Introduction

The synthesis of new elements is achieved in nuclear collisions, in which two nuclei come close to each other and merge to form a new compound nucleus. The two nuclei must come close enough for their matter distributions to overlap, allowing the attractive nuclear force to act. Then their kinetic energy is rapidly dissipated, and the can system transition to a single, compact, excited nucleus. Preventing their merger (fusion) is a potential barrier, created by the sum of the long-range repulsive Coulomb potential and short-range attractive nuclear potential (Fig. 1a), having a peak at radial separation RB. For fusion to occur, this barrier must be overcome, either by having sufficient energy to pass over it, or through it or via quantum tunnelling. Barrier-passing models of fusion construct this barrier and apply boundary conditions inside RB to simulate fusion, assuming that the identities (i.e. their proton and neutron numbers) of the nuclei are essentially unchanged prior to this point.

Fig. 1: Experimental principle and onset of complexity in reaction outcomes.
figure 1

a Depicted is the internuclear potential (blue) of 40Ca+208Pb nuclei (with centre-to-centre separation R), the nuclear potential Vnuc (red)52, and the sum of the Coulomb and centrifugal potentials Vcoul + Vcent (green). The yellow crosses show the deduced distance between the barrier RB and the distance of closest approach \({R}_{\min }\), \({R}_{\min }-{R}_{{{{{{{{\rm{B}}}}}}}}}\), at each measured energy Ecm, taking into account the change in angular momentum l at the measurement angle. b Left axis: proportion of the reflected flux P/Preflected that is made up of 40Ca (lilac squares), statistical errors are smaller than the points. Right axis: The smallest number of nuclide pairs required to make up 95% of the reflected flux (N95, green diamonds). c The deduced excitation energy distribution Ex. To show the evolution of the excitation energy with decreasing surface separation, the probabilities were normalised to the total reflected flux such that the integral at each \({R}_{\min }-{R}_{{{{{{{{\rm{B}}}}}}}}}\) is equal to 1. These distributions will be modulated by absorption at higher energies (above E/VB = 0.91, below \({R}_{\min }-{R}_{{{{{{{{\rm{B}}}}}}}}}=1.93\) fm (Supplementary Fig. 2a)) which will not be equally likely for all Ex. The data has been interpolated between measurement energies using Delaunay triangulation57. The black points show the mean excitation energy at each measured energy.

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A wealth of experimental results suggests that this picture is too simple. Fusion cross-sections measured very far below the barrier energy are smaller than model1,2 predictions3,4,5,6. Suggested explanations are nuclear incompressibility through Pauli repulsion7,8 or neck formation9 acting to widen the barrier. Measured above-barrier cross-sections are also systematically smaller than model calculations6,10. Experiments suggest that there may be a dynamical origin linking both energy domains—arising from the gradual loss of kinetic energy (energy dissipation) already outside the barrier, before the nuclei touch6. Significant kinetic energy loss will lead to substantially reduced cross-sections6,10,11. Understanding the early stages of the collision, and the state of the system at the point of fusion, is therefore key.

We cannot directly probe the system as it evolves towards fusion: the transition from isolated nuclei to a compound system is too fast, occurring on a 10−21 s timescale. However, we can probe the system by measuring the reflected (non-fused) flux at an energy well below the barrier, providing a snapshot of the system for a given minimum separation \({R}_{\min }\) (see Fig. 1a, described in the Methods). This approach has previously been successfully applied for light nuclei12,13. By increasing the energy in small steps, we map out how the colliding nuclei evolve as they come closer together.

The reflected flux at each energy represents the integral of all reaction outcomes along a trajectory with a given \({R}_{\min }\). The likelihood of transferring protons or neutrons increases exponentially with decreasing radial separation as the nuclear matter overlap increases. Thus the characteristics of the reflected flux should mainly represent processes occurring near the outer turning point of each trajectory. Critically, reactions that do lead to fusion must pass through the same sequence of separations. Probing the characteristics of collisions not resulting in fusion thus probes the early stages of the fusion process.

