Restricted Spin-Ranges in the Oslo Method
197
excitation energy bin j . Consequently, by subtracting the γ -ray spectra from bins
with lower excitation energy, only the primary γ rays remain.
3 Extraction of NLD and γSF
For γ rays emitted in the statistical regime (i.e., high level density) we can
determine the NLD at the excitation energy of the final state, ρ(E x,f ), and the γ -
ray transmission coefficient, T (E γ ) [2]:
P (E x,i , E γ ) ∝ ρ(E x,f )T (E γ ),
(1)
up to a transformation with the parameters A, B, and α,
˜
ρ(E i − E γ ) = A exp[α (E i − E γ )] ρ(E i − E γ ),
(2)
˜
T (E γ ) = B exp[α E γ ] T (E γ ).
(3)
To select the γ decay channel, only excitation energies E x below the neutron
separation energy (S n = 6.534 MeV [17]) must be considered. In this experiment,
we applied more stringent constrains due to the onset of sub-barrier fission events
at about 4.5 MeV [18, 19]. A more detailed analysis of the prompt fission γ
rays can be found in [20]. The final extraction regions were E min
γ
= 1.2 MeV,
E min
x
= 2.4 MeV, E max
x
= 4.0 MeV. It remained then to find the transformation
parameters corresponding to the correct physical solution.
The level density at low E x was normalized to the discrete level scheme [21]
was normalized to the discrete level scheme [21] up to an excitation energy E c ≈
1 MeV. Above this energy we expect that the low-lying level scheme is now known
completely anymore. At the neutron separation energy S n , we obtain ρ(S n ) from the
average neutron resonance spacing for s-waves, D 0 = 2.20(9) eV, taken from RIPL3 [22] following [2]. The latter conversion depends on the spin-parity distribution;
we assumed equal parities and used the spin distribution g(E x , I ) proposed by
Ericson [23, Eq. (3.29)] together with the rigid-body moment of inertia approach
for the spin cut-off parameter σ by von Egidy and Bucurescu [24]. Additionally, we
extrapolated from the highest E x data points up to S n . In accordance with findings
for other actinides [5], this was performed assuming a constant temperature level
density formula [25]. The resulting level density ρ is displayed in Fig. 1a.
The remaining parameter B for the normalization of the transmission coefficient T can be determined [29, 30] from the average total radiative width
γ (S n ) = 43(4) meV [22]. The γ -ray strength function f (E γ ) was obtained from
the transmission coefficient T assuming dominance of dipole strength, f (E γ ) =
T (E γ )/(2πE 3
γ ), and is shown in Fig. 1b.
197
excitation energy bin j . Consequently, by subtracting the γ -ray spectra from bins
with lower excitation energy, only the primary γ rays remain.
3 Extraction of NLD and γSF
For γ rays emitted in the statistical regime (i.e., high level density) we can
determine the NLD at the excitation energy of the final state, ρ(E x,f ), and the γ -
ray transmission coefficient, T (E γ ) [2]:
P (E x,i , E γ ) ∝ ρ(E x,f )T (E γ ),
(1)
up to a transformation with the parameters A, B, and α,
˜
ρ(E i − E γ ) = A exp[α (E i − E γ )] ρ(E i − E γ ),
(2)
˜
T (E γ ) = B exp[α E γ ] T (E γ ).
(3)
To select the γ decay channel, only excitation energies E x below the neutron
separation energy (S n = 6.534 MeV [17]) must be considered. In this experiment,
we applied more stringent constrains due to the onset of sub-barrier fission events
at about 4.5 MeV [18, 19]. A more detailed analysis of the prompt fission γ
rays can be found in [20]. The final extraction regions were E min
γ
= 1.2 MeV,
E min
x
= 2.4 MeV, E max
x
= 4.0 MeV. It remained then to find the transformation
parameters corresponding to the correct physical solution.
The level density at low E x was normalized to the discrete level scheme [21]
was normalized to the discrete level scheme [21] up to an excitation energy E c ≈
1 MeV. Above this energy we expect that the low-lying level scheme is now known
completely anymore. At the neutron separation energy S n , we obtain ρ(S n ) from the
average neutron resonance spacing for s-waves, D 0 = 2.20(9) eV, taken from RIPL3 [22] following [2]. The latter conversion depends on the spin-parity distribution;
we assumed equal parities and used the spin distribution g(E x , I ) proposed by
Ericson [23, Eq. (3.29)] together with the rigid-body moment of inertia approach
for the spin cut-off parameter σ by von Egidy and Bucurescu [24]. Additionally, we
extrapolated from the highest E x data points up to S n . In accordance with findings
for other actinides [5], this was performed assuming a constant temperature level
density formula [25]. The resulting level density ρ is displayed in Fig. 1a.
The remaining parameter B for the normalization of the transmission coefficient T can be determined [29, 30] from the average total radiative width
γ (S n ) = 43(4) meV [22]. The γ -ray strength function f (E γ ) was obtained from
the transmission coefficient T assuming dominance of dipole strength, f (E γ ) =
T (E γ )/(2πE 3
γ ), and is shown in Fig. 1b.