Negative Energy Resonances Research Articles

Universal disorder in Bi2Sr2CaCu2O8+x

The cuprates contain a range of nanoscale phenomena that consist of both LDOS(E) features and spatial excitations. Many of these phenomena can only be observed through the use of a SI-STM and their disorder can be mapped out through the fitting of a phenomenological model to the LDOS(E). We present a study of the nanometer scale disorder of single crystal cryogenically cleaved samples of Bi2Sr2CaCu2O8+x whose dopings range from p = 0.19 to 0.06. The phenomenological model used is the Tripartite model that has been successfully applied to the average LDOS(E) previously. The resulting energy scale maps show a structured patchwork disorder of three energy scales, which can be described by a single underlying disordered parameter. This spatial disorder structure is universal for all dopings and energy scales. It is independent of the oxygen dopant negative energy resonances and the interface between the different patches takes the form of a shortened lifetime pseudogap/superconducting gap state. The relationship between the energy scales and the spatial modulations of the dispersive QPI, static q1* modulation and the pseudogap shows that the energy scales signatures in the LDOS(E) are tied to the onset and termination of the spatial excitations. The static q1* modulations local energy range is measured and its signature in the LDOS(E) is the kink, whose number of states are modulated with a wave vector of q1*. This analysis of both the LDOS(r,E) and the spatial modulations in q-space show a picture of a single underlying disordered parameter that determines both the LDOS(E) structure as well as the energy ranges of the QPI, q1* modulation and the pseudogap states. This parameter for a single patch can be defined by the Fermi surface crossing of the parent compound anti-ferromagnetic zone boundary for a model homogeneous superconductor with the same electronic properties as the patch.

Resonantly Enhanced Pair Production in a Simple Diatomic Model

A new mechanism for the production of electron-positron pairs from the interaction of a laser field and a fully ionized diatomic molecule in the tunneling regime is presented. When the laser field is turned off, the Dirac operator has resonances in both the positive and the negative energy continua while bound states are in the mass gap. When this system is immersed in a strong laser field, the resonances move in the complex energy plane: the negative energy resonances are pushed to higher energies while the bound states are Stark shifted [F. Fillion-Gourdeau et al., J. Phys. A 45, 215304 (2012)]. It is argued here that there is a pair production enhancement at the crossing of resonances by looking at a simple one-dimensional model: the nuclei are modeled simply by Dirac delta potential wells while the laser field is assumed to be static and of finite spatial extent. The average rate for the number of electron-positron pairs produced is evaluated and the results are compared to the one and zero nucleus cases. It is shown that positrons are produced by the resonantly enhanced pair production mechanism, which is analogous to the resonantly enhanced ionization of molecular physics. This phenomenon could be used to increase the number of pairs produced at low field strength, allowing the study of the Dirac vacuum.

Negative energy resonances of bosons in a magnetic quadrupole trap

We investigate resonances of spin 1 bosons in a three-dimensional magnetic quadrupole field. Complementary to the well-known positive energy resonances it is shown that there exist short-lived, i.e. broad, negative energy resonances. The latter are characterized by an atomic spin that is aligned antiparallel to the local magnetic field direction. In contrast to the positive energy resonances the lifetimes of the negative energy resonances decreases with increasing total magnetic quantum number. We derive a mapping of the two branches of the spectrum.

Intrinsic charge radius of the neutron: Discrepancy between the Garching and Dubna results.

This Rapid Communication discusses possible reasons for the discrepancy between the results of the Garching and Dubna determinations of the mean square intrinsic charge radius of the neutron related to the inner structure of the neutron. It is shown that the most probable reason for the discrepancy between the values for bismuth is the differences in accounting for the influence of negative energy resonances on the (ne)-scattering length value measured in the experiments. The Dubna result seems to be more reliable for the present.

