From atomic nuclei to stars

Neutron stars are objects at the extremes. Measuring about 20 km in diameter, they are just about as large as a city the size of Darmstadt, but their mass is remarkable: a scoop out of a neutron star the size of a sugar cube would weigh about a hundred million tonnes on earth. “Basically, they’re densely packed atomic nuclei,” explains Achim Schwenk, theoretical nuclear physicist and professor at the TU Darmstadt.

Atoms are the building blocks of all matter on earth, and the defining structure of elements. They consist of a tiny nucleus that contains neutrons and protons and a voluminous shell of electrons. The mass of the atom almost entirely comes from the nucleus; the shell weighs virtually nothing. Normal stars are also made up of atoms. When they explode at the end of their life span, depending on the star’s mass, a compact neutron star can form. The negatively charged electrons are then pressed into the atomic nuclei during the star’s supernova explosion, where they combine with the positively charged protons to make neutrons. What remains is soup of atomic nuclei, that consists of 95% neutrons.

Astronomers have now tracked around 2000 neutron stars. “They are so small that they can only be detected, for example, with radio telescopes by their electromagnetic radiation,” explains Schwenk. So measuring neutron star radii is something of a challenge, which is where the theoretical nuclear physicists come in. Schwenk and his team are not astronomers, but their findings on the interactions among neutrons in atom nuclei can be transferred to the macrocosm. “We are particularly interested in exotic nuclei with a large excess of neutrons,” he adds. And the forces that act there also keep neutron stars in shape.

The number of neutrons of a chemical element is – unlike its number of protons – variable. Carbon, for instance, can contain between two and 16 neutrons, although almost 99 percent of the carbon atoms that occur on Earth contain six neutrons. We know that iron has 30 and lead 40 variants with different numbers of neutrons. However, most of these so-called isotopes are unstable, and decay radioactively. Until ten years ago, physicists could only calculate the energy, and thus the stability, of nuclei if they contained a maximum of 12 particles.

Calculations ended at carbon, which has six protons and six neutrons. But then new calculational methods coupled with improved computer power, plus an novel understanding of nuclear forces, gave this research field a big boost, explains Schwenk. Recently, an international collaboration that included theorists from Darmstadt managed for the first time to precisely calculate an atomic nucleus of 100 particles, tin-100, element 50 in the periodic table of a total of 118 chemical elements.

Unlike chemists, nuclear physicists are interested in the nuclear chart, which presents all the known isotopes graphically, rather than the periodic table. “Around 3000 isotopes have already been discovered,” explains Schwenk. “There are about 20 new ones every year, and about 4000 are still unknown.” In the region of extreme neutron-rich isotopes there are vast areas that haven’t been explored in the nuclear chart. The problem: these unstable nuclei are only created under extreme conditions in the Universe or with tremendous efforts in the laboratory.

The results of the artificial isotope synthesis are highly revealing for theoretical nuclear physicists like Schwenk: “We can use our colleagues’ measurements to check that we have understood the interaction between neutrons correctly, and whether we can use them to predict matter in astrophysics.” Only recently, an international consortium, which included the Darmstadt nuclear physicists, published a study on neutron-rich chrome isotopes.

Their production succeeded with a particle accelerator from the large research facility CERN near Geneva. The experimenters fired read more

a proton beam at a uranium target. The fission products included neutron-rich chrome isotopes, the mass of which could then be determined more precisely than ever before.

Schwenk emphasises that the method is so precise that it could be used to extrapolate the weight of a paper clip on a jumbo jet. Einstein’s formula E=mc2 can then be applied to calculate from the mass m the energy E that binds the neutrons and protons in the core.

The Darmstadt scientists had predicted this binding energy, which is closely related to the stability. A similar theoretical-experimental investigation into neutron-rich titanium isotopes was carried out by an international team in collaboration with Schwenk’s team in February.

In response to the question of whether experiment and theory matched up, Schwenk replied: “This still depends one where we are in the nuclear chart, whichis what makes it so exciting.” It worked well with titanium.

The isotopes examined here contained between 29 and 33 neutrons and 22 protons. Nuclei with this number of particles are almost spherical. With other elements, a deformation of the nucleus – for instance from the shape of a football to that of a rugby ball – has to be considered more strongly. Furthermore, we do not yet understand nuclear forces well enough, adds Schwenk. “Our calculations have a theoretical uncertainty that is like the uncertainty in an experiment.” There is another reason why the Darmstadt physicists won’t be suffering from a lack of work in the foreseeable future: “So far, we’ve only talked about neutrons and protons. However, for the fundamental understanding of nuclear structure, we want to go down another level.”

In other words, into the world of quarks and gluons. Quarks are the elementary particles from which protons and neutrons are made. Gluons (based on the word “to glue”) are what keeps them together into neutrons, protons, and other particles. Not only in the vast expanse of the Universe, but in the world of the tiniest particles, there is still much to discover. With the theoretical physicists in Darmstadt, both are starting to come together.