Na2 Molecule Research Articles

Dissociative Ionization of Na2 via Repulsive Rydberg States: Elucidating Femtosecond Dynamics with Nanosecond Lasers

We have studied the dissociative ionization behavior of Na2 molecules using two-color, three photon optical-optical double resonance enhanced excitation via the A(1)Sigma(u)(+) and the 2(1)Pi(g) states. Excess energy ranges from about 150 to about 1500 cm(-1) above threshold for dissociative ionization into ground-state Na and Na(+). Slow atomic Na(+) fragments and Na2(+) molecular ions are detected using a linear time-of-flight spectrometer operated in low field extraction, core sampling mode. To explain the observed energy dependence of the Na(+)/Na2(+) branching ratio, we introduce a semiclassical model for the underlying decay dynamics. Franck-Condon overlap densities for bound-free transitions starting in 2(1)Pi(g) vibrational levels indicate that atomic Na(+) fragments are primarily produced via Rydberg states, with principal quantum number n between 5 and 12, converging to the repulsive 1(2)Sigma(u)(+) first excited-state potential of Na2(+). Dynamics along these Rydberg curves involves competition between electronic (autoionizing) and nuclear (dissociative) degrees of freedom. Within the model, the autoionization lifetime tau auto is the only one free parameter available to fit calculated Na(+)/Na2(+) branching ratios as a function of excess energy to the observed values. The lifetime is assumed to be the same multiple c of the Bohr period of each Rydberg potential. A chi(2)-minimization procedure yields, for the range of principal quantum numbers involved, a most likely value of c = 1.5 +/- 0.3, implying that on average the Rydberg electron completes only 1 to 2 orbits before interaction with the excited core electron leads to autoionization.

Accurate studies of dissociation energies and vibrational energies on alkali metals

This paper studies full vibrational spectra {Ev} and molecular dissociation energies De by using conventional least-squares (LS) fitting and an algebraic method (AM) proposed recently for 10 diatomic electronic states of 7Li2, Na2, NaK and NaLi molecules based on some known experimental vibrational energies in a subset [Evexpt] respectively. Studies show that: (1) although both the full AM spectrum {EvAM} and the LS spectrum {EvLS} can reproduce the known experimental energies in [Evexpt], the {EvAM} is superior to the {EvLS} in that the high-lying AM vibrational energies which may not be available experimentally have better or much better accuracy than those LS counterparts in {EvLS}, and so is the AM dissociation energy DeAM; (2) the main source of the errors in the data obtained by using the LS fitting is that the fitting which is just a pure mathematical process does not use any physical criteria that must be satisfied by the full vibrational spectrum, while the AM method does. This study suggests that when fitting or solving a physical equation using a set of source data, it is important not only to apply a proper mathematical tool, but also to use correct physical criteria which measure the physical properties of the data, kick out those data having bigger errors, and impose conditional convergence on the numerical process.

Theoretical Investigation of Femtosecond-Resolved PhotoelectronSpectrum of Na2 Molecules

Effect of laser fields on Na2 interaction potentials is studiedby calculating the time-resolved photoelectron spectrum (TRPES) withthe time-dependent wave-packet method. It is shown that thephotoelectron spectrum at different delay times reflects the populationin different electronic states. We inspect the periodicity ofvibrational motion in neutral states, and map the vibrationalwave-packet propagation in corresponding internuclear coordinate.

Suppression of Decoherence in a Wave Packet via Nonlinear Resonance

We propose a simple approach for suppressing decoherence of a wave packet excited in an anharmonic oscillator. We show that when a resonant external field forces the oscillator to follow the driving force, motion around the resonant trajectory inside a stable resonant island can be made almost completely immune to the environment. As an example, we study suppression of decoherence due to coupling to thermally populated rotations in vibrational wave packets in a Na2 molecule.

New analysis of the D(4)1Π u state of Na2 using polarization labelling spectroscopy

The D(4)1Π u state in the Na2 molecule is experimentally investigated by using the polarization labelling spectroscopy technique. The D band system is observed under rotational resolution providing information of rovibrational levels in the D state up to v,′ = 72 (that covers 85% of the potential well depth). A set of Dunham coefficients is deduced to fit the spectroscopic data and the potential curve of the D state is constructed using the Inverted Perturbation Approach method.

