1
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Nakatsuji H, Nakashima H. Exact Theory Applied to the Lithium Atom. J Chem Theory Comput 2024. [PMID: 39225699 DOI: 10.1021/acs.jctc.4c00884] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/04/2024]
Abstract
The free complement (FC) theory for solving the scaled Schrödinger equation (SSE) was applied to the Li atom for calculating the exact wave functions, the energies, and the various properties of the ground doublet S and excited P states. The SSE is equivalent to the Schrödinger equation (SE) but does not have the divergence difficulty of the variational equation of the SE. Because the Li atom is a three-electron system, the variational exact FC calculations for solving the SSE are possible using the function g = 1 - exp(-γr) as the "correct" scaling function of the SSE. The "reasonable" scaling function g = r was also used as comparative calculations. We performed variational calculations to the order eight of the FC theory and could obtain essentially exact solutions of the SSE or SE with the "correct" g function of the FC theory. We report here the values of the exact energy, spin density, electron density, and electron-nuclear and electron-electron cusp values of the doublet S and P states. They agreed very well with the experimental values and the best theoretical values presented by Drake and collaborators. This is a simple example that the exact theory gives the exact solutions.
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Affiliation(s)
- Hiroshi Nakatsuji
- Quantum Chemistry Research Institute, Kyoto Technoscience Center 16, 14 Yoshida Kawaramachi, Sakyo-ku, Kyoto 606-8305, Japan
| | - Hiroyuki Nakashima
- Quantum Chemistry Research Institute, Kyoto Technoscience Center 16, 14 Yoshida Kawaramachi, Sakyo-ku, Kyoto 606-8305, Japan
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2
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Beutel M, Ahrens A, Huang C, Suzuki Y, Varga K. Deformed explicitly correlated Gaussians. J Chem Phys 2021; 155:214103. [PMID: 34879658 DOI: 10.1063/5.0066427] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Deformed explicitly correlated Gaussian (DECG) basis functions are introduced, and their matrix elements are calculated. All matrix elements can be calculated analytically in a closed form, except the Coulomb one, which has to be approximated by a Gaussian expansion. The DECG basis functions can be used to solve problems with nonspherical potentials. One example of such potential is the dipole self-interaction term in the Pauli-Fierz Hamiltonian. Examples are presented showing the accuracy and necessity of deformed Gaussian basis functions to accurately solve light-matter coupled systems in cavity QED.
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Affiliation(s)
- Matthew Beutel
- Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235, USA
| | - Alexander Ahrens
- Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235, USA
| | - Chenhang Huang
- Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235, USA
| | | | - Kálmán Varga
- Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235, USA
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3
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Ireland R, Jeszenszki P, Mátyus E, Martinazzo R, Ronto M, Pollak E. Lower Bounds for Nonrelativistic Atomic Energies. ACS PHYSICAL CHEMISTRY AU 2021; 2:23-37. [PMID: 35098243 PMCID: PMC8796283 DOI: 10.1021/acsphyschemau.1c00018] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/27/2021] [Indexed: 11/29/2022]
Abstract
A recently developed lower bound theory for Coulombic problems (E. Pollak, R. Martinazzo, J. Chem. Theory Comput. 2021, 17, 1535) is further developed and applied to the highly accurate calculation of the ground-state energy of two- (He, Li+, and H-) and three- (Li) electron atoms. The method has been implemented with explicitly correlated many-particle basis sets of Gaussian type, on the basis of the highly accurate (Ritz) upper bounds they can provide with relatively small numbers of functions. The use of explicitly correlated Gaussians is developed further for computing the variances, and the necessary modifications are here discussed. The computed lower bounds are of submilli-Hartree (parts per million relative) precision and for Li represent the best lower bounds ever obtained. Although not yet as accurate as the corresponding (Ritz) upper bounds, the computed bounds are orders of magnitude tighter than those obtained with other lower bound methods, thereby demonstrating that the proposed method is viable for lower bound calculations in quantum chemistry applications. Among several aspects, the optimization of the wave function is shown to play a key role for both the optimal solution of the lower bound problem and the internal check of the theory.
