High-resolution spectroscopy of He2+_2^+ using Rydberg-series extrapolation and Zeeman-decelerated supersonic beams of metastable He2_2

Recently, high-resolution spectroscopy of slow beams of metastable helium molecules (He$_2^*$) generated by multistage Zeeman deceleration was used in combination with Rydberg-series extrapolation techniques to obtain the lowest rotational interval in the molecular helium ion at a precision of 18 MHz [Jansen et al. Phys. Rev. Lett. 115 (13) (2015) 133202], limited by the temporal width of the Fourier-transform-limited laser pulses used to record the spectra. We present here an extension of these measurements in which we have (1) measured higher rotational intervals of He${_2}^+$, (2) replaced the pulsed UV laser by a cw UV laser and improved the resolution of the spectra by a factor of more than five, and (3) studied $M_J$ redistribution processes in regions of low magnetic fields of the Zeeman decelerator and shown how these processes can be exploited to assign transitions originating from specific spin-rotational levels ($N^{\prime\prime},J^{\prime\prime}$) of He$_2^*$.Comment: 28 pages, 8 figure

Precision measurement of the rotational energy-level structure of the three-electron molecule He2+_2^+

The term values of all rotational levels of the $^4$He{_2}^+\,X^+\,^2\Sigma_u^+\,(\nu^+=0) ground vibronic state with rotational quantum number $N^+\le 19$ have been determined with an accuracy of 8 x 10$^{-4}$ cm$^{-1}$ ($\sim{25}$ MHz) by MQDT-assisted Rydberg spectroscopy of metastable He$_2^*$. Comparison of these term values with term values recently calculated ab initio by Tung et al. [J. Chem. Phys. 136, 104309 (2012)] reveal discrepancies that rapidly increase with increasing rotational quantum number and reach values of 0.07 cm$^{-1}$ ($\sim{2.1}$ GHz) at $N^+=19$.Comment: 11 pages, 6 figure

FINE STRUCTURE OF METASTABLE 4He2 USING ZEEMAN-DECELERATED MOLECULAR-BEAM RESONANCE SPECTROSCOPY

The a\,^3\Sigma_u^+ state of $^{4}$He$_{2}$ is a metastable state with a lifetime of about $18$\,s. The spin-spin and spin-rotation interactions result in a splitting of each rotational level $N$ into three components $J=N, N\pm1$. The fine structure intervals of the $N=1$, $3$, $5$, $7 - 11$ and $25$ - $29$ have been measured by radio frequency (rf) spectroscopy\footnote{W. Lichten, M.V. McCusker and T. L. Vierima, \textit{J. Chem. Phys.}, \textbf{61}, 2200 (1974).} \footnote{W. Lichten and T. Wik, \textit{J. Chem. Phys.}, \textbf{69}, 98 (1978).} \footnote{M. Kristensen and N. Bjerre, \textit{J. Chem. Phys.}, \textbf{93}, 983 (1990).} \footnote{I. Hazell, A. N\o rregaard and N. Bjerre, \textit{J. Mol. Spectrosc.}, \textbf{172}, 135 (1995).} and were included in a global analysis of the a\,^3\Sigma_u^+ state \footnote{C. Focsa, P. F. Bernath and R. Colin, \textit{J. Mol. Spectrosc.}, \textbf{191}, 209, (1998).}. A new measurement of the fine structure of all rotational levels between $N=1$ and $21$ of the a\,^3\Sigma_u^+ ($v=0$) state will be presented. The $J=N$ fine-structure components, which are high-field seeking in magnetic fields, have been eliminated using a multistage Zeeman decelerator, and repopulated from the low-field-seeking $J=N\pm1$ components using rf radiation prior to detection by excitation to Rydberg states followed by pulsed-field ionization. The low velocity of the Zeeman decelerated beam\footnote{M. Motsch, P. Jansen, J. A. Agner, H. Schmutz and F. Merkt, Phys. Rev. A, \textbf{89}, 043420 (2014).} \footnote{P. Jansen, L. Semeria, L. E. Hofer, S. Scheidegger, J. A. Agner, H. Schmutz and F. Merkt, \textit{Phys. Rev. Lett.}, \textbf{115}, 133202 (2015).} enabled long interaction times of the molecules with the rf radiation and therefore a reduction of the transit-time broadening down to 10 kHz (FWHM), allowing the transition frequencies to be determined very accurately. The fine structure has been analyzed using an effective Hamiltonian to obtain improved values of the spin-spin and spin-rotation coupling constants for the a\,^3\Sigma_u^+ ($v=0$) metastable state of $^{4}$He$_{2}$, including centrifugal distortion corrections

