Complex cross sections of spin exchange in collisions of sodium and potassium atoms in the ground state

Complex cross sections of the spin exchange are calculated for the first time for interacting Na and K atoms based on the data on the singlet (X ¹Σ⁺) and triplet (a ³Σ⁺) potentials that describe the interaction of these alkali-metal atoms in the ground state. The obtained cross sections allow one to theoretically consider the polarization transfer processes and calculate the relaxation times and the magnetic resonance frequency shifts caused by Na-K spin-exchange collisions.     

Spin exchange during collisions of potassium atoms: Complex cross sections

Singlet (X ¹Σ⁺) and triplet (a ³Σ⁺) potentials of interaction of two potassium atoms residing in the ground state (4s ² S _1/2) are presented. Based on the given interaction potentials, the complex cross sections of spin exchange q = [`(q)] + i[`([`(q)])]q = \bar q + i\overline{\overline q} for the system under investigation are calculated. Obtained dependences of the real and imaginary parts of the spin-exchange cross section on temperature allow one to obtain information both on the broadening of a magnetic resonance line of K atoms and on the frequency shift of the magnetic resonance during collision.     

Spin exchange during collisions of two sodium atoms

Based on data on the singlet (X ¹Σ⁺) and triplet (a ³Σ⁺) potentials describing the interaction of two Na atoms in the ground state, the complex cross sections of spin exchange for the system under investigation are calculated. The obtained cross sections allow one to determine relaxation times, as well as magnetic-resonance frequency shifts caused by spin-exchange Na-Na collisions.     

Spectroscopy of the a3Σu + state and the coupling to the X1Σg + state of K2

We report on high resolution Fourier-transform spectroscopy of fluorescence to the a³Σ_u ⁺ state induced by two-photon or two-step excitation from the X¹Σ_g ⁺ state to the 2³Π_g state in the molecule K₂. These spectroscopic data are combined with recent results of Feshbach resonances and two-color photoassociation spectra for deriving the potential curves of X¹Σ_g ⁺ and a³Σ_u ⁺ up to the asymptote. The precise relative position of the triplet levels with respect to the singlet levels was achieved by including the excitation energies from the X¹Σ_g ⁺ state to the 2³Π_g state and the frequencies of the fluorescence down to the a³Σ_u ⁺ state in the simultaneous fit of both potentials. The derived precise potential curves allow for reliable modeling of cold collisions of pairs of potassium atoms in their ²S ground state. Electronic supplementary material Supplementary Online Material     

s-wave and p-wave scattering in a cold gas of Na and Rb atoms

Using improved experimentally based X¹Σ⁺ and a³Σ⁺ molecular potentials of NaRb, we apply the variable phase method to compute new data for low energy scattering of ²³Na atoms by ⁸⁵Rb atoms and ⁸⁷Rb atoms. These are the scattering lengths and volumes, numbers of bound states and effective ranges, which we use to obtain the low energy spin-change cross section as functions of the system temperature and the isotope masses. From an analysis of the contributions of s-wave and p-wave scatterings to the elastic cross section we estimate temperatures below which only s-wave scattering is dominant. We compare our quantal results to data obtained from the semiclassical approximation. We supply evidence for the existence of a near zero energy p-wave bound state supported by the singlet molecular potential.     

Echo spectroscopy of atomic dynamics in a Gaussian trap via phase imprints

We present a simultaneous analysis of the X¹ Σ ⁺ and the a³ Σ ⁺ electronic ground states of the NaK molecule. Excitation of the [B ¹ Π, c³ Σ ⁺]-system made it possible to record fluorescence to rovibrational levels of both ground states simultaneously with a Fourier-transform spectrometer. For the first time high lying levels in the triplet state with v = 17 and v = 18 were seen, the highest possible v = 19 for ²³Na-³⁹K was not observed. The joint evaluation of the retrieved data leads to accurate potential energy curves, that describe the experimental data within their experimental uncertainty of 0.005 cm⁻¹. Cold collision properties like scattering length and Feshbach resonance positions are calculated with these potentials and compared to other predictions.     