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Affiliation(s)
- Robbie
T. Ireland
- Institute
of Chemistry, ELTE, Eötvös
Loránd University, Pázmány Péter sétány 1/A, Budapest, H-1117, Hungary,School of
Chemistry, University of Glasgow, University Avenue, G12 8QQ, Glasgow, United Kingdom
| | - Peter Jeszenszki
- Institute
of Chemistry, ELTE, Eötvös
Loránd University, Pázmány Péter sétány 1/A, Budapest, H-1117, Hungary
| | - Edit Mátyus
- Institute
of Chemistry, ELTE, Eötvös
Loránd University, Pázmány Péter sétány 1/A, Budapest, H-1117, Hungary,E-mail:
| | - Rocco Martinazzo
- Department
of Chemistry, University of Milan, Milan, 20122, Italy,Institute of Molecular Science and Technologies
(ISTM), Consiglio
Nazionale delle Ricerche (CNR), Milan, 20133, Italy,
| | - Miklos Ronto
- Chemical
and Biological Physics Department, Weizmann
Institute of Science, 76100, Rehovot, Israel
| | - Eli Pollak
- Chemical
and Biological Physics Department, Weizmann
Institute of Science, 76100, Rehovot, Israel,
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4
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Stanke M, Palikot E, Sharkey KL, Adamowicz L. Benchmark calculations of the 2D Rydberg spectrum of lithium. Mol Phys 2021. [DOI: 10.1080/00268976.2021.1925765] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Monika Stanke
- Institute of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University, Toruń, PL, Poland
| | - Ewa Palikot
- Department of Chemistry and Biochemistry, University of Arizona, Tucson, AZ, USA
| | - Keeper L. Sharkey
- Department of Chemistry and Biochemistry, University of Arizona, Tucson, AZ, USA
| | - Ludwik Adamowicz
- Department of Chemistry and Biochemistry, University of Arizona, Tucson, AZ, USA
- Interdisciplinary Center for Modern Technologies, Nicolaus Copernicus University, Toruń, PL, Poland
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5
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Ferenc D, Korobov VI, Mátyus E. Nonadiabatic, Relativistic, and Leading-Order QED Corrections for Rovibrational Intervals of ^{4}He_{2}^{+} (X ^{2}Σ_{u}^{+}). PHYSICAL REVIEW LETTERS 2020; 125:213001. [PMID: 33274993 DOI: 10.1103/physrevlett.125.213001] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2020] [Accepted: 09/23/2020] [Indexed: 06/12/2023]
Abstract
The rovibrational intervals of the ^{4}He_{2}^{+} molecular ion in its X ^{2}Σ_{u}^{+} ground electronic state are computed by including the nonadiabatic, relativistic, and leading-order quantum-electrodynamics corrections. Good agreement of theory and experiment is observed for the rotational excitation series of the vibrational ground state and the fundamental vibration. The lowest-energy rotational interval is computed to be 70.937 69(10) cm^{-1} in agreement with the most recently reported experimental value, 70.937 589(23)(60)_{sys} cm^{-1} [L. Semeria et al., Phys. Rev. Lett. 124, 213001 (2020)PRLTAO0031-900710.1103/PhysRevLett.124.213001].
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Affiliation(s)
- Dávid Ferenc
- Institute of Chemistry, ELTE, Eötvös Loránd University, Pázmány Péter sétány 1/A, Budapest H-1117, Hungary
| | - Vladimir I Korobov
- Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, Russia
| | - Edit Mátyus
- Institute of Chemistry, ELTE, Eötvös Loránd University, Pázmány Péter sétány 1/A, Budapest H-1117, Hungary
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6
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Atomic fine-structure calculations performed with a finite-nuclear-mass approach and with all-electron explicitly correlated Gaussian functions. Chem Phys Lett 2020. [DOI: 10.1016/j.cplett.2020.137476] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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7
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Li R, Wu Y, Rui Y, Li B, Jiang Y, Ma L, Wu H. Absolute Frequency Measurement of ^{6}Li D Lines with khz-Level Uncertainty. PHYSICAL REVIEW LETTERS 2020; 124:063002. [PMID: 32109124 DOI: 10.1103/physrevlett.124.063002] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/28/2019] [Accepted: 12/03/2019] [Indexed: 06/10/2023]
Abstract
We report the precision measurement of the absolute frequencies, hyperfine splitting, and 2P fine structure splitting in cold atoms of ^{6}Li. Using the stabilized optical frequency comb and developed heterodyne detection technique, the photon shot-noise limited optical spectroscopy is achieved. The measurement of absolute frequencies of D_{1} lines is reached with an uncertainty of about 1 kHz, which is 1 order of magnitude more accurate than previous measurements. The hyperfine splitting of the D_{1} line and 2P fine structure splitting of ^{6}Li are 26.103 1 (14) and 10 052.780 4 (18) MHz, respectively, in agreement with recent theoretical calculations. Our results could provide a benchmark to test the theory at the higher precision and help to resolve large discrepancies among previous experiments.
