New Finite-Range Droplet Mass Model and Equation-of-State Parameters

The parameters in the macroscopic droplet part of the finite-range droplet model (FRDM) are related to the properties of the equation of state. In the FRDM (1992) version, the optimization of the model parameters was not sufficiently sensitive to variations of the compressibility constant $K$ and the density-symmetry constant $L$ to allow their determination. In the new, more accurate FRDM-2011a adjustment of the model constants to new and more accurate experimental masses allows the determination of $L$ together with the symmetry-energy constant $J$. The optimization is still not sensitive to $K$ which is therefore fixed at $K=240\mathrm{MeV}$. Our results are $J=32.5\pm 0.5\mathrm{MeV}$ and $L=70\pm 15\mathrm{MeV}$ and a considerably improved mass-model accuracy $\sigma =0.5700\mathrm{MeV}$, with respect to the 2003 Atomic Mass Evaluation (AME2003) for FRDM-2011a, compared to $\sigma =0.669\mathrm{MeV}$ for FRDM (1992).

Figure 1

Impact of successive enhancements to FRDM(1992) with $\sigma =0.669\mathrm{MeV}$, leading to FRDM-2011a with $\sigma =0.5700\mathrm{MeV}$. The line numbers in Table  corresponding to before and after enhancement are given in parentheses.

Figure 2

Differences between measured and calculated masses corresponding to line 7 in Table .

Figure 3

Calculated symmetry parameters $J$ and $L$ in a selection of different SHF (white circles) and RMF (black circles) models. The dashed lines indicate the one-$\sigma$ limits in our determination.