Identical Spin Research Articles

Gumbel statistics for the longest interval of identical spins in a one-dimensional Gibbs measure

We consider one-dimensional Gibbs measures on spin configurations σ ∈ {–1,+1}ℤ. For N ∈ ℕ let lN denote the length of the longest interval of consecutive spins of the same kind in the interval [0,N]. We show that the distribution of a suitable continuous modification lc(N) of lN converges to the Gumbel distribution, i.e., for some α, β ∈ (0, ∞) and γ ∈ ℝ,

The Angular Momentum of Gas in Protogalaxies. I. Implications for the Formation of Disk Galaxies

We use numerical simulations of structure formation in a cold dark matter cosmology to compare the angular momentum distributions of dark matter and nonradiative gas in a large sample of halos. We show that the two components have identical spin parameter distributions and that their angular momentum distributions within individual halos are very similar, all in excellent agreement with standard assumptions. Despite these similarities, however, we find that the angular momentum vectors of the gas and dark matter are poorly aligned, with a median misalignment angle of � 30 � , which might have important implications for spin correlation statistics used in weak lensing studies. We present distributions for the component of the angular momentum that is aligned with the total angular momentum of each halo and find that for between 5% and 50% of the mass, this component is negative. This disagrees with the generally adopted ‘‘ universal ’’ angular momentum distribution, for which the mass fraction with negative specific angular momentum is zero. We discuss the implications of our results for the formation of disk galaxies. Since galactic disks generally do not contain counterrotating stars or gas, disk formation cannot occur under detailed conservation of specific angular momentum. We suggest that the material with negative specific angular momentum combines with positive angular momentum material to build a bulge component, and we show that in such a scenario the remaining material can form a disk with a density distribution that is very close to exponential. Subject headings: dark matter — galaxies: formation — galaxies: halos — galaxies: structure — methods: n-body simulations

Erratum: Role of democratic SU2 × Sn dual-group carrier space and group structure in the superboson quantum-Liouville physics of identical spin ensembles: Maximal Sn tensor product reduction, via symbolic algebraic combinatorics

Structural aspects of superboson mappings and their dual group-based carrier spaces inherent in quantum-Liouville NMR formalisms are presented for their conceptual role in understanding the transfo...

On Uniform (1≤Ii≤3) n‐fold {∣IouterM(i1⋅⋅⋅in)〉} dual tensorial sets, spin irreps from SU(3≤m)×𝒮n⊃⋅⋅⋅⊃𝒮n weight sets: a direct role for 𝒩(λ⊢n)‐partitional catalogs of 𝒮n combinatorics in spin physics

AbstractA direct systematic approach is given to the derivation of outer M‐labeled ∣IM(⋅)〉 dual (spin) irreps for identical higher nuclear spin ensembles. This stresses the essential role of multipartite partitions in spin physics and the value of algorithmic tableau‐based decompositions of 𝒮n combinatorics. Additional purely 𝒮n projective modeling techniques for the numbers of independant ensemble scalar invariants are discussed briefly. Such uniform inner rank dual group basis sets (spin representations) are as central to NMR as they are to all isotopomer CNP aspects of spectral weighting. Three specific applications are presented: one involving \documentclass{article}\pagestyle{empty}\begin{document}$[A]_{6}^{(I_{i})}$\end{document} systems, whereas the others treat 2H‐cubane and the spin subensembles of the trans‐[2H11B]10(CH2)2 carborane isotopomer to illustrate recent algorithmic roles specifically for “sst” (𝒮n) encoding in (quantized) spin physics and quantum‐Liouville NMR spin dynamics. © 2002 John Wiley & Sons, Inc. Int J Quantum Chem, 2002

Quasi-Particle Dual Mappings on \(\widetilde{\mathbb{H}}_v\) Carrier Spaces for Dynamical Structures of S2n-Invariant-Based, Integer-Rank Tensorial Sets: A Democratic-Recoupling S2n-Compatible Overview of v-Auxiliary Labelling in Superboson Algebras of Uniform Multispin NMR Ensembles

