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Symmetry projection in atomic nuclei

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Abstract

In the present work, projection methods employed to restore the spontaneously broken symmetry in the mean-field approach to many-body problem are reviewed. The symmetry restoration is important to include correlations going beyond the mean-field approximation. Further, in order to cause a direct comparison with the experimental quantities, quantum states must have sharp values of the desired quantum numbers. For Hamiltonian based approaches, projection methods have been developed and applied for restoration of symmetries. Symmetry projected Hartree–Fock–Bogoliubov (HFB) equations have been derived in the Hamiltonian based approach, which have a similar structure to those of bare HFB equations. The explicit expressions for the projected Hartree-Fock (HF) and pairing fields are derived in the present work for a generalized projection operator. Approximations to the projection method, based on the work of Lipkin and Kamlah, are discussed with some technical details. Finally, problems associated in the application of the projection technique to the energy density functional approaches are highlighted.

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Authors and Affiliations

  1. Cluster University Srinagar, Jammu and Kashmir, Srinagar, 190008, India

    J. A. Sheikh

  2. Department of Physics, University of Kashmir, Srinagar, 190006, India

    J. A. Sheikh & R. N. Ali

  3. Department of Physics, Central University of Kashmir, Ganderbal, 191131, India

    R. N. Ali

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Sheikh, J.A., Ali, R.N. Symmetry projection in atomic nuclei. Eur. Phys. J. Spec. Top. 229, 2555–2602 (2020). https://doi.org/10.1140/epjst/e2020-000111-3

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