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.     

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.     

The group-theoretical structure of the atomic d shell and the energies of the corresponding terms

The icosahedral symmetry I?≈?A ₅ of the atomic d shell can arise from the symmetries of the five-dimensional d orbital space through the subgroup chain SO(5)???SO(3)???I or O(5)???S ₆???S ₅???I. In the latter case the symmetric group S ₅ can be generated from I?≈?A ₅ by addition of the period 4 kaleidoscope operator K, which mixes the d orbitals with m?=?±1 and those with m?=?±2. Furthermore, separation of the d ⁿ configurations into two sets according to the parity of n (even or odd) and the irreps of SO(5) is found to lead to new relationships between the multiplicities and seniorities of the corresponding terms. Thus the sums of the seniorities and multiplicities for even and odd n for a given irrep of SO(5) lead to a constant, namely 12. Furthermore, new pseudodegeneracies are found to arise when the energy expressions of pairs of otherwise equivalent terms with different seniorities for a given d ⁿ are adjusted to remove the radicals arising from solution of the quadratic secular equation. In addition to the well-known ²H/²P degeneracy for d³, ³F/³P degeneracies are found for d⁴ and a ²D/²S pseudodegeneracy is found for d⁵.     

Hyperfine structure in the atomic spectrum of niobium

A parametric analysis of the fine and the hyperfine structure for the three even configurations 4d^45s, 4d ⁴5s ² and 4d⁵ has been performed. Effective one-electron parameters a _nl ^kskl(k _s k _l = 01, 12 and 10) and b _nl ⁰² were determined for these three configurations. Extremely large ratios a _4d ¹⁰/a _4d ⁰¹ were found. Theoretical predictions for the hyperfine structure constants A and B for all levels of the configurations 4d^45s, 4d ⁴5s ² and 4d⁵ have been determined from experimental data. Additionally, the fine and hyperfine structure for the two energetically high lying even configurations 4d^46s and 4d^35s6s are discussed. The results presented here call into doubt the existence of the fine structure levels 4d ³5s6s ⁶ F _11/2 at an energy of 39 408.88 cm^-1 and 4d ³5s5p ⁶ G _13/2 at 18 876.46 cm^-1 given in the Moore tables.     

Model-independent analysis of the neutral-current interaction in the inclusive neutrino reactions

On the basis of some general assumptions on the deep inelastic structure functions, such as scaling and chiral symmetry we determine the values of {(H _V ³)²+(H _A ³)²}+η{(H _V ⁰)²+(H _A ⁰)²} andH _V ³ H _A ³+ηH _V ⁰ H _A ⁰ whereH _V ^3,0 andH _A ^3,0 are the four coupling constants characterizing the hadronic neutral current andη is the ratio of the isoscalar to isovector structure functions. General expressions are given for the kinematical averages 〈v〉 and 〈Q ²〉 for the neutral-current reactions in terms of the coupling constants. This analysis does not depend on the validity of the quark-parton model.     

On the spectrum of the hydrogen atom in an ultrastrong magnetic field

Various approaches to computing the energies of the ground state and excited levels of the hydrogen atom in an ultrastrong magnetic field B that considerably exceeds the field B _a = m _e ² e ³ c/ħ ³ ∼ 10⁹ G are considered. The effects of polarization of vacuum and anomalous magnetic moment of the electron on the position of the atomic levels are discussed. The vacuum polarization effects are negligibly weak for B < 10¹⁵ G but become significant in fields B ≫ 10¹⁶ G, in which these effects qualitatively modify the atomic spectrum in this range. The difference in the behaviors of the even and odd energy levels for B ≫ B _a is analyzed and the formulas for the energies of odd levels as a function of field B are refined.     

