Identifying structures in the continuum: Application to 16^{16}Be

The population and decay of two-nucleon resonances offer exciting new opportunities to explore dripline phenomena. The understanding of these systems requires a solid description of the three-body (core+N+N) continuum. The identification of a state with resonant character from the background of non-resonant continuum states in the same energy range poses a theoretical challenge. It is the purpose of this work to establish a robust theoretical framework to identify and characterize three-body resonances in a discrete basis. A resonance operator is proposed, which describes the sensitivity to changes in the potential. Resonances are then identified from the lowest eigenstates of the resonance operator. The operator is diagonalized in a basis of Hamiltonian pseudostates, built within the hyperspherical harmonics formalism using the analytical THO basis. The energy and width of the resonance are determined from its time dependence. The method is applied to 16Be in a 14Be+n+n model. An effective core+n potential, fitted to the available information on the subsystem 15Be, is employed. The 0+ ground state resonance of 16Be presents a strong dineutron configuration, which favors the picture of a correlated two-neutron emission. Fitting the three body interaction to the experimental two-neutron separation energy |S2n|=1.35(10) MeV, the computed width is Gamma(0+)=0.16 MeV. From the same Hamiltonian, a 2+ resonance is also predicted with E_r(2+)=2.42 MeV and Gamma(2+)=0.40 MeV. The dineutron configuration and the computed 0+ width are consistent with previous R-matrix calculations for the true three-body continuum. The extracted values of the resonance energy and width converge with the size of the pseudostate basis and are robust under changes in the basis parameters. This supports the reliability of the method in describing the properties of unbound core+N+N systems in a discrete basis.Comment: 11 pages, 14 figures. Accepted as PR

The Morse-Sard theorem revisited

Let $n, m, k$ be positive integers with $k=n-m+1$. We establish an abstract Morse-Sard-type theorem which allows us to deduce, on the one hand, a previous result of De Pascale's for Sobolev $W^{k,p}_{\textrm{loc}}(\mathbb{R}^n, \mathbb{R}^m)$ functions with $p>n$ and, on the other hand, also the following new result: if $f\in C^{k-1}(\mathbb{R}^n, \mathbb{R}^m)$ satisfies $$\limsup_{h\to 0}\frac{|D^{k-1}f(x+h)-D^{k-1}f(x)|}{|h|}<\infty$$ for every $x\in\mathbb{R}^n$ (that is, $D^{k-1}f$ is a Stepanov function), then the set of critical values of $f$ is Lebesgue-null in $\mathbb{R}^m$. In the case that $m=1$ we also show that this limiting condition holding for every $x\in\mathbb{R}^n\setminus\mathcal{N}$, where $\mathcal{N}$ is a set of zero $(n-2+\alpha)$-dimensional Hausdorff measure for some $0<\alpha<1$, is sufficient to guarantee the same conclusion.Comment: We corrected some misprints and made some changes in the introductio

Non-stochastic behavior of atomic surface diffusion on Cu(111) at all temperatures

Atomic diffusion is usually understood as a succession of random, independent displacements of an adatom over the surface's potential energy landscape. Nevertheless, an analysis of Molecular Dynamics simulations of self-diffusion on Cu(111) demonstrates the existence of different types of correlations in the atomic jumps at all temperatures. Thus, the atomic displacements cannot be correctly described in terms of a random walk model. This fact has a profound impact on the determination and interpretation of diffusion coefficients.Comment: 5 figure