Hyperfine-Induced Lifting of Parity Degeneracy in Noninverting Molecules

Abstract

We report experimental evidence for the splitting of E levels in 28 SiF 4 , which are degenerate in parity as far as the rovibrational Hamiltonian solely is concerned. The parity degeneracy of rovibrational levels is in fact lifted by hyperfine interactions, even though the associated total spin is I 0. We compare this situation with that in other molecules (SF 6 and PH 3 ) for which similar effects have already been reported. We also predict the splitting of the P͑7͒ E 0 ͑6͒ line of 12 CH 4 , a resonance used currently as a frequency standard, assumed up to now to be perfectly degenerate. [S0031-9007(96)00392-4] PACS numbers: 33.20. Ea, 33.25.+k Inversion of all space coordinates of every particle belonging to a given physical system is a relevant symmetry as long as weak interactions are not taken into account. Two stationary states completely identical, but for parity, in a semirigid (i.e., noninverting) molecule, should be perfectly degenerate. Such parity degenerate molecular states thus represent excellent candidates to detect a parity violating interaction, which should result in their splitting.We have observed such a splitting of parity degenerate E states of the molecule 28 SiF 4 . Although the total spin of the fluorines is zero, we show that hyperfine couplings with neighboring states are responsible for this splitting. A similar lifting of parity degeneracy has already been observed in the spectrum of SF 6 and PH 3 . We analyze in detail the different mechanisms involved. We point out that, in all cases, the Pauli principle forbids the existence of identical states but for parity in such molecules, and, thus, any degeneracy may be removed by mechanisms different from inversion and weak interactions.Extensive saturation spectra of the n 3 vibration-rotation band of 28 SiF 4 have been recorded in our laboratory with our ultrahigh resolution saturation spectrometer [1][2][3][4][5]. The current linewidth for these spectra was 1.5 kHz. We have used various isotopic species of CO 2 and a microwave electrooptic modulation technique [5] in order to increase the spectral coverage. In previous studies of SiF 4 [6], the hyperfine structure of the lines could not be resolved. Figures 1 and 2 display, respectively, the hyperfine structures of the R͑34͒F 0 1͑2͒ E 0 F 0 1͑1͒ and P͑22͒A 1 2͑1͒ F 5 1͑2͒ E 3 superfine clusters. It is well known that the Pauli principle limits drastically the number of existing states: The F 1 and A 2 rovibrational states are associated with total nuclear spins I respectively equal to 1 and 2 and give rise to partly resolved triplets and quintuplets in these spectra; moreover, only one of the two parity states is allowed. On the other hand, E states are associated with I 0 and may have both parities [7,8]. The observed splitting of the E lines correspond necessarily to the two parity labels. As we shall see, this degeneracy removal is related to the neighbor hyperfine states (with a symmetric neighborhood for Fig. 1 and an asymmetric one for Fig. 2). For isolated E lines no such ...

The Pauli principle and ultrahigh resolution spectroscopy of polyatomic molecules

“…The Pauli principle has important consequences on the hyperfine spectra of these molecules, which we have observed in the course of many studies. We have also emphasized on several examples that there was a strong link between these consequences and parity [26] and we have shown two spectacular examples where this link leads to a parity doubling in PH% [20] and SiF± [18] .…”

“…A simpler experiment is presently underway which can be performed with very high signal-to-noise and will be presented in the next section. Let us mention another important consequence of the Pauli principle in such spectra and discussed in detail in references [13,18,20,26]. Some lines are parity doublets while others are parity singlets, but states, which differ by their overall parity, differ also by some other part of their wave function, either through their rotational or through their nuclear spin wave functions.…”

“…Hilborn in this book and references therein). Thanks to modern techniques of ultra-high resolution spectroscopy (saturation spectroscopy, twophoton spectroscopy) it is now possible to resolve individual hyperfine components of vibration-rotation lines of molecules having three or more identical nuclei with a high degree of symmetry: spherical tops such as SFQ [8][9][10][11][12][13][14], OsO^ [9,12,[15][16][17], SiF± [18], symmetric tops such as NH 3 [12,19], PH 3 [20], PF 5 [12]...…”

Limit on the Parity Nonconserving Energy Difference between the Enantiomers of a Chiral Molecule by Laser Spectroscopy

“…It can provide a spectral purity of 6 Hz and a long-term stability of 0.1 Hz over 100 s with an OsO 4 saturation resonance in the 10 mm spectral region. This performance is degraded by a factor of 10 reference and the reduction of the finesse of our cavity at that wavelength. However, the residual drift of the laser frequency has no impact on the sensitivity of the test.…”

“…Theoretical background.-For nonchiral polyatomic molecules we have shown, experimentally and theoretically [8][9][10], that one of the two states, which differ only by their parity, does not exist because of the Pauli principle applied to identical nuclei. Thus, no strict parity degeneracy can occur even if inversion and parity violation are neglected.…”