The field of nuclear physics is well into its second century. From its initial experiment bombarding a gold foil with alpha particles, experimental techniques have become more sophisticated to keep pace with the technology and innovation that has allowed more detailed probes of the nucleus. Of particular interest to the nuclear physicist is the structure of the nucleus, which can be understood through the measurements of its excited states. Excited states in nuclei originate from the complex coupling of the neutrons and protons, which can be interpreted as simple rearrangements of the constituent particles (single-particle structure), changes in the collective motion of the nucleus (e.g. vibration and rotation), and sometimes a mixture of these effects.

Nuclear models have traditionally been created using stable nuclei that are abundant and straightforward (i.e. non-radioactive) to measure. While they have been applied to the excited states of stable nuclei, neutron- or proton-rich (exotic) nuclei provide excellent testing grounds for validating these models. In particular, mapping the evolution of nuclear structure as protons and/or neutrons are removed is able to demonstrate where these models succeed and where the gaps in our understanding remain.

A better understanding of radioactive nuclei has wider implications, not only for nuclear physics, but for many other fields: the understanding of stellar evolution in astrophysics, the treatment of various diseases using radioactive decays, and understanding the processes which govern nuclear power generation, to name a few. The goal of the ISOLDE (Isotope Separation On-Line DEvice) facility at CERN [1] is to enable these studies of nuclei.

ISOLDE is a world-leading ISOL facility, able to produce radioactive ion beams of different species, energies, and yields. Following upgrades to its high-energy LINAC before LS2, ISOLDE is able to provide beams of sufficiently high energy to perform transfer reactions, where a single neutron or proton is transferred from the target to the beam particle (or vice versa) in a single step. This is a particularly clean probe of single-particle structure, and, when coupled with the exotic nuclei provided by ISOLDE, provides a fertile testing ground for understanding the evolution of single-particle structure.

The ISOLDE Solenoidal Spectrometer (ISS) is a device that specialises in measuring transfer reactions. Fashioned from a repurposed MRI magnet, the uniform magnetic field at its centre forces any charged reaction products to undergo helical orbits and intersect with the beam axis again. Carefully placed detectors are able to capture these reaction products, and the focusing of the magnetic field provides excellent solid angle coverage for the reactions. The inside of the experiment is shown in Figure 1.

Figure 1: The ISOLDE Solenoidal Spectrometer, an experimental setup at HIE-ISOLDE (High-Intensity and Energy project of ISOLDE) [2]

The ISS had its first experiments before LS2 in 2018 and was then fully commissioned in 2021 [3]. Since then, it has had multiple successful experimental campaigns with a range of applications. The 2024 campaign was composed of five experiments.

Exploring the Tin Isotopes

Two recent experiments explored the structure of exotic tin isotopes, focusing on how nuclear properties change as neutrons are added or removed. Tin is a key element in nuclear physics due to its "magic" number of 50 protons, which makes certain isotopes particularly stable. It uniquely has two doubly-magic nuclei, ¹⁰⁰Sn (Z = N = 50) and ¹³²Sn (Z = 50, N = 82), serving as benchmarks for nuclear structure models. Understanding their single-particle properties is crucial for testing the shell model and investigating how nuclear forces evolve across a wide range of isospin.

One experiment examined shell evolution by measuring how energy levels shift near these magic numbers, while the other focused on neutron-rich tin isotopes beyond ¹³²Sn to probe isospin asymmetry and its effects on nuclear stability. These studies provide valuable insights into fundamental nuclear interactions, with implications for astrophysics, nuclear technology, and the refinement of theoretical models.

For the neutron-deficient side, the closest we can get for (d,p) reactions at suitable beam energies, to date, is ¹⁰⁶Sn. A single-neutron transfer (d,p) reaction was performed on ¹⁰⁸Sn in 2024 at ISS, with the goal of mapping the shell evolution using data from a previous measurement of the ¹¹⁰Sn(d,p) reaction at ISS, and with the hopes of doing a future measurement on ¹⁰⁶Sn. Unfortunately, there were some issues with the primary target, so statistics were limited for this experiment. It is hoped that this can be run again in 2025 to get more data.

On the neutron-rich side, the ISOLDE facility was able to produce beams of ¹³²Sn, the doubly-magic nucleus, for a (d,p) reaction at ISS. This measurement had been previously performed at Oak Ridge in 2010, albeit at a beam energy (4.77 MeV/u) in the proximity of the Coulomb barrier. This limited the measurement to probing the low angular momentum f and p states. However, the measurement at ISS was carried out at 7.65 MeV/u, which is above the Coulomb barrier in the entrance and exit channels, offering order-of-magnitude increases in yields for the ℓ = 5 and ℓ = 6 transfers to the h_9/2 and i_13/2 orbitals, respectively.