The true potential energy curves for different states of SiO and SiS molecules

The true potential energy curves forX ¹ Σ ⁺, a³ π _r,A ¹ π,e ³ Σ ⁻,E ¹ Σ ⁺,c ³ π _i states of astrophysically important molecule SiO, whose spectra were observed in the sunspots, have been constructed using the method of Lakshman and Rao. Dissociation energy and ionization potential have been estimated as 65,350 cm⁻¹ and 92,854 cm⁻¹ respectively and found to be in good agreement with the values cited in literature. The true potential energy curves forX ¹ Σ ⁺,D ¹ π andE ¹ Σ ⁺ states of SiS molecule have been constructed by the same method and its dissociation energy in the ground state has been estimated using Hulburt-Hirschfelder potential function as 54,765 cm⁻¹ in good agreement with 53,250.9 cm⁻¹ given by Herzberg.     

Combined analysis of the PFOODR data on the a 3Σ u+ , 23Πg, 23Σ g+ , 33Πg, and 43Σ g+ states of the K2 molecule

The known and new heterogeneous spectral data on the triplet states a ³Σ _u ⁺ , 2³Π_g, 2³Σ _g ⁺ , 3³Π_g, and 4³Σ _g ⁺ of the K₂ dimer are simultaneously fitted. The data published in J. Mol. Spectrosc. 234, 41 (2005) are refined. The new information used in the analysis contains the data on the 2³Σ _g ⁺ state, which have not been considered previously. The range of internuclear distances where the potential function of the lowest triplet state a ³Σ _u ⁺ is defined is extended. Original Russian Text ? V.B. Sovkov, V.S. Ivanov, D. Li, F. Xie, Li Li, 2007, published in Optika i Spektroskopiya, 2007, Vol. 103, No. 5, pp. 747–751.     

Influence of local spin polarization to the Kondo effect

We use the spin non-degenerate single impurity Anderson model to investigate the influence of the local spin polarization to the Kondo effect. By using the Schrieffer-Wolff transformation, we obtain a generalized s-d exchange Hamiltonian, which describes the interaction between a polarized local spin and conduction electrons. In this case, the singlet is no longer an eigenstate as shown by variational calculations where the splitting of the local energy Δ = ɛ _d↑ − ɛ _d↓ can be arbitrarily small. The local spin polarization generates the instability of the singlet ground state of the S = 1/2 s-d exchange model.      

Spin correlations of muons in the process of electron-positron pair annihilation e + e ? → μ+μ?

Using the technique of helicity amplitudes, the electromagnetic process e ⁺ e ⁻ → μ⁺μ⁻ is theoretically investigated in the one-photon approximation. The structure of the triplet states of the final (μ⁺μ⁻) system is analyzed. It is shown that in the case of unpolarized electron and positron the final muons are also unpolarized, but their spins are strongly correlated. Explicit expressions for the components of the correlation tensor of the final (μ⁺μ⁻) system are derived. The formula for the angular correlation at the decays of final muons μ⁺ and μ⁻, produced in the process e ⁺ e ⁻ → μ⁺μ⁻, is obtained. It is demonstrated that spin correlations of muons in the process of electron-positron pair annihilation have the purely quantum character, since one of the incoherence inequalities for the correlation tensor components is always violated. The additional contribution of the weak interaction of lepton neutral currents through the virtual Z ⁰ boson is considered; it is established that, taking into account the weak interaction, the qualitative character of the muon spin correlations does not change.     

On the spin correlations of muons generated in the annihilation process e + e ? → μ+μ?

Using the technique of helicity amplitudes, the electromagnetic process e ⁺ e ⁻ → μ⁺μ⁻ is theoretically investigated in the one-photon approximation. The structure of the triplet states of the final (μ⁺μ⁻) system is analyzed. It is shown that in the case of unpolarized electron and positron the finalmuons are also unpolarized, but their spins are strongly correlated. Explicit expressions for the components of the correlation tensor of the final (μ⁺μ⁻) system are derived. The formula for the angular correlation at the decays of final muons μ⁺ and μ⁻, produced in the process e ⁺ e ⁻ → μ⁺μ⁻, is obtained. It is demonstrated that spin correlations of muons in the process of electron-positron pair annihilation have the purely quantum character, since one of the incoherence inequalities for the correlation-tensor components is always violated. The additional contribution of the weak interaction of lepton neutral currents through the virtual Z ⁰ boson is considered; it is established that, taking into account the weak interaction, the qualitative character of the muon spin correlations does not change. The text was submitted by the authors in English.     

