Three Different Approaches to the Same Interaction: The Yukawa Model in Nuclear Physics

Abstract

Abstract. After a brief discussion of the meaning of the potential in quantum mechanics, we shall examine the results of the Yukawa model (scalar meson exchange) for the nucleonnucleon interaction in three different dynamical frameworks: the non-relativistic dynamics of the Schrodinger equation, the relativistic quantum mechanics of the Bethe-Salpeter and Light-Front equations and the lattice solution of the Quantum Field Theory, obtained in the quenched approximation.

Solving Bethe-Salpeter scattering state equation in Minkowski space

“…Beyond this region both dynamics are not compatible. This non matching between NR and relativistic equations was already pointed out in [32,33] when computing the binding energies B of a two scalar and two fermion system in the limit B → 0 with different relativistic approaches. A recent work [16] devoted to this problem proposes the construction of equivalent non relativistic potential using the technique of geometrical spectral inversion.…”

“…The sum over intermediate states in the product S † S is understood as integration with the measure given in (33). After substituting the partial waves decomposition (5) in the equation ( 33) the latter obtains the form:…”

The Interplay between Compact and Molecular Structures in Tetraquarks

“…Compared to the Coulomb potential, the Yukawa potential (4) is of the short-range type and hence not all values of g 2 may produce bound states. There exists a critical value of it, g 2 cr = 1.68 × (4π) [76,78], below which bound states do not exist. The existence of bound states is ensured by the inequality:…”

Calculation of screened Coulomb potential matrices and its application to He bound and resonant states

“…Investigation of the screened Coulomb potential (SCP) has attracted considerable attention in the past years due to its fundamental importance and wide applications in different areas, such as atomic physics, nuclear physics, plasma physics, semiconductors, and quantum chemistry [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. In a variety of formalism, the exponential type in the form Z i Z j e −λr ij /r ij with λ the screening parameter is of particular interest.…”

“…In a variety of formalism, the exponential type in the form Z i Z j e −λr ij /r ij with λ the screening parameter is of particular interest. For example, it can be used to describe the Coulomb interactions of atoms embedded in weakly coupled plasmas within the Debye-Hückel model where the screening parameter is a function of plasma temperature and number density of charged particles [1][2][3][4][5][6][7], the interactions of elementary particles in nuclear structure calculations where the SCP is always referred to as Yukawa potential [8,9], and the static field generated by impurity doping in semiconductor materials where the screening parameter is related to the impurity charge and electron and impurity concentrations [10,11]. The SCP has also shown its special advantages in implementation of the range-separated density-functional theory [12,13].…”