Single-Particle Density of States for the Aharonov-Bohm Potential and Instability of Matter with Anomalous Magnetic Moment in 2+1 Dimensions

الأصل · EN

In the nonrelativistic case we find that whenever the relation mc²/e² <X(,gₘ) is satisfied, where is a flux in the units of the flux quantum, gₘ is magnetic moment, and X(,gₘ) is some function that is nonzero only for gₘ>2 (note that gₘ=2.00232 for the electron), then the matter is unstable against formation of the flux. The result persists down to gₘ=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 gₘ>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