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We classify the nilpotent almost abelian Lie algebras admitting complex or symplectic structures. It turns out that if a nilpotent almost abelian Lie algebra admits a complex structure, then it necessarily admits a symplectic structure. Given an even dimensional almost abelian Lie algebra, we show that it always admits a complex structure when it is 2-step nilpotent and it always admits a symplectic structure when it is $k$-step nilpotent for $k=2, \, 3$ or $4$. Several consequences of the classification theorems are obtained.

We study $\gamma$-ray emission following $^{239}\mathrm{Pu}(n,\mathrm{f})$ over an incident neutron energy range of $2 < E_i < 40$ MeV. We present the first experimental evidence for positive correlations between the total angular momentum generated in fission and the excitation energy of the compound nucleus prior to fission. The $\gamma$-ray multiplicity increases linearly with incident energy below the 2\textsuperscript{nd}-chance fission threshold with a slope of $0.085 \pm 0.010$ MeV$^{-1}$. This linear trend appears to hold for the average excitation energy of the compound nucleus between $9 < \langle E_x \rangle < 19$ MeV. Most of the multiplicity increase comes from an enhancement around a $\gamma$-ray energy of 0.7 MeV, which we interpret as stretched quadrupole $\gamma$ rays that indicate an increase in total fission-fragment angular momentum with excitation energy., Comment: 9 pages, 5 figures

We differentiate the event-by-event n-$\gamma$ multiplicity data from \ce{^{252}Cf}(sf) with respect to the energies of the emitted particles as well as their relative angles of emission. We determine that neutron emission enhances $\gamma$-ray emission around $0.7$ and $1.2$ MeV, but the only directional alignment was observed for $E_\gamma \leq 0.7$ MeV and tended to be parallel and antiparallel to neutrons emitted in the same event. The emission of $\gamma$ rays at other energies was determined to be nearly isotropic. The presence of the emission and alignment enhancements is explained by positive correlations between neutron emission and quadrupole $\gamma$-ray emission along rotational bands in the de-exciting fragments. This observation corroborates the hypothesis of positive correlations between the angular momentum of a fragment and its intrinsic excitation energy. The results of this work are especially relevant in view of the recent theoretical and experimental interest in the generation of angular momentum in fission. Specifically, we have determined an alignment of the fragments angular momenta in a direction perpendicular to the direction of motion. We interpret the lack of $n$-$\gamma$ angular correlations for fission fragments near closed shells as a weakening of the alignment process for spherical nuclei. Lastly, we have observed that statistical $\gamma$ rays are emitted isotropically, indicating that the average angular momentum removed by this radiation is small. These results, and the analysis tools presented in this work, represent a stepping stone for future analysis of $n$-$\gamma$ emission correlations and their connection to angular momentum properties., Comment: 17 pages, 3 figures, no table

The emission of neutrons and gamma rays by fission fragments reveal important information about the properties of fragments immediately following scission. The initial fragment properties, correlations between fragments, and emission competition give rise to correlations in neutron-gamma emission. Neutron-gamma correlations are important in nonproliferation applications because the characterization of fissionable samples relies on the identification of signatures in the measured radiation. Furthermore, recent theoretical and experimental advances have proposed to explain the mechanism of angular momentum generation in fission. In this paper, we present a novel analysis method of neutrons and gamma rays emitted by fission fragments that allows us to discern structure in the observed correlations. We have analyzed data collected on \ce{^{252}Cf}(sf) at the Chi-Nu array at the Los Alamos Neutron Science Center. Through our analysis of the energy-differential neutron-gamma multiplicity covariance, we have observed enhanced neutron-gamma correlations, corresponding to rotational band gamma-ray transitions, at gamma-ray energies of $0.7$ and $1.2$ MeV. To shed light on the origin of this structure, we compare the experimental data with the predictions of three model calculations. The origin of the observed correlation structure is understood in terms of a positive spin-energy correlation in the generation of angular momentum in fission., Comment: 21 pages, 4 figures, 1 table

We give necessary conditions for the existence of degenerations between two complex Lie superalgebras of dimension $(m,n)$. As an application, we study the variety $\mathcal{LS}^{(2,2)}$ of complex Lie superalgebras of dimension $(2,2)$. First we give the algebraic classification and then obtain that $\mathcal{LS}^{(2,2)}$ is the union of seven irreducible components, three of which are the Zariski closures of rigid Lie superalgebras. As byproduct, we obtain an example of a nilpotent rigid Lie superalgebra, in contrast to the classical case where no example is known., Comment: 12 pages

We describe degenerations of three-dimensional Jordan superalgebras over $\mathbb{C}$. In particular, we describe all irreducible components in the corresponding varieties., Comment: arXiv admin note: text overlap with arXiv:1611.06454