We have studied 40Ca + 208Pb collisions, where systematics10 indicate that above-barrier fusion cross-sections will be ~40% lower than model predictions. Previous measurements at above-barrier energies have indicated substantial probabilities of multinucleon transfer and large kinetic energy losses14. Being a collision of two spherical closed-shell nuclei, 40Ca + 208Pb provides a good benchmark for model development. Using the PRISMA magnetic spectrometer15,16,17, we measured the distributions in mass (A), atomic number (Z) and kinetic energy of 40Ca + 208Pb reactions at 12 energies. We started at 20% below the fusion barrier, where there is negligible nuclear matter overlap (and fusion), increasing to 1% below the fusion barrier (see Methods). Measuring the kinetic energy as well as A and Z allowed us to reconstruct the excitation energy for each event, giving a complete characterisation of all the reflected nuclides.

Results and discussion

Rapidly increasing complexity

We find that there is a rapid change in the identities of the nuclei already outside the capture barrier, depending on \({R}_{\min }-{R}_{{{{{{{{\rm{B}}}}}}}}}\), the separation between the distance of closest approach \({R}_{\min }\) and the barrier radius RB. This is shown in Fig. 1b. The fraction of reflected flux P/Preflected remaining as 40Ca + 208Pb (lilac squares) is only 11.6 ± 0.1% at the closest separation distance measured \({R}_{\min }-{R}_{{{{{{{{\rm{B}}}}}}}}}=0.46\) fm. Correlated with this, the smallest number of projectile-like and target-like nuclide pairs making up 95% of the reflected flux rapidly increases (N95, green diamonds), reaching 31 different nuclide pairs. In Supplementary Fig. 1, we show the full distribution of the reflected flux in N, Z, and in Supplementary Fig. 2. the probability for 1–2 nucleon transfer and for multinucleon transfer. It is not just one or two channels contributing—there is a multitude of different mass and charge transfer processes occurring. In contrast, in a typical coupled-channels calculation1 for this system, only states in 40Ca and 208Pb and a few simple transfer reactions would be approximately included.

Added to this complexity is the number of quantum states populated in the nuclei, revealed by the excitation energy Ex distribution, shown in Fig. 1c. At large surface separations (low collision energies), the excitation energies are strongly peaked at Ex = 0 (the reflected nuclei are in their ground-states), but a tail extends to high Ex, becoming stronger as the nuclei approach closer (\({R}_{\min }-{R}_{{{{{{{{\rm{B}}}}}}}}}\,\lesssim \,2.5\) fm). Here also the number of different nuclides produced rapidly increases. At the closest separation measured, the mean excitation energy (shown by the black circles) reaches 〈Ex〉 = 19.4 MeV, where there a high density of (overlapping) quantum states in the interacting nuclei. The excitation energy is largest when multiple nucleons are transferred, with 〈Ex〉 = 29.5 MeV (Supplementary Fig. 2c). Even the inelastic plus one & two nucleon transfer component shows a mean excitation energy of 〈Ex〉 = 10.0 MeV (Supplementary Fig. 2b). Ground-state to ground-state transfers, as usually included in coupled-channels calculations, represent a negligible fraction of the reflected flux. Measuring at energies below the (l-dependent) barrier ensures that the probability of this reflected flux arising from capture is minimal. This is supported by the fact that signatures of capture are not yet present: the majority of the flux does not show mass flow towards symmetry nor are the mean excitation energies high enough for the kinetic energies to have been fully damped.

Significant amounts of multinucleon transfer products with high excitation energies have been previously observed at above-barrier energies18,19,20,21, and seem to be a general feature of near-barrier heavy ion collisions. Significant energy loss (up to hundreds of MeV), associated with complex multinucleon transfers both towards and away from the target, is known as deep-inelastic scattering14,22,23. It has been identified as the energy loss mode in heavy-ion collisions24 and has been modelled classically22,25,26,27. However, it has long been known22 (also seen here) that deep-inelastic scattering evolves smoothly from few-nucleon transfer and inelastic scattering, which must be treated quantum-mechanically28.

How can we resolve this transition? In principle, when processes are fully reversible, coupled channels calculations will reproduce experiments if every coupling can be included. However, at high excitation energies where the density of states is very high, very many overlapping states will couple to each other in a complex scheme that results in a coupling that is effectively irreversible on the time scale of the nuclear collision (i.e. has a recurrence time longer than 10−21 s). This effective irreversibility leads to quasi-classical behaviour. An example of the scaling of recurrence times with system size in 1D superfluids is found in ref. 29.

