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DOE OSTI2022

Rare Higgs Processes at CMS and Precision Timing Detector Studies for HL-LHC CMS Upgrade

This thesis describes the search for two rare Higgs processes. The first analysis describes the CMS Run 2 search for $H$ $\rightarrow$ $\mu$$\mu$ decays, with 137.3 fb$^{-1}$ of data at $\sqrt{s}$ = 13 TeV. The analysis targeted four different Higgs production modes: the gluon fusion (ggH), the vector boson fusion (VBF), the Higgs-strahlung process (VH), and the production in association with a pair of top quarks (ttH). Each category used a dedicated machine learning based classifier to separate the signal from the background processes. A combined fit from all these categories saw a slight excess in the data corresponding to 3.0 standard deviations at $M$$_{H}$ = 125.38 GeV, and gave the first evidence for the Higgs boson decay to second-generation fermions. The best-fit signal strength and the corresponding 68% CL interval was found to be +0.17?????? = 1.19 $_{-0.39}^{+0.41}$ (stat)$_{-0.16}^{+0.17}$(syst) at $M$$_{H}$ = 125.38 GeV. The second analysis describes the CMS Run 2 search for 𝐻𝐻 → 𝑏𝑏𝑏𝑏 with highly boosted Higgs bosons. This analysis used a dedicated jet identification algorithm based on graph neural networks (ParticleNet) to identify boosted H→ bb jets. This search targeted the gluon fusion and the vector boson fusion HH production modes, and put constraints on the allowed values of the various Higgs couplings as: 𝜅𝜆 ∈ [−9.9, 16.9] when 𝜅𝑉 = 1, 𝜅2𝑉 = 1; 𝜅𝑉 ∈ [−1.17, −0.79] ∪ [0.81, 1.18] when 𝜅𝜆 = 1, 𝜅2𝑉 = 1; 𝜅2𝑉 ∈ [0.62, 1.41] when 𝜅𝜆 = 1, 𝜅𝑉 = 1. A scenario with 𝜅2𝑉 = 0 was excluded with a significance of 6.3 standard deviations for the first time, when other H couplings are fixed to their SM values. The combined observed (expected) 95% upper limit on the HH production cross section was found to be 9.9 (5.1) × SM. Finally, this thesis also discusses the planned MIP Timing Detector (MTD) upgrade for CMS at the HL-LHC. The MTD will be a time-of-flight (TOF) detector, designed to provide a precision timing information for charged particles using SiPMs + LYSO scintillating crystals, with a time resolution of ∼30 ps. This thesis describes several R&D tests that have been performed for characterizing the sensor properties (time resolution, light yield, etc.) and optimizing the sensor design geometry. This thesis also contains a description of mock test setups for cooling the sensors, since it is known to be an effective way of mitigating the increased dark current rates in the sensors due to radiation damage.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

Charge Symmetry Violation Quark Distributions Via Precise Measurement of p+/p- Rations in Semi-Inclusive Deep Inelastic Scattering

Charge symmetry in the nucleon parton distributions assumes the distribution of quarks in the proton is related to those in the neutron. Indirect experimental evidence constrains Charge Symmetry Violation (CSV) to be less than 9%. In Quantum Chromo-Dynamics (QCD), charge symmetry is broken by the mass difference between the up and down quarks. CSV in the valence region can be extracted from precision measurements of the cross section ratio of charged pion production in semi-inclusive deep inelastic scattering (SIDIS) from deuterium. Such measurements were proposed and carried out in experiment E12-09-002 at Jefferson Lab. The experiment was conducted in Hall C from fall 2018 to spring 2019 using the upgraded 10.6 GeV incident electron beam. In this SIDIS experiment, charged pions are detected in coincidence with scattered electrons covering the four-momentum transfer of the virtual photon Q2 from 4 to 5.5 GeV2, the Bjorken variable x for 0.35-0.65, and the fraction of energy transfer carried by the outgoing pion z from 0.4-0.7.

