Griesemer M., Lutgen J.
Accumulation of Discrete Eigenvalues of the Radial Dirac Operator
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ABSTRACT. For bounded potentials which behave like \(-cx^{-\gamma}\) at
infinity we investigate whether discrete eigenvalues of the radial
Dirac operator $H_{\kappa}$ accumulate at +1 or not. It is well
known that $\gamma=2$ is the critical exponent. We show that
\(c=1/8+\kappa(\kappa+1)/2\) is the critical coupling constant in
the case $\gamma=2$. 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.