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Survey of ground-state octupole deformations of atomic nuclei

This study explores the ground-state octupole deformations of atomic nuclei, examining the evidence for non-spherical nuclear shapes and the stability of pear-shaped nuclear deformations. It also discusses the correlation between Schiff moments and octupole moments in light actinides. The findings provide valuable insights into the structure of atomic nuclei.

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Survey of ground-state octupole deformations of atomic nuclei

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  1. Survey of ground-state octupole deformations of atomic nuclei Yuchen Cao and Witold Nazarewicz, Michigan State University/FRIB FRIB-TA Topical Program: Hadronic Electric Dipole Moments in the FRIB Era: From the Proton to Protactinium MSU, August 12-23, 2019 • Menu • Nuclear shapes • Ground-state octupole deformations: a survey • Conclusions FRIB-TA Topical Program 2019

  2. Shapes FRIB-TA Topical Program 2019

  3. Nuclear shapes • The first evidence for a non-spherical nuclear shape came from the observation of a quadrupole component in the hyperfine structure of optical spectra. The analysis showed that the electric quadrupole moments of the nuclei concerned were more than an order of magnitude greater than the maximum value that could be attributed to a single proton and suggested a deformation of the nucleus as a whole. • Schüler, H., and Schmidt, Th., Z. Physik 94, 457 (1935) • Casimir, H. B. G., On the Interaction Between Atomic Nuclei and Electrons, Prize Essay, Taylor’s TweedeGenootschap, Haarlem (1936) • The question of whether nuclei can rotate became an issue already in the very early days of nuclear spectroscopy • Thibaud, J., Comptesrendus 191, 656 ( 1930) • Teller, E., and Wheeler, J. A., Phys. Rev. 53, 778 (1938) • Bohr, N., Nature 137, 344 ( 1936) • Bohr, N., and Kalckar, F., Mat. Fys. Medd. Dan. Vid. Selsk. 14, no, 10 (1937) FRIB-TA Topical Program 2019

  4. Reflection-asymmetric nuclear shapes Remarks on pear-shaped nuclei, VilenStrutinsky, At. Energ. 4, 150 (1956) Physica, 22, 1166 (1956) FRIB-TA Topical Program 2019

  5. Stability of Pear-Shaped Nuclear Deformations, K. Lee and D. R. Inglis Phys. Rev. 108, 774 (1957) FRIB-TA Topical Program 2019

  6. P. Butler and WN, Rev. Mod. Phys. 68,349 (1996) FRIB-TA Topical Program 2019

  7. FRIB-TA Topical Program 2019

  8. Intrinsic dipole moment P. Butler, J. Phys. G 43, 073002 (2016) P. Butler and WN, Nucl. Phys. A 533, 249 (1991) FRIB-TA Topical Program 2019

  9. Mean-Field Theory ⇒ Density Functional Theory Degrees of freedom: nucleonic densities • mean-field ⇒ one-body densities • zero-range ⇒ local densities • finite-range ⇒ gradient terms • particle-hole and pairing channels • Does not have to be related to a force • Has been extremely successful. A broken-symmetry generalized product state does surprisingly good job for nuclei. • Nuclear DFT • two fermi liquids • self-bound • superfluid • Constrained by microscopic theory: ab-initio functionals provide quasi-data! • Not all terms are equally important. Usually ~12 terms considered • Some terms probe specific experimental data • Pairing functional poorly determined. Usually 1-2 terms active • Most popular: Skyrme, Gogny, Covariant, Fayans, DME-based • Can be extended into multi-reference DFT (GCM) and projected DFT FRIB-TA Topical Program 2019

  10. Shell correction approach FRLDM (2002) Axial and reflection asymmetry of the nuclear ground state P. Möller et al, Atomic Data and Nuclear Data Tables 94, 758 (2008) FRIB-TA Topical Program 2019

  11. DFT: Gogny vs. Barcelona-Catania-Paris Ba Axial octupole collective Hamiltonian Ra FRIB-TA Topical Program 2019 L.M. Robledo et al., Phys. Rev. C 81, 034315 (2010)

  12. RDFT: DD-PC1 FRIB-TA Topical Program 2019 K. Nomura et al., Phys. Rev. C 89, 024312 (2014)

  13. S.E. Agbemava, A.V. Afanasjev, P. Ring, Octupole deformation in the ground states of even-even nuclei: A global analysis within the covariant density functional theory, Phys. Rev. C 93, 044304 (2016) FRIB-TA Topical Program 2019

  14. L. M. Robledo, J. Phys. G 42, 055109 (2015) Gogny D1M L. M. Robledo and R. R. Rodrıguez-Guzman, J. Phys. G 39, 105103 (2012) FRIB-TA Topical Program 2019

  15. Robledo & Bertsch, PRC84, 054302 (2011) FRIB-TA Topical Program 2019

  16. Global calculations of octupole deformations Y. (Maxwell) Cao, WN, E. Olsen, S. Agbemava FRIB-TA Topical Program 2019

  17. Equilibrium deformation 224Th 154Dy 114Ba 146Ba FRIB-TA Topical Program 2019

  18. Equilibrium deformation FRIB-TA Topical Program 2019

  19. Octupole energy FRIB-TA Topical Program 2019

  20. Number of cases (based on 7 models) 114Ba 146Ba 200Gd (170Gd is the heaviest known) FRIB-TA Topical Program 2019

  21. Number of cases, heavy nuclei (9 models) 224,226Ra, 226,228Th, 228Pu FRIB-TA Topical Program 2019

  22. FRIB-TA Topical Program 2019

  23. FRIB-TA Topical Program 2019

  24. FRIB-TA Topical Program 2019

  25. FRIB-TA Topical Program 2019

  26. Correlating Schiff Moments in the Light Actinides with Octupole Moments J. Dobaczewski et al., Phys. Rev. Lett. 121, 232501 (2018) The result is a dramatically reduced uncertainty in intrinsic Schiff moments. Direct measurements of octupole moments in odd nuclei will reduce the uncertainty even more. The only significant source of nuclear-physics error in the laboratory Schiff moments will then be the intrinsic matrix elements of the time-reversal noninvariant interaction produced by CP-violating fundamental physics. FRIB-TA Topical Program 2019

  27. Conclusions • Very rich data; need to be fully analyzed. • Octupole softness • Systematic uncertainties • The usual suspects remain the best cases • To be done: • Search for best parity doublet candidates in odd-A nuclei • Schiff moment calculations FRIB-TA Topical Program 2019

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