⁺ though some weaker ones are assigned as excitations to ⁴ A _1g on the Fe³⁺ of the pair. There is also a strong, broad underlying absorption probably due to t _2g → t _2g charge transfer in the pair.     

Electric Dipole Oscillator Strength and Radiative Lifetimes in the Magnesium Isoelectronic Sequence

Oscillator strengths for the singlet 3sns(¹S)-3smp(¹P); (n, m = 3-7), 3snp(¹P)-3smd(¹D); (n = 4-7, m = 3-6) and the triplet 3sns(³S)-3smp(³P); (n = 4-7, m = 3-7), 3snp(³P)-3smd(³D); (n = 4-7, m = 3-6) transitions in the Mg I sequence are calculated in LS-coupling scheme. The Coulomb approximation is used in calculating the radial part of the wave functions, while the angular part is determined using the Racah technique. Lifetimes of the upper 3sns(³S, ¹S); (n = 4-7) and 3snp(³P, ¹P); (n = 3-7) excited states are obtained and compared with the available experimental data.     

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.     

() reaction studies of Dy and Hf

Angular distributions for the ¹⁶³Dy(t,p) and ¹⁷⁷Hf(t,p) reactions were measured using 17 MeV tritons from the McMaster University Tandem Van de Graaff accelerator. Reaction products were analyzed with a magnetic spectrograph and detected with photographic emulsions. Favored L=0 transitions confirmed assignments of the 5/2⁻[523] band in ¹⁶⁵Dy and 7/2⁻[514] band in ¹⁷⁹Hf. Additional L=0 transitions in each nuclide identified previously unknown 5/2⁻ levels in ¹⁶⁵Dy and 7/2⁻ ones in ¹⁷⁹Hf. Overall trends of L=0 strengths support the existence of subshell closures at neutron numbers 98 and 108. On the basis of a relatively strong L=2 transition, the K^π=11/2⁻ γ-vibration based on the 7/2⁻[514] state is identified at 1689 keV in ¹⁷⁹Hf, about 440 keV above its previously-assigned K^π=3/2⁻ partner.     

Improvement of perturbation theory in QCD for e + e − →hadrons and the problem of α s freezing

A method of improving perturbation theory in QCD is developed which can be applied to any polarization operator. The case of the polarization operator Π(q ²), corresponding to the process e ⁺ e ⁻→ hadrons, is considered in detail. By the use of the analytical properties of Π(q ²) and a perturbation expansion of Π(q ²) for q ²<0, the function ImΠ(q ²) at q ²>0 is defined in such a way that the infrared pole is eliminated. The convergence of the perturbation series for R(q ²)=σ(e ⁺ e ⁻ →hadrons)/(e ⁺ e ⁻→μ ⁺ μ ⁻) is improved. After substitution of R(q ²) into the dispersion relation an improved Adler function D(q ²) is obtained, having no infrared pole and a frozen α _s (q ²). Good agreement with experiment is achieved. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 3, 167–170 (10 August 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

基于火焰发射光谱的转动温度和振动温度的测量

利用光学多通道分析仪(OMA)对酒精和煤油在大气中燃烧时的火焰发射光谱进行了分析.实验发现上述火焰发射光谱在275-600 nm波段范围内存在多支辐射强度很大的带状分子光谱,其中以OH自由基A²Σ⁺→X²Π_r(300-330 nm),CH自由基A²Δ→X²Π(410-440 nm)和C₂自由基A³Π_g→X³Π_u(500-520 nm)电子带系的发射光谱最为强烈.实验中采用高分辨率光栅对OH自由基A²Σ⁺→X²Π_r和CH自由基A²Δ→X²Π电子带系发射光谱的精细结构进行了分析.与此同时,本文基于分子光谱理论计算了不同转动温度和振动温度条件下OH自由基A²Σ⁺→X²Π_r和CH自由基A²Δ→X²Π电子带系发射光谱的强度分布,同时通过理论计算光谱和实验光谱进行比较确定了酒精燃烧火焰的转动温度和振动温度. 关键词： 火焰发射光谱 谱线强度 转动温度 振动温度     

Effect of substituents in phenol and aniline nucleophiles on activation parameters in SNAr reactions

Changes of activation parameters, ΔH^≠ and ΔS^≠, with σ constants of substituents in the phenol and aniline nucleophiles for their S_NAr reactions in various solvents give the δΔH^≠ and δΔS^≠ reaction constants which are linearly related. The dependence obtained, δΔH^≠ versus δΔS^≠, allow estimation of the contribution of changes of the internal enthalpy, δΔH^≠_int, to the enthalpy reaction constant, δΔH^≠, which give a linear dependence on the Hammett reaction constants, ρ. The results obtained show that the substituent effects on the charge development in the transition state (TS) are governed by the magnitude of δΔH^≠_int. Copyright © 2009 John Wiley & Sons, Ltd.     

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°.