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Nuclear Schiff Moments and CP Violation

This article reviews the calculation of nuclear Schiff moments, which one must know in order to interpret experiments that search for time-reversal-violating electric dipole moments in certain atoms and molecules. After briefly reviewing the connection between dipole moments and CP violation in and beyond the Standard Model of particle physics; Schiff's theorem, which concerns the screening of nuclear electric dipole moments by electrons; Schiff moments; and experiments to measure dipole moments in atoms and molecules, this review examines attempts to compute Schiff moments in nuclei such as 199 Hg and octupole-deformed isotopes such as 225 Ra, which are particularly useful in experiments. It then turns to ab initio nuclear-structure theory, describing ways in which both the in-medium similarity renormalization group and coupled-cluster theory can be used to compute important Schiff moments more accurately than the less controlled methods that have been applied so far.

CP violation↗

Schiff Moment of 129 Xe and 199 Hg [Slides]

Using Chicoma in 2025, we advanced DFT-based calculations needed to connect fundamental T violating interactions to measurable Schiff moments in heavy nuclei. We implemented DFT for polarized odd nuclear systems, a first step toward treating the time-reversal-breaking mean fields required for Schiff moment calculations. As a validation test, we computed polarizabilities using a perturbation with the dipole operator (see figure to the right) for the odd systems shown in Table 1; while no odd-system effect is expected for polarizabilities, this capability is essential for Schiff moments. Initial mean-field solutions for 129 Xe Schiff moment calculations were also generated.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

New Platinum Complexes from Salen- and Hydroxy-Substituted Salpn-Naphthalene Ligands with CO 2 Reduction Activity

The electrocatalytic reduction of carbon dioxide (CO 2 ) into added-value products is a promising alternative to completing the cycle of atmospheric CO 2 . We report two new platinum complexes—a salen-like naphthalene (PtL1) and a hydroxy-substituted salpn naphthalene (PtL2)—that are capable of activating CO 2 to produce carbon monoxide (CO). The predominant keto tautomer of the non-innocent ligands was determined using DFT calculations and UV-Vis spectroscopy. The PtL2 complex has a CO Faradaic efficiency >40% in the presence of water as a sacrificial proton source at -2.5 V vs. Fc/Fc + . The addition of the hydroxy group in combination with water as a proton source decreased the reduction potential and increased the CO formation tenfold when compared to PtL1.

30 DIRECT ENERGY CONVERSION↗

Measurement of the angle between jet axes in Pb-Pb collisions at $\sqrt{s_{NN}}$ =5.02 TeV

This paper presents the first measurement of the angle between different jet axes (denoted as Δ⁢𝑅 axis ) in Pb-Pb collisions. The measurement is carried out in the 0–10 % most-central events at $\sqrt{s_{NN}}$ = 5.02 TeV. Jets are assembled by clustering charged particles at midrapidity using the anti-𝑘 T algorithm with resolution parameters 𝑅 = 0.2 and 0.4 and transverse momenta in the intervals 40 < 𝑝$^{ch jet}_{T}$ < 140 GeV/𝑐 and 80 < 𝑝$^{ch jet}_{T}$ < 140 GeV/𝑐, respectively. Measurements at these low transverse momenta enhance the sensitivity to quark-gluon plasma (QGP) effects. A comparison to models implementing various mechanisms of jet energy loss in the QGP suggests that the observed narrowing of the Pb-Pb distribution relative to 𝑝𝑝 can be explained if quark-initiated jets are more likely to emerge from the medium than gluon-initiated jets. These new measurements disfavor intrajet 𝑝 T broadening as implemented in a simple model calculation with the Baier-Dokshitzer-Mueller-Peigne-Schiff formalism for energy loss in the QGP. The comparison of Pb-Pb and 𝑝𝑝 collisions shows sensitivity to the angular scale at which the QGP can resolve two independent splittings, favoring mechanisms that incorporate incoherent energy loss.

