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     

Cold rubidium molecule formation through photoassociation: A spectroscopic study of the 0 g - long-range state of 87 Rb 2

We report the detailed analysis of translationally cold rubidium molecule formation through photoassociation. Cold molecules are formed after spontaneous decay of photoexcited molecules from a laser cooled atomic sample, and are detected by selective mass spectroscopy after two-photon ionization into Rb ₂ ⁺ ions. A spectroscopic study of the 0 _g ^- (5 S + 5 P _3/2 ) pure long-range state of ⁸⁷Rb₂ is performed by detecting the ion yield as a function of the photoassociation laser frequency; the spectral data are theoretically analyzed within the semiclassical RKR approach. Molecular ionization is resonantly enhanced through either the 2 ³ Π _g or the 2 ³ Σ ⁺ _g intermediate molecular states. Some vibrational levels of the latter electronic state are observed and assigned here for the first time. Finally, cold molecules formation rates are calculated and compared to the experimentally measured ones, and the vibrational distribution of the formed molecules in the a ³ Σ ⁺ _u ground triplet state is discussed. Received 18 January 2001 and Received in final form 10 April 2001     

Li2分子自旋一致激发态a3Σ+u和b3Πu的分析势能函数的从头算

使用对称性匹配簇-组态相互作用方法首次计算了Li₂分子自旋一致激发态a³Σ⁺_u和b³Π_u的离解能、平衡几何及其谐振频率。使用最小二乘法、利用Murrell-Sorbie函数形式拟合出了Li₂分子三重态的第一激发态a³Σ⁺_u 和第二激发态b³Π_u的完整势能函数，并计算了这两个态的光谱常数 (B_e, α_e, ω_e 和 ω_eχ_e) 和力常数 (f₂, f₃和f₄)。得到了Murrell-Sorbie函数形式既适用于基态、又适用于激发态的结论。将计算得到的激发态（a³Σ⁺_u和b³Π_u）的离解能、平衡几何及其谐振频率与实验结果及其它理论计算结果进行了比较。从比较的结果中可以清楚地看出，本文的计算结果在计算精度方面有很大的改进。     

Photoelectron spectroscopic assignment of symmetry to the ground state and first excited state of the 1,4-cyclohexadiene radical cation

The empirical correlation of the photoelectron spectra of 1,4-cyclohexadiene (molecule 4), 1, 4, 5, 8-tetrahydronaphthalene (molecule 5), 1, 4, 5, 6, 9, 1 0-hexahydroanthracene (molecule 6), and 1, 4, 5, 6, 7, 10, 11, 12-octahydronaphthacene (molecules 6) proves that the electronic ground state of these molecules is ²B_1u, assuming that they have D_2h symmetry. In particular this confirms previous predictions for 1,4-cyclohexadiene (molecule 4), for which the “inverted” orbital sequence 2b_1u(π) above lb_3g(π) had been proposed under the assumption that hyperconjugative “through-bond” interaction dominates the “through-space” interaction of the two semi-localized π-orbitals.     

Long-range Rydberg-Rydberg interactions and molecular resonances

We present a detailed theoretical treatment to describe the lineshape of molecular resonances in a cold dense gas of rubidium Rydberg atoms. Molecular potentials in Hund's case (c) are calculated by diagonalization of an interaction matrix. We show how the strong ℓ-mixing due to long-range Rydberg-Rydberg interactions can lead to resonances in excitation spectra. Such resonances were first reported in [S.M. Farooqi et al., Phys. Rev. Lett. 91, 183002 (2003)], where single UV photon excitations from the 5s ground state occurred at energies corresponding to normally forbidden transitions or very far detuned from the atomic energies. Here, we focus our attention on resonances at energies corresponding to excited atom pairs (n - 1)p_3/2+(n + 1)p_3/2. Very good agreement between the theoretical and experimental lineshapes is found.     

Additional symmetry for the electronic shell in its ground state and many-electron effects

The additional symmetry for the properties related to the ground state of the atom is considered taking into account many-electron effects. Calculations of the I _4f, I _3d,I _2p,I _3p binding energies, 4f ^N-15d - 4f^N system differences and 2p, 3p electron affinities in the second order of perturbation theory and in the configuration interaction approximation have been performed for the ground configurations with one open shell. The analysis of separate many-electron corrections for these quantities and their variation along the sequences of atoms and ions shows that the main corrections maintain the considered symmetry. Received 18 January 1999 and Received in final form 17 July 1999     

Calculation of the elastic scattering properties for cold and ultracold 39K atoms in a triplet state

The elastic scattering properties for collisions between cold and ultracold 39K atoms in a triplet state are investigated. Based on the recent theoretical and experimental results, the improved hybrid potential is presented for a triplet α3∑u^＋ ground state of K2. Our calculated value of the s-wave scattering length a by using the Numerov method for the triplet state is 79.578α0 and found to be in good agreement with the previous ones. The numbers of bound states are supported by the molecular potential. Pronounced shape resonances appear for the l = 3 partial waves for the α3∑u^＋ state. Furthermore, the s-wave scattering cross section, the total cross section and energy positions of shape resonances for the α3∑u^＋ state are calculated.     

