Cluster radioactivity — the emission of a light nucleus heavier than an alpha particle — is established only in the trans-lead region (21 known emitters, from 221Fr down to 242Cm). The fission approach of Poenaru and Gherghescu (Pramana 85, 415, 2015) reproduces this data but explicitly leaves open whether cluster decay competes with alpha decay and spontaneous fission in superheavy nuclei: spontaneous-fission half-lives remain uncertain by many orders of magnitude because inertia prescriptions (Werner–Wheeler versus cranking and beyond) are incompletely validated, predicted half-lives inherit large, unquantified spread from divergent atomic mass tables through exponentially sensitive Q-values, potential-energy-surface mapping has not been extended systematically to superheavy nuclei near the beta-stability line and to neutron-rich isotopes, and rare emitter classes (odd–odd) plus detection limits constrain testability. The open question left by this program is whether cluster radioactivity actually occurs in superheavy nuclei and competes with alpha decay and spontaneous fission — a prediction of the alpha/cluster/spontaneous-fission half-lives and branching ratios of superheavy nuclei in the program's range (Z approximately 104–124) — and it remains open: a decade of later work (microscopic density-functional-theory fission studies, empirical-formula systematics, mass-model comparisons, sub-microsecond detection advances) has refined pieces but left the predictions mutually contradictory and the uncertainties unquantified.

Background

Cluster radioactivity (CR) is a radioactive decay mode in which a nucleus emits a light fragment heavier than a helium nucleus but lighter than a typical fission fragment — from carbon-14 up to silicon-34 in observed cases — leaving a daughter near the doubly magic 208Pb (a nucleus with closed shells of both protons and neutrons, and hence exceptional stability). It was predicted in 1980 by Sandulescu, Poenaru and Greiner and first observed in 1984; all 21 known cluster emitters lie in the trans-lead region between 221Fr and 242Cm, and no cluster emission has ever been observed from a superheavy nucleus. Superheavy nuclei (SHE) are nuclei with proton number around and above Z=104, whose existence against prompt disintegration rests on quantum shell effects rather than the liquid-drop barrier; the known ones reach oganesson (Z=118). A superheavy nucleus can decay by alpha decay (emission of a 4He nucleus), by spontaneous fission (SF, splitting into two comparable fragments through quantum tunneling through the fission barrier), or — hypothetically — by cluster radioactivity, and the observed decay chains of SHE synthesis experiments are interpreted by assuming which of these modes dominates isotope by isotope. The half-life of a tunneling decay depends exponentially on the decay energy Q (the mass difference between parent and fragments, supplied by atomic mass tables where not measured) and on the action integral across the barrier, which involves the collective inertia of the deforming nucleus. The macroscopic–microscopic method computes a potential-energy surface (PES) — the energy of the nucleus as a function of deformation coordinates such as mass-asymmetry eta and quadrupole moment — by adding shell corrections to a liquid-drop-like macroscopic energy; the inertia tensor along the fission path can be approximated by the irrotational-flow Werner–Wheeler formula or computed microscopically by the cranking model (perturbing single-particle states by the collective velocity). Poenaru and Gherghescu and co-workers developed the Analytical SuperAsymmetric Fission Model (ASAF), in which CR is treated as a very asymmetric fission process with an analytic barrier, and the Universal (UNIV) and Universal Decay Law (UDL) formulas, and benchmarked them on hundreds of alpha emitters and the known cluster branches. Their companion calculations for superheavy nuclei (e.g. a PES of 286Fl showing two valleys corresponding to 208Pb + 78Ge and 132Sn + 154Gd-type splits) predicted that for some charge numbers around Z=118–124 cluster decay could compete with or dominate alpha decay. The 2015 Pramana review of this program states its acknowledged limitations as open issues: SF half-lives computed with Werner–Wheeler inertia can be wrong by many orders of magnitude (their cranking-inertia study of 282Cn required a fitted zero-point energy to reproduce experiment); theoretical mass tables give divergent Q-values in unmeasured regions, which propagate exponentially into half-lives; detailed PES calculations had not been extended to superheavy nuclei closer to the beta-stability line (the locus of nuclei longest-lived against beta decay on a chart of neutron number versus proton number) and to neutron-rich isotopes; and experimental scarcity of certain emitter classes (notably odd–odd emitters, where unpaired nucleons complicate the theory) plus a practical detection limit around one microsecond constrain which predictions can be tested. Whether cluster radioactivity actually occurs in superheavy nuclei, and with what half-life relative to alpha decay and SF, is therefore not a settled question: it is a quantitative prediction problem whose inputs — masses, shell corrections, inertia, and cluster preformation probabilities (the probability that the emitted fragment already exists as a preformed cluster inside the parent nucleus before tunneling) — are each uncertain at the level that matters, because the answer depends on them exponentially.

Problem Statement

Determine whether cluster (heavy-particle) radioactivity occurs in superheavy nuclei and competes with alpha decay and spontaneous fission, as posed by the fission approach of Poenaru and Gherghescu (Pramana 85, 415, 2015) and its acknowledged limitations. The objective is a prediction of the cluster-decay, alpha-decay and spontaneous-fission partial half-lives and of the cluster-to-alpha and cluster-to-SF branching ratios for superheavy nuclei in the program's range (Z approximately 104–124), and, for each element Z=104–124 and the isotope or isotopes on or nearest the beta-stability line, a determination of whether — separately for alpha decay and for spontaneous fission — cluster emission dominates that competitor, is comparable to it (within one order of magnitude in partial half-life), or is subdominant to it. The theoretical mass table used for masses that are unmeasured and the inertia prescription used for the barrier must be named, and each such comparison must be stated as conditional on those named inputs. Extending these predictions toward neutron-rich isotopes and, as they become accessible, superheavy nuclei off the beta-stability line forms a separate, secondary target. The prediction is confronted by the obstacles the program itself acknowledges: calculated spontaneous-fission half-lives can deviate from experiment by up to ten orders of magnitude because the Werner–Wheeler inertia is too small (cranking inertia with a fitted zero-point vibration energy reproduces the measured 282Cn half-life), and cluster Q-values depend on which mass model is used for unmeasured superheavy isotopes — inputs that propagate exponentially into half-lives. The same masses, shell corrections, inertias, and preformation factors enter all three decay modes, so a prediction of the competition is only as credible as the treatment of these obstacles behind it. An experimental observation of cluster emission from a superheavy parent would settle the question empirically; the program explicitly awaits decay-mode information for Z>120, where cluster decay is predicted to become observable (Z>121). Experimental scarcity of certain emitter classes (notably odd–odd nuclei) and the practical detection window (now extending below one microsecond) constrain which predictions can be tested.

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