Long-range interactions in the ozone molecule: spectroscopic and dynamical points of view

Using the multipolar expansion of the electrostatic energy, we have characterized the asymptotic interactions between an oxygen atom O$(^3P)$ and an oxygen molecule O$_2(^3\Sigma_g^-)$, both in their electronic ground state. We have calculated the interaction energy induced by the permanent electric quadrupoles of O and O$_2$ and the van der Waals energy. On one hand we determined the 27 electronic potential energy surfaces including spin-orbit connected to the O$(^3P)$ + O$_2(^3\Sigma_g^-)$ dissociation limit of the O--O$_2$ complex. On the other hand we computed the potential energy curves characterizing the interaction between O$(^3P)$ and a O$_2(^3\Sigma_g^-)$ molecule in its lowest vibrational level and in a low rotational level. Such curves are found adiabatic to a good approximation, namely they are only weakly coupled to each other. These results represent a first step for modeling the spectroscopy of ozone bound levels close to the dissociation limit, as well as the low energy collisions between O and O$_2$ thus complementing the knowledge relevant for the ozone formation mechanism.Comment: Submitted to J. Chem. Phys. after revisio

Long-range interactions between polar bialkali ground-state molecules in arbitrary vibrational levels

We have calculated the isotropic $C\_6$ coefficients characterizing the long-range van der Waals interaction between two identical heteronuclear alkali-metal diatomic molecules in the same arbitrary vibrational level of their ground electronic state $X^1\Sigma^+$. We consider the ten species made up of $^7$Li, $^{23}$Na, $^{39}$K, $^{87}$Rb and $^{133}$Cs. Following our previous work [M.~Lepers \textit{et.~al.}, Phys.~Rev.~A \textbf{88}, 032709 (2013)] we use the sum-over-state formula inherent to the second-order perturbation theory, composed of the contributions from the transitions within the ground state levels, from the transition between ground-state and excited state levels, and from a crossed term. These calculations involve a combination of experimental and quantum-chemical data for potential energy curves and transition dipole moments. We also investigate the case where the two molecules are in different vibrational levels and we show that the Moelwyn-Hughes approximation is valid provided that it is applied for each of the three contributions to the sum-over-state formula. Our results are particularly relevant in the context of inelastic and reactive collisions between ultracold bialkali molecules, in deeply bound or in Feshbach levels

Photoassociation of a cold atom-molecule pair: long-range quadrupole-quadrupole interactions

The general formalism of the multipolar expansion of electrostatic interactions is applied to the calculation the potential energy between an excited atom (without fine structure) and a ground state diatomic molecule at large separations. Both partners exhibit a permanent quadrupole moment, so that their mutual quadrupole-quadrupole long-range interaction is attractive enough to bind trimers. Numerical results are given for an excited Cs(6P) atom and a ground state Cs2 molecule. The prospects for achieving photoassociation of a cold atom/dimer pair is thus discussed and found promising. The formalism can be easily generalized to the long-range interaction between molecules to investigate the formation of cold tetramers.Comment: 5 figure

Analysis of the world record time for combined father and son marathon.

The aim of this study was to examine the physiological profiles and the pacing strategies of the father (59 yr old) and son (34 yr old) who broke the World Record time (4:59:22; father: 2:27:52, son: 2:31:30) for combined father and son marathon in 2019. Oxygen uptake (V̇o2), heart rate (HR), ventilation (V̇e), blood lactate concentration (La), and running economy (RE) were measured during treadmill-running tests. The total distance of the marathon was divided into eight sections of 5 km and one last section of 2.195 km, and the relative average running velocity on each section was calculated individually. V̇o2max, HRmax, V̇emax, and Lamax were 65.4 mL·kg-1·min-1, 165 beats/min, 115 L/min, 5.7 mmol/L for the father and 66.9 mL·kg-1·min-1, 181 beats/min, 153 L/min, 11.5 mmol/L for the son, respectively. At 17 km/h, RE was 210 mL·kg-1·km-1 for the father and 200 mL·kg-1·km-1 for the son, and % V̇o2max sustained was 90.9% for the father and 84.5% for the son, respectively. The father maintained an even running velocity during the marathon (running velocity CV <1%), while the son ran the second half-marathon 7% slower than the first one, and his running velocity markedly dropped from the 35th kilometer. Father and son who broke the World record time for combined father and son marathon had a similar level of performance, but their physiological profiles and pacing strategies during the marathon were different. A more even speed for the son could help them to improve their own record in the near future.NEW & NOTEWORTHY We provide novel data demonstrating that different physiological profiles can lead to the same level of performance in a marathon, even at different ages. The novelty of our study is that we report on the physiological characteristics, training routine, and in-race pacing strategy that allowed a father (59 yr old) and son (34 yr old) to break the World Record time for combined father and son marathon. The father also established a new World record marathon time for the age of 59

Predictor variables for half marathon race time in recreational female runners

Anthropometric and training variables were related to half-marathon race time in recreational female runners. Skin-fold thicknesses at various upper body locations were related to training intensity. High running speed in training appears to be important for fast half-marathon race times and may reduce upper body skin-fold thicknesses in recreational female half marathoners

Breaking the marathon world record with your father? The superpower of lifelong endurance training

Are you looking for a training buddy to prepare for your next marathon race? Have you ever considered that your father could be the right person? Would it not be great to cross the finish line side by side and get on the podium together? You probably think that he is not young enough for such an effort, don’t you? and if I tell you that your father is also able of exceptional physical performances despite his older age. In the following article, we are going to see how a father and son (with a 25-year age difference) managed to break the world record for combined father and son marathon in 2019

Photoassociation of a cold-atom-molecule pair. II. Second-order perturbation approach

The electrostatic interaction between an excited atom and a diatomic ground-state molecule in an arbitrary rovibrational level at large mutual separations is investigated with a general second-order perturbation theory, in the perspective of modeling the photoassociation between cold atoms and molecules. We find that the combination of quadrupole-quadrupole and van der Waals interactions competes with the rotational energy of the dimer, limiting the range of validity of the perturbative approach to distances larger than 100 Bohr radii. Numerical results are given for the long-range interaction between Cs and Cs-2, showing that the photoassociation is probably efficient for any Cs-2 rotational energy