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Background: Nuclear pasta, emerging due to the competition between thelong-range Coulomb force and the short-range strong force, is believed to bepresent in astrophysical scenarios, such as neutron stars and core-collapsesupernovae. Its structure can have a high impact e.g. on neutrino transport orthe tidal deformability of neutron stars.  Purpose: We study several possible pasta configurations, all of them minimalsurface configurations, which are expected to appear in the mid-density regimeof nuclear pasta, i.e. around 40% of the nuclear saturation density. Inparticular we are interested in the energy spectrum for different pastaconfigurations considered.  Method: Employing the density functional theory (DFT) approach, we calculatethe binding energy of the different configurations for three values of theproton content XP = 1/10, 1/3 and 1/2, by optimizing their periodic length. Westudy finite temperature effects and the impact of electron screening.  Results: Nuclear pasta lowers the energy significantly compared to uniformmatter, especially for $X_P \geq 1/3$. However, the different configurationshave very similar binding energies. For large proton content, $X_P \geq 1/3$,the pasta configurations are very stable, for lower proton content temperaturesof a few MeV are enough for the transition to uniform matter. Electronscreening has a small influence on the binding energy of nuclear pasta, butincreases its periodic length.  Conclusion: Nuclear pasta in the mid-density regime lowers the energy of thematter for all proton fractions under study. It can survive even largetemperatures of several MeV. Since various configurations have very similarenergy, it is to expected that many configurations can coexist simultaneouslyalready at small temperatures.

A Survey of Nuclear Pasta in the Intermediate Density Regime I: Shapes and Energies