Search for variation of fundamental constants and violations of fundamental symmetries using isotope comparisons

Abstract

Atomic microwave clocks based on hyperfine transitions, such as the caesium standard, tick with a frequency that is proportional to the magnetic moment of the nucleus. This magnetic moment varies strongly between isotopes of the same atom, while all atomic electron parameters remain the same. Therefore the comparison of two microwave clocks based on different isotopes of the same atom can be used to constrain variation of fundamental constants. In this paper, we calculate the neutron and proton contributions to the nuclear magnetic moments, as well as their sensitivity to any potential quark-mass variation, in a number of isotopes of experimental interest including 201,199 Hg and 87,85 Rb, where experiments are underway. We also include a brief treatment of the dependence of the hyperfine transitions to variation in nuclear radius, which in turn is proportional to any change in quark mass. Our calculations of expectation values of proton and neutron spin in nuclei are also needed to interpret measurements of violations of fundamental symmetries.

Perspective: Tipping the scales: Search for drifting constants from molecular spectra

“…Crosses, also shown in the figure, indicate sensitivity coefficients that were calculated using a full molecular Hamiltonian. 63 From the figure, it can be seen that resonances occur near A/B ∼ 25 which is close to the A/B values for the 12 13 C 16 O have a sensitivity that is almost 500 times that of a pure rotational transition. An experiment to measure these transitions in a double-resonance molecular beam machine using a two-photon microwave absorption is currently under construction in our laboratory.…”

“…While electronic transitions, including spinorbit interactions, are sensitive to α, vibrational, rotational, and tunneling modes in molecules are sensitive to μ. Hyperfine effects, such as in the Cs-atomic clock 12,13 and the 21-cm line of atomic hydrogen, 14 depend on both α and μ, as do -doublet transitions in molecules. 15 The same holds for combined high-redshift observations of a rotational transition in CO and a fine structure transition in atomic carbon, 16 placing a tight constraint on the variation of the combination α 2 μ at a redshift as high as z = 5.2.…”

Particle-hole configuration interaction and many-body perturbation theory: Application toHg+

“…Here all shells are closed, but in general we can sometimes obtain better starting orbitals by including a partially-filled closed shell as was done in previous works, e.g. [6,23]. However, we must then include MBPT subtraction diagrams (see Section III).…”

“…Indeed, one of the purposes of this work is to avoid the large subtraction diagrams in Σ (1) that are partially cancelled by terms in Σ (2) (see [6] for details). Subtraction diagrams are not present in the particle-hole calculation since in that caseĥ CI =ĥ DF and there are no off-diagonal matrix elements of (6) (at least until MBPT corrections are included).…”

“…Since then it has been remarkably successful in treating a wide variety of two and threevalence-electron atoms and ions, and even some with four (e.g. [2][3][4][5]) and five valence electrons (Cr II [6]). Generally, as the number of valence electrons increases the method becomes less effective and one must revert to usual CI and estimate the core-valence correlations some other way (see, e.g.…”