A Study of Perturbations of the A1Σu + State of Na2

High resolution Fourier spectrometry techniques have been used to study the A1Σ+ u state, which is perturbed by the b3Πu state of the Na2 molecule. This study was achieved by means of exciting the B1Πu state from the X1Σ+ g ground state by 4880 Å and 4965 Å lines of an Ar+ laser. The excitation is followed by collisional transfer energy produced between B1Πu and (2)1Σ+ g states ν, which led to the population of the vibrational levels of the (2)1Σ+ g state v. The analysis of the collision-induced system (2)1Σ+ g −A1Σ+ g enabled us to study, in detail, the perturbations of 11 vibrational levels from v = 0 to v = 10 of the A1Σ+ u state.

Controlling Population Transfer and Dissociation Rate ofNa2 Molecules with Ultra-Short Intense Laser Pulses

A scheme used for controlling the population transfer and thedissociation rate of Na2 molecules is described by usingthe quantum wavepacket dynamical method. It is theoretically shown thatthe population transfer and the dissociation rate of Na2molecules can be controlled by pump and probe laser pulses withappropriate widths of pulses, sequence and intensities.

Studies on full vibrational spectra and dissociation energies of some diatomic molecular electronic states using algebraic approaches

An algebraic energy method (AEM) is suggested as an alternative theoretical approach to generate molecular dissociation energy D e 's. The AEM is used to evaluate accurate full vibrational energy spectra {E υ} and D e in this study for 14 diatomic electronic states of Li2, Na2, Rb2, K2 and Sr2 molecules: the 11Π g , , 23Πg, 13Δg and 23Δg states of Li2; the , , 13Δg and 23Δgstates of Na2; the and states of K2; the and 11Πg states of Rb2 and the state of Sr2 molecule. Studies show that present vibrational energies in the full spectrum {E υ} are accurate, and the AEM D e have an accuracy better than one percent when they are compared with experimental dissociation energies. The AEM can generate reliable D e 's for electronic states whose molecular dissociation energies may be difficult to obtain experimentally and/or theoretically.

Absorption spectrum of Na–K–He mixture: experiment and theory

We present experimental and theoretical studies of the absorption spectrum of Na–K–He mixture. Semiclassical spectral simulations in the 400–850 nm wavelength range were performed, on the basis of available interaction potential curves for Na2, K2, NaK, NaHe and KHe molecules. Calculated absorption spectra were analysed and compared to the experimental absorption spectrum of Na–K–He mixture generated in a gravitational heat pipe oven.

Control of Population Flow in Coherently Driven Quantum Ladders

A technique for adiabatic control of the population flow through a preselected decaying excited level in a three-level quantum ladder is presented. The population flow through the intermediate or upper level is controlled efficiently and robustly by varying the pulse delay between a pair of partly overlapping coherent laser pulses. The technique is analyzed theoretically and demonstrated in an experiment with Na2 molecules.

Studies on the full vibrational energy spectra and molecular dissociation energies for some electronic states of Na2 molecule

Modern experimental methods or accurate quantum theory methods usually may obtain a vibrational energy subset［Ev］ containing m energies, but it may be very difficult to have all the excited highlying vibrational energies f or the electronic states of most diatomic molecules. Since the full vibrational spectrum and the molecular dissociation energies of the electronic states of Na 2 molecule are very important in many studies and applications, the vibrationa l spectroscopic constants and the full vibrational spectra of some electronic st ates of Na2 molecules are acqnired using the algebraic method (AM), and the di ssociation energy (DE) of these states are obtained using the algebraic energy m ethod (AEM). The results show that AM can give accurate vibrational spectroscopi c constants and correct full vibrational energy spectrum {Ev} from experim ental vibrational energy subset［Ev］, and the molecular dissociation energies obtained using the AEM have much better accuracy than those generated u sing the vibrational constants given in the literature. The AEM can give reliabl e values of the dissociation energies for some excited electronic states whose D E may not be available in the literture.

