  In the nonrelativistic case we find that whenever the relation $mc^2/e^2
<X(\al,g_m)$ is satisfied, where $\al$ is a flux in the units of the flux
quantum, $g_m$ is magnetic moment, and $X(\al,g_m)$ is some function that is
nonzero only for $g_m>2$ (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. 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