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Affiliation(s)
- Rui Li
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, People's Republic of China
| | - Yuelong Wu
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, People's Republic of China
| | - Yang Rui
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, People's Republic of China
| | - Bo Li
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, People's Republic of China
| | - Yanyi Jiang
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, People's Republic of China
| | - Longsheng Ma
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, People's Republic of China
| | - Haibin Wu
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, People's Republic of China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
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8
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Maaß B, Hüther T, König K, Krämer J, Krause J, Lovato A, Müller P, Pachucki K, Puchalski M, Roth R, Sánchez R, Sommer F, Wiringa RB, Nörtershäuser W. Nuclear Charge Radii of ^{10,11}B. PHYSICAL REVIEW LETTERS 2019; 122:182501. [PMID: 31144867 DOI: 10.1103/physrevlett.122.182501] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/18/2019] [Indexed: 06/09/2023]
Abstract
The first laser spectroscopic determination of the change in the nuclear charge radius for a five-electron system is reported. This is achieved by combining high-accuracy ab initio mass-shift calculations and a high-accuracy measurement of the isotope shift in the 2s^{2}2p ^{2}P_{1/2}→2s^{2}3s ^{2}S_{1/2} ground state transition in boron atoms. Accuracy is increased by orders of magnitude for the stable isotopes ^{10,11}B and the results are used to extract their difference in the mean-square charge radius ⟨r_{c}^{2}⟩^{11}-⟨r_{c}^{2}⟩^{10}=-0.49(12) fm^{2}. The result is qualitatively explained by a possible cluster structure of the boron nuclei and quantitatively used to benchmark new ab initio nuclear structure calculations using the no-core shell model and Green's function Monte Carlo approaches. These results are the foundation for a laser spectroscopic determination of the charge radius of the proton-halo candidate ^{8}B.
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Affiliation(s)
- Bernhard Maaß
- Institut für Kernphysik, TU Darmstadt, 64289 Darmstadt, Germany
| | - Thomas Hüther
- Institut für Kernphysik, TU Darmstadt, 64289 Darmstadt, Germany
| | - Kristian König
- Institut für Kernphysik, TU Darmstadt, 64289 Darmstadt, Germany
| | - Jörg Krämer
- Institut für Kernphysik, TU Darmstadt, 64289 Darmstadt, Germany
| | - Jan Krause
- Institut für Kernphysik, TU Darmstadt, 64289 Darmstadt, Germany
| | - Alessandro Lovato
- Physics Division, Argonne National Laboratory, Lemont, Illinois 60439, USA
- INFN-TIFPA Trento Institute of Fundamental Physics and Applications, Via Sommarive 14, 38123 Trento, Italy
| | - Peter Müller
- Physics Division, Argonne National Laboratory, Lemont, Illinois 60439, USA
| | - Krzysztof Pachucki
- Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
| | - Mariusz Puchalski
- Faculty of Chemistry, Adam Mickiewicz University, Umultowska 89b, 61-614 Poznań, Poland
| | - Robert Roth
- Institut für Kernphysik, TU Darmstadt, 64289 Darmstadt, Germany
| | - Rodolfo Sánchez
- GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt, Germany
| | - Felix Sommer
- Institut für Kernphysik, TU Darmstadt, 64289 Darmstadt, Germany
| | - R B Wiringa
- Physics Division, Argonne National Laboratory, Lemont, Illinois 60439, USA
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9
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Nakatsuji H, Nakashima H. Solving the Schrödinger equation with the free-complement chemical-formula theory: Variational study of the ground and excited states of Be and Li atoms. J Chem Phys 2019; 150:044105. [PMID: 30709316 DOI: 10.1063/1.5065565] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The chemical formula theory (CFT) proposed in Paper I of this series [H. Nakatsuji et al., J. Chem. Phys. 149, 114105 (2018)] is a simple variational electronic structure theory for atoms and molecules. The CFT constructs simple, conceptually useful wave functions for the ground and excited states, simultaneously, from the ground and excited states of the constituent atoms, reflecting the spirits of the chemical formulas. The CFT wave functions are also designed to be used as the initial wave functions of the free complement (FC) theory, that is, the exact theory producing the exact wave functions of the Schrödinger accuracy. This combined theory is referred to as the FC-CFT. We aim to construct an exact wave function theory that is useful not only quantitatively but also conceptually. This paper shows the atomic applications of the CFT and the FC-CFT. For simplicity, we choose the small atoms, Be and Li, and perform variational calculations to essentially exact levels. For these elements, a simple Hylleraas CI type formulation is known to be potentially highly accurate: we realize it with the CFT and the FC-CFT. Even from the CFT levels, the excitation energies to the Rydberg excited states were calculated satisfactorily. Then, with increasing the order of the FC theory in the FC-CFT, all the absolute energies and the excitation energies of the Be and Li atoms were improved uniformly and reached rapidly to the essentially exact levels in order 3 or 4 with moderately small calculational labors.
