Static electric dipole moments of nondegenerate systems probe mass scales for physics beyond the Standard Model well beyond those reached directly at high energy colliders. Discrimination between different physics models, however, requires complementary searches in atomic-molecular-and-optical, nuclear and particle physics. In this report, we discuss the current status and prospects in the near future for a compelling suite of such experiments, along with developments needed in the encompassing theoretical framework.

Generalized relativistic pseudopotentials (GRPP) of atomic cores implying the use of different potentials for atomic electronic shells with different principal quantum numbers give rise to accurate and reliable relativistic electronic structure models of atoms, molecules, clusters, and solids. These models readily incorporate the effects of Breit electron-electron interactions and one-loop quantum electrodynamics effects. Here we report the computational procedure for evaluating one-electron integrals of GRPP over contracted Gaussian functions. This procedure was implemented in a library of routines named LIBGRPP, which can be integrated into existing quantum chemistry software, thus enabling the application of various methods to solve the many-electron problem with GRPPs. Pilot applications to electronic transitions in the ThO and UO2 molecules using the new library and intermediate-Hamiltonian Fock space relativistic coupled cluster method are presented. The results clearly demonstrate that rather economical tiny-core GRPP models can exceed in accuracy relativistic all-electron models defined by Dirac-Coulomb and Dirac-Coulomb-Gaunt Hamiltonians.

Relativistic study of xenotime, YPO4, containing atoms thorium and uranium as point defects is performed in the framework of cluster model with using the compound-tunable embedding potential (CTEP) method proposed by us recently [1]. The Y-(PO4)6-Y'22-O'104 cluster for xenotime is considered, in which central part, [Y-(PO4)6] −15 , is the main cluster, whereas outermost 22 atoms of yttrium and 104 atoms of oxygen are treated as its environment and compose electron-free CTEP with the total charge of +15. The P and O atoms of the orthophosphate groups nearest to the central Y atom are treated at all-electron level. The central Y, its substitutes, Th and U, together with environmental Y atoms are described within different versions of the generalized relativistic pseudopotential method [2]. Correctness of our cluster and CTEP models, constructed in the paper, is justified by comparing the Y-O and P-O bond lengths with corresponding periodic structure values of the YPO4 crystal, both experimental and theoretical.Using this cluster model, chemical properties of solitary point defects, X = U, Th, in xenotime are analyzed. It has been shown that the oxidation state +3 is energetically more profitable than +4 not only for thorium but for uranium as well (∆E ≈ 5 eV) despite the notably higher ionic radius of U +3 compared to Y +3 , whereas ionic radii of U +4 and Y +3 are close. This leads to notable local deformation of crystal geometry around the U +3 impurity in xenotime and contradicts to widespread opinion about favorite oxidation state of uranium in such kind of minerals [3].

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Molecules containing short-lived, radioactive nuclei are uniquely positioned to enable a wide range of scientific discoveries in the areas of fundamental symmetries, astrophysics, nuclear structure, and chemistry. Recent advances in the ability to create, cool, and control complex molecules down to the quantum level, along with recent and upcoming advances in radioactive species production at several facilities around the world, create a compelling opportunity to coordinate and combine these efforts to bring precision measurement and control to molecules containing extreme nuclei. In this manuscript, we review the scientific case for studying radioactive molecules, discuss recent atomic, molecular, nuclear, astrophysical, and chemical advances which provide the foundation for their study, describe the facilities where these species are and will be produced, and provide an outlook for the future of this nascent field.