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Setting the Bar for the Replacement of the Probability of Collision Metric

To date, satellite conjunction assessment (CA) risk analysis has largely embraced the probability of collision (Pc) as the omnibus metric to evaluate collision likelihood, and its use in such assessments has mostly been straightforward: at the point at which a conjunction mitigation decision is required, the calculated Pc is compared to a threshold; and if the calculated Pc exceeds that threshold, then a mitigation action is warranted. With only minor variation, this approach is employed by major CA risk assessment centers (e.g., NASA, EUSST, CNES, JAXA) and is advanced as the preferred method in the published CA best practices handbooks. Despite this near unanimity of operational practice, there is a major strain of secondary literature critical of the Pc and willing to propose alternatives. Alfano (2005) pointed out the ability of the Pc to underrepresent the risk in certain situations and counselled a maximum Pc construct. Carpenter (2017, 2019) reiterated this criticism and proposed using instead a confidence interval on the miss distance. Balch et al. (2019) identified what they argued was a defect in the entire Bayesian Pc construct and believed that the use of a more conservative methodology based on covariance ellipsoid overlap was necessary. Delande (2022) introduced the framework of collision “plausibility” to the risk assessment process and sketched out how this might be used operationally. Elkantassi (2022) published a full development of the miss distance confidence interval approach and applied it to several worked examples. While these different approaches to collision risk assessment do differ in their details, they all converge on two central points: first, the Pc’s failure to give an adequate expression of the risk in dilution region situations is a fatal flaw; and second, a conjunction should be presumed risky and in need of mitigation until the evidence of the situation can establish otherwise. These criticisms, if correct, would counsel a number of modifications to current CA operational practice; as such, they force a re-examination of fundamental aspects of the CA problem, including the following: 1. Is the CA risk assessment a probability problem, a statistics problem, or something else? 2. If it is a statistics problem, does it lend itself naturally to a hypothesis test construction? 3. If it can be construed as a hypothesis test, what form should the null hypothesis take, to wit: what constraints exist on the choice of the null hypothesis, what selections are in best alignment with all of the attendant parameters of the problem, and what is implied philosophically by different choices? 4. What are the implications of using the different proposed risk assessment parameters for CA? This question should be answered both in determining how frequently the dilution region situation cited by the critics of the Pc actually appears in an operationally significant manner and the missed detection and false alarm rates of all of the proposed risk assessment metrics, compared both to the Pc and to each other. This paper explores and offers preliminary answers to the above questions, presenting a researched treatment of the philosophical nature of the CA problem and the null hypothesis choice that achieves the greatest consistency with all of the different aspects of operational CA conduct. It then profiles all of the different proposed risk assessment metrics enumerated in the earlier paragraph against an extremely large database of conjunction events at both the 550km and 700km altitudes. The combination of the philosophical exploration of the CA problem and the results of the profiling activity articulates what a risk assessment metric will need to demonstrate, in terms of both innate construction and performance, in order to be a true competitor to the Pc.

conjunction assessment↗
DOE OSTI2023

Dense nuclear matter equation of state from heavy-ion collisions

The nuclear equation of state (EOS) is at the center of numerous theoretical and experimental efforts in nuclear physics. With advances in microscopic theories for nuclear interactions, the availability of experiments probing nuclear matter under conditions not reached before, endeavors to develop sophisticated and reliable transport simulations to interpret these experiments, and the advent of multi-messenger astronomy, the next decade will bring new opportunities for determining the nuclear matter EOS, elucidating its dependence on density, temperature, and isospin asymmetry. Among controlled terrestrial experiments, collisions of heavy nuclei at intermediate beam energies (from a few tens of MeV/nucleon to about 25 GeV/nucleon in the fixed-target frame) probe the widest ranges of baryon density and temperature, enabling studies of nuclear matter from a few tenths to about 5 times the nuclear saturation density and for temperatures from a few to well above a hundred MeV, respectively. Collisions of neutron-rich isotopes further bring the opportunity to probe effects due to the isospin asymmetry. However, capitalizing on the enormous scientific effort aimed at uncovering the dense nuclear matter EOS, both at RHIC and at FRIB as well as at other international facilities, depends on the continued development of state-of-the-art hadronic transport simulations. Furthermore, this white paper highlights the essential role that heavy-ion collision experiments and hadronic transport simulations play in understanding strong interactions in dense nuclear matter, with an emphasis on how these efforts can be used together with microscopic approaches and neutron star studies to uncover the nuclear EOS.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Jet modification via 𝜋 0 -hadron correlations in Au + Au collisions at $\sqrt{s_{NN}}$ = 200 GeV