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Affiliation(s)
- Hiroshi Nakatsuji
- Quantum Chemistry Research Institute, Kyoto Technoscience Center 16, 14 Yoshida Kawaramachi, Sakyo-ku, Kyoto 606-8305, Japan
| | - Hiroyuki Nakashima
- Quantum Chemistry Research Institute, Kyoto Technoscience Center 16, 14 Yoshida Kawaramachi, Sakyo-ku, Kyoto 606-8305, Japan
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10
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Kumar P, Natarajan V. Precise measurement of hyperfine structure in the 3S 1/2 state of 7Li. Sci Rep 2017; 7:13204. [PMID: 29038442 PMCID: PMC5643324 DOI: 10.1038/s41598-017-13531-9] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/16/2017] [Accepted: 09/25/2017] [Indexed: 12/05/2022] Open
Abstract
We report a precise measurement of hyperfine structure in the 3S1/2 state of the odd isotope of Li, namely 7Li. The state is excited from the ground 2S1/2 state (which has the same parity) using two single-photon transitions via the intermediate 2P3/2 state. The value of the hyperfine constant we measure is A = 93.095(52) MHz, which resolves two discrepant values reported in the literature measured using other techniques. Our value is also consistent with theoretical calculations.
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Affiliation(s)
- Pushpander Kumar
- Department of Physics, Indian Institute of Science, Bangalore, 560012, India
| | - Vasant Natarajan
- Department of Physics, Indian Institute of Science, Bangalore, 560012, India.
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11
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Nörtershäuser W, Geppert C, Krieger A, Pachucki K, Puchalski M, Blaum K, Bissell ML, Frömmgen N, Hammen M, Kowalska M, Krämer J, Kreim K, Neugart R, Neyens G, Sánchez R, Yordanov DT. Precision Test of Many-Body QED in the Be+ 2p Fine Structure Doublet Using Short-Lived Isotopes. PHYSICAL REVIEW LETTERS 2015; 115:033002. [PMID: 26230786 DOI: 10.1103/physrevlett.115.033002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/10/2015] [Indexed: 06/04/2023]
Abstract
Absolute transition frequencies of the 2s 2S{1/2}→2p2P{1/2,3/2} transitions in Be^{+} were measured for the isotopes ^{7,9-12}Be. The fine structure splitting of the 2p state and its isotope dependence are extracted and compared to results of ab initio calculations using explicitly correlated basis functions, including relativistic and quantum electrodynamics effects at the order of mα(6) and mα(7) ln α. Accuracy has been improved in both the theory and experiment by 2 orders of magnitude, and good agreement is observed. This represents one of the most accurate tests of quantum electrodynamics for many-electron systems, being insensitive to nuclear uncertainties.
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Affiliation(s)
| | - Christopher Geppert
- Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany
- Institut für Kernchemie, Johannes Gutenberg-Universität Mainz, D-55128 Mainz, Germany
| | - Andreas Krieger
- Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany
- Institut für Kernchemie, Johannes Gutenberg-Universität Mainz, D-55128 Mainz, Germany
| | - Krzysztof Pachucki
- Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
| | - Mariusz Puchalski
- Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
- Faculty of Chemistry, Adam Mickiewicz University, Umultowska 89b, 61-614 Poznań, Poland
| | - Klaus Blaum
- Max-Planck-Institut für Kernphysik, D-69117 Heidelberg, Germany
| | - Mark L Bissell
- Instituut voor Kern- en Stralingsfysica, KU Leuven, B-3001 Leuven, Belgium
| | - Nadja Frömmgen
- Institut für Kernchemie, Johannes Gutenberg-Universität Mainz, D-55128 Mainz, Germany
| | - Michael Hammen
- Institut für Kernchemie, Johannes Gutenberg-Universität Mainz, D-55128 Mainz, Germany
| | | | - Jörg Krämer
- Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany
| | - Kim Kreim
- Max-Planck-Institut für Kernphysik, D-69117 Heidelberg, Germany
| | - Rainer Neugart
- Institut für Kernchemie, Johannes Gutenberg-Universität Mainz, D-55128 Mainz, Germany
| | - Gerda Neyens
- Instituut voor Kern- en Stralingsfysica, KU Leuven, B-3001 Leuven, Belgium
| | - Rodolfo Sánchez
- GSI Helmholtzzentrum für Schwerionenforschung GmbH, D-64291 Darmstadt, Germany
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12
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Tajitsu A, Sadakane K, Naito H, Arai A, Aoki W. Explosive lithium production in the classical nova V339 Del (Nova Delphini 2013). Nature 2015; 518:381-4. [DOI: 10.1038/nature14161] [Citation(s) in RCA: 89] [Impact Index Per Article: 9.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/02/2014] [Accepted: 12/16/2014] [Indexed: 11/09/2022]
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13
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Wang L, Li C, Yan ZC, Drake GWF. Fine structure and ionization energy of the 1s2s2p 4P state of the helium negative ion He-. PHYSICAL REVIEW LETTERS 2014; 113:263007. [PMID: 25615325 DOI: 10.1103/physrevlett.113.263007] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/24/2014] [Indexed: 06/04/2023]
Abstract
The fine structure and ionization energy of the 1s2s2p (4)P state of the helium negative ion He(-) are calculated in Hylleraas coordinates, including relativistic and QED corrections up to O(α(4)mc(2)), O((μ/M)α(4)mc(2)), O(α(5)mc(2)), and O((μ/M)α(5)mc(2)). Higher order corrections are estimated for the ionization energy. A comparison is made with other calculations and experiments. We find that the present results for the fine structure splittings agree with experiment very well. However, the calculated ionization energy deviates from the experimental result by about 1 standard deviation. The estimated theoretical uncertainty in the ionization energy is much less than the experimental accuracy.
