Scientists have showcased a novel technique to utilize high-energy particle collisions at the Relativistic Heavy Ion Collider (RHIC) to uncover intricate details about the forms of atomic nuclei. This new approach complements existing lower energy methods used to ascertain nuclear structures and enhances researchers’ comprehension of the nuclei that constitute most of the observable universe.
Scientists have showcased a novel technique to utilize high-energy particle collisions at the Relativistic Heavy Ion Collider (RHIC) — a U.S. Department of Energy (DOE) Office of Science user facility for nuclear physics located at DOE’s Brookhaven National Laboratory — to uncover intricate details about the forms of atomic nuclei. This new approach, detailed in a recent paper published in Nature, serves as a complement to lower energy methods for defining nuclear structures. It promises to enrich researchers’ knowledge of the nuclei that comprise the majority of visible matter.
“In this new measurement, we not only capture the overall shape of the nucleus — whether it’s elongated like a football or compressed like a tangerine — but also the nuanced triaxiality, which describes the relative differences among its three principal axes, depicting forms that fall between the ‘football’ and ‘tangerine’,” explained Jiangyong Jia, a professor at Stony Brook University (SBU) and a co-author on the STAR Collaboration publication.
Understanding the shapes of nuclei is significant for various physics inquiries, including predicting which atoms are more prone to splitting during nuclear fission, how heavy atomic elements arise from neutron star collisions, and which nuclei may serve as indicators for uncovering exotic particle decay phenomena. Improved insights into nuclear shapes will also enhance scientists’ grasp of the initial conditions present in the particle soup akin to the early universe, generated by RHIC’s high-energy particle collisions. This technique can be utilized to analyze additional data from RHIC as well as data collected from nuclear interactions at Europe’s Large Hadron Collider (LHC). It will also play a role in future studies of nuclei at the Electron-Ion Collider, a nuclear physics facility currently under design at Brookhaven Lab.
Ultimately, with 99.9% of the visible matter comprising people, stars, and planets stemming from the nuclei at the core of atoms, comprehending these nuclear components is fundamental to understanding our existence.
“The most effective way to affirm the validity of the nuclear physics insights gained at RHIC is to demonstrate their application in other domains,” Jia stated. “Now that we’ve established a robust method for imaging nuclear structures, a plethora of applications awaits.”
From long exposure to freeze-frame snapshots
For many years, researchers relied on low-energy experiments to deduce nuclear forms, typically by exciting the nuclei and observing photons — light particles — released as the nuclei revert to their ground state. This traditional method looked at the general spatial distribution of protons within the nucleus but was limited to longer time scales.
“In low-energy experiments, it’s akin to capturing a long-exposure photograph,” remarked Chun Shen, a theorist at Wayne State University whose calculations were part of the new analysis.
Due to the extended exposure, low-energy techniques often miss the subtle variations in how protons are arranged in the nucleus over very quick time scales. Furthermore, since most of these methods rely on electromagnetic interactions, they are unable to directly “see” the uncharged neutrons contained within the nucleus.
“You only obtain an average of the overall system,” commented Dean Lee, a low-energy theorist at the Facility for Rare Isotope Beams, a DOE Office of Science user facility at Michigan State University. While Lee and Shen are not co-authors of this study, they, alongside other theorists, contributed to the development of this innovative nuclear imaging technique.
“The high-energy imaging technique, which captures numerous freeze-frame pictures revealing details about both protons and neutrons, operates at speeds that are exponentially faster,” shared Chunjian Zhang, a former SBU postdoc and now a junior faculty member at Fudan University, who co-led the STAR analysis.
Significantly, the images generated by RHIC’s STAR detector originate from varied collision events.
“Reimaging the same nuclei isn’t feasible since they are destroyed during the collision,” Jia pointed out. However, by examining the entire set of images from multiple collisions, researchers can reconstruct the nuanced features of the 3D structure of the disrupted nuclei.
As Lee elaborated, “In each collision, you’re essentially freezing time momentarily to observe the arrangement of all protons and neutrons. Each attempt yields a different distribution owing to the quantum properties of atomic nuclei. Thus, the high-energy method captures an immense amount of information and complexity that we typically don’t explore in low-energy experiments.”
Reconstructing shapes from debris
How does STAR observe this complexity if the nuclei get obliterated? By monitoring the trajectories and velocities of particles emitted from direct, head-on nuclear collisions.
As the STAR researchers note in their Nature paper, “In a twist of irony, this effectively demonstrates the renowned physicist Richard Feynman’s analogy of the seemingly impossible task of ‘figuring out a pocket watch by smashing two together and observing the flying debris.'”