Acharya, S. [LPC] (ORCID:0000000292135329)↗

Effective electric field: Quantifying the sensitivity of searches for new -odd physics with EuCl 3 ∙ 6H 2 O

Laboratory-scale precision experiments are a promising approach to searching for physics beyond the standard model. Noncentrosymmetric solids offer favorable statistical sensitivity for efforts that search for new fields, whose interactions violate the discrete parity and time-reversal symmetries. One example is the cosmic axion spin precession experiment (CASPEr), which can be sensitive to the defining interaction of the quantum chromodynamics (QCD) axion dark matter with gluons in atomic nuclei. The effective electric field is the parameter that quantifies the sensitivity of such experiments to new physics. We describe the theoretical approach to calculating the effective electric field for noncentrosymmetric sites in ionic insulating solids. We consider the specific example of the crystal, which is a particularly promising material. The optimistic estimate of the effective electric field for the isotope in this crystal is . The calculation uncertainty is estimated to be two orders of magnitude, dominated by the evaluation of the europium nuclear Schiff moment.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Steric effects in light-induced solvent proton abstraction

The significance of solvent structural factors in the excited-state proton transfer (ESPT) reactions of Schiff bases with alcohols is reported here. In this work, we use the super photobase FR0-SB and a series of primary, secondary, and tertiary alcohol solvents to illustrate the steric issues associated with solvent to photobase proton transfer. Steady-state and time-resolved fluorescence data show that ESPT occurs readily for primary alcohols, with a probability proportional to the relative –OH concentration. For secondary alcohols, ESPT is greatly diminished, consistent with the barrier heights obtained using quantum chemistry calculations. ESPT is not observed in the tertiary alcohol. We explain ESPT using a model involving an intermediate hydrogen-bonded complex where the proton is “shared” by the Schiff base and the alcohol. The formation of this complex depends on the ability of the alcohol solvent to achieve spatial proximity to and alignment with the FR0-SB* imine lone pair stabilized by the solvent environment.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Co(salen)-Catalyzed Oxidation of Lignin Models to Form Benzoquinones and Benzaldehydes: A Computational and Experimental Study

Lignin is a highly abundant polyphenolic polymer that imparts mechanical strength to plant biomass. Transition-metal complexes can catalyze lignin oxidation to produce value-added products, but low catalytic efficiency has hampered their use in industry. Identifying the chemical and structural factors that govern catalytic activity is a prerequisite to rational design of catalysts with improved activity. In this study, we combine computational and experimental approaches to investigate the mechanism of Co(salen)-catalyzed oxidation of the monomeric lignin models syringyl (S), vanillyl (G), and 4-hydroxybenzyl alcohol (H) to produce benzoquinone and benzaldehyde products. Experimentally, S oxidation to form dimethoxybenzoquinone proceeded efficiently with a Co(salen) catalyst coordinated by a pyridine ligand, but G and H did not undergo oxidation. Density functional theory calculations reveal that catalyst regeneration is energetically unfavorable in the presence of H, which prevents oxidation. In contrast, S readily facilitates catalyst regeneration. Formation of methoxybenzoquinone from G was achieved experimentally by adding bulky, noncoordinating bases. These findings provide a fundamental baseline for enhancing the activity of Co-Schiff base catalysts toward lignin-like molecules by adding sterically hindered nitrogenous bases or potentially by including a cocatalyst that promotes catalyst regeneration.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Nuclear Structure Studies for Schiff Moment Enhancement

