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NASA NTRS2003

XTE J1946+274 = GRO J1944+26: An Enigmatic Be/X-Ray Binary

XTE J1946+274 = GRO J1944+26 is a 15.8 s Be/X-ray pulsar discovered simultaneously in 1998 September with the Burst and Transient Source Experiment (BATSE) on the Compton Gamma Ray Observatory (CGRO) and the All-Sky Monitor (ASM) on the Rossi X-Ray Timing Explorer (RXTE). Here we present new results from BATSE and RXTE including a pulse timing analysis, spectral analysis, and evidence for an accretion disk. Our pulse timing analysis yielded an orbital period of 169.2 days, a moderate eccentricity 0.33, and implied a mass function of 9.7 solar masses. We observed evidence for an accretion disk, a correlation between measured spin-up rate and flux, which was fitted to obtain a distance estimate of 9.5 +/- 2.9 kpc. XTE J1946+274 remained active from 1998 September to 2001 July, undergoing 13 outbursts that were not locked in orbital phase. Comparing RXTE Proportional Counter Array observations from the initial bright outburst in 1998 and the last pair of outbursts in 2001, we found energy and intensity-dependent pulse profile variations in both outbursts and hardening spectra with increasing intensity during the fainter 2001 outbursts. In 2001 July, optical H alpha observations indicated that a density perturbation appeared in the Be disk as the X-ray outbursts ceased. We propose that the equatorial plane of the Be star is inclined with respect to the orbital plane in this system and that this inclination may be a factor in the unusual outburst behavior of the system.

Wilson, Colleen A.↗

DOE OSTI2024

Probing the Isospin Composition of Short-Range Correlated Pairs at Jefferson Lab Hall B

Nucleons in short-range correlated (SRC) pairs, due to their close proximity and high relative momentum, can provide insight into the short-range part of the strong nuclear interaction. In particular, the prevalence of np pairs is due to the dominance of a tensor term for correlated nucleons with momenta of approximately 400?600 MeV/c. This dissertation comprises two studies advancing the community?s understanding of the isospin composition of SRC pairs. First, I performed a study of proton and neutron knockout from initially low-momentum and high-momentum states in 3He. Previous work has shown that protons are disproportionately represented in high-momentum states in neutron-rich nuclei. I demonstrate that spectral functions for the proton-rich nucleus 3He predict, in agreement with data, that neutrons are disproportionately represented in high-momentum states, but that 3He does not display the same strong prevalence of np pairs that is observed in larger nuclei. Second, Generalized Contact Formalism (GCF), a well-supported theory for predicting SRC behavior, predicts the transition from an isospin-dependent, tensor-dominant interaction at intermediate distances to a scalar-dominant, isospin-independent interaction at very short distances. This dissertation uses data from the CLAS12 Nuclear Targets Experiments in Hall B at Jefferson Lab to measure the relative abundances of pp and pn pairs for increasing relative momentum and decreasing separation. I provide an independent confirmation of the previously-observed increase in pp pairs at increasing momentum of the struck nucleon. I also contribute to the application of the new CLAS12 Central Neutron Detector by precisely measuring the neutron detection efficiency and developing a machine learning model for rejecting charged particle background.

Seroka, Erin↗

DOE OSTI2025

Self-Assembled Magnetic Nanoparticle Layers: Structural Control for Reconfigurable Magnetism and Functional Applications

We advance soft X-ray vector ptychographic tomography to map the 3D magnetization field in self-assembled superparamagnetic nanoparticles at a liquid–liquid interface, revealing how layered structures influence magnetic ordering. We observe that monolayers with low coordination numbers exhibit weak magnetic order, with magnetic vortices disrupting spin alignment. In contrast, bilayers and trilayers with higher coordination numbers display long-range magnetic order with strong spin correlations across larger distances and a suppression of magnetic vortices. We further quantify the average distance for vortex–antivortex pairs as 26.0 ± 2.0 nm, while vortex–vortex and antivortex–antivortex pairs exhibit larger separations, averaging 44.9 ± 5.2 and 54.1 ± 7.4 nm, respectively. These experimental results are supported by micromagnetic Monte Carlo simulations. Our findings illustrate how layered structures enhance magnetic order and spin correlation in superparamagnetic nanoparticle assemblies, providing a promising approach for tuning magnetic properties in applications such as data storage, microrobotics, and biomedicine.

