1. Parity and time reversal violation in heavy and superheavy atoms
Jacek Bieroń
Universitas Iagellonica Cracoviensis
Zakład Optyki
Atomowej
Institute of Physics
Discrete Symmetries and Entanglement 2017

3. MCDHF approach to CPT symmetries in heavy atoms
Zakład Optyki
Atomowej
Jacek Bieroń
Uniwersytet Jagielloński
Instytut Fizyki

4. CPT theorem
Define product symmetries, like CP (parity and charge conjugation)  a system of antiparticles in the reverse-handed coordinate system symmetry
Combined CPT symmetry is absolutely exact: for any process,
its mirror image with antiparticles and time reversed
should look exactly as the original  CPT theorem
If any one individual (or pair) of the symmetries is broken, there must be a compensating asymmetry in the remaining operation(s) to ensure exact symmetry under CPT operation
CPT symmetry was checked through the possible difference in masses, lifetimes, electric charges and magnetic moments of particle vs antiparticle and was confirmed experimentally with accuracy (relative difference in masses)

6. discrete symmetry violation

7. reflection in mirror represents reversal of the axis perpendicular to the mirror
reversal of the other two axes is equivalent to the rotation about the axis perpendicular to the mirror

8. Parity
parity reversal

9. (a comment) on (non)equivalence of mirror and parity transformations

10. Parity
Chen Ning Yang
Tsung-Dao Lee

11. Parity
Chien-Shiung Wu

12. Charge conjugation
C operation - interchange of particle with its antiparticle.
C symmetry in classical physics - invariance of Maxwell’s equations under change in sign of the charge, electric and magnetic fields.
C symmetry in particle physics - the same laws for a set of particles and their antiparticles: collisions between electrons and protons are described in the same way as collisions between positrons and antiprotons. The symmetry also applies for neutral particles.
Cy = ± y: even or odd symmetry.
Example: particle decay into two photons, for example
p o  2g, by the electromagnetic force. Photon is odd under C symmetry; two photon state gives a product (-1)2 and is even. So, if symmetry is exact, then 3 photon decay is forbidden. In fact it has not been observed.
C symmetry holds in strong and electromagnetic interactions.

13. C-symmetry violation
C invariance was violated in weak interactions because parity was violated, if CP symmetry was assumed to be preserved.
Under C operation left-handed neutrinos should transform into left-handed antineutrino, which was not found in nature. However, the combined CP operation transforms left-handed neutrino into right-handed antineutrino, which does exist.

14. CP and Time-reversal symmetry
CP invariance was violated in neutral kaon system

15. CP and Time-reversal symmetry
CP invariance was violated in neutral kaon system
… and in decays of meson B: … It is a classic example of the question to ask aliens from a distant galaxy to discover if they are made from what we on Earth define as matter or antimatter. Tell them to make neutral B mesons and anti-mesons and measure the decays to Kπ pairs. Then ask whether the sign of the kaon in the most frequent decay has the same or opposite sign to the lepton orbiting the atoms that make up the galaxy's matter. If the answer is "yes", then the aliens are made from what we know of as antimatter, and it might be better not to invite them to visit Earth. …
[CERN Courier, Sep 6, 2004]

16. CP and Time-reversal symmetry
CP invariance was violated in neutral kaon system.
T operation - connects a process with a reversed process obtained by running backwards in time, i.e. reverses the directions of motion of all components of the system.
T symmetry: "initial state final state" can be converted to "final state initial state" by reversing the directions of motion of all particles.
Time reversal invariance is simply the statement that two processes related to one another by a reversal of all momenta and angular momenta have equal rates

17. Howto observe Time Reversal Violation
Asymmetry of particle energy-momentum distributions (after (high-energy) collision); for instance - compare cross sections of scattering process [running in ‘real’ time] and ‘time-reversed’ scattering process [running in ‘reversed’ time]
2. Detect an Electric Dipole Moment of an elementary particle

19. Time reversal violation and the Electric Dipole Moment
QM: J//d
any particle will do
dn  em
de < em
de (SM) < em
find suitable object
Schiff
need amplifier
atomic (Z3)
nuclear
suitable structure
Consider all nuclides
Why is EDM a TRV observable J d
time
time
EDM violates parity and time reversal

20. Electric dipole moments exist !? they are listed in handbooks
Feynman lectures III chapter 9 will give the answer
|1
Energy
more? p
J1=J2
|I p
|1
split  tunnel probability
Electric field 
|2
|II p
-p
definite energy eigenstates |I / |II =
(|1  |2)
|2
have no dipole moment

