Colliding heavy nuclei take multiple identities on the path to fusion

The study addresses how heavy-ion collisions evolve on the path to fusion, particularly whether the colliding nuclei preserve their identities (proton and neutron numbers) up to the capture barrier as commonly assumed in barrier-passing models. Standard coupled-channels approaches construct an interaction barrier from Coulomb, centrifugal, and nuclear potentials and usually assume minimal change in Z and N prior to reaching the barrier radius RB. However, extensive experimental evidence shows discrepancies: sub-barrier fusion cross sections are hindered relative to models, and above-barrier cross sections are also systematically lower. These observations suggest dynamical energy dissipation and nucleon transfer processes already outside the barrier, before nuclear contact. Because the transition to fusion occurs on a ~10^-21 s timescale and cannot be directly observed, the study probes reflected (non-fused) flux at well below-barrier energies to infer the system’s state at specific closest-approach separations Rmin, thereby mapping the early dynamics relevant to fusion.

Prior work has documented fusion hindrance at deep sub-barrier energies, potentially due to nuclear incompressibility, Pauli repulsion, or neck formation widening the barrier (e.g., Mişicu & Esbensen; Simenel et al.). Systematic failures of Woods–Saxon potentials to jointly describe fusion and elastic scattering indicated a need for dynamical treatments (Newton et al.). Deep-inelastic scattering studies at and above the barrier revealed significant multinucleon transfer with large kinetic energy loss and a smooth evolution from few-nucleon transfer to deep-inelastic processes, implying a quantum-to-quasi-classical transition with effective irreversibility at high excitation energies. Coupled-channels methods can capture reversible couplings but struggle when many overlapping high-density states interact, leading to effectively irreversible couplings on collision timescales. Semi-classical models such as GRAZING incorporate aspects of transfer effects on fusion probabilities but typically assume ground-state to ground-state transfer or limited excitations. These backgrounds motivate a more comprehensive experimental characterization of Z, N, and excitation energy distributions prior to capture.

