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Neutron stars are extreme and mysterious objects that astrophysicists cannot see inside. With a radius of about 12 kilometers, they can have more than twice the mass of the sun. The matter in them is packed up to five times more tightly than in an atomic nucleus; with black holes they are the densest objects in the universe.

Under extreme conditions, matter can assume exotic states. One hypothesis is that the building blocks of atomic nuclei – protons and neutrons – deform into plates and strings, like lasagna or spaghetti, which is why experts call this “nuclear pasta”.

Researchers from TU Darmstadt’s Department of Physics and the Niels Bohr Institute in Copenhagen have now taken a new theoretical approach to study the state of nuclear matter in the inner core of neutron stars. They showed that both neutrons and protons can “leak” from atomic nuclei and stabilize the “nuclear paste”. Their findings are reported in Physical examination letters.

Neutron stars form when massive stars explode in a supernova: as the star’s outer envelopes are ejected into space, its interior disintegrates. Atoms are literally crushed by the massive gravitational force. Despite their repulsion, the negatively charged electrons are squeezed so close to the positively charged protons in the atomic nucleus that they transform into neutrons.

The strong nuclear force then prevents further collapse. The result is an object that consists of about 95% neutrons and 5% protons – a “neutron star”.

The Darmstadt researchers, led by Achim Schwenk, are experts in theoretical nuclear physics, with neutron stars as one of their research interests. In their current work, they focus on the crust of these extreme objects. The matter in the outer crust is not as dense as in the interior and still has atomic nuclei.

As the density increases, an excess of neutrons is formed in atomic nuclei. Neutrons can then “drip” from the nuclei, a phenomenon known as “neutron dripping”. Therefore, atomic nuclei “float” in a kind of neutron sauce.

“We asked ourselves whether protons can also drip from nuclei,” says Achim Schwenk. “The literature was not clear on this,” the physicist continues. The team with Jonas Keller and Kai Hebeler of TU Darmstadt and Christopher Pettik of the Niels Bohr Institute in Copenhagen calculated the state of nuclear matter under the conditions in the neutron star crust.

Unlike before, they directly calculated its energy as a function of proton fraction. In addition, they included pairwise interactions between particles in their calculations, as well as those between three nucleons.

The method was successful: The researchers were able to demonstrate that protons in the inner crust also drip from the cores. So “proton drip” does exist. This phase consisting of protons coexists with neutrons.

“We were also able to show that this phase favors the nuclear paste phenomenon,” says Schwenk. Thanks to protons sprinkled in the “sauce,” nucleons can exist better in spaghetti and lasagna shapes. This allowed the team to refine the image of nuclear matter in the crust of neutron stars.

“The better we can describe neutron stars, the better we can compare with astrophysical observations,” says Schwenk. Neutron stars are difficult to understand from an astrophysical point of view. For example, we know their radius only indirectly from the gravitational effects on another neutron star. In addition, other phenomena can be observed, such as pulsating radio emission from neutron stars.

The team’s result improves the theoretical understanding of neutron stars and contributes to gaining new insights into these mysteries of the universe from astrophysical measurements.