Relativistic decay of atomic states. Energy approach. Allowance for angular symmetry

M. N. Driker, Л. Н. Иванов

Takaharu Otsuka, Yusuke Tsunoda

An isolated quantum system generally exhibits rotational symmetry, i.e., conserved spin (angular momentum) in its eigenstates. Non-spherical quantum objects such as many of molecules and atomic nuclei are not exceptions. However, these objects are not rotationally invariant by definition. Such an object therefore restores, as a consequence of the action of Hamiltonian, the rotational symmetry by superposing states of the same object orienting in different directions, where each component represents one direction. We show the time evolution of an individual component of this superposition: this component remains almost unchanged for finite time, called standing time. This implies that if the object is found to be in this component, it basically remains so for the standing time. This feature is shown to be relevant in a variety of cases, such as atomic nuclei, polymers (proteins), and electron drops in atoms. The shapes of many nuclei are ellipsoids with variations. The "viewing" of the ellipsoidal shape is not straightforward, because this ellipsoid is not at rest. A "snapshot" of a nucleus is highly desired as a direct information. Recent experimental approaches with Relativistic Heavy-ion Collision (RHC) are promising for taking such a snapshot. The present work depicts that the standing time, some 10^{-23} sec for typical ellipsoidal nuclei, is much longer than the time scale of RHC, some 10^{-25} sec. This implies that an ellipsoidal nucleus remains practically unchanged for this critical period. As the standing time will be intimately related, through a relation like the energy-time uncertainty relation, to the energy scales involved, we can also explore this concept and its applications in a variety of physical cases such as fusion (tunneling process), fission, alpha-decay/emission, polymers and electron drop in atom.

Spencer R. Klein

Ultra-peripheral collisions (UPCs) involving relativistic heavy ions are a unique laboratory to study quantum correlations. The intense electromagnetic fields generate high rates of photonuclear interactions, including events involving multiple photon exchange. Multiple photon exchange can result in the production of multiple vector mesons and/or nuclear excitations. These interactions share a common impact parameter, so the photons have the same linear polarization. The shared polarization entangles the particles, leading to unique quantum correlations. The decays of these vector excitations are sensitive to this polarization, allowing for the study of these correlations. This letter will compare classical and quantum calculations of the correlations between these azimuthal directions. The two approaches predict vert different angular correlations. The differences are akin to those seen with polarized photons in tests of Bells inequality. Uniquely, UPC photoproduction can produce final states containing three or more particles, all entangled with the same polarization. These more complex states exhibit additional unique phenomenology, allowing new tests of multi-particle entanglement.

JOSIP SEKE

Л. Н. Иванов

F. Fratini

The angular and polarization properties of the photon pair emitted in the two--photon decay of $2s$ hyperfine states in hydrogenlike ions are investigated within the relativistic Dirac framework and second order perturbation theory. The studied transitions are $2s_{1/2}\,(F=1,0)\to1s_{1/2}\,(F=1,0)$ in Hydrogen atom and $2s_{1/2}\,(F=4,3)\to1s_{1/2}\,(F=4,3)$ in hydrogenlike Uranium ion. Two different emission patterns are found: For non-spin-flip transitions, the angular correlation ($i.e.$ the angular distribution of the emitted photons) is of the type $\sim 1+\cos^2θ$, while the linear polarizations of the emitted photons are approximately parallel one another; For spin-flip transitions, the angular correlation is of the type $\sim 1-1/3\cos^2θ$, while the linear polarizations of the emitted photons are approximately orthogonal one another.