Correlations between charge radii differences of mirror nuclei and stellar observables

P. Bano, S. P. Pattnaik, M. Centelles, X. Viñas, and T. R. Routray

Phys. Rev. C 108, 015802 – Published 13 July 2023

Abstract

The correlation between the charge radii differences in mirror nuclei pairs and the neutron skin thickness has been studied with the so-called finite range simple effective interaction over a wide mass region. The so far precisely measured charge radii difference data within their experimental uncertainty ranges in the ${}^{34}{Ar} − {}^{34}S$ , ${}^{36}{Ca} − {}^{36}S$ , ${}^{38}{Ca} − {}^{38}{Ar}$ , and ${}^{54}{Ni} − {}^{54}{Fe}$ mirror pairs are used to ascertain an upper limit for the slope parameter of the nuclear symmetry energy $L \approx 100$ MeV. This limiting value of $L$ is found to be consistent with the upper bound of the NICER PSR $J 0740 + 6620$ constraint at $1 σ$ level for the radius $R_{1.4}$ of $1.4 M_{⊙}$ neutron stars. The lower bound of the NICER $R_{1.4}$ data constrains the lower limit of $L$ to $\approx 70$ MeV. Within the range for $L = 70 - 100$ MeV the tidal deformability $Λ^{1.4}$ constraint, which is extracted from the GW170817 event at $2 σ$ level, and the recent PREX-2 and CREX data on the neutron skin thickness are discussed.

Received 5 April 2023
Accepted 22 June 2023

DOI:https://doi.org/10.1103/PhysRevC.108.015802

Physics Subject Headings (PhySH)

Nuclear astrophysics Nuclear charge radii Nuclear matter Nuclear matter in neutron stars

Nuclear Physics

Authors & Affiliations

P. Bano ¹, S. P. Pattnaik ¹, M. Centelles ², X. Viñas ^2,3, and T. R. Routray ^1,*

¹School of Physics, Sambalpur University, Jyotivihar 768 019, India
²Departament de Física Quàntica i Astrofísica (FQA) and Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona (UB), Martí i Franquès 1, E-08028 Barcelona, Spain
³Institut Menorquí d'Estudis, Camí des Castell 28, 07702 Maó, Spain

^*Corresponding author: trr1@rediffmail.com

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Issue

Vol. 108, Iss. 1 — July 2023

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Images

Figure 1
Linear correlation between the neutron skin $Δ R_{n p}$ and the proton rms radii difference $Δ R_{p}$ for mirror nuclei pairs shown for the SEI EoS $(γ = 0.42)$ in the isotonic chains of (a) $N = 14$ , (b) $N = 28$ , and (c) $N = 50$ and isotopic chains of (d) $Z = 10$ , (e) $Z = 28$ , and (f) $Z = 50$ . The results of SkM*, SLy4 [65] and $N {}^{3}{LO}$ [6] forces are given by symbols plus (indigo), square (red), and diamond (magenta), respectively.
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Figure 2
$Δ R_{CH}$ as a function of the symmetry energy slope $L$ for the mirror pairs (a) ${}^{34}{Ar} − {}^{34}S$ , (b) ${}^{36}{Ca} − {}^{36}S$ , (c) ${}^{38}{Ca} − {}^{38}{Ar}$ , and (d) ${}^{54}{Ni} − {}^{54}{Fe}$ . The experimental results, shown in horizontal bands in each panel, are taken from Brown, 2017 [4], Brown et al., 2020 [7], and Pineda et al., 2021 [9]. The SEI characteristic EoS ( $γ = 0.42$ and $L_{c} = 76.71$ MeV) results are shown by filled squares in the four panels, whereas the results for SEI EoSs other than $L = L_{C}$ are black filled circles. The results of other models are displayed by symbols as mentioned in the legends [65, 66].
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Figure 3
Neutron skin thickness $Δ R_{n p}$ as a function of $L$ for (a) ${}^{208}{Pb}$ , (b) ${}^{132}{Sn}$ , (c) ${}^{78}{Ni}$ , and (d) ${}^{48}{Ca}$ for SEI-G ( $γ = 0.42$ ). The results extracted from theoretical analyses of the experiments are shown in horizontal bands in each panel where available and are taken from PREX I [12], PREX II [27], Piekarewicz et al., 2012 [14], Klimkiewicz et al., 2007 [48], Birkhan et al., 2017 [68], RIKEN [69], and CREX [28].
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Figure 4
Stellar radii for neutron stars having masses (b) $M = 0.8 M_{⊙}$ , (c) $1.0 M_{⊙}$ , (d) $1.2 M_{⊙}$ , (e) $1.4 M_{⊙}$ , and (f) $1.8 M_{⊙}$ as a function of the charge radii difference $Δ R_{CH}^{54}$ in the ${}^{54}{Ni} − {}^{54}{Fe}$ mirror pair. The correlation coefficient $r$ obtained from linear regression is given in each panel. The correlation between $Δ R_{CH}^{54}$ and $Δ R_{n p}^{208}$ is shown in panel (a).
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Figure 5
Predictions of SEI-G ( $γ = 0.42$ ) for the tidal deformability, $Λ^{1.4}$ , in $1.4 M_{⊙}$ NSs shown by filled black circles versus (a) the radius $R_{1.4}$ of $1.4 M_{⊙}$ NSs, (b) charge radii difference $Δ R_{CH}^{54}$ of the ${}^{54}{Ni} − {}^{54}{Fe}$ mirror pair, and (c) neutron skin thickness $Δ R_{n p}^{208}$ in ${}^{208}{Pb}$ . The black squares correspond to the SEI calculation with characteristic slope parameter $L_{C} = 76.71$ MeV. The GW170817 $2 σ$ limits on $Λ^{1.4}$ [46] are shown between the blue horizontal lines and the earlier upper limit [84] by the pink line. In panel (a), the $1 σ$ limits on $R_{1.4}$ from pulsar PSR $J 0740 + 6620$ data [45] are shown by red vertical lines. In (b) the experimental data for $Δ R_{CH}^{54}$ [9] are shown between maroon lines, and in (c) the PREX-2 limits [27] are shown by green vertical lines. In each panel the vertical yellow bands correspond to the SEI values in the range of $L = 70 - 100$ MeV for the respective variables $R_{1.4}$ , $Δ R_{CH}^{54}$ , and $Δ R_{n p}^{208}$ .
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