An analytical solution of the Klein–Fock–Gordon equation for a 2D pion atom moving in a constant uniform magnetic field

The Klein–Fock–Gordon equation is solved for a 2D pion moving in a constant uniform magnetic field. A relativistic energy spectrum is calculated for fixed values of the angular momentum and magnetic field Н. An analysis of the results of these calculations allows us to conclude that the Klein–Fock–Gordon equation, unlike the Schr?dinger equation, cannot describe the energy of the particle s-state in the magnetic field. It is elucidated that a correction for the relativistic energy level caused by the constant magnetic field is noticeable for the magnetic field H > 100. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 91–96, March, 2009.     

Isospin-breaking corrections in the pion–deuteron scattering length

It is shown that isospin-breaking corrections to the pion–deuteron scattering length can be very large, because of the vanishing of the isospin-symmetric contribution to this scattering length at leading order in chiral perturbation theory. We further demonstrate that these corrections can explain the bulk of the discrepancy between the recent experimental data on pionic hydrogen and pionic deuterium. We also give the first determination of the electromagnetic low-energy constant f₁$f_1$.     

Isospin breaking in the pion–nucleon scattering lengths

We analyze isospin breaking through quark mass differences and virtual photons in the pion–nucleon scattering lengths in all physical channels in the framework of covariant baryon chiral perturbation theory.     

The pion–nucleon scattering lengths from pionic hydrogen and deuterium

This is the final publication of the ETH Zurich–Neuchatel–PSI collaboration on the pionic hydrogen and deuterium precision X-ray experiments. We describe the recent hydrogen 3p–1s measurement, report on the determination of the Doppler effect correction to the transition line width, analyze the deuterium shift measurement and discuss implications of the combined hydrogen and deuterium results. From the pionic hydrogen 3p–1s transition experiments we obtain the strong-interaction energy level shift eV and the total decay width eV of the state. Taking into account the electromagnetic corrections we find the hadronic s-wave scattering amplitude for elastic scattering and for single charge exchange, respectively. We then combine the pionic hydrogen results with the 1s level shift measurement on pionic deuterium and test isospin symmetry of the strong interaction: our data are still compatible with isospin symmetry. The isoscalar and isovector scattering lengths (within the framework of isospin symmetry) are found to be and , respectively. Using the GMO sum rule, we obtain from a new value of the coupling constant () from which follows the Goldberger–Treiman discrepancy . The new values of and imply an increase of the nucleon sigma term by at least 9 MeV. Received: 20 April 2001 / Revised version: 6 July 2001 / Published online: 24 August 2001     

Quadrupole polarizabilities of the pion in the Nambu–Jona-Lasinio model

The electromagnetic dipole and quadrupole polarizabilities of the neutral and charged pions are calculated in the Nambu–Jona-Lasinio model. Our results agree with the recent experimental analysis of these quantities based on dispersion sum rules. Comparison is made with the results from the chiral perturbation theory.     

The super-heat-kernel expansion and the renormalization of the pion–nucleon interaction

A recently proposed super-heat-kernel technique is applied to heavy baryon chiral perturbation theory. A previous result for the one-loop divergences of the pion–nucleon system to is confirmed, giving at the same time an impressive demonstration of the efficiency of the new method. The cumbersome and tedious calculations of the conventional approach are now reduced to a few simple algebraic manipulations. The present computational scheme is not restricted to chiral perturbation theory, but can easily be applied or extended to any (in general non-renormalizable) theory with boson–fermion interactions. Received: 21 July 1998 / Published online: 5 October 1998     

Positivity constraints on the low-energy constants of the chiral pion–nucleon Lagrangian

Positivity constraints on the pion–nucleon scattering amplitude are derived in this article with the help of general S-matrix arguments, such as analyticity, crossing symmetry, and unitarity, in the upper part of the Mandelstam triangle, $\mathcal{R}$ . Scanning inside the region $\mathcal{R}$ , the most stringent bounds on the chiral low-energy constants of the pion–nucleon Lagrangian are determined. When just considering the central values of the fit results from covariant baryon chiral perturbation theory using the extended-on-mass-shell scheme, it is found that these bounds are well respected numerically both at the $O(p^3)$ and the $O(p^4)$ level. Nevertheless, when taking the errors into account, only the $O(p^4)$ bounds are obeyed in the full error interval, while the bounds on the $O(p^3)$ fits are slightly violated. If one disregards the loop contributions, the bounds always fail in certain regions of $\mathcal{R}$ . Thus, at a given chiral order these terms are not numerically negligible and one needs to consider all possible contributions, i.e., both tree-level and loop diagrams.We have provided the constraints for special points in $\mathcal {R}$ where the bounds are nearly optimal in terms of just a few chiral couplings, which can easily be implemented and employed to constrain future analyses. Some issues concerned with calculations with an explicit $\Delta $ resonance are also discussed.     

