Fluctuations of atomic energy levels due to axion dark matter

The amplitude of the pseudoscalar (axion) or scalar field fluctuates on a time scale of order of million field oscillation periods which is a typical coherence time in the virialized axion galactic dark matter halo model. This causes fluctuations of frequencies of atomic clocks on the same time scale. We show that this effect may be employed to search for the axion and scalar field dark matter with atomic and nuclear clocks. We re-purpose the results of the atomic clocks experiments comparing the variations of frequencies of hyperfine transitions in Rb and Cs atoms as well as in hydrogen atom vs cavity frequency fluctuations, and extract new limits on the axion coupling constant $f_a$ for masses in the range $2\times 10^{-17}\text{ eV}\lesssim m \lesssim 10^{-13}\text{ eV}$. We also show that similar energy shifts arise in the second-order perturbation theory with linear in the pseudoscalar field interaction. These shifts may be potentially measured with nuclear clocks based on the low-energy transition in $^{229}$Th nucleus. We propose a procedure which could, in principle, help determine the axion mass if the axion dark matter signal is present in experimental data sets.Comment: New section about difference between axion signal and white nois

A multishell solution in the Skyrme model

We consider multishell configurations in the Skyrme model within the rational map ansatz. We show that equations for the Skyrme field are linearized in the limit of large number of shells, thus allowing for a simple analytic solution. Although this solution is approximate, it provides an accurate description of multishell configurations in the Skyrme model in the region where the Skyrme field is large, $F\gg1$. We use this solution to calculate the mass and the root mean square radius of multishell skyrmion configurations. In particular, for solutions with one unit of baryon charge per shell (the ``hedgehog'' solution) the mass scales as $M\propto B^2$, and its rms radius scales as $B^{1/2}$ with the baryon charge $B$. This scaling for the mass can be reduced to $M\propto B^{4/3}$ in the model with many units of baryon charge per shell. Although this solution is unstable against decays into single-shell or single-skyrmion configurations, it may be useful for modelling skyrmion stars or compact composite objects in some models of dark matter if the decay of such configurations is prevented by some mechanism.Comment: 5 pages, 1 figur