One of the major open questions in modern physics is the origin of the matter-antimatter asymmetry observed in the universe. While the Standard Model contains sources of charge-parity (CP) violation, they appear insufficient to explain the observed dominance of matter over antimatter. As a result, searches for additional sources of CP violation are an important area of contemporary nuclear and particle physics. Atomic electric dipole moments (EDMs) provide sensitive probes of CP-violating interactions. In heavy nuclei, the observable atomic EDM can be enhanced through the presence of a nuclear Schiff moment, which arises from CP-violating nuclear forces and nuclear structure effects. The review paper Nuclear Schiff Moments and CP Violation by Jonathan Engel provides an overview of the theoretical framework connecting CP violation, nuclear structure, and Schiff moments. The long-term goal of this project is to contribute to the identification and characterization of nuclei that may exhibit enhanced Schiff moments. Such nuclei are often associated with strong octupole correlations or low-energy parity-doublet structures that can amplify CP-violating effects. This report summarizes progress made during the initial phase of the project, including a survey of candidate isotopes and preparation for nuclear-structure calculations using the HFODD code.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

High-resolution spectroscopy of barium monofluoride: Odd isotopologues, hyperfine structure, and isotope shifts

Barium monofluoride (BaF) is a promising molecular species for precision tests of fundamental symmetries and interactions. We present a combined theoretical and experimental study of BaF spectra and isotope shifts, focusing in particular on the poorly understood odd isotopologues 137 BaF and 135 BaF. By comparing state-of-the-art ab initio calculations with high-resolution fluorescence and absorption spectroscopy data, we provide a benchmark for electronic structure theory and disentangle the hyperfine and rovibrational spectra of the five most abundant isotopologues, from 138 BaF to 134 BaF. The comprehensive knowledge gained enables a King plot analysis of the isotope shifts that reveals the odd-even staggering of the barium nuclear charge radii. It also paths the way for improved laser cooling of rare BaF isotopologues and crucially supports future measurements of nuclear anapole and Schiff moments.

Kogel, Felix [Univ. of Stuttgart (Germany)] (ORCID↗

Influence of Peripheral Substituents on Fe(II) Spin State in Complexes with Tridentate Schiff‐Base Ligands

Abstract Six Fe(II) complexes with substituted 6‐((quinoline‐8‐ylimino)methyl)phenolates (R 2 qsal) were synthesized. X‐ray crystal structure determination for [Fe(R 2 qsal) 2 ], where R=F ( 1 ), Cl ( 2 ), Br ( 3 ), I ( 4 ), CF 3 /H ( 5 ), or CN/H ( 6 ), revealed mononuclear complexes that crystallize either solvent‐free in case of 1 , 5 , and 6 or as CH 2 Cl 2 solvates in the case of 2 , 3 , and 4 . Complexes 1 – 4 , which contain π‐donating substituents, exhibit only high‐spin (HS) state, as shown by crystal structure analysis and magnetic measurements. In contrast, complexes 5 and 6 , which contain electron‐withdrawing substituents, exist in the low‐spin (LS) state at lower temperatures but exhibit crossover to the HS state above 300 K. Electronic structure calculations show a good correlation between the relative energies of the LS and HS states and the experimentally observed behavior.

Gakiya‐Teruya, Miguel↗

Rare isotope-containing diamond colour centres for fundamental symmetry tests

Detecting a non-zero electric dipole moment in a particle would unambiguously signify physics beyond the Standard Model. A potential pathway towards this is the detection of a nuclear Schiff moment, the magnitude of which is enhanced by the presence of nuclear octupole deformation. However, due to the low production rate of isotopes featuring such ‘pear-shaped’ nuclei, capturing, detecting and manipulating them efficiently is a crucial prerequisite. Incorporating them into synthetic diamond optical crystals can produce defects with defined, molecule-like structures and isolated electronic states within the diamond band gap, increasing capture efficiency, enabling repeated probing of even a single atom and producing narrow optical linewidths. In this study, we used density functional theory to investigate the formation, structure and electronic properties of crystal defects in diamond containing 229 ⁢Pa, a rare isotope that is predicted to have an exceptionally strong nuclear octupole deformation. In addition, we identified and studied stable lanthanide-containing defects with similar electronic structures as non-radioactive proxies to aid in experimental methods. Our findings hold promise for the existence of such defects and can contribute to the development of a quantum information processing-inspired toolbox of techniques for studying rare isotopes.

07 ISOTOPE AND RADIATION SOURCES↗