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A. Voinov
which is referred to as the Hauser-Feshbach theory of nuclear reactions. This
theory is phenomenological in the sense that it uses input parameters to calculate
reaction cross sections. Input parameters are based on nuclear structure quantities
which determine probability of creation and decay of a compound nucleus. These
are particle and γ transmission coefficients, and the nuclear level density. These
quantities are largely based on models and are source of uncertainties in cross
section calculations. For review of the present status of these quantities we refer
to Ref. [7].
HF theory is used as a main tool to calculate reaction cross sections in different
areas of basic and applied physics (examples are astrophysics and data evaluations).
Therefore the problem of the uncertainties of the input parameters is considered to
be important. This calls for specific studies of input parameters both experimentally
and theoretically. For the present, the level density and γ -strength functions are
considered to be the most uncertain inputs since particle transmission coefficients
are derived from the optical model and are based on much broader experimental
data sets compared to the level density and γ -strength. Here we will focus on level
density problems.
2 Understanding the Source of Level Density Model
Uncertainties
The reason for uncertainties in level density models is basically the same as
the reason of uncertainties of any other theoretical model in nuclear physics,
namely the lack of experimental data which are used to constrain these models.
Majority of nuclear physics models use parameters which are adjusted to fit
experimental data. Such models are usually referred to as phenomenological or
semi-phenomenological models depending on fraction of the microscopic approach
used in these models. Even some models which appear to be based on microscopic
approach usually have adjustable parameters which require experimental data to fit.
Most of all, the following types of level density models are currently used in
reaction codes for practical calculations: the first one is phenomenological models
which are based on analytical formulas and the second type of models is based
on microscopic calculations. Phenomenological models mainly use two types of
analytical formulas: the first one is based on Fermi-gas model (FGM) of Ref.[8] and
the other uses a combination of Fermi-gas at higher excitation energies, typically
above the neutron separation energy, and the constant temperature formula at low
excitation energies. The latter model is referred to as a Gilbert and Cameron model
(GCM) [9]. FGM and GCM have different excitation energy dependence because of
inclusion of the constant temperature model formula in GCM. This has a physical
implication of whether a nucleus undergoes a first-order phase transition when it is
excited. In macro-physics the first-order phase transition is observed in the process
of melting ice when the heat is received but the temperature remains constant.
A. Voinov
which is referred to as the Hauser-Feshbach theory of nuclear reactions. This
theory is phenomenological in the sense that it uses input parameters to calculate
reaction cross sections. Input parameters are based on nuclear structure quantities
which determine probability of creation and decay of a compound nucleus. These
are particle and γ transmission coefficients, and the nuclear level density. These
quantities are largely based on models and are source of uncertainties in cross
section calculations. For review of the present status of these quantities we refer
to Ref. [7].
HF theory is used as a main tool to calculate reaction cross sections in different
areas of basic and applied physics (examples are astrophysics and data evaluations).
Therefore the problem of the uncertainties of the input parameters is considered to
be important. This calls for specific studies of input parameters both experimentally
and theoretically. For the present, the level density and γ -strength functions are
considered to be the most uncertain inputs since particle transmission coefficients
are derived from the optical model and are based on much broader experimental
data sets compared to the level density and γ -strength. Here we will focus on level
density problems.
2 Understanding the Source of Level Density Model
Uncertainties
The reason for uncertainties in level density models is basically the same as
the reason of uncertainties of any other theoretical model in nuclear physics,
namely the lack of experimental data which are used to constrain these models.
Majority of nuclear physics models use parameters which are adjusted to fit
experimental data. Such models are usually referred to as phenomenological or
semi-phenomenological models depending on fraction of the microscopic approach
used in these models. Even some models which appear to be based on microscopic
approach usually have adjustable parameters which require experimental data to fit.
Most of all, the following types of level density models are currently used in
reaction codes for practical calculations: the first one is phenomenological models
which are based on analytical formulas and the second type of models is based
on microscopic calculations. Phenomenological models mainly use two types of
analytical formulas: the first one is based on Fermi-gas model (FGM) of Ref.[8] and
the other uses a combination of Fermi-gas at higher excitation energies, typically
above the neutron separation energy, and the constant temperature formula at low
excitation energies. The latter model is referred to as a Gilbert and Cameron model
(GCM) [9]. FGM and GCM have different excitation energy dependence because of
inclusion of the constant temperature model formula in GCM. This has a physical
implication of whether a nucleus undergoes a first-order phase transition when it is
excited. In macro-physics the first-order phase transition is observed in the process
of melting ice when the heat is received but the temperature remains constant.