High-momentum two-particle correlations are a useful tool for studying jet-quenching effects in the quark-gluon plasma. Angular correlations between neutral-pion triggers and charged hadrons with transverse momenta in the range 4–12 GeV/𝑐 and 0.5–7 GeV/𝑐, respectively, have been measured by the PHENIX experiment in 2014 for Au + Au collisions at $\sqrt{s_{NN}}$ = 200 GeV. Suppression is observed in the yield of high-momentum jet fragments opposite the trigger particle, which indicates jet suppression stemming from in-medium partonic energy loss, while enhancement is observed for low-momentum particles. The ratio and differences between the yield in Au + Au collisions and 𝑝 + 𝑝 collisions, 𝐼 𝐴⁢𝐴 and Δ 𝐴⁢𝐴 , as a function of the trigger-hadron azimuthal separation, Δ⁢𝜙, are measured for the first time at the BNL Relativistic Heavy Ion Collider. Finally, these results better quantify how the yield of low-𝑝 𝑇 associated hadrons is enhanced at wide angle, which is crucial for studying energy loss as well as medium-response effects.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Multiplicity-dependent production of Σ(1385) ± and Ξ(1530) 0 in pp collisions at $\sqrt{s}$ = 13 TeV

The production yields of the Σ(1385) ± and Ξ(1530) 0 resonances are measured in pp collisions at $\sqrt{s}$ = 13 TeV with ALICE. The measurements are performed as a function of the charged-particle multiplicity $\langle$dN ch /dη$\rangle$, which is related to the energy density produced in the collision. The results include transverse momentum (p T ) distributions, p T - integrated yields, mean transverse momenta of Σ(1385) ± and Ξ(1530) 0 , as well as ratios of the p T - integrated resonance yields relative to yields of other hadron species. The Σ(1385) ± /π ± and Ξ(1530) 0 /π ± yield ratios are consistent with the trend of the enhancement of strangeness production from low to high multiplicity pp collisions, which was previously observed for strange and multi-strange baryons. The yield ratio between the measured resonances and the long-lived baryons with the same strangeness content exhibits a hint of a mild increasing trend at low multiplicity, despite too large uncertainties to exclude the flat behaviour. The results are compared with predictions from models such as EPOS-LHC and PYTHIA 8 with Rope shoving. The latter provides the best description of the multiplicity dependence of the Σ(1385) ± and Ξ(1530) 0 production in pp collisions at $\sqrt{s}$ = 13 TeV.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Jet angularities in dijet production in proton-proton and heavy-ion collisions at RHIC

We study jet angularities for dijet production at the Relativistic Heavy Ion Collider (RHIC) in proton-proton (pp) and nucleus-nucleus (AA) collisions at 200 GeV nucleon-nucleon center-of-mass collision energy. In particular, we provide NLL resummed predictions for angularity observables of groomed and ungroomed jets produced in pp collisions matched to next-to-leading order QCD calculations resulting in NLO + NLL ' accuracy. Our parton-level predictions are corrected for non-perturbative effects, such as hadronization and underlying event, using parton-to-hadron level transfer matrices obtained with the Sherpa event generator. Furthermore, we use the Q-PYTHIA and JEWEL generators to estimate the impact of the interaction between quarks and gluons produced by the parton shower with the dense medium formed in heavy-ion collisions on the considered jet angularities.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Light neutral-meson production in pp collisions at $\sqrt{\text{s}}$ = 13 TeV