The independent cardinalities of invariants (SIs) of the dual group and its (2n)-fold uniform spin ensembles are derived via S2n-decompositional approaches. The fundamental terms arise from character theory, whereas the (2i < 2n) subsidary statistical subsets arise from arguments based on time-reversal symmetry (TRV) in the context of democratic recoupling – an approach consistent with a projective view and also with the nature of (Weyl) (I • I)1⋅⋅⋅() i ⋅⋅⋅(I • I) n single pairwise exchange yielding TRV spin symmetry. In contrast to traditional |D0(U)|((⊗SU(2))(2n)) formalisms, democratic sampling and recoupling now play important roles. As derived via superboson algebra, the dual tensorial properties of [A...](2n) uniform 2n-fold NMR spin systems are seen also as fundamental in defining aspects of quantum computing via NMR analogues. Representational aspects of (quasiparticle) pattern algebras are given for superbosons over dual projective carrier subspaces of Liouville space. Hence an independent Lie-algebraic proof is derived of the fundamental “sign” structure of superbosons acting on {\(\sum_v \oplus_{\tilde\lambda}\widetilde{\mathbb{H}}_v^(\tilde\lambda)|[\tilde\lambda]\)\({\mathcal{S}}_n\);vaux. SU(2) × \({\mathcal{S}}_n\)} carrier subspaces. This constitutes a direct extension of earlier work [Physica A 198 (1993) 245]. The explicit SI-based tensorial v-auxiliary labels of the latter are defined via the dual action \(\tilde U \times {\mathcal{P}}:\tilde {\mathbb{H}} \to \tilde {\mathbb{H}}\left\{ { \cdot \left| {\tilde U \in SU\left( 2 \right),} \right.{\mathcal{P}}\left( {\tilde \Gamma } \right) \in {\mathcal{S}}_n } \right\}\)for the dual group and [A...] n (S n ) identical spin ensembles involving high degeneracies. Motivation for the work arose from certain fundamental quantum questions for dual group actions on multiple invariant-based systems, themselves subject to projective-compatible, S n democratic recoupling. to graph-based results for such specialised uniform systems. Attention is drawn to various correspondences to geometric, quasiparticle (or superboson) and Lie-algebraic concepts for these systems, as being of topical interest both to quantum physics and to computing.

A many-body analysis of the effects of the matrix protons and their diffusional motion on electron spin resonance line shapes and electron spin echoes

The method for treating the evolution of the density matrix developed in the accompanying paper for many-spin systems is applied here for calculating magnetic resonance signals of a spin A interacting with a bath of N identical spins B. Spins B are assumed to have much smaller gyromagnetic ratios than the spin A (e.g., the former are nuclear spins, I and the latter is an electron spin, S). The experimentally observed quadratic dependence of the spin-echo envelope decay on concentration and time is explained from considering the dipolar coupling of spin A to all the B spins in the presence of B–B dipolar interactions. It is shown that the spin-echo envelope decay in the rigid limit is due to the interaction of the A spin with the coherent many-body states of the coupled spins B via the nuclear flip-flop terms I±I∓, which becomes a dissipative mechanism in the thermodynamic limit. This represents a more rigorous analysis than simplified models based on an incoherent version of “spin diffusion,” and it leads to good quantitative agreement with experiment. Moreover, this analysis represents a unified description of both the modulation and decay of the A-spin echoes. Spin echoes and line shapes for the A–BN systems are also calculated for finite motions which randomize the B spins. Even for very slow motions (modeled as translational diffusion) an effective mechanism for spin-echo envelope decay is generated, which readily overtakes the coherent mechanism in importance. The intensity distribution for the forbidden components in the A-spin line shape resulting from multiquantum transitions of the B spins caused by the pseudosecular interaction terms SzI±, is calculated. In the rigid limit it is found to behave like a Poisson distribution.

Resonance in Axisymmetric Jet Under Controlled Helical, Fundamental, and Axisymmetric Subharmonic Forcing

An axisymmetric jet is forced with two helical fundamental waves of identical frequency spinning in the opposite directions and an additional axisymmetric subharmonic wave. The subharmonic component rapidly grows downstream from resonant interaction with the fundamental, significantly depending on the initial phase difference between the subharmonic and the fundamental. The variation of the subharmonic amplitude with the initial phase difference shows a cusplike shape. The amplification of the subharmonic results in a vortex pairing of helical modes. Furthermore, the azimuthal variation of the amplification induces an asymmetric jet cross section. When the initial subharmonic is imposed with an initial phase difference close to a critical value, the jet cross section evolves into a three-lobed shape. The lobes are generated by vortex pairing. Therefore, the conclusion is made that the initial phase difference between the fundamental and the subharmonic plays an important role in controlling the jet cross section