How high does the excitation energy need to be to lead to (effective) irreversibility? As a concrete example, actinide nuclei having excitation energies larger than their fission barrier (Bf ~ 6 MeV) can fission (in ≲ 10−16 s) indicating thermalisation. For heavy systems we may thus expect that energy losses ≳ 6 MeV (or perhaps lower) lead to (effectively) irreversible energy loss. A significant fraction of the reflected flux satisfies this condition. Crucially, we have shown that this energy loss begins outside the fusion barrier radius.

To briefly summarise: at the barrier radius, (i) the system consists of broad Z, N distributions, with only a small probability of remaining as 40Ca and 208Pb nuclei and (ii) a significant fraction of collisions have high excitation energies consistent with (effective) energy dissipation. Neither condition is consistent with coherent coupled channels calculations, so how can they give even approximately correct results if they miss so much of the physics? We show that the answer lies in the correlation between Z, N and Ex.

Reconciling with barrier-passing models of fusion

We introduce a generalised variable that can quantify the effect of (multi-nucleon) transfer on fusion. A change in Z before (i) and after (f) transfer results in a change in the Coulomb potential \({V}_{{{{{{{{\rm{i}}}}}}}}}({R}_{\min })-{V}_{{{{{{{{\rm{f}}}}}}}}}({R}_{\min })\) at the distance of closest approach \({R}_{\min }\). Additionally, transfer of nucleons (i.e changes in Z and/or N) changes the nuclear binding energy, defined by the ground-state to ground-state Q-value Qgg. The available energy for a given transfer (relative to the new potential) is thus

$$\Delta {E}_{{{{{{{{\rm{gg}}}}}}}}}={Q}_{{{{{{{{\rm{gg}}}}}}}}}+({V}_{{{{{{{{\rm{i}}}}}}}}}({R}_{\min })-{V}_{{{{{{{{\rm{f}}}}}}}}}({R}_{\min })).$$
(1)

This energy may be in the form of kinetic or excitation energy (Ex). We can thus determine the kinetic energy with respect to the new potential at \({R}_{\min }\) as:

$$\Delta {E}_{{{{{{{{\rm{fi}}}}}}}}}=\Delta {E}_{{{{{{{{\rm{gg}}}}}}}}}-{E}_{{{{{{{{\rm{x}}}}}}}}}.$$
(2)

This is identical to \(\Delta {E}_{{{{{{{{\rm{fi}}}}}}}}}=({K}_{{{{{{{{\rm{f}}}}}}}}}-{V}_{{{{{{{{\rm{f}}}}}}}}}({R}_{\min }))-({K}_{{{{{{{{\rm{i}}}}}}}}}-{V}_{{{{{{{{\rm{i}}}}}}}}}({R}_{\min }))\), where Ki,f are the total kinetic energies in the initial and final states. Thus, ΔEfi > 0 means that there is an increase in kinetic energy relative to the (new) potential, which increases fusion. ΔEfi < 0 decreases the kinetic energy relative to the new potential, resulting in reduced fusion. This idea is connected to what is partly incorporated in the semi-classical model GRAZING30.

The ΔEgg are shown by the red lines in Fig. 2a, b, with the height corresponding to the measured \({P}_{{{{{{{{\rm{reflected}}}}}}}}}^{{{{{{{{\rm{Z,N}}}}}}}}}\) for each measured Z, N. At \({R}_{\min }-{R}_{B}=3.87\) fm (E/VB = 0.80) (Fig. 2a), the transfer probabilities are low, and ΔEgg is strongly peaked at 0 MeV. At \({R}_{\min }-{R}_{B}=1.93\) fm (E/VB = 0.91) (Fig. 2b) significant multinucleon transfer has begun, but there is little absorption by fusion to distort the overall distribution. Only 34% of the flux remains as 40Ca (seen at ΔEgg = 0), the rest being largely distributed between ΔEgg = 0 to 10 MeV, with a small fraction of events between 0 and − 15 MeV (Fig. 2b, red lines). Since ΔEgg is largely positive, for higher beam energies, one would expect enhanced fusion and at least a 10 MeV wide fusion barrier distribution31 if nuclides were produced in their ground-states.