The momentum-differential invariant cross sections of π 0 and η mesons are reported for pp collisions at $\sqrt{s}$ = 13 TeV at midrapidity (|y| < 0.8). The measurement is performed in a broad transverse-momentum range of 0.2 < p T < 200 GeV/c and 0.4 < p T < 60 GeV/c for the π 0 and η, respectively, extending the p T coverage of previous measurements. Transverse-mass-scaling violation of up to 60% at low transverse momentum has been observed, agreeing with measurements at lower collision energies. Transverse Bjorken x (x T ) scaling of the π 0 cross sections at LHC energies is fulfilled with a power-law exponent of n = 5.01 ± 0.05, consistent with values obtained for charged pions at similar collision energies. The data are compared to predictions from next-to-leading order perturbative QCD calculations, where the π 0 spectrum is best described using the CT18 parton distribution function and the NNFF1.0 or BDSS fragmentation function. Expectations from PYTHIA8 and EPOS LHC overestimate the spectrum for the π 0 and are not able to describe the shape and magnitude of the η spectrum. The charged-particle multiplicity dependent π 0 and η p T spectra show the expected change of the spectral shape, characterized by a flatter slope with increasing multiplicity. This is demonstrated across a broad transverse-momentum range and up to events with a charged-particle multiplicity exceeding five times the mean value in minimum bias collisions. The η/π 0 ratio depends on the charged-particle multiplicity for p T < 4 GeV/c. PYTHIA8 and EPOS LHC qualitatively explain this behavior with an increasing contribution from the feed-down of heavier particles to the π 0 spectrum.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Measurement of beauty production via non-prompt charm hadrons in p–Pb collisions at $\sqrt{s_{\textrm{NN}}}$ = 5.02 TeV

The production cross sections of D 0 , D + , and Λ$^{+}_{c}$ hadrons originating from beauty-hadron decays (i.e. non-prompt) were measured for the first time at midrapidity in proton–lead (p–Pb) collisions at the center-of-mass energy per nucleon pair of $\sqrt{s_{\textrm{NN}}}$ = 5.02 TeV. Nuclear modification factors (R pPb ) of non-prompt D 0 , D + , and Λ$^{+}_{c}$ are calculated as a function of the transverse momentum (p T ) to investigate the modification of the momentum spectra measured in p–Pb collisions with respect to those measured in proton–proton (pp) collisions at the same energy. The R pPb measurements are compatible with unity and with the measurements in the prompt charm sector, and do not show a significant p T dependence. The p T -integrated cross sections and p T -integrated R pPb of non-prompt D 0 and D + mesons are also computed by extrapolating the visible cross sections down to p T = 0. The non-prompt D-meson R pPb integrated over p T is compatible with unity and with model calculations implementing modification of the parton distribution functions of nucleons bound in nuclei with respect to free nucleons. The non-prompt Λ$^{+}_{c}$/D 0 and D + /D 0 production ratios are computed to investigate hadronisation mechanisms of beauty quarks into mesons and baryons. The measured ratios as a function of p T display a similar trend to that measured for charm hadrons in the same collision system.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Ab-initio nucleon-nucleon correlations and their impact on high energy 16 O+ 16 O collisions

Investigating nucleon-nucleon correlations inherent to the strong nuclear force is one of the core goals in nuclear physics research. We showcase the unique opportunities offered by collisions of 16 O nuclei at high-energy facilities to reveal detailed many-body properties of the nuclear ground state. We interface existing knowledge about the geometry of 16 O coming from ab-initio calculations of nuclear structure with transport simulations of high-energy 16 O+ 16 O collisions. Bulk observables in these processes, such as the elliptic flow or the fluctuations of the mean transverse momentum, are found to depend significantly on the input nuclear model and to be sensitive to realistic clustering and short-range repulsive correlations, effectively opening a new avenue to probe these features experimentally. This finding demonstrates collisions of oxygen nuclei as a tool to elucidate initial conditions of small collision systems while fostering connections with effective field theories of nuclei rooted in quantum chromodynamics (QCD).

