Could the static properties of nuclei be deduced from the dynamics of a single quark?

Abstract

We show that the static properties of a nucleus could arise from a single quark moving in a mean field generated by all other constituents of this nucleus. The resulting model provides a way for determining the nuclear sizes characteristic of the liquid drop model, and reasonably accurate values of magnetic moments of different nuclei with the aid of two parameters α s and σ appearing in the Cornell potential intended for use in quarkonium physics.

Correspondence between the physics of extremal black holes and that of stable heavy atomic nuclei

“…We found the energy levels ε nr for κ = −1, −2 and the corresponding sizes of the cavities r sc (n r ). To a good approximation the energy levels ε nr turn out to be proportional to √ n r [6]. By assuming that n r is proportional to A 2/3 , where A is the nucleus mass number, we came to the relationship r sc = R 0 A 1/3 with R 0 ≈ 1 fm for the chosen values of the α s and σ, which is consistent with Eq.…”

“…What this means is the quark Q orbits the center of mass, being driven by central potentials A 0 (r) and Φ(r), and roams around the nucleus, that is, the quark Q is affected not only by the neighbouring quarks of the "parent" nucleon, but the combined potentials of the entire nucleus. The arguments in support of this assumption closely resemble those taken in the single-particle shell model of atomic nuclei [6]. We thus take, as the starting point, the Dirac Hamiltonian…”

“…Reasonably accurate results for the spectrum of quarkonia can then be found with the use of the discussed Dirac equation machinery [5], [6].…”

“…The paper is organized as follows. The treatment of nuclear physics in terms of quark degrees of freedom, developed in [5] and [6], is briefly reviewed in Sec. 2.…”

Spin and Pseudo-Spin Symmetries in Radial Dirac Equation and Exceptional Hermite Polynomials

“…Spin symmetry shows up in the spectrum of mesons with one heavy quark, also hadrons, antinucleons have spin symmetry [7]. Pseudospin symmetry in heavy nuclei originates from the nucleons in a nucleus move in an attractive scalar and repulsive vector potential [8], [9] which is used to explain the observed degeneracies of some shell-model orbitals in nuclei. Pseudospin symmetry is an approximation in a real nuclei and it is shown that the pseudospin symmetry is examined in the framework of relativistic Hartree-Bogoliubov theory for some examples [10].…”