Have you ever wondered how long it took our sun to form in its stellar nursery? An international collaboration of scientists is now closer to an answer. They succeeded in the measurement of the bound-state beta decay of fully-ionized thallium (²⁰⁵Tl⁸¹⁺) ions at the Experimental Storage Ring (ESR) of GSI/FAIR.

This measurement has profound effects on the production of radioactive lead (²⁰⁵Pb) in asymptotic giant branch (AGB) stars and can be used to help determine the sun’s formation time. The results have been published in the journal Nature.

Current calculations estimate that the formation of our sun from the progenitor molecular cloud took about a few tens of million years. Scientists derive this number from long-lived radionuclides produced just before the sun’s formation by what is called the astrophysical s-process.

The s-process had operated in the solar neighborhood in asymptotic giant branch (AGB) stars—intermediate mass stars at the end of their burning cycles. The radionuclides, all long decayed since the birth of the sun 4.6 billion years ago, left their imprints as small excess abundances of the decay products in meteorites where they can now be detected.

The ideal candidate is a radionuclide that is purely produced by the s-process and does not have pollutions from other nucleosynthesis processes. The “s-only” nucleus ²⁰⁵Pb is the sole candidate that fulfills these properties.

On Earth, it is atomic ²⁰⁵Pb that decays to ²⁰⁵Tl by converting one of its protons and an atomic electron into a neutron and an electron neutrino. The energy difference between ²⁰⁵Pb and its daughter ²⁰⁵Tl is so tiny that the larger binding energies of the electrons in ²⁰⁵Pb (with charge Z=82 compared to only 81 electrons in ²⁰⁵Tl) tip the scale.

In other words, if all electrons are removed, the role of daughter and mother in the decay is inverted, and ²⁰⁵Tl undergoes a beta minus decay to ²⁰⁵Pb. This is what happens in AGB stars where the temperatures of a few 100 million Kelvin are sufficient to fully ionize the atoms. The amount of ²⁰⁵Pb being produced in AGB stars depends crucially on the rate at which ²⁰⁵Tl decays to ²⁰⁵Pb. But this decay cannot be measured under normal laboratory conditions because there ²⁰⁵Tl is stable.

The decay of ²⁰⁵Tl is only energetically possible if the produced electron is captured into one of the bound atomic orbits in ²⁰⁵Pb. This is an exceptionally rare decay mode known as bound-state beta decay. Moreover, the nuclear decay leads to an excited state in ²⁰⁵Pb which is situated only by a minuscule 2.3 kiloelectronvolt above the ground state but is strongly favored over the decay to the ground state.

The ²⁰⁵Tl–²⁰⁵Pb pair can be imagined as a stellar seesaw model, as both decay directions are possible, and the winner depends on the stellar environment conditions of temperature and (electron) density—and on the nuclear transition strength which was the great unknown in this stellar competition.

This unknown has now been unveiled in an ingenious experiment conducted by an international team of scientists coming from 37 institutions representing twelve countries. Bound-state beta decay is only measurable if the decaying nucleus is stripped of all electrons and is kept under these extraordinary conditions for several hours. Worldwide this is only possible at the GSI/FAIR heavy-ion Experimental Storage Ring (ESR) combined with the fragment separator (FRS).

“The measurement of ²⁰⁵Tl⁸¹⁺ had been proposed in the 1980s, but it has taken decades of accelerator development and the hard work of many colleagues to bring it to fruition,” says Professor Yury Litvinov of GSI/FAIR, spokesperson of the experiment. “A plethora of groundbreaking techniques had to be developed to achieve the required conditions for a successful experiment, like production of bare ²⁰⁵Tl in a nuclear reaction, its separation in the FRS and accumulation, cooling, storage and monitoring in the ESR.”

“Knowing the transition strength, we can now accurately calculate the rates at which the seesaw pair ²⁰⁵Tl–²⁰⁵Pb operates at the conditions found in AGB stars,” says Dr. Riccardo Mancino, who performed the calculations as a post-doctoral researcher at the Technical University of Darmstadt and GSI/FAIR.

The ²⁰⁵Pb production yield in AGB stars has been derived by researchers from the Konkoly Observatory in Budapest (Hungary), the INAF Osservatorio d’Abruzzo (Italy), and the University of Hull (UK), implementing the new ²⁰⁵Tl/²⁰⁵Pb stellar decay rates in their state-of-the-art AGB astrophysical models.

“The new decay rate allows us to predict with confidence how much ²⁰⁵Pb is produced in AGB stars and finds its way into the gas cloud which formed our sun,” explains Dr. Maria Lugaro, researcher at Konkoly Observatory. “By comparing with the amount of ²⁰⁵Pb we currently infer from meteorites, the new result gives a time interval for the formation of the sun from the progenitor molecular cloud of 10 to 20 million years that is consistent with other radioactive species produced by the slow neutron capture process.”

“Our result highlights how groundbreaking experimental facilities, collaboration across many research groups, and a lot of hard work can help us understand the processes in the cores of stars. With our new experimental result, we can uncover how long it took our sun to form 4.6 billion years ago,” says Guy Leckenby, doctoral student from TRIUMF and first author of the publication.

The measured bound-state beta decay half-life is essential to analyzing the accumulation of ²⁰⁵Pb in the interstellar medium. However, other nuclear reactions are also important, including the neutron capture rate on ²⁰⁵Pb for which an experiment is planned utilizing the surrogate reaction method in the ESR. These results clearly illustrate the unique possibilities offered by the heavy-ion storage rings at GSI/FAIR allowing scientists to bring the universe to the lab.

The work is dedicated to deceased colleagues Fritz Bosch, Roberto Gallino, Hans Geissel, Paul Kienle, Fritz Nolden, and Gerald J. Wasserburg, who supported this research for many years.