Showing papers on "Ground state published in 1994"

Theory of high-harmonic generation by low-frequency laser fields.

Abstract: We present a simple, analytic, and fully quantum theory of high-harmonic generation by low-frequency laser fields. The theory recovers the classical interpretation of Kulander et al. in Proceedings of the SILAP III Works hop, edited by B. Piraux (Plenum, New York, 1993) and Corkum [Phys. Rev. Lett. 71, 1994 (1993)] and clearly explains why the single-atom harmonic-generation spectra fall off at an energy approximately equal to the ionization energy plus about three times the oscillation energy of a free electron in the field. The theory is valid for arbitrary atomic potentials and can be generalized to describe laser fields of arbitrary ellipticity and spectrum. We discuss the role of atomic dipole matrix elements, electron rescattering processes, and of depletion of the ground state. We present the exact quantum-mechanical formula for the harmonic cutoff that differs from the phenomenological law Ip+3.17Up, where Ip is the atomic ionization potential and Up is the ponderomotive energy, due to the account for quantum tunneling and diffusion effects.

Strongly Geometrically Frustrated Magnets

Abstract: The study of cooperative phenomena in magnetism has provided fertile ground for testing theories of interacting systems that possess different spatial dimensions, ranges, and sign of interactions, and that exhibit local anisotropy of the basic interacting unit, the magnetic spin. This study has also motivated the development of new classes of materials, from the oldest known type of magnets, namely ferromagnets, to modern substances embodied in the unusual random field and spin glass compounds. In this context, we use the term material class to mean a set of compounds that share both microscopic, as well as macroscopic, or bulk, properties. Thus for example, ferro magnets possess the microscopic uniform ferromagnetic­ type exchange or dipolar interaction between spins, in addition to a bulk low temperature magnetization approaching the theoretical saturated moment value, and characteristic critical behavior at the Curie, or order­ ing, temperature. Among the known classes of magnets, spin glasses are among the most fascinating, displaying in their bulk properties simul­ taneous sharp ordering features in their magnetic response while exhibiting no such anomalies in their thermal response (1). These properties are thought to arise from a ground state characterized not by a single potential well representing the uniform arrangement of perfectly ordered spins, as in a ferromagnet, but rather by an energy landscape with many nearly degenerate ground state configurations separated by barriers of random height ( 1 ). The microscopic parameters empirically associated with spin glass

Spectroscopy of quantum levels in charge-tunable InGaAs quantum dots.

Abstract: Imbedding self-assembled lens-shaped InGaAs quantum dots in a suitably designed field-effect-type GaAs/AlAs heterostructure allows us to charge the lowest discrete quantum levels in the dots with single electrons. Because of their small diameters of about 20 nm the Coulomb charging energy is significantly smaller than the quantization energies. We extract energy spacings of about 41 meV between the $s$-like ground state and the first excited $p$-like state from capacitance as well as infrared transmission spectroscopy at low temperatures and under application of high magnetic fields.

Local-density functional and on-site correlations: The electronic structure of La2CuO4 and LaCuO3

Abstract: State-of-the-art electronic-structure calculations based on the local-density approximation (LDA) to the density functional fail to reproduce the insulating antiferromagnetic ground state in the parent compounds of the high-temperature oxide superconductors. Similar problems have been observed earlier in classical transition-metal oxides such as FeO, CoO, and NiO. In this work we present the method which delivers the correct insulating antiferromagnetic ground state in the correlated oxides preserving other properties as well as the efficiency of the standard LDA. The method embeds the relevant (for a given system of electrons) part of the Hubbard Hamiltonian into the Kohn-Sham LDA equation. The resulting Hamiltonian attempts to fix two intrinsic problems of the LDA: the deficiency in forming localized (atomiclike) moments and the lack of discontinuity of the effective one-particle potential when going from occupied to unoccupied states. We present the detailed study of La2CuO4 and LaCuO3. In the case of La2CuO4 the energy gap and the value of the localized magnetic moment in the stable insulating antiferromagnetic solution are in good agreement with experiment. We compare our results with the standard local spin density approximation calculation and multiband Hubbard model calculations, as well as with results of spectroscopy: inverse photoemission, valence photoemission, and x-ray absorption at the K edge of oxygen. In the case of LaCuO3 such an extensive comparison is limited due to the limited data available for this compound. We discuss, however, the electric and magnetic properties and the insulator-metal-insulator transitions upon increase of oxygen deficiency.

