Statistical features of the thermal neutron capture cross sections

We discuss the existence of huge thermal neutron capture cross sections in several nuclei. The values of the cross sections are several orders of magnitude bigger than expected at these very low energies. We lend support to the idea that this phenomenon is random in nature and is similar to what we have learned from the study of parity violation in the actinide region. The idea of statistical doorways is advanced as a unified concept in the delineation of large numbers in the nuclear world. The average number of maxima per unit mass, $$ in the capture cross section is calculated and related to the underlying cross section correlation function and found to be $= 3/(\pi \sqrt{2}\gamma_{A})$, where $\gamma_{A}$ is a characteristic mass correlation width which designates the degree of remnant coherence in the system. We trace this coherence to nucleosynthesis which produced the nuclei whose neutron capture cross sections are considered here.Comment: 7 pages, 6 figures. To appear in Acta Physica Polonica B as a Contribution to the proceedings of:Jagiellonian Symposium of Fundamental and Applied Subatomic Physics, June 7- 12, 2015 Krakow, Polan

Nonlinear Schrodinger equation with chaotic, random, and nonperiodic nonlinearity

In this paper we deal with a nonlinear Schr\"{o}dinger equation with chaotic, random, and nonperiodic cubic nonlinearity. Our goal is to study the soliton evolution, with the strength of the nonlinearity perturbed in the space and time coordinates and to check its robustness under these conditions. Comparing with a real system, the perturbation can be related to, e.g., impurities in crystalline structures, or coupling to a thermal reservoir which, on the average, enhances the nonlinearity. We also discuss the relevance of such random perturbations to the dynamics of Bose-Einstein Condensates and their collective excitations and transport.Comment: 4 pages, 6 figure

Matrix Elements of Random Operators and Discrete Symmetry Breaking in Nuclei

It is shown that several effects are responsible for deviations of the intensity distributions from the Porter-Thomas law. Among these are genuine symmetry breaking, such as isospin; the nature of the transition operator; truncation of the Hilbert space in shell model calculations and missing transitionsComment: 8 pages, 3 figure

Inclusive Breakup Theory of Three-Body Halos

We present a recently developed theory for the inclusive breakup of three-fragment projectiles within a four-body spectator model \cite{CarPLB2017}, for the treatment of the elastic and inclusive non-elastic break up reactions involving weakly bound three-cluster nuclei in $A\,(a,b)\,X$ / $a = x_1 + x_2 + b$ collisions. The four-body theory is an extension of the three-body approaches developed in the 80's by Ichimura, Autern and Vincent (IAV) \cite{IAV1985}, Udagawa and Tamura (UT) \cite{UT1981} and Hussein and McVoy (HM) \cite{HM1985}. We expect that experimentalists shall be encouraged to search for more information about the $x_{1} + x_{2}$ system in the elastic breakup cross section and that also further developments and extensions of the surrogate method will be pursued, based on the inclusive non-elastic breakup part of the $b$ spectrum.Comment: 8 pages, 3 figures, Contribution to the Proceedings of Fusion17: "International Conference on Heavy-Ion Collisions at Near-Barrier Energies", 20-24 February 2017 Hobart, Tasmania, Australi

Role of virtual break-up of projectile in astrophysical fusion reactions

We study the effect of virtual Coulomb break-up, commonly known as the dipole polarizability, of the deuteron projectile on the astrophysical fusion reaction 3He(d,p)4He. We use the adiabatic approximation to estimate the potential shift due to the E1 transition to the continuum states in the deuteron, and compute the barrier penetrability in the WKB approximation. We find that the enhancement of the penetrability due to the deuteron break-up is too small to resolve the longstanding puzzle observed in laboratory measurements that the electron screening effect is surprisingly larger than theoretical prediction based on an atomic physics model. The effect of the 3He break-up in the 3He(d,p)4He reaction, as well as the 7Li break-up in the 7Li(p,alpha)4He reaction is also discussed.Comment: 9 pages, 2 eps figure

Effective Widths and Effective Number of Phonons of Multiphonon Giant Resonances

We discuss the origin of the difference between the harmonic value of the width of the multiphonon giant resonances and the smaller observed value. Analytical expressions are derived for both the effective width and the average cross-section. The contribution of the Brink-Axel mechanism in resolving the discrepancy is pointed out.Comment: 9 pages, 4 figure