Nuclear Level Densities: From Empirical
Models to Microscopic Methods
Y. Alhassid
1 Introduction
The nuclear level density is among the most important statistical nuclear properties.
It appears in Fermi’s golden rule for transition rates. Along with gamma strength
functions, it is a required input to the Hauser–Feshbach theory [1] of compound
nuclear reactions. The excited compound nucleus can decay into various channels,
and its decay rate in any given channel is proportional to the available phase
space, i.e., the corresponding level density of the residual nucleus. The level density
has many applications in diverse areas such as stellar nucleosynthesis and nuclear
reactor technology.
The state density at total energy E is defined as the number of states per unit
energy
ρ(E) = Tr δ(E − ˆ
H ),
(1)
where ˆ
H is the system’s Hamiltonian. For a system with discrete energy levels E i ,
the state density ρ(E) =
i δ(E − E i ) is singular. Usually we are interested in a
smoothed version of this density, i.e., the average state density.
While qualitative features of level densities can be understood by simple models,
a quantitative understanding presents a major challenge, in particular in the presence
of correlations beyond the mean-field approximation.
Y. Alhassid ()
Center for Theoretical Physics, Sloane Physics Laboratory, Yale University, New Haven,
CT, USA
e-mail: yoram.alhassid@yale.edu
https://alhassidgroup.yale.edu
© This is a U.S. government work and not under copyright protection
in the U.S.; foreign copyright protection may apply 2021
J. Escher et al. (eds.), Compound-Nuclear Reactions, Springer Proceedings in
Physics 254, https://doi.org/10.1007/978-3-030-58082-7_12
97
Models to Microscopic Methods
Y. Alhassid
1 Introduction
The nuclear level density is among the most important statistical nuclear properties.
It appears in Fermi’s golden rule for transition rates. Along with gamma strength
functions, it is a required input to the Hauser–Feshbach theory [1] of compound
nuclear reactions. The excited compound nucleus can decay into various channels,
and its decay rate in any given channel is proportional to the available phase
space, i.e., the corresponding level density of the residual nucleus. The level density
has many applications in diverse areas such as stellar nucleosynthesis and nuclear
reactor technology.
The state density at total energy E is defined as the number of states per unit
energy
ρ(E) = Tr δ(E − ˆ
H ),
(1)
where ˆ
H is the system’s Hamiltonian. For a system with discrete energy levels E i ,
the state density ρ(E) =
i δ(E − E i ) is singular. Usually we are interested in a
smoothed version of this density, i.e., the average state density.
While qualitative features of level densities can be understood by simple models,
a quantitative understanding presents a major challenge, in particular in the presence
of correlations beyond the mean-field approximation.
Y. Alhassid ()
Center for Theoretical Physics, Sloane Physics Laboratory, Yale University, New Haven,
CT, USA
e-mail: yoram.alhassid@yale.edu
https://alhassidgroup.yale.edu
© This is a U.S. government work and not under copyright protection
in the U.S.; foreign copyright protection may apply 2021
J. Escher et al. (eds.), Compound-Nuclear Reactions, Springer Proceedings in
Physics 254, https://doi.org/10.1007/978-3-030-58082-7_12
97