Electronic Angular Momentum Research Articles

Generation of 10 kT axial magnetic fields using multiple conventional laser beams: A sensitivity study for kJ PW-class laser facilities

Strong multi-kilotesla magnetic fields have various applications in high-energy density science and laboratory astrophysics, but they are not readily available. In our previous work [Y. Shi et al., Phys. Rev. Lett. 130, 155101 (2023)], we developed a novel approach for generating such fields using multiple conventional laser beams with a twist in the pointing direction. This method is particularly well-suited for multi-kilojoule petawatt-class laser systems like SG-II UP, which are designed with multiple linearly polarized beamlets. Utilizing three-dimensional kinetic particle-in-cell simulations, we examine critical factors for a proof-of-principle experiment, such as laser polarization, relative pulse delay, phase offset, pointing stability, and target configuration, and their impact on magnetic field generation. Our general conclusion is that the approach is very robust and can be realized under a wide range of laser parameters and plasma conditions. We also provide an in-depth analysis of the axial magnetic field configuration, azimuthal electron current, and electron and ion orbital angular momentum densities. Supported by a simple model, our analysis shows that the axial magnetic field decays owing to the expansion of hot electrons.

Photoelectron momentum distribution in structured strong fields

Abstract In this study, a reaction microscope is used to explore the behavior of electrons in shaped beams under strong field conditions. Photoelectron momentum spectra indicate that the inclusion of orbital angular momentum (OAM) of light does not significantly impact the available electron angular momentum states. However, the distinctive donut shape of the beam plays a crucial role in determining the observed Photoelectron Angular Distributions (PADs). TDSE simulations, incorporating focal volume averaging indicates that the geometric properties of the focal region of the OAM and the Gaussian beams affect the photoelectron spectra differently. By averaging the spectra across different intensity regions, we have provided a qualitative explanation for the variations in photoelectron spectra resulting from the shapes of the individual beams. This result shows that the transfer of OAM in ultrashort light pulses cannot be detected in gas ensembles due to the ionization being overwhelmed by atoms in the most intense region with minimal spatial phase variation within the laser field. We demonstrate that the differences in the momentum spectra arising from shaped beams can be qualitatively explained using models that incorporate the spatial averaging of the beam, rather than focusing on the OAM content.

Prospects of a thousand-ion Sn2+ Coulomb-crystal clock with sub-10−19 inaccuracy

Optical atomic clocks are the most accurate and precise measurement devices of any kind, enabling advances in international timekeeping, Earth science, fundamental physics, and more. However, there is a fundamental tradeoff between accuracy and precision, where higher precision is achieved by using more atoms, but this comes at the cost of larger interactions between the atoms that limit the accuracy. Here, we propose a many-ion optical atomic clock based on three-dimensional Coulomb crystals of order one thousand Sn2+ ions confined in a linear RF Paul trap with the potential to overcome this limitation. Sn2+ has a unique combination of features that is not available in previously considered ions: a 1S0 ↔ 3P0 clock transition between two states with zero electronic and nuclear angular momentum (I = J = F = 0) making it immune to nonscalar perturbations, a negative differential polarizability making it possible to operate the trap in a manner such that the two dominant shifts for three-dimensional ion crystals cancel each other, and a laser-accessible transition suitable for direct laser cooling and state readout. We present calculations of the differential polarizability, other relevant atomic properties, and the motion of ions in large Coulomb crystals, in order to estimate the achievable accuracy and precision of Sn2+ Coulomb-crystal clocks.

Electrically Induced Angular Momentum Flow between Separated Ferromagnets.

Converting angular momentum between different degrees of freedom within a magnetic material results from a dynamic interplay between electrons, magnons, and phonons. This interplay is pivotal to implementing spintronic device concepts that rely on spin angular momentum transport. We establish a new concept for long-range angular momentum transport that further allows us to address and isolate the magnonic contribution to angular momentum transport in a nanostructured metallic ferromagnet. To this end, we electrically excite and detect spin transport between two parallel and electrically insulated ferromagnetic metal strips on top of a diamagnetic substrate. Charge-to-spin current conversion within the ferromagnetic strip generates electronic spin angular momentum that is transferred to magnons via electron-magnon coupling. We observe a finite angular momentum flow to the second ferromagnetic strip across a diamagnetic substrate over micron distances, which is electrically detected in the second strip by the inverse charge-to-spin current conversion process. We discuss phononic and dipolar interactions as the likely cause to transfer angular momentum between the two strips. Moreover, our Letter provides the experimental basis to separate the electronic and magnonic spin transport and thereby paves the way towards magnonic device concepts that do not rely on magnetic insulators.