Sharp-line photoluminescence and two-photon absorption of zero-dimensional biexcitons in a GaAs/AlGaAs structure.

Abstract: Using a micron-sized photoluminescence (PL) probe enables us to study single islandlike interface defects of a thin GaAs/AlGaAs quantum well. The bound exciton ground state locally emits a distinct sharp line. With increasing excitation of this quantum dot level additional transition lines emerge at lower energy. They are attributed to localized biexciton states. The biexciton correlation energy is about 4 meV. A distinct two-photon resonant absorption peak of the biexciton ground state is observed in PL excitation spectroscopy. Its linewidth is only about 30 \ensuremath{\mu}eV. The spectra and their polarization properties are discussed on the basis of a discrete level scheme and the Pauli exclusion principle.

Nonparabolicity and a sum rule associated with bound-to-bound and bound-to-continuum intersubband transitions in quantum wells

Abstract: A sum rule for electronic intersubband transitions has been derived following Kane's model, beyond the quadratic dispersion relations The sum rule takes into account the effects of nonparabolicity and the different effective masses in the well and barrier materials; it depends on the property of the ground state of the system and, as such, on the shape of the potential The boundaries of the validity of matrix element computations are also discussed in the case where only the conduction band is included Experimental results are presented for bound-to-bound and bound-to-continuum intersubband transitions in various types of ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{In}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As/${\mathrm{Ga}}_{\mathit{y}}$${\mathrm{In}}_{1\mathrm{\ensuremath{-}}\mathit{y}}$As quantum well systems (single wells, coupled wells and quantum wells with Bragg confinement); the agreement with theory is excellent In the last section of the paper, the effect of the electric field on the sum rule is investigated

Experimental Demonstration of the Dependence of the First Hyperpolarizability of Donor-Acceptor-Substituted Polyenes on the Ground-State Polarization and Bond Length Alternation

Abstract: It has been suggested that optimizing the first hyperpolarizability, β, of donor-acceptor compounds requires a specific donor-acceptor strength for a given conjugated bridge. For donor-acceptor polyenes, β can be maximized when an optimal degree of mixing between neutral and charge-separated canonical resonance forms This degree of mixing is related to the donor-acceptor strength and a molecular parameter, bond length alternation (BLA), defined as the difference between the average carbon-carbon single and double bond lengths in the polymethine backbone. The degree of BLA arises from the linear combination, or mixing, of the two-limiting charge-transfer resonance forms of the molecule (Figure 1).4 For unsubstituted polyenes or chromophores with weak donors-acceptors, the neutral canonical form is the dominant contributor to the ground state, resulting in large positive BLA. As the donor-acceptor strength increases, the charge-separated resonance structure contributes more to the ground state, resulting in smaller BLA, until both resonance forms contribute equally and the ground-state structure possesses essentially zero BLA, analogous to a symmetrical cyanine. Increasing the ground-state polarization further results in the charge-separated canonical form dominating the ground-state structure, leading to negative BLA.

The dynamics of spin-density waves

Abstract: Spin-density waves (SDWs) are broken-symmetry ground states of metals, the name referring to the periodic modulation of the spin density with period, ${\ensuremath{\lambda}}_{0}=\frac{\ensuremath{\pi}}{{k}_{F}}$, determined by the Fermi wave vector ${k}_{F}$. The state, originally postulated by Overhauser, has been found in several organic linear-chain compounds. The development of the SDW state opens up a gap in the single-particle excitation spectrum, and the ground state is close to that of an antiferromagnet, as shown by a wide range of magnetic studies. Because of the magnetic ground state and of the incommensurate periodic spin modulation (which can be thought of as two periodic charge modulations in the two spin subbands), both collective charge and spin excitations may occur. These couple to ac magnetic and electric fields, which leads to antiferromagnetic resonances and frequency-dependent collective-mode conductivity. Both have been observed in the spin-density-wave ground state. The interaction of the collective mode with impurities pins the mode to the underlying lattice, and therefore the collective-mode charge excitations occur at finite frequencies in the long-wavelength limit. The mode can also be induced to execute a translational motion upon the application of a dc field which exceeds the threshold field ${E}_{T}$. Many of the observations on the ac, and on the nonlinear dc, response are similar to those which occur in materials with a charge-density-wave ground state. At low temperatures a novel type of collective transport suggestive of a tunneling process is observed. These low-temperature phenomena remain unexplained.

