Sensitivity of transitions in internal rotor molecules to a possible variation of the proton-to-electron mass ratio

Abstract

Recently, methanol was identified as a sensitive target system to probe variations of the proton-to-electron mass ratio μ [Jansen et al., Phys. Rev. Lett. 106, 100801 (2011)]. The high sensitivity of methanol originates from the interplay between overall rotation and hindered internal rotation of the molecule; that is, transitions that convert internal rotation energy into overall rotation energy, or vice versa, have an enhanced sensitivity coefficient, K μ . As internal rotation is a common phenomenon in polyatomic molecules, it is likely that other molecules display similar or even larger effects. In this paper we generalize the concepts that form the foundation of the high sensitivity in methanol and use this to construct an approximate model which makes it possible to estimate the sensitivities of transitions in internal rotor molecules with C 3v symmetry, without performing a full calculation of energy levels. We find that a reliable estimate of transition sensitivities can be obtained from the three rotational constants (A, B, and C) and three torsional constants (F , V 3 , and ρ). This model is verified by comparing obtained sensitivities for methanol, acetaldehyde, acetamide, methyl formate, and acetic acid with a full analysis of the molecular Hamiltonian. Of the molecules considered, methanol is by far the most suitable candidate for laboratory and cosmological tests searching for a possible variation of μ.

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

“…It was shown by Jansen et al 37,93 that a pure torsional transition in methanol has a sensitivity coefficient of K μ = −2.5. However, pure torsional transitions are forbidden, since they possess a different torsional symmetry.…”

“…Higher order parameters pose a problem since their physical interpretation is not always clear. Jansen et al 37,93 derived the scaling relations for these higher-order constants by considering them as effective products of lower-order torsional and rotational operators. Ilyushin et al 94 showed that the scaling of the higher order constants only contributes marginally to the sensitivity coefficient of a transition.…”

“…93 The dimensionless parameter s = 4V 3 /9F , with V 3 the height of the barrier, is a measure of the effective potential. The sensitivity of a pure torsional transition is given by…”

“…Jansen et al 37,93 employed the state-of-the art effective Hamiltonian that is implemented in the BELGI code 95 together with a set of 119 molecular parameters. 96,97 Similar calculations were performed by Levshakov et al 91 The large number of both positive and negative sensitivity coefficients makes methanol a preferred target system for probing a possible variation of μ, since this makes it possible to test variation of μ using transitions in a single molecular species, thereby avoiding the many systematic effects that plague tests that are based on comparing transitions in different molecules.…”

Sensitivity to a possible variation of the proton-to-electron mass ratio of torsion-wagging-rotation transitions in methylamine CH3NH2

“…Kozlov et al [1] showed that transitions that convert rotational motion into inversion motion, and vice versa, in the different isotopologues of hydronium (H 3 O + ) have K μ coefficients ranging from −219 to +11 [2]. Similarly, Jansen et al [3,4] and Levshakov et al [5] showed that transitions that convert internal rotation into overall rotation in the different isotopologues of methanol have K μ coefficients ranging from −88 to +330. Here, the sensitivity coefficient K μ is defined by…”