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Affiliation(s)
- Liming Wang
- Department of Physics, Henan Normal University, Xinxiang, Henan, People's Republic of China 453007
| | - Chun Li
- Department of Mathematics, Nanjing University, Nanjing, Jiangsu, People's Republic of China 210093
| | - Zong-Chao Yan
- Department of Physics, University of New Brunswick, Fredericton, New Brunswick, Canada E3B 5A3 and State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan, People's Republic of China 430071
| | - G W F Drake
- Department of Physics, University of Windsor, Windsor, Ontario, Canada N9B 3P4
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14
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Salam A. Quantum electrodynamics effects in atoms and molecules. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2014. [DOI: 10.1002/wcms.1211] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Affiliation(s)
- A. Salam
- Department of Chemistry; Wake Forest University; Winston-Salem NC USA
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15
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Puchalski M, Pachucki K. Quantum electrodynamics corrections to the 2P fine splitting in Li. PHYSICAL REVIEW LETTERS 2014; 113:073004. [PMID: 25170705 DOI: 10.1103/physrevlett.113.073004] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2014] [Indexed: 06/03/2023]
Abstract
We consider quantum electrodynamics (QED) corrections to the fine splitting E(2P_{3/2})-E(2P_{1/2}) in the Li atom. We derive complete formulas for the mα^{6} and mα^{7}lnα contributions and calculate them numerically using highly optimized, explicitly correlated basis functions. The obtained results are in agreement with the most recent measurement, helping to resolve discrepancies between former ones and lay the foundation for the investigation of QED effects in light, many-electron atoms.
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Affiliation(s)
- Mariusz Puchalski
- Faculty of Chemistry, Adam Mickiewicz University, Umultowska 89b, 61-614 Poznań, Poland
| | - Krzysztof Pachucki
- Faculty of Physics, University of Warsaw, Hoża 69, 00-681 Warsaw, Poland
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16
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Strasburger K. High angular momentum states of lithium atom, studied with symmetry-projected explicitly correlated Gaussian lobe functions. J Chem Phys 2014; 141:044104. [PMID: 25084878 DOI: 10.1063/1.4890373] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Abstract
Method of construction of wave functions approximating eigenfunctions of the [Formula: see text] operator is proposed for high angular momentum states of few-electron atoms. Basis functions are explicitly correlated Gaussian lobes, projected onto irreducible representations of finite point groups. Variational calculations have been carried out for the lowest states of lithium atom, with quantum number L in the range from 1 to 8. Nonrelativistic energies accurate to several dozens of nanohartree have been obtained. For 2(2)P, 3(2)D, and 4(2)F states they agree well with the reference results. Transition frequencies have been computed and compared with available experimental data.
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Affiliation(s)
- Krzysztof Strasburger
- Theoretical Chemistry Group, Institute of Physical and Theoretical Chemistry, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
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17
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Bubin S, Adamowicz L. Prediction of (1)P Rydberg energy levels of beryllium based on calculations with explicitly correlated Gaussians. J Chem Phys 2014; 140:024301. [PMID: 24437871 DOI: 10.1063/1.4858275] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Benchmark variational calculations are performed for the seven lowest 1s(2)2s np ((1)P), n = 2...8, states of the beryllium atom. The calculations explicitly include the effect of finite mass of (9)Be nucleus and account perturbatively for the mass-velocity, Darwin, and spin-spin relativistic corrections. The wave functions of the states are expanded in terms of all-electron explicitly correlated Gaussian functions. Basis sets of up to 12,500 optimized Gaussians are used. The maximum discrepancy between the calculated nonrelativistic and experimental energies of 1s(2)2s np ((1)P) →1s(2)2s(2) ((1)S) transition is about 12 cm(-1). The inclusion of the relativistic corrections reduces the discrepancy to bellow 0.8 cm(-1).