Theoretical study of the electronic states and transition dipole moments of the LiK molecule

The adiabatic potential energy, the spectroscopic constants and the transition dipole moments of the lowest electronic states of the LiK⁺ molecule, dissociating into Li(2s, 2p, 3s, 3p, 3d, 4s, and 4p) + K⁺ and Li⁺ + K(4s, 4p, 5s, 3d, 5p, 4d, and 6s), have been investigated. We have used an ab initio approach involving a non-empirical pseudopotential for the Li (1s²) and K (1s²2s²2p⁶3s²3p⁶) cores and core valence correlation correction. A very good agreement has been obtained for the ground state for the spectroscopic constants with the available theoretical works. The transition dipole moment from X²Σ, 2²Σ, 3²Σ, and 4²Σ states to higher excited states have been determined. Numerous avoided crossing between electronic states of ²Σ and ²Π symmetries, have been localised and analysed. Their existences are related to the charge transfer process between the two ionic systems Li⁺K and LiK⁺.     

Effect of the Structure of Light Loosely Bound Nuclei on the Mechanisms of Nuclear Reactions

The results of experiments devoted to studying fusion and transfer reactions in beams of loosely bound (³He) and cluster (⁶Li, ⁷Li) nuclei, as well as nuclei that have a halo structure (⁶He and ⁸He), with nuclei of light and heavy elements are generalized. Special features in the behavior of cross sections for the formation of evaporation residues and transfer-reaction products at energies near the barrier are revealed. The behavior of cross sections for nucleon- and cluster-transfer reactions leads to different populations of single-particle and collective states in target-like nuclei. The effect of various channels of nuclear reactions involving light nuclei on the population of the ^195mHg and ^197mHg(13/2⁺), ^198mTl and ^196mTl(7⁺), and ^196mAu and ^198mAu(12⁻) pairs of isomeric states is considered. The values of the isomeric ratios (σ_m/σ_g) for reaction products originating from fusion reactions followed by particle evaporation and from nucleon-and cluster-transfer reactions are explained.

     

On the Variation of a Functional when the Boundary of the Domain is not Fixed

The formula for the variation of a functional is obtained where the integrand depends on several independent variables x ^j , several functions of these variables u ^k and a finite number of partial derivatives of any order of the functions u ^k with respect to x ^j . Besides the functions u ^k , the boundary of the domain can also move. The formula generalizes the well-known case when only first-order partial derivatives are admitted.      

Dispersion and polarization interactions of the strontium atom

Dispersion coefficients involving the 5s ^{2 1} S ^e and 5s5p ^1,3P ^o states of strontium are determined from a large basis configuration interaction calculation. Dispersion coefficients are presented for the strontium dimer and also for strontium interactions with hydrogen and the rare gases. Polarizabilities and oscillator strengths from some low lying states are also given. The ground state polarizability and that of the 5s5p ¹P ^o and 5s4d ¹D ^e states are very similar in size.     

Perturbation allowed transitions in the infrared spectrum of 14ND3: determination of the K-dependent parameters in the ground state

ABSTRACT

Accurate values of the K-dependent constants ^{( i )} C, ^{( i )} D_K and ^{( i )} H_K in the ground state of ¹⁴ND₃, with i = s, a, have been determined for the first time thanks to the detections of ‘perturbation allowed’ transitions in the ν₁, ν₂, ν₃, ν₄ and 2ν₄ infrared bands. The rotation–inversion and inversion transitions from the literature, together with 7289 ground state combination differences from the infrared vibration–rotation–inversion transitions have been simultaneously analysed. The adopted rotation–inversion Hamiltonian includes distortion constants up to the eighth power and the Δk = ±3 and Δk = ±6 interaction terms. Precise values of the diagonal constants and of the Δk = ±3 interaction coefficients have been obtained. Accurate values of the ground state term values have been calculated for both s and a levels up to J = 21.     

Energy levels of the Schrödinger equation for some rational potentials in two-dimensional space using the inner product technique

The energy levels of a two-dimensional system are calculated for the rational potential,V(x, y; λ, g)=x ²+y ²+λ[x ²/(1+gx ²)+y ²/(1+gy ²)+a _xxx⁴+a _xyx² y ²+a _yyy⁴] using the inner product technique over a wide range of values of the perturbation parameters (g, λ) and for various eigenstates.     

