arXiv : Cool molecular highly charged ions for precision tests of fundamental physics

Zülch, Carsten; Garcia Ruiz, Ronald F.; Giesen, Steffen M.; Berger, Robert; Gaul, Konstantin

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Preprint
Report number	arXiv:2203.10333
Title	Cool molecular highly charged ions for precision tests of fundamental physics
Author(s)	Zülch, Carsten (Philipps U. Marburg) ; Gaul, Konstantin (Philipps U. Marburg) ; Giesen, Steffen M. (Philipps U. Marburg) ; Garcia Ruiz, Ronald F. (MIT ; CERN) ; Berger, Robert (Philipps U. Marburg ; CERN)
Imprint	2022-03-19
Number of pages	18
Note	18 pages, 3 figures, 6 tables
Subject category	physics.comp-ph ; Other Fields of Physics ; physics.atom-ph ; Other Fields of Physics ; physics.chem-ph ; Chemical Physics and Chemistry
Abstract	Molecules and atomic highly charged ions provide powerful low-energy probes of the fundamental laws of physics: Polar molecules possess internal fields suitable to enhance fundamental symmetry violation by several orders of magnitudes, whereas atoms in high charge states can feature large relativistic effects and compressed level structures, ideally posed for high sensitivity to variations of fundamental constants. Polar, highly charged molecules could benefit from both: large internal fields and large relativistic effects. However, a high charge dramatically weakens chemical bonding and drives systems to the edge of Coulomb explosion. Herein, we propose multiply-charged polar molecules, that contain actinides, as promising candidates for precision tests of physics beyond the standard model. Explicitly, we predict PaF$^{3+}$ to be thermodynamically stable, coolable and well-suited for precision spectroscopy. The proposed class of compounds, especially with short-lived actinide isotopes from the territory of pear-shaped nuclei, has potential to advance our understanding of molecules under extreme conditions, to provide a window into unknown properties of atomic nuclei, and to boost developments in molecular precision spectroscopy in various areas, such as optical clocks and searches for new physics.
Other source	Inspire
Copyright/License	preprint: (License: CC BY-NC-ND 4.0)

$Schematics of a search for $P,T$-violation in the quark-sector with the stable highly charged molecule \ce{PaF^3+}. (\textbf{A}) Sketch of an experimental set-up for precision spectroscopy with \ce{PaF^3+}. A decelerated beam of \ce{PaF^3+} is trapped in a Paul trap, sympathetically cooled by \ce{Sr+} ions and probed by the dark red laser. Further lasers for a potential direct cooling of the molecular ion \ce{PaF^3+} are omitted for clarity. (\textbf{B}) Sketch of dissociation channels of \ce{PaF^3+} (solid lines) and \ce{PaF^4+} (dashed lines) as diabatic potentials. Ground state electronic potentials of \ce{PaF^3+} and \ce{PaF^4+} are shown as a spline interpolation of points computed at the level of ZORA-cGKS-PBE0, indicated as circles (molecular calculations) and crosses (separate atomic calculations). Potential curves for the repulsive channels \ce{Pa^2+} $+$ \ce{F+} and \ce{Pa^3+} $+$ \ce{F+} as well as the attractive channel \ce{Pa^4+} $+$ \ce{F-} are represented with the model described in the methods section. Total electronic densities and Mulliken partial charges computed at the level of ZORA-cGKS-PBE0 are shown for the electronic ground states. (\textbf{C}) The parameters of the $P,T$-odd spin-rotational Hamiltonian of \ce{PaF^3+} at the level of ZORA-cGHF relative to those of RaF computed in Ref.~\cite{gaul:2020} scaled by $6/1.16$ (for details see the methods section).$ $Potential energy curves for the eight energetically lowest electronic states relative to the ground state of \ce{PaF^3+} computed at the level of DC-FSCCSD/ANO-RCC. Lines between the points are shown to guide the eye. The two lowest dissociation channels \ce{Pa^2+} $+$ \ce{F+} and \ce{Pa^3+} $+$ \ce{F}, as computed on a highler level of theory (RECP-UCCSD(T)-SOC), are indicated by black horizontal lines. The various electronic states are additionally characterized by the complex two-component ZORA-cGHF spinor $\psi=(\psi_\uparrow,\psi_\downarrow)$ of the unpaired electron and compared to the upper component of the analytic solution of the Dirac equation for the hydrogen atom. Atomic hydrogen spinors are labelled as $\ell_{j,m_j}$, where $\ell$ is the symbol for the electronic orbital angular momentum quantum number, $j$ is the total electronic angular momentum quantum number and $m_j$ is the magnetic total electronic angular momentum quantum number.$ $Visualization of enhancement of $P,T$-violation in the quark-sector within the PMHCI \ce{PaF^3+} compared to isoelectronic RaF, illustrated by example of the nuclear Schiff moment. This moment would induce an energy shift propotional to $\mathcal{S}W_\mathcal{S}\mathcal{I}$ (see text). (\textbf{A}) Enhancement as per the electronic structure parameter $W_\mathcal{S}$ is shown. Non-vanishing $W_\mathcal{S}$ stems from a shift of the maximum electron density away from the nuclear center by polarization, which in good approximation is characterized by the slope of the four-component (4c) electron density (indicated by a line in the plots in the middle) at the position of the Pa or Ra nucleus. Contributions from the SOMO, the highest doubly occupied orbital (SOMO--1) and uncompensated contributions from core electrons are shown. Approximate 4c electron densities computed at the ZORA-cGHF level are plotted with contour value of $0.035^2~a_0^{-3}$, with lower component density contributions (right isodensities) being magnified by $\alpha^{-2}$ to enhance visibility as compared to the upper component (left isodensities). In each isodensity plot, the heavy nucleus (Pa, Ra) is located on the left, the fluorine nucleus on the right as indicated by the ball-and-stick structures. (\textbf{B}) Visualization of the strong enhancement of a collective Schiff moment $\mathcal{S}$ in octupole deformed nuclei. Large octupole deformations accumulate in the highlighted region of the nuclide chart. Nuclear charge densities with deformation of order $n$ and corresponding angular densities of the Schiff operator are modeled in spherical plots (for details on how this is realized see the methods section). The resulting collective Schiff moments $\mathcal{S}$ are indicated by a vector of length $\mathcal{S}$ along the deformation axis in the intrinsic frame. The precession of the intrinsic moment around the $z$-axis is also indicated.$ Show more plots

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ჩანაწერი შექმნილია 2022-04-06, ბოლოს შესწორებულია 2024-09-18

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