Jia, Shuo↗
DOE OSTI2024

Towards Precision Photometric Type ia Supernova Cosmology With Machine Learning

The revolutionary discovery of dark energy and accelerating cosmic expansion was made with just 42 type Ia supernovae (SNe Ia) in 1999. Since then, large synoptic surveys, e.g., Dark Energy Survey (DES), have observed thousands more SNe Ia and the upcoming Rubin Legacy Survey of Space and Time (LSST) and Roman Space Telescope promise to deliver millions in the next decade. This unprecedented data volume can produce the required precision to unambiguously test concordance cosmology which could represent a monumental shift in our understanding of dark energy and its role in cosmic history. However, extracting a pure SN Ia sample with accurate redshifts for such a large dataset will be a challenge. Specifically, spectroscopic classification will not be possible for the vast majority of discovered objects, and only ~25% will have spectroscopic redshifts. This thesis presents a series of observational and methodological studies designed to address the questions associated with this new era of photometric SN Ia cosmology. First, we present a machine learning method for photometric classification of SNe, Supernova Classification with a COnvolutional Neural Network (SCONE). Photometric classification enables SNe with no spectroscopic information to be confidently categorized, and is a critical component of current and future analysis pipelines. SCONE achieves >99% accuracy distinguishing simulated SNe Ia from non-Ia SNe, and has been integrated into DES, LSST, and Roman analysis pipelines. We also demonstrate the efficacy of SCONE on early-time photometric classification, which will be vital for optimal allocation of spectroscopic resources. We show that SCONE can distinguish between 6 SN types with 75% accuracy on the night of initial discovery, comparable to results in the literature for full-phase SNe. Next, we study current methods for estimating SN Ia redshifts and propose a machine learning alternative that uses SN photometry alone to extract redshift information. Most SNe Ia inherit redshift information from their host galaxy, but the process of matching SNe to the correct host galaxy can be challenging. We systematically analyze the impact of incorrect redshifts from host galaxy mismatch on 5 years of DES SN data, and conclude that improved host matching or redshift estimation methods can reduce our systematic errors by ~10%. In response to this finding, we present a SN photometry-only method for estimating redshifts independent of host galaxy information, Photo-zSNthesis. We show that Photo-zSNthesis redshift estimates are accurate to within 2% across the full redshift range of LSST, a first in the literature. Finally, we focus on the robustness of machine learning (ML) algorithms for real-world and scientific applications. ML models generalize poorly beyond their training set and often experience severe performance degradation when deployed on new data. We demonstrate a general method for improving robustness that achieves new state-of-the-art results on astronomical object classification, wildlife identification, and tumor detection.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

An Integrated Electrochemical Approach to the Precision Synthesis of Sustainable Catalyst Materials

There is a pressing need to replace critical materials such as platinum group elements (PGE) in applications related to energy. This work responds to the need for fundamental principles of materials design to replace these metals by addressing a gap in the understanding of how to precisely control the surface structure of nanoscale materials. Electrochemical nanomaterials synthesis, such as techniques developed in the PI’s research group, expands the toolbox of available synthetic handles to include both electrochemical and chemical parameters, providing access to control over synthetic conditions in ways that are not possible in purely chemical nanoparticle growth. However, electrochemical materials synthesis (electrodeposition) is inherently serial, limiting throughput and preventing widespread implementation. Initial efforts in the short period of this award resulted in an innovative, high throughput, parallel approach to synthetic discovery for the electrodeposition of shaped metal nanoparticles that overcomes this limitation. Looking ahead, this work establishes an important capability that will enable researchers to push boundaries in the shape control of nanoparticles composed of non-PGE such as copper, iron, nickel, or cobalt.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Precision Measurements of the Neutron Magnetic Form Factor to High Momentum Transfer using Durand’s Method

Protons and neutrons, collectively known as nucleons, along with electrons, constitute the fundamental building blocks of the visible universe. Understanding their internal structure is crucial for addressing key scientific questions about our origin and existence. Elastic electron-nucleon scattering provides insights into the spatial distributions of charge and current within nucleons through their electromagnetic form factors. Accurate knowledge of these form factors over a broad range of Q2, the squared four-momentum transfer in the scattering process, reveals details about the nucleon's internal structure. However, high-Q2 data of the nucleon electromagnetic form factor is scarce due to the challenges associated with such measurements. This thesis reports preliminary results from high-precision measurements of the neutron magnetic form factor (GMn) to unprecedented Q2 using Durand's method, also known as the "ratio" method. Systematic errors are greatly reduced by ext