A ligand field theory analysis of the spectra of the t 2g 3 levels of IrF6

Calculations and experimental data are presented for the t _2g ³ molecular levels of IrF₆ which imply that a substantial interaction takes place between these 5d³-configuration states and charge transfer states at ca. 20 000 cm^-1. This t _2g ³-charge transfer state configuration interaction is so extensive that the five t _2g ³ levels can only be fit with physically unreasonable values of the Racah (electrostatic) parameters and a spin orbit coupling parameter that is not consistent with expectations for 5d-series transition metal hexafluorides. Parameter values presented for IrF₆ are thus determined from the lowest three levels only, as these should experience the smallest relative shift due to configuration interaction: B = 297 cm^-1, C = 1167 cm^-1, ζ_5d = 4182 cm^-1, and 10Dq = 35 000 cm^-1. In order to corroborate the assertion that t _2g ³-charge transfer configuration interaction is an important factor for the determination of IrF₆ crystal and molecular properties, a number of t _2g ³ spectroscopic properties, which turn out to be quite sensitive to charge transfer state admixture, were studied theoretically and experimentally. These include gas-to-crystal shifts, site splittings, and Jahn-Teller interactions; comparison of calculated and experimental values clearly substantiate the conclusion that there is a strong influence of charge transfer states on the nature of the 5d³-t _2g ³ manifold. Finally, new data for the Γ_8g (² E_g ) and Γ_6g (² T _1g ) states at 1·2 μm are given, completing the data set for the t _2g ³ transitions of IrF₆.     

Influence of the three-body coulomb effects on the values of asymptotic normalization coefficients (nuclear vertex constants) of astrophysical interest extracted from the modified DWBA approach for the peripheral proton-transfer reactions

From the exact three-body distorted wave amplitude obtained by other authors for the one-charged-particle-transfer reaction A(x, y)B within the strict three-body (x = y + a and B = A + a, where a is a transferred particle) model, its part is separated in which the three-body Coulomb dynamics of the transfer mechanism is taken into account correctly. The contribution of the three-body Coulomb dynamics of the transfer mechanism to the partial wave amplitudes at l ≫ 1 for the peripheral proton-transfer reactions ¹³C(³He, d)¹⁴N, ¹³C(¹⁴N, ¹³C)¹⁴N, and ⁹Be(¹⁰B, ⁹Be)¹⁰B is estimated within the three-body approach combining the dispersion method and the DWBA approach. For these reactions, the Coulomb renormalization factors, arising owing to correctly taking into account the three-body Coulomb dynamics of the proton-transfer mechanism in the DWBA cross sections, are calculated. A new estimate is obtained for the values of the asymptotic normalization factors for p + ¹³C → ¹⁴N, which also have astrophysical interest. The text was submitted by the authors in English.     

Antikaon angular distributions in the reaction γd → K −Θ+ p → K − K + np near the threshold and the parity of the Θ+ Pentaquark

Within the spectator model, we study the reaction γd → K ⁻Θ⁺ p → K ⁻ K ⁺ np in the threshold energy region. We present the predictions for the exclusive and inclusive K ⁻-meson angular distributions in the laboratory system for this reaction calculated for two possible parity states of the Θ⁺ resonance at 1.5-and 1.75-GeV beam energies with and without imposing the relevant kinematical cuts on those parts of the sampled phase space where the contribution from the main background sources, associated with the ϕ(1020), Λ(1520) production as well as with the K ⁻ p rescattering in the final state, is expected to be dominant. We show that, under the chosen kinematics, these distributions are sensitive to the Θ⁺ parity and, therefore, can be used as a filter for the determination of its parity. The text was submitted by the author in English.     