Dipolar relaxation in a many-body system of spins of 1/2

The method utilized in Paper I [J. Chem. Phys. 112, 1413 (2000)] for treating the density matrix equation for a two-spin system in the presence of the dipolar interaction that is randomly modulated by translational diffusion, is extended to a many-body system of identical spins of 1/2. Generalized cumulant expansions are used, which allow one to take full advantage of the statistical independence of the motions of spins. In the high-temperature approximation (appropriate for dilute solutions), for a single nonselective pulse, the symmetry of the problem allows one to obtain a compact ordered binomial expression for the free-induction decay signal that is related to the two-particle solution, and it still contains the two spin-isochromat components. The latter are evaluated by solving the corresponding stochastic Liouville equation, which allows one to recover in a unified way the two limiting cases including Anderson’s result for statistical broadening in a rigid lattice and the classical Torrey–Bloembergen–Redfield expression for the motional narrowing, as corrected by Hwang and Freed. The line shape expression in the thermodynamic limit, i.e., for large numbers of particles in a macroscopic volume, is obtained. It is found that the many-body dipolar line shapes are very close to Lorentzians over the entire motional range studied, with the linewidths proportional to the spin concentration, as predicted earlier for the limiting cases. Linewidths plotted versus the values of the translational diffusion coefficient clearly show the solid-state limit, the motional-narrowing limit, and the intermediate region. The method is extended to describe the behavior of the many-body system in a solid-echo sequence. This enables one to obtain the homogeneous T2’s over the whole range of motions. A minimum in T2 is found at approximately the same value of translational diffusion coefficient as was found for the two-spin case in Paper I.

Levels of187Au: A detailed study of shape coexistence in an odd-mass nucleus

The decays of ${}^{187}$Hg (2.2 min; ${J}^{\ensuremath{\pi}}$=13/2${}^{+})$ and ${}^{187}$Hg (2.4 min; ${J}^{\ensuremath{\pi}}$=3/2${}^{\ensuremath{-}})$ have been studied with mass-separated sources at the UNISOR facility. Multiscaled spectra of $\ensuremath{\gamma}$ rays, x rays, and conversion electrons, as well as $\ensuremath{\gamma}\ensuremath{\gamma}t$, $\ensuremath{\gamma}\mathrm{xt}$, $e\ensuremath{\gamma}t$, and $\mathrm{ext}$ coincidences were obtained. Decay schemes have been constructed incorporating $&gt;$99$%$ of the decay intensities assigned to the high-spin and low-spin decays. The $\ensuremath{\gamma}$-ray gated conversion-electron spectra permitted determination of 367 conversion coefficients. A variety of coexisting band structures are established in ${}^{187}$Au. Some of these have near-identical analogs in the heavier odd-mass Au isotopes. The remaining bands reveal new degrees of freedom at low excitation energy in ${}^{187}$Au. Nine electric monopole $(E$0) transitions are observed to deexcite members of these new bands. The work represents an undertaking to achieve a benchmark in complete spectroscopy following radioactive decay. The most notable band structure in ${}^{187}$Au has two bands with identical spins, nearly identical relative energies, and electric monopole transitions connecting the favored members. These bands can be understood as $\ensuremath{\pi}{h}_{9/2}$ and $\ensuremath{\pi}{f}_{7/2}$ intruder configurations coupled to coexisting prolate or near-prolate $(\ensuremath{\gamma}$ $&lt;~$ 20$\ifmmode^\circ\else\textdegree\fi{})$ cores having diabatic configurations that differ only in the number of protons occupying the $N$=5 intruder configurations.