Flux phase of the half-filled band

Abstract: The conjecture is verified that the optimum, energy minimizing, magnetic flux for a half-filled band of electrons hopping on a planar, bipartite graph is π per square plaquette. We require only that the graph has periodicity in one direction and the result includes the hexagonal lattice (with flux 0 per hexagon) as a special case. The theorem goes beyond previous conjectures in several ways: (1) It does not assume, a priori, that all plaquettes have the same flux (as in Hofstadter’s model). (2) A Hubbard-type on-site interaction of any sign, as well as certain longer range interactions, can be included. (3) The conclusion holds for positive temperature as well as the ground state. (4) The results hold in D ≥ 2 dimensions if there is periodicity in D — 1 directions (e.g., the cubic lattice has the lowest energy if there is flux π in each square face).

Excited-State Intramolecular Proton Transfer in 2-(2-Hydroxyphenyl)benzimidazole and -benzoxazole: Effect of Rotamerism and Hydrogen Bonding

Abstract: An excited-state intramolecular proton transfer (ESIPT) process in 2-(2’-hydroxyphenyl) benzimidazole and -benzoxazole (HPBI and HBO, respectively) has been studied using steady-state and time-resolved emission spectroscopy at various temperatures and by semiempirical quantum chemical methods. For both of them two distinct ground-state rotamers I and I1 respectively responsible for the “normal” and the “tautomer” emission have been detected. In hydrocarbon solvents at room temperatureand at 77 K the tautomer emission predominates over the normal emission for both HPBI and HBO. This indicates that rotamer 11, responsible for the tautomer emission, is intrinsically stabler than rotamer I, which causes the normal emission. In alcoholic glass at 77 K for HPBI a dramatic enhancement of the normal emission is observed. It is suggested that due to the increased solvation, the more polar rotamer I becomes stabler than I1 for HPBI in alcohol and the substantial temperature variation is due to the change in the population of the two rotamers with temperature. From the detailed temperature variation in alcoholic medium the ground-state energy difference between rotamers I and I1 is determined. In dioxane-water mixtures it is observed that with the addition of water the quantum yield of the normal emission increases, which is ascribed to the inhibition of the ESIPT process due to the formation of an intermolecular hydrogen bond involving water. CNDO/S-CI calculations were performed optimizing thegroundstate geometry by the AM1 method. Details of the energy, dipole moment, and charge distribution of the rotamers in the ground state (SO) and the first excited singlet state (SI) and the barrier for the interconversion of I and I1 in SO, SI, and first excited triplet state are discussed. The calculation indicates that the barrier for the interconversion of the two rotamers is too high in the excited state (SI and TI) for free interconversion.

Quasi-one-dimensional electronic structure in orthorhombic RbC60.

Abstract: X-ray diffraction studies show that the stable phase of the alkali fullerene RbC[sub 60] is orthorhombic ([ital o]-RbC[sub 60]) below 350 K. C[sub 60] molecules form chains along [bold a] with an unusually short spacing of 9.12 A and magnetic properties suggest that [ital o]-RbC[sub 60] is a quasi-1D metal with a transition to a spin density wave ground state at 50 K. The high temperature fcc phase of RbC[sub 60] may be stabilized below 300 K by quenching from 500 K; it is paramagnetic above 300 K and transforms into a nonmagnetic ground state beween 300 and 250 K.

Precision laser spectroscopy of the ground state hyperfine splitting of hydrogenlike ^209 Bi^82+

Abstract: The first direct observation of a hyperfine splitting in the optical regime is reported. The wavelength of the $M1$ transition between the $F=4$ and $F=5$ hyperfine levels of the ground state of hydrogenlike $^{209}\mathrm{Bi}^{82+}$ was measured to be ${\ensuremath{\lambda}}_{0}=243.87(4)$ nm by detection of laser induced fluorescence at the heavy-ion storage ring ESR at GSI. In addition, the lifetime of the laser excited $F=5$ sublevel was determined to be ${\ensuremath{\tau}}_{0}=0.351(16)$ ms. The method can be applied to a number of other nuclei and should allow a novel test of QED corrections in the previously unexplored combination of strong magnetic and electric fields in highly charged ions.

