abstract

In this paper, we exhibited the ground and excited state masses of doubly heavy \({\mit \Omega }\) baryons. For this purpose, we have analytically solved the six-dimensional radial Schrödinger equation for three identical particles with the hypercentral potential by using the Ansatz method. The hypercentral potential is considered as a combination of the hypercoulomb, linear confining, and the harmonic oscillator terms which has a two-body character and turns out to be exactly hypercentral. We also incorporated the first order correction and the spin-dependent part to the confinement potential. Our calculations have been performed for the radial excited states as well as orbital excited states masses of \({\mit \Omega }_{cc}\), \({\mit \Omega }_{bb}\) and \({\mit \Omega }_{bc}\) baryons. The obtained masses are compared with other theoretical predictions, which could be a useful tool for the interpretation of experimentally unknown doubly heavy baryons spectrum.

abstract

Angular distributions of the \(^{15}\)N+\(^{12}\)C elastic and inelastic scattering were measured at \(E_{\rm lab}\)(\(^{15}{\mathrm {N}})=81\) MeV to study the nuclear–nuclear interactions and possible transfer contributions to the scattering. The data were analyzed with the coupled-reaction-channels (CRC) method using the \(^{15}\)N+\(^{12}\)C optical potential of Woods–Saxon shape. The elastic and inelastic scattering as well as the most obvious one- and two-step transfer reactions were included in the channel-coupling scheme. The \(^{15}\)N+\(^{12}\)C optical potential and deformation parameters of \(^{15}\)N were deduced. The transfer reaction contributions to the \(^{15}\)N+\(^{12}\)C elastic and inelastic scattering channels were estimated. The \(^{15}\)N+\(^{12}\)C elastic scattering at 81 MeV was compared with the \(^{14}\)N+\(^{12}\)C elastic scattering of \(^{14}\)N beam energy 78 MeV.

abstract

A solution of the Einstein equations for a multi-string system having a layered structure is found. It is shown that the influence of the gravitational field of such a multi-string system can lead to stable in time oscillations of the test null-string in the vicinity of fixed point of space. This situation can be interpreted as a particle localized in space with an effective nonzero rest mass.

abstract

A nonlinear wave equation is investigated via the Riemann–Hilbert approach. Based on the spectral analysis for the Lax pair, a Riemann–Hilbert problem of the nonlinear wave equation is established. For the reflectionless cases, we obtain \(N\)-soliton solutions of the nonlinear wave equation and discuss the dynamic behavior of its soliton solutions.

abstract

Beginning with addition and multiplication intrinsic to a Koch-type curve we formulate and solve wave equation describing wave propagation along a fractal coastline. As opposed to examples known from the literature, we do not replace the fractal by the continuum in which it is embedded. This seems to be the first example of a truly intrinsic description of wave propagation along a fractal curve. The theory is relativistically covariant under an appropriately defined Lorentz group.