EDM

Despite its spectacular phenomenological success, it is recognized that the Standard Model is incomplete and may eventually be incorporated into a more fundamental framework. For example, the excess of matter over antimatter in the Universe indicates the presence of baryon-number-violating interactions and most likely of new sources of CP violation. At present, the Standard Model does not violate the CP symmetry sufficiently strongly to account for this excess. The observation of a permanent electric dipole moment (EDM) would indicate time-reversal (T) or charge-parity (CP) violation, most likely due to physics beyond the Standard Model [Eng13, Pos05].

As shown by the most sensitive EDM search to date, performed on ¹⁹⁹Hg [Gri09], the present upper limits already constrain various extensions of the Standard Model. In the past few decades, it has been realized that nuclear structure can strongly amplify the sensitivity of nuclear EDM measurements to the underlying physics [Eng13]. The occurrence of octupole deformation and enhanced octupole vibrations in nuclei lead to closely-spaced parity doublets and considerably larger Schiff moments (proportional to the difference between the mean-square radius of the nuclear dipole moment distribution and the nuclear charge distribution). Because a CP-violating Schiff moment induces a contribution to the atomic EDM, a large enhancement due to octupole effects translates into an improved sensitivity to an atomic EDM when compared to atomic systems without this deformation (such as ¹⁹⁹Hg). Enhancement factors of 10²-10³ have been calculated [Eng13, Dob05, Spe97].

A signature of the rotation of an octupole-deformed, even-even nucleus is the presence of rotational bands with levels of alternating parity, connected by strong electric-dipole transitions (i.e., both (I⁺ --> (I-1)^- and I^- --> (I-1)⁺ transitions) where the large B(E1) values of the connecting transitions are interpreted as resulting from the presence of an intrinsic electric dipole moment [But96]. Bands with these properties have been reported in both ²²⁴Ra and ²²⁶Ra [Wol93, Coc97]. Furthermore, a pioneering Coulomb excitation measurement was performed at REX-ISOLDE with ²²⁰Rn and ²²⁴Ra radioactive beams [Gaf13], which provided the E2 and E3 intrinsic moments for the two nuclei. The data provide evidence for stronger octupole deformation in ²²⁴Ra and the results enable discrimination between some of the available calculations. Inverse-kinematics, barrier-energy Coulomb excitation, with GRETA for γ-ray detection, is best suited to search for the regular band structures that serve as a fingerprint for static octupole deformation. With multiple Coulomb excitation at beam energies near the Coulomb barrier, the nucleus can be excited to states of relatively high spins: spins as high as 36 have been observed in ²³²Th and ²³⁸U, for example. In the near-term, with GRETINA at ATLAS/ANL, pioneering exploratory measurements with long-lived, radioactive Ra isotopes will be performed. Specifically, the ²²⁵Ra nucleus will be investigated first, in order to provide input for the

EDM measurement currently being prepared at ANL using atom-trapping technology. The focus of the GRETINA experiment is on the identification of the collective octupole band sequences that would be built on the so-called parity-doublet states; i.e., pairs of bands with the same K quantum number, but opposite parity where states of the same spin are rather close in excitation energy so that they can be described as the projections from a single intrinsic state of mixed parity.

At FRIB, using reaccelerated beams, high-statistics multi-step Coulomb excitation with GRETA will be possible for the ²²⁵Ra and ²²³Rn nuclei; e.g, for both nuclei where efforts to measure the EDM are currently underway. With the available beam intensities, detailed, quantitative studies of octupole collectivity will become possible, including the precise determination of static moments and transition strengths. Furthermore, new candidate nuclei will be probed for the presence or absence of octupole deformation as inferred from properties of the excited levels, including spin-parity assignments and electromagnetic transition rates. One such possible candidate, which is out of reach for the required detailed studies at present generation facilities, is ²²⁹Pa. In this nucleus, the EDM contribution induced by the Schiff moment is predicted to be 3 x 10⁴ times larger than the one for (spherical) ¹⁹⁹Hg and 40 times larger than the contribution to one of the most promising candidates today, ²²⁵Ra [Fla08]. Little is known about the structure of 229Pa to date: most spin-parity assignments are uncertain and no information exists on transition strengths or moments. At FRIB, ²²⁹Pa will be available at reaccelerated-beam 10⁶/s allowing for first-rate, inverse-kinematics Coulomb excitation measurements. In addition to the high detection efficiency, the angular coverage and tracking ability of GRETA will be invaluable to exploit linear polarization and angular distributions in the characterization of possible new, game-changing EDM candidate nuclei like 229Pa and, perhaps, entirely new candidates not envisioned today.

The gains in sensitivity for multiple Coulomb excitation measurements with GRETA at FRIB's reaccelerator are illustrated in Figure 1 for the case of ²²⁰Rn that was studied at REX-ISOLDE [Gaf13]. The efficiency and position resolution of GRETA combined with the FRIB reaccelerated beam intensity and energy provide a 100-fold or higher increase in the intensity of transitions characterizing higher-spin states, sufficient for the detailed and quantitative coincidence spectroscopy of collective structures at high-spin values. With this, GRETA at FRIB's reaccelerator will afford unprecedented discovery potential on the quest for the identification and characterization of octupole-collective candidate nuclei for EDM searches.

References:

[But96] P. A. Butler and W. Nazarewicz, Rev. Mod. Phys. 68, 349 (1996).

[Fla08] V. V. Flambaum, Phys. Rev. A 77, 024501 (2008).

[Pos05] M. Pospelov and A. Ritz, Ann. Phys. 318, 119 (2005).

[Gaf13] L. Gaffney et al., Nature 497, 199 (2013).

[Gri09] W. C. Griffith et al., Phys. Rev. Lett. 102, 101601 (2009).

[Spe97] V. Spevak, N. Auerbach, V. V. Flambaum, Phys. Rev. C 56, 1357 (1997).

[Eng13] J. Engel, M. J. Ramsey-Musolf, and U. van Kolck, Prog. Part. Nucl. Phys. 71, 21 (2013).

[Dob05] J. Dobaczewski and J. Engel, Phys. Rev. Lett. 94, 232502 (2005).

[Wol93] H. J. Wollersheim et al., Nucl. Phys. A556, 262 (1993).