Reflected flux measurements were performed at the INFN Legnaro National Laboratory XTU Tandem–ALPI accelerator using the PRISMA magnetic spectrometer positioned at θ_lab = 115°. PRISMA specifications: large solid angle 80 msr (Δθ_lab = ±6°, Δφ = ±11°), momentum acceptance Δp/p = ±10%, mass resolution ΔA/A ≈ 1/200, and energy resolution up to 1/1000 via time-of-flight. Beams of 40Ca were delivered in 12 center-of-mass energies E_cm = 189.0–230.5 MeV. For E_cm above 213 MeV (with ALPI), carbon degraders of 135 or 205 µg/cm^2 provided three beam energies per tune. Targets were ~150 µg/cm^2 208PbS, oriented with normals at 60° to the beam; 20 µg/cm^2 carbon backings were upstream so accepted particles did not traverse the backing. The spectrometer fields were tuned to maximize transmission for the dominant charge state of elastically scattered beam, emphasizing quasi-elastic to multinucleon-transfer evolution. Due to Δp/p acceptance, channels with much larger N,Z changes (binary reactions beyond ±10%) were not observed, so near-barrier multinucleon transfer and dissipation extents are lower limits. Possible sticking/rotation in multinucleon transfer could bias θ_lab = 115° yields toward trajectories with smaller angular momentum; onset of multinucleon transfer at E/V_B = 0.88 (θ_lab = 115°) corresponds to E/V_B = 0.94 for l = 0, still below barrier. Identification and kinematic reconstruction used the TOF–Bρ–ΔE technique. Ions passed through a large-area MCP timing detector before quadrupole/dipole magnets; at the focal plane, a MWPPAC and a segmented ionization chamber yielded positions and energy loss. From Bρ, ΔE, and TOF, Z and charge state q were determined; together with trajectory reconstruction, A and thus N = A − Z, and kinetic energy of projectile-like fragments were obtained. Event-wise ground-state Q-values (Q_gg) were computed from Z,N, and two-body kinematics provided total excitation energy E_x via E_x = Q_gg − Q. Absolute probabilities P_reflected were normalized to Rutherford yields measured by two forward silicon monitors; PRISMA transmission was referenced by assuming P_reflected/dσ_reflected/dσ_Rutherford = 1 at the lowest energy (E/V_B ≈ 0.80). Mapping beam energy to distance of closest approach R_min: The total potential V_tot(R) = V_nuc + V_coul + V_cent was constructed. V_nuc used the São Paulo double-folding potential with Pauli non-locality; V_coul was for a point charge interacting with a finite sphere (radius from São Paulo systematics). V_cent = l(l+1)ħ^2/(2μR^2), with l determined for scattering to 115° at each energy assuming Rutherford trajectories (l = μv_0 b; v_0 = √(2E_cm/μ); b = Z_1 Z_2 e^2 / (2E_cm)). R_min at each E_cm was the outer intersection of E_cm with V_tot; barrier radius R_B and height V_B for each l_115 were determined from the local maximum of V_tot. The deduced separations R_min − R_B (or R_min − R_g as referenced in figures) were used to order measurements. Fission/quasifission mass distributions: Additional measurements were carried out at the Heavy Ion Accelerator Facility (ANU) using beams of 36S and 40Ca on 208PbS targets (100–170 µg/cm^2), target normals at 60°. Energies were 6–7% above the fusion barrier for each system. Fragments were detected in coincidence with the CUBE spectrometer comprising two large MWPCs (active areas 279×357 mm^2) at 180 mm from target; angular coverages were 55°–130° (backwards) and 5°–80° (forwards) with ~70° azimuthal coverage. Position (φ, ψ) and timing gave fragment velocities, energies, and mass ratios M_R in the c.m. frame using energy–momentum conservation; source analysis selected binary events consistent with full momentum transfer from 208Pb reactions (v_⊥ ≈ 0, v_∥ = v_CN sinθ_CM). Silicon monitors at θ = 30°, φ = 90°, 270° provided elastic yields for absolute cross sections. Analysis framework for fusion impact: A generalized energy variable was introduced to quantify how multinucleon transfer modifies the kinetic energy relative to the post-transfer potential at R_min: ΔE_gg = Q_gg + (V_i(R_min) − V_f(R_min)); ΔE_k = ΔE_gg − E_x. Positive ΔE_k increases kinetic energy relative to the new potential (favoring fusion); negative ΔE_k decreases it (hindering fusion). Event-by-event ΔE_k distributions were built across Z,N,E_x at each energy.

• Rapid identity changes outside the capture barrier: At the closest measured separation (R_min − R_g = 0.46 fm), only 11.6 ± 0.1% of the reflected flux remained as the original 40Ca + 208Pb pair. The minimum number of projectile-like/target-like nuclide pairs accounting for 95% of the reflected flux (N_95) reached 31, demonstrating extensive multinucleon transfer pathways.
• Broad excitation energy distributions: As surface separation decreases, E_x distributions develop long high-energy tails. At the closest separation, the mean E_x reached 19.4 MeV. Events with multiple-nucleon transfer showed mean E_x ≈ 29.5 MeV, while the inelastic plus one- and two-nucleon transfer component had mean E_x ≈ 10.0 MeV. Ground-state to ground-state transfers constitute a negligible fraction of reflected flux at near-barrier separations.
• Evidence of early energy dissipation: Significant fractions of events have E_x above thresholds associated with effective irreversibility (≳6 MeV), indicating quasi-classical dissipative behavior beginning outside the barrier radius.
• ΔE framework reconciles model successes and failures: At E/V_B = 0.91 (R_min − R_B ≈ 1.93 fm), transfer probabilities are substantial; only ~34% of flux remains as 40Ca (ΔE_gg = 0). Although many channels have positive ΔE_gg, accounting for E_x yields ΔE_k distributions peaked near 0 MeV due to the optimum Q-value condition favoring continuous trajectories, with an exponential tail extending to at least ΔE_k ≈ −40 MeV that reduces fusion probability at higher energies.
• Consequences for superheavy synthesis: Multinucleon transfer before capture produces a distribution of charge products Z_1 Z_2 even for events with ΔE < 5 MeV (similar capture likelihood to entrance channel), including a tail to lower Z_1 Z_2. Comparative fission-like mass-ratio vs angle distributions show that lower Z_1 Z_2 systems (e.g., 36S + 208Pb, Z_1 Z_2 = 1312) exhibit narrow, angle-uncorrelated distributions consistent with longer sticking and larger P_CN, whereas higher Z_1 Z_2 (40Ca + 208Pb, Z_1 Z_2 = 1640) show strong mass–angle correlations indicative of short sticking (< half rotation) and smaller P_CN.