21. EDM Now and in the Future
The more Winnie the Pooh looked inside the more Piglet wasn’t there.
NUPECC list
1.610-27 • •
199Hg
Radium potential
Start TRIP
de (SM) < 10-37

22. Principle of EDM measurement
detection -
=   E E
precession B B
state
preparation

23. ~ 1 order of magnitude / decade
EDM Limits as of summer 2004
spring 2011
summer 2009
1.05
0.031
~ 1 order of magnitude / decade
if the electron were magnified to the size of the solar system,
its EDM would be no bigger than the width of a human hair.
Courtesy Klaus Jungmann 23

25. atomic EDM for the ground state with J=0 the summation runs over
all states of opposite parity with J=1

26. Schiff theorem

27. a neutral system composed of charged objects rearranges in an external electric field such that the net force on it cancels on average

28. introduced by Ramsey and Purcell
Schiff Theorem -
introduced by Ramsey and Purcell
a neutral system composed of charged objects re-arranges in an external electric field such that the net force on it cancels on average

29. Can an atom have an EDM ?

30. Schiff theorem

31. atomic EDM for the ground state with J=0 the summation runs over
all states of opposite parity with J=1

32. introduced by Ramsey and Purcell
Schiff Theorem -
introduced by Ramsey and Purcell
A neutral system composed of charged objects re-arranges in an external electric field such that the net force on it cancels on average.
This may give rise to
significant shielding of the field at the location of the particle of interest
(strong) enhancement of the EDM effect
“Schiff corrections” - need for theoretical support

33. electric dipole operator
presence of r
weigths in the outer parts of the wavefunction

34. nuclear charge density distribution

35. TPT operator presence of rho(r) weighs the parts of
the wavefunction inside the nucleus
and effectively cuts off the outer parts

36. PSS operator presence of derivative of rho(r)
weighs the region of nuclear skin
and effectively cuts off the other regions

37. electron electric dipole moment
presence of r^3
weighs the inner parts of the wavefunction
and effectively cuts off the outer parts

38. Schiff operator presence of rho(r).r weighs the nuclear-skin
region of the wavefunction
and effectively cuts off the outer parts

39. EDM - role of atomic theory
P,T-odd
interactions E
Schiff moment
MQM
E octupole
atomic enhancement factor

40. analogy: hyperfine interaction
structure
magnetic dipole
electric quadrupole …

41. regularities in the PTE
digression::
regularities in the PTE
hydrogenic
isoelectronic
Z-dependence in neutral atoms
n-dependence in Rydberg series
n-dependence along a group

42. ns contraction in coinage metal group
copper
silver
gold

43. -dependence in neutral atoms
total energy
fine splitting
hyperfine splitting
transition energy
correlation energy
correlation energy
relativistic effects
spin-orbit parameter
of p electrons in excited
subshells of neutral atoms:

44. hydrogenic Z-dependence

45. n-dependence of electric dipole ME

46. n-dependence of P,Q near origin

47. n-dependence of atomic EDMIE

48. EDM in group 12 of PTE zinc cadmium mercury beryllium copernicium E162
Uhb

49. EDM of Zn, Cd, Hg, Cn, Uhb

50. (in alphabetical order)
Co-Producers
(in alphabetical order)
Jacek Bieroń Uniwersytet Jagielloński ( )
Charlotte Froese Fischer Vanderbilt University (38) & NIST
Stephan Fritzsche GSI
Gediminas Gaigalas Vilniaus Universitetas
Erikas Gaidamauskas Vilniaus Universitetas
Ian Grant University of Oxford (9)
Paul Indelicato l’Université Paris VI (41)
Per Jönsson Malmö Högskola
Pekka Pyykkö Helsingin Yliopisto (72)
T-foils = thanks to Klaus Jungmann & Hans Wilschut (KVI)

51. (in alphabetical order)
Co-Producers
(in alphabetical order)
Jacek Bieroń Uniwersytet Jagielloński
Charlotte Froese Fischer Vanderbilt University & NIST
Stephan Fritzsche Universität Jena
Gediminas Gaigalas Vilniaus Universitetas
Michel Godefroid Université Libre Bruxelles
Ian Grant University of Oxford
Paul Indelicato l’Université Paris VI
Per Jönsson Malmö Högskola
Pekka Pyykkö Helsingin Yliopisto
Thank you for your attention

52. CPT invariance by M. C. Escher
identical
to start
start
matter
anti-matter
time   time
mirror image
Thank you for your attention
anti-particle particle
e e-
From H.W. Wilschut