Surface coverage studies of the icosahedron by Li using density based molecular dynamics

Density based molecular dynamics has been used to investigate the ground state structures of heterogeneous binary clusters Al₁₃Li_n, n = 1, 2, 3, 4, 10, 19, 20, 21. Some of these structures have also been investigated by full Kohn-Sham based calculations. Our earlier investigations have shown that in the Al-Li cluster, the ground state configurations are the ones where the Al atoms form a core around which the Li atoms form a “cage”. In the present work, we have chosen the well-known Al₁₃ icosahedron as the surface over which we study the evolution of the surface coverage as the number of Li atoms increases. On the basis of the earlier work, we expect that the Al₁₃Li₂₀ cluster would be the most stable and indeed our simulations do yield such a novel fivefold symmetric stable structure formed out of purely metal atoms. This icosahedral substrate is also used to study the coverage of the aluminum surface by lithium atoms. For a small number of Li atoms, these studies suggest that the Li-Li dimerisation is not particularly favored. Received: 24 October 1997 / Revised: 7 April 1998 / Accepted: 29 June 1998     

Ab initio calculation of excited state dipole polarizability - Application to the first 1, 3 Σ + g,u states of Li 2

Firstly, imaginary frequency-dependent dipole polarizabilities of Li in its ² S ground state and the first ² P excited state are calculated from a time-dependent gauge-invariant method using effective core pseudo-potentials and the multi-configuration one-electron wave function. C₆ dispersion coefficients of the 2 s + 2 s and 2 s + 2 p dissociations are deduced and also compared with all-electron values. Then, static polarizabilities of Li₂ in its ground and first excited ^{1, 3} Σ ⁺ _g,u states are obtained at interatomic distance corresponding to the energy minimum of each state. Received 10 May 2001 and Received in final form 14 September 2001     

Formation of Cs molecules via Feshbach resonances stabilized by spontaneous emission: theoretical treatment with the Fourier grid method

This paper proposes a general method to investigate Feshbach resonances in atomic collisions similar to Cs(6 s ) + Cs(6 p ) in the thermal or cold regime. In order to compute the predissociation widths of the C ¹ Π _u (6 s + 5 d ) bound vibrational levels of Cs₂, coupled both with the (2) ³ Σ ⁺ _u (6 s + 6 p ) continuum and with the (2) ³ Π _u (6 s + 5 d ) vibrational series, a Fourier grid method is implemented, with an optical potential. A convenient way of optimizing the latter is proposed. A large number of resonances are found and calculations of their cross-sections for stabilization into ground state molecules show that the rate may be important. This confirms the interpretation of Lintz and Bouchiat [Phys. Rev. Lett. 80, 2570 (1998)] who observed dimer formation in cell experiments. Possible generalization to the cold regime relies on the possibility to tune the position of a resonance to coincide with the maximum of the collisional energy distribution. Received 14 February 2002 Published online 28 June 2002     

Photoassociative spectroscopy of the long-range state

The photoassociative spectroscopy of the Cs₂ 0 g ^- long-range molecular state dissociating into the asymptote is performed, using cold cesium atoms in a vapor-cell magneto-optical trap (MOT). Vibrational levels from v =0 to v =132 are identified, and their rotational structure is well resolved up J =8 for levels below v =74. These data are analyzed in terms of the Rydberg-Klein-Rees (RKR) procedure, and correspond to 99.6% of an effective potential curve with a minimum at ? and a cm^-1 depth. Both ab initio calculations and simple model estimations predict a double-well structure for this potential curve, which cannot be reproduced presently by the RKR approach but which is confirmed by the presence of giant structures in the spectrum. The 1_u()long-range state is also observed for the first time in Cs₂.     