Femtosecond quantum dynamics of diatomic molecules in optically dense gaseous media

A consistent quantum theory of a two-pulse pump-probe experiment in the femto-and picosecond spectroscopy of diatomic molecules is developed. The theory aims at the use of weak quantum femtosecond light pulses to excite molecular coherence. It is suggested that the experiment be realized using a double-frequency excitation scheme that is feasible for Na2 molecules. On the basis of the theory developed, the luminescence signals are calculated at different temperatures and different optical densities of the medium for the time range from 100 fs to ~ 100 ps. The results obtained show the presence of a strong dependence of the time and frequency spectra of a luminescence signal on the optical density of the medium at temperatures from 50 to 300 K. The proposed approach makes it possible to use the quantum coherence properties of optically dense media for more detailed study of the vibronic dynamics of diatomic molecules, in particular, detection of weak optical transitions.

Sensitivity of the dynamics of Na + Na $\mathsf{_2}$ collisions on the three-body interaction at ultralow energies

We have studied the quantum dynamics of collisions between spin-stretched Na atoms and Na2 molecules. Cross-sections and rate coefficients for vibrational relaxation of Na2(v,j = 0) have been computed in the 1 nK-0.1 mK energy range using an accurate time-independent method based on hyperspherical coordinates. The complex scattering length and the extension of the Wigner region have been determined. A detailed study of the sensitivity of collisional quantities on the three-body interaction at short distance has been performed. They are very sensitive to three-body effects for the vibrational state v = 1 of Na2. Rotational distributions have also been calculated and show a more pronounced sensitivity on the three-body interaction, even for v = 2 and 3.

Determination of the parameters of the potential well of a diatomic molecule with the use of the experimental spectrum of an electronic transition to a repulsive branch of the state under study

It is shown that the lack of information on the rotational structure of the vibrational terms of a diatomic molecule in the problem of determination of the potential well of the molecule can be compensated by information on the intensity distribution in the spectrum of a bound-free transition to a repulsive branch of the state under study. The accuracy characteristics of the method proposed are studied on the example of a potential whose parameters are close to those of the state a3Σu+ of the Na2 molecule.

Velocity redistribution of excited atoms by radiative excitation transfer. II. Theory of radiation trapping in collimated beams

We have developed a theory of resonance radiation imprisonment in collimated atomic beams. Treating the integral master equation describing imprisonment as a generalized wave (Schrödinger) equation and using the geometrical quantization technique for its solution, we obtained analytical representations for the effective radiative lifetime, mean scattering number, and trapping factors. We apply this theory to explain the recent observation of a dramatic velocity redistribution of excited atoms by radiative excitation transfer after the photofragmentation of Na2. In this process, the fast Na(3p) photofragments transfer their excitation energy efficiently via radiation to the abundant Na(3s) atoms from the primary particle beam. The influence of the hyperfine splitting of the ground state of Na atoms on this process is discussed. The ratio of the number of Na(3p) atoms produced by the radiative excitation transfer to the number of Na(3p) photofragments was found to be 0.13 and 0.19 for photodissociation of Na2 molecules in the vibrational levels v″=17 and v″=23, respectively. This is in good agreement with the corresponding experimental values of 0.16 and 0.22.

Observation of the long-range potential well of the $\mathsf{(6)^1\Sigma^+_g(3s+5s)}$ state of Na $\mathsf{_2}$

We report on the first observation of the outer well of the \((6)^1\Sigma^+_g\) state of Na2 molecule. The levels are populated in a molecular beam experiment with a three step laser excitation. The fact that these levels predissociate allows an almost background free detection by the appearance of atomic fluorescence. With this method almost all vibrational levels of the outer well are observed. The corresponding predissociation line widths show an oscillating behaviour. The theoretical description of the predissociation is presented in the framework of mapped Fourier grid Hamiltonian representation with optical potential, involving two coupled electronic states. Combining the spectroscopic information on energy positions and predissociation widths, a Rydberg-Klein-Rees potential curve is given for the outer well. Such a state could offer a reliable path for photoassociation of cold Na atoms and formation of ultracold Na2 molecules.

