62
D. Brown et al.
Our work also shows how and where superradiance may impact nuclear reactions. The effects of superradiance in the compound nuclear cross section appear to
be small in most cases and are only evident in systems with a small number of open
channels with large transmission coefficients. In practice, there are many effects that
could mask superradiance: (a) direct reactions will lower the effective transmission
coefficient because of the Englebrecht-Weidenmueller transform, (b) strong level
repulsion prevents small D, (c) Γ c → ∞ is unphysical, and (d) odd cross section
behavior may be washed out by the cross section fluctuations. However, the right
optical model potential could lead to T c ≈ 1 as in Fig. 1.
The effects of superradiance might be easier to see in the incoming channel
because it is easier to control this channel experimentally. Blindly substituting
the sum rule transmission coefficient into the absorption cross section we have
σ abs
a
→
2π 2 g a
k 2
a
T a
√
1−T a
, which clearly is singular when T a → 1. The Moldauer–
Simonius transmission coefficient is also singular as T a → 1. As the results of Ref.
[12] strongly disfavor both and favor the SPRT parameterization, we think a possible
resolution requires a detailed re-examination of how the WFC must be modified to
account for level repulsion. Such a study might also help us understand the variance
of the cross section in the URR.
Acknowledgments Work at Brookhaven National Laboratory was sponsored by the Office of
Nuclear Physics, Office of Science of the U.S. Department of Energy under Contract No. DEAC02- 98CH10886 with Brookhaven Science Associates, LLC. Work at Los Alamos National
Laboratory was carried out under the auspices of the National Nuclear Security Agency of the U.S.
Department of Energy under Contract No. DE-AC52- 06NA25396.
References
1. J.J.M. Verbaarschot, H.A. Weidenmüller, M.R. Zirnbauer, Phys. Rep. 129, 367 (1985)
2. P.A. Moldauer, Phys. Rev. C 11, 426 (1975)
3. A.M. Lane, J.E. Lynn, Proc. Phys. Soc. A70, 557 (1957); F.H. Fröhner, JEFF Report 18 (2000)
4. G.R. Satchler Introduction to Nuclear Reactions (Wiley, New York, 1980); P. Fröbrich, R.
Lipperheide, Theory of Nuclear Reactions (Oxford Studies in Nuclear Physics) (Clarendon
Press, Oxford, 1996) ISBN-13: 978-0198537830
5. D.A. Brown, G.P.A. Nobre, M.W. Herman, Phys. Rev. C 98, 024616 (2018)
6. G. Noguere et al., EPJ Web Conf. 146, 02036 (2017)
7. M. Simonius, Phys. Lett. 52B, 279 (1974); P.A. Moldauer, Phys. Rev. 157, 907 (1967)
8. P.A. Moldauer, Phys. Rev. Lett. 19, 1047 (1967)
9. S.F. Mughabghab, Atlas of Neutron Resonances: Resonance Parameters and Neutron Cross
Sections, Z = 1-100 (Elsevier, Amsterdam 2006); D.A. Brown et al., Nucl. Data Sheets 148, 1
(2018)
10. J. Raynal, ECIS code, distributed by the NEA DATA Bank, Paris, France (2003)
11. R. Capote et al., Nucl. Data Sheets 110 (12), 3107 (2009)
12. Y. Alhassid et al, Phys. Rev. C 99, 024621 (2019)
13. N. Auerbach, V. Zelevinsky, Rep. Prog. Phys. 74 106301 (2011)
D. Brown et al.
Our work also shows how and where superradiance may impact nuclear reactions. The effects of superradiance in the compound nuclear cross section appear to
be small in most cases and are only evident in systems with a small number of open
channels with large transmission coefficients. In practice, there are many effects that
could mask superradiance: (a) direct reactions will lower the effective transmission
coefficient because of the Englebrecht-Weidenmueller transform, (b) strong level
repulsion prevents small D, (c) Γ c → ∞ is unphysical, and (d) odd cross section
behavior may be washed out by the cross section fluctuations. However, the right
optical model potential could lead to T c ≈ 1 as in Fig. 1.
The effects of superradiance might be easier to see in the incoming channel
because it is easier to control this channel experimentally. Blindly substituting
the sum rule transmission coefficient into the absorption cross section we have
σ abs
a
→
2π 2 g a
k 2
a
T a
√
1−T a
, which clearly is singular when T a → 1. The Moldauer–
Simonius transmission coefficient is also singular as T a → 1. As the results of Ref.
[12] strongly disfavor both and favor the SPRT parameterization, we think a possible
resolution requires a detailed re-examination of how the WFC must be modified to
account for level repulsion. Such a study might also help us understand the variance
of the cross section in the URR.
Acknowledgments Work at Brookhaven National Laboratory was sponsored by the Office of
Nuclear Physics, Office of Science of the U.S. Department of Energy under Contract No. DEAC02- 98CH10886 with Brookhaven Science Associates, LLC. Work at Los Alamos National
Laboratory was carried out under the auspices of the National Nuclear Security Agency of the U.S.
Department of Energy under Contract No. DE-AC52- 06NA25396.
References
1. J.J.M. Verbaarschot, H.A. Weidenmüller, M.R. Zirnbauer, Phys. Rep. 129, 367 (1985)
2. P.A. Moldauer, Phys. Rev. C 11, 426 (1975)
3. A.M. Lane, J.E. Lynn, Proc. Phys. Soc. A70, 557 (1957); F.H. Fröhner, JEFF Report 18 (2000)
4. G.R. Satchler Introduction to Nuclear Reactions (Wiley, New York, 1980); P. Fröbrich, R.
Lipperheide, Theory of Nuclear Reactions (Oxford Studies in Nuclear Physics) (Clarendon
Press, Oxford, 1996) ISBN-13: 978-0198537830
5. D.A. Brown, G.P.A. Nobre, M.W. Herman, Phys. Rev. C 98, 024616 (2018)
6. G. Noguere et al., EPJ Web Conf. 146, 02036 (2017)
7. M. Simonius, Phys. Lett. 52B, 279 (1974); P.A. Moldauer, Phys. Rev. 157, 907 (1967)
8. P.A. Moldauer, Phys. Rev. Lett. 19, 1047 (1967)
9. S.F. Mughabghab, Atlas of Neutron Resonances: Resonance Parameters and Neutron Cross
Sections, Z = 1-100 (Elsevier, Amsterdam 2006); D.A. Brown et al., Nucl. Data Sheets 148, 1
(2018)
10. J. Raynal, ECIS code, distributed by the NEA DATA Bank, Paris, France (2003)
11. R. Capote et al., Nucl. Data Sheets 110 (12), 3107 (2009)
12. Y. Alhassid et al, Phys. Rev. C 99, 024621 (2019)
13. N. Auerbach, V. Zelevinsky, Rep. Prog. Phys. 74 106301 (2011)