Kinetic energy dependence and potential energy surface of the spin-forbidden reaction Sm+ (8F) + N2O (1Σ+) → SmO+ (6Δ) + N2 (1Σg+).

The kinetic energy dependence of the title reaction is examined using guided ion beam tandem mass spectrometry. Because this reaction is spin-forbidden, crossings between octet and sextet hypersurfaces presumably must occur. Furthermore, Sm+ must transition from a 4f66s1 configuration in the reactant to 4f55d2 in order to have the orbital occupancy required to form the triple bond in SmO+ (6Δ). Despite being strongly exothermic (∼4eV), the reaction proceeds with low efficiency (18% ± 4%) via a barrierless process at low energies. Below ∼0.3eV, the cross section follows a kinetic energy dependence that roughly parallels that of the collision rate for ion-dipole reactions. At higher collision energies, the reaction cross section increases until it follows the trajectory cross section closely from 3 to 5eV, indicating that another pathway opens on the reaction hypersurface. Modeling this increase yields a threshold energy for this new pathway at 0.54 ± 0.05eV. Theoretical potential energy surfaces that do not include spin-orbit interactions for the reaction show that there is a barrier of height 1.19eV (MP2) or 0.49eV [CCSD(T)] to insertion of Sm+ into the N2-O bond and that there are several places where octet and sextet surfaces can intersect and interact. By considering the distribution of spin-orbit states generated in the ion source, the internal energy of the N2O reactant, and the influence of coupling between electronic, orbital, and rotational angular momentum, the low-efficiency, exothermic behavior as well as the increase in efficiency at higher energies can plausibly be explained.

Comprehensive Bicubic Formalism of Ordinary and Novel (dm) Particles With Substituted Virtual Novel Electron Describing the Bohr Atom

The particle limiting velocity solutions from the bicubic limiting velocity equation ( Soln, J., 2021.1.2, 2022) have been very useful in carrying out parallel studies of ordinary and novel particles. This study is facilitated with the help of evolutionary congruent parameters, ordinaryz1 ⪯ 1, novel z2 = 1/z1 ⪰ 1 and congruent phase-angle α ⪯ π/2. At smooth matching point z1 = z2 = 1 and α = π/2, there is no physical difference between an ordinary and novel particle as they have the same limiting velocities. At α = π/3 ≺ π/2, they have already different limiting velocities with different other physical characteristics. Ordinary photon γ and novel doubly photon γN are indistinguishable at α = π/2, while at α = π/3 ≺ π/2, they are already physically different. That applies to any other particle, ordinary proton p versus novel proton pN, etc. Through trial and error, one finds that c3 the ordinary particle limiting velocity solution has ratio value of 1 at the comprehensive congruent phase-angle αO = π/5.1 = 0.616 which an ordinary particle of velocity v can satisfy at v ≃ c3, in fact, defining the value of c3. The quantum jump from the ordinary particle comprehensive congruent phase-angle αO to the novel particle comprehensive congruent phase-angle αN = 2αO = 2π/5.1 = 1.232 yields novel particle limiting velocity solution doubly Rc1,3 with ratio value of 1 which a novel particle velocity vN can satisfy with doublyRc1,3 ≃ vN, simply defining the value of doubly Rc1,3. This comprehensive quantum jump with fixed comprehensive congruent phase-angles αO and αN apply to any free and interacting ordinary particle (γ, e, ν,etc.) when connecting to the corresponding free and interacting novel particle (γN, eN, νN, etc.). Concerning the Bohr’s atom, we wish to address the question of negative energy electron e emitting positive energy radiation. To this end we simply substitute e with the virtual novel electron eN with the same radius r and velocity v. This virtual eN, due to the Coulomb potential energy V from the sitting proton p plus the centrifugal force, with the quantized orbital virtual novel electron angular momentum yields the positive virtual novel electron energy in the bicubic formalism. The frequencies of emitted radiation from virtual novel electron is practically the same as from the negative energy electron e.

