Problem of Level Densities
117
Although, the original ρ(E ∗ ) oslo is not able to provide model independent
absolute level density values, it delivers very unique information about the excitation
energy dependence of the level density function. As it is seen from Eq. 1, ρ(E ∗ ) oslo
is able to show deviations from the exponential form of the excitation energy
dependence A exp(BE ∗ ) or from the constant temperature level density formula
if we express A = 1/(t exp(x 0 /t)) and B = 1/t. Indeed, if we assume that
the “true” level density has the constant temperature energy dependence, we
will get ρ(E ∗ ) oslo = 1 when A and B are adjusted to minimize the ratio
ρ(E ∗ ) true /(A exp(BE)). Any deviations from one would show the deviations from
the constant temperature energy dependence. Such an analysis has been performed
in Ref. [14] which showed the preference of the constant temperature model over
FGM for the range of nuclei studied with Oslo technique.
Also, the Oslo method delivers very unique information about the level density
behavior between discrete and continuum excitation energy regions. This region
can still be affected by nuclear structure properties resulting in the level density
functions being not as smooth as phenomenological models (FGM or GCM)
suggest.
3.3 The Particle Evaporation
The method is based on measurements of particle evaporation spectra from compound nuclear reactions [15]. Spectra are interpreted in framework of the HauserFeshbach theory of nuclear reactions [6] according to which the differential cross
section of an outgoing particle in respect to its energy is proportional to the product
of particle transmission coefficients T and the level density ρ of a residual nucleus
populated by this particle. Schematically, it can be written as σ ∝ T · ρ, but a
more complete and accurate formula is presented in Ref. [6]. Since the accuracy
of transmission coefficients calculated from optical models usually exceeds the
accuracy of level density models, the latter can be benchmarked using experimental
differential cross sections σ (or spectra) of outgoing particles. Moreover, the
level density excitation energy function can be obtained by direct unfolding of
experimental cross sections [15].
The advantage of this method is that it, firstly, allows obtaining the level density
in a wide spin and excitation energy intervals compared to the method based on
the neutron resonance counting. Secondly, the method is capable of determining
the absolute values of level densities. This feature distinguishes it from the Oslo
method which requires data on neutron resonance spacings and model dependent
spin distribution function.
The systematic uncertainties of the method can potentially be caused by possible contribution of pre-equilibrium processes which distort the shape of particle
evaporation spectra, especially their high energy parts that might lead to incorrect
determination of the level density or its parameters. This is considered to be
the main drawback of the method. Also, the uncertainties arising from unknown
117
Although, the original ρ(E ∗ ) oslo is not able to provide model independent
absolute level density values, it delivers very unique information about the excitation
energy dependence of the level density function. As it is seen from Eq. 1, ρ(E ∗ ) oslo
is able to show deviations from the exponential form of the excitation energy
dependence A exp(BE ∗ ) or from the constant temperature level density formula
if we express A = 1/(t exp(x 0 /t)) and B = 1/t. Indeed, if we assume that
the “true” level density has the constant temperature energy dependence, we
will get ρ(E ∗ ) oslo = 1 when A and B are adjusted to minimize the ratio
ρ(E ∗ ) true /(A exp(BE)). Any deviations from one would show the deviations from
the constant temperature energy dependence. Such an analysis has been performed
in Ref. [14] which showed the preference of the constant temperature model over
FGM for the range of nuclei studied with Oslo technique.
Also, the Oslo method delivers very unique information about the level density
behavior between discrete and continuum excitation energy regions. This region
can still be affected by nuclear structure properties resulting in the level density
functions being not as smooth as phenomenological models (FGM or GCM)
suggest.
3.3 The Particle Evaporation
The method is based on measurements of particle evaporation spectra from compound nuclear reactions [15]. Spectra are interpreted in framework of the HauserFeshbach theory of nuclear reactions [6] according to which the differential cross
section of an outgoing particle in respect to its energy is proportional to the product
of particle transmission coefficients T and the level density ρ of a residual nucleus
populated by this particle. Schematically, it can be written as σ ∝ T · ρ, but a
more complete and accurate formula is presented in Ref. [6]. Since the accuracy
of transmission coefficients calculated from optical models usually exceeds the
accuracy of level density models, the latter can be benchmarked using experimental
differential cross sections σ (or spectra) of outgoing particles. Moreover, the
level density excitation energy function can be obtained by direct unfolding of
experimental cross sections [15].
The advantage of this method is that it, firstly, allows obtaining the level density
in a wide spin and excitation energy intervals compared to the method based on
the neutron resonance counting. Secondly, the method is capable of determining
the absolute values of level densities. This feature distinguishes it from the Oslo
method which requires data on neutron resonance spacings and model dependent
spin distribution function.
The systematic uncertainties of the method can potentially be caused by possible contribution of pre-equilibrium processes which distort the shape of particle
evaporation spectra, especially their high energy parts that might lead to incorrect
determination of the level density or its parameters. This is considered to be
the main drawback of the method. Also, the uncertainties arising from unknown