Zhang, Chunjian [Fudan University, Shanghai (China↗
DOE OSTI2025

Evidence of isospin-symmetry violation in high-energy collisions of atomic nuclei

Strong interactions preserve an approximate isospin symmetry between up (u) and down (d) quarks, part of the more general flavor symmetry. In the case of K meson production, if this isospin symmetry were exact, it would result in equal numbers of charged (K + and K − ) and neutral (K 0 and ${\overline{K}}^{0}$) mesons produced in collisions of isospin-symmetric atomic nuclei. Here, we report results on the relative abundance of charged over neutral K meson production in argon and scandium nuclei collisions at a center-of-mass energy of 11.9 GeV per nucleon pair. We find that the production of K + and K − mesons at mid-rapidity is (18.4 ± 6.1)% higher than that of the neutral K mesons. Although with large uncertainties, earlier data on nucleus-nucleus collisions in the collision center-of-mass energy range $2.6 \, < \, \sqrt{{s}_{NN}} \, < \, 200$ GeV are consistent with the present result. Using well-established models for hadron production, we demonstrate that known isospin-symmetry breaking effects and the initial nuclei containing more neutrons than protons lead only to a small (few percent) deviation of the charged-to-neutral kaon ratio from unity at high energies. Thus, they cannot explain the measurements. The significance of the flavor-symmetry violation beyond the known effects is 4.7σ when the compilation of world data with uncertainties quoted by the experiments is used. New systematic, high-precision measurements and theoretical efforts are needed to establish the origin of the observed large isospin-symmetry breaking.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

A Proof of the Asymptotic Variance of Path Length Estimators for Single-Collision Monte Carlo Source Iteration in the Thick Diffusion Limit

Here, we prove a theorem relating the variance of path length estimators for single-collision Monte Carlo source iteration to a parameter that becomes infinitesimally small in an important physical regime arising in radiative transfer. In our usage, “single-collision Monte Carlo source iteration” refers to Monte Carlo Boltzmann transport methods in which each Monte Carlo particle history includes no more than a single collision, and the physics of multiple scattering is modeled by lagging the scattering source term and iterating until this term converges. Our theorem can be used to construct variance reduction techniques which improve the order of the estimator variance. This enables calculations that would otherwise require impractically large sample sizes to achieve practical estimator uncertainties. We believe this is the first postulation of a theorem relating estimator variance to a limiting case parameter for single-collision Monte Carlo source iteration, and the first proof of such a theorem. We illustrate the theorem’s value with an example in which the authors of a transport method used the theorem to design a variance reduction technique that improved the uncertainty of their solution by a factor of about 500 for a proxy problem from radiative transfer that contains both optically-thick and optically-thin material.

Mathematics and Computing↗
DOE OSTI2024

Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC

Abstract Ultrarelativistic nuclear collisions create a strongly interacting state of hot and dense quark–gluon matter that exhibits a remarkable collective flow behavior with minimal viscous dissipation. To gain deeper insights into its intrinsic nature and fundamental degrees of freedom, we determine the speed of sound in an extended volume of quark–gluon plasma using lead–lead (PbPb) collisions at a center-of-mass energy per nucleon pair of 5.02 TeV. The data were recorded by the CMS experiment at the CERN LHC and correspond to an integrated luminosity of 0.607 nb −1 . The measurement is performed by studying the multiplicity dependence of the average transverse momentum of charged particles emitted in head-on PbPb collisions. Our findings reveal that the speed of sound in this matter is nearly half the speed of light, with a squared value of 0.241 ± 0.002 ( stat ) ± 0.016 ( syst ) in natural units. The effective medium temperature, estimated using the mean transverse momentum, is 219 ± 8 ( syst ) MeV . The measured squared speed of sound at this temperature aligns precisely with predictions from lattice quantum chromodynamic (QCD) calculations. This result provides a stringent constraint on the equation of state of the created medium and direct evidence for a deconfined QCD phase being attained in relativistic nuclear collisions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Semi-inclusive direct photon + jet and 𝜋 0 + jet correlations measured in 𝑝 + 𝑝 and central Au + Au collisions at $\sqrt{s_{NN}}$ = 200GeV

