Actinide collisions for QED and superheavy elements with the time-dependent Hartree-Fock theory and the Balian-V\'en\'eroni variational principle

Collisions of actinide nuclei form, during very short times of few zs ($10^{-21}$ s), the heaviest ensembles of interacting nucleons available on Earth. Such collisions are used to produce super-strong electric fields by the huge number of interacting protons to test spontaneous positron-electron pair emission (vacuum decay) predicted by the quantum electrodynamics (QED) theory. Multi-nucleon transfer in actinide collisions could also be used as an alternative way to fusion in order to produce neutron-rich heavy and superheavy elements thanks to inverse quasifission mechanisms. Actinide collisions are studied in a dynamical quantum microscopic approach. The three-dimensional time-dependent Hartree-Fock (TDHF) code {\textsc{tdhf3d}} is used with a full Skyrme energy density functional to investigate the time evolution of expectation values of one-body operators, such as fragment position and particle number. This code is also used to compute the dispersion of the particle numbers (e.g., widths of fragment mass and charge distributions) from TDHF transfer probabilities, on the one hand, and using the Balian-Veneroni variational principle, on the other hand. A first application to test QED is discussed. Collision times in $^{238}$U+$^{238}$U are computed to determine the optimum energy for the observation of the vacuum decay. It is shown that the initial orientation strongly affects the collision times and reaction mechanism. The highest collision times predicted by TDHF in this reaction are of the order of $\sim4$ zs at a center of mass energy of 1200 MeV. According to modern calculations based on the Dirac equation, the collision times at $E_{cm}>1$ GeV are sufficient to allow spontaneous electron-positron pair emission from QED vacuum decay, in case of bare uranium ion collision. A second application of actinide collisions to produce neutron-rich transfermiums is discussed. A new inverse quasifission mechanism associated to a specific orientation of the nuclei is proposed to produce transfermium nuclei ($Z>100$) in the collision of prolate deformed actinides such as $^{232}$Th+$^{250}$Cf. The collision of the tip of one nucleus with the side of the other results in a nucleon flux toward the latter. The probability distributions for transfermium production in such a collision are computed. The produced nuclei are more neutron-rich than those formed in fusion reactions, thus, leading to more stable isotopes closer to the predicted superheavy island of stability. In addition to mass and charge dispersion, the Balian-Veneroni variational principle is used to compute correlations between $Z$ and $N$ distributions, which are zero in standard TDHF calculations.Comment: Proceeding of the FUSION11 conferenc

A new inverse quasifission mechanism to produce neutron-rich transfermium nuclei

Based on time-dependent Hartree-Fock theory, a new inverse quasifission mechanism is proposed to produce neutron-rich transfermium nuclei, in collision of prolate deformed actinides. Calculations show that collision of the tip of one nucleus with the side of the other results in a nucleon flux toward the latter. The role of nucleon evaporation and impact parameter, as well as the collision time are discussed.Comment: 8 pages, 7 figure

Soliton solutions of an integrable nonlinear Schrödinger equation with quintic terms

We present the fifth-order equation of the nonlinear Schrodinger hierarchy. This integrable partial differential ¨ equation contains fifth-order dispersion and nonlinear terms related to it. We present the Lax pair and use Darboux transformations to derive exact expressions for the most representative soliton solutions. This set includes two-soliton collisions and the degenerate case of the two-soliton solution, as well as beating structures composed of two or three solitons. Ultimately, the new quintic operator and the terms it adds to the standard nonlinear Schrodinger equation (NLSE) are found to primarily affect the velocity of solutions, with complicated ¨ flow-on effects. Furthermore, we present a new structure, composed of coincident equal-amplitude solitons, which cannot exist for the standard NLSE.The authors acknowledge the support of the Australian Research Council (Discovery Project No. DP140100265). N.A. and A.A. acknowledge support from the Volkswagen Stiftung and A.C. acknowledges Endeavour Postgraduate Award support

Triangular rogue wave cascades

By numerically applying the recursive Darboux transformation technique, we study high-order rational solutions of the nonlinear Schrödinger equation that appear spatiotemporally as triangular arrays of Peregrine solitons. These can be considered as rogue wave cascades and complement previously discovered circular cluster forms. In this analysis, we reveal a general parametric restriction for their existence and investigate the interplay between cascade and cluster forms. As a result, we demonstrate how to generate many more hybrid rogue wave solutions, including semicircular clusters that resemble claws

Second-order nonlinear Schrödinger equation breather solutions in the degenerate and rogue wave limits

We present an explicit analytic form for the two-breather solution of the nonlinear Schrödinger equation with imaginary eigenvalues. It describes various nonlinear combinations of Akhmediev breathers and Kuznetsov-Ma solitons. The degenerate case, when the two eigenvalues coincide, is quite involved. The standard inverse scattering technique does not generally provide an answer to this scenario. We show here that the solution can still be found as a special limit of the general second-order expression and appears as a mixture of polynomials with trigonometric and hyperbolic functions. A further restriction of this particular case, where the two eigenvalues are equal to i, produces the second-order rogue wave with two free parameters considered as differential shifts. The illustrations reveal a precarious dependence of wave profile on the degenerate eigenvalues and differential shifts. Thus we establish a hierarchy of second-order solutions, revealing the interrelated nature of the general case, the rogue wave, and the degenerate breathers

Classifying the hierarchy of nonlinear-Schrödinger-equation rogue-wave solutions

We present a systematic classification for higher-order rogue-wave solutions of the nonlinear Schrödinger equation, constructed as the nonlinear superposition of first-order breathers via the recursive Darboux transformation scheme. This hierarchy is subdivided into structures that exhibit varying degrees of radial symmetry, all arising from independent degrees of freedom associated with physical translations of component breathers. We reveal the general rules required to produce these fundamental patterns. Consequently, we are able to extrapolate the general shape for rogue-wave solutions beyond order 6, at which point accuracy limitations due to current standards of numerical generation become non-negligible. Furthermore, we indicate how a large set of irregular rogue-wave solutions can be produced by hybridizing these fundamental structures

Ks band secondary eclipses of WASP-19b and WASP-43b with the Anglo-Australian Telescope

We report new Ks band secondary eclipse observations for the hot-Jupiters WASP-19b and WASP-43b. Using the IRIS2 infrared camera on the Anglo-Australian Telescope (AAT), we measured significant secondary eclipses for both planets, with depths of 0.287 -0.020/+0.020% and 0.181 -0.027/+0.027% for WASP-19b and WASP-43b respectively. We compare the observations to atmosphere models from the VSTAR line-by-line radiative transfer code, and examine the effect of C/O abundance, top layer haze, and metallicities on the observed spectra. We performed a series of signal injection and recovery exercises on the observed light curves to explore the detection thresholds of the AAT+IRIS2 facility. We find that the optimal photometric precision is achieved for targets brighter than Kmag = 9, for which eclipses as shallow as 0.05% are detectable at >5 sigma significance.Comment: Accepted for publication in MNRAS, 13 pages, 10 figure