200
F. Zeiser et al.
The lower panel displays the derived ratio to the input NLD. As expected, it was
observed that the NLD in the quasi-continuum (i.e., above the discrete levels)
was well reproduced when g pop = g int ; the assumptions of the first-generation
method are fulfilled. However, when populating the nucleus by the more realistic,
but narrower distribution g pop = g int , we underestimated the derived NLD in the
quasi-continuum by up to approximately 40% at 2 MeV.
This deviation may be qualitatively explained by the smaller fraction of levels
populated when decaying with a distribution g pop much narrower than g int (see also
Fig. 2). At higher excitation energies, the ratio is forced to converge to unity due
to the normalization at S n . Note that for the normalization of the γ SF specified in
the next paragraphs, we also display the NLD with g pop = g int where the upper
normalization point ρ tot (S n ) obtained from Eq. (28) in [2] was reduced by
ρ red (S n ) = rρ tot (S n ), r ≤ 1.
(4)
We now turn to the extraction of the γ SF. For g pop = g int , we observed about
10% difference between the absolute values of the extracted strength and the
input function. This difference is mainly attributed to a small mismatch of the true
and best-fit temperature for the NLD, which propagates to the γ SF absolute values
through the normalization.
For the more realistic spin distribution g pop = g int , we first naively extracted
the γ SF assuming that we had populated all intrinsic levels. Here the shape of the
NLD curve is off since it is forced to match the calibration point at S n . Figure 3b
compares the results to the input γ SF and although the general shape is preserved,
both the slope and absolute value are considerably off as compared to the input.
Next, we applied a correction inspired by [4], which is based on the assumption
that the transmission coefficient T is spin independent. The first generation matrix,
P , should then be fit by P ∝ ρ red T to extract the correct T , where ρ red is obtained
from Eq. (4) and indicates that we can decay only to a fraction of all intrinsic levels.
This will affect the common transformation parameter α, see Eq. ((2), (3)), which
determines the slope of the γ SF: The smaller r, the smaller α, which translates to a
flatter slope.
The determination of the remaining scaling parameter B depends on T as
extracted with ρ red . However, the level density available for γ decay following
neutron capture is not affected by this reduction, thus we used ρ tot in the γ
normalization integral.
We varied the correction factor r of Eq. (4) and found that for r = 0.3 we
obtained the best match between the (slope of) input and analyzed γ SF. There
remained a constant off-set of about 5–10%, which could be attributed to deviations
in the NLD, which propagated to the γ SF via the normalization procedure. Besides,
the larger deviation towards lower γ -ray energies was traced back to a failure of the
first-generation method.
F. Zeiser et al.
The lower panel displays the derived ratio to the input NLD. As expected, it was
observed that the NLD in the quasi-continuum (i.e., above the discrete levels)
was well reproduced when g pop = g int ; the assumptions of the first-generation
method are fulfilled. However, when populating the nucleus by the more realistic,
but narrower distribution g pop = g int , we underestimated the derived NLD in the
quasi-continuum by up to approximately 40% at 2 MeV.
This deviation may be qualitatively explained by the smaller fraction of levels
populated when decaying with a distribution g pop much narrower than g int (see also
Fig. 2). At higher excitation energies, the ratio is forced to converge to unity due
to the normalization at S n . Note that for the normalization of the γ SF specified in
the next paragraphs, we also display the NLD with g pop = g int where the upper
normalization point ρ tot (S n ) obtained from Eq. (28) in [2] was reduced by
ρ red (S n ) = rρ tot (S n ), r ≤ 1.
(4)
We now turn to the extraction of the γ SF. For g pop = g int , we observed about
10% difference between the absolute values of the extracted strength and the
input function. This difference is mainly attributed to a small mismatch of the true
and best-fit temperature for the NLD, which propagates to the γ SF absolute values
through the normalization.
For the more realistic spin distribution g pop = g int , we first naively extracted
the γ SF assuming that we had populated all intrinsic levels. Here the shape of the
NLD curve is off since it is forced to match the calibration point at S n . Figure 3b
compares the results to the input γ SF and although the general shape is preserved,
both the slope and absolute value are considerably off as compared to the input.
Next, we applied a correction inspired by [4], which is based on the assumption
that the transmission coefficient T is spin independent. The first generation matrix,
P , should then be fit by P ∝ ρ red T to extract the correct T , where ρ red is obtained
from Eq. (4) and indicates that we can decay only to a fraction of all intrinsic levels.
This will affect the common transformation parameter α, see Eq. ((2), (3)), which
determines the slope of the γ SF: The smaller r, the smaller α, which translates to a
flatter slope.
The determination of the remaining scaling parameter B depends on T as
extracted with ρ red . However, the level density available for γ decay following
neutron capture is not affected by this reduction, thus we used ρ tot in the γ
normalization integral.
We varied the correction factor r of Eq. (4) and found that for r = 0.3 we
obtained the best match between the (slope of) input and analyzed γ SF. There
remained a constant off-set of about 5–10%, which could be attributed to deviations
in the NLD, which propagated to the γ SF via the normalization procedure. Besides,
the larger deviation towards lower γ -ray energies was traced back to a failure of the
first-generation method.