Datta, Provakar↗
DOE OSTI2024

Precise Measurement of the Neutron Magnetic Form Factor Using Super-BigBite Spectrometer at Jefferson Lab

The GMn experiment (E12-09-019) was conducted at Jefferson Laboratory from late 2021 into early 2022. The goal was to make high-precision measurement of the neutron’s magnetic form factor (GMn) at multiple kinematic points, including Q2 = 3.5, 4.5, 6.5, 8.5, 10, 12, 13.5, 16, and 18 (GeV/c)2. Limited data exist for GMn in the region up to about Q2 = 10 (GeV/c)2, with existing data having large systematic uncertainty. In this experiment, the ratio method was employed to reduce systematic uncertainty by measuring the ratio of neutron and proton yields. The experiment took place at Jefferson Laboratory in Hall A, where the BigBite spectrometer was used to detect the scattered electrons, while the HCal in the SuperBigbite spectrometer was used to detect both neutrons and protons. The protons were deflected slightly upwards with the use of a large-aperture dipole magnet named BigBen, allowing for enhanced particle identification. Extraction of GMn requires taking the ratio of proton and neutron yields. Analysis efforts are still currently underway to refine corrections to the data, including detector efficiencies, radiative corrections, neutron and proton mass identification, and charge exchange.

Lashley-Colthirst, Nathaniel↗
DOE OSTI2025

Revisiting Gauge Ambiguities for DUNE Precision

The de Forest prescription for handling off-shell initial states in the impulse approximation for lepton-nucleus scattering breaks gauge invariance. We discuss existing methods to address this problem and handle the form factor scale ambiguity. We demonstrate that the irreducible differences between the prescriptions are significant compared to the precision expected of next-generation accelerator neutrino experiments. A novel approach directly using the off-shell currents is proposed as a systematically improvable alternative.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Jefferson Lab High Precision Proton Radius Measurement Experiment: PRad

Proton is not a point-like particle; it has a finite size and an internal structure. The proton charge radius is usually measured through two different methods: using spectroscopy of hydrogen atoms, or through electron-proton (e - p) elastic scattering at low momentum transfer. In 2010, Phol et al [1] published a new measurement for proton charge radius obtained using the spectroscopy method from muonic hydrogen atoms. An ordinary hydrogen (H) atom is a bound state of an electron orbiting a proton. Likewise, a muonic hydrogen atom has a muon orbiting a proton. Since a muon has 200 times more mass than an electron, resulting in a much smaller orbiting radius, its orbit is much more sensitive to the proton charge distribution in space than the electron’s of an ordinary H-atom. Thus, the measurement from muonic hydrogen provides a 10 times more precise result than the previous methods. The radius from the muonic hydrogen measurement reported in [1] was significantly smaller than all the p

Bai, Xinzhan↗
DOE OSTI2025

Precision Measurement of the Neutron Magnetic Form Factor via the Ratio Method at Jefferson Lab Hall A

Protons and neutrons, collectively known as nucleons, are composed of quarks and gluons. The Sachs electromagnetic form factors encode information about the spatial distributions of charge and magnetization in the nucleon, particularly at low momentum transfer. In particular, the neutron magnetic form factor (GMn) provides crucial information about the distribution of magnetization inside the neutron and helps constrain theoretical models of nucleon structure. Quasi-elastic electron scattering from deuterium was measured up to Q^2=13.5 GeV^2 using the Super BigBite Spectrometer in Hall A at Jefferson Lab. In this work, the neutron magnetic form factor GMn was extracted at Q^2 = 3.0 GeV^2 and Q^2=4.5 GeV^2 using the Ratio Method. These results represent a subset of the full dataset collected in this experiment, which extended to significantly higher Q^2. The extracted GMn values agree with the existing global fit within approximately two standard deviations at Q^2=3.0 and show excellent agreement at Q^2=4.5. The measurements achieved systematic uncertainties of about 2% and statistical uncertainties below 0.5%, among the most precise determinations of GMn at these kinematics. These results demonstrate the robustness of the experimental technique and provide an important validation point for future extractions at higher Q^2, where data remain scarce. In addition, the GRINCH heavy gas Cherenkov detector—a key component of the experimental apparatus—was commissioned and achieved an electron detection efficiency of approximately 97%, supporting reliable particle identification. Together, the analysis presented here advances both our understanding of nucleon structure and the validation of the experimental methods and instrumentation used to access it.