Lu, Xingyuan↗

NASA NTRS1992

On the performance of large Gaussian basis sets for the computation of total atomization energies

The total atomization energies of a number of molecules have been computed using an augmented coupled-cluster method and (5s4p3d2f1g) and 4s3p2d1f) atomic natural orbital (ANO) basis sets, as well as the correlation consistent valence triple zeta plus polarization (cc-pVTZ) correlation consistent valence quadrupole zeta plus polarization (cc-pVQZ) basis sets. The performance of ANO and correlation consistent basis sets is comparable throughout, although the latter can result in significant CPU time savings. Whereas the inclusion of g functions has significant effects on the computed Sigma D(e) values, chemical accuracy is still not reached for molecules involving multiple bonds. A Gaussian-1 (G) type correction lowers the error, but not much beyond the accuracy of the G1 model itself. Using separate corrections for sigma bonds, pi bonds, and valence pairs brings down the mean absolute error to less than 1 kcal/mol for the spdf basis sets, and about 0.5 kcal/mol for the spdfg basis sets. Some conclusions on the success of the Gaussian-1 and Gaussian-2 models are drawn.

Martin, J. M. L.↗

NASA NTRS2011

Initiating Molecular Growth in the Interstellar Medium via Dimeric Complexes of Observed Ions and Molecules

A feasible initiation step for particle growth in the interstellar medium (ISM) is simulated by means of ab quantum chemistry methods. The systems studied are dimer ions formed by pairing nitrogen containing small molecules known to exist in the ISM with ions of unsaturated hydrocarbons or vice versa. Complexation energies, structures of ensuing complexes and electronic excitation spectra of the encounter complexes are estimated using various quantum chemistry methods. Moller-Plesset perturbation theory (MP2, Z-averaged perturbation theory (ZAP2), coupled cluster singles and doubles with perturbative triples corrections (CCSD(T)), and density functional theory (DFT) methods (B3LYP) were employed along with the correlation consistent cc-pVTZ and aug-cc-pVTZ basis sets. Two types of complexes are predicted. One type of complex has electrostatic binding with moderate (7-20 kcal per mol) binding energies, that are nonetheless significantly stronger than typical van der Waals interactions between molecules of this size. The other type of complex develops strong covalent bonds between the fragments. Cyclic isomers of the nitrogen containing complexes are produced very easily by ion-molecule reactions. Some of these complexes show intense ultraviolet visible spectra for electronic transitions with large oscillator strengths at the B3LYP, omegaB97, and equations of motion coupled cluster (EOM-CCSD) levels. The open shell nitrogen containing carbonaceous complexes especially exhibit a large oscillator strength electronic transition in the visible region of the electromagnetic spectrum.

Bera, Partha P.↗

NASA NTRS1999

Effective Forces Between Colloidal Particles

Colloidal suspensions have proven to be excellent model systems for the study of condensed matter and its phase behavior. Many of the properties of colloidal suspensions can be investigated with a systematic variation of the characteristics of the systems and, in addition, the energy, length and time scales associated with them allow for experimental probing of otherwise inaccessible regimes. The latter property also makes colloidal systems vulnerable to external influences such as gravity. Experiments performed in micro-ravity by Chaikin and Russell have been invaluable in extracting the true behavior of the systems without an external field. Weitz and Pusey intend to use mixtures of colloidal particles with additives such as polymers to induce aggregation and form weak, tenuous, highly disordered fractal structures that would be stable in the absence of gravitational forces. When dispersed in a polarizable medium, colloidal particles can ionize, emitting counterions into the solution. The standard interaction potential in these charged colloidal suspensions was first obtained by Derjaguin, Landau, Verwey and Overbeek. The DLVO potential is obtained in the mean-field linearized Poisson-Boltzmann approximation and thus has limited applicability. For more precise calculations, we have used ab initio density functional theory. In our model, colloidal particles are charged hard spheres, the counterions are described by a continuum density field and the solvent is treated as a homogeneous medium with a specified dielectric constant. We calculate the effective forces between charged colloidal particles by integrating over the solvent and counterion degrees of freedom, taking into account the direct interactions between the particles as well as particle-counterion, counterion-counterion Coulomb, counterion entropic and correlation contributions. We obtain the effective interaction potential between charged colloidal particles in different configurations. We evaluate two- and three-body forces in the bulk as well as study the influence of soft walls. We qualitatively explain the effects of the walls on the forces and demonstrate that many-body effects are negligible in our system. With adjustments in the parameters, the DLVO pair-potential can describe the results quantitatively. Besides electrostatic interactions, entropic depletion effects that arise from (hard-core) exclusion play an important role in determining the behavior of multi-component colloidal suspensions. A standard theory for depletion forces is due to Asakura and Oosawa and is based on the ideal gas approximation. To go beyond this approximation, we have studied entropic forces in molecular dynamics simulations of systems of hard spheres (the effects of the solvent have been ignored). The effective depletion forces for these systems can be found either from equilibrium distribution functions or from direct momentum transfer calculations. Our results obtained by either method show qualitative differences from the Asakura-Oosawa forces, indicating a longer range, higher value at contact and most importantly a more complicated structure, comprising of several maxima and minima. Our calculations include the determination of effective forces between two spheres, a hard sphere and a wall, and the behavior of a hard sphere near a step-edge and a corner. We also demonstrate that such entropic forces do not necessarily satisfy pairwise additivity.

