Parity Violating Energy Shifts in Atoms, I

Abstract

We present a study of parity (P) violating contributions to the eigenenergies of stationary systems containing atoms in spatially inhomogeneous external electric fields. In this context the subtle interplay of P-violation and time reversal (T) invariance plays an important role. If the entire field configuration is chosen to exhibit chirality the energies are in general shifted by pseudoscalar contributions which change sign under a planar reflection of the field. In part I we consider sudden variations of the fields and calculate P-violating energy shifts using perturbation theory. In part II the adiabatic case will be treated and the connection to geometrical (Berry-) phases will be elucidated. To calculate the effects we use the standard model of elementary particle physics where the P-odd interaction arises through the exchange of Z-bosons between the quarks in the nucleus and the atomic electrons. We consider in detail hydrogen-like systems in unstable levels of principal quantum number n = 2. We study atoms with vanishing nuclear spin like $$_{1}^{1}{\rm He}^{+}$$ and with nuclear spin I = 1/2 like $$_{1}^{1}{\rm H}$$ . The nominal order of P-violating effects is 10−5...10−9 Hz which is determined by the mixing of the 2S1/2 and 2P1/2 states. However we point out that with certain configurations of the external fields, it is possible to enhance the P-violating energy shifts dramatically! Instead of energy shifts linear in the P-violation parameters we get then shifts proportional to the square root of these parameters. Numerically we find such energy shifts which only appear for unstable states to be of order 10−5...1 Hz. Under a reversal of the handedness of the external field configuration these P-violating shifts get multiplied by a phase factor i, i.e. the shifts in the real and imaginary part of the complex eigenenergies are exchanged. Application of our technique to hydrogen-like atoms with a nucleus of spin I = 1/2 yields P-violating energy shifts which are very sensitive to the nuclear spin dependent P-odd force, which receives a rather large contribution from the polarized strange quark density in polarized nuclei. Thus, a measurement of these energy shifts could provide an important tool to elucidate nuclear properties connected to the so called “spin crisis”. We also present a method for treating degenerate perturbation theory which combines advantages of both, Kato’s and Bloch’s methods.