4D-imaging of drip-line radioactivity by detecting proton emission from $^{54m}$Ni pictured with ACTAR TPC

The study of nuclear stability and structure is strongly influenced by magic numbers of protons and neutrons, with doubly magic nuclei providing key benchmarks for shell-model descriptions. For N = Z systems near 56Ni, isospin symmetry and its breaking by Coulomb and parts of the strong interaction play central roles. Proton emission, analogous to alpha decay, probes quantum tunnelling through Coulomb and centrifugal barriers and highlights coupling to the continuum, especially for nuclei beyond the proton drip line. In this context, the 10+ isomer in 54Ni, mirror to the well-known 54mFe isomer, presented a puzzle: prior gamma-ray studies inferred an unexpected proton branch to the first excited state of 53Co, yet theoretical and experimental decay patterns remained inconsistent unless a comparable-strength proton branch to the 53Co ground state was also present. Simple barrier-penetration estimates predicted comparable probabilities for l = 5 emission to the first excited state (Ep ≈ 1.20 MeV) and l = 7 emission to the ground state (Ep ≈ 2.50 MeV). The research question is to directly observe, in a single experiment, both high-l proton-emission branches from 54mNi, quantify their branching ratios precisely, and confront shell-model plus barrier-penetration theory to test isospin symmetry and decay dynamics near 56Ni.

Proton radioactivity from isomeric and ground states has been a cornerstone in defining the proton drip line and understanding quantum tunnelling in nuclei. The first observation from 53mCo (Jπ = 19/2−, l = 9) established high-angular-momentum tunnelling. Two-proton radioactivity was later discovered in 45Fe, 48Ni, and 54Zn. Near doubly magic 56Ni, rotational structures and isomers have been extensively studied, and the shell model describes this region well. For the mirror pair 54Fe/54Ni, the 54Fe 10+ isomer’s decay is well reproduced, whereas for 54mNi, gamma spectroscopy suggested a significant l = 5 proton branch to the first excited state of 53Co but could not directly observe a ground-state l = 7 branch of similar strength, leading to discrepancies between theory and experiment. Mass and Q-value precision data and barrier-penetration estimates indicated that both branches should be of comparable probability, motivating a detector capable of directly resolving and quantifying each branch.

Production and identification: A 58Ni primary beam at 75 MeV/nucleon impinged on a Be target at GANIL’s LISE3 line to produce 54Ni fragments. Event-by-event identification used ΔE in a silicon diode and ToF (RF start and CFA stop). About 0.4% of implanted 54Ni populated the 10+ isomer (E* = 6457 keV; T1/2 ≈ 155 ns). Instrumentation: The ACTAR TPC (25×25×20 cm3 active volume, 16384 pads) operated as a time projection chamber with GET electronics. Gas: Ar(95%)+CF4(5%) at 900 mbar, chosen to avoid hydrogen-induced recoil protons. Signals above threshold were sampled at 25 MHz. Pad-plane amplification induced cross-pad signals; control channels corrected distortions. Pads along the beam axis were biased to reduce gain and avoid saturation, rendering those pads insensitive to small proton signals. Data taking and processing: Trigger from the CFA detector initiated a ≈10 μs pad-plane readout window. GET data processing reconstructed the time distribution of charge per pad with gain/time alignment calibrated by pulser. Event selection: (1) Fragment selection via ΔE–ToF contour for 54Ni; (2) Proton-emission identification by removing pads attributed to the implantation ion track using an iterative high-threshold search, then clustering remaining pad signals to form tracks. Events were kept if a single proton track extrapolated to the ion stopping point and met quality criteria (amplitudes, number of pads, length) to reject reactions/noise. 3D reconstruction: Drift time provided Z after estimating the drift velocity via L2 = Lxy2 + (vaΔt)2, yielding va = 53.1±0.4 mm/μs (consistent with GARFIELD). Proton tracks were fit with a 3D Bragg-peak-based model (validated with Geant4), including diffusion and amplification effects; the proton start point was obtained by extrapolating the fitted trajectory to the ion stopping position, as the initial segment is obscured by the ion track. The decay time was the time difference at the proton start between ion and proton signals. Efficiency and simulation: Detection efficiency for each proton energy accounted for pad-plane attenuation-zone occultation and escape from active volume. A Monte Carlo combined (i) implantation/start-point and ion-direction distributions from data, (ii) Geant4 tracking at tuned gas pressure to reproduce measured track lengths, (iii) drift, diffusion, amplification, and pad response, and (iv) identical selection cuts as data to extract global efficiencies. Systematic uncertainties were dominated by simulation-parameter uncertainties. Dataset and statistics: Over 17 h, ~2×10^6 54Ni implants were recorded; ~3000 proton-emission events were identified. Distributions of proton track lengths and decay times were built; decay-time spectra were fitted by an exponential convolved with a Gaussian resolution function.