The emission band system c2 Σ + — x2 Π of NH+

Five red degraded bands belonging to theC ² Σ ⁺ —X ² Π system of NH⁺ were excited in a mild condensed discharge through flowing ammonia and were photographed on a 3.4 meter Ebert grating spectrograph at a dispersion of 2.5 A/mm. The rotational analyses of these bands enabled us to evaluate the vibrational and rotational constants accurately. The rotational energy levels of theΠ ⁺ andΠ ⁻ levels of theν=0 and 1 levels of the ground state,X ² Π, were fitted in James expression using two sets of rotational constants. The perturbations observed in theX ² Π state caused by thea ⁴ Σ ⁻ state were examined in greater detail.     

Experimental determination of the rate constant for spin exchange in collisions of polarized metastable helium atoms with ground-state cesium atoms

The rate constant for spin exchange in a system consisting of a metastable helium atom and an alkali-metal atom is determined. An experiment on optical orientation of atoms established that the rate constant for spin exchange in a collision of a metastable 2³ S ₁ helium atom with a cesium atom in the 6² S _1/2 ground state equals (2.8±0.8)×10⁻⁹ cm³ s⁻¹. The rate constant for chemoionization of cesium atoms by metastable helium atoms was determined at the same time to be (1.0±0.3)×10⁹ cm³s⁻¹. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 3, 145–148 (10 August 1997)     

Influence of two-particle excited states on the interatomic exchange interaction in La<Subscript>2</Subscript>CuO<Subscript>4</Subscript>

The effective spin Hamiltonian for undoped cuprates is constructed in the framework of the realistic multiband p-d model with the parameters calculated from first principles. The exchange interaction parameter is defined as the sum of the antiferromagnetic and ferromagnetic contributions, which are determined by the two-hole triplet terms. The ferromagnetic and antiferromagnetic contributions of the excited terms compensate each other to a large extent. It is shown that the antiferromagnetic contribution of the two-hole ground singlet ¹ A _1g to the exchange interaction is dominant. Original Russian Text. V.A. Gavrichkov, S.G. Ovchinnikov, 2008, published in Fizika Tverdogo Tela, 2008, Vol. 50, No. 6, pp. 1037–1041.     

Electron collisions with the BeH<Superscript>+</Superscript> molecular ion in the R-matrix approach

The R-matrix method is used to study electron collisions with the BeH⁺ molecular ion. The diatomic version of the UK Molecular R-matrix codes is used and a configuration-interaction calculation is first performed for the BeH⁺ target to obtain its potential energy curves for 19 lowest singlet and triplet states. Scattering calculations are then done to yield excitation and rotational excitation cross sections in the energy range 0 − 14 eV. Additionally we also obtain bound states of BeH and their quantum defects at the BeH equilibrium bond length 2.5369a ₀. Resonance positions and widths for Feshbach resonances in the e-BeH⁺ system are also obtained and presented at the equilibrium bond length 2.5369a ₀.     

Calculation of the quenching rate constants for electronically excited singlet molecular nitrogen

The quenching rate constants for the singlet states (a′)⁽¹⁾Σ _u ⁻ (v = 1−17), a ⁽¹⁾Π _g (v = 0−14), and w ⁽¹⁾Δ _u (v = 0−13) of molecular nitrogen colliding with an N₂ molecule are calculated using quantum-chemical approximations. It is shown for the first time that both the intramolecular and intermolecular processes of electronic excitation transfer are significant for these states. Calculated rate constants are in satisfactory agreement with experimental data.     

Calculation of adiabatic potentials of Li<Subscript>2</Subscript><Superscript>+</Superscript>

We report adiabatic potential energy curves of the Li₂ ⁺ molecule. Our curves are tabulated according to internuclear distance from 2 a₀ to 100 a₀. We compare our theoretical results with the ones calculated by other authors and potential energy curves derived from experiments. For the ground state and 17 excited states we calculate spectroscopic parameters and compare them with parameters obtained by other authors. For the first time we present three new minima for 3²Σ_u ⁺, 4²Σ_u ⁺ and 2²Π_g excited states. In our approach we use the configuration interaction method where only the valence electrons of Li atoms are treated explicitly. The core electrons are represented by pseudopotential. All calculations are performed by means of MOLPRO program package.     

