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From Fredholm to Schrödinger via Eikonal: A New Formalism for Revealing Unknown Properties of Natural Orbitals.
J Chem Theory Comput
November 2021
Department of Physical and Quantum Chemistry, Faculty of Chemistry, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland.
Previously unknown properties of the natural orbitals (NOs) pertaining to singlet states (with natural parity, if present) of electronic systems with even numbers of electrons are revealed upon the demonstration that, at the limit of → ∞, the NO ψ() with the th largest occupation number ν approaches the solution ψ̃() of the zero-energy Schrödinger equation that reads ([(, )] (r⃗)) - (π/) [ρ(, )] ([ρ(, )] (r⃗)) = 0 (where is the kinetic energy operator), whereas ν approaches ν̃. The resulting formalism, in which the "on-top" two-electron density ρ(, ) solely controls the asymptotic behavior of both ψ() and ν at the limit of the latter becoming infinitesimally small, produces surprisingly accurate values of both quantities even for small . It opens entirely new vistas in the elucidation of their properties, including single-line derivations of the power laws governing the asymptotic decays of ν and ⟨ψ()||ψ()⟩ with , some of which have been obtained previously with tedious algebra and arcane mathematical arguments.
View Article and Find Full Text PDFNonperturbative shell-model interactions from the in-medium similarity renormalization group.
Phys Rev Lett
October 2014
Institut für Kernphysik, Technische Universität Darmstadt, 64289 Darmstadt, Germany.
We present the first ab initio construction of valence-space Hamiltonians for medium-mass nuclei based on chiral two- and three-nucleon interactions using the in-medium similarity renormalization group. When applied to the oxygen isotopes, we find experimental ground-state energies are well reproduced, including the flat trend beyond the drip line at (24)O. Similarly, natural-parity spectra in (21,22,23,24)O are in agreement with experiment, and we present predictions for excited states in (25,26)O.
View Article and Find Full Text PDFObservation of a J(PC)=1-+ exotic resonance in diffractive dissociation of 190 GeV/c π- into π- π- π+.
Phys Rev Lett
June 2010
Torino Section of INFN, 10125 Turin, Italy.
The COMPASS experiment at the CERN SPS has studied the diffractive dissociation of negative pions into the π- π- π+ final state using a 190 GeV/c pion beam hitting a lead target. A partial wave analysis has been performed on a sample of 420,000 events taken at values of the squared 4-momentum transfer t' between 0.1 and 1 GeV2/c2.
View Article and Find Full Text PDFNovel manifestation of alpha-clustering structures: new "alpha+208Pb" states in 212Po revealed by their enhanced E1 decays.
Phys Rev Lett
January 2010
CSNSM, IN2P3-CNRS and Université Paris-Sud, 91405 Orsay, France.
Excited states in 212Po were populated by alpha transfer using the 208Pb(18O,14C) reaction, and their deexcitation gamma rays were studied with the Euroball array. Several levels were found to decay by a unique E1 transition (Egamma<1 MeV) populating the yrast state with the same spin value. Their lifetimes were measured by the Doppler-shift attenuation method.
View Article and Find Full Text PDFObservation of exotic meson production in the reaction pi- p --> eta'pi- p at 18 GeV/c.
Phys Rev Lett
April 2001
University of Notre Dame, Notre Dame, Indiana 46556, USA.
An amplitude analysis of an exclusive sample of 5765 events from the reaction pi- p-->eta'pi- p at 18 GeV/c is described. The eta'pi- production is dominated by natural parity exchange and by three partial waves: those with J(PC) = 1(-+), 2(++), and 4(++). A mass-dependent analysis of the partial-wave amplitudes indicates the production of the a2(1320) meson as well as the a4(2040) meson, observed for the first time decaying to eta'pi-.
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