Spectroscopic properties of aromatic dicarboximides. Part1.—N—H and N-methyl-substituted naphthalimides

Abstract: The photophysical properties of the N—H and N-methyl derivatives of 1,2-, 2,3- and 1,8-naphthalimides have been studied. The shift of the fluorescence emission position as a function of the solvent polarity indicates only a weak variation of dipole moment for the excited state compared with the corresponding value in the ground state (5.7 D for 2b, 2.8 D for 3b and <2 D for 4b, 1 D ≈ 3.335 64 × 10–30 C m, and 2b, 3b and 4b are N-methyl-1,2- naphthalimide, N-methyl-2,3-napthalimide and N-methyl-1,8-naphthalimide). However, important modifications of the photophysical properties are observed which depend on the relative position of the dicarboximide moiety on the naphthalene ring: the intersystem crossing rate constant of 4b increases dramatically by three orders of magnitude compared with that of 2b; simultaneously, the fluorescence quantum yield decreases from 0.77 to 0.03, although the corresponding rate constant, kf, increases. This difference is found to arise from the energy gap between the lowest1(π, π*) singlet excited state and the upper 3(n,π*) triplet state, which is of the order of 9 kcal mol–1 for 2b and less than 2 kcal mol–1 for 4b in acetonitrile solution. Protic solvents increase the energy difference between the n,π* and π,π* states thus decreasing the mixing of the two levels; as a consequence, the lifetime of 4b is increased, i.e. from <60 ps in hexane to 2.1 ns in trifluoroethanol. A triplet–triplet annihilation process occurs with the N-methyl derivatives 3b and 4b which leads to a monomer delayed fluorescence with the former, and mainly to a delayed excimer emission with the latter.

Partially asymmetric exclusion process with open boundaries.

Abstract: Exclusive diffusion on a one-dimensional lattice is studied. In the model, particles hop stochastically in both directions but with different rates. At the ends of the lattice, particles are injected and removed. The exact stationary probability measure is represented in the form of a matrix product, as a generalization of the solution given by Derrida et al. [J. Phys. A 26, 1493 (1993)] for the fully asymmetric process. The phase diagram of the current on the infinite lattice is obtained. Analytic expressions for the current in the different phases are derived. The model is equivalent to an XXZ-Heisenberg chain with a certain type of boundary terms, the ground state of which corresponds to the stationary solution of the master equation.

A multireference coupled‐cluster study of the ground state and lowest excited states of cyclobutadiene

Abstract: The electronic structure of the ground state and several low‐lying excited states of cyclobutadiene are studied using the new state‐universal multireference coupled‐cluster method with single and double excitations (MR‐CCSD) augmented by a noniterative inclusion of the triple excitations [MR‐CCSD(T)]. Two possible ground state configurations are examined, namely the square and the distorted rectangular geometries, and the multireference coupled‐cluster energy barrier for the interconversion between the two rectangular ground state structures is estimated to be 6.6 kcal mol−1 compared with the best theoretical value, 6.4 kcal mol−1 obtained using the highly accurate coupled‐cluster method with full inclusion of the triple excitations (CCSDT). The ordering of electronic states for the square geometry is determined, with the ground state singlet being located 6.9 kcal mol−1 below the lowest triplet electronic state. We also examine the potential energy surface for the interconversion between the two equivalent second‐order Jahn–Teller rhombic structures for the first excited singlet state. When comparing the MRCC energies with the results provided by various single‐ and multireference correlation methods, the critical importance of including both the dynamic and nondynamic correlation for a qualitatively correct description of the electronic structure of cyclobutadiene is emphasized. We also address the invariance properties of the present MRCC methods with respect to the alternative selections of reference orbital spaces.

Geometric aspects of quantum spin states

Abstract: A number of interesting features of the ground states of quantum spin chains are analyzed with the help of a functional integral representation of the system's equilibrium states. Methods of general applicability are introduced in the context of the SU(2S+1)-invariant quantum spin-S chains with the interaction −P(o), whereP(o) is the projection onto the singlet state of a pair of nearest neighbor spins. The phenomena discussed here include: the absence of Neel order, the possibility of dimerization, conditions for the existence of a spectral gap, and a dichotomy analogous to one found by Affleck and Lieb, stating that the systems exhibit either slow decay of correlations or translation symmetry breaking. Our representation elucidates the relation, evidence for which was found earlier, of the −P(o) spin-S systems with the Potts and the Fortuin-Kasteleyn random-cluster models in one more dimension. The method reveals the geometric aspects of the listed phenomena, and gives a precise sense to a picture of the ground state in which the spins are grouped into random clusters of zero total spin. E.g., within such structure the dichotomy is implied by a topological argument, and the alternatives correspond to whether, or not, the clusters are of finite mean length.