Fig. 2: Quantifying the change in available and kinetic energies.
figure 2

The change in available energy ΔEgg (red) and in kinetic energy ΔEfi (blue) is shown for all transfer channels at (a) E/VB = 0.80 (\({R}_{\min }-{R}_{{{{{{{{\rm{B}}}}}}}}}=3.87\) fm) and (b) E/VB = 0.91 (\({R}_{\min }-{R}_{{{{{{{{\rm{B}}}}}}}}}=1.93\) fm). Cases for all other measured energies are shown in Supplementary Fig. 3. Statistical errors are shown. The red lines show ΔEgg, the maximum extra energy available to the colliding nuclei following transfer, which comprises kinetic and excitation energy. After subtracting the excitation energy, the blue curves show ΔEfi, the distribution of kinetic energies following transfer with respect to their potential. c Illustration showing how ground-state to ground-state transfers (red) result in discontinuities in the trajectories resulting from the change in potential after transfer. The reflected flux clustering to zero change in energy when the excitation energy is included (blue) is due to transfers preferentially producing excitation energies Ex that ensure a smooth match between entrance and exit channels.

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However, the nuclei are not produced in their ground states, but at a range of excitation energies. Taking Ex into account event-by-event, the ΔEfi distributions are shown by blue curves in Fig. 2, showing the actual change in kinetic energy relative to the new potential. Our determination of Ex is critical to this interpretation. The many transfer channels with positive ΔEgg at E/VB = 0.91 now peak around ΔEfi = 0. Significantly, there is also an exponentially falling tail extending at least as far as ΔEfi = − 40 MeV, that will reduce fusion at higher beam energies.

The peak at ΔEfi = 0 is due to favouring of continuous trajectories. Probabilities for transfer generally peak in a window around the Q-value (Q = Qgg − Ex) that ensures that the linear and angular momenta in the entrance and exit mass partitions join smoothly, approximated by \(Q+({V}_{{{{{{{{\rm{i}}}}}}}}}({R}_{\min })-{V}_{{{{{{{{\rm{f}}}}}}}}}({R}_{\min }))\approx 0\) MeV. This is known as the optimum Q-value21,32,33,34 and is illustrated in Fig. 2c. Provided that the optimum Q-value is <Qgg, the equality can be satisfied if the fragments are excited, resulting in a peak at ΔEfi = 0. The tail for ΔEfi < 0 arises from (1) the exponential increase in the density of states with Ex that will enhance transfer probabilities towards the high Ex (low ΔEfi) side of the Q-window and (2) effectively irreversible multiple nucleon transfers in both directions (deep-inelastic scattering) that build up excitation energy22,25. While these measurements were made at a laboratory angle of 115°, the essential results are not expected to change if a different backwards angle (different ℓ) was chosen35,36, following corrections for the change in centrifugal energy36.

Consequences for superheavy element synthesis

Superheavy element synthesis requires that the captured nuclei evolve in shape to a compact equilibrated compound nucleus. The probability of doing so (\({P}_{{{{{{{{\rm{CN}}}}}}}}}\)) is very small because of strong competition from quasifission, in which the system re-separates into two heavy fragments before equilibration. The characteristics of quasifission, and by implication \({P}_{{{{{{{{\rm{CN}}}}}}}}}\), depend most sensitively on the charge product Z1Z2 of the colliding nuclei, but also on deformation, closed shells and matching of neutron to proton ratios of the colliding nuclei37,38,39,40,41. Our observations of the multitude of identities resulting from multinucleon transfer mean that each of these variables may be changed enroute to capture.

How could the fragmentation of flux observed here impact on superheavy element synthesis? Before capture, multinucleon transfer results in a distribution of Z1Z2. Shown in Fig. 3a is the Z1Z2 distribution for collisions with ∣ΔEfi∣ < 5 MeV (those having similar probabilities of capture to the starting value) at E/VB = 0.91 (\({R}_{\min }-{R}_{{{{{{{{\rm{B}}}}}}}}}=1.93\) fm). The charge product distribution has a tail to much lower Z1Z2. For the lower Z1Z2 collisions (shown for 36S+208Pb in Fig. 3b) the fragments show narrow fission-like mass distributions having no correlation with angle. This indicates many rotations and long sticking times, associated with larger \({P}_{{{{{{{{\rm{CN}}}}}}}}}\). In contrast for 40Ca+208Pb with higher Z1Z2 (Fig. 3c), there is a strong correlation of fragment mass with angle, showing that the system typically comes apart in less than half a rotation. This is associated with smaller \({P}_{{{{{{{{\rm{CN}}}}}}}}}\).