High-resolution investigation of the spin-rotation doublets of 14NO2 at 6.2 µm mid-infrared region using cavity ring-down spectroscopy

Nitrogen dioxide (14NO2) exhibits a unique doublet structure due to the presence of its unpaired electron, which results in a nonzero electronic angular momentum in the ground electronic state of the molecule. In this study, an investigation into high-resolution rovibrational spectral features associated with the spin-rotation doublets of 14NO2 was conducted using an external-cavity quantum cascade laser (EC-QCL)-coupled cavity ring-down spectrometer operating at 6.2 μm. Four spin-split doublets belonging to the RR branch of the (001)-(000) fundamental band were probed in the mid-IR spectral region. The air broadening and self-broadening coefficients were reported explicitly for each doublet component for the first time, to the best of our knowledge. The line-intensities were also quantified, and they were compared to the HITRAN database, revealing good agreement (<4% discrepancy).

Dipolar Coupling as a Mechanism for Fine Control of Magnetic States in ErCOT-Alkyl Molecular Magnets.

The design of molecular magnets has progressed greatly by taking advantage of the ability to impart successive perturbations and control vibronic transitions in 4fn systems through the careful manipulation of the crystal field. Herein, we control the orientation and rigidity of two dinuclear ErCOT-based molecular magnets: the inversion-symmetric bridged [ErCOT(μ-Me)(THF)]2 (2) and the nearly linear Li[(ErCOT)2(μ-Me)3] (3). The conserved anisotropy of the ErCOT synthetic unit facilitates the direction of the arrangement of its magnetic anisotropy for the purposes of generating controlled internal magnetic fields, improving control of the energetics and transition probabilities of the electronic angular momentum states with exchange biasing via dipolar coupling. This control is evidenced through the introduction of a second thermal barrier to relaxation operant at low temperatures that is twice as large in 3 as in 2. This barrier acts to suppress through-barrier relaxation by protecting the ground state from interacting with stray local fields while operating at an energy scale an order of magnitude smaller than the crystal field term. These properties are highlighted when contrasted against the mononuclear structure ErCOT(Bn)(THF)2 (1), in which quantum tunneling of the magnetization processes dominate, as demonstrated by magnetometry and ab initio computational methods. Furthermore, far-infrared magnetospectroscopy measurements reveal that the increased rigidity imparted by successive removal of solvent ligands when adding bridging methyl groups, along with the increased excited state purity, severely limits local spin-vibrational interactions that facilitate magnetic relaxation, manifesting as longer relaxation times in 3 relative to those in 2 as temperature is increased.

Prospective Optical Lattice Clocks in Neutral Atoms with Hyperfine Structure

Optical lattice clocks combine the accuracy and stability required for next-generation frequency standards. At the heart of these clocks are carefully engineered optical lattices tuned to a wavelength where the differential AC Stark shift between ground and excited states vanishes—the so called ‘magic’ wavelength. To date, only alkaline-earth-like atoms utilizing clock transitions with total electronic angular momentum J=0 have successfully realized these magic wavelength optical lattices at the level necessary for state-of-the-art clock operation. In this article, we discuss two additional types of clock transitions utilizing states with J≠0, leveraging hyperfine structure to satisfy the necessary requirements for controlling lattice-induced light shifts. We propose realizing (i) clock transitions between same-parity clock states with total angular momentum F=0 and (ii) M1/E2 clock transitions between a state with F=0 and a second state with J=1/2, mF=0. We present atomic species which fulfill these requirements before giving a detailed discussion of both manganese and copper, demonstrating how these transitions provide the necessary suppression of fine structure-induced vector and tensor lattice light shifts for clock operations. Such realization of alternative optical lattice clocks promises to provide a rich variety of new atomic species for neutral atom clock operation, with applications from many-body physics to searches for new physics.