Observation of parity-induced suppression of Josephson tunneling in the superconducting single electron transistor.

Abstract: We have measured the supercurrent branch of a superconducting single electron transistor as a function of gate charge, temperature, and magnetic field. At low temperature and magnetic field, the switching current goes from a minimum to a maximum when the gate charge is varied from 0 to e, as expected for an island in the ground state with an even electron number. When the odd electron number ground state becomes populated by an increase of temperature or field, the Josephson tunneling is strongly suppressed, in agreement with theoretical predictions.

Modeling harmonic generation by a zero-range potential

Abstract: High-order harmonic emission by one electron in a laser field bound to a zero-range potential is extensively discussed. The model yields an expression for the emission rates in the form of a one-dimensional integral that has to be calculated numerically. The solution is based on the quasienergy wave function of the ground state. The approach is very significantly facilitated by suppressing the harmonic components of the wave function at the position of the zero-range potential. This approximation is found to be very accurate except for the third harmonic. In spite of the simplicity of the model, the harmonic spectrum exhibits a very involved structure, occasional harmonics being strongly suppressed, with cusps and spikes for certain evenly spaced intensities. The latter are due to channel closings for the same intensities in above-threshold ionization. The harmonics near and beyond the cutoff of the plateau are amenable to a completely analytical approximation. This approximation shows how the classical model of Krause, Schafer, and Kulander [Phys. Rev. Lett. 68, 3535 (1992)] is embedded in a fully-quantum-mechanical description. Results are also given for the harmonic production rates in an elliptically polarized laser field; they display fair agreement with recent measurements. The model should adequately describe harmonic emission by negative ions with just one bound s state. Moreover, it also gives a fair description of harmonic emission by an atom, particularly if the ground-state energy of the zero-range potential is adjusted not to the binding energy of the atom, but rather to the energy difference between the ground state and the first excited state. The reason why this is appropriate is found in lowest-order perturbation theory, which sheds some light on the physical origin of the plateau.

Charged spin-texture excitations and the Hartree-Fock approximation in the quantum Hall effect

Abstract: We develop a Hartree-Fock approach to the charged spin-texture excitations (CSTE's) of the ferromagnetic incompressible ground state, which occurs in the quantum Hall effect at Landau-level filling factor [nu]=1. The CSTE's are the appropriate generalization of skyrmions to the situation when there is a nonzero Zeeman coupling. We find for Coulomb interactions that the charged spin-texture excitation energies are always smaller than the excitation energies of localized spin 1/2 quasiparticles and quasiholes. However, the amount by which the energy is lowered is quite small for typical experimental situations. The net spin of the CSTE's is always much larger than 1/2, suggesting that adding or removing charge from a filled Landau level rapidly degrades its spin polarization.

Ultrafast Transient Absorption Spectroscopy of the Solvated Electron in Water

Abstract: Ultrafast near-infrared (NIR)-pump/variable wavelength probe transient absorption spectroscopy has been performed on the aqueous solvated electron. The photodynamics of the solvated electron excited to its p-state are qualitatively similar to previous measurements of the dynamics of photoinjected electrons at high energy. This result confirms the previous interpretation of photoinjected electron dynamics as having a rate-limiting bottleneck at low energies presumably involving the p-state. The absorption transients of our NIR-pump experiments obtained probing between 540 and 1060 nm reveal complicated dynamics that cannot be strictly reproduced using a two-state kinetic model, necessitating modification of the two-state model to include ground-state transient solvation and local heating following electronic relaxation. This modified kinetic model was found to quantitatively reproduce the observed spectral dynamics, yielding an excited-state lifetime of 310 [+-] 80 fs and a 1.1 [+-] 0.2 ps time scale for ground-state cooling and solvation. This model preserves a two-state electronic relaxation but adds ground-state relaxation dynamics. Excited-state solvation has been neglected in the model, and it remains to be proven whether the observed relaxation processes result from solvation in the ground state, the excited state, or both. 83 refs., 8 figs., 1 tab.