Relation between the charged and neutral pion–nucleon coupling constants in the Yukawa model

In the Yukawa-model framework for NN forces, a simple relation between the charged and neutral pion–nucleon coupling constants is derived. The relation implies that the charged pion–nucleon constant is larger than the neutral one since the np interaction is stronger than the pp interaction. The derived value of the charged pion–nucleon constant shows a very good agreement with one of the recent measurements. In relative units, the splitting between the charged and neutral pion–nucleon constants is predicted to be practically the same as that between the charged and neutral pion masses. The charge dependence of the NN scattering length arising from the mass difference between the charged and neutral pions is also analyzed.     

Parametrization of Bose–Einstein correlations and reconstruction of the space–time evolution of pion production in ee annihilation

A parametrization of the Bose–Einstein correlation function of pairs of identical pions produced in hadronic e⁺e⁻ annihilation is proposed within the framework of a model (the τ-model) in which space–time and momentum space are very strongly correlated. Using information from the Bose–Einstein correlations as well as from single-pion spectra, it is then possible to reconstruct the space–time evolution of pion production.     

Two-body deuteron photodisintegration above pion threshold with a dynamical treatment of δ degrees of freedom

The two-body photo break-up of the deuteron above pion threshold is calculated treating the final state interaction in a coupled channel approach with inclusion of Δ degrees of freedom. For the electromagnetic interaction nucleon, isobar and meson exchange currents are taken into account. Various observables (total and differential cross sections, γ-asymmetry and nucleon polarization) are influenced by the dynamical treatment of Δ degrees of freedom. Especially for the proton polarization it leads to an improved agreement with experiment. However, the situation for the shape of the differential cross section remains problematic.     

Towards a Skyrme–Hartree–Fock–Bogolyubov Mass Formula

In this work, we explain our astrophysical motivations for deriving a mass formula based on HFB calculations with a Skyrme interaction. We give an overview of existing mass formulae and present briefly the last HF+BCS mass formula [1]. The Skyrme force MSk7 [1] is considered in the study of shell effects at N=82, in the neutron-rich region far from stability, within the HFB and HF+BCS theories, and compared with results obtained using the forces SkP^δ and SkP^δρ [2]. This revised version was published online in July 2006 with corrections to the Cover Date.     

Propagation of a Hermite–Laguerre–Gaussian beam in a turbulent atmosphere

The propagation and spreading of a Hermite–Laguerre–Gaussian (HLG) beam in a turbulent atmosphere has been investigated. Based on the extended Huygens–Fresnel integral and some mathematical techniques, analytical expressions for the average intensity, the effective beam size, and the kurtosis parameter of an HLG beam in a turbulent atmosphere are derived, respectively. The average intensity distribution and the spreading properties of HLG beams in a turbulent atmosphere are numerically demonstrated. Upon propagation in a turbulent atmosphere, the central lobes in the beam spot of the HLG beam will evolve into the dominant lobes, and the peripheral lobes around the central lobes will evolve into the subdominant lobes. The influences of the additional angle parameter and the transversal mode numbers on the propagation of HLG beams in a turbulent atmosphere are also discussed. As the coherence length of the turbulence is determined by the propagation distance, the effect of the additional angle parameter on the effective beam size is related to the propagation distance. The kurtosis parameter generally increases with increasing the additional angle parameter. The influence of the transversal mode numbers on the kurtosis parameter is related to the additional angle parameter and the propagation distance. According to the practical need of free-space optical communications and remote sensing, the HLG beam in a turbulent atmosphere can be controlled by choice of the additional angle parameter and the transversal mode numbers.     

Left–right asymmetry for pion and kaon production in the semi-inclusive deep-inelastic scattering process

We analyze the left–right asymmetry in the semi-inclusive deep-inelastic scattering (SIDIS) process without introducing any weighting functions. With the current theoretical understanding, we find that the Sivers effect plays a key role in our analysis. We use the latest parametrization of the Sivers and fragmentation functions to reanalyze the π ^± production process and find that the results are sensitive to the parametrization. We also extend our calculation on the K ^± production, which can help us know more about the Sivers distribution of the sea quarks and the unfavored fragmentation processes. HERMES kinematics with a proton target, COMPASS kinematics with a proton, deuteron, and neutron target (the information on the neutron target can be effectively extracted from the ³He target), and JLab kinematics (both 6 GeV and 12 GeV) with a proton and neutron target are considered in our paper.     

