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تسجيل مستخدم جديدThe Statistical Model of Nuclear Reactions: Open Problems
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Several experiments [1-3] show significant deviations from predictions of the statistical model of nuclear reactions. We summarize unsuccessful recent theoretical efforts to account for such disagreement in terms of a violation of orthogonal invariance caused by the Thomas-Ehrman shift. We report on numerical simulations involving a large number of gamma decay channels that also give rise to violation of orthogonal invariance but likewise do not account for the discrepancies. We discuss the statistical model in the light of these results.
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Is there a connection between the branch point singularity at the particle emission threshold and the appearance of cluster states which reveal the structure of a corresponding reaction channel? Which nuclear states are most impacted by the coupling
to the scattering continuum? What should be the most important steps in developing the theory that will truly unify nuclear structure and nuclear reactions? The common denominator of these questions is the continuum shell-model approach to bound and unbound nuclear states, nuclear decays, and reactions.
The statistical model of compound-nucleus reactions predicts that the fluctuations of the partial $gamma$-decay widths for a compound-nucleus resonance are governed by the Porter-Thomas distribution (PTD), and that consequently the distribution of to
tal $gamma$-decay widths is very narrow. However, a recent experiment [Koehler, Larsen, Guttormsen, Siem, and Guber, Phys. Rev. C 88, 041305(R) (2013)] reported large fluctuations of the total $gamma$-decay widths in the $^{95}$Mo$(n,gamma)^{96}$Mo* reaction, contrary to this expectation. Furthermore, in recent theoretical works it was argued that sufficiently strong channel couplings can cause deviations of the partial width distributions from PTD. Here, we investigate whether the combined influence of a large number of nonequivalent $gamma$-decay channels, each of which couples weakly to the compound-nucleus resonances, can modify the statistics of the partial widths. We study this effect in neutron scattering off $^{95}$Mo within a random-matrix model that includes coupling to the entrance neutron channel and to the large number of $gamma$ channels. Using realistic coupling parameters obtained from empirical models for the level density and the $gamma$ strength function, we find that the PTD describes well the distribution of partial widths for all decay channels, in agreement with the statistical-model expectation. Furthermore, we find that the width of the distribution of the total $gamma$-decay widths is insensitive to wide variations in the parameters of the $gamma$ strength function, as well as to deviations of the partial-width distributions from the PTD. Our results rule out an explanation of the recent experimental data within a statistical-model description of the compound nucleus.
This contribution gives a short review of recent theoretical advances in most topics of nuclear cluster physics concentrating, however, around {$alpha$} particle clustering. Along the route, the point of view will be critical mentioning not only progress but also failures and open problems.
We propose alternatives to coupled-channels calculations with loosely-bound exotic nuclei (CDCC), based on the the random matrix (RMT) and the optical background (OPM) models for the statistical theory of nuclear reactions. The coupled channels equat
ions are divided into two sets. The first set, described by the CDCC, and the other set treated with RMT. The resulting theory is a Statistical CDCC (CDCC$_S$), able in principle to take into account many pseudo channels.
Proceedings of the workshop Boundary and Defect Conformal Field Theory: Open Problems and Applications, Chicheley Hall, Buckinghamshire, UK, 7-8 Sept. 2017.
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