Emission of twisted photons by a Dirac electron in a strong magnetic field

We study the spontaneous emission of a photon during the transitions between relativistic Landau states of an electron in a constant magnetic field that can reach the Schwinger value of Hc=4.4×109 T. In contrast to the conventional method, in which detection of both the final electron and the photon are implied in a certain basis, here we derive the photon state as it evolves from the process itself. It is shown that the emitted photon state represents a twisted Bessel beam propagating along the field axis with a total angular momentum (TAM) projection onto this axis ℓ−ℓ′, where ℓ and ℓ′ are the TAM of the initial electron and of the final one, respectively. Thus, the majority of the emitted photons turn out to be twisted, with ℓ−ℓ′≳1, even when the magnetic field reaches the critical value of H∼Hc. The transitions without a change of the electron angular momentum, ℓ′=ℓ, are possible, yet much less probable. We also compare our findings with those for a spinless charged particle and demonstrate their good agreement for the transitions without change of the electron spin projection even in the critical fields, while the spin-flip transitions are generally suppressed. In addition, we argue that whereas the ambiguous choice of an electron spin operator affects the differential probability of emission, this problem can partially be circumvented for the photon evolved state because it is the electron TAM rather than the spin alone that defines the TAM of the emitted twisted photon. Published by the American Physical Society 2024

An ab initio spectroscopic model of the molecular oxygen atmospheric and infrared bands.

We present a unified variational treatment of the magnetic dipole matrix elements, Einstein coefficients and line strength for general open-shell diatomic molecules in the general purpose diatomic code Duo. Building on previous work in which similar expressions for the electric quadrupole transitions were developed, we also present a complete ab initio spectroscopic model for the infrared, electric dipole-forbidden, spectrum of the 16O2 molecule. The model covers seven states, namely the X 3Σ-g, a 1Δg, b 1Σ+g, I 1Πg, II 1Πg, I 3Πg and II 3Πg states, for which 7 potential energy, 6 electronic angular momentum, 7 spin-orbit, and 14 quadrupole moment curves are calculated using ic-MRCI theory and an aug-cc-pV5Z basis set. These curves are diabatised to remove avoided crossings between the excited Π states, and the resultant properties are used to produce a line list for higher-order transitions of astrophysical interest.

Probing Coupled Rotational and Electronic Dynamics during Laser-Induced Molecular Fragmentation

Coupled nuclear and electronic dynamics within a molecule are key to understanding a broad range of fundamental physical and chemical processes. Although probing the coupled vibrational and electronic dynamics was demonstrated, it has so far been challenging to observe the coupling interactions between the rotational and electronic degrees of freedom. Here, we report the first observation of Coriolis coupling, a coupling interaction between nuclear rotational angular momentum and electronic axial angular momentum, during laser-induced molecular fragmentation by tracing the electronic structure of a dissociating O 2 + molecule. We observe that the electron density changes its shape from that of a molecular σ orbital to a nearly isotropic shape as the internuclear distance goes up to ∼20 Å, which results from the transition between nearly degenerate electronic states associated with different rotational angular momenta. Our experiment demonstrates that the breaking of a chemical bond does not occur suddenly during molecular dissociation. Instead, it lasts for a long time of several hundred femtoseconds due to the Coriolis coupling interaction. Our experiment can be extended to complicated molecules, holding the potential of revealing yet unobserved electron–nuclear coupling interactions during ultrafast processes.

An ab initio diabatic study of rovibronic spectra of CN.

An ab initio study of the rovibronic spectra for the cyano radical (CN) based on a diabatic representation is presented. This work considers 17 electronic states, 59 dipole moment curves, 88 spin-orbit coupling curves, and 30 electronic angular momentum coupling curves, which are obtained using the internally contracted multireference configuration interaction method including the Davidson correction (icMRCI + Q) with the aug-cc-pwCV5Z-DK basis set. The diabatic transformations are performed based on a property-based diabatization method to remove the avoided crossings for the D2Π-H2Π and b4Π-24Π pairs. Ab initio potential energy curves of the X2Σ+, B2Σ+, E2Σ+, A2Π, D2Π, H2Π, F2Δ and J2Δ electronic states are shifted to match the experimental electronic excitation energies and the equilibrium internuclear distances. The coupled nuclear motion Schrödinger equations are then solved to obtain the rovibronic spectra of CN for wavenumbers from 0 to 80 000 cm-1. At wavenumbers of 0-30 000 cm-1, our absorption cross sections agree well with available theoretical data. For wavenumbers above 30 000 cm-1, our cross sections are larger than previous data in view of the fact that the transitions involving high-lying electronic states are considered. This work provides an overall prediction of the rovibronic spectrum of CN. Our results are suitable for temperatures below 8000 K and could be useful for the investigations of planetary exploration.