Long-range antiferromagnetic couplings in [ZnTe|MnTe] superlattices

Magnetic semiconductor superlattices consisting of x monolayers of ZnTe alternated with y monolayers of MnTe [(ZnTe)x|(MnTe)y] have been grown in the zinc-blende structure by molecular beam epitaxy. For relative thin ZnTe nonmagnetic interlayers (3⩽x⩽6), neutron diffraction data show long range order within the MnTe layers and also an interlayer magnetic coupling across the semiconducting ZnTe interlayer extending over multiple bilayers. For the x=5, y=10; and x=4, 5, y=20 superlattices at low temperature (10 K), the spins in adjacent MnTe layers couple in an inphase antiferromagnetic structure with identical spin orientations in all MnTe layers. As the temperature is raised, this ordering slowly transforms into an antiphase coupling in which alternate MnTe layers have spin directions reversed. For increasing ZnTe layer thickness, a systematic reduction in the magnetic correlation range is observed, with the correlation range reducing to approximately one MnTe layer for x=6 and 7.

Classical Heisenberg model of magnetic molecular ring clusters: Accurate approximants for correlation functions and susceptibility

We show that the measured magnetic susceptibility of molecular ring clusters can be accurately reproduced, for all but low temperatures T, by a classical Heisenberg model of N identical spins S on a ring that interact with isotropic nearest-neighbor interactions. While exact expressions for the two-spin correlation function, CN(n,T), and the zero-field magnetic susceptibility, χN(T), are known for the classical Heisenberg ring, their evaluation involves summing infinite series of modified spherical Bessel functions. By contrast, the formula CN(n,T)=(un+uN−n)/(1+uN), where u(K)=coth K−K−1 is the Langevin function and K=JS(S+1)/(kBT) is the nearest-neighbor dimensionless coupling constant, provides an excellent approximation if N⩾6 for the regime |K|&amp;lt;3. This choice of approximant combines the expected exponential decay of correlations for increasing yet small values of n, with the cyclic boundary condition for a finite ring, CN(n,T)=CN(N−n,T). By way of illustration, we show that, for T&amp;gt;50 K, the associated approximant for the susceptibility derived from the approximate correlation function is virtually indistinguishable from both the exact theoretical susceptibility and the experimental data for the “ferric wheel” molecular cluster ([Fe(OCH3)2(O2CCH2Cl)]10), which contains N=10 interacting Fe3+ ions, each of spin S=5/2, that are symmetrically positioned in a nearly planar ring.

NUCLEAR MAGNETIC PROPERTIES OF SOLID 3HE FILMS

A brief review on the thermodynamic properties of 3 He films adsorbed on graphite is presented. The second solid layer of 3 He adsorbed on graphite is a particularly interesting two-dimensional system of localized identical spin- $$\frac{1}{2} $$ fermions, which evolves from antiferromagnetism to ferromagnetism as a function of increasing density. This striking behavior is interpreted within a generalized Heisenberg model including competing ring-exchange interactions. While ferromagnetic three-particle exchange dominates at the highest densities, higher order antiferromagnetic ring-exchange processes become significant at low densities leading to highly frustrated antiferromagnetic or ferromagnetic phases. At low temperature, the frustrated antiferromagnetic and ferromagnetic states may correspond to unique examples of new quantum phases as suggested by recent theoretical results. The relevance of this ring-exchange model for other systems of localized fermions is also discussed.

Three-Body Systems with Square-Well Potentials in L = 0 States

The angular part of the Faddeev equations is solved analytically for s-states for two-body square-well potentials. The results are, still analytically, generalized to arbitrary short-range potentials for both small and large distances. We consider systems with three identical bosons, three non-identical particles and two identical spin-1/2 fermions plus a third particle with arbitrary spin. The angular wave functions are in general linear combinations of trigonometric and exponential functions. The Efimov conditions are obtained at large distances. General properties and applications to arbitrary potentials are discussed. Gaussian potentials are used for illustrations. The results are useful for numerical calculations, where for example large distances can be treated analytically and matched to the numerical solutions at smaller distances. The saving is substantial.

Covariant equations for the three-body bound state

The covariant spectator (or Gross) equations for the bound state of three identical spin 1/2 particles, in which two of the three interacting particles are always on shell, are developed and reduced to a form suitable for numerical solution. The equations are first written in operator form and compared to the Bethe-Salpeter equation, then expanded into plane wave momentum states, and finally expanded into partial waves using the three-body helicity formalism first introduced by Wick. In order to solve the equations, the two-body scattering amplitudes must be boosted from the overall three-body rest frame to their individual two-body rest frames, and all effects which arise from these boosts, including Wigner rotations and p-spin decomposition of the shell-particle, are treated exactly. In their final form, the equations reduce to a coupled set of Faddeev-like double integral equations with additional channels arising from the negative p-spin states of the off-shell particle.