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Affiliation(s)
- Sergiy Bubin
- Department of Chemistry, University of Rochester, Rochester, New York 14627, USA
| | - Ludwik Adamowicz
- Department of Chemistry and Biochemistry and Department of Physics, University of Arizona, Tucson, Arizona 85721, USA
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18
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Sharkey KL, Kirnosov N, Adamowicz L. An algorithm for quantum mechanical finite-nuclear-mass variational calculations of atoms with L = 3 using all-electron explicitly correlated Gaussian basis functions. J Chem Phys 2013; 138:104107. [PMID: 23514465 DOI: 10.1063/1.4794192] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023] Open
Abstract
A new algorithm for quantum-mechanical nonrelativistic calculation of the Hamiltonian matrix elements with all-electron explicitly correlated Gaussian functions for atoms with an arbitrary number of s electrons and with three p electrons, or one p electron and one d electron, or one f electron is developed and implemented. In particular the implementation concerns atomic states with L = 3 and M = 0. The Hamiltonian used in the approach is obtained by rigorously separating the center-of-mass motion from the laboratory-frame all particle Hamiltonian, and thus it explicitly depends on the finite mass of the nucleus. The approach is employed to perform test calculations on the lowest (2)F state of the two main isotopes of the lithium atom, (7)Li and (6)Li.
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Affiliation(s)
- Keeper L Sharkey
- Department of Chemistry, University of Arizona, Tucson, Arizona 85721, USA
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19
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Huang YC, Chen HC, Chen SE, Shy JT, Wang LB. Precise frequency measurements of iodine hyperfine transitions at 671 nm. APPLIED OPTICS 2013; 52:1448-1452. [PMID: 23458797 DOI: 10.1364/ao.52.001448] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/2012] [Accepted: 01/31/2013] [Indexed: 06/01/2023]
Abstract
We report absolute frequency measurements on the a(1), a(10), and a(15) hyperfine components of the R(78) 4-6 line of (127)I(2). An external-cavity diode laser system at 671 nm is frequency-stabilized to the saturated absorption center obtained by modulation transfer spectroscopy in an iodine vapor cell. Its absolute frequency is measured by an optical frequency comb. The effect of pressure shift is investigated to obtain the absolute transition frequency at zero pressure. Our determination of the line centers reaches a precision of better than 40 kHz and will provide useful input for theoretical calculations. This frequency-stabilized laser can be used as a reference laser for the spectroscopy of lithium D lines.
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Affiliation(s)
- Yao-Chin Huang
- Department of Physics and Frontier Research Center on Fundamental and Applied Sciences of Matters, National Tsing Hua University, Hsinchu, Taiwan
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20
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Bubin S, Pavanello M, Tung WC, Sharkey KL, Adamowicz L. Born–Oppenheimer and Non-Born–Oppenheimer, Atomic and Molecular Calculations with Explicitly Correlated Gaussians. Chem Rev 2012; 113:36-79. [DOI: 10.1021/cr200419d] [Citation(s) in RCA: 115] [Impact Index Per Article: 9.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Sergiy Bubin
- Department
of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235,
United States
| | - Michele Pavanello
- Department
of Chemistry, Rutgers University Newark, Newark, New Jersey 07102,
United States
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21
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Bubin S, Adamowicz L. Assessment of the accuracy the experimental energies of the 1P(o) 1s(2)2s6p and 1s(2)2s7p states of 9Be based on variational calculations with explicitly correlated Gaussians. J Chem Phys 2012; 137:104315. [PMID: 22979867 DOI: 10.1063/1.4742764] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023] Open
Abstract
Benchmark variational calculations are performed for the six lowest states of the (1)P(o) 1s(2)2snp state series of the (9)Be atom. The wave functions of the states are expanded in terms of all-particle, explicitly correlated Gaussian basis functions and the effect of the finite nuclear mass is directly included in the calculations. The exponential parameters of the Gaussians are variationally optimized using the analytical energy gradient determined with respect to those parameters. Besides providing reference non-relativistic energies for the considered states, the calculations also allow to assess the accuracy of the experimental energies of the (1)P(o) 1s(2)2s6p and 1s(2)2s7p states and suggest their refinement.
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Affiliation(s)
- Sergiy Bubin
- Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235, USA
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22
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Bubin S, Adamowicz L. Explicitly correlated Gaussian calculations of the 2P(o) Rydberg spectrum of the lithium atom. J Chem Phys 2012; 136:134305. [PMID: 22482550 DOI: 10.1063/1.3698584] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023] Open
Abstract
Accurate quantum-mechanical nonrelativistic variational calculations are performed for the nine lowest members of the (2)P(o) Rydberg series (1s(2)np(1), n = 2, ..., 10) of the lithium atom. The effect of the finite nuclear mass is included in the calculations allowing for determining the isotopic shifts of the energy levels. The wave functions of the states are expanded in terms of all-electron explicitly correlated Gaussian functions. The exponential parameters of the Gaussians are variationally optimized with the aid of the analytical energy gradient determined with respect to those parameters. The calculated state energies are compared with the available experimental data.
