Alexander MOROZ
SINGLE-PARTICLE DENSITY OF STATES FOR THE AHARONOV-BOHM POTENTIAL
AND INSTABILITY OF MATTER WITH ANOMALOUS MAGNETIC MOMENT IN 2+1
DIMENSIONS
(25K, latex)
ABSTRACT. In the nonrelativistic case we find that whenever the relation
$mc^2/e^2 2$ (note that $g_m=2.00232$ for the electron),
then the matter is unstable against formation of the flux $\al$.
The result persists down to $g_m=2$ provided the Aharonov-Bohm
potential is supplemented with a short range attractive potential.
We also show that whenever a bound state is present in the spectrum it
is always accompanied by a resonance with the energy proportional to
the absolute value of the binding energy.
In the relativistic case the instability along with
the resonance disappear as long as the minimal coupling is
considered. For the Klein-Gordon equation with the Pauli coupling
which exists in (2+1) dimensions without any reference to a spin
the matter is again unstable for $g_m>2$.
The results are obtained by calculating the change of the density of states
induced by the Aharonov-Bohm potential. The Krein-Friedel formula for this
long-ranged potential is shown to be valid when supplemented with zeta
function regularization.
PACS : 03.65.Bz, 03-70.+k, 03-80.+r, 05.30.Fk