Hyperfine structure and Zeeman splitting in two-fermion bound-state systems (original) (raw)
Related papers
2008
A relativistic theory of the Zeeman splitting of hyperfine levels in two-fermion systems is presented. The approach is based on the variational equation for bound states derived from quantum electrodynamics [1]. Relativistic corrections to the g-factor are obtained up to O(alpha^2). Calculations are provided for all quantum states and for arbitrary fermionic mass ratio. In the one-body limit our calculations reproduce the formula for the g-factor (to O((Z*alpha)^2)) obtained from the Dirac equation. The results will be useful for comparison with high-precision measurements.
Journal of Physics: Conference Series, 2010
A relativistic theory of the Zeeman splitting of hyperfine levels in two-fermion systems is presented. The approach is based on the variational equation for bound states derived from quantum electrodynamics . Relativistic corrections to the g-factor are obtained up to O (α) 2 . Calculations are provided for all quantum states and for arbitrary fermionic mass ratio. In the one-body limit our calculations reproduce the formula for the g-factor (to O (Zα) 2 ) obtained from the Dirac equation. The results will be useful for comparison with high-precision measurements. (S 1 ) J and f (S 1 ) J are taken as f (S 1 ) J =
Relativistic two fermion treatment of hyperfine transitions
Journal of Physics B: Atomic, Molecular and Optical Physics, 2015
A system of two fermions with different masses and interacting by the Coulomb potential is presented in a completely covariant framework. The spin-spin interaction, including the anomalous magnetic moments of the two fermions, is added by means of a Breit term. We solve the resulting fourth order differential system by evaluating the spectrum and the eigenfunctions. The interaction vertex with an external electromagnetic field is then determined. The relativistic eigenfunctions are used to study the photon emission from a hyperfine transition and are checked for the calculation of the Lamb shift due to the electron vacuum polarization in the muonic Hydrogen.
Two-fermion relativistic bound states: hyperfine shifts
Journal of Physics A: Mathematical and General, 2006
We discuss the hyperfine shifts of the Positronium levels in a relativistic framework, starting from a two fermion wave equation where, in addition to the Coulomb potential, the magnetic interaction between spins is described by a Breit term. We write the system of four first order differential equations describing this model. We discuss its mathematical features, mainly in relation to possible singularities that may appear at finite values of the radial coordinate. We solve the boundary value problems both in the singular and non singular cases and we develop a perturbation scheme, well suited for numerical computations, that allows to calculate the hyperfine shifts for any level, according to well established physical arguments that the Breit term must be treated at the first perturbative order. We discuss our results, comparing them with the corresponding values obtained from semi-classical expansions. pacs03.65.Pm, 03.65.Ge
Hyperfine spin-spin interaction and Zeeman effect in the pure bound field theory
The European Physical Journal Plus, 2012
We carry out a joint analysis of the hyperfine spin-spin splitting (HFS) and the Zeeman effect in the framework of Pure Bound Field Theory (PBFT) we recently suggested (A.L. Kholmetskii et al. Eur. Phys. J. Plus 126 (2011) 33; 126 (2011) 35), where the PBFT corrections to the known results have a similar form due to the common physical origin of both effects. We consequently consider the hydrogen atom, positronium, muonium and muonic hydrogen atom and show that for the Zeeman effect in muonic hydrogen, the PBFT correction occurs measurable and its presence/absence can be subjected to an experimental test, which thus will be crucial for the verification of PBFT versus the common theory. Concurrently we derive the PBFT correction to the muon mass, which is cancelled in the joint analysis of HFS and Zeeman effect, but can be revealed in muon-spin-precession-resonance experiments with enhanced precision. As a result, we achieve better agreement between the estimations of the muon mass in different experiments. In addition, we have shown that the PBFT correction to the proton Zemach radius is one order of magnitude smaller than the measurement uncertainty and can be well ignored, unlike the case of the proton charge radius.
The quadratic Zeeman effect for highly excited hydrogen atoms in weak magnetic fields
Journal of Physics B: Atomic and Molecular Physics, 1984
The hydrogen Rydberg states in the presence of weak magnetic fields areanalytically investigated by using quantum mechanical first-order perturbation theory. The unperturbed hydrogenic wavefunctions, which diagonalise the quadratic Zeeman interaction within the subspace of states with fixed principal quantum number n, are obtained by separation of variables on the Fock hypersphere in momentum space. By considering n as a large parameter, the comparison equation method is employed to find the uniform asymptotics of eigenfunctions and asymptotic expansions of quadratic Zeeman energies corresponding to the outermost components of the Zeeman n manifold. The results obtained are compared with other theoretical predictions.
Relativistic self-consistent field theory for muonic atoms: The muonic hyperfine anomaly
Hyperfine Interactions, 1981
The relativistic Hartree-Fock-Roothaan equation for closed-shell configurations of atoms is derived. The relativistic Hamiltonian consists of the sum of the Dirac Hamiltonians and the interelectronic Coulomb repulsion terms. The atomic wave function is assumed to be an antisymmetrized product of 4-component orbitals whose radial functions are expanded in terms of the Slater-type basis functions. The Breit interaction operator is used as the relativistic interelectronic interaction term, and is treated as the first-order perturbation. Expressions for the matrix elements of the Breit interaction operator are given for the closedshell configurations. Numerical results for the ground states of He, Be, and Ne atoms computed according to this formalism are also presented. '7 We call Jgg "the direct integral of the Coulomb repulsion term" to distinguish it from the direct integrals of the magnetic interaction and the retardation terms in the Breit operator. Obviously, Jgg is the relativistic counterpart of the nonrelativistic Coulomb integral.
Foundations of the relativistic theory of many-electron bound states
International Journal of Quantum Chemistry, 1984
Most of the existing calculations of relativistic effects in many-electron atoms or molecules are based on the Dirac-Coulomb Hamiltonian HDc. However, because the electron-electron interaction mixes positive-and negative-energy states, the operator HDc has no normalizable eigenfunctions.
2007
The variational method, within the Hamiltonian formalism of reformulated QED is used to determine relativistic wave equations for a system of three fermions of arbitrary mass interacting electromagnetically. The interaction kernels of the equations are, in essence, the invariant M matrices in lowest order. The equations are used to obtain relativistic O(α 2) corrections to the non-relativistic ground state energy levels of the Muonium negative ion (µ + e − e −) as well as of Ps − and H − , using approximate variational three-body wave functions. The results are compared with other calculations, where available. The relativistic correction for Mu − is found to be −1.0773×10 −4 eV.
Two fermion relativistic bound states
Journal of Physics A: Mathematical and General, 2005
We consider the relativistic quantum mechanics of a two interacting fermions system. We first present a covariant formulation of the kinematics of the problem and give a short outline of the classical results. We then quantize the system with a general interaction potential and deduce the explicit equations in a spherical basis. The case of the Coulomb interaction is studied in detail by numerical methods, solving the eigenvalue problem for j = 0, j = 1, j = 2 and determining the spectral curves for a varying ratio of the mass of the interacting particles. Details of the computations, together with a perturbative approach in the mass ratio and an extended description of the ground states of the Para-and Orthopositronium are given in Appendix.