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Affiliation(s)
- Sergiy Bubin
- Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235, USA
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23
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Krieger A, Blaum K, Bissell ML, Frömmgen N, Geppert C, Hammen M, Kreim K, Kowalska M, Krämer J, Neff T, Neugart R, Neyens G, Nörtershäuser W, Novotny C, Sánchez R, Yordanov DT. Nuclear charge radius of 12Be. PHYSICAL REVIEW LETTERS 2012; 108:142501. [PMID: 22540787 DOI: 10.1103/physrevlett.108.142501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2011] [Indexed: 05/31/2023]
Abstract
The nuclear charge radius of (12)Be was precisely determined using the technique of collinear laser spectroscopy on the 2s(1/2)→2p(1/2,3/2) transition in the Be(+) ion. The mean square charge radius increases from (10)Be to (12)Be by δ<r(c)(2)>(10,12)=0.69(5) fm(2) compared to δ<r(c)(2)>(10,11)=0.49(5) fm(2) for the one-neutron halo isotope ^{11}Be. Calculations in the fermionic molecular dynamics approach show a strong sensitivity of the charge radius to the structure of ^{12}Be. The experimental charge radius is consistent with a breakdown of the N=8 shell closure.
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Affiliation(s)
- A Krieger
- Institut für Kernchemie, Johannes Gutenberg-Universität Mainz, D-55128 Mainz, Germany
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24
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Hättig C, Klopper W, Köhn A, Tew DP. Explicitly Correlated Electrons in Molecules. Chem Rev 2011; 112:4-74. [DOI: 10.1021/cr200168z] [Citation(s) in RCA: 401] [Impact Index Per Article: 30.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Christof Hättig
- Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, D-44780 Bochum, Germany
| | - Wim Klopper
- Abteilung für Theoretische Chemie, Institut für Physikalische Chemie, Karlsruher Institut für Technologie, KIT-Campus Süd, Postfach 6980, D-76049 Karlsruhe, Germany
| | - Andreas Köhn
- Institut für Physikalische Chemie, Johannes Gutenberg-Universität Mainz, D-55099 Mainz, Germany
| | - David P. Tew
- School of Chemistry, University of Bristol, Bristol BS8 1TS, United Kingdom
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25
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Komasa J, Piszczatowski K, Łach G, Przybytek M, Jeziorski B, Pachucki K. Quantum Electrodynamics Effects in Rovibrational Spectra of Molecular Hydrogen. J Chem Theory Comput 2011; 7:3105-15. [DOI: 10.1021/ct200438t] [Citation(s) in RCA: 153] [Impact Index Per Article: 11.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Jacek Komasa
- Faculty of Chemistry, A. Mickiewicz University, Grunwaldzka 6, 60-780 Poznań, Poland
| | | | - Grzegorz Łach
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
| | - Michał Przybytek
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
| | - Bogumił Jeziorski
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
| | - Krzysztof Pachucki
- Faculty of Physics, University of Warsaw, Hoża 69, 00-681 Warsaw, Poland
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26
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Sansonetti CJ, Simien CE, Gillaspy JD, Tan JN, Brewer SM, Brown RC, Wu S, Porto JV. Absolute transition frequencies and quantum interference in a frequency comb based measurement of the (6,7)Li D lines. PHYSICAL REVIEW LETTERS 2011; 107:023001. [PMID: 21797599 DOI: 10.1103/physrevlett.107.023001] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/14/2011] [Indexed: 05/31/2023]
Abstract
Optical frequencies of the D lines of (6,7)Li were measured with a relative accuracy of 5 × 10⁻¹¹ using an optical comb synthesizer. Quantum interference in the laser induced fluorescence for the partially resolved D2 lines was found to produce polarization dependent shifts as large as 1 MHz. Our results resolve large discrepancies among previous experiments and between all experiments and theory. The fine-structure splittings for ⁶Li and ⁷Li are 10052.837(22) MHz and 10053.435(21) MHz. The splitting isotope shift is 0.599(30) MHz, in reasonable agreement with recent theoretical calculations.
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Affiliation(s)
- Craig J Sansonetti
- National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
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27
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King FW, Quicker D, Langer J. Compact wave functions for the beryllium isoelectronic series, Li− to Ne6+: A standard Hylleraas approach. J Chem Phys 2011; 134:124114. [PMID: 21456652 DOI: 10.1063/1.3569565] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023] Open
Affiliation(s)
- Frederick W King
- Department of Chemistry, University of Wisconsin-Eau Claire, Eau Claire, Wisconsin 54702, USA.
