Realistic calculations for $c$ coefficients of the isobaric mass multiplet equation in $1p0f$ shell nuclei

We present calculations for the $c$ coefficients of the isobaric mass multiplet equation for nuclei from $A=42$ to $A=54$ based on input from three realistic nucleon-nucleon interactions. We demonstrate that there is a clear dependence on the short-range charge-symmetry-breaking (CSB) part of the strong interaction and that there is significant disagreement in the CSB part between the commonly used CD-Bonn, chiral effective field theory at next-to-next-to-next-to-leading-order, and Argonne V18 nucleon-nucleon interactions. In addition, we show that all three interactions give a CSB contribution to the $c$ coefficient that is too large when compared to experiment.

Figure 1

Results for the CD-Bonn potential up to first (red), second (blue), and third (green) order. The black circles are the experimental data. The solid lines in the left-hand panels show the Coulomb contribution to the $c$ coefficients. In the right-hand panels, the dashed lines show the CSB contribution from the CD-Bonn potential, while the solid line represents the full calculation, CSB + Coulomb.

Figure 2

First-order calculations compared to experiment. The black circles are the experimental data. The solid lines show the sum of the Coulomb and CSB contributions. The dashed lines show only the CSB contribution.

Figure 3

Calculations up to third order compared to experiment. See caption to Fig 2.

Figure 4

First-order calculations for ${\mathrm{N}}^3\mathrm{LO}$ with the CSB part multiplied by 0.8 and compared to experiment. See caption to Fig 2.