Multipolar Graviton in the Hydrogen Atoms

Abstract

We derive multipolar gravitational radiation in the framework of quantum field theory in which the atomic states are treated nonrelativistically, and the gravitational waves are quantized. By relaxing the constraint e^ik·x ≈ 1, the multipolar transition rate is calculated when one graviton is emitted. As a consistency check, we recover the semiclassical result in the dipole approximation regime. Besides, we show that the dynamical mechanism that gives rise to spontaneous graviton emission by an atom, has a profound consequence on the lifetime of the atomic electron.