Microscopic Description of Fission for the r-Process in Neutron Star Mergers
287
Fig. 1 (Color online)
Comparison of D1M,
Skyrme-BSk14 [9], and
FRLDM [10] primary fission
barrier heights with empirical
values [11] as a function of
the fissibility parameter Z 2 /A
points and their neighboring wells. More details can be found in [8] and references
therein.
The highest (or primary) fission barrier, which is crucial for the calculation of
fission probabilities, can directly be extracted from the LEP. It corresponds to the
difference between the energy of the highest saddle point and the ground-state 0 +
level energy of the even–even fissioning nuclei. In Fig. 1, we compare the primary
barrier height of the 14 even–even nuclei for which empirical values have been
extracted from fission cross section measurements [11]. A good agreement is found
with empirical data with the root-mean-square (rms) deviation of 0.52 MeV. The
agreement is particularly good for 232 U, 234 U, 236 U, and 238 Pu. D1M fission barrier
heights are in better agreement with the empirical values than the ones obtained
with the Skyrme-HFB calculations based on the BSk14 force [9] (rms = 0.75 MeV)
as well as with the finite-range liquid-drop model (FRLDM) [10] (rms = 0.77 MeV).
2.2 Least-Action Fission Path: Fission Lifetime
The Dijkstra’s algorithm [13] is used to minimize the action of the fission path.
The action depends on the inertia tensor, the potential energy of the system (i.e. the
PES), the total energy of the system (which depends on its excitation energy), and
the trajectory of the LAP. The inner turning point is close to the ground-state well
while the outer turning point is located in the high Q 20 region of the PES. More
details can be found in Ref. [8] and references therein. The spontaneous fission
half-life can be obtained within the WKB formalism as
T
sf
1/2 [s] = 2.86 × 10
−21 (1 + e
2S(E ∗ )/¯ h )
(1)
287
Fig. 1 (Color online)
Comparison of D1M,
Skyrme-BSk14 [9], and
FRLDM [10] primary fission
barrier heights with empirical
values [11] as a function of
the fissibility parameter Z 2 /A
points and their neighboring wells. More details can be found in [8] and references
therein.
The highest (or primary) fission barrier, which is crucial for the calculation of
fission probabilities, can directly be extracted from the LEP. It corresponds to the
difference between the energy of the highest saddle point and the ground-state 0 +
level energy of the even–even fissioning nuclei. In Fig. 1, we compare the primary
barrier height of the 14 even–even nuclei for which empirical values have been
extracted from fission cross section measurements [11]. A good agreement is found
with empirical data with the root-mean-square (rms) deviation of 0.52 MeV. The
agreement is particularly good for 232 U, 234 U, 236 U, and 238 Pu. D1M fission barrier
heights are in better agreement with the empirical values than the ones obtained
with the Skyrme-HFB calculations based on the BSk14 force [9] (rms = 0.75 MeV)
as well as with the finite-range liquid-drop model (FRLDM) [10] (rms = 0.77 MeV).
2.2 Least-Action Fission Path: Fission Lifetime
The Dijkstra’s algorithm [13] is used to minimize the action of the fission path.
The action depends on the inertia tensor, the potential energy of the system (i.e. the
PES), the total energy of the system (which depends on its excitation energy), and
the trajectory of the LAP. The inner turning point is close to the ground-state well
while the outer turning point is located in the high Q 20 region of the PES. More
details can be found in Ref. [8] and references therein. The spontaneous fission
half-life can be obtained within the WKB formalism as
T
sf
1/2 [s] = 2.86 × 10
−21 (1 + e
2S(E ∗ )/¯ h )
(1)