136
G. P. A. Nobre et al.
10
0
10
1
10
2
10
3
10
4
10
5
10
6
10
7
0
5
10
15
20
56 Mn
Level density (1/MeV)
Excitation Energy (MeV)
Exp. level densities
Gilbert-Cameron
HFB (RIPL)
HFB (fitted
56 Mn LD)
HFB (Smoothed, fitted
56
Mn LD)
10
0
10
1
10
2
0
0.5
1
1.5
2
2.5
56 Mn
Cumulative number of levels
Excitation Energy (MeV)
Exp. discrete levels
Gilbert-Cameron
HFB (RIPL)
HFB (fitted
56
Mn LD)
HFB (Smoothed, fitted
56
Mn LD)
Fig. 2 Level densities and cumulative number of levels of 56 Mn for the different LD approaches
explained in Sect. 3
Fig. 3 56 Fe(n,p) 56 Mn cross
section obtained from the
adoption of the different LD
approaches explained in
Sect. 3. Experimental data
from EXFOR [9]
0.00
0.05
0.10
0.15
4
6
8
10
12
14
16
18
20
56 Fe(n,p)
Cross Section (b)
Incident Neutron Energy (MeV)
EXFOR
Gilbert-Cameron
HFB (RIPL)
HFB (fitted
56 Mn LD)
HFB (Smoothed
56 Fe LD)
HFB (Smoothed, fitted
56 Mn LD)
4 Discussion
By comparing the green and red curves in Fig. 1 we see that while the GC LD
is smooth (as it comes from constant-temperature analytical forms), the HFB LD
present fluctuations, or structures, in the range 5 E x 9 MeV. Both GC and
HFB (from RIPL) models approximately reproduce reasonably well the number
of levels at around 4.5 MeV which is around where one would normally impose
the transition from the discrete levels to LD. This transition point, or excitation
energy cut-off, can however be rather arbitrary. One can clearly see from Fig. 1 that
the HFB predicted cumulative number of levels yields a much better agreement
with the overall behavior of observed discrete levels, which makes it much more
independent from the choice of excitation energy at which the transition to LD is
made. Even though these two apparently similarly reasonable (from the perspective
of discrete-level matching) LD models, they lead to dramatically different (n,p)
cross sections (Fig. 3). Even after fitting 56 Mn LD parameters (blue curve), the
G. P. A. Nobre et al.
10
0
10
1
10
2
10
3
10
4
10
5
10
6
10
7
0
5
10
15
20
56 Mn
Level density (1/MeV)
Excitation Energy (MeV)
Exp. level densities
Gilbert-Cameron
HFB (RIPL)
HFB (fitted
56 Mn LD)
HFB (Smoothed, fitted
56
Mn LD)
10
0
10
1
10
2
0
0.5
1
1.5
2
2.5
56 Mn
Cumulative number of levels
Excitation Energy (MeV)
Exp. discrete levels
Gilbert-Cameron
HFB (RIPL)
HFB (fitted
56
Mn LD)
HFB (Smoothed, fitted
56
Mn LD)
Fig. 2 Level densities and cumulative number of levels of 56 Mn for the different LD approaches
explained in Sect. 3
Fig. 3 56 Fe(n,p) 56 Mn cross
section obtained from the
adoption of the different LD
approaches explained in
Sect. 3. Experimental data
from EXFOR [9]
0.00
0.05
0.10
0.15
4
6
8
10
12
14
16
18
20
56 Fe(n,p)
Cross Section (b)
Incident Neutron Energy (MeV)
EXFOR
Gilbert-Cameron
HFB (RIPL)
HFB (fitted
56 Mn LD)
HFB (Smoothed
56 Fe LD)
HFB (Smoothed, fitted
56 Mn LD)
4 Discussion
By comparing the green and red curves in Fig. 1 we see that while the GC LD
is smooth (as it comes from constant-temperature analytical forms), the HFB LD
present fluctuations, or structures, in the range 5 E x 9 MeV. Both GC and
HFB (from RIPL) models approximately reproduce reasonably well the number
of levels at around 4.5 MeV which is around where one would normally impose
the transition from the discrete levels to LD. This transition point, or excitation
energy cut-off, can however be rather arbitrary. One can clearly see from Fig. 1 that
the HFB predicted cumulative number of levels yields a much better agreement
with the overall behavior of observed discrete levels, which makes it much more
independent from the choice of excitation energy at which the transition to LD is
made. Even though these two apparently similarly reasonable (from the perspective
of discrete-level matching) LD models, they lead to dramatically different (n,p)
cross sections (Fig. 3). Even after fitting 56 Mn LD parameters (blue curve), the