Satnik, Maria [College of William and Mary, Willia↗
DOE OSTI2025

Accurate Dark Energy Constraints via the Precise Characterization of Galaxy Intrinsic Alignment Coupled with Shear and Redshift Interference

One of the most fundamental mysteries we face in physics is understanding what the nature of the dark energy component of our Universe is that causes the accelerated expansion of space. A powerful way to study dark energy is via weak gravitational lensing due to large-scale structure in the Universe, which we observe as tiny distortions in the shapes of very distant galaxies due to the bending of light by foreground mass. The Dark Energy Survey (DES) and Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) were designed to enable unprecedented measurements of these distortions in the shapes of galaxies to study dark energy. The intrinsic shapes of galaxies before they are distorted by weak gravitational lensing can cancel out some of the effects of lensing to obscure or bias what we infer about the nature of dark energy. This research program has led to improved image-level simulations of the Rubin Observatory LSST data. These simulations have made it possible to characterize for the first time the cosmic impact of these intrinsic shapes on biasing weak gravitational lensing calibration. This work will inform crucial improvements in methodology for studying dark energy with weak gravitational lensing at the precision promised by the the Rubin Observatory LSST over the next decade to ensure we are able to infer unbiased information about the nature of dark energy.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Precision Kinematic Sunyaev--Zel'dovich Measurements Across Halo Mass and Redshift with DESI DR2 and ACT DR6: Part I. Luminous Red Galaxies

We present the most precise measurements of the kinetic Sunyaev-Zel'dovich (kSZ) effect around luminous red galaxies to date, detecting the signal at $18σ$ significance in both harmonic and configuration space. Our analysis cross-correlates 2.4 million spectroscopic LRGs from the Dark Energy Spectroscopic Instrument (DESI) DR2 sample with Data Release 6 (DR6) of the Atacama Cosmology Telescope (ACT). We develop a novel harmonic-space cross-correlation approach using momentum-weighted kSZ templates, yielding nearly uncorrelated bandpowers within a framework consistent with other large-scale structure analyses. By incorporating the LRG halo occupation distribution (HOD) and its uncertainty, we convert measured galaxy gas profiles into halo gas profiles and provide generalized Navarro-Frenk-White (GNFW) fitting profiles, providing empirical targets for tuning feedback efficiency in hydrodynamical simulations and for baryonic modeling in large-scale structure analyses. We find strong evidence that gas profiles do not trace dark matter, providing direct evidence for gas redistribution beyond gravitational collapse. Comparing to hydrodynamical simulations, our measurements favor feedback efficiencies exceeding those in the Battaglia profile, suggesting more efficient gas ejection in group-scale halos than previously predicted. Splitting by redshift, we detect the kSZ signal at SNR $\approx 5$--$10$ in each of four bins and find amplitude evolution consistent with the expected decline in mean halo mass at fixed comoving number density. Splitting by stellar mass, we study the scaling of kSZ amplitude with galaxy properties. Together with BGS and ELG measurements in Paper II, these results span $0.1 \lesssim z \lesssim 1.6$ across three galaxy populations, demonstrating the potential of spectroscopic kSZ to map circumgalactic gas and constrain baryonic feedback.

