On the Invariance of G\"odel's Second Theorem with regard to Numberings

The prevalent interpretation of G\"odel's Second Theorem states that a sufficiently adequate and consistent theory does not prove its consistency. It is however not entirely clear how to justify this informal reading, as the formulation of the underlying mathematical theorem depends on several arbitrary formalisation choices. In this paper I examine the theorem's dependency regarding G\"odel numberings. I introduce deviant numberings, yielding provability predicates satisfying L\"ob's conditions, which result in provable consistency sentences. According to the main result of this paper however, these "counterexamples" do not refute the theorem's prevalent interpretation, since once a natural class of admissible numberings is singled out, invariance is maintained.Comment: Forthcoming in The Review of Symbolic Logi

The electric form factor of the neutron and its chiral content

Considering the nucleon as a system of confined valence quarks surrounded by pions we derive a Galster-like parameterization of the neutron electric form factor $G_E^n$. Furthermore, we show that the proposed parameterization can be linked to properties of the pion cloud. By this, the high quality data for the pion form factor can be used in predictions of $G_E^n$ in the low $Q^2$ region, where the direct double polarization measurements are not available.Comment: 11 pages, 3 figure

Self-reference Upfront: A Study of Self-referential G\"odel Numberings

In this paper we examine various requirements on the formalisation choices under which self-reference can be adequately formalised in arithmetic. In particular, we study self-referential numberings, which immediately provide a strong notion of self-reference even for expressively weak languages. The results of this paper suggest that the question whether truly self-referential reasoning can be formalised in arithmetic is more sensitive to the underlying coding apparatus than usually believed. As a case study, we show how this sensitivity affects the formal study of certain principles of self-referential truth

Low-Lying 2+ states in neutron-rich oxygen isotopes in quasiparticle random phase approximation

The properties of the low-lying, collective 2+ states in neutron-rich oxygen isotopes are investigated in the framework of self-consistent microscopic models with effective Skyrme interactions. In RPA the excitation energies E2+ can be well described but the transition probabilities are much too small as compared to experiment. Pairing correlations are then accounted for by performing quasiparticle RPA calculations. This improves considerably the predictions of B(E2) values and it enables one to calculate more reliably the ratios Mn/Mp of neutron-to-proton transition amplitudes. A satisfactory agreement with the existing experimental values of Mn/Mp is obtained.Comment: 8 pages, 3 figure

Three-nucleon mechanisms in photoreactions

The $^{12}$C$(\gamma,ppn)$ reaction has been measured for E$_{\gamma}$=150-800 MeV in the first study of this reaction in a target heavier than $^3$He. The experimental data are compared to a microscopic many body calculation. The model, which predicts that the largest contribution to the reaction arises from final state interactions following an initial pion production process, overestimates the measured cross sections and there are strong indications that the overestimate arises in this two-step process. The selection of suitable kinematic conditions strongly suppresses this two-step contribution leaving cross sections in which up to half the yield is predicted to arise from the absorption of the photon on three interacting nucleons and which agree with the model. The results indicate $(\gamma,3N)$ measurements on nuclei may be a valuable tool for obtaining information on the nuclear three-body interaction.Comment: 5 pages, 3 figure

Magnetization screening from gluonic currents and scaling law violation in the ratio of magnetic form factors for neutron and proton

The ratio ${\mu_p}G_E^p/G_M^p$ exhibits a decrease for four-momentum transfer Q^2 increasing beyond 1 GeV^2 indicating different spatial distributions for charge and for magnetization inside the proton. One-gluon exchange currents can explain this behaviour. The SU(6) breaking induced by gluonic currents predicts furthermore that the ratio of neutron to proton magnetic form factors ${\mu_p}G_M^n/{\mu_n}G_M^p$ falls with increasing Q^2. We find that the experimental data are consistent with our expectations of an almost linear decrease of the ratio ${\mu_p}G_M^n/{\mu_n}G_M^p$ with increasing Q^2, supporting the statement that the spatial distributions of magnetization are different for protons and for neutrons.Comment: 10 pages, 3 figure

Correlations in Nuclei: Self-Consistent Treatment and the BAGEL Approach

An approach is presented which allows a self-consistent description of the fragmentation of single-particle strength for nucleons in finite nuclei employing the Greens function formalism. The self-energy to be considered in the Dyson equation for the single-particle Greens function contains all terms of first (Hartree-Fock) and second order in the residual interaction. It is demonstrated that the fragmentation of the single-particle strength originating from the terms of second order can efficiently be described in terms of the so-called BAGEL approximation. Employing this approximation the self-energy can be evaluated in a self-consistent way, i.e. the correlations contained in the Greens function are taken into account for the evaluation of the self-energy. As an example this scheme is applied to the nucleus $^{16}O$, using a realistic nucleon nucleon interaction. The effects of the correlations on the occupation probabilities and the binding energy are evaluated.Comment: 9 page

Direct Test of the Scalar-Vector Lorentz Structure of the Nucleon- and Antinucleon-Nucleus Potential

Quantum Hadrodynamics in mean field approximation describes the effective nucleon-nucleus potential (about -50 MeV deep) as resulting from a strong repulsive vector (about 400 MeV) and a strong attractive scalar (about -450 MeV) contribution. This scalar-vector Lorentz structure implies a significant lowering of the threshold for $p\bar{p}$ photoproduction on a nucleus by about 850 MeV as compared to the free case since charge conjugation reverses the sign of the vector potential contribution in the equation of motion for the $\bar{p}$ states. It also implies a certain size of the photon induced $p\bar{p}$ pair creation cross section near threshold which is calculated for a target nucleus $^{208}$Pb. We also indicate a measurable second signature of the $p\bar{p}$ photoproduction process by estimating the increased cross section for emission of charged pions as a consequence of $\bar{p}$ annihilation within the nucleus.Comment: 18 pages latex, 5 PS figure

124-Color Super-resolution Imaging by Engineering DNA-PAINT Blinking Kinetics

Optical super-resolution techniques reach unprecedented spatial resolution down to a few nanometers. However, efficient multiplexing strategies for the simultaneous detection of hundreds of molecular species are still elusive. Here, we introduce an entirely new approach to multiplexed super-resolution microscopy by designing the blinking behavior of targets with engineered binding frequency and duration in DNA-PAINT. We assay this kinetic barcoding approach in silico and in vitro using DNA origami structures, show the applicability for multiplexed RNA and protein detection in cells, and finally experimentally demonstrate 124-plex super-resolution imaging within minutes.We thank Martin Spitaler and the imaging facility of the MPI of Biochemistry for confocal imaging support

First measurements of the ^16O(e,e'pn)^14N reaction

This paper reports on the first measurement of the ^16O(e,e'pn)^14N reaction. Data were measured in kinematics centred on a super-parallel geometry at energy and momentum transfers of 215 MeV and 316 MeV/c. The experimental resolution was sufficient to distinguish groups of states in the residual nucleus but not good enough to separate individual states. The data show a strong dependence on missing momentum and this dependence appears to be different for two groups of states in the residual nucleus. Theoretical calculations of the reaction using the Pavia code do not reproduce the shape or the magnitude of the data.Comment: 10 pages, 11 figures, 2 tables, Accepted for publication in EPJ