Information content of the differences in the charge radii of mirror nuclei

Abstract

Differences in the charge radii of mirror nuclei have been recently suggested to contain information on the slope of the symmetry energy L. To test this hypothesis, we perform statistical correlation analysis using quantified energy density functionals that are consistent with our previous knowledge on global nuclear observables such as binding energies and charge radii. We conclude that the difference in charge radii between a mirror pair, ∆R mir ch , is an inferior isovector indicator compared to other observables, such at the neutron skin or electric dipole polarizability αD. In particular, this quantity correlates poorly with both the neutron skin and L. We demonstrate that ∆R mir ch is influenced by pairing correlations in the presence of low-lying proton continuum in the proton-rich mirror-partner nucleus. Considering the large theoretical uncertainties on ∆R mir ch , we conclude that the precise data on mirror charge radii cannot provide a stringent constraint on L.Introduction.-A cursory information on properties of atomic nuclei is offered by the droplet model [1,2] whose key parameters are the nuclear matter (or bulk) characteristics such as volume energy E/A, equilibrium density ρ eq , incompressibility K, symmetry energy J, and symmetry energy slope L. These quantities are widely used to characterize and compare nuclear models. The isoscalar parameters (E/A, ρ eq , K) are well determined by empirical data because the chart of nuclei extends over a large range of mass numbers. However, the isovector parameters J and L are poorly constrained because available isotopic chains are fairly short. This is an uncomfortable situation because extrapolations to very neutron rich isotopes and to neutron stars are crucial in nuclear astrophysics [3][4][5][6]. Consequently, there is a great demand for isovector-sensitive data that can be used for constraining the symmetry energy in the various nuclear models. The most promising isovector indicators [7] include neutron radii, neutron skins, dipole polarizability, and parity-violating asymmetry, see, e.g., .Recently, it has been suggested [17] that a difference in the charge radii of mirror nuclei, ∆R mir ch, can serve as an isovector indicator that can be used to estimate the symmetry energy parameter L. Such estimates can be found in Refs. [17][18][19][20][21] for the 50 Ni/Ti, 52 Ni/Cr, 54 Ni/Fe, and 36 Ca/S mirror pairs. It was concluded [17,18] that the precise data on mirror charge radii can provide a stringent constraint on L. In this study, we examine this finding.

Isospin symmetry breaking in the charge radius difference of mirror nuclei

“…In the present work, we concentrate on a different source of systematic uncertainty with respect to those discussed in Ref. [23]. It will be shown that nuclear ISB contributions cannot be neglected in the study of the difference of charge radii in mirror nuclei if analysed on the basis of current EDFs.…”

“…Our results indicate that one must expect a correction: given ∆R ch , the estimated value of L must be decreased whenever ISB are neglected. The correction due to nuclear ISB based on our calculations of the mirror pair 48 Ca- 48 Ni would correspond to a shift of about 10 MeV and, even if not large, it needs to be incorporated -among other corrections [23]by a sound study of ∆R ch . For the same reasons, the neutron skin thickness ∆R np in a neutron-rich nucleus is also affected by ISB effects.…”

“…Those studies neglect ISB effects as well as pairing correlations, and also deformation is not treated microscopically. Actually, in a recent study based on quantified EDFs [23], ∆R ch has been shown to be influenced by pairing correlations in the presence of low-lying proton continuum -in the proton-rich partner-and the authors concluded that, considering the large theoretical uncertainties, precise data on mirror charge radii cannot provide a stringent constraint on L.…”