The solenoidal-spectrometer approach with ISS also provides over a factor of two improvement in Q-value resolution over the previous attempt. Thus, for the first time, all the valence single-neutron orbitals outside the doubly-magic core (0h_9/2, 1f_7/2, 1f_5/2, 2p_3/2, 2p_1/2, 0i_13/2) have been measured. Knowledge of these orbitals allows the properties of large numbers of medium-mass nuclei to be calculated using nuclear shell models – before this result, the high-angular momentum orbitals had to be guessed. This represents a significant achievement and was only possible due to the excellent beams provided by the ISOLDE facility.

Figure 2: Comparison of preliminary ISS spectrum to that from the previous measurement [4].

Exploiting the Properties of Mirror Nuclei

Two experiments at ISS in 2024 focused on exploiting the unique properties of mirror nuclei—pairs of nuclei where the number of protons in one matches the number of neutrons in the other, and vice versa. Because the strong nuclear force acts identically on protons and neutrons, the excited energy states of these mirror pairs are nearly identical, with only slight differences arising due to the electromagnetic interaction.

This fundamental symmetry allows researchers to infer details about a nucleus by studying its mirror partner, especially in cases where direct measurements of one are difficult or impractical. By precisely measuring the properties of one nucleus, constraints can be placed on the structure and behavior of its counterpart, refining nuclear models and deepening our understanding of fundamental nuclear interactions. These experiments provide valuable insights into the forces shaping atomic nuclei and have important implications for both nuclear physics and astrophysical processes such as stellar nucleosynthesis.

The first experiment was the ⁶¹Zn(d,p) reaction to measure states in ⁶²Zn (N = 32, Z = 30), acting as the mirror of the astrophysical reaction ⁶¹Ga(p,γ) ⁶²Ge (N = 30, Z = 32). This reaction on gallium plays a crucial role in the understanding of Type-I X-ray bursts in neutron stars, but the direct study of ⁶²Ge is not presently possible with transfer reactions. Therefore, the ISS populated states in the mirror nucleus, and analysis is ongoing.

The second was the ³⁸K(d,p) reaction, looking at the mirror energy differences (MEDs) between ³⁹K and its mirror, ³⁹Ca. It has been conjectured that the root cause for the large MEDs in the A = 39 mirror nuclei occurs due to a substantial increase in the single-particle aspects of wave functions as higher spins are reached. As no experimental data were available, this system was measured for the first time at ISOLDE in 2024, and the angular dependence of states has been extracted, forecasting a positive outcome for the extraction of the single-neutron overlaps.

Exploration of Different Reaction Channels

The final experiment of the 2024 campaign was an inelastic scattering reaction, (d,d’), where ejectiles are focused downstream of the target compared to the upstream focusing in (d,p) reactions. Therefore, the standard setup in ISS had to be physically rotated 180˚ to be able to place detectors to measure these particles.

The goal of this inelastic-scattering measurement was to measure octupole collectivity in ¹⁴⁶Ce, with the hopes of measuring more collectivity in this region in future experiments. While there were some issues with the beam (we ended up measuring ¹⁴⁴Ba instead) and gathering statistics, this experiment was an excellent proof-of-principle for other proposed experiments where ejectiles are forward-focused. Analysis for this is ongoing with a complementary reaction of the same beam in the Miniball setup that measured Coulomb excitation.

Looking to the Future

As ISS prepares for its 2025 campaign, the final one before LS3, several exciting opportunities lie ahead. One key goal is to measure a (d,pf) reaction, where the transfer of a single neutron induces fission in the resulting nucleus. If successful, this experiment could offer a direct measurement of the fission barrier, providing valuable insights into nuclear stability and reaction dynamics.

Alongside a number of proposed (d,p) measurements at ISS, it is hoped that this year will also mark the first measurement of (t,p) reactions using a tritiated target.

References

[1] ISOLDE facility website

[2] J. M. Ordan, The ISOLDE Solenoidal Spectrometer (ISS), CDS 2800900, 2022

[3] D. Sharp, ISOLDE's Solenoidal Spectrometer (ISS): a new tool for studying exotic nuclei, CERN EP newsletter, 2022

[4] Jones, K., Adekola, A., Bardayan, D. et al. The magic nature of ¹³²Sn explored through the single-particle states of ¹³³Sn. Nature 465, 454–457 (2010).