Qu, F. J. [KIPAC, Menlo Park; Stanford U., HEPL; S↗
DOE OSTI2026

Precise 2D electric field density simulations for superconducting quantum devices

Dielectric loss due to two-level systems is a limiting factor for superconducting qubit relaxation times. These losses arise mostly from nanometer-scale interfacial defect regions in superconducting devices with planar dimensions of microns to millimeters, thus making it resource intensive to accurately simulate the electric field density in these regions with traditional electromagnetic solvers. In this work, we demonstrate a fast boundary integral equation solver that allows precise simulation of electric field density in these thin regions, showing a speedup of around two orders of magnitude over traditional solvers, with relative errors around $10^{-7}$ for a ten-minute solution runtime. By computing participation ratios through Green's first identity without squaring the electric field, our approach is less susceptible to the field singularities near conductor corners. We apply this solver to a basic untrenched coplanar waveguide cross-section, showing that the common assumption of participation ratio linearity with dielectric constant holds well for some interfaces and not others; in particular, while the metal-air (MA) top and corner follow this linear relationship strongly, the MA sidewall does not. We then compare isotropic and anisotropic etching, showing that the MA sidewall and the metal-air-substrate triple junction are the most strongly affected. We are currently leveraging this solver to explore geometries that will uniquely isolate the participation ratios of the different dielectrics. Finally, we are working to combine this solver framework with a full 3D microwave solver to accurately calculate participation ratios for the thin dielectrics that are known sources of loss in superconducting qubits.

Gimbutas, Z. [NIST, Boulder] (ORCID:00000003320982↗
DOE OSTI2021

Boosting CO 2 Electrochemical Reduction with Atomically Precise Surface Modification on Gold Nanoclusters

Thiolate-protected gold nanoclusters (NCs) are promising catalytic materials for the electrochemical CO 2 reduction reaction (CO 2 RR). In this work an atomic level modification of a Au 23 NC is made by substituting two surface Au atoms with two Cd atoms, and it enhances the CO 2 RR selectivity to 90–95 % at the applied potential between -0.5 to -0.9 V, which is doubled compared to that of the undoped Au 23 . Additionally, the Cd-doped Au 19 Cd 2 exhibits the highest CO 2 RR activity (2200 mA mg -1 at -1.0 V vs. RHE) among the reported NCs. This synergetic effect between Au and Cd is remarkable. Density-functional theory calculations reveal that the exposure of a sulfur active site upon partial ligand removal provides an energetically feasible CO 2 RR pathway. The thermodynamic energy barrier for CO formation is 0.74 eV lower on Au 19 Cd 2 than on Au 23 . Here these results reveal that Cd doping can boost the CO 2 RR performance of Au NCs by modifying the surface geometry and electronic structure, which further changes the intermediate binding energy. This work offers insights into the surface doping mechanism of the CO 2 RR and bimetallic synergism.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Contribution of the Sub-Surface to Electrocatalytic Activity in Atomically Precise La 0.7 Sr 0.3 MnO 3 Heterostructures

Electrocatalytic reactions are known to take place at the catalyst/electrolyte interface. Whereas recent studies of size-dependent activity in nanoparticles and thickness-dependent activity of thin films imply that the sub-surface layers of a catalyst can contribute to the catalytic activity as well, most of these studies consider actual modification of the surfaces. Here, in this study, the role of catalytically active sub-surface layers was investigated by employing atomic-scale thickness control of the La 0.7 Sr 0.3 MnO 3 (LSMO) films and heterostructures, without altering the catalyst/electrolyte interface. The activity toward the oxygen evolution reaction (OER) shows a non-monotonic thickness dependence in the LSMO films and a continuous screening effect in LSMO/SrRuO 3 heterostructures. The observation leads to the definition of an “electrochemically-relevant depth” on the order of 10 unit cells. This study on the electrocatalytic activity of epitaxial heterostructures provides new insight in designing efficient electrocatalytic nanomaterials and core-shell architectures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Estimation of soil classes and their relationship to grapevine vigor in a Bordeaux vineyard: advancing the practical joint use of electromagnetic induction (EMI) and NDVI datasets for precision viticulture

