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Discerning nuclear pairing properties from magnetic dipole excitation

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Abstract

Pairing correlation of Cooper pair is a fundamental property of multi-fermion interacting systems. For nucleons, two modes of the Cooper-pair coupling may exist, namely of \(S_{12}=0\) with \(L_{12}=0\) (spin-singlet s-wave) and \(S_{12}=1\) with \(L_{12}=1\) (spin-triplet p-wave). In nuclear physics, it has been an open question whether the spin-singlet or spin-triplet coupling is dominant, as well as how to measure their role. We investigate a relation between the magnetic-dipole (M1) excitation of nuclei and the pairing modes within the framework of relativistic nuclear energy-density functional (RNEDF). The pairing correlations are taken into account by the relativistic Hartree-Bogoliubov (RHB) model in the ground state, and the relativistic quasi-particle random-phase approximation (RQRPA) is employed to describe M1 transitions. We have shown that M1 excitation properties display a sensitivity on the pairing model involved in the calculations. The systematic evaluation of M1 transitions together with the accurate experimental data enables us to discern the pairing properties in finite nuclei.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: Raw data supporting our conclusions are available from the corresponding author T.O. on request.]

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Acknowledgements

We especially thank Tamara Nikšić and Dario Vretenar for fruitful discussions. This work is supported by the “QuantiXLie Centre of Excellence”, a project co-financed by the Croatian Government and European Union through the European Regional Development Fund, the Competitiveness and Cohesion Operational Programme (KK.01.1.1.01).

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Authors and Affiliations

  1. Department of Physics, Faculty of Science, University of Zagreb, Bijenička c. 32, 10000, Zagreb, Croatia

    Tomohiro Oishi, Goran Kružić & Nils Paar

  2. Research department, Ericsson - Nikola Tesla, Krapinska 45, 10000, Zagreb, Croatia

    Goran Kružić

Authors
  1. Tomohiro Oishi
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  2. Goran Kružić
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Correspondence to Tomohiro Oishi.

Additional information

Communicated by Michael Bender.

Appendix A: Comparison of pairing models

Appendix A: Comparison of pairing models

In the main text, we have utilized the D1S and S1P-pairing models combined with the relativistic DD-PC1 interaction for the RHB calculations. In this Appendix, we check the consistency between D1S and S1P in terms of the binding energies for open-shell nuclei. We perform the RHB calculations for the Sn and Pb isotopes by keeping the same setting and parameters used in the main text for Ca isotopes.

In Fig. 7, our RHB results for Sn and Pb isotopes are displayed. The D1S and S1P-pairing models show a good agreement in terms of the binding energies per nucleon, E/A. Namely, they have the same quality on the reproduction of the ground-state energies of open-shell nuclei. Notice also that their results exactly coincide for the doubly-magic nuclei. The error from the experimental E/A data is, even at maximum, less than 0.1 MeV throughout the Ca, Sn, and Pb isotopes. We have also checked that the RHB results, which include the pairing strength, quasiparticle spectrum, and charge radii, are well equivalent between the DD-PC1+D1S and DD-PC1+S1P cases.

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Oishi, T., Kružić, G. & Paar, N. Discerning nuclear pairing properties from magnetic dipole excitation. Eur. Phys. J. A 57, 180 (2021). https://doi.org/10.1140/epja/s10050-021-00488-7

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