Radiative lifetimes of the NaRb C(3)1Σ+ state: experiment and theory

Radiative lifetimes for 2≤v^′≤44 rovibronic C¹Σ⁺ state levels of NaRb and quenching collision cross-sections with Rb atoms have been directly measured in a thermal cell by detecting time resolved laser induced fluorescence after pulsed excitation. Many body multipartitioning theory was applied to calculate C¹Σ⁺-X¹Σ⁺ and C¹Σ⁺-A¹Σ⁺ transition dipole moments. The relevant ab initio matrix elements were converted to the C¹Σ⁺ state radiative lifetimes. The strong spin-orbit A¹Σ⁺∼ b³Π coupling effect on the total C → A transition probabilities and lifetimes of the C¹Σ⁺ state is discussed. The measured radiative lifetimes show a decrease from 61 to 34 ns as the v^′ values increase, the results being in good agreement with calculations. The averaged collisional quenching cross-section value σ=(3±1)×10^-14 cm² was determined for NaRb (C¹Σ⁺) + Rb collisions from the Stern-Volmer plots.     

Quantum-chemical modeling of structural,electronic, and spin characteristics of NV centers in nanostructured diamond: Surface effect

The effect of the surface of diamond on atomic, electronic, and spin properties of diamond nanocrystals containing single nitrogen-vacancy defects ([NV]⁻ centers) is studied. The surface was modeled with clusters C₃₃H₃₀[NV]⁻, C₆₆H₇₂[NV]⁻, which were constructed based on bulk clusters C₃₃H₃₆[NV]⁻ and C₆₉H₈₄[NV]⁻, respectively. In all cases, clusters in the triplet state S = 1 are considered with the cluster charge being −1. The geometric structure of clusters is optimized using the principle of minimization of the total energy of the system; then, the electronic and spin characteristics of clusters are calculated by the density functional theory. The isotropic and anisotropic hyperfine interaction constants of the electron spin of the NV center with the nuclear spin of the nitrogen atom and ¹³C atoms located at different sites in the cluster are calculated. It is found that, in contrast to bulk clusters with [NV]-centers in which the spin density is mainly localized at the three carbon atoms that are the nearest neighbors of the vacancy of the center, upon arrangement of the NV center in the immediate proximity to the surface, the spin density is redistributed such that it is mainly localized at the three carbon atoms that are the nearest neighbors of the nitrogen atom of the center and at C atoms that form the first atomic layer of the (111) surface of the nanocrystal.     

Electron-vibrational energy exchange in collisions of Ar atoms in the 3P2 metastable state with N2(X1S g+ ) molecules

Rate constants for electron-vibrational energy exchange Ar(³ P ₂) + N₂(X ¹Σ _g ⁺, ν = 0) → Ar(¹ S ₀) + N₂(C ³Π _u , ν′), where ν′ = 0, 1, 2, were calculated. Calculations were performed taking into account the presence of a resonance in electron scattering by N₂(X ¹Σ _g ⁺). As a result, the interaction of Ar(³ P ₂) with N₂(X ¹Σ _g ⁺, ν = 0) was characterized by attraction and, in the end, intersection of electron-vibrational potential surfaces correlating with Ar(³ P ₂) + N₂(X ¹Σ _g ⁺, ν = 0) and Ar(¹ S ₀) + N₂(C ³Π _u , ν′) at interparticle distances of 2.5–3.5 ?. Exchange interaction at which electron-vibrational transitions in the region of intersection of electron-vibrational transitions in the region of intersection of electron-vibrational potential surfaces accompanied by spin exchange were induced was calculated by the asymptotic method. The rate constants determined at 300–600 K were on the order of 10⁻¹¹−10⁻¹² cm³/s and weakly increased as the temperature grew. Mainly the C ³Π _u , ν′ = 0 state of the N₂ molecule was populated. The calculation results were in satisfactory agreement with the experimental data obtained at 300 K.