Atomic Many-Body Theory with Applications

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The research centers on the development of next-generation high-precision methods of many-body relativistic theory for univalent atoms. A new partial summation scheme to all-orders of many-body perturbation theory will be implemented. This ab initio summation scheme will improve accuracy and convergence of a recently derived and computed 1,648 fourth-order diagram calculation. Second, an incorporation of valence triple and disconnected quadruple excitations into a hierarchy of coupled-cluster equations is proposed.The development of many-body formalisms has a long-term goal of improving accuracyof calculations of atomic parity-violating amplitudes. These amplitudes are important forrevealing possible new physics beyond the Standard Model of elementary particles. Applications to the design of ultrastable optical clocks is also discussed.