Cosmological Implications of the Planck Aether Model for a Unified Field Theory

Abstract In the previously proposed Planck aether model of a unified theory, the vacuum ground state consists of a dense assembly of positive and negative Planck masses obeying an exactly nonrelativistic law of motion. The Planck aether is superfluid, and it can without expenditure of energy form a tangle of quantized vortex filamants permitting the transmission of two types of waves: One associated with a symmetric displacement of the vortex lattice leading to gravitational waves, and one associated with an antisymmetric displacement leading to electromagnetic waves. Dirac spinors are explained in this model as excitons made up from positive and negative energy resonances of the vortex lattice. Because the number of positive and negative Planck masses is assumed to be equal, the cosmological constant is equal to zero. With the Dirac spinors formed as bound states from the Planck aether, the sum of the positive kinetic energy and negative gravitational energy must remain exactly equal to zero, resulting in ß = l as the exact value for the cosmological mass parameter. To make up for the unobserved missing mass, estimated to be about 10 times larger than the baryonic mass, it is conjectured that this mass consists of rotons, which in the superfluid Planck aether would come from the cut-off of the energy spectrum near the Planck energy. Because of their unusual dispersion relation, rotons possess a large momentum, even if their velocity vanishes. They are, for this reason, a promising candidate for the nonbaryonic dark matter, combining properties of hot and cold dark matter. The critical value Ω = 1 requires that the number density of the rotons is equal to nr ≃ 2 x 10-25 cm-3 . This value corresponds to an average distance of separation between the rotons of the order nr -1/3 ≃ 6000 km. The small number of rotons per unit volume combined with their weak gravitational coupling constant would make it difficult to detect them directly, but the gravitational field these roton masses generate in the vicinity of galaxies could explain the observed flat rotation curves of disc galaxies. Finally, because the gravitational waves have a cut-off at the vortex lattice scale at 1015 -1016 GeV, there can be no singularity in the course of a gravitational collapse, as it happens for solutions of Einstein's gravitational field equations. A generalization of Einstein's gravitational field Lagrangian, taking into account the existence of a smallest wave length, rather predicts a conversion of all mass into electromagnetic (or gravitational) radiation in approaching the singularity. The predicted conversion of mass into radiation in the course of gravitational collapse may provide an explanation for the large energy release of quasars.

Precision measurement of the bound-coherent-neutron scattering length of 235U.

With use of the neutron interferometric technique, the real parts of the bound-coherent scattering length, b, of /sup 235/U have been precisely measured for five different incident neutron energies in the range of 30 to 92 meV. The value of b at each incident neutron energy was obtained from the average of two independent measurements using two samples of different thicknesses. The results are b = 10.47 +- 0.04 fm (E = 30.34 meV), b = 10.47 +- 0.03 fm (E = 41.02 meV), b = 10.51 +- 0.03 fm (E = 51.43 meV), b = 10.39 +- 0.03 fm (E = 74.90 meV), b = 10.41 +- 0.03 fm (E = 91.39 meV). The uncertainty in these results is about an order of magnitude smaller than the present literature value. The small energy dependence of the observed scattering lengths has been used to establish the parameters of the negative energy resonance level (-1.4 eV) using the Breit-Wigner formalism.

Thermal Westcott g-Factor Measurement for Thorium-232

The shape of the thorium absorption cross section near thermal energies was investigated. This shape is dominated by one or more negative energy resonances whose parameters are not directly known but must be inferred from higher energy data. Since the integral quantity most conveniently describing the thermal cross-section shape is the Westcott g-factor, effort was directed toward establishing this quantity to high precision. Three nearly independent g-factor estimates were obtained from measurements on a variety of foils in three different neutron spectra provided by polyethylene-moderated neutrons from a 252Cf source and from irradiations in the National Bureau of Standards “Standard Thermal Neutron Density.” The weighted average of the three measurements was 0.990 ± 0.009. This is in good agreement with two recent evaluations and supports the adequacy of the current cross-section descriptions.

Prediction of a new type of threshold effects

Threshold effect can be expected in the proton spectrum from (d,p) reactions at the neutron threshold. The investigation of the anomaly may contribute to our knowledge about the very extended, puffy states e.g. “negative energy resonances”.

Total Neutron Cross Section and Resonance Parameters of Promethium-147

The total neutron cross section of 147Pm has been measured from 0.01 to 1000 eV, using compacted oxide samples in the Materials Testing Reactor (MTR) fast chopper. After correcting the data for decay product 147Sm content and water contaminant bias, the total cross section of 147Pm at 0.0253 eV was found to be b. Resonance parameters were determined up to 250 eV by shape-fitting and area analysis, and a negative energy resonance has been postulated to fit the data at thermal. From these parameters a resonance absorption integral of 2192 ± 100 b and a neutron s-wave strength function have been obtained.

Negative energy resonances and potential capture in the 59Co (n, γ) reaction

Abstract Gamma-ray circular polarization measurements of the 59 Co(n, γ ) reaction with polarized neutrons indicate the presence of a negative energy resonance with J π = 4 − . It is shown that interference measurements on partial radiative capture can be explained without introducing potential capture.

The 149Sm(n, α) 146Nd reactions with low energy neutrons

The α-spectrum from the 149Sm(n, α) 146Nd reaction with slow neutrons has been measured for three different incident neutron energies. The results confirm that the spin of the 0.0976 eV resonance of 149Sm is 4 and show the existence of a negative energy resonance with spin 3.

