The elements present on Earth and their relative abundances are important observables in fundamental physics. The nuclei of the elements that populate the periodic table were produced in different phases. The lightest ones (hydrogen, deuterium, helium, and lithium) were created during what is known as Big Bang Nucleosynthesis, which took place within a few minutes of the Big Bang. In a process of expansion and cooling, this led to the transition from elementary degrees of freedom—quarks and gluons—to more complex ones, such as nucleons, and by combining them, to light nuclei.

The subsequent phase of synthesis, which produced elements up to iron, takes place inside stellar cores. Here, thermodynamic conditions allow for densities and energies high enough to overcome the Coulomb barrier and give rise to the fusion process. This process is energetically favorable up to iron; after this element, however, the binding energy tends to decrease with atomic number, and the fusion process is no longer spontaneous.

Therefore, the synthesis of elements beyond iron occurs through different processes, based on neutron capture by heavy nuclei. When a neutron is added to an atomic nucleus, there are two different possible outcomes. If the beta decay of the resulting nucleus is less probable than a further neutron capture, the element will tend to form a heavier isotope by capturing another neutron, but its electromagnetic properties will remain unchanged. If, on the contrary, the nucleus undergoes beta decay, one of the neutrons will transform into a proton, increasing the atomic number and changing the starting element into the next one on the periodic table.

Nuclear physics thus plays a fundamental role in studying the relative abundances of elements in the universe. An accurate measurement of the cross-sections for fusion processes, neutron capture, and the half-lives for beta decay is strategic for evaluating the competition between possible processes and estimating which one will take place.

To date, measurements of cross-sections and half-lives have been conducted with neutral elements. However, in a stellar environment, elements appear in their ionized form—that is, with the bare nucleus no longer surrounded by an electron cloud. To produce realistic models of the phenomena that occur in a stellar environment, it is necessary to account for the element’s state of ionization. It has been predicted—and observed in experiments with storage rings—that the half-lives for beta decay change significantly if the element in question is ionized. The absence of electrons in the atomic orbitals widens the phase space accessible to the electron from the neutron’s beta decay. The electron no longer has to necessarily reach the continuum—that is, leave the atomic system—but can occupy the atom’s free orbitals (Takahashi et al. 1987, Phys Rev C36 (1987) 1522; Takahashi and Yokoi, Nucl. Phys. A404 (1983) 578). At the same time, the measurement of the cross-sections of fusion processes seems to be influenced by electron screening, so the absence of the electron cloud could alter the electromagnetic potential that is established between the two nuclei involved in the fusion process.

In light of the previous considerations, the project aims to outline an experimental campaign for measuring fusion processes and beta decay half-lives in an ionized environment. The latter can be created using a high-intensity laser that hits a target composed of the isotope to be analyzed. This produces immediate ionization, leading to the formation of a plasma. The characteristics of this plasma can be controlled by appropriately calibrating the laser intensity and the properties of the target to reproduce the stellar environment as accurately as possible.

To date, there are existing measurements of fusion process cross-sections with neutral elements, and only one measurement in a plasma environment (Lattuada et al., Phys. Rev. C 93, 045808 (2016)). While this latter measurement produced a systematically lower reaction rate compared to the others (black markers in the following figure), it is still compatible within experimental uncertainties. Therefore, a measurement campaign is needed to collect enough data to significantly estimate the presence of an effect on the fusion process caused by electron screening.

Regarding the study of changes in beta decay half-lives in plasma, initial observations have been made with storage rings, for example, for 163Dy66+ (Jung et al., First observation of bound-state β− decay, Phys. Rev. Lett. 69, 1992), for 187Re75+ (F. Bosch et al., Observation of Bound-State β− Decay of Fully Ionized $187\text{Re}$: $187\text{Re}$–$187\text{Os}$ Cosmochronometry, Phys. Rev. Lett. 77, 1996), and for 140Pr58+ (Y. Litvinov et al., Measurement of the $\beta +$ and orbital electron capture decay rates in fully ionized, hydrogen-like and helium-like $140\text{Pr}$ Ions, Phys. Rev. Lett. 99, 2007, 262501). These studies confirmed the onset of radioactive behavior in the first case (Dy is stable in its neutral form) and the lowering of the half-life by significant factors (9 orders of magnitude for Re) in the other two.

To extend these previous measurements by estimating the change in beta decay half-lives in a plasma environment, the National Institute for Nuclear Physics is launching an experimental program with the PANDORA experiment. This project aims to measure the beta decay of astrophysically relevant isotopes in a plasma produced using the Electron Cyclotron Resonance (ECR) method. The apparatus is under construction, and the first data are expected by the end of 2026.

This project, planned in collaboration with the PANDORA experimental group, aims to extend PANDORA’s scientific program. In particular, the project seeks to expand the thermodynamic domain of the plasma produced by the ECR method by performing measurements in a laser-produced plasma. While the ion bath in the former remains cold—with ion temperatures on the order of 1 eV—and cannot be expected to achieve Full Thermodynamical Equilibrium, the higher energy transmitted to the target by the laser in the latter case can lead to the thermalization of the ionic system and the attainment of temperatures that can result in the population of excited nuclear states. This scenario would allow for a more accurate study of beta decay variations in an ionized environment, decoupling the effects due to the atomic system from those of the nucleus.

Study of Deuterium Fusion Processes in a Laser-Produced Plasma

Our first measurement campaign will be conducted at the Frascati National Laboratories of the National Institute for Nuclear Physics, using the FLAME laser, which operates at a power of 300 TW.

This laser will be directed at a gaseous deuterium target maintained under controlled thermodynamic conditions. In particular, at specific pressure and temperature configurations, the D2​ gas forms clusters. This setup maximizes the absorption of energy transmitted by the laser, leading to a Coulomb repulsion regime. This repulsion is induced by the complete ionization of the deuterium atoms, which lose their electrons and, therefore, experience immediate electrostatic repulsion from other ions. This regime accelerates the ions, allowing them to overcome the Gamow barrier and initiate fusion processes.

To identify an optimized detection system for reconstructing the fusion processes, several preliminary steps are necessary. These will form the core activities for the next three years:

• Characterizing the gaseous target through preliminary measurements at FLAME.

• Designing a detection system for identifying ions and neutrons.

• Estimating the effect of the electromagnetic pulse on the experimental apparatus and identifying suitable instrumentation for operating in a laser environment.

• Characterizing the detectors.

Study of Beta Decays in a Laser-Produced Plasma

Defining a scientific program to measure beta decay half-lives in a laser-produced plasma is a new initiative in nuclear physics and requires a preliminary feasibility study.

First, we need to set up a simulation-based study to characterize the laser-produced plasma in terms of its established thermodynamic regimes, the duration of the ionized state, and its reproducibility. Second, based on the study of measurement apparatuses suitable for operating in a laser environment (as described in the previous section), we will identify potential experimental challenges. We will then explore possible configurations that would allow us to measure the decay products needed to identify the beta process.