Fig. 3: Potential impact of transfer on superheavy element formation.
figure 3

a The distribution of charge products between the projectile-like and target-like nuclides Z1Z2 at the below-barrier energy of E/VB = 0.91, with corresponding to a separation of \({R}_{\min }-{R}_{{{{{{{{\rm{B}}}}}}}}}=1.93\) fm. Shown are the reflected nuclei that maintain similar kinetic energies with respect to the barrier, i.e. ∣ΔEfi∣ < 5. Other energies are shown in Supplementary Fig. 4. The y-axis shows the absolute probability of the flux being reflected and having charge product Z1Z2, Preflected(Z1Z2). Fission-like fragment mass-ratio MR vs scattering angle θcm distributions for (b) 36S+208Pb (E/VB = 1.067) and (c) 40Ca+208Pb (E/VB = 1.058). The intense vertical bands at the extremes of the MR distributions arise from (quasi)elastic scattering. The blue dashed lines guide the eye, indicating the degree of mass-angle correlation and thus sticking times.

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For reactions forming superheavy elements with much larger Z1Z2, and \({P}_{{{{{{{{\rm{CN}}}}}}}}}\) values perhaps as low as 10−6, a much stronger dependence of \({P}_{{{{{{{{\rm{CN}}}}}}}}}\) on Z1Z2 would be expected, making the larger \({P}_{{{{{{{{\rm{CN}}}}}}}}}\) for lower Z1Z2 significantly more impactful. We thus speculate that the multinucleon transfer processes occurring outside the capture barrier radius may provide a mechanism for superheavy element synthesis. Multinucleon transfer yields and N, Z distributions depend strongly on the colliding system42,43,44,45, and this may also explain the observed isotopic difference in fusion probabilities40. These ideas need to be tested quantitatively through further experimental measurements, in particular for deformed actinide nuclei, to see whether the characteristics agree with the present measurements with closed-shell spherical nuclei.

In summary, in collisions of 40Ca and 208Pb nuclei, we find that the nuclei reach the fusion barrier radius with a multitude of proton and neutron numbers, having broad distributions of excitation energies reaching tens of MeV. In contrast, standard models of fusion have assumed that nuclei reach the point of capture essentially unchanged—in just a handful of low-lying states.

The effect of these distributions on fusion can be seen through a variable we introduce, ΔEfi, showing how the energies with respect to the barrier change after multinucleon transfer. Due to transfer favouring smooth trajectories, most events have a similar energy with respect to their barrier, and thus a similar fusion probability to that of the initial 40Ca and 208Pb collision. This explains why standard models of fusion work as well as they do, despite missing the major physical processes occurring in the dynamics. We attribute the observed correlation to the favouring of smooth trajectories before and after transfer.

Importantly, we observe a significant tail of events having much higher excitation energies (negative ΔEfi) and thus lower kinetic energies. These will reduce fusion, explaining long-standing experimental observations6,10. The distribution of ΔEfi is the reason that fusion barrier distributions for higher Z1Z2 reactions are smoothed and have a tail extending to high energies. Such a barrier distribution is seen in 20Ne+208Pb35, which cannot be reproduced in a reasonably constrained coupled-channels calculation even when a very large number of states are included46.

Our results thus explain both why standard models of fusion seem to work at all, and also why they fail. Our results offer a framework to develop more realistic models of nuclear fusion, including the processes actually occurring in the early stages of the pathway to fusion.

Methods

Reflected flux

Experimental details

The measurements of the reflected flux were performed at Legnaro National Laboratory XTU Tandem-ALPI accelerator complex, using the PRISMA magnetic spectrometer15,16,17. PRISMA features a large solid angle (80 msr, Δθlab = ± 6°, Δϕ = ± 11°), momentum acceptance Δp = ± 10%, mass-resolution ΔA/A ~ 1/200, and energy resolution up to 1/1000 (via time-of-flight measurement). In this experiment, PRISMA was located at θlab = 115°.

