Threshold Anomalies Research Articles

Threshold effects in multichannel coupling and spectroscopic factors in exotic nuclei

In the threshold region, the cross section and the associated overlap integral obey the Wigner threshold law that results in the Wigner-cusp phenomenon. Due to flux conservation, a cusp anomaly in one channel manifests itself in other open channels, even if their respective thresholds appear at a different energy. The shape of a threshold cusp depends on the orbital angular momentum of a scattered particle; hence, studies of Wigner anomalies in weakly bound nuclei with several low-lying thresholds can provide valuable spectroscopic information. In this work, we investigate the threshold behavior of spectroscopic factors in neutron-rich drip-line nuclei using the Gamow shell model, which takes into account many-body correlations and the continuum effects. The presence of threshold anomalies is demonstrated and the implications for spectroscopic factors are discussed.

COMMENT ON "NONCOMMUTATIVITY AS A POSSIBLE ORIGIN OF THE ULTRAHIGH-ENERGY COSMIC RAY AND THE TEV PHOTON PARADOXES"

A Lorentz-noninvariant modification of the kinematic dispersion law was proposed in Ref. 1, claimed to be derivable from q-deformed noncommutative theory, and argued to evade ultrahigh energy threshold anomalies (trans-GKZ-cutoff cosmic rays and TeV-photons) by raising the respective thresholds. It is pointed out that such dispersion laws do not follow from deformed oscillator systems, and the proposed dispersion law is invalidated by tachyonic propagation, as well as photon instability, in addition to the process considered.

REPLY TO THE COMMENT ON "NONCOMMUTATIVITY AS A POSSIBLE ORIGIN OF THE ULTRAHIGH-ENERGY COSMIC RAY AND THE TEV PHOTON PARADOXES"

A cogitative comment on Ref. 1 was given by the author of Ref. 2 arguing that the Lorentz-noninvariant modification of the kinematic dispersion law does not follow from deformed oscillator systems, and it cannot evade ultrahigh energy threshold anomalies by raising the respective thresholds. It is pointed out that the dispersion relations of a q-deformed boson and fermion are derived heedlessly and further study on noncommutative theories is necessary. However if such dispersion relations are assumed tenable, the tachyonic propagation and photon instability do not exist at all because the deviation from 1 in q must be imaginary.

NONCOMMUTATIVITY AS A POSSIBLE ORIGIN OF THE ULTRAHIGH ENERGY COSMIC RAY AND THE TeV-PHOTON PARADOXES

In this paper, we present a general modified dispersion relation derived from q-deformed noncommutative theory and apply it to the ultrahigh energy cosmic ray and the TeV-photon paradoxes — threshold anomalies. Our purpose is not only trying to solve these puzzles by noncommutative theory but also to support noncommutative theory through the coincidence of the region in the parameter space for resolving the threshold anomalies with the one from the q-deformed noncommutative theory.

SELECTED TOPICS IN PLANCK-SCALE PHYSICS

We review a few topics in Planck-scale physics, with emphasis on possible manifestations in relatively low energy. The selected topics include quantum fluctuations of spacetime, their cumulative effects, uncertainties in energy–momentum measurements, and low energy quantum-gravity phenomenology. The focus is on quantum-gravity-induced uncertainties in some observable quantities. We consider four possible ways to probe Planck-scale physics experimentally: (i) looking for energy-dependent spreads in the arrival time of photons of the same energy from GRBs; (ii) examining spacetime fluctuation-induced phase incoherence of light from extragalactic sources; (iii) detecting spacetime foam with laser-based interferometry techniques; (iv) understanding the threshold anomalies in high energy cosmic ray and gamma ray events. Some other experiments are briefly discussed. We show how some physics behind black holes, simple clocks, simple computers, and the holographic principle is related to Planck-scale physics. We also discuss a formulation of the Dirac equation as a difference equation on a discrete Planck-scale spacetime lattice, and a possible interplay between Planck-scale and Hubble-scale physics encoded in the cosmological constant (dark energy).