PRECISION MEASUREMENT OF THE ROVIBRATIONAL ENERGY-LEVEL STRUCTURE OF 4He+2

He$_{2}^{+}$ is a three-electron system for which highly accurate textit{ab initio} calculations are possible._x000d_ The latest calculations of the rovibrational energies of He$_{2}^{+}$ by Tung emph{et al.} footnote{W.-C. Tung, M. Pavanello and L. Adamowicz, textit{J. Chem. Phys.}, 136, 104309, 2012.} have a reported accuracy of 120 MHz, although they do not include relativistic and quantum electrodynamics (QED) effects. _x000d_ _x000d_ We determined the rovibrational structure of $^{4}$He$^{+}_{2}$ from measurements of the Rydberg spectrum of metastable $a,^3Sigma_u^+$ He$_{2}$ (He$^{*}_{2}$ hereafter) and Rydberg-series extrapolation using multichannel quantum-defect-theory footnote{C. Jungen, textit{Elements of Quantum Defect Theory, in : Handbook of High-resolution Spectroscopy}, 2001.} footnote{D. Sprecher, J. Liu, T. Krähenmann, M. Schäfer, and F. Merkt, textit{J. Chem. Phys.}, 140, 064304, 2014.}._x000d_ He$^{*}_{2}$ molecules are produced in supersonic beams with velocities tunable down to about 100 m/s by combining a cryogenic supersonic-beam source with a multistage Zeeman decelerator footnote{A. W. Wiederkehr, S. D. Hogan, M. Andrist, H. Schmutz, B. Lambillotte, J. A. Agner, and F. Merkt., J. Chem. Phys., 135, 214202, 2011.} footnote{M. Motsch, P. Jansen, J. A. Agner, H. Schmutz, and F. Merkt, textit{Phys. Rev. A}, 89, 043420, 2014.}. They are then excited to high-$n$p Rydberg states by single-photon excitation._x000d_ In the experiments, we use a pulsed uv laser system, with a near Fourier-transform-limited bandwidth of 150 MHz. The Zeeman deceleration reduces the systematic uncertainty arising from a possible Doppler shift and greatly simplifies the spectral assignment because of its spin-rotational state selectivity footnote{P. Jansen, L. Semeria, L. E. Hofer, S. Scheidegger, J. A. Agner, H. Schmutz, and F. Merkt. Phys. Rev. Lett., 115, 133202, 2015.}._x000d_ _x000d_ Results will be presented on the rotational structure of the lowest three vibrational levels of He$^{+}_{2}$. The unprecedented accuracy that we have obtained for the v$^{+}=0$ rotational intervals of He$_{2}^{+}$ footnote{L. Semeria, P. Jansen and F. Merkt, J. Chem. Phys., 145, 204301, 2016.} enables the quantification of the relativistic and QED corrections by comparison with the results of Tung emph{et al.}$^a

Precision Measurements in Few-Electron Molecules: The Ionization Energy of Metastable 4\mathbf{^4}He2\mathbf{{_2}} and the First Rotational Interval of 4\mathbf{^4}He2+\mathbf{{_2}^+}

Molecular helium represents a benchmark system for testing $\textit{ab initio}$ calculations on few-electron molecules. We report on the determination of the adiabatic ionization energy of the a\,^3\Sigma_u^+ state of He$_2$, corresponding to the energy interval between the a\,^3\Sigma_u^+ ($v''=0$, $N''=1$) state of He$_2$ and the X^+\,^2\Sigma_u^+ ($v^+=0$, $N^+=1$) state of He${_2}^+$, and of the lowest rotational interval of He${_2}^+$. These measurements rely on the excitation of metastable He$_2$ molecules to high Rydberg states using frequency-comb-calibrated continuous-wave UV radiation in a counter-propagating-laser-beam setup. The observed Rydberg states were extrapolated to their series limit using multichannel quantum-defect theory. The ionization energy of He$_2$ (a\,^3\Sigma_u^+) and the lowest rotational interval of He${_2}^+$ (X^+\,^2\Sigma_u^+) are 34301.207002(23)$\pm 0.000037_{\mathrm{sys}}$ cm$^{-1}$ and 70.937589(23)$\pm 0.000060_{\mathrm{sys}}$ cm$^{-1}$, respectively