Tehver, Riina↗

DOE OSTI2025

Experimental and Theoretical Confirmation of Covalent Bonding in α‐Pu

Plutonium's radioactivity provides functionality for nuclear batteries, nuclear reactors, etc., but its complex electronic properties harbor strongly correlated behavior giving rise to a host of interesting phenomena including the presence of a ca. 25% volume collapse between δ-Pu and α-Pu. The complex bonding environments of the ground state allotrope, α-Pu, serve as a unique testing ground for new computational and experimental approaches within the Pu science community. For the first time, a combination of novel ansatzes is used in all-electron density functional theory (DFT) and pair distribution functions (PDF) obtained from high-Q X-ray diffraction to study the bonding behavior in α-Pu. This first experimental and theoretical co-informed description of local bonding behavior for α-Pu reveals covalent bonds, which is a topic that remains of interest in this allotrope. The covalent bonding present at the atomistic level accounts for several of α-Pu's macropscopic properties (e.g., Poisson's ratio) that in turn explains its physical functionalities relative to other allotropic phases like δ-Pu.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Cu site differentiation in tetracopper(I) sulfide clusters enables biomimetic N 2 O reduction

Copper clusters feature prominently in both metalloenzymes and synthetic nanoclusters that mediate catalytic redox transformations of gaseous small molecules. Such reactions are critical to biological energy conversion and are expected to be crucial parts of renewable energy economies. However, the precise roles of individual metal atoms within clusters are difficult to elucidate, particularly for cluster systems that are dynamic under operating conditions. Here, we present a metal site-specific analysis of synthetic Cu 4 (μ 4 -S) clusters that mimic the Cu Z active site of the nitrous oxide reductase enzyme. Leveraging the ability to obtain structural snapshots of both inactive and active forms of the synthetic model system, we analyzed both states using resonant X-ray diffraction anomalous fine structure (DAFS), a technique that enables X-ray absorption profiles of individual metal sites within a cluster to be extracted independently. Using DAFS, we found that a change in cluster geometry between the inactive and active states is correlated to Cu site differentiation that is presumably required for efficient activation of N 2 O gas. More precisely, we hypothesize that the Cu δ+ ∙∙∙Cu δ- pairs produced upon site differentiation are poised for N 2 O activation, as supported by computational modeling. These results provide an unprecedented level of detail on the roles of individual metal sites within the synthetic cluster system and how those roles interplay with cluster geometry to impact the reactivity function. We expect this fundamental knowledge to inform understanding of metal clusters in settings ranging from (bio)molecular to nanocluster to extended solid systems involved in energy conversion.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Quantum chromodynamics resolution of the ATOMKI anomaly in 4 He nuclear transitions