Information gains expected from separate and joint measurements of N identical spin-1/2 systems: Noninformative Bayesian analyses

An investigator is assumed to have N replicas of a spin-1/2 system, but lacks any specific knowledge pertinent to constructing a 2×2 density matrix for it. We compute—within a noninformative Bayesian framework—the expected information gains for various measurement schemes, first, separate and, then, joint in nature. In particular, we obtain a result which fully accords with a certain plausibility argument of Peres, while the parallel result in a recent analysis of Massar and Popescu does not.

Experimental Separation of Geometric and Dynamical Phases Using Neutron Interferometry

We present results of the first experiment clearly demarcating geometric and dynamical phases. These two phases arise from two distinct physical operations, a rotation and a linear translation, respectively, performed on two identical spin flippers in a neutron interferometer. A reversal of the current in one flipper results in a pure geometric phase shift of \ensuremath{\pi} radians. This observation constitutes the first direct verification of Pauli anticommutation, implemented in neutron interferometry.

Substitutional disorder and the ground state spectroscopy of gallogermanate crystals

Electron spin resonance (ESR) spectra at X-band microwave frequencies are reported for dopant ions in (CGGO), (SGGO), (LGGO) and (LGS). The ESR measurements identify two distinct sites for in CGGO and SGGO and a single site in LGGO and LGS characterized by spin S = 3/2 for ions in the ground state. In CGGO a sharp line ESR spectrum, fitted to an axially symmetric spin Hamiltonian with , and , is assigned to substituents at trigonally distorted octahedral sites with a regular array of and ions in second-nearest-neighbour sites. A second spectrum of broader lines, due to ions in orthorhombically distorted sites associated with random occupation of the second-nearest-neighbour sites by and ions, has slightly different spin Hamiltonian parameters; , and . In this spectrum the principal axis is rotated by about from the c-axis towards the a-axis. In SGGO there are also ESR spectra from ions in trigonal and orthorhombic symmetry sites with almost identical spin Hamiltonian parameters. The ground state splittings of the trigonal centres measured optically by fluorescence line narrowing gives for both crystals. In contrast, only the trigonal centres are identified in LGGO and LGS, their ESR spectra being very similar to those of the trigonal centres in CGGO and SGGO. These results are discussed in terms of the substitutional disorder in these crystals and the nature of the site environment of substituents. The spectra correspond to ions in strong and weak crystal field sites, respectively, in agreement with earlier optical studies.

Magnetization steps of spin quartets.

Magnetization steps (MST's) arising from quartets consisting of four identical spins, each of magnitude $S$, are discussed. It is assumed that the only interactions are (1) antiferromagnetic exchange bonds between quartet members, with only one exchange constant $J$, and (2) the Zeeman interaction with the magnetic field H. There are six quartet types. Each type gives rise to steps in the magnetization curve at low temperatures, ${k}_{B}T&lt;|J|$. For five quartet types analytical expressions for the magnetic fields ${H}_{n}$ at the MST's are given, for any $S$. These results are based on expressions for the quartets' energy levels. For the sixth quartet type (called "string"), numerical results for ${H}_{n}$ are given assuming $S=\frac{5}{2}$, which is appropriate for ${\mathrm{Mn}}^{2+}$ and ${\mathrm{Fe}}^{3+}$ ions. The probabilities that a magnetic ion is in any of the six quartet types are given for an fcc lattice. Magnetization curves for ${\mathrm{Zn}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{S}$ ($x=2.5 \mathrm{and} 3.8%$) and ${\mathrm{Zn}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{Se}$ ($x=3.1 \mathrm{and} 5.3%$) were measured at 0.6 K in dc magnetic fields up to 190 kOe. The data show an MST which is a superposition of the first MST from "string quartets" and the first MST from "funnel quartets" (two of the six quartet types). The predicted fields for these two MST's differ by only 5%, so that the two MST's overlap in the experiment. The magnetic field at the center of the observed MST is close to the predicted value in all cases. The size of the magnetization rise at the observed MST is consistent with the calculated probabilities of finding a spin in strings and funnels.

Investigation of the spatial distribution of dangling bonds in light-soaked hydrogenated amorphous silicon.