The magnetic fields were set for each energy to maximise the transmission for the dominant charge state of the elastically scattered beam. Thus, the measurements focus on the evolution of quasi-elastic scattering to multinucleon transfer (or deep-inelastic scattering). The finite momentum acceptance of PRISMA means that binary reaction channels with Δp > ± 10%—those with much larger changes in N, Z—cannot be observed. In particular, the expected smooth evolution from multinucleon transfer to quasifission38,47,48 will not be observed. This makes our near-barrier measurements lower limits for the extent of multinucleon transfer in Z, N, and thus also energy dissipation. Additionally, if present, sticking and rotation in the multinucleon transfer component may mean that the measurement at θlab = 115° may be contaminated by trajectories originating from smaller angular momenta, closer to their effective barrier. This is difficult to quantify without knowledge of the sticking times, which can vary widely depending on the model interpretation. However, we note that the onset of multinucleon transfer at E/VB ~ 0.88 (for θlab = 115°) corresponds to E/VB = 0.94 for ℓ = 0, still well below the barrier.

Beams of 40Ca were produced in 12 energy steps between Ecm = 189.0 and 230.5 MeV. For the energies above 213 MeV, where the ALPI booster accelerator was used, carbon degrader foils of 135 μg/cm2 or 205 μg/cm2 were employed to provide three beam energies for each accelerator tune. The 40Ca beams were delivered onto ~150 μg/cm2208PbS targets oriented with their normals at 60° to the beam axis. The targets had 20 μg/cm2 carbon backings which were placed upstream of the target such that the particles accepted into PRISMA did not pass through the carbon backing.

Data analysis

Absolute probabilities of the integrated reflected flux Preflected were determined by normalising to Rutherford scattering yields in two silicon beam monitoring detectors placed at forward angles on either side of the beam axis (see Supplementary Fig. 2a). To account for the transmission through PRISMA, it was assumed that at the lowest energy (E/VB = 0.80), Preflected = dσreflected/dσRutherford = 1. The efficiency of PRISMA is rather flat, except for at the edges of its acceptance49. Therefore, the overall shape of the measured distributions are not substantially moderated by acceptance effects, thus allowing qualitative comparisons of their evolution with energy.

The atomic (proton) number Z, mass number A and energies of the scattered beam-like particles passing through PRISMA were determined using the TOF − Bρ − ΔE technique15. Ions pass through a position-sensitive microchannel plate timing detector (MCP)50 before entering the quadrupole and dipole magnets. At the focal plane, ions first pass through a multi-wire parallel plate avalanche counter (MWPPAC) then into a segmented ionisation chamber51. The measured positions of the ions in the MCP and MWPPAC define the trajectory of the ions through the magnetic elements, determining the magnetic rigidity Bρ. The energy loss of ions in the ionisation chamber enables the determination of Z, and with Bρ, the charge-state q. Together with time-of-flight (TOF), this allows determination of A (and hence neutron number N = A − Z) and the kinetic energy of the projectile-like nuclei. The resulting (Z, N) distributions are shown in Supplementary Fig. 1.

Following Z, N determination, the ground-state to ground-state energy difference (Q-value, Qgg) could be obtained for each event. With the kinetic energy information, the total excitation energy Ex could be derived (Ex = Qgg − Q), making use of two-body kinematics. Crucially, determining Z, N and Ex rather than total kinetic energy loss (TKEL) allowed us to calculate the change in energy with respect to the barrier after transfer relative to that of the entrance channel. This allowed a direct link to fusion hindrance to be made (Supplementary Figs. 2b, c, 3).

Determination of distance of closest approach

Mapping from a beam energy to a distance of closest approach requires that we determine the point at which the incoming kinetic energy is matched by the potential, as illustrated in Fig. 1 of the main text. We begin by constructing the total inter-nuclear potential Vtot, being the sum of an attractive nuclear potential Vnuc, and the repulsive Coulomb Vcoul and centrifugal Vcent potentials, \({V}_{{{{{{{{\rm{tot}}}}}}}}}={V}_{{{{{{{{\rm{nuc}}}}}}}}}+{V}_{{{{{{{{\rm{coul}}}}}}}}}+{V}_{{{{{{{{\rm{cent}}}}}}}}}.\) Vnuc was calculated using the São Paulo potential52, a density dependent double-folding potential, with an energy dependent correction arising from Pauli non-locality, determined from heavy-ion scattering data. This potential has no free parameters.

Vcoul is the repulsive Coulomb potential between a positively charged finite sphere and a positive-point charge, where the radius of the sphere (the Coulomb radius) is determined using São Paulo systematics52.