Spins of levels in N 15, Fe 57, Cu 64, Zr 92 and Hg 200 by neutron capture γ-ray directional correlations

Neutron capture γ-ray directional correlations, with the assumption of negligible M2 admixture in high energy E1 transitions, are used to deduce spins of levels in N 15, Fe 57, Cu 64, Zr 92 and Hg 200. For several of the correlations studied, multipolarities of primary γ-rays, and hence parities of certain levels, are inferred from the systematics of neutron capture γ-ray radiation strengths and other information. On this basis, the following assignments are made: N 15: 6.32 MeV level, 3 2 or 5 2 ; Fe 57: 0.365 MeV level, 3 2 ; Cu 64: 0.277 and 0.607 MeV levels, 1 or 2 +; Zr 92: 2.33 MeV level, 3 -, negative energy resonance dominating thermal capture, 2; Hg 200: 1.59 MeV and 2.10 MeV levels, 1 +, resonance at −2 eV, 0. In Hg 200, as a consequence of the spin 0 capturing state assignment and E1 multipolarity assignments for primary γ-rays, levels at 2.39, 2.64, 2.97, 3.09, 3.21 and 3.38 MeV are tentatively concluded to be 1 +. Information concerning γ-ray multipole mixtures is also obtained in N 15 and Fe 57.

Multilevel Analysis of the Slow Neutron Cross Sections ofU233

A multilevel analysis of the slow neutron total and fission cross sections of ${\mathrm{U}}^{233}$ from thermal energies to 11 ev has been carried out, under the assumption that in one of the two spin states the nucleus undergoes fission primarily through a small number of channels. The cases of one and of two fission channels for this spin state have been investigated in detail. Although the analysis does not yield an exact value for the number of available fission channels, the data are adequately fit with a two fission channel formula. It is not necessary to invoke any negative energy resonances in the analysis. The presence of a noninterfering component in the cross sections, having a $\frac{1}{v}$ energy variation, is indicated. At thermal energies, this component accounts for approximately 80% of the total and fission cross sections. An interpretation of this component as being due to one spin state of the compound nucleus is presented. Under this assumption, the fission characteristics of the two spin states of the compound nucleus formed by $s$-wave neutrons are quite different.

Resonance Theory of Neutron Cross Sections of Fissionable Nuclei

The general Wigner-Eisenbud resonance theory is used to develop a method of analysis for the neutron cross sections of fissionable nuclei. The method is employed in giving a reasonable description of the low-energy cross sections in ${\mathrm{U}}^{235}$. The single-level fit for ${\mathrm{U}}^{235}$ is known to be unreasonable. Many-level expressions for the cross sections are derived---the only approximation to the general theory being the neglect of all but a small group of resonances. No explicit reference to fission channels is needed and the many-level expressions require few level parameters: the ${E}_{\ensuremath{\lambda}}$, ${\ensuremath{\Gamma}}_{\ensuremath{\lambda}n}$, ${\ensuremath{\Gamma}}_{\ensuremath{\lambda}\ensuremath{\gamma}}$, and ${\ensuremath{\Gamma}}_{\ensuremath{\lambda}f}$ of the single-level theory for each resonance and a few additional parameters pertinent to the interference between levels. The interference terms are described and shown to be important. Their average value yields information about the number of channels involved in fission. The shape and size of the ${\mathrm{U}}^{235}$ cross sections below 2 ev are fitted to within one or two percent using: (a) only one negative energy resonance of smaller size than in the single-level fit; (b) no additional levels to fit the shape other than the observed levels at positive energies; (c) three interference parameters whose size suggests that there are several fission channels in ${\mathrm{U}}^{235}$.

The slow neutron total cross-section of 143Nd

Crystal spectrometers covering the energy range 0·01–10 eV have been used to measure the transmission of neodymium oxide enriched in the isotope 143Nd. Analysis of the energy dependence of the 143Nd. total cross-section gives the 2200 m/sec cross-sections as 335 ± 20 barns for absorption and 75 ± 7 barns for scattering, and the parameters of a negative energy resonance are E 0 = −6 ± 1 eV, Δ γ = 86 ± 15 mV, Δ n 0 = 68 ± 15 mV.

The 2.85 keV neutron resonance of sodium

The measurement of the total neutron cross-section of sodium in the region 600 eV to 15 keV using the Harwell 15 MeV linear electron accelerator is described. Analysis of the results in conjunction with the known values of the low energy elastic and radiative capture cross-sections leads to the following conclusions. The cross-section up to 15 keV may be described in terms of a potential scattering cross-section of 2.4 barn and two s-wave resonances, one at 2.85±0.04 keV neutron energy and the other at negative energy. The 2.85 keV resonance has parameters σ 0 = 370±5 barn, Γ n = 405±12 eV, Γ γ ≦ 0.34±0.01 eV and spin J = 1+. The negative energy resonance has a ratio of reduced width to resonance energy of γ n 2/ E R = −0.5 while | E R| ⪢1 keV. The spin of this resonance is J = 2+.