The STAR experiment at RHIC reports new measurements of jet quenching based on the semi- inclusive distribution of charged-particle jets recoiling from direct photon (γ dir ) and neutral pion (π 0 ) triggers in pp and central Au + Au collisions at $\sqrt{s_{NN}}$ = 200 GeV, for triggers in the range 9 < $E$$^{trig}_{T}$ < 20 GeV. The datasets have integrated luminosities of 3.9nb −1 for Au + Au and 23pb −1 for 𝑝𝑝 collisions. Jets are reconstructed using the anti-𝑘 𝑇 algorithm with resolution parameters 𝑅 = 0.2 and 0.5. The large uncorrelated jet background in central Au + Au collisions is corrected using a mixed-event approach, which enables precise charged-particle jet measurements at low transverse momentum 𝑝$^{ch}_{𝑇,jet}$ and large 𝑅. Recoil-jet distributions are reported in the range 𝑝$^{ch}_{𝑇,jet}$ < 25 GeV/𝑐. Comparison of the distributions measured in 𝑝𝑝 and Au + Au collisions reveals strong medium-induced jet yield suppression for 𝑅 = 0.2 with markedly less suppression for 𝑅 = 0.5. Comparison is also made to theoretical models incorporating jet quenching. Furthermore, these data provide new insight into the mechanisms underlying jet quenching and the angular dependence of medium-induced jet-energy transport and provide new constraints on modeling such effects.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Measurement of forward charged hadron flow harmonics in peripheral PbPb collisions at s N N = 5.02 TeV with the LHCb detector

Flow harmonic coefficients, v n , which are the key to studying the hydrodynamics of the quark-gluon plasma (QGP) created in heavy-ion collisions, have been measured in various collision systems and kinematic regions and using various particle species. The study of flow harmonics in a wide pseudorapidity range is particularly valuable to understand the temperature dependence of the shear viscosity to entropy density ratio of the QGP. This paper presents the first LHCb results of the second- and the third-order flow harmonic coefficients of charged hadrons as a function of transverse momentum in the forward region, corresponding to pseudorapidities between 2.0 and 4.9, using the data collected from PbPb collisions in 2018 at a center-of-mass energy of 5.02 TeV . The coefficients measured using the two-particle angular correlation analysis method are smaller than the central-pseudorapidity measurements at ALICE and ATLAS from the same collision system but share similar features. ©2024 CERN, for the LHCb Collaboration 2024 CERN

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Correlations of event activity with hard and soft processes in p + Au collisions at $\sqrt{s_{NN}}$ = 200 GeV at the RHIC STAR experiment

With the STAR experiment at the BNL Relativistic Heavy Ion Collider, we characterize $\sqrt{s_{NN}}$ = 200GeV p + Au collisions by event activity (EA) measured within the pseudorapidity range η ϵ[–5,–3.4] in the Au-going direction and report correlations between this EA and hard- and soft-scale particle production at midrapidity (η ϵ[–1,1]). At the soft scale, charged particle production in low-EA p + Au collisions is comparable to that in p + p collisions and increases monotonically with increasing EA. At the hard scale, we report measurements of high transverse momentum (p T ) jets in events of different EAs. In contrast with the soft particle production, high-p T particle production and EA are found to be inversely related. Furthermore, to investigate whether this is a signal of jet quenching in high-EA events, we also report ratios of p T imbalance and azimuthal separation of dijets in high- and low-EA events. Within our measurement precision, no significant differences are observed, disfavoring the presence of jet quenching in the highest 30% EA p + Au collisions at $\sqrt{s_{NN}}$ = 200GeV.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

First measurement of 𝐷 𝑠⁢1 ⁡(1 + )⁢(2536) + and 𝐷$^{*}_{𝑠⁢2}$⁡(2 + )⁢(2573) + production in proton-proton collisions at $\sqrt{s}$ = 13 TeV at the LHC

