46,842 research outputs found
Identifying structures in the continuum: Application to 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 be positive integers with . 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 functions with and, on the other hand, also the following
new result: if satisfies
for every
(that is, is a Stepanov function), then the set
of critical values of is Lebesgue-null in . In the case that
we also show that this limiting condition holding for every
, where is a set of zero
-dimensional Hausdorff measure for some , 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
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