The measurements reveal that, contrary to standard barrier-passing assumptions, colliding 40Ca and 208Pb nuclei arrive at the barrier with a multitude of Z,N configurations and broad excitation energies, implying that effective energy dissipation and complex multinucleon transfers commence outside the barrier. This helps explain reduced fusion cross sections both below and above the barrier. Introducing the ΔE (ΔE_k) measure shows why coupled-channels models can perform reasonably: the most probable transfers favor the optimum Q-value, leading to ΔE_k ≈ 0 and thus fusion probabilities similar to the entrance channel. However, the significant negative ΔE_k tail, arising from high E_x and deep-inelastic-like transfers, decreases kinetic energy relative to the post-transfer potential and hinders fusion, smoothing and extending fusion barrier distributions to higher energies (as observed, e.g., in 20Ne + 208Pb). The observed fragmentation into many Z,N partitions also modifies key variables (Z_1 Z_2, shell structure, N/Z matching, deformation) that govern quasifission and compound nucleus formation probability P_CN, suggesting that pre-capture transfer can substantially influence superheavy element synthesis. Overall, the results both rationalize the partial success of coherent coupled-channels approaches (through ΔE_k ≈ 0 events) and clarify their failures (through missing dissipative, high-E_x channels), providing a physically grounded framework for improved fusion modeling that includes early-stage transfer and dissipation.

Collisions of 40Ca + 208Pb evolve to the fusion barrier through a complex landscape of multinucleon transfers that generate broad Z,N and excitation-energy distributions. Only a small fraction of events preserve the entrance-channel identities at the closest separations, and significant effective energy dissipation occurs before reaching the barrier. The introduced ΔE (ΔE_k) variable connects event-wise transfer, excitation, and kinetic energy relative to the post-transfer potential, explaining why standard fusion models sometimes succeed (dominant ΔE_k ≈ 0 component) yet also underpredict or overpredict in regimes impacted by the negative ΔE_k tail. The fragmentation of flux into a Z_1 Z_2 distribution prior to capture likely impacts compound nucleus formation probability P_CN, potentially aiding superheavy element synthesis via pathways with reduced Z_1 Z_2. Future research should develop quantitative models that incorporate event-by-event transfer with excitation energy and dissipation, and extend measurements to deformed actinide systems to test generality and assess isotopic dependencies of pre-capture transfer effects.

• Spectrometer acceptance: PRISMA’s Δp/p = ±10% acceptance excludes binary channels with very large momentum changes (and thus large N,Z changes), making reported multinucleon transfer and dissipation extents conservative lower limits. The smooth evolution to quasifission is not observed within this setup.
• Angular coverage: Measurements were taken at a single backward laboratory angle (115°). Although essential trends are expected to hold at other backward angles after centrifugal corrections, angle-dependent sticking and rotation could bias yields.
• Possible contamination by sticking/rotation: If multinucleon transfer involves sticking and rotation, selected events at 115° may originate from trajectories with smaller angular momentum (closer to their effective barrier), which is difficult to quantify without detailed sticking-time distributions.
• Mapping to R_min assumptions: Determination of l at each energy assumes Rutherford trajectories and employs the São Paulo potential; systematic uncertainties in potentials and angular momentum determination can affect R_min and barrier inferences.
• Ground-state properties and Q-values: Event-by-event Q_gg and E_x rely on nuclear mass tables and two-body kinematics; uncertainties therein can propagate to ΔE_k distributions.
• System specificity: Results are for closed-shell spherical 40Ca + 208Pb; extrapolation to deformed actinides and other systems requires further dedicated measurements.