# Finding the best candidates for atomic EDM searches

The search for hints of new physics Beyond the Standard Model (BSM) calls for a combination of experimental strategies including both direct searches but also a number of very high-precision measurements of certain quantities looking for deviations that could be interpreted in the framework of BSM physics. As experimental techniques advance, sophisticated devices allow for ultra-precise measurements that can probe higher scales where new physics may be at play.

Searches for the permanent electric dipole moments (EDMs) of molecules, atoms, nucleons and nuclei provide powerful probes of charge-parity (CP) violation both within and beyond the Standard Model. The minimal SUSY extension of the SM (MSSM) already contains many possible CP-violating phases, even in its minimally flavour-violating (MFV) version while the maximally CP-violating MFV version, the MCPMFV model has six CP-violating phases, to which may be added the QCD vacuum phase θ_{QCD}. Some CP-violating phases may manifest themselves at the TeV scale and be accessible to contemporary collider experiments, e.g. at the LHC. However, baryogenesis could equally well be achieved via CP-violating phases appearing at higher energy scales, and EDMs have the potential to probe beyond the TeV scale, in particular because the Standard Model Kobayashi–Maskawa predictions for EDMs are quite small. At present the best experimental limits for EDMs of diamagnetic systems are for the neutron and for ^{199}Hg, while the best limits for paramagnetic systems are for HfF+ and for ThO. These limits have placed severe constraints on CP-violating parameters in models extending the SM.

Diamagnetic atoms with octupole-deformed (pear-shaped) nuclei are very important in the search for EDMs, because odd-A nuclei having this reflection-asymmetric shape will have an enhanced nuclear Schiff moment (the *r*^{2}-weighted electric dipole charge distribution in a nucleus) that induces the atomic EDM. The enhancement arises from the presence of the large octupole collectivity and the occurrence of nearly degenerate parity doublets in pear-shaped nuclei – two states of the same spin but opposite parity, one of which is the ground state. For such nuclei the sensitivity of the EDM measurement to CP violation over non-octupole-enhanced systems such as ^{199}Hg can be improved by a factor of 100–1,000.

The number of observed cases where the octupole correlations are strong enough to induce a static pear-shape is small. Strong evidence for this type of deformation comes from the observation of a particular behaviour of the energy levels for the rotating quantum system and from an enhancement in the electric octupole moment. So far there are only two cases, ^{224}Ra and ^{226}Ra for which both experimental signatures have been observed. The presence of a parity doublet of 55keV at the ground state of ^{225}Ra makes this nucleus therefore a good choice for EDM searches, and a programme to look for EDMs in this atomic system is well underway at the Argonne National Laboratory. In contrast to the radium isotopes, much less is known about the behaviour of radon (Rn) nuclei, also proposed as candidates for atomic EDM searches on account of possible enhancement of their Schiff moments.

Therefore the team studied the low-lying quantum states in ^{224}Rn and ^{226}Rn by accelerating beams of these radioactive nuclei to understand their potential for EDM searches capable of probing new physics.

*Recent ISOLDE results *

In order to determine the shape of nuclei, the rotational model can be used to connect the intrinsic deformation, which is not directly observable, to the electric charge moments that arise from the non-spherical charge distribution. Twenty five years ago Coulomb excitation was applied to the detailed measurements of the octupole shape of ^{148}Nd in the Z ~ 56, N ~ 88 region and of ^{226}Ra in the Z ~ 88 and N ~134 region, but measurements of other nuclei in the latter mass region have had to wait for the development of accelerated beams of heavy radioactive nuclei. This was realised in 2010 when ^{224}Ra beams were accelerated for the first time and ^{220}Rn beams accelerated in 2011. The collaboration published the results on the octupole characteristics of the latter two nuclei in 2013. These ISOLDE measurements and the new measurements discussed here all used the Miniball detector array to detect g-rays following the Coulomb excitation of the radioactive beam by the target, usually a thin foil of an enriched (stable) isotope of Ni or Sn. Miniball is an array of 24 high-purity germanium detectors, each with six-fold segmentation and arranged in eight triple-clusters. The scattered projectiles and target recoils were detected in a highly segmented silicon detector, defining the kinematics of the two-body reaction and enabling the energy of the Doppler corrected g-rays to be measured precisely.

**Figure 1: The Miniball spectrometer in the ISOLDE experimental hall.**

In the new measurements ISOLDE produced ^{224}Rn (Z = 86, N = 138) and ^{226}Rn (Z = 86, N = 140) ions by bombarding a thick thorium carbide target with ~10^{13} protons s^{−1} at 1.4 GeV from the CERN PS Booster. The ions were accelerated in HIE-ISOLDE to an energy of 5.08 MeV per nucleon and bombarded secondary targets of ^{120}Sn. By looking at time-ordered coincident relationships between pairs of g-rays, their decay sequence and the energies and spins of excited states in ^{224,226}Rn were determined for the first time. To verify the identification technique, the team used another isotope of radon, ^{222}Rn that was accelerated to 4.23 MeV/u. The results from these measurements are shown in the figure. Here Di_{x} (figure c) is calculated by subtracting from the value of spin for each negative parity state an interpolated, smoothed value for the positive parity spin at the same value of rotational frequency w. For a nucleus with stable octupole deformation the value of Di_{x} is expected to be zero. For octupole-vibrational nuclei in which the negative-parity states arise from the coupling of an octupole phonon to the positive-parity states, the value of Di_{x} can approach three if the phonon becomes aligned with the rotational axis. This appears to be the case for all radon isotopes.

**Figure 2: (a) Systematics of the energies for different spins of low-lying positive-parity (black) and negative-parity states (red) in radon isotopes; (b) cartoon illustrating how the octupole phonon vector aligns with the rotation (R) vector (which is orthogonal to the rotating body’s symmetry axis) so that I=R+3 and; (c) difference in aligned spin for negative- and positive-parity states in ^{218-224}Rn). **

The observation of octupole-vibrational bands in the even-even radon isotopes is consistent with several theoretical calculations, which predict that only nuclei with Z > 86 have stable octupole deformation. The study concluded that there are no isotopes of radon that have static octupole deformation, so that any parity doublets in the odd-mass neighbours will not be closely spaced in energy. Therefore radon atoms provide less favourable conditions for the enhancement of a measurable atomic EDM. The next steps will be to attempt to measure the properties of the excited quantum states in odd-A radon isotopes directly populated by β-decay, by taking advantage of contamination-free astatine beams that will be available after LS2. In addition, the collaboration is currently analysing data that will determine the electric octupole strength in ^{222,224}Rn, necessary to determine the Schiff moment in these nuclei vital for any future EDM measurement.

**Further Reading:**

P. Butler, L.P. Gaffney, M. Zielinska., "Observation of vibrating pear-shapes in radon nuclei' (doi: 10.1038/s41467-019-10494-5)*: *https://www.nature.com/articles/s41467-019-10494-5