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Register a new userApproaching meV level for transition energies in the radium monofluoride molecule RaF and radium cation Ra$^+$ by including quantum-electrodynamics effects
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Authors
Leonid V. Skripnikov
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Highly accurate theoretical predictions of transition energies in the radium monofluoride molecule, $^{226}$RaF and radium cation, $^{226}$Ra$^+$, are reported. The considered transition $X~^2Sigma_{1/2} to A~^2Pi_{1/2}$ in RaF is one of the main features of this molecule and can be used to laser cool RaF for subsequent measurement of the electron electric dipole moment. For molecular and atomic predictions we go beyond the Dirac-Coulomb Hamiltonian and treat high-order electron correlation effects within the coupled cluster theory with the inclusion of quadruple and ever higher amplitudes. Effects of quantum electrodynamics (QED) are included non-perturbatively using the model QED operator that is implemented now for molecules. It is shown that the inclusion of QED effects in molecular and atomic calculations is a key ingredient in resolving the discrepancy between the theoretical values obtained within the Dirac-Coulomb-Breit Hamiltonian and the experiment. The remaining deviation from the experimental values is within a few meV. This is more than an order of magnitude better than the chemical accuracy, 1 kcal/mol=43 meV, that is usually considered as a guiding thread in theoretical molecular physics.
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The diatomic molecule radium monofluoride (RaF) has recently been proposed as a versatile probe for physics beyond the current standard model. Herein, a route towards production of a RaF molecular beam via radium ions is proposed. It takes advantage of the special electronic structure expected for group 2 halides and group 2 hydrides: The electronic ground state of neutral RaF and its monocation differ in occupation of a non-bonding orbital of $sigma$ symmetry. This implies similar equilibrium distances and harmonic vibrational wavenumbers in the two charge states and thus favourable Franck--Condon factors for neutralisation without dissociation in neutralising collisions. According to the calculated ionisation energy of RaF, charge exchange collisions of RaF$^+$ with sodium atoms are almost iso-enthalpic, resulting in large cross-sections for the production of neutral radium monofluoride.
Energy levels, wavelengths, lifetimes and hyperfine structure constants for the isotopes of the first and second spectra of radium, Ra I and Ra II have been compiled. Wavelengths and wave numbers are tabulated for 226Ra and for other Ra isotopes. Isotope shifts and hyperfine structure constants of even and odd-A isotopes of neutral radium atom and singly ionized radium are included. Experimental lifetimes of the states for both neutral and ionic Ra are also added, where available. The information is beneficial for present and future experiments aimed at different physics motivations using neutral Ra and singly ionized Ra.
Isotope shifts of $^{223-226,228}$Ra$^{19}$F were measured for different vibrational levels in the electronic transition $A^{2}{}{Pi}_{1/2}leftarrow X^{2}{}{Sigma}^{+}$. The observed isotope shifts demonstrate the particularly high sensitivity of radium monofluoride to nuclear size effects, offering a stringent test of models describing the electronic density within the radium nucleus. Ab initio quantum chemical calculations are in excellent agreement with experimental observations. These results highlight some of the unique opportunities that short-lived molecules could offer in nuclear structure and in fundamental symmetry studies.
There is sparse direct experimental evidence that atomic nuclei can exhibit stable pear shapes arising from strong octupole correlations. In order to investigate the nature of octupole collectivity in radium isotopes, electric octupole ($E3$) matrix elements have been determined for transitions in $^{222,228}$Ra nuclei using the method of sub-barrier, multi-step Coulomb excitation. Beams of the radioactive radium isotopes were provided by the HIE-ISOLDE facility at CERN. The observed pattern of $E$3 matrix elements for different nuclear transitions is explained by describing $^{222}$Ra as pear-shaped with stable octupole deformation, while $^{228}$Ra behaves like an octupole vibrator.
Parity (P) and time (T) invariance violating effects in the Ra atom are strongly enhanced due to close states of opposite parity, the large nuclear charge Z and the collective nature of P,T-odd nuclear moments. We have performed calculations of the atomic electric dipole moments (EDM) produced by the electron EDM and the nuclear magnetic quadrupole and Schiff moments. We have also calculated the effects of parity non-conservation produced by the nuclear anapole moment and the weak charge. Our results show that as a rule the values of these effects are much larger than those considered so far in other atoms (enhancement is up to 10^5 times).
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