Cross Section Correlation Functions and
Deviations from the Porter-Thomas
Distribution
Edward D. Davis
Given the importance of the Porter-Thomas distribution [1] to statistical models of
the compound nucleus, the identification [2] of resonance data sets that are almost
certainly statistically inconsistent with the PTD has prompted several attempts to
account for these findings within standard models of CN processes (for recent
overviews, see [3, 4]). The only issue on which theorists seem to concur at present
is that more data is needed to guide their considerations.
With a few exceptions (viz., Ref. [5]), autocorrelation function studies of nuclear
reactions have previously been confined to the regime of strongly overlapping
resonances, but, in this short contribution, I want to advocate that the autocorrelation
function involving the total cross section
R tot (ε) =
σ tot
E +
1
2 ε
σ tot
E −
1
2 ε
σ tot 2
− 1,
(1)
be investigated in the unresolved but not strongly overlapping resonance regime. 1
Via the optical theorem, R tot (ε) is a linear superposition of (two-point) measures
C ab (ε) =
S fl∗
aa (E +
1
2 ε)S fl
bb (E −
1
2 ε)
of fluctuations in elastic elements of the Smatrix (S fl ≡ S − S). The relation between R tot (ε) and the C ab (ε)’s has two
desirable consequences. First, for neutron-induced reactions, there are contributions
to R tot (ε) sensitive to a key statistic of neutron partial width amplitudes, namely the
1 In (1), the angle brackets denote an average over the scattering energy E.
E. D. Davis ()
North Carolina State University, Raleigh, NC, USA
e-mail: dedavis4@ncsu.edu
© This is a U.S. government work and not under copyright protection
in the U.S.; foreign copyright protection may apply 2021
J. Escher et al. (eds.), Compound-Nuclear Reactions, Springer Proceedings in
Physics 254, https://doi.org/10.1007/978-3-030-58082-7_6
53
Deviations from the Porter-Thomas
Distribution
Edward D. Davis
Given the importance of the Porter-Thomas distribution [1] to statistical models of
the compound nucleus, the identification [2] of resonance data sets that are almost
certainly statistically inconsistent with the PTD has prompted several attempts to
account for these findings within standard models of CN processes (for recent
overviews, see [3, 4]). The only issue on which theorists seem to concur at present
is that more data is needed to guide their considerations.
With a few exceptions (viz., Ref. [5]), autocorrelation function studies of nuclear
reactions have previously been confined to the regime of strongly overlapping
resonances, but, in this short contribution, I want to advocate that the autocorrelation
function involving the total cross section
R tot (ε) =
σ tot
E +
1
2 ε
σ tot
E −
1
2 ε
σ tot 2
− 1,
(1)
be investigated in the unresolved but not strongly overlapping resonance regime. 1
Via the optical theorem, R tot (ε) is a linear superposition of (two-point) measures
C ab (ε) =
S fl∗
aa (E +
1
2 ε)S fl
bb (E −
1
2 ε)
of fluctuations in elastic elements of the Smatrix (S fl ≡ S − S). The relation between R tot (ε) and the C ab (ε)’s has two
desirable consequences. First, for neutron-induced reactions, there are contributions
to R tot (ε) sensitive to a key statistic of neutron partial width amplitudes, namely the
1 In (1), the angle brackets denote an average over the scattering energy E.
E. D. Davis ()
North Carolina State University, Raleigh, NC, USA
e-mail: dedavis4@ncsu.edu
© This is a U.S. government work and not under copyright protection
in the U.S.; foreign copyright protection may apply 2021
J. Escher et al. (eds.), Compound-Nuclear Reactions, Springer Proceedings in
Physics 254, https://doi.org/10.1007/978-3-030-58082-7_6
53