Ultrafast charge transfer in an electron donor–acceptor complex

Abstract: Ultrafast pump–probe measurements on the electron donor–acceptor complex of tetracyanoethylene with hexamethylbenzene in polar and nonpolar solvents are reported. Ground state coherence in the complex stretching mode at 165 cm−1 excited by impulsive stimulated Raman scattering is observed as well as decay of the ground state bleaching signal due to return electron transfer to the ground state. The experimental electron‐transfer rates are compared with nonadiabatic and adiabatic electron‐transfer theories using a previously published analysis of all the vibrational modes active in the reaction. It is shown that a breakdown of the Born–Oppenheimer approximation can give rise to a coupling that leads to the observed electron‐transfer reaction. The non‐Born–Oppenheimer matrix element is estimated using information obtained from the absorption and Raman spectra. Using this coupling, good agreement is found between the experimentally observed and theoretically predicted rates. Caveats of the various theories, the reliability of the normal mode analysis, and aspects of electron transfer that theory should address are discussed.

Ab initio studies of the copper(I) tetramers Cu4X4L4 (X = I, Br, Cl). Effects of cluster structure and of halide on photophysical properties

Abstract: Ab initio calculations at the Hartree-Fock level are described for various compounds of the type Cu 4 X 4 L 4 , in order to gain a better understanding of the rich luminescence behavior of these cuprous halide clusters. The calculations clearly demonstrate a relationship between the Cu-Cu distances (d Cu-Cu ) in these «cubane» type clusters and the energies and distortions (from the ground state) expected for the «cluster-center» (CC) excited states, which arise primarily from a redistribution of charge within the Cu 4 I 4 cluster core

An excited state of Th 229 at 3.5 eV

Abstract: It has been known for many years that the first excited state of $^{229}\mathrm{Th}$ lies close to the ground state. Originally this energy was given as 0.1 keV; later, the authors reported a value of -1\ifmmode\pm\else\textpm\fi{}4 eV. In an attempt to improve the value for this level energy, we have remeasured the energies of a number of \ensuremath{\gamma} rays from $^{223}\mathrm{U}$ whose positions in the $^{229}\mathrm{Th}$ level scheme can be used to establish it. Compared with our earlier study, we have considered more \ensuremath{\gamma} rays in $^{229}\mathrm{Th}$, used more well-measured energy calibration and reference lines, used more detectors, used detectors with better low-energy resolution, more closely matched the counting rates in the \ensuremath{\gamma}-ray peaks whose relative energy is measured, and specifically considered certain systematic errors. More than 111 \ensuremath{\gamma}-ray spectra have been measured. From this large set of measurements we have deduced a value of 3.5\ifmmode\pm\else\textpm\fi{}1.0 eV for the energy of this level.

Kondo effect in a Tomonaga-Luttinger liquid.

Abstract: The Kondo effect in a repulsively interacting electron system (Tomonaga-Luttinger liquid) is studied. By using the poor man's scaling method it is shown that the Kondo coupling in this model flows to the strong-coupling regime not only for the antiferromagnetic but also for the ferromagnetic case. The ground state is governed by stable strong-coupling fixed points where the impurity spin is completely screened; the fixed-point Hamiltonian consists of two semi-infinite Tomonaga-Luttinger liquids and a spin singlet. Specific heat, susceptibility, and conductance are calculated for low temperatures.

Rotationally inelastic and hyperfine resolved cross sections for OH–H2 collisions. Calculations using a new ab initio potential surface

Abstract: Cross sections and rate constants are presented for the rotational excitation of OH in collision with ortho and para‐H2, using a new ab initio interaction potential [Offer and Van Hemert, J. Chem. Phys. 99, 3836 (1993)]. The cross sections are given at a number of energies and are compared with those calculated using an earlier potential energy surface, and with the available experimental results. A strong oscillatory behavior is found in the cross sections for collisions with ground state para‐H2 which was not apparent in earlier calculations. The oscillatory behavior is very much reduced in collisions with ortho‐H2. Rate constants obtained by averaging the cross sections over a Maxwell–Boltzmann velocity distribution are given at a temperature of 300 K. Expressions for calculating the hyperfine resolved cross sections by transforming the S‐matrices are discussed for the case where H2 is no longer constrained to its rotational ground state, and cross sections for transitions between the hyperfine resolved levels are given for collisions with both para and ortho‐H2.