  Nowdays, modern microscopic approaches for fission are generally based on the
framework of nuclear density functional theory (DFT), which has enabled a
self-consistent treatment of both static and dynamic aspects of fission. The
key issue is a DFT solver with high precision and efficiency especially for the
large elongated configurations. Purpose: To develope a DFT solver with high
precision and efficiency based on the point coupling covariant density
functional theory (CDFT), which has achieved great success in describing
properties of nuclei for the whole nuclear chart. Method: We have extended the
point-coupling CDFT to be based on the two-center harmonic oscillator (TCHO)
basis, which matches well with the large elongated configurations during the
fission process. Multi-dimensional constraint and time-dependent generator
coordinate method (TDGCM) have been used to analyze the fission potential
energy surface and fission dynamics, respectively. To simulate the splitting
process of the nascent fragments beyond scission, we also introduce a density
constraint into the new CDFT framework. Results: Illustrative calculations have
been done for the PESs and induced fission dynamics of two typical examples:
$^{226}$Th and $^{240}$Pu. A more reasonable PES is obtained in the new
framework compared to that based on the once-center harmonic oscillator (OCHO)
with the same basis space. An optimization of about $0.2\sim0.3$ MeV has been
achieved for the outer fission barriers and large elongated configurations. The
dynamical simulations based on TCHO basis presents a trend to improve the
description for fission yields. Conclusions: The new developed CDFT solver
optimizes the elongated configurations, improves the calculation efficiency,
and provides a basis for large-scale multi-dimensional constraint calculations
and dynamical simulations.