Observations of anomalous angular correlations in electron-positron pairs produced from excited states of 4 He, 8 Be, and 12 C nuclei have been suggested as being due to the creation and subsequent decay of a new light particle of mass ~17MeV. In this work, we investigate the possibility that the source of the observed signals is a set of new excitation channels created by the 12-quark hidden-color Fock state within the 4 He nuclear wave function dubbed the “hexadiquark.” We calculate the invariant e + ⁢ e - mass spectrum for the electromagnetic transition from a new excitation of 4 He, estimating its differential and total decay width. We find that we can fit the shape of the anomalous signal with the QCD Fock state at excitation energy E* = 17.9 ± 1MeV and a Gaussian form factor for the electromagnetic decay. We address the physical issues with the fit parameters using properties of the hexadiquark state, in particular the three weakly repulsive 6 C interactions of SU⁡(3) C between diquark pairs. Experimental tests of our model are described in detail. In light of this work, we emphasize the need for independent experimental confirmation or refutation of the ATOMKI results as well as dedicated experiments to search for the proposed new excitations of 4 He and other a-cluster nuclei.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS2024

Decade-Long Ozone Profile Record from Suomi NPP OMPS Limb Profiler: Assessment of Version 2.6 Data

We evaluate a decadal ozone profile record derived from the Suomi National Polar-orbiting Partnership (SNPP) Ozone Mapping and Profiler Suite (OMPS) Limb Profiler (LP) satellite instrument. In 2023, the OMPS LP data were re-processed with the new version 2.6 retrieval algorithm that combines measurements from the ultraviolet (UV) and visible (VIS) parts of the spectra and employs the second order Tikhonov regularization to retrieve a single vertical ozone profile between 12.5 km (or cloud tops) and 57.5 km with the vertical resolution of about 1.9 - 2.5 km between 20-55 km. The algorithm uses radiances measured at six UV ozone-sensitive wavelengths (295, 302, 306, 312, 317 and 322 nm) paired with 353 nm, and one VIS wavelength at 606 nm combined with 510 nm and 675 nm to form a triplet. Each wavelength pair or triplet is used over a limited range of tangent altitudes where the sensitivity to ozone changes are strongest. A new implemented aerosol correction scheme is based on a gamma-function particle size distribution. Numerous calibration changes that affected ozone retrievals were also applied to measured LP radiances, including updates in altitude registration, radiometric calibration, stray light, and spectral registration. The key version 2.6 improvement is the reduction in relative drifts between LP ozone and correlative measurements, linked previously to a drift in the version 2.5 LP altitude registration. We compare LP ozone profiles with those from Aura Microwave Limb Sensor (MLS) to quantify ozone changes in version 2.6.

Limb scattering↗

NASA NTRS1999

Scaling features of noncoding DNA

We review evidence supporting the idea that the DNA sequence in genes containing noncoding regions is correlated, and that the correlation is remarkably long range--indeed, base pairs thousands of base pairs distant are correlated. We do not find such a long-range correlation in the coding regions of the gene, and utilize this fact to build a Coding Sequence Finder Algorithm, which uses statistical ideas to locate the coding regions of an unknown DNA sequence. Finally, we describe briefly some recent work adapting to DNA the Zipf approach to analyzing linguistic texts, and the Shannon approach to quantifying the "redundancy" of a linguistic text in terms of a measurable entropy function, and reporting that noncoding regions in eukaryotes display a larger redundancy than coding regions. Specifically, we consider the possibility that this result is solely a consequence of nucleotide concentration differences as first noted by Bonhoeffer and his collaborators. We find that cytosine-guanine (CG) concentration does have a strong "background" effect on redundancy. However, we find that for the purine-pyrimidine binary mapping rule, which is not affected by the difference in CG concentration, the Shannon redundancy for the set of analyzed sequences is larger for noncoding regions compared to coding regions.

Non-NASA Center↗

DOE OSTI2024

Investigating the composition of the $K$$^{*}_{0}$(700) state with π ± $K$$^{0}_{S}$ correlations at the LHC

The first measurements of femtoscopic correlations with the particle pair combinations π ± $K$$^{0}_{S}$ in pp collisions at $\sqrt{s}$ = 13 TeV at the Large Hadron Collider (LHC) are reported by the ALICE experiment. Using the femtoscopic approach, it is shown that it is possible to study the elusive $K$$^{*}_{0}$(700) particle that has been considered a tetraquark candidate for over forty years. Source and final-state interaction parameters are extracted by fitting a model assuming a Gaussian source to the experimentally measured two-particle correlation functions. The final-state interaction in the π ± $K$$^{0}_{S}$ system is modeled through a resonant scattering amplitude, defined in terms of a mass and a coupling parameter, The extracted mass and Breit–Wigner width, derived from the coupling parameter, of the final-state interaction are found to be consistent with previous measurements of the $K$$^{*}_{0}$ (700). The small value and increase of the correlation strength with increasing source size support the hypothesis that the $K$$^{*}_{0}$(700) is a four-quark state, i.e. a tetraquark state of the form (q 1 , $\bar{q}$ 2 , q 3 , $\bar{q}$ 3 ) in which q 1 , q 2 and q 3 indicate the flavor of the valence quarks of the π and $K$$^{0}_{S}$. This latter trend is also confirmed via a simple geometric model that assumes a tetraquark structure of the $K$$^{*}_{0}$(700) resonance.

