A new way of calculating the size of atomic nuclei has helped solve a longstanding problem in nuclear theory. Previously, all so-called ab initio approaches to this problem “under-predicted” the sizes of nuclear radii, but the new method produces answers in line with experimental results for the radii of elements with atomic numbers from 2 to 58. Among other possibilities, the improved method should enable astrophysicists to make more precise calculations of how stars convert helium into heavier elements via nuclear fusion, which the researchers who developed the method describe as a “holy grail” of nuclear astrophysics.
To study atomic nuclei, physicists often use ab initio calculations. These calculations begin with the nucleons – neutrons and protons – that make up the nucleus, and incorporate the strong force, which is one of the four known fundamental forces. The strong force is responsible for binding protons and neutrons together, and it is also responsible for “gluing” together the quarks that make up protons, neutrons and other baryons. At very short distances, the strong force is attractive and much stronger than the electromagnetic force, which works to push protons and other like-charged particles apart.
While ab initio calculations are excellent at describing the properties of atomic nuclei and how their structure affects their interactions when the number of nucleons is small, they fail when the number of nucleons gets too high or when the nucleons’ interactions become too complex. In particular, a class of ab initio calculations known as quantum Monte Carlo simulations, which use stochastic (random) processes to calculate desired quantities, suffers from something called the sign problem. This problem appears when positive and negative statistical weights of a certain configuration of components start to cancel each other out. The result is a huge increase in statistical errors that severely limits the size of the systems physicists can study.
Simple method
Researchers at the University of Bonn, Germany, together with an international team of collaborators at other institutions in Germany, the US, Korea, China, France, Georgia and Turkey, have now solved this problem using an approach called wavefunction matching. “The method is simple,” says Ulf-G Meißner, who co-led the team together with Serdar Elhatisari. “Below some radius R, we substitute the wavefunction of a complex interaction [with] one that is simpler (and free from ‘sign oscillations’), assuming that such a simple interaction does exist.”
This transformation is done in a way that preserves all the important properties of the original, more realistic interaction, he adds. Any errors introduced into the new wavefunction can be dealt with using a standard method known as perturbation theory.
The researchers applied their new technique to quantum Monte Carlo simulations for light- and medium-mass nuclei, neutron matter and nuclear matter and found that they could predict the nuclear radii of elements with atomic numbers ranging from 2 to 58 (hydrogen, with atomic number 1, is a special case). Their results agree with experimental measurements in the existing literature.
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The new approach will allow physicists to make precision calculations in nuclear structure and dynamics, Meißner says. “One much sought after issue is in determining the structure and the precise locations of the neutron and proton drip lines (the so-called edges of stability which describe the maximum number of nucleons an isotope of each element can contain),” he explains. “Another is in reaction theory for the calculation of radiative alpha-capture on 12C at the ‘Gamov peak’ (astrophysical energies), which is the ‘holy grail’ of nuclear astrophysics.”
The researchers now plan to test their framework on structure and reaction calculations. “We will eventually refine the values of the three-nucleon forces in our calculations if disagreements appear,” Meißner tells Physics World.
The team reports its work in Nature.