• Direct 4D visualization and separation of two proton-emission branches from 54mNi(10+): • l = 7 to 53Co ground state at Ep = 2.5002(43) MeV with 1411 ± 40 counts. • l = 5 to 53Co first excited state at Ep = 1.1979(44) MeV with 1459 ± 40 counts.
• Measured detection efficiencies (from simulation): • Ep ≈ 1.20 MeV (p1): 58.8 ± 3.8%. • Ep ≈ 2.50 MeV (p2): 81.7 ± 2.2%.
• Branching within proton emission: The 1.20 MeV branch constitutes 57.3 ± 1.9% of total proton emission.
• Absolute branching fractions for the isomeric decay (combining with previous gamma spectroscopy): • Total proton emission bp = 49.5 ± 2.3%. • Electromagnetic decay bγ = 50.5 ± 2.3%.
• Isomer half-life from decay-time distribution: T1/2 = 156.6 ± 3.6 ns.
• No evidence for two-proton emission; estimated 2p barrier-penetration half-life is ~10^6 times longer than for 1p emission, consistent with non-observation.
• Theoretical comparison: Using GXPF1A and KB3G shell-model Hamiltonians with M3Y coupling to high-l orbitals and Woods–Saxon proton scattering for Γsp: • For decay to 7/2− (ground state, l ≈ 7): calculated partial T1/2 ≈ 0.34/0.52 μs (GXPF1A/KB3G), reasonably close to experimental 0.73 ± 0.06 μs. • For decay to 9/2+ (first excited state, l ≈ 5): experimental partial T1/2 = 0.55 ± 0.03 μs is much shorter than calculated; deduced C2S ≈ 4.6×10−6 if using calculated Γsp. • Small mixing between two nearby 10+ states (one ~2 MeV higher) could reconcile both branches with experiment.

The study directly addresses whether both theoretically expected high-l proton-emission branches from 54mNi(10+) occur with comparable probabilities and quantifies their branching with minimal model dependence via track imaging. The observations confirm two branches: l = 5 to the 9/2+ first excited state (Ep ≈ 1.20 MeV) and l = 7 to the 7/2− ground state (Ep ≈ 2.50 MeV), with the lower-energy branch contributing 57.3% of proton decays. The total proton-decay probability bp = 49.5% establishes near-equal competition between proton emission and electromagnetic de-excitation, supporting isospin symmetry arguments drawn from the mirror 54mFe case. Comparison with shell-model plus barrier-penetration calculations shows reasonable agreement for the l = 7 branch but a significant underestimation of the l = 5 branch unless configuration mixing between two 10+ states is included. This suggests sensitivity to high-l continuum couplings and to details of the fp-shell Hamiltonians and model-space truncations. The 4D imaging approach provides precise decay times and kinematics, enabling stringent tests of tunnelling through high centrifugal barriers and informing improvements in spectroscopic-factor and potential modeling relevant to few-body quantum systems and astrophysical proton-capture mirror processes.

A new 4D time-projection-chamber technique (ACTAR TPC) enabled the first direct imaging and quantification of both high-angular-momentum proton-emission branches from the 10+ isomer in 54mNi. The two branches at Ep = 1.1979(44) MeV (l = 5) and 2.5002(43) MeV (l = 7) were separated and their efficiencies corrected, yielding that the 1.20 MeV branch accounts for 57.3 ± 1.9% of total proton emission and establishing an absolute proton-emission fraction of 49.5 ± 2.3% for the isomer, consistent with isospin symmetry when compared to the mirror 54mFe decay. Theoretical analysis combining shell-model spectroscopic factors with Woods–Saxon barrier penetration reproduces the l = 7 branch reasonably and points to state mixing to explain the l = 5 strength. The work completes the decay scheme of 54mNi, validates a powerful method for studying short-lived high-l decays at the drip line, and motivates refined calculations including less truncated spaces, improved interactions, and explicit continuum coupling. Future studies could apply the technique to other isomers and proton emitters near 56Ni and to probe potential two-proton emission limits.

Experimental: (i) Portions of the pad plane were blind due to charge-collection issues and intentional gain reduction along the beam axis to prevent saturation, reducing sensitivity to proton signals in those regions; (ii) although charge (dE/dx) was recorded, missing pads limited energy reconstruction by charge so proton energies were determined more precisely via track-length fits; (iii) detection efficiencies rely on simulations subject to systematic uncertainties in gas properties, diffusion, amplification, and geometry. Theoretical: (i) High-l orbital potentials approximated by varying Woods–Saxon depths alter single-particle energies and wave functions, affecting spectroscopic factors; (ii) truncations in the fp-shell model space; (iii) use of the M3Y interaction to connect high-l to fp shells introduces uncertainties. These factors impact quantitative agreement for partial half-lives and branching ratios.