Microscopic Description of Fission for the r-Process in Neutron Star Mergers
289
individual binding energies of the two fragments and the interaction energy between
the fragments composed of the Coulomb repulsion and the nuclear attraction. The
system at scission is treated as a microcanonical ensemble where all available states
are equiprobable. In this framework, the number of available states of a given
fragmentation is the product of the state densities of the two isolated fragments.
The yield of a fragmentation is the number of available states associated with this
fragmentation whatever the deformation of the fragments.
The new version of the SPY model, called SPY2 [14], is based on fully
microscopic nuclear ingredients to describe the fragments properties at the scission
point. The scission configuration of the fissioning nucleus is no more defined by two
uniformly charged fragments without diffusivity separated by a scission distance,
like in the original version SPY1 [7], but rather on the basis of the fragments’
proton density derived from HFB proton spatial distributions. The proton density
at the scission neck is used as a separation criterion for the nascent fragments
which is the same whatever the fissioning system. The Coulomb repulsion is
numerically computed from the HFB proton spatial distributions of the fragments.
The state densities are no more described in the framework of a Fermi gas but in the
framework of the statistical BCS model of nuclear state densities on the basis of the
discrete single-particle level scheme obtained in the same microscopic framework
as the one used to estimate individual binding and Coulomb energies, which takes
pairing and shell effects coherently into account on the basis of the same nuclear
structure properties.
All SPY2 inputs are computed within the same self-consistent microscopic HFB
framework on the basis of the BSk27 Skyrme interaction [15].
3.2 Fission of 236 U, 240 Pu, and 252 Cf
We compare in Fig. 3 the experimental yield distributions of the three fissioning
systems 236 U, 240 Pu, and 252 Cf with those predicted by SPY1 and SPY2. With SPY1
(Fig. 3a–c, blue dashed lines), the yield distribution is peaked around A 1 = 132
and A 2 = A CN − 132, particularly for U and Pu. These peaked distributions can
be explained by the high sensitivity to the fragments shell effect, in particular
to the doubly magic nucleus 132
50 Sn 82 which is associated with the soft fragment
104
42 Mo 62 in the 236 U case. Compared to SPY1, the SPY2 yield distributions (Fig. 3a–
c, green thin lines) are much wider and also in better agreement with experimental
data but present strong staggering patterns. To compare the overall structure with
experimental data, the yield distributions are smoothed by a normalized Gaussian
function.
In the U case (Fig. 3a, red line), the symmetric part of the distribution is overestimated compared to experimental data. This is partially due to an underestimate
of the highly asymmetric part of the yields distribution, which, in turn, is due to
an overestimate of the kinetic energy (KE) for asymmetric fragments. A lower
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individual binding energies of the two fragments and the interaction energy between
the fragments composed of the Coulomb repulsion and the nuclear attraction. The
system at scission is treated as a microcanonical ensemble where all available states
are equiprobable. In this framework, the number of available states of a given
fragmentation is the product of the state densities of the two isolated fragments.
The yield of a fragmentation is the number of available states associated with this
fragmentation whatever the deformation of the fragments.
The new version of the SPY model, called SPY2 [14], is based on fully
microscopic nuclear ingredients to describe the fragments properties at the scission
point. The scission configuration of the fissioning nucleus is no more defined by two
uniformly charged fragments without diffusivity separated by a scission distance,
like in the original version SPY1 [7], but rather on the basis of the fragments’
proton density derived from HFB proton spatial distributions. The proton density
at the scission neck is used as a separation criterion for the nascent fragments
which is the same whatever the fissioning system. The Coulomb repulsion is
numerically computed from the HFB proton spatial distributions of the fragments.
The state densities are no more described in the framework of a Fermi gas but in the
framework of the statistical BCS model of nuclear state densities on the basis of the
discrete single-particle level scheme obtained in the same microscopic framework
as the one used to estimate individual binding and Coulomb energies, which takes
pairing and shell effects coherently into account on the basis of the same nuclear
structure properties.
All SPY2 inputs are computed within the same self-consistent microscopic HFB
framework on the basis of the BSk27 Skyrme interaction [15].
3.2 Fission of 236 U, 240 Pu, and 252 Cf
We compare in Fig. 3 the experimental yield distributions of the three fissioning
systems 236 U, 240 Pu, and 252 Cf with those predicted by SPY1 and SPY2. With SPY1
(Fig. 3a–c, blue dashed lines), the yield distribution is peaked around A 1 = 132
and A 2 = A CN − 132, particularly for U and Pu. These peaked distributions can
be explained by the high sensitivity to the fragments shell effect, in particular
to the doubly magic nucleus 132
50 Sn 82 which is associated with the soft fragment
104
42 Mo 62 in the 236 U case. Compared to SPY1, the SPY2 yield distributions (Fig. 3a–
c, green thin lines) are much wider and also in better agreement with experimental
data but present strong staggering patterns. To compare the overall structure with
experimental data, the yield distributions are smoothed by a normalized Gaussian
function.
In the U case (Fig. 3a, red line), the symmetric part of the distribution is overestimated compared to experimental data. This is partially due to an underestimate
of the highly asymmetric part of the yields distribution, which, in turn, is due to
an overestimate of the kinetic energy (KE) for asymmetric fragments. A lower