Related papers: Solving the two-center nuclear shell-model problem…
It is shown that the operator methods of supersymmetric quantum mechanics and the concept of shape invariance can profitably be used to derive properties of spherical harmonics in a simple way. The same operator techniques can also be…
A numerical method using implicit surface representations is proposed to solve the linearized Poisson-Boltzmann equations that arise in mathematical models for the electrostatics of molecules in solvent. The proposed method used an implicit…
The determination of nucleus-nucleus potentials is important not only to describe the properties of the colliding system, but also to extract nuclear-structure information and for modelling nuclear reactions for astrophysics. We present the…
The complex scaling method is commonly used to describe decaying states, but its applications are limited because the Hamiltonian operator must contain only relative coordinates. This has hindered the use of complex scaling in models…
In calculations of heavy-atom molecules with the shape-consistent Relativistic Effective Core Potential (RECP), only valence and some outer-core shells are treated explicitly, the shapes of spinors are smoothed in the atomic core regions…
Unpolarized 800 MeV proton inelastic scatterings from an s-d shell nucleus $^{22}$Ne are analyzed using phenomenological optical potentials in the Dirac coupled channel formalism. The first-order rotational collective model is used to…
The potential model for nuclear astrophysical reactions requires a considerably shallow nuclear potential when a square-well potential is employed to fit experimental data. We discuss the origin of this apparently different behavior from…
We develop a systematic procedure for constructing quantum many-body problems whose spectrum can be partially or totally computed by purely algebraic means. The exactly-solvable models include rational and hyperbolic potentials related to…
The hyperspherical adiabatic expansion is combined with complex scaling and used to calculate low-lying nuclear resonances of $^{12}$C in the $3\alpha$-model. We use Ali-Bodmer potentials and compare results for other potentials…
The asymptotic behavior of the molecular continuum wave function has been analyzed within a model of non-overlapping atomic potentials. It is been shown that the representation of the wave function far from a molecule as a plane wave and…
A set of moderately deformed $s-d$ shell nuclei is employed for testing the reliability of the nuclear ground state wave functions which are obtained in the context of a BCS approach and offer a simultaneous consideration of deformation and…
A theoretical method for treating collisions in the presence of multiple potentials is developed by employing the Schwinger variational principle. The current treatment agrees with the local (regularized) frame transformation theory and…
The supersymmetric intertwining relations with second order supercharges allow to investigate new two-dimensional model which is not amenable to standard separation of variables. The corresponding potential being the two-dimensional…
Alpha elastic scattering of p-nuclei were studied for calculating optical potentials. Choice of the $\alpha$-optical potentials are important to measure the reaction rates of p-process. $^{106}$Cd$(\alpha,\alpha)^{106}$Cd and…
We investigate the isovector component in the phenomenological mean field model of nuclei. Lane's isospin dependence, initially proposed for the nuclear optical potential, is reexamined within the context of bound states using the…
Analytical expressions for spectra and wave functions are derived for a Bohr Hamiltonian, describing the collective motion of deformed nuclei, in which the mass is allowed to depend on the nuclear deformation. Solutions are obtained for…
We present a precise fully relativistic numerical solution of the two-center Coulomb problem. The special case of unit nuclear charges is relevant for the accurate description of the ${\rm H}_2^+$ molecular ion and its isotopologues,…
$0s$-orbit $\Lambda$ states in $p$-shell double-$\Lambda$ hypernuclei ($^{\ \,A}_{\Lambda\Lambda}Z$), $^{\ \,8}_{\Lambda\Lambda}\textrm{Li}$, $^{\ \,9}_{\Lambda\Lambda}\textrm{Li}$, $^{10,11,12}_{\ \ \ \ \ \Lambda\Lambda}\textrm{Be}$,…
Two different methods of the covariant relativistic separable kernel construction in the Bethe-Salpeter approach are considered. One of them leads in the center-of-mass system of two particles to the quasipotential equation. The constructed…
In this paper, motivated by diffraction of traveling light waves, a simple mathematical model is proposed, both for the multivariate super-resolution problem and the problem of blind-source separation of real-valued exponential sums. This…