Anomalous population of 10^{10}He states in reactions with 11^{11}Li

Structure with the lowest energy observed in the $^{10}$He spectrum populated in the proton knockout reaction with $^{11}$Li beam has a peak at $1.2-1.5$ MeV. This peak is usually interpreted as a resonant $0^+$ ground state of $^{10}$He. Our theoretical calculations indicate that this peak is likely to be a pileup of $1^-$, $0^+$, and $2^+$ excitations with very similar shapes. %We predict a very specific nature of the $1^-$ excitation in $^{10}$He. Moreover, the ``soft'' $1^-$ excitation appears to be the lowest one in energy. Such an anomalous continuum response is traced to the halo structure of $^{11}$Li providing extreme low energy shift to all the expected continuum excitations. Competitions of the initial state structure (ISS) and the final state interaction (FSI) effects on the spectrum and three-body correlations in $^{10}$He are discussed. Analogous effect of the extreme low-energy shift could also be expected in other cases of $2n$ emitters populated in reactions with halo nuclei. Simplified example of the $^{10}$He spectrum in $\alpha$ knockout from $^{14}$Be, is given. We also discuss limits on the properties of $^{9}$He stemming from the observed $^{10}$He spectrum.Comment: 10 pages, 13 figure

Scattering theory with finite-gap backgrounds: Transformation operators and characteristic properties of scattering data

We develop direct and inverse scattering theory for Jacobi operators (doubly infinite second order difference operators) with steplike coefficients which are asymptotically close to different finite-gap quasi-periodic coefficients on different sides. We give necessary and sufficient conditions for the scattering data in the case of perturbations with finite second (or higher) moment.Comment: 23 page

Two-proton radioactivity and three-body decay. V. Improved momentum distributions

Nowadays quantum-mechanical theory allows one to reliably calculate the processes of 2p radioactivity (true three-body decays) and the corresponding energy and angular correlations up to distances of the order of 1000 fm. However, the precision of modern experiments has now become sufficient to indicate some deficiency of the predicted theoretical distributions. In this paper we discuss the extrapolation along the classical trajectories as a method to improve the convergence of the theoretical energy and angular correlations at very large distances (of the order of atomic distances), where only the long-range Coulomb forces are still operating. The precision of this approach is demonstrated using the "exactly" solvable semianalytical models with simplified three-body Hamiltonians. It is also demonstrated that for heavy 2p emitters, the 2p decay momentum distributions can be sensitive to the effect of the screening by atomic electrons. We compare theoretical results with available experimental data.Comment: 13 pages, 18 figure

Scattering Theory for Jacobi Operators with Steplike Quasi-Periodic Background

We develop direct and inverse scattering theory for Jacobi operators with steplike quasi-periodic finite-gap background in the same isospectral class. We derive the corresponding Gel'fand-Levitan-Marchenko equation and find minimal scattering data which determine the perturbed operator uniquely. In addition, we show how the transmission coefficients can be reconstructed from the eigenvalues and one of the reflection coefficients.Comment: 14 page

Inverse scattering transform for the Toda hierarchy with steplike finite-gap backgrounds

We provide a rigorous treatment of the inverse scattering transform for the entire Toda hierarchy for solutions which are asymptotically close to (in general) different finite-gap solutions as $n\to\pm\infty$.Comment: 10 page

From Coulomb excitation cross sections to non-resonant astrophysical rates in three-body systems: 17^{17}Ne case

Coulomb and nuclear dissociation of $^{17}$Ne on light and heavy targets are studied theoretically. The dipole E1 strength function is determined in a broad energy range including energies of astrophysical interest. Dependence of the strength function on different parameters of the $^{17}$Ne ground state structure and continuum dynamics is analyzed in a three-body model. The discovered dependence plays an important role for studies of the strength functions for the three-body E1 dissociation and radiative capture. The constraints on the $[s^2]/[d^2]$ configuration mixing in $^{17}$Ne and on $p$-wave interaction in the $^{15}$O+$p$ channel are imposed based on experimental data for $^{17}$Ne Coulomb dissociation on heavy target.Comment: 12 pages, 13 figure