Problem of Level Densities
115
Variations arising from employing of different (FGM or GCM) level density models
represent the first source of uncertainties. Both FGM and GCM model prescriptions
have parameters which are traditionally determined based on comprehensive data on
neutron resonances [10] (discussed in the next section). For details about specific
formulas and their parameterizations recommended for practical applications one
can refer to the Refs.[1, 7].
Microscopic level density calculations used as input in Talys and Empire are
those from Refs.[11, 12]. Calculations are available in table form for all nuclei.
These level density model calculations might be consistent, depending on a specific
nucleus, with either FGM or GCM models or might exhibit completely different
excitation energy dependence. So, again, the difference in an excitation energy
dependence in different models is a key factor which determines level density
uncertainties.
Parameters for all level density models including microscopic ones from Refs.
[11, 12] (which also use renormalization parameters) are determined based on
comprehensive, but a single data set only which is data set on neutron resonance
spacings. Data on neutron resonances are available for all stable plus one neutron
nuclei, however, they are very limited in terms of spin, parity, and excitation energy
ranges. Thus, the limitation of experimental data set on which models (model
parameterizations) are based is the main source of level density model uncertainties.
More specific discussion on limitation of neutron resonance and other experimental
data is presented in the next section.
3 Review of Available Experimental Data Sets and Their
Limitations
3.1 Neutron Resonance Spacings
As already mentioned in the previous section the data on neutron resonance spacings
is the only data set the current level density models use for their parameterizations. Therefore, understanding of limitations of these data and their influence on
uncertainties of level density models is important. The neutron resonances represent
individual nuclear levels excited in low-energy neutron induced reactions. The
energy of neutrons is in eV range for heavy nuclei and in keV range for middle
mass and light ones. Therefore, the excitation energy range for neutron resonances
is very limited and is just above the neutron separation energy. Reactions with lowenergy neutrons are dominated by reactions with zero orbital momentum, so the
spins of the neuron resonances (the so called s-resonances) are in a very narrow
range of (I t ± 1/2), where I t is the spin of a target nucleus. All s-wave resonances
have one parity only equal to the parity of the ground state target nucleus. For middle
mass and light nuclei, contribution of p-wave resonances (for neutrons with orbital
momentum equal one) becomes apparent which creates difficulties of distinguishing
115
Variations arising from employing of different (FGM or GCM) level density models
represent the first source of uncertainties. Both FGM and GCM model prescriptions
have parameters which are traditionally determined based on comprehensive data on
neutron resonances [10] (discussed in the next section). For details about specific
formulas and their parameterizations recommended for practical applications one
can refer to the Refs.[1, 7].
Microscopic level density calculations used as input in Talys and Empire are
those from Refs.[11, 12]. Calculations are available in table form for all nuclei.
These level density model calculations might be consistent, depending on a specific
nucleus, with either FGM or GCM models or might exhibit completely different
excitation energy dependence. So, again, the difference in an excitation energy
dependence in different models is a key factor which determines level density
uncertainties.
Parameters for all level density models including microscopic ones from Refs.
[11, 12] (which also use renormalization parameters) are determined based on
comprehensive, but a single data set only which is data set on neutron resonance
spacings. Data on neutron resonances are available for all stable plus one neutron
nuclei, however, they are very limited in terms of spin, parity, and excitation energy
ranges. Thus, the limitation of experimental data set on which models (model
parameterizations) are based is the main source of level density model uncertainties.
More specific discussion on limitation of neutron resonance and other experimental
data is presented in the next section.
3 Review of Available Experimental Data Sets and Their
Limitations
3.1 Neutron Resonance Spacings
As already mentioned in the previous section the data on neutron resonance spacings
is the only data set the current level density models use for their parameterizations. Therefore, understanding of limitations of these data and their influence on
uncertainties of level density models is important. The neutron resonances represent
individual nuclear levels excited in low-energy neutron induced reactions. The
energy of neutrons is in eV range for heavy nuclei and in keV range for middle
mass and light ones. Therefore, the excitation energy range for neutron resonances
is very limited and is just above the neutron separation energy. Reactions with lowenergy neutrons are dominated by reactions with zero orbital momentum, so the
spins of the neuron resonances (the so called s-resonances) are in a very narrow
range of (I t ± 1/2), where I t is the spin of a target nucleus. All s-wave resonances
have one parity only equal to the parity of the ground state target nucleus. For middle
mass and light nuclei, contribution of p-wave resonances (for neutrons with orbital
momentum equal one) becomes apparent which creates difficulties of distinguishing