Dirac spinor orbits.

It is supposed that a single fermion with Hamiltonian H=α·p+βμ(r)+[lowercase_phi_synonym](r), where μ(r) and [lowercase_phi_synonym](r) are central potentials, obeys the Dirac equation. If ψ1(r) and ψ2(r) are the radial factors in the Dirac spinor, then the graph {ψ1(r), ψ2(r)} for r∈(0,∞) is called a spinor orbit. In cases where discrete eigenvalues exist, the corresponding spinor orbit eventually returns to the origin. However, if there is a constant a≥0 such that, for r>a, the three functions [lowercase_phi_synonym](r), [lowercase_phi_synonym](r)/μ(r), and rμ(r) increase monotonically without bound, then it is proved that the spinor orbit must eventually be confined to an annular region excluding the origin. Consequently, the spinor orbit approaches a ‘‘spinor circle,’’ the spinor is not L2, and there are no eigenvalues. This happens, for example, if μ is constant and [lowercase_phi_synonym](r) is any monotone increasing and unbounded potential. In such cases the radius of the spinor circle is sensitive to the energy, and instead of eigenvalues one finds a sequence of resonant energies for which the radii of the spinor circles are local minima. [ABSTRACT FROM AUTHOR]