FINE STRUCTURE OF METASTABLE 4He2 USING ZEEMAN-DECELERATED MOLECULAR-BEAM RESONANCE SPECTROSCOPY

The a\,^3\Sigma_u^+ state of $^{4}$He$_{2}$ is a metastable state with a lifetime of about $18$\,s. The spin-spin and spin-rotation interactions result in a splitting of each rotational level $N$ into three components $J=N, N\pm1$. The fine structure intervals of the $N=1$, $3$, $5$, $7 - 11$ and $25$ - $29$ have been measured by radio frequency (rf) spectroscopy\footnote{W. Lichten, M.V. McCusker and T. L. Vierima, \textit{J. Chem. Phys.}, \textbf{61}, 2200 (1974).} \footnote{W. Lichten and T. Wik, \textit{J. Chem. Phys.}, \textbf{69}, 98 (1978).} \footnote{M. Kristensen and N. Bjerre, \textit{J. Chem. Phys.}, \textbf{93}, 983 (1990).} \footnote{I. Hazell, A. N\o rregaard and N. Bjerre, \textit{J. Mol. Spectrosc.}, \textbf{172}, 135 (1995).} and were included in a global analysis of the a\,^3\Sigma_u^+ state \footnote{C. Focsa, P. F. Bernath and R. Colin, \textit{J. Mol. Spectrosc.}, \textbf{191}, 209, (1998).}. A new measurement of the fine structure of all rotational levels between $N=1$ and $21$ of the a\,^3\Sigma_u^+ ($v=0$) state will be presented. The $J=N$ fine-structure components, which are high-field seeking in magnetic fields, have been eliminated using a multistage Zeeman decelerator, and repopulated from the low-field-seeking $J=N\pm1$ components using rf radiation prior to detection by excitation to Rydberg states followed by pulsed-field ionization. The low velocity of the Zeeman decelerated beam\footnote{M. Motsch, P. Jansen, J. A. Agner, H. Schmutz and F. Merkt, Phys. Rev. A, \textbf{89}, 043420 (2014).} \footnote{P. Jansen, L. Semeria, L. E. Hofer, S. Scheidegger, J. A. Agner, H. Schmutz and F. Merkt, \textit{Phys. Rev. Lett.}, \textbf{115}, 133202 (2015).} enabled long interaction times of the molecules with the rf radiation and therefore a reduction of the transit-time broadening down to 10 kHz (FWHM), allowing the transition frequencies to be determined very accurately. The fine structure has been analyzed using an effective Hamiltonian to obtain improved values of the spin-spin and spin-rotation coupling constants for the a\,^3\Sigma_u^+ ($v=0$) metastable state of $^{4}$He$_{2}$, including centrifugal distortion corrections

A multi-level network tool to trace wasted water from farm to fork and backwards

Food loss and waste (FLW) is an issue of great public concern, due to its major impact on food security and on the social, economic and environmental resources involved in food production, trade and consumption. In this work, we put the lens on water resources, as those lost in the different stages of FLW represent about a quarter of the total freshwater resources used in food crop production. To this end, we propose the NETFLOW model (Network-based Evaluation Tool for Food LOss and Waste) as an innovative tool capable of reconstructing, for each commodity, the complex global multi-layered network linking FLW at each stage of the value chain with the corresponding wasted water resources. Food re-exports, nested supply chains, telecoupling of food markets, and different levels of food transformation are taken into account. Focusing on the emblematic case of wheat and its derived food commodities (e.g. flour, bread, pasta), we show the complexity and extent of the FLW-linked water network. For example, in 2016, more than 100 countries used their water resources (almost 3 km ^3 ) to produce wheat which was ultimately lost or wasted along the food consumption value chain in Italy, with almost half of this amount being directly attributable to the bread value chain. On the supply side, we show that about 18.3 km ^3 of water resources in the U.S. were lost through wheat-related FLW in 144 countries, about 40% for flour, 27% for raw wheat (mainly used for feed), and 24% for bread. The NETFLOW model proves useful in unravelling the complex links between (i) product-specific global trade networks, (ii) primary and derived products, (iii) country- and stage-dependent FLW, and (iv) country- and product-specific virtual water content

Fundamental vibration frequency and rotational structure of the first excited vibrational level of the molecular helium ion (He2+)

ISSN:0021-9606ISSN:1089-769

Determination of the Spin-Rotation Fine Structure of He2+

ISSN:0031-9007ISSN:1079-711