Rotational Enhancement Factor for
Nuclear Level Density
S. M. Grimes
1 Introduction
Bethe was the first to examine the nuclear level density problem. He showed [1] that
the density of nuclear states per MeV was given by
ρ T (E) =
√
π
12
exp(2
√
aE)
a 1/4 E 5/4 .
(1)
In this equation, E is the energy of excitation in MeV and a is the constant called the
level density parameter which is normally found to be approximately A/8 MeV
−1 ,
where A is the mass number. By making the assumption that a nucleus is spherical,
Bethe was able to show that
ρ(E, J ) =
ρ T (E)(J + 1/2)
√
2πσ 3
exp(−
(J + 1/2) 2
2σ 2
) = ρ L (E)S(J ).
(2)
In this equation, ρ L (E, J ) (=ρ T (E)/
√
2πσ ) is the total number of levels per MeV
and σ is the spin cutoff parameter (expectation of < J 2
z > 1/2 ). S(J ) is the fraction
of the levels which have spin J:
S(J ) =
(J + 1/2)
σ 2
exp
−
(J + 1/2) 2
2σ 2
.
(3)
If the nucleus is spherical,
S. M. Grimes ()
Department of Physics and Astronomy, Ohio University, Athens, OH, USA
e-mail: grimes@ohio.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_16
139