Vcent is the effective centrifugal potential depending on the angular momentum l, \({V}_{{{{{{{{\rm{cent}}}}}}}}}=\frac{{\hslash }^{2}l(l+1)}{2\mu {R}^{2}}=\frac{{L}^{2}}{2\mu {R}^{2}},\) where μ is the reduced mass of the colliding nuclei. Since the measurements of the reflected flux were performed at a fixed laboratory angle θlab = 115°, an increase in energy Ecm corresponds to a small decrease in l (and thus a small decrease in the centrifugal potential) for particles scattered to θlab.

We thus determine the angular momentum for particles scattered to 115° at each energy, \({l}_{{E}_{{{{{{{{\rm{cm}}}}}}}}},\theta=11{5}^{\circ }}\), assuming Rutherford trajectories. In Rutherford scattering, L is related to the impact parameter b via L = μv0b, where \({v}_{0}=\sqrt{2{E}_{{{{{{{{\rm{cm}}}}}}}}}/\mu }\), and \(b=\frac{{Z}_{{{{{{{{\rm{1}}}}}}}}}{Z}_{{{{{{{{\rm{2}}}}}}}}}{e}^{2}}{2{E}_{{{{{{{{\rm{cm}}}}}}}}}\tan \theta /2}.\)

Once Vtot have been constructed for each \({l}_{{E}_{{{{{{{{\rm{cm}}}}}}}}},\theta=11{5}^{\circ }}\), the distance of closest approach between centers \({R}_{\min }\) at each Ecm at θlab = 115° was determined by solving to find the outside intersection of Ecm and Vtot. RB and VB are found as the local maxima of Vtot. The inter-nuclear potentials as a function of \({R}_{\min }-{R}_{B}\) are shown by the blue curves in Fig. 1 of the main text, and the summed Vcent + Vcoul in green. The distances of closest approach for each energy indicated by the yellow crosses, and these, and the energies with respect to the (\({l}_{{E}_{{{{{{{{\rm{cm}}}}}}}}},\theta=11{5}^{\circ }}\)) barrier are tabulated in Supplementary Table 1.

Fission and quasifission mass distributions

The measurements of the fission and quasifission mass distributions were performed at the Heavy Ion Accelerator Facility, located at the Australian National University, Canberra, Australia. Beams of 36S, 40Ca were delivered by the 14UD 15 MV electrostatic pelletron accelerator. The beams were delivered to a 208PbS targets ranging in thickness from 100 to 170 μg/cm2. The targets were placed with their normals oriented at 60° to the beam axis to minimise energy loss of the fission fragments in the targets, and avoid shadowing of the detectors by the target frame. In order to compare the fission mass distributions across the two different systems, the energies were chosen to be between 6% and 7% above the fusion barrier53 for each system.

Fission and quasi-fission fragments were detected in coincidence using the CUBE spectrometer, in this experiment consisting of two multiwire proportional counters (MWPCs) with active areas of 279 × 357 mm2. The MWPCs were placed 180 mm from the target, with one detector at backwards angles centered at 90° continuously covering 55° to 130° and the other at forward angles, centered at 45°, covering 5° to 80°54. The typical azimuthal coverage was 70°.

Position information (θ, ϕ) was extracted from the X and Y anode planes of each MWPC, comprising grids of 20 μm gold-plated tungsten wires with 1 mm spacing. The central 0.9 μm gold-coated mylar cathode provided the timing information. From the position and timing information, the fission fragment velocities, energies and mass ratios (MR) were determined in the center-of-mass frame using energy-momentum conservation37,55. Fission fragment source analysis, confirming the fission fragments as being binary events originating with the 208Pb in the targets was performed. This is done by selecting the events where the components of the fission fragment velocities in the perpendicular v⊥ and parallel v∥ directions relative to the beam are consistent with full-momentum transfer fission after reactions with 208Pb. That is, the events are tightly centered around v⊥ = 0 and \([{v}_{\parallel }-{v}_{{{{{{{{\rm{CN}}}}}}}}}]\sin {\theta }_{cm}=0\), where \({v}_{{{{{{{{\rm{CN}}}}}}}}}\) is the velocity of the compound nucleus, and \(\sin {\theta }_{cm}\) the scattering angle56.

Two silicon monitor detectors were placed at laboratory angles of θ = 30° and ϕ = 90°, 270° to measure elastically scattered events for absolute cross-section determination dσ2/dMRdθ.