Planck-scale deformation of Lorentz symmetry as a solution to the ultrahigh energy cosmic ray and the TeV-photon paradoxes

One of the most puzzling current experimental physics paradoxes is the arrival on Earth of Ultra High Energy Cosmic Rays with energies above the GZK threshold. The recent observation of 20TeV photons from Mk 501 is another somewhat similar paradox. Several models have been proposed for the UHECR paradox. No solution has yet been proposed for the TeV-$\gamma$ paradox. Remarkably, the drastic assumption of a violation of ordinary Lorentz invariance would resolve both paradoxes. We present a formalism for the description of the type of Lorentz-invariance deformation (LID) that could be induced by non-trivial short-distance structure of space-time, and we show that this formalism is well suited for comparison of experimental data with LID predictions. We use the UHECR and TeV-$\gamma$ data, as well as bounds on time-of-flight differences between photons of different energies, to constrain the LID parameter space. A model with only two parameters, an energy scale and a dimensionless parameter characterizing the functional dependence on the energy scale, is shown to be sufficient to solve both the UHECR and the TeV-$\gamma$ threshold anomalies while satisfying the time-of-flight bounds. The allowed region of the two-parameter space is relatively small, but, remarkably, it fits perfectly the expectations of the quantum-gravity-motivated space-time models known to support such deformations of Lorentz invariance: integer value of the dimensionless parameter and characteristic energy scale constrained to a narrow interval in the neighborhood of the Planck scale.

Energy–momentum uncertainties as possible origin of threshold anomalies in UHECR and TeV- γ events

A threshold anomaly refers to a theoretically expected energy threshold that is not observed experimentally. Here we offer an explanation of the threshold anomalies encountered in the ultra-high energy cosmic ray events and the TeV- γ events, by arguing that energy–momentum uncertainties due to quantum gravity, too small to be detected in low-energy regime, can affect particle kinematics so as to raise or even eliminate the energy thresholds.

Energy–momentum uncertainties as possible origin of threshold anomalies in UHECR and TeV-γ events

Energy–momentum uncertainties as possible origin of threshold anomalies in UHECR and TeV-γ events

Barriers, thresholds, and resonances: Spectral quantization of the transition state for the collinear D+H2 reaction

We have analyzed the quantum dynamics of the collinear D+H2 reaction in the region of the transition state on the DMBE potential energy surface. Using the spectral quantization method, the dynamical features of the transition state are mapped out through a sequence of hypothetical Franck–Condon spectra. These spectra are generated by time-dependent wave packet dynamics. A comprehensive analysis of the spectra has revealed three distinct classes of peaks associated with (1) conventional reactive resonances, (2) threshold anomalies, and (3) barrier resonances. Individual peaks in the spectra are assigned through the use of time-independent wave functions which are obtained by Fourier transformation of the wave packet at the peak energies. The positions, lifetimes, and wave functions are extracted for all 23 conventional and barrier resonances. A new analytic line shape formula is developed to fit the spectral peaks of the barrier resonances. The exact quantum analysis is also supplemented with a semiclassical treatment based on periodic orbits. Most of the resonance states are found to be associated with single quantized periodic orbits in the transition state region.

Multichannel neutralization and reionization in scattering of slow ions

A simple kinetic model is proposed for the multichannel neutralization of slow ions scattered on a metal surface. The “V” shape peculiarities observed recently in scattering of Ar +, He +, N 2 +, CO +, CO 2 + on Pt(100) are interpreted as classic threshold anomalies arising from crossing of the Fermi level by the ground electron levels of the particles. The model predicts two new types of peculiarities (“h” and “α” types) connected with the competition of multichannel neutralization, reionization and deexcitation. The possibility of spectroscopy of the surface collisional complexes (“spectroscopy of threshold anomalies”) is also pointed out in this report.

