Description
Theoretical descriptions of heavy-ion nuclear fusion remain largely phenomenological, often exploiting complex-valued potentials to absorb flux and associating the deficit in the norm of outgoing waves with fusion observables. This makes it challenging to simultaneously and consistently describe related reaction outcomes, such as exchange of nucleons at large distances prevalent in super-heavy element formation reactions [1]. We discuss our recent efforts towards formulating physically motivated alternative approaches to modelling fusion that naturally account for effects inaccessible or artificially imposed in present theories.
Fusion occurs on much larger timescales than quasi-elastic scattering. Webber [2] attempted to simulate this effect within the time-dependent coupled channels framework, using many couplings at short distances to trap flux for long periods, mimicking formation of a fused system. The norm of the wave function at short distances indicated that this indeed leads to temporal separation from the (fast) scattered flux. However, these calculations were unable to energy-resolve the wave packet and a more complete theoretical treatment is required to calculate the $S$-matrix and scattering observables.
This work provides a rigorous description and a numerically convenient method to apply the wave packet time-correlation function formulation of the $S$-matrix with time-independent Hamiltonians [3], that include the long-range Coulomb potential [4]. Illustrative numerical examples show excellent agreement with the static solver FRESCO. While the $S$-matrix can be obtained using static methods in such cases, we emphasise potential numerical advantages of using wave packet propagation. We highlight how the time-correlation function can be a useful tool for the time-separated analysis underpinning Webber’s approach to modelling fusion, while retaining a direct link to the $S$-matrix required to obtain observables.
[1] K.J. Cook, et. al. Nat.Commun.14,7988 (2023). [2] M. Webber. Honours thesis, Australian National University (2025). [3] D.J. Tannor and D.E. Weeks. J.Chem.Phys.98,3884 (1993). [4] A.S. Tejas and E.C. Simpson. EPJ.Web.Conf.368,00023 (2026).
| I am the presenting author | Yes |
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