We report on a detailed investigation of the spatial distribution of dangling bonds (DB's) in light-soaked hydrogenated amorphous silicon (a-Si:H) films. The results for light soaking at different light intensities (3 W/${\mathrm{cm}}^{2}$ and 300 mW/${\mathrm{cm}}^{2}$) show that the inverse power-law DB distribution, ${\mathit{N}}_{\mathit{v}}$(x)=${\mathit{C}}_{\mathit{vx}}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\alpha}}}$, holds regardless of the light soaking intensity. Here, ${\mathit{N}}_{\mathit{v}}$(x) is the volume density of DB's at depth x measured from the surface, and ${\mathit{C}}_{\mathit{v}}$ and \ensuremath{\alpha}(\ensuremath{\approxeq}0.6) are constants. The nonuniform spatial distribution of DB's in light-soaked a-Si:H is thought to originate from a nonuniform distribution of photocarriers during light soaking rather than from an inhomogeneity of the material. The same annealing behavior of light-induced DB's was observed regardless of the thickness of the sample and regardless of whether the sample was light soaked from one side or from both sides. This result, together with the observation of identical spin characteristics, indicates that the light-induced DB's at various depths of a given a-Si:H sample are identical in nature. The surface DB density is found to be much less sensitive to light soaking than the bulk DB density and can be assumed unchanged if the light-soaking intensity is not much higher than 300 mW/${\mathrm{cm}}^{2}$ and the light-soaking time is shorter than \ensuremath{\sim}10 h. We show that the conventional method of estimating the surface DB density is no longer appropriate for light-soaked a-Si:H, due to the highly nonuniform distribution of DB's in the material. The nonuniform distribution of DB's can lead to significant disagreements between different techniques in quantifying the Staebler-Wronski effect and should therefore be taken into account in studies of the SW effect. \textcopyright{} 1996 The American Physical Society.

Generation of reactive oxygen species during the enzymatic oxidation of polycyclic aromatic hydrocarbon trans-dihydrodiols catalyzed by dihydrodiol dehydrogenase.

Dihydrodiol dehydrogenase (DD; EC 1.3.1.20) catalyzes the oxidation of polycyclic aromatic hydrocarbon (PAH) trans-dihydrodiols (proximate carcinogens) to catechols which rapidly autoxidize to yield o-quinones (Smithgall, T. E., Harvey, R. G., and Penning, T. M. (1988) J. Biol. Chem 263, 1814-1820). Although this pathway suppresses the formation of the PAH anti- and syn-diol epoxides (ultimate carcinogens), the process of autoxidation is anticipated to yield reactive oxygen species (ROS). We now show that the NADP+ dependent oxidation of (+/-)-trans-1,2-dihydroxy-1,2-dihydronaphthalene (Npdiol) and (+/-)-trans-7,8-dihydroxy-7,8-dihydrobenzo[a]pyrene (Bpdiol) catalyzed by homogeneous DD is accompanied by the consumption of molecular oxygen and the production of H2O2. With both trans-dihydrodiol substrates, oxygen consumption was stoichiometric with H2O2 production consistent with the reaction: QH2 + O2 = H2O2 + Q, where QH2 is the catechol and Q is the o-quinone. Using Npdiol or Bpdiol as substrates, a burst of superoxide anion production is catalyzed by DD which can be detected as the rate of cyt c reduction that is inhibited by superoxide dismutase. Using 5,5-dimethyl-1-pyrroline N-oxide (DMPO) as spin-trapping agent, secondary spin adducts corresponding to DMPO-CH3 were formed during the enzymatic oxidation of Npdiol and Bpdiol. The formation of the CH3. radical arises from the OH. attack of DMSO, which was used as cosolvent. These spin adducts were attenuated by superoxide dismutase and catalase, implying that O2-. and H2O2 are obligatory for the formation of DMPO-CH3. It is proposed that O2-. is the radical that propagates autoxidation and that the resultant H2O2 undergoes Fenton chemistry to produce the OH. radical. Identical spin adducts were observed using a superoxide anion generating system (hypoxanthine/xanthine oxidase) and DMPO as spin-trapping agent in the presence of DMSO. The ability of DD to generate ROS during the oxidation of PAH trans-dihydrodiols (proximate carcinogens) may have important implications for tumor initiation and promotion.