ExoMol line lists – LIII: empirical rovibronic spectra of yttrium oxide

ABSTRACT Empirical line lists BRYTS for the open shell molecule 89Y16O (yttrium oxide) and its isotopologues are presented. The line lists cover the six lowest electronic states: $X\, {}^{2}\Sigma ^{+}$, $A\, {}^{2}\Pi$, $A^{\prime }\, {}^{2}\Delta$, $B\, {}^{2}\Sigma ^{+}$, $C\, {}^{2}\Pi$, and $D\, {}^{2}\Sigma ^{+}$ up to 60 000 cm−1 (&amp;lt;0.167 $\mu$m) for rotational excitation up to J = 400.5. An ab initio spectroscopic model consisting of potential energy curves (PECs), spin–orbit, and electronic angular momentum couplings is refined by fitting to experimentally determined energies of YO, derived from published YO experimental transition frequency data. The model is complemented by empirical spin-rotation and Λ-doubling curves and ab initio dipole moment and transition dipole moment curves computed using multireference configuration interaction (MRCI). The ab initio PECs computed using the complete basis set limit extrapolation and the coupled-cluster CCSD(T) method with its higher quality provide an excellent initial approximation for the refinement. Non-adiabatic coupling curves for two pairs of states of the same symmetry A/C and B/D are computed using a state-averaged complete active space self-consistant field theory (CASSCF) and used to build diabatic representations for the $A\, {}^{2}\Pi$, $C\, {}^{2}\Pi$, $B\, {}^{2}\Sigma ^{+}$, and $D\, {}^{2}\Sigma ^{+}$ curves. The experimentally derived energies of 89Y16O utilized in the fit are used to replace the corresponding calculated energy values in the BRYTS line list. Simulated spectra of YO show excellent agreement with the experiment, where it is available. Calculated lifetimes of YO are tuned to agree well with the experiment, where available. The BRYTS YO line lists are available from the ExoMol database (www.exomol.com).

Multielectronic and multiatomic effects in the U O4,5 x-ray absorption spectroscopy of uranium dioxide

In order to explain all of the spectral features observed in the U O4,5 x-ray absorption spectrum of uranium dioxide (UO2), it is necessary to include both multielectron effects and multiatomic effects. The 5d (core hole)-5f (electron) angular momentum coupling that gives rise to the giant resonance has been treated within ligand field density functional theory, and the electron scattering that generates the extended x-ray absorption fine structure has been included via the spectral simulation program FEFF: both within a UO8 fluorite cluster picture. An atomic model is insufficient to explain all of the observed spectral features.

Surface hopping, electron translation factors, electron rotation factors, momentum conservation, and size consistency.

For a system without spin-orbit coupling, the (i) nuclear plus electronic linear momentum and (ii) nuclear plus orbital electronic angular momentum are good quantum numbers. Thus, when a molecular system undergoes a nonadiabatic transition, there should be no change in the total linear or angular momentum. Now, the standard surface hopping algorithm ignores the electronic momentum and indirectly equates the momentum of the nuclear degrees of freedom to the total momentum. However, even with this simplification, the algorithm still does not conserve either the nuclear linear or the nuclear angular momenta. Here, we show that one way to address these failures is to dress the derivative couplings (i.e., the hopping directions) in two ways: (i) we disallow changes in the nuclear linear momentum by working in a translating basis (which is well known and leads to electron translation factors) and (ii) we disallow changes in the nuclear angular momentum by working in a basis that rotates around the center of mass [which is not well-known and leads to a novel, rotationally removable component of the derivative coupling that we will call electron rotation factors below, cf. Eq. (96)]. The present findings should be helpful in the short term as far as interpreting surface hopping calculations for singlet systems (without spin) and then developing the new surface hopping algorithm in the long term for systems where one cannot ignore the electronic orbital and/or spin angular momentum.

