The spinless relativistic Yukawa problem

Abstract

Noticing renewed or increasing interest in the possibility to describe semirelativistic bound states (of either spin-zero constituents or, upon confining oneself to spin-averaged features, constituents with nonzero spin) by means of the spinless Salpeter equation generalizing the Schrödinger equation towards incorporation of effects caused by relativistic kinematics, we revisit this problem for interactions between bound-state constituents of Yukawa shape, by recalling and applying several well-known tools enabling to constrain the resulting spectra.

The semi-relativistic scattering states of the two-body spinless Salpeter equation with the Varshni potential model

“…The solution of this spinless Salpeter equation is limited to certain potentials due to the square of potential term in the equation. These potentials include: Yukawa potential [5,6,15,16], generalized Hulthén potential [7,12], Hulthén potential [11,13], Cornell and Kratzer potential [17], Woods-Saxon potential [18][19][20][21], Coulomb potential [22] among the fewer ones. The solution of this equation with some potential models is of scientific interest as the semi-relativistic nature and two-body effects find their applications in particle and nuclear physics.…”

The spinless relativistic Hellmann problem

“…Fourier transformation immediately provides the momentum-space representation of these basis states; explicit expressions of these functions can be found in, e.g., Refs. [6,8,9,20,23]. Table 1 illustrates the application of the variational technique recalled above to spinless relativistic Hellmann problems by presenting the set of upper limits on the binding energies…”

“…Needless to say, upon having a set of solutions at one's disposal, its significance can be easily examined by various really powerful tools, for instance, the generalization of the virial theorem of nonrelativistic quantum theory to the incorporation of relativistic kinematics [4,5]. Utilizing techniques of this kind has proven extremely efficient in the separation of the wheat from the chaff [6][7][8][9][10].…”

Bethe–Salpeter-Motivated Modelling of Pseudo-Goldstone Pseudoscalar Mesons

“…With the explicit behaviour of the effective interquark potential V (r) at our disposal, we are in a position to embark on the intended simplified description of meson properties: for M B = 0, inserting any of Eqs. (3.3) into the other, takes us to a single eigenvalue equation for eigenvalues M 2 B [2][3][4][5]17], which can be easily solved by expanding its solutions over suitable bases in function space [18][19][20][21][22][23][24][25].…”