Accumulation of Discrete Eigenvalues of the Radial Dirac Operator

For bounded potentials which behave like −cx−γat infinity we investigate whether discrete eigenvalues of the radial Dirac operatorHκaccumulate at +1 or not. It is well known thatγ=2 is the critical exponent. We show thatc=1/8+κ(κ+1)/2 is the critical coupling constant in the caseγ=2. Our approach is to transform the radial Dirac equation into a Sturm–Liouville equation nonlinear in the spectral parameter and to apply a new, general result on accumulation of eigenvalues of such equations.