From extensive experiments conducted at RHIC, researchers have found that high-energy nuclear collisions break apart protons and neutrons from the nuclei, freeing their constituent components, quarks and gluons. The shape and expansion of each heated blob of this melted nuclear substance — referred to as quark-gluon plasma (QGP) — is defined by the shape of the colliding nuclei. The configuration and dimensions of each QGP blob directly impact the pressure gradients within the plasma, influencing the collective flow and momentum of particles released as the QGP transitions back to its cooler state.
The STAR researchers deduced that they could “reverse engineer” this relationship to glean insights into nuclear structures. They investigated the flow and momentum of particles emitted from collisions and compared these results with hydrodynamic expansion models for various QGP shapes to ascertain the shapes of the nuclei that collided.
To validate their method, they contrasted central collisions of gold nuclei — which are assumed, based on low-energy studies, to be nearly spherical — with central collisions of uranium nuclei, known for their elongated, football-like shape. Since gold nuclei are almost spherical, collision-to-collision variations in the emitted particles’ flow patterns should be minimal.
“Central collisions of gold nuclei generate a circular, consistently sized QGP that expands uniformly in all directions,” explained Shengli Huang, a research scientist at SBU who co-led the STAR analysis. “In contrast, oblong uranium nuclei can collide in various orientations, producing QGP droplets of differing shapes and sizes,” he noted. Thus, the researchers anticipated that central collisions of uranium nuclei would show significantly greater variability in their flow patterns.
This prediction held true in their observations.
By analyzing the differences between uranium-uranium and gold-gold collisions — and aligning those findings with hydrodynamic models that have previously accurately depicted other characteristics of the QGP — the scientists managed to deduce a quantitative description of the uranium nucleus’s shape. Additionally, this analysis yielded a first quantification of the relative lengths of the Three main axes of the elongated uranium nucleus.
Computing tools
Generating accurate predictions from different hydrodynamic models, such as Shen’s model, presented notable computational hurdles. This endeavor took over a year, with Zhang executing calculations on the Open Science Grid. He utilized over 20 million CPU hours to create more than ten million collision events from the hydrodynamic models, which were then aligned with the experimental data.
“Numerous characteristics in the STAR data reveal significant differences in shape between uranium and gold nuclei, but our comparisons of computational data with models have certainly refined our ability to quantify these nuclear shapes,” Zhang stated.
While the goal of this study was to introduce a new nuclear imaging technique, the data also uncovered fresh insights regarding uranium nuclei. Instead of detecting distortion in merely one principal axis that leads to “prolate” elongation, researchers identified variations in all three axes, indicating that uranium nuclei are more intricate than previously believed.
Expanded impacts
The new method enhances physicists’ comprehension of the initial conditions in heavy ion collisions that produce quark-gluon plasma (QGP) at both RHIC and the LHC. Nuclear structures obtained from low-energy experiments were crucial for linking these initial conditions with hydrodynamic flow patterns, confirming that the QGP generated in such collisions behaves like a nearly perfect liquid. Now, scientists can apply this new method to validate low-energy approaches using familiar nuclei such as uranium, which will further decrease uncertainties regarding initial state conditions and improve the understanding of QGP characteristics.
This technique can also be utilized to ascertain the shapes of other nuclei, particularly those for which low-energy experiments have yielded limited insights. For example, it can be applied to isobar nuclei—nuclei that contain the same total number of protons and neutrons (nucleons) but in different amounts. Such pairs are relevant when two neutrons in a higher-neutron-number “parent” nucleus convert into protons through a nuclear weak decay process, resulting in a lower-neutron-number “daughter” nucleus. Understanding the shape differences between the parent and daughter nuclei could help minimize model uncertainties in experiments looking for a rare form of decay called neutrinoless double beta decay.
“This research has many interdisciplinary elements,” Jia explained. “Nuclear physics encompasses various subfields, each typically utilizing its own methodologies—both theoretical and experimental. However, due to these findings, the global low-energy nuclear structure and nuclear reaction communities have taken notice. Several workshops, meetings, and conferences have been organized to investigate the links between the high-energy and low-energy spheres of nuclear physics, fostering a better mutual understanding,” he noted.
This research was made possible with support from the DOE Office of Science, the U.S. National Science Foundation (NSF), and numerous international agencies and organizations mentioned in the scientific paper. In addition to leveraging the Open Science Grid, backed by the NSF, the researchers also utilized computational facilities at the Scientific Data and Computing Center at Brookhaven Lab, and the National Energy Research Scientific Computing Center (NERSC), another user facility of the DOE Office of Science at DOE’s Lawrence Berkeley National Laboratory.
