Relativistic neutron interaction with electric fields revisited
- PDF / 410,640 Bytes
- 9 Pages / 595.276 x 790.866 pts Page_size
- 37 Downloads / 231 Views
Regular Article -Theoretical Physics
Relativistic neutron interaction with electric fields revisited S. A. Bruce1,a , J. F. Diaz-Valdes2,b 1 2
Complex Systems Group, Facultad de Ingenieria y Ciencias Aplicadas, Universidad de Los Andes, Santiago, Chile Departamento de Fisica, Facultad de Ciencias Fisicas y Matematicas, Universidad de Concepcion, Concepción, Chile
Received: 27 February 2020 / Accepted: 8 July 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020 Communicated by Eulogio Oset
Abstract We address the bound-state dynamics of a neutron with anomalous magnetic dipole moment in the presence of certain static electric fields. We show that the involved quantum systems can be described by an exactly solvable single particle model realized as: (i) the so-called Dirac oscillator; (ii) a particular kind of hydrogen atom-like system; (iii) an axial harmonic oscillator; where the Aharonov–Casher (AC) discrete states in 3 + 1 space-time dimensions are analyzed within the framework of supersymmetric quantum mechanics (SUSYQM).
1 Introduction We investigate the relativistic bound-state dynamics of a neutron with ‘anomalous’ gyromagnetic ratio, i.e. endowed with magnetic dipole moment μn = −1.91μN , where μN is the nuclear magneton. We begin by considering the relativistic quantum mechanical model of introducing anomalous magnetic moment: the Dirac–Pauli equation (DPE), namely, the Dirac equation with the addition of a Pauli term in which the magnetic moment does not vary independently of charge and mass. The ‘Dirac’ magnetic moment can be calculated from the Dirac equation. It is usually expressed in terms of the g-factor; the Dirac equation predicts g = 2. For charged particles such as the proton, this result differs from the observed value, either due to their composite structure, or, for (fundamental) point-like particles, due to the quantum vacuum fluctuation phenomenon. The magnetic moment sign choice is implicitly made when writing the Dirac Hamiltonian operator, choosing minus sign in the mass term we choose the conventional magnetic moment sign, the other sign leads to opposite magnetic moment sign. The incorporation of both magnetic moment signs in the DPE for relativistic fermion a e-mail:
[email protected] (corresponding author)
b e-mail:
[email protected]
0123456789().: V,-vol
dynamics needs to maintain the number of degrees of freedom 4 in the Dirac spinor [1]. The DPE in natural units (h¯ = 1 = c) describing the interaction of a neutron with an external electromagnetic (EM) field has a magnetic moment interaction constituting its observed anomalous magnetic moment [2–4]
γ μ i∂μ − en Aμ +
κn |e| 2Mn
1 μν F μν − Mn (q,t) = 0, 2
(1) with e the electron charge, where en = 0, i.e. κn = gn /2. The EM field tensor can be written as F μν = ∂ μ Aν − ∂ ν Aμ , where Aμ = (V, A) is the EM 4-vector potential applied on the neutron. Here we use Jackson’s convention for the global sign of F μν [5], which implies that |e| (instead occurs of
Data Loading...
