Speaker
Description
The isospin symmetry of atomic nuclei is broken due to the Coulomb interaction and the isospin symmetry breaking part of the nuclear interaction. The former gives the dominant contribution to the isospin symmetry breaking of atomic nuclei, and the latter is a small part of the whole; however, it sometimes gives important contributions to nuclear properties, such as the mass difference of mirror nuclei and the isobaric analog states [1, 2]. Especially, it has been a long-standing problem that the Coulomb interaction is not enough to describe the mass difference of mirror nuclei, which is known as the Okamoto-Nolen-Schiffer anomaly [3, 4], and some other properties [2].
The isospin symmetry breaking can be classified into two parts: the charge symmetry breaking (CSB) and the charge independence breaking (CIB). The CSB originates from the mass difference between protons and neutrons and rho-omega and pi-eta mixing in the meson exchange picture and the CIB originates from mass difference between charged pions and neutral ones. These origins are related to the mass difference of up- and down-quarks. Therefore, it is related to the fundamental study on the quarks and strong interaction; for instance, it is indispensable to estimate the isospin symmetry breaking of nuclear interaction properly to test the unitarity of the Cabibbo-Kobayashi-Maskawa matrix.
The CSB term of the effective interaction, i.e., the energy density functional (EDF), can be determined phenomenologically based on experimental data [1, 5] or theoretically based on ab initio calculation. However, we found that the CSB strength determined phenomenologically is about ten times larger than that by ab initio calculation [6]. Therefore, we have pin down the isospin symmetry breaking terms of the EDF based on more fundamental theory.
We pinned down the CSB EDF using the effective mass in medium of nucleons calculated based on the quantum chromodynamics sum rule [7]. We found that the QCD-based CSB EDF can reproduce experimental data of the mass difference of mirror nuclei of $ N = Z \pm 1 $ nuclei quite nicely. We also estimated the CIB term of the EDF based on the quantum electrodynamics effects in the one-pion exchange potential (OPEP) [8], where we can, in principle, consider the effective mass of pions in medium. We found that even without the in-medium effect of pions, the OPEP-based CIB EDF can reproduce the CIB contribution to the equation of state obtained phenomenologically.
In this talk, I will report our recent progress on the derivation of the isospin symmetry breaking energy density functional based on quantum chromodynamics.
References
[1] X. Roca-Maza, G. Colò, and H. Sagawa. "Nuclear Symmetry Energy and the Breaking of the Isospin Symmetry: How Do They Reconcile with Each Other?" Phys. Rev. Lett. 120, 202501 (2018).
[2] T. Naito, G. Colò, H. Liang, X. Roca-Maza, and H. Sagawa. "Effects of Coulomb and isospin symmetry breaking interactions on neutron-skin thickness" Phys. Rev. C 107, 064302 (2023).
[3] K. Okamoto. "Coulomb energy of $ \mathrm{He}^3 $ and possible charge asymmetry of nuclear forces" Phys. Lett. 11, 150 (1964).
[4] J. A. Nolen, Jr. and J. P. Schiffer. "Coulomb energies" Annu. Rev. Nucl. Sci. 19, 471 (1969).
[5] P. Bączyk, J. Dobaczewski, M. Konieczka, W. Satuła, T. Nakatsukasa, and K. Sato. "Isospin-symmetry breaking in masses of $ N \simeq Z $ nuclei" Phys. Lett. B 778, 178 (2018).
[6] T. Naito, G. Colò, T. Hatsuda, H. Liang, X. Roca-Maza, and H. Sagawa. "Possible inconsistency between phenomenological and theoretical determinations of charge symmetry breaking in nuclear energy density functionals" Nuovo Cim. C 47, 52 (2024).
[7] H. Sagawa, T. Naito, X. Roca-Maza, and T. Hatsuda. "QCD-based charge symmetry breaking interaction and the Okamoto-Nolen-Schiffer anomaly" Phys. Rev. C 109, L011302 (2024).
[8] T. Naito, G. Colò, T. Hatsuda, X. Roca-Maza, and H. Sagawa. To be submitted.