New investigation of the decay of the high-spin isomer in 151Er

The decay of the T _1/2 = 420 ns isomer in ¹⁵¹Er has been reinvestigated. The multipolarities of the decaying transitions have been established by measuring the electron conversion coefficients. An I ^π = 67/2⁻ assignment is proposed for this isomer with a π[h ₁₁^2/4 d ₃^2/1 d ₅^2/−1]⊗ν[f _7/2 h _9/2 h ₁₁^2/−1] configuration.     

Effect of Coulomb forces on the position of the pole in the scattering amplitude and on its residue

The vertex constant for the virtual decay of a nucleus to two charged particles having an arbitrary orbital angular momentum l was explicitly obtained for the first time in the case of a standard expansion of the effective-range function K _l (k ²), as well as in the case where the function K ₀(k ²) has a pole. The bound state of the 3He nucleus and the resonance states of the ²He and ³He nuclei in the S wave, as well as the resonance states of the ⁵He and ⁵Li nuclei in the P wave, are studied as physical examples. For the Np and N d systems, the trajectories of the pole in the complex planes of the momentum and the corresponding renormalized vertex constant are constructed for the transition from a resonance state to a virtual state as the Coulomb interaction is switched off gradually.     

The Isobaric-Analogue Resonance States in the Fe56 Nucleus

Gamma ray spectra from the reaction Mn⁵⁵(p, γ) Fe^56ß have been measured at the isobaric-analogue resonances at E_p = 1769 ± 4 keV and 1806 ± 4 keV respectively with a 15 cm³ Ge(Li) dedector. Double correlation for the transition from the resonance level to the second excited state of Fe⁵⁶ has been measured for the two cases. Proton elastic scattering was also studied at each resonance at the angle 150°. Analysis of the (p, y) and (p, p) works yields a J^π assignment 4⁺ or 5⁺ and 3⁺ for the two mentioned resonance states, respectively, which are the isobaric-analogues of the 0.454 MeV and 0.486 MeV states of Mn⁵⁶. The proton partial width and the total width for each resonance state were also determined.     

New search for T violation in the decays of the charged kaon

We report the results of the measurement of T-violating transverse muon polarization in the decays K ⁺→μ ⁺ ν _μ π ⁰ (K _μ3) and K ⁺→μ ⁺ ν _μ γ(K _μ2γ) performed in experiment E246 at KEK. The preliminary results obtained for the entire data set taken in the period 1996–2000 are consistent with no T violation in both decays.

     

The Q-dependence of the generalised Gerasimov-Drell-Hearn integral for the deuteron,proton and neutron

The Gerasimov-Drell-Hearn (GDH) sum rule connects the anomalous contribution to the magnetic moment of the target nucleus with an energy-weighted integral of the difference of the helicity-dependent photoabsorption cross sections. Originally conceived for real photons, the GDH integral can be generalised to the case of photons with virtuality Q². For spin-1/2 targets such as the nucleon, it then represents the non-perturbative limit of the first moment of the spin structure function g ₁ (x,Q ² ) in deep inelastic scattering (DIS). The data collected by HERMES with a deuterium target are presented together with a re-analysis of previous measurements on the proton. This provides an unprecedented and complete measurement of the generalised GDH integral for photon-virtuality ranging over 1.2&lt;Q ² &lt;12.0 GeV² and for photon-nucleon invariant mass squared W² ranging over 1&lt;W ² &lt;45 GeV², thus covering simultaneously the nucleon-resonance and the deep inelastic scattering regions. These data allow the study of the Q²-dependence of the full GDH integral, which is sensitive to both the Q²-evolution of the resonance form factors and contributions of higher twist. The contribution of the nucleon-resonance region is seen to decrease rapidly with increasing Q². The DIS contribution is sizeable over the full measured range, even down to the lowest measured Q². As expected, at higher Q² the data are found to be in agreement with previous measurements of the first moment of g₁. From data on the deuteron and proton, the GDH integral for the neutron has been derived and the proton-neutron difference evaluated. This difference is found to satisfy the fundamental Bjorken sum rule at Q ² = 5 GeV². Received: 20 October 2002 / Published online: 15 January 2003