The production yields of the orbitally excited charm-strange mesons D s⁢1 ⁡(1 + )⁢(2536)+ and 𝐷$^{*}_{𝑠⁢2}$⁡(2 + )⁢(2573) + were measured for the first time in proton-proton (pp) collisions at a center-of-mass energy of $\sqrt{s}$ =13 TeV with the ALICE experiment at the LHC. The D$^{+}_{s⁢1}$ and D$^{*+}_{s⁢2}$ mesons were measured at midrapidity (|𝑦| < 0.5) in minimum-bias and high-multiplicity pp collisions in the transverse-momentum interval 2< 𝑝 T < 24 GeV/𝑐. Their production yields relative to the D$^{+}_{s}$ ground-state yield were found to be compatible between minimum-bias and high-multiplicity collisions, as well as with previous measurements in e ± ⁢p and e + ⁢e − collisions. The measured D$^{+}_{s⁢1}$/D$^{+}_{s}$ and D$^{*+}_{s⁢2}$/D$^{+}_{s}$ yield ratios are described by statistical hadronization models and can be used to tune the parameters governing the production of excited charm-strange hadrons in Monte Carlo generators, such as pythia 8.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Medium-induced modification of azimuthal correlations of electrons from heavy-flavor hadron decays with charged particles in Pb–Pb collisions at $\mathbf {\sqrt{s_{\textrm{NN}}} = 5.02}$ TeV

The azimuthal-correlation distributions between electrons from the decays of heavy-flavor hadrons and associated charged particles in Pb–Pb collisions at $\sqrt{s_{\textrm{NN}}} = 5.02$ TeV are reported for the 0–10% and 30–50% centrality classes. This measurement provides access to the jet-like correlation observables in the heavy-flavor sector in Pb–Pb collisions. The analysis is performed for trigger electrons from heavy-flavor hadron decays with transverse momentum $4< p_\textrm{T}^\textrm{e} < 16~\textrm{GeV}/c$, considering associated particles within the transverse-momentum range $1< p_\textrm{T}^\textrm{assoc} < 7$ GeV/c, and a pseudorapidity difference of $|\Delta \eta |<1$ between the trigger electron and associated particles. The per-trigger nuclear modification factor ( I AA ) is calculated to compare the near- and away-side peak yields to those in pp collisions at $\sqrt{s} = 5.02$ TeV. In 0–10% central collisions, the indicates a hint of enhancement of associated-particle yields with $p_\textrm{T}<3$ GeV/c on the near side, and a suppression of yields with $p_\textrm{T}>4$ GeV/c on the away side. The I AA for electron triggers from heavy-flavor hadron decays is compared with that for light-flavor and strange-particle triggers to investigate the dependence on different fragmentation processes and parton-medium dynamics, and is found to be the same within uncertainties.

Abualrob, I. J. [University of Houston] (ORCID:000↗
NASA NTRS1972

Examination of the collision force method for analyzing the responses of simple containment/deflection structures to impact by one engine rotor blade fragment

An approximate collision analysis, termed the collision-force method, was developed for studying impact-interaction of an engine rotor blade fragment with an initially circular containment ring. This collision analysis utilizes basic mass, material property, geometry, and pre-impact velocity information for the fragment, together with any one of three postulated patterns of blade deformation behavior: (1) the elastic straight blade model, (2) the elastic-plastic straight shortening blade model, and (3) the elastic-plastic curling blade model. The collision-induced forces are used to predict the resulting motions of both the blade fragment and the containment ring. Containment ring transient responses are predicted by a finite element computer code which accommodates the large deformation, elastic-plastic planar deformation behavior of simple structures such as beams and/or rings. The effects of varying the values of certain parameters in each blade-behavior model were studied. Comparisons of predictions with experimental data indicate that of the three postulated blade-behavior models, the elastic-plastic curling blade model appears to be the most plausible and satisfactory for predicting the impact-induced motions of a ductile engine rotor blade and a containment ring against which the blade impacts.

Zirin, R. M.↗
NASA NTRS1972

Broadening of the D lines and the relaxation of the resonance levels of sodium due to collisions with helium.

Calculated potentials for the NaHe molecule are used to obtain collision-induced widths and shifts for the sodium D lines together with cross sections for fine-structure transitions and the relaxation of the multipole polarizations of the resonance levels. The atomic collision is treated in an adiabatic approximation in which the colliding atoms form a molecular system which rotates during the collision. We find the resonance lines to be broadened equally and to be approximately 70% wider, and with associated shifts of an order of magnitude smaller, than expected on the basis of van der Waals forces. The dependence of the cross sections for relaxation of the multipole polarizations of the resonance levels on the molecular-coupling conditions and the rotation of the system during collision is discussed and indicates a limitation of the sum rule for these cross sections.

Lewis, E. L.↗