A Grand Tour of Nuclear Fission Physics
265
by the fragments which tend to be peaked in the recoil direction of those fragments.
Scission neutrons were first identified by their angular distributions [42], but the
neutron energy spectrum may also be affected by their presence [43]. However, a
great deal of work has since shown that some scission neutrons could be reabsorbed
by the moving fragments, resulting in an anisotropic distribution not so different
from that of the neutrons emitted by the fragments themselves [44], thus a word of
caution is warranted so that scission neutrons are not automatically equated with
an additional isotropic source of neutrons in the data (see also [45]). Finally, when
the secondary fragment undergoes beta decay, the resulting nucleus may on rare
occasions be left with sufficient excitation energy to emit a neutron. Because they
are delayed by the relatively slow beta-decay process, these are known as delayed
neutrons [46].
The gamma-ray energies and multiplicities have been recently measured for
several fissioning systems [47–49]. The measured properties of these gamma rays
can be used to estimate the energy they remove from the excitation energies of the
fragments. By adding the energies removed by both neutrons and gammas, the initial
excitation energies of the fragments can be reconstructed. Because they also carry
away angular momentum, the prompt gammas can be used to deduce the initial
angular momentum of the fragments [50].
3 Fission Theory and Modeling
The liquid-drop model (LDM) was the first approach used to describe the fission
process [8, 9]. The LDM has since evolved into the macroscopic-microscopic model
that is widely used today [51, 52]. The remarkable success of the LDM can be
attributed to the fact that it gives a good description of the bulk behavior of the
nucleus (i.e., the properties that vary smoothly with the number of nucleons),
and any deviations from this bulk behavior are due primarily to the contribution
from nucleons in the thin surface region of the nucleus [53]. The macroscopicmicroscopic model starts from a family of curves that describe the surface of the
nucleus as a geometrical object. The total energy of the nucleus is then obtained as
the sum of a macroscopic energy, a shell correction, and a pairing correction. The
macroscopic contribution often consists primarily of a surface energy, proportional
to the surface integral of the nuclear shape, and a Coulomb energy calculated as
the volume integral of the inverse-distance potential inside the nucleus, assuming a
uniform charge distribution [53, 54]. There are additional terms that can be added
to improve the accuracy of the macroscopic-energy term, and various liquid-drop
prescriptions have been developed depending on which terms are included, such
as the standard LDM [55], the generalized liquid-drop model [56, 57], the LublinStrasbourg liquid drop [58], and the finite-range liquid-drop model [51, 52]. The
shell correction term was introduced by Strutinsky [59, 60] to account for quantum
effects. In order to calculate this correction, it is necessary to construct a potential
function that can be used in the Schrödinger equation to calculate a set of single-
265
by the fragments which tend to be peaked in the recoil direction of those fragments.
Scission neutrons were first identified by their angular distributions [42], but the
neutron energy spectrum may also be affected by their presence [43]. However, a
great deal of work has since shown that some scission neutrons could be reabsorbed
by the moving fragments, resulting in an anisotropic distribution not so different
from that of the neutrons emitted by the fragments themselves [44], thus a word of
caution is warranted so that scission neutrons are not automatically equated with
an additional isotropic source of neutrons in the data (see also [45]). Finally, when
the secondary fragment undergoes beta decay, the resulting nucleus may on rare
occasions be left with sufficient excitation energy to emit a neutron. Because they
are delayed by the relatively slow beta-decay process, these are known as delayed
neutrons [46].
The gamma-ray energies and multiplicities have been recently measured for
several fissioning systems [47–49]. The measured properties of these gamma rays
can be used to estimate the energy they remove from the excitation energies of the
fragments. By adding the energies removed by both neutrons and gammas, the initial
excitation energies of the fragments can be reconstructed. Because they also carry
away angular momentum, the prompt gammas can be used to deduce the initial
angular momentum of the fragments [50].
3 Fission Theory and Modeling
The liquid-drop model (LDM) was the first approach used to describe the fission
process [8, 9]. The LDM has since evolved into the macroscopic-microscopic model
that is widely used today [51, 52]. The remarkable success of the LDM can be
attributed to the fact that it gives a good description of the bulk behavior of the
nucleus (i.e., the properties that vary smoothly with the number of nucleons),
and any deviations from this bulk behavior are due primarily to the contribution
from nucleons in the thin surface region of the nucleus [53]. The macroscopicmicroscopic model starts from a family of curves that describe the surface of the
nucleus as a geometrical object. The total energy of the nucleus is then obtained as
the sum of a macroscopic energy, a shell correction, and a pairing correction. The
macroscopic contribution often consists primarily of a surface energy, proportional
to the surface integral of the nuclear shape, and a Coulomb energy calculated as
the volume integral of the inverse-distance potential inside the nucleus, assuming a
uniform charge distribution [53, 54]. There are additional terms that can be added
to improve the accuracy of the macroscopic-energy term, and various liquid-drop
prescriptions have been developed depending on which terms are included, such
as the standard LDM [55], the generalized liquid-drop model [56, 57], the LublinStrasbourg liquid drop [58], and the finite-range liquid-drop model [51, 52]. The
shell correction term was introduced by Strutinsky [59, 60] to account for quantum
effects. In order to calculate this correction, it is necessary to construct a potential
function that can be used in the Schrödinger equation to calculate a set of single-