The First Born Approximation in Estimates of the Threshold Anomalies in the X‐Ray Spectra of Simple Metals

AbstractThe XPS core line asymmetries and the XAS threshold singularities of Zn, Cd, In, Mg, and Na metals are considered. The singularity indices and threshold exponents, calculated by using the “Z + 1” approximation are compared with experimental values. Furthermore, the results obtained by a partial‐wave method are compared with those estimated by the first Born approximation. It is found that the Born approximation values are in agreement with those within the partialwave method.

Threshold phenomena in R-matrix theory

An R-matrix treatment of threshold phenomena in nuclear reactions is developed. It results, in addition to cusp phenomena, in a class of threshold anomalies induced by a resonance located at the threshold of the opening channel. The influence of compound nucleus and single-particle resonances and of direct interaction on threshold phenomena is discussed for s- and p- waves.

X-ray spectra of aluminum

The x-ray emission and absorption spectra of aluminum are examined in the light of the many-electron theory of Mahan threshold anomalies. The ${K}_{\ensuremath{\beta}}$ emission, ${L}_{2,3}$ emission, ${L}_{2,3}$ satellite emission, and ${L}_{2,3}$ absorption spectra exhibit threshold shapes which cannot all be consistently explained using the present form of the theory.

K-edge x-ray spectra of Mg and other simple metals: Absence of evidence for orthogonality catastrophes

It is shown that those simple free-electron metals (e.g., Li, Na, Mg, Al), whose x-ray emission spectra do not reveal bound-exciton states, generally cannot exhibit the significantly rounded $K$-edge threshold anomalies associated with the "orthogonality catastrophe." Thus, the recently measured rounded $K$-emission spectrum of magnesium cannot be interpreted as evidence for the orthogonality-catastrophe effect.

Measurement of the Li K absorption threshold anomaly in Li1-xCuxalloys: Evidence against a many electron interpretation

Measurements of the soft X-ray K absorption threshold of lithium in Li1-xCux alloys indicate that the present many electron theory of the threshold anomalies does not describe the Li threshold.

X-ray spectra of metallic alloys: many electron effects

The authors show that measurements of the soft X-ray absorption threshold at the K edge of lithium in alloys should provide a striking test of the many electron theory of threshold anomalies.

Thresholds and Resonances in a Three-Body Model

An exactly soluble three-body model is constructed which consists of two light particles and an infinitely heavy one having internal degrees of freedom. This model is designed to simulate various phenomena associated with isobaric-analog states, showing up in scattering and transfer reactions. The formulation and solution are done in the framework of Faddeev's theory using nonlocal separable potentials. The cross sections are calculated in the neighborhood of the channel thresholds. The effect of a resonance on the threshold is studied in detail and threshold anomalies are searched.

A theory of anomalies observed in (d,p) excitation curves at thresholds for neutron analogue channels

It is shown that several essential features of the (d,p) threshold anomalies observed with targets A ≈ 90 may be understood physically without elaborate calculations. In particular, their narrow width and their occurence on threshold over the mass range 80 – 100 results from a remarkable energy compression effect operating on the single particle 3p-neutron state which is basically responsible for the anomaly. It is remarked that the wide variety of observed anomalies are classified very neatly by the Q-values of the (d,p) reactions.

Threshold anomalies as manifested by coupling constants

Threshold anomalies as manifested by coupling constants

Elastic scattering of protons at the threshold for the quasi-elastic (p, n) process

The excitation functions for elastic scattering of protons from 48Ca and 91Zr have been measured at several observation angles for proton energies in the vicinity of the threshold for the quasi-elastic (p, n) scattering process. For 91Zr, the excitation function for the quasi-elastic (p, n) reaction has been measured by observing the decay protons from the analogue state. A theoretical investigation of the threshold effects in the framework of the coupled-channel Lane model is carried out, and the calculated cross sections are compared to the measured ones. The present results suggest that the expected energy dependence of the proton wave function due to the isovector coupling in the nucleon channel does not explain the threshold anomalies observed previously in the 90Zr(d, p) reaction.