This paper proposes a new, more microscopic way to model the fusion step that makes superheavy elements. The authors combine a nuclear-structure method, the Hartree–Fock–Bogoliubov (HFB) approach, with a dynamical model called fusion by diffusion (FBD). The result is a self-consistent way to find where the two nuclei first form a neck (the “injection point”) and how high the inner fusion barrier is, using the calculated potential-energy surface (PES) of the combined system.

To make the PES the authors perform constrained HFB calculations with a Skyrme energy density functional (SkM*). They constrain three shape coordinates: elongation (quadrupole Q20), mass asymmetry (octupole Q30) and neck thickness (hexadecapole Q40). Pairing of nucleons is treated with the Lipkin–Nogami approximation. These microscopic PES maps let the authors feed physically motivated injection points and barrier heights into the FBD diffusion step. For the test case 48Ca + 208Pb they report that the calculated evaporation‑residue cross section (the final yield after particle evaporation) reproduces experimental data reasonably well.

A key finding is a strongly asymmetric valley in the PES that is anchored by the doubly magic nucleus 208Pb. This “hyper‑asymmetric” valley links the incoming two‑body configuration to the compact compound nucleus. The same valley also provides an energetically favored path back out toward asymmetric split patterns known as cluster decay, in which a nucleus emits a cluster heavier than an alpha particle. The authors therefore emphasize that cold fusion (low‑excitation fusion using a compact target like 208Pb) and cluster decay are related processes along the same microscopic valley. The fast formation of a neck between projectile and target — the “neck‑zip” mechanism — drives the system into that valley.

Why this matters: the fusion step is the main source of uncertainty when predicting production rates of new superheavy elements. In the commonly used factorization of the production cross section, the probability to form a compact compound nucleus (PCN) is typically tiny and controls the final yield. By extracting the injection point and inner barrier directly from the microscopic PES, the hybrid HFB+FBD framework reduces reliance on phenomenological tuning. The authors also apply the method to cold‑fusion reactions with 54Cr + 208Pb and 58Fe + 208Pb and find that PCN falls roughly exponentially with the compound‑nucleus charge Z, in line with known systematics.