118
A. Voinov
spin distributions of populated nuclei can also take place for some of reactions.
To minimize these uncertainties, the careful selection of beam species and their
energies is needed to ensure the compound mechanism is dominant and effect of the
spin dependence is minimized. Spectra measured at backward angles are used for
these purposes.
Existing experimental information on the level density from particle evaporation
is scarce. There were few groups involved in these kinds of experiments in 60s–80s
using reactions such as (α, p), (p, α) [16, 17], (p, n), (α, n) [18], and (n, α) [19] on
nuclei from 50–70 mass range. Unfortunately, available data do not allow making
some general conclusions on level density regularities. The quality of data points in
some of these works is poor (small number of points, large binning interval, pointto-point fluctuations). The analysis of these data was made with different techniques
and assumptions. Some experiments were analyzed with the simple Weisskopf
model [20] which does not account for angular momentum values of compound and
residual nuclei. Many experimental spectra have not been measured in the region
of discrete known levels populated by evaporated particles or population of discrete
levels was not included in statistical model calculations at that time.
Experiments conducted by our group suggested improvements and showed
capability of this technique to extract level densities for individual nuclei and to
benchmark existing level density models [21–24].
3.4 Spin Distribution
The spin distribution of the nuclear level density ρ(J) is an important and most
uncertain parameter in level density calculations. Model level densities use the
Gaussian form of the spin distribution with the spin cutoff parameter σ determining
the widths of this distribution:
ρ(J ) =
1
√
2πσ
(J + 1/2)
σ 2
exp
−
(J + 1/2) 2
2σ 2
.
(2)
The spin cutoff parameter is coupled with level density parameters, namely
the parameter a and δ (see Ref. [7] for details). The spin distribution and its
parameterization are based on FGM [8] and currently have a little support from
experimental data. Different model formulas for the spin cutoff parameters can be
found in Refs.[1, 7, 25, 26]. Although there is a general consensus that the spin cutoff
estimates based on the rigid body model of inertia [7, 25] work at the excitation
energy near the neutron binding energy range and higher, there are indications that
they overestimate the spin cutoff values at low excitation energies. For example, it
overestimates spin cutoff values derived from low-energy discrete levels with known
spins [7]. Therefore reaction codes such as Empire and Talys, for some of their
models, use linear interpolation for the spin cutoff parameter between the region
A. Voinov
spin distributions of populated nuclei can also take place for some of reactions.
To minimize these uncertainties, the careful selection of beam species and their
energies is needed to ensure the compound mechanism is dominant and effect of the
spin dependence is minimized. Spectra measured at backward angles are used for
these purposes.
Existing experimental information on the level density from particle evaporation
is scarce. There were few groups involved in these kinds of experiments in 60s–80s
using reactions such as (α, p), (p, α) [16, 17], (p, n), (α, n) [18], and (n, α) [19] on
nuclei from 50–70 mass range. Unfortunately, available data do not allow making
some general conclusions on level density regularities. The quality of data points in
some of these works is poor (small number of points, large binning interval, pointto-point fluctuations). The analysis of these data was made with different techniques
and assumptions. Some experiments were analyzed with the simple Weisskopf
model [20] which does not account for angular momentum values of compound and
residual nuclei. Many experimental spectra have not been measured in the region
of discrete known levels populated by evaporated particles or population of discrete
levels was not included in statistical model calculations at that time.
Experiments conducted by our group suggested improvements and showed
capability of this technique to extract level densities for individual nuclei and to
benchmark existing level density models [21–24].
3.4 Spin Distribution
The spin distribution of the nuclear level density ρ(J) is an important and most
uncertain parameter in level density calculations. Model level densities use the
Gaussian form of the spin distribution with the spin cutoff parameter σ determining
the widths of this distribution:
ρ(J ) =
1
√
2πσ
(J + 1/2)
σ 2
exp
−
(J + 1/2) 2
2σ 2
.
(2)
The spin cutoff parameter is coupled with level density parameters, namely
the parameter a and δ (see Ref. [7] for details). The spin distribution and its
parameterization are based on FGM [8] and currently have a little support from
experimental data. Different model formulas for the spin cutoff parameters can be
found in Refs.[1, 7, 25, 26]. Although there is a general consensus that the spin cutoff
estimates based on the rigid body model of inertia [7, 25] work at the excitation
energy near the neutron binding energy range and higher, there are indications that
they overestimate the spin cutoff values at low excitation energies. For example, it
overestimates spin cutoff values derived from low-energy discrete levels with known
spins [7]. Therefore reaction codes such as Empire and Talys, for some of their
models, use linear interpolation for the spin cutoff parameter between the region