13 TeV pp collisions↗

DOE OSTI2024

An Attractive Way to Correct for Missing Singles Excitations in Unitary Coupled Cluster Doubles Theory

Coupled cluster methods based exclusively on double excitations are comparatively “cheap” and interesting model chemistries, as they are typically able to capture the bulk of the dynamic electron correlation effects. The trade-off in such approximations is that the effect of neglected excitations, particularly single excitations, can be considerable. Using standard and electron-pair-restricted T 2 operators to define two flavors of unitary coupled cluster doubles (UCCD) methods, we investigate the extent to which missing single excitations can be recovered from low-order corrections in many-body perturbation theory (MBPT) within the unitary coupled cluster (UCC) formalism. Here, our analysis includes the derivations of finite-order UCC energy functionals, which are used as a basis to define perturbative estimates of missed single excitations. This leads to the novel UCCD[4S] and UCCD[6S] methods, which consider energy corrections for missing single excitations through fourth- and sixth-order in MBPT, respectively. We also apply the same methodology to the electron-pair-restricted ansatz, but the improvements are only marginal. Our findings show that augmenting UCCD with these post hoc perturbative corrections can lead to UCCSD-quality results.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1984

Sum rules and static local-field corrections of electron liquids in two and three dimensions

The dielectric functions of electron liquids which take into account short-range electron-electron correlations via the static local-field corrections are examined in the light of the frequency-moment sum rules. The formation is given for degenerate as well as classical electron liquids in arbitrary (d) spatial dimensions, which is suitable for comparison between the two- and three-dimensional cases. By using the virial equations of state it is shown that such dielectric functions cannot satisfy the compressibility sum rule and the third-frequency-moment sum rule simultaneously. In the degenerate case, the plasmon, single-pair, and multipair contributions to the sum rules are analyzed, and the reason for this incompatibility is discussed.

Iwamoto, N.↗

NASA NTRS2015

Regional Rates of Young US Forest Growth Estimated From Annual Landsat Disturbance History and IKONOS Stereo Imagery

Forests of the Contiguous United States (CONUS) have been found to be a large contributor to the global atmospheric carbon sink. The magnitude and nature of this sink is still uncertain and recent studies have sought to define the dynamics that control its strength and longevity. The Landsat series of satellites has been a vital resource to understand the long-term changes in land cover that can impact ecosystem function and terrestrial carbonstock. We combine annual Landsat forest disturbance history from 1985 to 2011 with single date IKONOS stereoimagery to estimate the change in young forest canopy height and above ground live dry biomass accumulation for selected sites in the CONUS. Our approach follows an approximately linear growth rate following clearing over short intervals and does not estimate the distinct non-linear growth rate over longer intervals.We produced canopy height models by differencing digital surface models estimated from IKONOS stereo pairs with national elevation data (NED). Correlations between height and biomass were established independently using airborne LiDAR, and then applied to the IKONOS-estimated canopy height models. Graphing current biomass against time since disturbance provided biomass accumulation rates. For 20 study sites distributed across five regions of the CONUS, 19 showed statistically significant recovery trends (p is less than 0.001) with canopy growth from 0.26 m yr-1to 0.73 m yr-1. Above ground live dry biomass (AGB) density accumulation ranged from 1.31 t/ha yr-1 to 12.47 t/ha yr-1. Mean forest AGB accumulationwas 6.31 t/ha yr-1 among all sites with significant growth trends. We evaluated the accuracy of our estimates by comparing to field estimated site index curves of growth, airborne LiDAR data, and independent model predictions of C accumulation. Growth estimates found with this approach are consistent with site index curves and total biomass estimates fall within the range of field estimates. This is aviable approach to estimate forest biomass accumulation in regions with clear-cut harvest disturbances.