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28
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Sharkey KL, Adamowicz L. Exponentially and pre-exponentially correlated Gaussians for atomic quantum calculations. J Chem Phys 2011; 134:094104. [DOI: 10.1063/1.3553177] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023] Open
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29
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Sharkey KL, Bubin S, Adamowicz L. An algorithm for calculating atomic D states with explicitly correlated Gaussian functions. J Chem Phys 2011; 134:044120. [DOI: 10.1063/1.3523348] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
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30
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Sharkey KL, Bubin S, Adamowicz L. Analytical energy gradient in variational calculations of the two lowest P3 states of the carbon atom with explicitly correlated Gaussian basis functions. J Chem Phys 2010. [DOI: 10.1063/1.3419931] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023] Open
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31
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Bubin S, Komasa J, Stanke M, Adamowicz L. Isotope shifts of the three lowest S1 states of the B+ ion calculated with a finite-nuclear-mass approach and with relativistic and quantum electrodynamics corrections. J Chem Phys 2010; 132:114109. [DOI: 10.1063/1.3358999] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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32
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Zhang P, Bodo E, Dalgarno A. Near resonance charge exchange in ion-atom collisions of lithium isotopes. J Phys Chem A 2009; 113:15085-91. [PMID: 19746948 DOI: 10.1021/jp905184a] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Collisions of ions and atoms of (6)Li and (7)Li are explored theoretically over a wide range of energy from 10(-14) to 1 eV. Accurate ab initio calculations are carried out of the Born-Oppenheimer potentials and the nonadiabatic couplings that are responsible for the near resonance charge exchange. Scattering studies show that the calculated charge exchange cross section follows Wigner's law for inelastic processes for energies below 10(-10) eV and that the zero temperature rate constant for it is 2.1 x 10(-9) cm(3) s(-1). At collision energies much larger than the isotope shift of the ionization potentials of the atoms, we show that the near resonance charge exchange process is equivalent to the resonance charge exchange with cross sections having a logarithmic dependence on energy. A comparison with the Langevin model at intermediate energies is also presented.
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Affiliation(s)
- Peng Zhang
- Institute for Theoretical Atomic, Molecular and Optical Physics, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, USA
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33
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Bubin S, Komasa J, Stanke M, Adamowicz L. Isotope shift in the electron affinity of lithium. J Chem Phys 2009; 131:234112. [DOI: 10.1063/1.3275804] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023] Open
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34
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Nörtershäuser W, Tiedemann D, Záková M, Andjelkovic Z, Blaum K, Bissell ML, Cazan R, Drake GWF, Geppert C, Kowalska M, Krämer J, Krieger A, Neugart R, Sánchez R, Schmidt-Kaler F, Yan ZC, Yordanov DT, Zimmermann C. Nuclear charge radii of 7,9,10Be and the one-neutron halo nucleus 11Be. PHYSICAL REVIEW LETTERS 2009; 102:062503. [PMID: 19257582 DOI: 10.1103/physrevlett.102.062503] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/06/2008] [Indexed: 05/27/2023]
Abstract
Nuclear charge radii of ;{7,9,10,11}Be have been determined by high-precision laser spectroscopy. On-line measurements were performed with collinear laser spectroscopy in the 2s_{1/2}-->2p_{1/2} transition on a beam of Be+ ions. Collinear and anticollinear laser beams were used simultaneously, and the absolute frequency determination using a frequency comb yielded an accuracy in the isotope-shift measurements of about 1 MHz. Combining this with accurate calculations of the mass-dependent isotope shifts yields nuclear charge radii. The charge radius decreases from 7Be to 10Be and then increases for the halo nucleus 11Be. When comparing our results with predictions of ab initio nuclear-structure calculations we find good agreement. Additionally, the nuclear magnetic moment of 7Be was determined to be -1.3995(5)micro_{N} and that of 11Be was confirmed with an accuracy similar to previous beta-NMR measurements.
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Affiliation(s)
- W Nörtershäuser
- GSI Helmholtzzentrum für Schwerionenforschung GmbH, D-64291 Darmstadt, Germany
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35
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Smith M, Brodeur M, Brunner T, Ettenauer S, Lapierre A, Ringle R, Ryjkov VL, Ames F, Bricault P, Drake GWF, Delheij P, Lunney D, Sarazin F, Dilling J. First Penning-trap mass measurement of the exotic halo nucleus 11Li. PHYSICAL REVIEW LETTERS 2008; 101:202501. [PMID: 19113333 DOI: 10.1103/physrevlett.101.202501] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/21/2008] [Indexed: 05/27/2023]
Abstract
In this Letter, we report a new mass for 11Li using the trapping experiment TITAN at TRIUMF's ISAC facility. This is by far the shortest-lived nuclide, t_{1/2}=8.8 ms, for which a mass measurement has ever been performed with a Penning trap. Combined with our mass measurements of ;{8,9}Li we derive a new two-neutron separation energy of 369.15(65) keV: a factor of 7 more precise than the best previous value. This new value is a critical ingredient for the determination of the halo charge radius from isotope-shift measurements. We also report results from state-of-the-art atomic-physics calculations using the new mass and extract a new charge radius for 11Li. This result is a remarkable confluence of nuclear and atomic physics.
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Affiliation(s)
- M Smith
- TRIUMF, 4004 Wesbrook Mall, Vancouver, British Columbia, Canada
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