ELECTRIC DIPOLE MOMENT IN DEFORMED NUCLEI • Electric dipole moment in atoms with deformed nuclei
Time Reversal Symmetry Classically : The equations of motion are invariant with respect to inversion of time, that is with respect to a transformation that reverses the motion of all the components of the system. In quantum mechanics the transformation of time reversal obeys:
Time Reversal Wigner showed that it needs to be anti-unitary Time Reversal
T-P-odd electromagnetic moments In the absence of parity (P) and time (T) reversal violation the T P-odd moments for a quantum particle (system) will be zero. For example, the electric dipole moment: A direction in space is defined by the spin j. The electric dipole d=dj. But d=er, is a polar vector while j is an axial vector, so one changes sign under a parity transformation, the other not. Because of parity, d=0. But also under time reversal d does not change sign, but j does. In order to have a non-zero d both P and T must be violated.
Permanent Electric Dipole Moments Violate Discrete Fundamental Symmetries EDM violates: • Parity • Timereversal • CP- conservation (if CPT conservation assumed) Standard Model values are tiny, hence: An observedEDM would be Sign of New Physics beyond Standard Theory
Sakharov’s paper • According to our hypothesis, the occurrence of C asymmetry is the consequence of violation of CP invariance in the nonstationary expansion of the hot universe during the superdense stage, as manifest in the difference between the partial probabilities of the charge-conjugate reactions.
P C T matter anti-matter start end time time mirror image from H.W. Wilschut The World according to Escher anti-particle particle e+ e- back
Polar molecules "Some molecules are constructed so that they have electric dipole moments even in the absence of an electric field (HCl)” (undergraduate text book). + - + + - + - - + + -
NH3 molecule Undergraduate text book. (Eisberg and Resnick)
|+ |- - = (|+ - |-)/2 + = (|+ + |-)/2 DE Pear shaped nuclei and time reversal violation Parity doublets
6 Rotation Reflection 4 2 - 0 + Rotational band Parity doublet I(I+1) spectrum
Octupole Deformations Physics Letters B 359 (1995) 254-260 PHYSICS LETTERS B Parity mixing and time reversal violation in nuclei with octupole deformations V. Spevak, N. Auerbach School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel Received 29 May 1995; revised manuscript received 3 August 1995 Editor: GE Bertsch Abstract: Parity non-conserving and time reversal violating matrix elements between parity doublets occurring in nuclei that possess intrinsic octupole deformations are studied. In some cases the mixing coefficients turn out to be large due to the near degeneracy of the doublets and in the case of time reversal violation also due to the enhancement in the symmetry violating matrix elements.
Skyrme Hartee-Fock calculations of Ra isotopesM.Bender et al. Shapes of various Ra isotopes
CERN- COURIER • EDM search goes pear-shaped • Permanent electric dipole moments (EDMs) of particles are excellent test beds for the Standard Model. Nonzero EDMs imply that both P and T, and by implication CP, are violated. Nuclear physicists have thus been seeking to measure atomic EDMs since the 1980s, with pear-shaped nuclei the most promising candidates. More correctly termed a static octupole distortion, the pear shape was first seen at CERN’s ISOLDE facility in radium-isotope 224Ra in 2013 (Nature 497 199). However, Peter Butler of the University of Liverpool and coworkers, using beams from the upgraded HIE-ISOLDE, have now established that radon-isotopes 224Rn and 226Rn do not possess static pear shapes in their ground states, and are thus not promising candidates to have measurable atomic EDMs (Nat. Commun. 10 2473), inducing the team to switch focus to other isotopes.
Measuring Atomic EDMs A TRV component in the N-N interaction EDMs of of individual nucleons EDM+Schiff moment of the nucleus TRV in the electric field Atomic EDM Experiment External E and B
Schiff moment The Schiff-Purcell-Ramsey-Hellman-Feynman theorem. • The nuclear dipole moment causes the atomic electrons to rearrange themselves so that they develop a dipole moment opposite that of the nucleus. In the limit of non-relativistic electrons and a point nucleus the electrons’ dipole moment exactly cancels the nuclear moment, so that the net atomic dipole moment vanishes! • For a finite size nucleus the screening is not complete and one is left with a vector called the Schiff moment
Experimental Evidence • Present experimental studies of nuclei in the actinide region (Z around 88 and N around 134) indicate that these nuclei possess octupole shapes in the ground state. • The existence of octupole deformations in the actinide nuclei is manifested in the existence of parity doublet states and parity doublet bands. The E1 and E3 transitions between these states are relatively strong, of the order of a Weisskopf unit. These experimental findings are supported by theoretical studies. Some isotopes of Rn, Fr, Ra, Ac, Th, and Pa in the 218<A<230 region are predicted theoretically to be reflection asymmetric in the g.s. • More experimental work is needed in this area.
Three labs are presently actively pursuing experiments with radioactive nuclei in the actinide region: • 1. Argonne National Lab -Trapping of 225Ra • 2. KVI -Trapping of Ra isotopes • 3. TRIUMF-223Rn
Recent developments It was suggested that soft octupole vibrations observed in some regions of the nuclear chart more frequently than static octupole deformation may produce a similar enhancement of the Schiff moment. Estimates of the Schiff moment generated in nuclei with a quadrupole deformation and soft octupole mode showed that the resulting Schiff moments are indeed enhanced. A related idea was explored recently. It is known that some nuclei are soft with respect to both quadrupole and octupole modes. The light isotopes of Rn and Ra are spherical but with a soft quadrupole mode. The spectra of the nuclei display quasi-vibrational bands based on the ground state and on the octupole phonon, with positive and negative parity, respectively. These bands are connected via low-energy electric dipole transitions. This situation seems a-priori to be favorable for the enhancement of T,P-odd effects.
Particle phonon coupling The approach used was based on the QRPA that allows one to define microscopically the structure of collective modes and coupling of the odd particle to quadrupole and octupole phonons. We confirmed the effect of enhancement of the Schiff moment for very small quadrupole and octupole frequencies. The even-even system close to onset of deformation acts essentially similarly to the statically deformed system, where the enhancement was established earlier.
In the realistic cases there is a large fragmentation of s.p. strength (in both the positive and negative parity states) so that the final results for the Schiff moment are similar to the ones obtained for Hg or Xe.
An estimate shows that this contribution is by order of magnitude comparable to single-particle contributions and can be enhanced if the low-lying resonance has collective nature