Prospects for the formation of ultracold ground state polar molecules from mixed alkali atom pairs

Photoassociation rates of mixed cold alkali atom pairs and formation rates of cold heteronuclear alkali dimers in their ground state are computed within an approach where the wave functions are calculated exactly, and the laser field is treated as a perturbation. These rates are predicted to have the same magnitude for all heteronuclear species involving either Rb or Cs atoms. Moreover, these rates are found slightly smaller than, or similar to, the same rates for Cs₂ molecules, which is encouraging for future experiments. We studied the specific case of the photoassociation into excited molecular states coupled with spin-orbit interaction, emphasizing the role of the so-called resonant coupling in the formation of stable ultracold molecules with low vibrational levels. The comparison with recent experimental results on RbCs photoassociation and cold molecule formation show their reasonable agreement with our calculations.Received: 2 July 2004, Published online: 23 November 2004PACS: 32.80.Pj Optical cooling of atoms; trapping - 33.20.Tp Vibrational analysis - 33.70.Ca Oscillator and band strengths, lifetimes, transition moments, and Franck-Condon factors     

Frequency measurements in the b <Superscript>3</Superscript>Π(0<Subscript>u</Subscript><Superscript>+</Superscript>) - X <Superscript>1</Superscript>Σ<Subscript>g</Subscript><Superscript>+</Superscript> system of K<Subscript>2</Subscript>

Absolute transition frequencies of the b ³Π(0_u ⁺) - X ¹Σ_g ⁺ system of K₂ were measured in a molecular beam with Lamb dip absorption spectroscopy applying a frequency comb from a femtosecond pulsed laser. Both, K atoms and K₂ molecules are present in the beam and are expected to interact by collisions. The atoms can be deflected optically out of the beam, and thus the collision rate between K atoms and K₂ molecules is changed by about an order of magnitude. The molecular transition frequencies for low collisional rate are compared with those for high one. Limits for the collisional frequency shift within the beam are determined.     

Electronic structure of lanthanide dimers

Relativistic energy-consistent small-core lanthanide pseudopotentials of the Stuttgart-Bonn variety and extended valence basis sets have been used for the investigation of some selected lanthanide dimers with open 4f shell, that is Ce₂, Pr₂ and Gd₂. Comparison is made with results of corresponding previous studies of La₂ and Lu₂ as well as to available experimental data. The trends in the molecular constants of the dimers of the lanthanide series are discussed. The ground state candidates of Ce₂(4f¹4f¹σ² _gπ⁴ _u ¹Σ⁺ _g, ¹Σ^? _u, ³Σ^? _g, ³Σ⁺ _u, ¹6_g, ³6_u) and Pr₂(4f²4f²σ² _gπ⁴ _u ⁵Σ⁺ _g, ⁵Σ^? _u, ⁵10_g) are degenerate within 20cm^?1 and have the same valence subconfiguration σ² _g π⁴ _u, which was previously found to give rise to the La₂(4f⁰4f⁰σ² _gπ⁴ _u ¹Σ⁺ _g) ground state. In the case of Gd₂ the 4f⁷4f⁷σ² _gσ¹ _uσ² _u; ¹⁹Σ^? _g ground state found previously is confirmed. The derived molecular constants are the best theoretical estimates available at present and show a satisfactory agreement with experimental data. Discrepancies in the vibrational constants of La², Ce² and Pr² are shown to be probably related to quite large Ar-matrix shifts.     

Determination of the calcium ground state scattering length by photoassociation spectroscopy at large detunings

Photoassociation spectroscopy was used to determine the s-wave scattering length of ⁴⁰Ca atoms in their electronic ground state. Vibrational levels were observed in an extended range of up to 182 GHz below the dissociation limit 4s^{2 1}S₀–4s4p ¹P₁. Thus, the frequency interval was nearly tripled, in which photoassociation was observed compared to previous measurements. The spectra were analyzed by means of quantum mechanical simulations. With the new data it was possible to resolve the discrepancy concerning the ground state scattering length presented in earlier publications [Phys. Rev. A 67, 043408 (2003); Eur. Phys. J. D 26, 155 (2003)]. An improved dipole-dipole coupling constant C₃ ^Σ = 0.52306(20) ×10³ cm^-1 nm³ is obtained.     

