Kink-antikink interactions in the double sine-Gordon equation and the problem of resonance frequencies

We studied the kink-antikink collision process for the "double sine-Gordon" (DSG) equation in 1+1 dimensions at different values of the potential parameter $R>0$. For small values of $R$ we discuss the problem of resonance frequencies. We give qualitative explanation of the frequency shift in comparison with the frequency of the discrete level in the potential well of isolated kink. We show that in this region of the parameter $R$ the effective long-range interaction between kink and antikink takes place.Comment: 9 pages, LaTeX, 4 figures (eps

KKbar molecules with momentum-dependent interactions

It is shown that the momentum-dependent kaon-antikaon interactions generated via vector meson exchange from the standard SU_V(3) x SU_A(3) interaction Lagrangian lead to a non-local potential in coordinate space that can be incorporated without approximation into a non-relativistic version of the Bethe-Salpeter wave equation containing a radial-dependent effective kaon mass appearing in a fully symmetrized kinetic energy operator, in addition to a local potential. Estimates of the mass and decay widths of f_0(980) and a_0(980), considered as KKbar molecules of isospin 0 and 1, as well as for K^+K^- atomic bound states (kaonium) are presented, and compared with previous studies of a similar nature. It is argued that without a better knowledge of hadronic form factors it is not possible to distinguish between the molecular versus elementary particle models for the structure of the light scalar mesons.Comment: 14 pages, 2 tables, 5 figures. Added subsection on s-channel exchange, additional remarks on the possible effect of gluon exchange, and 1 additional figur

The Zel'dovich effect and evolution of atomic Rydberg spectra along the Periodic Table

In 1959 Ya. B. Zel'dovich predicted that the bound-state spectrum of the non-relativistic Coulomb problem distorted at small distances by a short-range potential undergoes a peculiar reconstruction whenever this potential alone supports a low-energy scattering resonance. However documented experimental evidence of this effect has been lacking. Previous theoretical studies of this phenomenon were confined to the regime where the range of the short-ranged potential is much smaller than Bohr's radius of the Coulomb field. We go beyond this limitation by restricting ourselves to highly-excited s states. This allows us to demonstrate that along the Periodic Table of elements the Zel'dovich effect manifests itself as systematic periodic variation of the Rydberg spectra with a period proportional to the cubic root of the atomic number. This dependence, which is supported by analysis of experimental and numerical data, has its origin in the binding properties of the ionic core of the atom.Comment: 17 pages, 12 figure

The variation of the magnetic field of the Ap star HD~50169 over its 29 year rotation period

Context. The Ap stars that rotate extremely slowly, with periods of decades to centuries, represent one of the keys to the understanding of the processes leading to the differentiation of stellar rotation. Aims. We characterise the variations of the magnetic field of the Ap star HD 50169 and derive constraints about its structure. Methods. We combine published measurements of the mean longitudinal field of HD 50169 with new determinations of this field moment from circular spectropolarimetry obtained at the 6-m telescope BTA of the Special Astrophysical Observatory of the Russian Academy of Sciences. For the mean magnetic field modulus , literature data are complemented by the analysis of ESO spectra, both newly acquired and from the archive. Radial velocities are also obtained from these spectra. Results. We present the first determination of the rotation period of HD 50169, Prot = (29.04+/-0.82) y. HD 50169 is currently the longest-period Ap star for which magnetic field measurements have been obtained over more than a full cycle. The variation curves of both and have a significant degree of anharmonicity, and there is a definite phase shift between their respective extrema. We confirm that HD 50169 is a wide spectroscopic binary, refine its orbital elements, and suggest that the secondary is probably a dwarf star of spectral type M. Conclusions. The shapes and mutual phase shifts of the derived magnetic variation curves unquestionably indicate that the magnetic field of HD 50169 is not symmetric about an axis passing through its centre. Overall, HD 50169 appears similar to the bulk of the long-period Ap stars.Comment: 10 pages, 3 figures, accepted for publication in A&

Example of a self-consistent solution for a fermion on domain wall

We discuss a self-consistent solution for a fermion coupled to static scalar field in the form of a kink (domain wall). In particular, we study the case when the fermion occupies an excited non-zero frequency level in the presence of the domain wall field. The effect of the domain wall profile distortion is calculated analytically.Comment: 9 pages, no figures; minor corrections, one reference added, results unchange

Angular asymmetries in the reactions pp \to d\pi^+\eta and pn \to d\pi^0\eta and a_0-f_0 mixing

The reactions pp\to d\pi^+\eta and pn\to d\pi^0\eta are of special interest for investigating the a_0(980) (J^P=0^+) resonance in the process NN \to da_0 \to d\pi\eta. We study some aspects of those reactions within a general formalism and also in a concrete phenomenological model. In particular, it is shown that the presence of nonresonant (i.e. without excitation of the a_0 resonance) contributions to these reactions yields nonvanishing values for specific polarization observables, i.e. to effects like those generated by a_0-f_0 mixing. An experimental determination of these observables for the reaction pp\to d\pi^+\eta would provide concrete information on the magnitude of those nonresonant contributions to \pi\eta production. We discuss also the possibility of extracting information about a_0-f_0 mixing from the reaction pn \to d\pi^0\eta with polarized proton beam.Comment: 14 pages, 3 figure

Proposed Search for a00(980)−f0(980)a^0_0(980)-f_0(980) Mixing in Polarization Phenomena

The $K^+$ and $K^0$ meson mass difference induces the mixing of the $a^0_0(980)$ and $f_0(980)$ resonances, the amplitude of which, between the $K^+K^-$ and $K^0\bar K^0$ thresholds, is large in magnitude, of the order of $m_{K}\sqrt{m^2_{K^0}-m^2_{K^+}}\approx\sqrt\alpha m^2_K$, and possesses the phase sharply varying by about 90$^\circ$. We suggest performing the polarized target experiments on the reaction $\pi^-p\to\eta\pi^0n$ at high energy in which the fact of the existence of $a^0_0(980)-f_0(980)$ mixing can be unambiguously and very easily established through the presence of a strong jump in the azimuthal asymmetry of the $\eta\pi^0$ $S$ wave production cross section near the $K\bar K$ thresholds. The presented estimates of the polarization effect to be expected in experiment are to a great extent model independent.Comment: RevTeX, 9 pages, 1 figure. A number of typographical and grammatical errors correcte

Formation of active-effective attitude of 12-13 years’ judo athletes to sports functioning in competition period

The purpose of the research is to theoretically and experimentally substantiate methodic of active-effective attitude to sports functioning formation in 12-13 years’ judo athletes (youngster categories) in competition perio