A study on the electric dipole moment of atoms a thesis submitted for the degree of Doctor of Philosophy in the faculty of science Bangalore University [Ph.D Thesis] Angom Dilip Kumar Singh - Bangalore Indian Institute of Astrophysics 1998 - xii, 134p.

Thesis Supervisor B. P. Das

The forms of symmetries exhibited by physical systems can be classified as continuous and

discrete. With each symmetry there is an associated transformation and these obey characteristic group structures. The continuous symmetries are associated with transformations which has the concept of infinitesimal transformation and a finite transformation can be achieved by applying a sequence of infinitesimal transformations. Whereas in discrete symmetries, there is no concept of infinitesimal transformations, instead the transformation takes the physical system from one state to another. The state of the system before and after the transformation can be same or different. If the system remains the same after

the transformation then it is invariant under the particular symmetry, if the state is different after the transformation then the symmetry is said to be violated by the system[3}. In classical physics the discrete symmetries figure less prominently than they do in quantum physics [2]. The three important discrete symmetries of interest in physical studies are charge

conjugation(C), space-inversion/parity (P) and time-reversal(T). According to the CPT

theorem[3} all physical systems described in local field theories are invariant under the

combined CPT transformation. A physical system/process can violate each of these symmetries individually such that it is compensated by another of the symmetry but when

combined the CPT-theorem is still valid. It has been now established that the weak interaction violates parity but to date no concrete evidence of T violation has been observed

apart from the decay of kaons. Symmetry violations can be observed in laboratory by

looking for their signatures in physical systems. For a single particle or a composite system

the intrinsic Electric Dipole Moment(EDM) in a non-degenerate state is the signature of

P and T violation. The significance of observing such an EDM is that it could lead to a

better understanding of the origin of T or CP violation.

Neutral Atomic systems are good candidates to search for EDM as it is a composite system of leptons and hadrons. The collective many-body effects can enhance the EDM arising

from interaction in a certain sector or due to intrinsic EDM of the constituent particles

either constructively or destructively. The effect of a particular interaction (property ) can

be studied by an appropriate choice of atomic system. The enhancement factor is proportional to the atomic number Z and hence heavier atoms are preferred. Once an atom

is chosen based on the physical effect of interest, the intrinsic EDM can be measured by

subjecting the atom to a constant external electric field E. The interaction Hamiltonian

between E and Da is -Da ·E. Experimentally Da is measured as the linear response to

a constant external electric field. Though all the theoretical descriptions are applicable to

both atomic systems as well as ionic systems, ions cannot be used in experiments as the

external field gives rise to a net force acting on it. From now on only atomic systems will

be considered.

The atomic Hamiltonian is the sum of kinetic energy part of the electrons, electronnucleus coulomb interaction, .electron-electron coulomb interaction and the PT-violating

interaction Hamiltonian HpTV ' The presence of HpTV implies that the eigen states of

the atomic Hamiltonian are no more eigen-states of parity operator P. The theoretical

computation is done by treating HpTV as the perturbation which mixes opposite parity

eigen states of the unperturbed Hamiltonian Hatom , which has the kinetic energy of the

electrons, electron-electron coulomb interaction and electron-nucleus coulomb interaction.

This gives a mixed parity ground state of the atom, from which the intrinsic atomic EDM

Da is computed as linear response to the external field.

Atomic systems

Ele ctric dipole moment

Many - body theories

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