Neigh, Christopher S. R.↗

NASA NTRS1990

A simulation survey of galaxy interactions

Many carefully selected samples of interacting galaxies have been observed extensively in attempts to clarify whether interaction produces activity in galaxies. Because the sample members represent a wide range of encounter parameters and times, one can then study whether there are correlations between observable encounter features and, for example, Seyfert activity. On the other hand, in theoretical studies, simulations typically deal with either time-consuming detailed modelling of single galaxy pairs or tracing a few model encounters over time. The authors extend the observational survey approach by combining it with a simulation survey. The authors are conducting a survey of model encounters, covering the most important encounter parameters over a wide range. Some parameters, such as companion structure and initial velocity, are demonstratably less important and can be ignored in a first pass. The parameter range must be richly enough sampled so that the authors can evaluate the uniqueness of the observable morphology and velocity structure of the resulting simulated pairs to diagnose unobservable companion orbit parameters. They are using a self-gravitating polar n-body code run on the Cray X-MP at the Alabama Supercomputer Network. For each simulation, the authors have stellar and gas distributions predicted over, typically, a billion years, along with information on gas motions within the disk and any material captured by the companion or lost to the system. Features of disturbed spiral galaxies are sensitive enough to time and encounter parameters so that a match of the simulation survey results to observations can be applied as starting points to infer unobservable orbital or system parameters in actual sample members. This should enable them to examine whether interesting observed properties (Seyfert activity, nuclear star-formation rate) are functions of unobservable dynamical properties which characterize each encounter. Any correlations (or lack of some expected ones) will provide strong clues as to how or whether these phenomena are related to interactions. Aside from its use with such observed samples, this survey should greatly speed determination of initial orbital parameters for more detailed subsequent simulations of individual systems.

Byrd, Gene G.↗

DOE OSTI2025

Breaking the Brønsted–Evans–Polanyi Relation with Dual-Metal Sites

Linear scaling relationships impose inherent limitations on catalyst activity; the Brønsted−Evans−Polanyi (BEP) relation, which correlates activation and reaction energies, is a prominent example. Here we report a dual-metal site catalyst (DMSC) on ceria that breaks the BEP relation for C−C coupling of methyl intermediates an elementary step in methane coupling to form ethane. The DMSC structure on CeO 2 (111) was discovered by density-functional theory (DFT) structural exploration and confirmed to be stable via ab initio thermodynamics and ab initio molecular dynamics. Homonuclear and heteronuclear DMSCs of Ni, Pd, Pt, Fe, Ru, Os, Co, Rh, and Ir (45 pairs in total) were examined for methyl affinity and methyl−methyl coupling activation energy. We found that many heteronuclear DMSCs break the BEP linear scaling due to a mixed low-affinity/high-affinity coadsorption of the two methyl groups, decoupling the step responsible for the activation energy (E a ) at the low-affinity site from the overall reaction energy (ΔE) determined by both sites. This mechanism of breaking the BEP relationship via the DMSCs offers a catalyst design principle for C−C coupling reactions.

Chen, Yiming [Vanderbilt Univ., Nashville, TN (Uni↗

NASA NTRS1993

The high-energy diffuse cosmic gamma-ray background radiation from blazars

We predict the spectrum and flux of the high-energy diffuse cosmic gamma-ray background radiation produced by blazars. Our calculations are based on the Compton Observatory EGRET observations of high-energy gamma-rays from these objects, the Whipple observation of TeV gamma-rays from Mrk 421, and radio population studies of flat-spectrum radio sources. Our statistical analysis gives a result consistent with a linear correlation. We then use the radio luminosity function and redshift evolution to calculate the gamma-ray background. We find that blazars cannot account for the flux level or steep spectrum of the background observed by SAS 2 in the sub-GeV range, but could likely provide the dominant background component in the multi-GeV energy range and above. We predict a differential photon spectral index for this component of about 2 up to about 10 GeV. Above that energy, the spectrum should gradually steepen owing to pair production by interactions of the gamma-rays with intergalactic infrared photons. Using the calculations of this effect by Stecker et al. (1992), we estimate a spectral index of about 3.5 for energies above a TeV.

Stecker, F. W.↗