Multiphoton ionization of iodine atoms and CF<Subscript> 3</Subscript>I molecules by XeCl laser radiation

We report about effective ionization of iodine atoms and CF₃I molecules under the action of intense XeCl laser radiation (308 nm). The only ion fragment resulting from the irradiation of the CF₃I molecules is the I⁺ ion. We have studied the influence of the intensity, spectral composition, and polarization of the laser radiation used on the intensity of the ion signal and the shape of its time-of-flight peak. Based on the analysis of the results obtained, we have suggested the mechanism of this effect. The conclusion drawn is that the ionization of the iodine atoms by the ordinary XeCl laser with a nonselective cavity results from a three- (2 + 1)-photon REMPI process. This process is in turn due to the presence of accidental two-photon resonances between various spectral components of the laser radiation and the corresponding intermediate excited states of the iodine atom. The probability of ionization of the atoms from their ground state I(²P_3/2) by the radiation of the ordinary XeCl laser is more than two orders of magnitude higher than the probability of their ionization from the metastable state I^*(²P_1/2). The ionization of the CF₃I molecules by the XeCl laser radiation occurs as a result of a four-photon process involving the preliminary one-photon dissociation of these molecules and the subsequent (2 + 1)-photon REMPI of the resultant neutral iodine atoms.     

AlxOy(x=1—2,y=1—3)分子几何结构与稳定性的DFT研究

用密度泛函理论(DFT)的B31yp方法在6-311++g^水平上对Al_xO_y(x=1—2,y=2—3)分子的几何构型、电子结构、振动频率等性质进行了理论研究. 通过对基态结构的几何参数分析发现，它们的基态结构趋于直线或平面结构. 对基态结构的绝热电离能讨论表明，金属铝原子数一定时，氧原子数从1增加到3，其气态分子越来越稳定，铝原子数少的分子体系更稳定. 系统给出了该系列分子基态的几何参数、电子结构、光谱性质. Al₂O₃的C_2V三重态是该分子的能量最低结构. 关键词： xO_y分子')" href="#">Al_xO_y分子 密度泛函理论 结构与稳定性     

Kinematically complete final state investigations of molecular photodissociation: two- and three-body decay of laser-prepared H 3 3 s ? 2 A 1 '

We have performed kinematically complete investigations of molecular photodissociation of triatomic hydrogen in a fast beam translational spectrometer recently built in Freiburg. The apparatus allows us to investigate laser-induced dissociation of neutral molecules into two, three, or more neutral products. The fragments are detected in coincidence and their vectorial momenta in the center-of-mass frame are determined. We demonstrate the potential of the method at the fragmentation of the 3 s ² A ₁ ^′ ( N = 1, K = 0) state of triatomic hydrogen. In this state, three-body decay into ground state hydrogen atoms H+H+H, two-body predissociation into H+H ₂ (v , J), and photoemission to the H ₃ ground state surface with subsequent two-body decay are competing channels. In the case of two-body predissociation, we determine the rovibrational population in the H ₂ (v , J) fragment. The vibrational distribution of H ₂ is compared with approximate theoretical predictions. For three-body decay, we measure the six-fold differential photodissociation cross-section. To determine accurate final state distributions, the geometric collection efficiency of the apparatus is calculated by a Monte Carlo simulation, and the raw data are corrected for apparatus efficiency. The final state momentum distribution shows pronounced correlation patterns which are characteristic for the dissociation mechanism. For a three-body decay process with a discrete kinetic energy release we have developed a novel data reduction procedure based on the detection of two fragments. The final state distribution determined by this independent method agrees extremely well with that observed in the triple-coincidence data. In addition, this method allows us to fully explore the phase space of the final state and to determine the branching ratios between the two- and three-body decay processes. Received 29 March 2001     

High sensitive photoassociation spectroscopy based on modulated ultra-cold Cs atoms

In this paper, a high sensitive photoassociation spectroscopy based on modulated ultra-cold cesium atoms is reported. The cold cesium gas in the magneto-optical trap is illuminated by a photoassociation laser with red detuning 40 cm^-1 below the 6S _1/2+6P _3/2 dissociation limit and photoassociation to the excited state ultra-cold molecules is observed. The rotationally bound levels of 0_g ^- state are well resolved using the lock-in detection. The 0_g ^-, 1_g and 0_u ⁺ long range states which connect to this dissociation limit are measured. The long-range dipole–dipole interaction constants are determined through a fit of the experimental energy levels. PACS 33.15.Mt; 33.20.Vq; 32.80.Pj     

Temperature dependence of Rb2 molecule formation rate constant in a magneto-optical trap

In this paper, we report the measurement of Rb₂ molecule formation rate constant due to a two body process in a magneto-optical trap as a function of the sample temperature. The ground state molecules are detected by two-photon ionization, through the intermediate a ³Σ _u ⁺ → 2³Π _g molecular band. Our results show that the Rb₂ molecules formed in the MOT could be due to a wave shape resonance, which enhances the molecule formation rate. This effect may be used to enhance the molecule production; and therefore it maybe important to future experiments involving production and trapping of cold ground state molecules.