Working within a vineyard in the Pessac Léognan Appellation of Bordeaux, France, this study documents the potential of using simple statistical methods with spatially-resolved and increasingly available electromagnetic induction (EMI) geophysical and normalized difference vegetation index (NDVI) datasets to accurately estimate Bordeaux vineyard soil classes and to quantitatively explore the relationship between vineyard soil types and grapevine vigor. First, co-located electrical tomographic tomography (ERT) and EMI datasets were compared to gain confidence about how the EMI method averaged soil properties over the grapevine rooting depth. Then, EMI data were used with core soil texture and soil-pit based interpretations of Bordeaux soil types (Brunisol, Redoxisol, Colluviosol and Calcosol) to estimate the spatial distribution of geophysically-identified Bordeaux soil classes. A strong relationship (r = 0.75, p < 0.01) was revealed between the geophysically-identified Bordeaux soil classes and NDVI (both 2 m resolution), showing that the highest grapevine vigor was associated with the Bordeaux soil classes having the largest clay fraction. The results suggest that within-block variability of grapevine vigor was largely controlled by variability in soil classes, and that carefully collected EMI and NDVI datasets can be exceedingly helpful for providing quantitative estimates of vineyard soil and vigor variability, as well as their covariation. The method is expected to be transferable to other viticultural regions, providing an approach to use easy-to-acquire, high resolution datasets to guide viticultural practices, including routine management and replanting.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Precision Measurement of the Microwave Dielectric Loss of Sapphire in the Quantum Regime with Parts-per-Billion Sensitivity

Dielectric loss is known to limit state-of-the-art superconducting qubit lifetimes. Recent experiments imply upper bounds on bulk dielectric loss tangents on the order of 100 parts per billion but because these inferences are drawn from fully fabricated devices with many loss channels, these experiments do not definitely implicate or exonerate the dielectric. To resolve this ambiguity, we devise a measurement method capable of separating and resolving bulk dielectric loss with a sensitivity at the level of 5 ×10 –9 . The method, which we call the dielectric dipper, involves the in situ insertion of a dielectric sample into a high-quality microwave cavity mode. Smoothly varying the participation of the sample in the cavity mode enables a differential measurement of the dielectric loss tangent of the sample. The dielectric dipper can probe the low-power behavior of dielectrics at cryogenic temperatures and does so without the need for any lithographic process, enabling controlled comparisons of substrate materials and processing techniques. We demonstrate the method with measurements of sapphire grown by edge-defined film-fed growth (EFG) in comparison to high-grade sapphire grown by the heat-exchanger method (HEMEX). For EFG sapphire, we infer a bulk loss tangent of 63⁢(8) ×10 –9 and a substrate-air interface loss tangent of 15⁢(3) ×10 –4 (assuming a sample surface thickness of 3 nm). For a typical transmon, this bulk loss tangent would limit device quality factors to Q ≲20 ×10 6 , suggesting that bulk loss is likely the dominant loss mechanism in the longest-lived transmons on sapphire. We also demonstrate this method on HEMEX sapphire and bound its bulk loss tangent to be less than 19⁢(6) ×10 –9 . As this bound is about 3 times smaller than the bulk loss tangent of EFG sapphire, the use of HEMEX sapphire as a substrate would lift the bulk dielectric coherence limit of a typical transmon qubit to several milliseconds.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Precision Mass Measurement of the Proton Dripline Halo Candidate 22 Al

Here, we report the first mass measurement of the proton-halo candidate 22 Al performed with the low energy beam ion trap facility’s 9.4 T Penning trap mass spectrometer at facility for rare isotope beams. This measurement completes the mass information for the lightest remaining proton-dripline nucleus achievable with Penning traps. 22 Al has been the subject of recent interest regarding a possible halo structure from the observation of an exceptionally large isospin asymmetry [J. Lee et al ., Large isospin asymmetry in Si22/O22 Mirror Gamow-Teller transitions reveals the halo structure of 22 Al , Phys. Rev. Lett. 125, 192503 (2020).]. The measured mass excess value of ME=18 092.5⁢(3) keV, corresponding to an exceptionally small proton separation energy of 𝑆𝑝=100.4⁢(8) keV, is compatible with the suggested halo structure. Our result agrees well with predictions from 𝑠⁢𝑑-shell USD Hamiltonians. While USD Hamiltonians predict deformation in the 22 Al ground state with minimal 1⁢𝑠 1/2 occupation in the proton shell, a particle-plus-rotor model in the continuum suggests that a proton halo could form at large quadrupole deformation. These results emphasize the need for a charge radius measurement to conclusively determine the halo nature.

binding energy↗