Study of inverse a.c. Josephson effect in Y–Ba–Cu–O and Y–8a–Sr–Cu–O

Microwave induced d.c. voltage due to inverse a.c. Josephson effect has been observed across bulk samples of Y-Ba-Cu-O and Y-Ba-Sr-Cu-O. The d.c. voltage is found to vary with microwave power, frequency and also with small external magnetic fields. Although the resistivity curve of Y-Ba-Cu-O does not show any appreciable resistance drop around 230 K, the microwave induced d.c. voltage due to the inverse a.c. Josephson effect has been found to exist upto 230 K. The resistivity behaviour of Y-Ba-Sr-Cu-O shows a sharp resistivity drop above 230 K. In this sample the inverse Josephson effect is found to exist upto +26 °C, indicating the presence of a phase having a superconducting onset around this temperature.     

Study of the charge dependence of the pion–nucleon coupling constant on the basis of data on low-energy nucleon–nucleon interactions

The relation between quantities that characterize the pion–nucleon and nucleon–nucleon interactions is studied with allowance for the fact that, at low energies, nuclear forces in nucleon–nucleon systems are mediated predominantly by one-pion exchange. On the basis of the values currently recommended for the low-energy parameters of the proton–proton interaction, the charged pion–nucleon coupling constant is evaluated at g_π²±/4π = 14.55(13). This value is in perfect agreement with the experimental value of g_π²±/4π = 14.52(26) found by the Uppsala Neutron Research Group. At the same time, the value obtained for the charged pion–nucleon coupling constant differs sizably from the value of the pion–nucleon coupling constant for neutral pions, which is g_π² 0/4π = 13.55(13). This is indicative of a substantial charge dependence of the coupling constant.     

In-medium pion dispersion relation and medium correction of Nπ■Δ near the threshold energy of pion production

Transport models cannot simultaneously explain very recent data on pion multiplicities and pion charged ratios from central collision of Sn+Sn at 0.27 A GeV.This stimulates further investigations on the pion dispersion relation,in-medium Nπ→Δ cross sections,and Δ→Nπ decay widths near the threshold energy or at subthreshold energy of pion production in isospin asymmetric nuclear matter.In this study,the pion dispersion relation,in-medium Nπ→Δ cross section,and Δ→Nπ decay width near the threshold energy are investigated in isospin asymmetric nuclear matter by using the one-boson-exchange model.With the consideration of the energy conservation effect,the in-medium Nπ→Δ cross sections are enhanced at s1/2 <1.11 GeV in a nuclear medium.The prediction of pion multiplicity and π-/π+ ratios near the threshold energy could be modified if this effect is considered in transport model simulations.     

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.     

Instability of a flame front propagating through a fuel-rich droplet–vapour–air cloud

A simple model of a flame front propagating through a fuel-rich droplet–vapour–air mixture is presented in which the fuel droplets are assumed to evaporate in a sharp front ahead of the reaction front. By performing a linear stability analysis neutral stability boundaries are determined. It is shown that the presence of the spray of droplets in the fresh mixture can have a profound effect by causing cellularization of the flame front. Specifically, we demonstrate that under certain circumstances a spray flame can be cellular when its equivalent non-spray flame is completely stable. Furthermore, it is shown that even when the non-spray flame is itself cellular the equivalent spray flame will have a finer cellular structure. These theoretical predictions verify qualitatively for the first time independent experimental observations from the literature. It is thus shown that the primary effect of the spray on the stability of these flames is due to heat loss from the absorption of heat by the droplets for vaporization. The influence of the initial liquid fuel loading and the latent heat of vaporization on the critical wavenumber associated with cellularity provide further evidence of the responsibility of the heat loss mechanism for these spray-related phenomena. Finally, the cellularity of the spray flames with their attendant increase in flame front area suggest a plausible rationale for the experimentally observed burning velocity enhancement induced by the use of a spray of fuel droplets.     

Current–phase relations of a ring-trapped Bose–Einstein condensate with a weak link

The current–phase relations of a ring-trapped Bose–Einstein condensate interrupted by a rotating rectangular barrier are extensively investigated with an analytical solution. A current–phase diagram, single and multi-valued relation, is presented with a rescaled barrier height and width. Our results show that the finite size makes the current–phase relation deviate a little bit from the cosine form for the soliton solution in the limit of a vanishing barrier, and the periodic boundary condition selects only the plane wave solution in the case of high barrier. The reason for multi-valued current–phase relation is given by investigating the behavior of soliton solution.