A Century Ago the Stern–Gerlach Experiment Ruled Unequivocally in Favor of Quantum Mechanics

AbstractIn 1921, Otto Stern conceived the idea for an experiment that would decide between a classical and a quantum description of atomic behavior, as epitomized by the Bohr–Sommerfeld–Debye model of the atom. This model entailed not only the quantization of the magnitude of the orbital electronic angular momentum but also of the projection of the angular momentum on an external magnetic field – the so‐called space quantization. Stern recognized that space quantization would have observable consequences: namely, that the magnetic dipole moment due to the orbital angular momentum would be space quantized as well, taking two opposite values for atoms whose only unpaired electron has just one quantum of orbital angular momentum. When acted upon by a suitable inhomogeneous magnetic field, a beam of such atoms would be split into two beams consisting of deflected atoms with opposite projections of the orbital angular momentum on the magnetic field. In contradistinction, if atoms behaved classically, the atomic beam would only broaden along the field gradient and have maximum intensity at zero deflection, i. e., where there would be a minimum or no intensity for a beam split due to space quantization. Stern anticipated that, although simple in principle, the experiment would be difficult to carry out – and invited Walther Gerlach to team up with him. Gerlach's realism and experimental skills together with his sometimes stubborn determination to make things work proved invaluable for the success of the Stern–Gerlach experiment (SGE). After a long struggle, Gerlach finally saw, on 8 February 1922, the splitting of a beam of silver atoms in a magnetic field. The absence of the concept of electron spin confused and confounded the interpretation of the SGE, as the silver atoms were, in fact, in a 2S state, with zero orbital and spin angular momentum. However, a key quantum feature whose existence the SGE was designed to test – namely space quantization of electronic angular momentum – was robust enough to transpire independent of whether the electronic angular momentum was orbital or due to spin. The SGE entails other key aspects of quantum mechanics such as quantum measurement, state preparation, coherence, and entanglement. Confronted with the outcome of the SGE, Stern noted: “I still have objections to the idea of beauty of quantum mechanics. But she is correct.”

High resolution electronic spectroscopy of uranium mononitride, UN.

The isoelectronic molecules UN and UO+ are known to have Ω = 3.5 and Ω = 4.5 ground states, respectively (where Ω is the unsigned projection of the electronic angular momentum along the internuclear axis). A ligand field theory model has been proposed to account for the difference [Matthew and Morse, J. Chem. Phys. 138, 184303 (2013)]. The ground state of UO+ arises from the U3+(5f3(4I4.5))O2- configuration. Owing to the higher nominal charge of the N3- ligand, the U3+ ion in UN is stabilized by promoting one of the 5f electrons to the more polarizable 7s orbital, reducing the repulsive interaction with the ligand and rendering U3+(5f27s(4H3.5))N3- the lowest energy configuration. In the present work, we have advanced the characterization of the UN ground state through studies of two electronic transitions, [18.35]4.5-X(1)3.5 and [18.63]4.5-X(1)3.5, using sub-Doppler laser excitation techniques with fluorescence detection. Spectra were recorded under field-free conditions and in the presence of static electric or magnetic fields. The ground state electric dipole moment [μ = 4.30(2) D] and magnetic ge-factor [2.160(9)] were determined from these data. These values were both consistent with the 5f27s configurational assignment. Dispersed fluorescence measurements were used to determine vibrational constants for the ground and first electronically excited states. Electric dipole moments and magnetic ge-factors are also reported for the higher-energy electronically excited states.

The gravitational form factors of the electron in quantum electrodynamics

We calculate the gravitational form factors of the electron at one loop in quantum electrodynamics, decomposing these into contributions from the electron and photon parts of the energy momentum tensor. Ultraviolet divergences are removed through renormalization in the MS‾ scheme. Infrared divergences are isolated and results are given in both dimensional regularization and photon-mass regularization. The form factors contain information about the electron's energy and angular momentum structure in QED, as well as its mass radius. Whenever possible, we compare our results with the existing literature.

ExoMol line lists – XLVII. Rovibronic spectrum of aluminium monochloride (AlCl)

ABSTRACT A line list for two isotopologues of aluminium monochloride, Al35Cl and Al37Cl, is presented covering the wavelength range &amp;lt;0.2 µm, J up to 400, and applicable for temperatures up to 5000 K. The line lists are built using an empirical spectroscopic model consisting of potential energy curves, spin–orbit coupling curves, electronic angular momentum curves, and Born–Oppenheimer breakdown correction curves combined with ab initio dipole moments and cover the four lowest electronic states, ${X}\, ^1\Sigma ^+$, ${A}\, ^1\Pi$, ${a}\, ^3\Pi$, and ${b}\, ^3\Sigma ^+$. Considerable problems with the assignments of some laboratory rovibronic spectra are identified. Treatment of the states lying in the continuum is discussed. The YNAT line list is available from the ExoMol data base at www.exomol.com.