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P. Koehler et al.
the NLD. Below E c = 0.626 MeV, values of E f , J f , and π f determined from
experiments are used. Spin and parity selection rules are properly taken into account
for individual transitions. Partial radiation widths are then calculated by random
sampling from PTDs characterized by the corresponding expectation values. To
obtain a distribution of γ values, this process is repeated numerous times using
the same level scheme but new PTD sampling each time.
Results of calculating γ distributions for 1 + and 2 + resonances in 198 Au using
published NLDs [3] and PSFs [4] measured with the Oslo technique are compared
to our new data in Fig. 2. From this figure, it can be seen that the calculated
distributions are significantly narrower and closer together than the data. Below,
we describe how the Oslo NLD and PSF can be adjusted, within the confines of the
technique, to obtain agreement between calculation and data.
The width of the γ distribution is a consequence of sampling from the PTD
but the magnitude of the width depends on details of the NLD and PSF. Transitions
to levels near the ground state tend to have the greatest influence on the width of
the distribution because they have the largest partial widths. The spin distribution
of the NLD can affect the width of the γ distributions in several ways. For
example, increasing the number of levels of a given spin (to which resonance
transitions can occur) near the ground state can make the distribution narrower
because the fluctuations will be damped by averaging over more contributions. The
spin distribution also affects the slope of the PSF, which affects the widths of the
γ distributions. For example, a PSF with steeper energy dependence (due to a
broader spin distribution at higher excitations) can lead to a wider γ distribution,
by increasing the relative sizes of the largest partial widths.
The spin distribution of the NLD also affects the separation between the γ distributions for the two s-wave-resonance spins in at least two ways. First, the expectation value is inversely proportional to the average level density, ρ(E λ , J λ , π λ ), for
resonances of a given spin. Because there are more J = 2 than J = 1 resonances, the
expectation value is smaller for the larger spin and hence the cumulative distribution
for J = 2 is, on average, to the left of the J = 1 distribution in Fig. 2. In the present
work, this component is fixed because the relative number of resonances of the two
spins is obtained from our R-matrix analysis.
The second way the spin distribution affects the separation between the γ
distributions for the two spins is through the relative number of J = 0 to J = 3
final states. This is because, assuming dipole transition dominate, only J = 1
(J = 2) resonances can decay to J = 0 (J = 3) levels. Therefore, increasing the
number of J = 0 relative to J = 3 levels, especially near the ground state where
the corresponding partial widths are larger, will increase the separation between the
two γ distributions. On the other hand, too many low-spin levels near the ground
state can lead to a narrowing of the distributions as explained above. So, the spin
distribution is constrained in opposite directions by the widths and relative spacing
between the γ distributions for the two s-wave-resonance spins.
P. Koehler et al.
the NLD. Below E c = 0.626 MeV, values of E f , J f , and π f determined from
experiments are used. Spin and parity selection rules are properly taken into account
for individual transitions. Partial radiation widths are then calculated by random
sampling from PTDs characterized by the corresponding expectation values. To
obtain a distribution of γ values, this process is repeated numerous times using
the same level scheme but new PTD sampling each time.
Results of calculating γ distributions for 1 + and 2 + resonances in 198 Au using
published NLDs [3] and PSFs [4] measured with the Oslo technique are compared
to our new data in Fig. 2. From this figure, it can be seen that the calculated
distributions are significantly narrower and closer together than the data. Below,
we describe how the Oslo NLD and PSF can be adjusted, within the confines of the
technique, to obtain agreement between calculation and data.
The width of the γ distribution is a consequence of sampling from the PTD
but the magnitude of the width depends on details of the NLD and PSF. Transitions
to levels near the ground state tend to have the greatest influence on the width of
the distribution because they have the largest partial widths. The spin distribution
of the NLD can affect the width of the γ distributions in several ways. For
example, increasing the number of levels of a given spin (to which resonance
transitions can occur) near the ground state can make the distribution narrower
because the fluctuations will be damped by averaging over more contributions. The
spin distribution also affects the slope of the PSF, which affects the widths of the
γ distributions. For example, a PSF with steeper energy dependence (due to a
broader spin distribution at higher excitations) can lead to a wider γ distribution,
by increasing the relative sizes of the largest partial widths.
The spin distribution of the NLD also affects the separation between the γ distributions for the two s-wave-resonance spins in at least two ways. First, the expectation value is inversely proportional to the average level density, ρ(E λ , J λ , π λ ), for
resonances of a given spin. Because there are more J = 2 than J = 1 resonances, the
expectation value is smaller for the larger spin and hence the cumulative distribution
for J = 2 is, on average, to the left of the J = 1 distribution in Fig. 2. In the present
work, this component is fixed because the relative number of resonances of the two
spins is obtained from our R-matrix analysis.
The second way the spin distribution affects the separation between the γ
distributions for the two spins is through the relative number of J = 0 to J = 3
final states. This is because, assuming dipole transition dominate, only J = 1
(J = 2) resonances can decay to J = 0 (J = 3) levels. Therefore, increasing the
number of J = 0 relative to J = 3 levels, especially near the ground state where
the corresponding partial widths are larger, will increase the separation between the
two γ distributions. On the other hand, too many low-spin levels near the ground
state can lead to a narrowing of the distributions as explained above. So, the spin
distribution is constrained in opposite directions by the widths and relative spacing
between the γ distributions for the two s-wave-resonance spins.