arXiv subjects
Publications and source records attributed to Vladimir B. Belyaev.
We present an application of a nonstandard approximate method---the finite-rank approximation---to solving the time-independent Schrödinger equation for a bound-state problem. The method is illustrated on the example of a three-dimensional isotropic quantum anharmonic oscillator with additive cubic or quartic anharmonicity. Approximate energy eigenvalues are obtained and convergence of the method is discussed.
We present a method for treatment of three charged particles. The proposed method has universal character and is applicable both for bound and continuum states. A finite rank approximation is used for Coulomb potential in three-body system Hamiltonian, that results in a system of one-dimensional coupled integral equations. Preliminary numerical results for three-body atomic and molecular systems like $H^{-}$, He, $ppμ$ and other are presented.
Binding energies of three-body systems of the type ϕ+2N are estimated. Due to the strong attraction between ϕ-meson and nucleon, suggested in different approaches, bound states can appear in systems like ϕ+np (singlet and triplet) and ϕ+pp. This indicates the principal possibility of the formation of new nuclear clusters.
We consider finite linear or cyclic crystalline structures with molecular cells having narrow pre-threshold nuclear resonance. We prove that if the real part of such a nuclear resonance lies within the energy band (the convex hull of the energy levels) of the crystalline structure arising of a separated molecular level, then there exist molecular crystalline states that decay exponentially in time and the decay rate $Γ_R^{(m)}$ of these states in the main order is described by the formula $Γ_R^{(m)}\cong 4\frac{\mathop{\rm Re} a}{Γ_R^{(n)}}$ where $a$ is the value of the residue of the molecular channel transfer function at the nuclear resonance point and $Γ_R^{(n)}$ is the nuclear resonance width.