Velocity redistribution of excited atoms by radiative excitation transfer. I. Experimental demonstration by photodissociation of Na2 and field-free imaging

Photodissociation of state-selected sodium molecules, Na2(X 1Σg+,v″)+hν→Na2*(B 1Πu)→Na*(3p3/2)+Na(3s1/2) has been studied theoretically and experimentally using a novel “field-free” ion imaging design. The experiment uses a supersonic Na/Na2 beam in combination with the stimulated Raman adiabatic passage technique to prepare Na2 molecules in selected rovibronic levels of the electronic ground state. The Na(3p3/2) fragments are photoionized (or excited to high Rydberg states) in a permanently field-free reaction zone. The fragments enter the ion optics because of the flow velocity of the beam and are focused onto a position sensitive detector, which provides an energy resolution of about 50 meV. The measured anisotropic photofragment angular distributions reflect the alignment of the molecules prior to dissociation and are well explained by the anisotropic nature of the photodissociation by polarized laser light. The measured images show not only the expected relatively fast photodissociation fragments, but also the efficient formation of slow Na(3p3/2) atoms. Fast and slow refer to the atomic velocity relative to the center of-mass of the dissociating molecule. The ratio of the numbers of slow atoms and fast photofragments is 0.16 and 0.22 for the dissociation of Na2 from levels v″=17 and v″=23, respectively. Several models are analyzed to explain the observations. Calculations show that the dramatic velocity redistribution is caused by radiation trapping: the excitation is efficiently radiatively transferred from the fast Na(3p) photofragments to the abundant Na(3s) atoms from the primary beam, whereby the hyperfine splitting of the 3s state must be taken into account. Analytical formulas describing this mechanism show a ratio of slow to fast Na(3p) atoms of 0.13 for v″=17 and 0.19 for v″=23, which is in very good agreement with the experimental observations.

Photodissociation and photoionization of sodium coated C $_\mathsf{60}$ clusters

(C60) m Na n clusters are produced in a tandem laser vaporization source and analyzed by photoionization and photofragmentation time-of-flight mass spectroscopy. At low sodium coverage, the special behavior of (C60) m=1,2Na n clusters $(n\leq 6m)$ is consistent with a significant electron transfer from the first six adsorbed atoms towards each of the C60 fullerenes and an ionic-like bonding in this size range. However, the stability of the (C60)Na3 + cation is found much more pronounced than the one of (C60)Na7 + predicted to be a magic size under the hypothesis of a full charge transfer from the metal atoms to the C60 molecule. When more sodium atoms are present, metal-metal bonds tend to become preponderant and control the cluster properties. Relative to the number of sodium atoms, an odd-even alternation in their stability is explained by the high dissociation rates for even-numbered clusters. The even clusters evaporate neutral sodium atoms whereas odd ones prefer to evaporate Na2 molecules. The hypotheses for the growth of a sodium droplet that does not wet the fullerene surface or for the formation of a concentric metallic layer are discussed in the light of this study.

Photoassociation of Ultracold Sodium Atoms

Using ultra-cold atoms a new technique of photoassociation spectroscopy has been developed. The technique has an unprecedented resolution and can be used to obtain high-resolution data on singly and doubly excited states of diatomic molecules. We describe the principle of the technique and show results for one specific case, namely the Na2 molecule.

Study of Electron Impact Ionization Cross-sections of Sodium-containing Molecules.

Electron impact ionization is a common way to provide positive ions for mass spectrometry. For most of molecular vapor species, however, experimental values of their electron impact ionization cross-sections are so limited that theoretic estimations become necessary. It is found that classic model such as additive rule or its modified version is no longer valid near the ionization threshold. Knowledge in this area is important for alkaline metals like sodium because their molecules may reach the maximum cross-section just a few eV above the ionization potential and easily crack in higher incident energies. A Binary-Encounter-Bethe (BEB) model developed by NIST was employed to calculate the cross-sections of NaO, NaOH, Na2, and Na2O molecules. The total ionization cross-section is computed from partial cross-sections of molecular orbitals. Gaussian and GAMESS code were employed to calculate the necessary molecular orbital parameters in the ground state. Calculated cross-sections were plotted as a function of electron impact energy. Reliability of the data predicted by BEB model was investigated by measuring corresponding ionization efficiency curves for some of the molecules. It was found that I(E)/Imax is generally equal to σ(E)/σmax within 15% in the testing range from 5 to 30 eV for sodium-containing molecules. It indicates that the BEB predictions seem correct at low electron incident energies.