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

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

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 10-19 accuracy (relative difference in masses)

discrete symmetry violation

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

Parity parity reversal

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

Parity Chen Ning Yang Tsung-Dao Lee

Parity Chien-Shiung Wu

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.

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.

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

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]

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

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

Time reversal violation and the Electric Dipole Moment QM: J//d any particle will do dn  0.6 10-27 em de < 1.6 10-29 em de (SM) < 10-39 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

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

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

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

~ 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

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

Schiff theorem

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

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

Can an atom have an EDM ?

Schiff theorem

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

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

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

nuclear charge density distribution

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

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

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

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

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

analogy: hyperfine interaction structure magnetic dipole electric quadrupole …

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

ns contraction in coinage metal group copper silver gold

-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:

hydrogenic Z-dependence

n-dependence of electric dipole ME

n-dependence of P,Q near origin

n-dependence of atomic EDM IE

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

EDM of Zn, Cd, Hg, Cn, Uhb

(in alphabetical order) Co-Producers (in alphabetical order) Jacek Bieroń Uniwersytet Jagielloński (300-400) 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)

(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

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