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In the theoretical description of the nuclear fission, the potential energy surface (PES) plays a vital role in analyzing the process. One crucial region of this process is just before scission, where pre-fragments develop their near-final configuration [1]. It has been demonstrated that employing multiple constraints on collective variables can be beneficial in obtaining a more detailed and continuous PES compared to projecting on only one or two collective degrees of freedom, which can lead to discontinuities and less informative fission barriers [2]. Using the necking constraint, along with constraints on multiple moments can help study this specific region and obtain a continuous PES through this approach [3].
We study saddle to the scission region by employing necking constraints using necking operator [4] with the analysis of its parameters: the width and the position of the necking gaussian. This study aims to understand the influence of these parameters on final results. We conduct the study for $^{236}$Pu in both asymmetric and super-asymmetric fission modes, as well as for $^{264}$Rf in symmetric fission modes. The constrained Hartree–Fock–Bogoliubov model is used with the Gogny D1S parametrization.
In this study, we demonstrate that the position of the minimum neck remains fixed for a given quadrupole deformation, irrespective of the chosen value of the Gaussian width. The minimum neck position can be detected by either using a Gaussian of width 1 fm to precisely capture the local structure of the neck or by performing the calculation with a dynamically determined neck position. However, some discrepancies are observed in the minimum neck position between these two methods.
[1] Younes W and Gogny D, 2011 Phys. Rev. Lett. 107 132501.
[2] A. Zdeb, M. Warda, and L. M. Robledo, Phys. Rev. C 104, 014610 (2021).
[3] R. Han, M. Warda, A. Zdeb, and L. M. Robledo, Scission configuration in self-consistent calculations with neck constraints, Phys. Rev. C 104, 064602 (2021).
[4] J. F. Berger, J. D. Anderson, P. Bonche, and M. S. Weiss, Phys. Rev. C 41, R2483 (1990).