286
J.-F. Lemaître et al.
by fission during the neutron irradiation. Phenomenological models are not suited
to determine such quantities due to the exotic nature of the nuclei involved and the
low reliability of such models far away from the experimentally known region. The
importance of reliable predictions is discussed in Refs. [5, 6].
Detailed fission paths, from which fission probability can be deduced, can be
determined on the basis of the Hartree–Fock–Bogoliubov (HFB) model which has
proven its capacity to estimate the potential energy surface (PES), hence the static
fission barrier heights and widths, with a relatively high degree of accuracy [4]. In
this case, the static aspect of fission is treated via the least-energy path (LEP) where
from the fission barrier is deduced, while the dynamical approach can be described
through the least-action path (LAP) taking into account the inertia tensor.
Fission yields of the heavy neutron-rich elements are also fundamental ingredients in r-process calculations. Microscopic approaches, like the Scission Point Yield
(SPY) model [7], may predict eventually new fission modes such as the doubly
asymmetric fission of the nuclei in the region of 278 Cf which impacts the final
abundances of rare-earth elements [2]. In addition, the SPY model provides the
mean number of evaporated neutrons per fissioning nucleus which may also affect
the neutron flux, especially during the late neutron irradiation.
Our latest effort to improve the prediction of fission paths, spontaneous fission
half-lives, and fission yields are described in the next sections.
2 Potential Energy Surface and Fission Path
The PES is explored in the deformation space by imposing constraints to the
standard HFB variational procedure with respect to the axial quadrupole deformation Q 20 related to nucleus elongation and the octupole deformation Q 30 related
to the mass (or left-right) asymmetry. All calculations in the present study are
performed with the Gogny D1M interaction. The final PES in the (Q 20 , Q 30 ) plane
is constructed by correcting the mean-field energy E HFB for the triaxiality degree
of freedom at small deformations and for the collective correlation effects beyond
mean field. All details concerning the HFB calculations with the Gogny interaction
including the basis expansion, convergence criteria, the variational procedure, and
corrections of the mean field can be found in Ref. [8] and references therein. For the
time being, only PES for even–even nuclei has been estimated.
2.1 Least-Energy Fission Path and Fission Barriers
The method used to determine the LEP of a PES is inspired from the flooding
method. It is based on a comprehensive approach, proceeding by dichotomy, to
determine the LEP using a binary search tree to store information about the saddle
J.-F. Lemaître et al.
by fission during the neutron irradiation. Phenomenological models are not suited
to determine such quantities due to the exotic nature of the nuclei involved and the
low reliability of such models far away from the experimentally known region. The
importance of reliable predictions is discussed in Refs. [5, 6].
Detailed fission paths, from which fission probability can be deduced, can be
determined on the basis of the Hartree–Fock–Bogoliubov (HFB) model which has
proven its capacity to estimate the potential energy surface (PES), hence the static
fission barrier heights and widths, with a relatively high degree of accuracy [4]. In
this case, the static aspect of fission is treated via the least-energy path (LEP) where
from the fission barrier is deduced, while the dynamical approach can be described
through the least-action path (LAP) taking into account the inertia tensor.
Fission yields of the heavy neutron-rich elements are also fundamental ingredients in r-process calculations. Microscopic approaches, like the Scission Point Yield
(SPY) model [7], may predict eventually new fission modes such as the doubly
asymmetric fission of the nuclei in the region of 278 Cf which impacts the final
abundances of rare-earth elements [2]. In addition, the SPY model provides the
mean number of evaporated neutrons per fissioning nucleus which may also affect
the neutron flux, especially during the late neutron irradiation.
Our latest effort to improve the prediction of fission paths, spontaneous fission
half-lives, and fission yields are described in the next sections.
2 Potential Energy Surface and Fission Path
The PES is explored in the deformation space by imposing constraints to the
standard HFB variational procedure with respect to the axial quadrupole deformation Q 20 related to nucleus elongation and the octupole deformation Q 30 related
to the mass (or left-right) asymmetry. All calculations in the present study are
performed with the Gogny D1M interaction. The final PES in the (Q 20 , Q 30 ) plane
is constructed by correcting the mean-field energy E HFB for the triaxiality degree
of freedom at small deformations and for the collective correlation effects beyond
mean field. All details concerning the HFB calculations with the Gogny interaction
including the basis expansion, convergence criteria, the variational procedure, and
corrections of the mean field can be found in Ref. [8] and references therein. For the
time being, only PES for even–even nuclei has been estimated.
2.1 Least-Energy Fission Path and Fission Barriers
The method used to determine the LEP of a PES is inspired from the flooding
method. It is based on a comprehensive approach, proceeding by dichotomy, to
determine the LEP using a binary search tree to store information about the saddle