scholarly journals Study of the Influence of Different Methods of Taking into Account the Coulomb Interaction on Determining Asymptotic Normalization Coefficients within the Framework of Exactly Solvable Model

2021 ◽  
Vol 84 (4) ◽  
pp. 401-407
Author(s):  
L. D. Blokhintsev ◽  
D. A. Savin
Keyword(s):  
Coulomb Interaction ◽  
Nuclear Charge ◽  
Solvable Model ◽  
Asymptotic Normalization ◽  
Exactly Solvable Model ◽  
Point Distribution ◽  
Exactly Solvable ◽  
Nuclear Systems ◽  
Square Well ◽  
Asymptotic Normalization Coefficients

Abstract It is shown that the Schrödinger equation for the sum of the potential of a square well and the Coulomb potential of a uniformly charged sphere admits an analytical solution for arbitrary values of the orbital angular momentum. An explicit form of this solution has been found. Using the obtained solution, the influence of the Coulomb interaction for both point and distributed nuclear charges on the values of asymptotic normalization coefficients for various nuclear systems is investigated. It is shown that taking into account the non-point distribution of the nuclear charge has little effect on the calculated values of the asymptotic normalization coefficients, provided that the binding energy of the system is assumed to be fixed.

scholarly journals A quasi-exactly solvable model: Two charges in a magnetic field subject to a non-Coulomb mutual interaction

2015 ◽  
Vol 29 (29) ◽  
pp. 1550204
Author(s):  
Michael Kreshchuk
Keyword(s):  
Magnetic Field ◽  
Exact Solutions ◽  
Coulomb Interaction ◽  
Differential Form ◽  
Uniform Magnetic Field ◽  
Solvable Model ◽  
Mutual Interaction ◽  
Planar Motion ◽  
Exactly Solvable Model ◽  
Exactly Solvable

In this paper, we extend the class of QM problems which permit for quasi-exact solutions. Specifically, we consider planar motion of two interacting charges in a constant uniform magnetic field. While Turbiner and Escobar–Ruiz (2013) addressed the case of the Coulomb interaction between the particles, we explore three other potentials. We do this by reducing the appropriate Hamiltonians to the second-order polynomials in the generators of the representation of SL(2, C) group in the differential form. This allows us to perform partial diagonalization of the Hamiltonian and to reduce the search for the first few energies and the corresponding wavefunctions to an algebraic procedure.

The reduced α-amplitude in an exactly solvable model

1979 ◽  
Vol 324 (1) ◽  
pp. 173-181 ◽  
Author(s):  
T. Fliessbach ◽  
P. Manakos
Keyword(s):  
Solvable Model ◽  
Exactly Solvable Model ◽  
Exactly Solvable
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