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Physical Review A

l -changing collision of a high-Rydberg atom with a polar molecule

Michio Matsuzawa

Published Oct 1, 1978• 19 citations
Publisher

Abstract

Cross sections of the title process are theoretically evaluated to be of order of ${10}^{\ensuremath{-}14}$ - ${10}^{\ensuremath{-}11}$ ${\mathrm{cm}}^{2}$, using the model in which an excited Rydberg electron behaves as if it were "free" and slow, with interaction between the excited electron and a polar molecule playing a decisive role. The $n$ dependence of the cross section shows a sharp peak as the energy defect becomes small.

DOI
10.1103/physreva.18.1396

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Thermal collisions between high-Rydberg atoms and rare-gas atoms

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The title processes are theoretically investigated based on the model in which an excited Rydberg electron behaves as if it were 'free' and slow, with its interaction with the rare-gas atom playing a decisive role. The cross sections of l-changing collisions of the Rydberg atoms with the rare-gas atoms are evaluated for small angular momentum changes. They are compared with experimental data available at present, under the assumption that there is no selection rule for the distribution over the final angular momentum states of the Rydberg atom, and are found to be consistent with experimental findings. The relation between this approach and some others is examined. The possibility of learning about low-energy electron-rare-gas collisions from refined experimental data on the title processes is briefly discussed.

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Quasielastic state-changing collisions of high-Rydberg atoms with rare-gas atoms

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For $20\ensuremath{\le}n\ensuremath{\le}45$, two types of quasielastic state-changing-collisional (QESCC) processes, i.e., (i) $l$-changing and (ii) $n$-and $l$-changing processes, have been theoretically investigated based on the free-electron model in which an excited Rydberg electron behaves as if it were "free" and slow with its interaction with a rare-gas atom playing a decisive role. It is shown that a parameter ${u}_{min}[=\frac{\ensuremath{\nu}{\ensuremath{\nu}}^{\ensuremath{'}}\ensuremath{\Delta}E{a}_{0}}{(\ensuremath{\hbar}V)}]$ is quite useful for characterizing both of these QESCC processes in a unified way where $\ensuremath{\nu}(\ensuremath{\simeq}{\ensuremath{\nu}}^{\ensuremath{'}})$ is an effective principal quantum number of the initial (final) state, $\ensuremath{\Delta}E$ is an energy defect, and $V$ is a relative velocity. It is theoretically found that higher-angular-momentum states are dominantly populated in the final channel of these QESCC processes with $1<{u}_{min}\ensuremath{\lesssim}\ensuremath{\nu}$ such as in the $n$- and $l$-changing collision of ${\mathrm{Rb}}^{**}(\mathrm{ns})+\mathrm{He}$. This is in contrast with the uniform distribution over the final angular-momentum states for the usual $l$-changing processes, i.e., ${u}_{min}\ensuremath{\lesssim}1$. The calculated cross sections of these QESCC processes with $1<{u}_{min}\ensuremath{\lesssim}\ensuremath{\nu}$ are found to be in reasonable agreement with experimental findings available at present.

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m- andl-Changing Collisions of High-Rydberg Atoms with Rare-Gas Atoms

Takashi Yoshizawa, Michio Matsuzawa

State changing of high-Rydberg atoms by collisions with rare-gas atoms have been theoretically investigated using the free-electron model. The non-selective character of transitions arising from the short range of the interaction between the high-Rydberg atoms and the rare-gas atoms is found to be strongly modified in the following two cases. First, for the high-Rydberg atoms in the circular states with | m |= l ≃ n , it has been found that transitions take place overwhelmingly between the circular states. This propensity rule originates from a highly anisotropic electron-density distribution of the initial circular states. Second, for the high-Rydberg states with large quantum defects (modulo 1), suppression of the yield of the lower angular momentum states have been observed. This cancels out the fair enhancement of the production of the high-Rydberg states with small | m | seen for the hydrogenic case with small quantum defects. It leads to the m distribution of the final states apparently proportional to their statistical weight.

Journal of the Physical Society of Japan•Mar 15, 1985•17 citations
Cross sections of the title process are theoretically evaluated to be of order of 10\ensuremath−14{10}^{\ensuremath{-}14}10\ensuremath−14 - 10\ensuremath−11{10}^{\ensuremath{-}11}10\ensuremath−11 cm2{\mathrm{cm}}^{2}cm2, using the model in which an excited Rydberg electron behaves as if it were "free" and slow, with interaction between the excited electron and a polar molecule playing a decisive role. The nnn dependence of the cross section shows a sharp peak as the energy defect becomes small.
The title processes are theoretically investigated based on the model in which an excited Rydberg electron behaves as if it were 'free' and slow, with its interaction with the rare-gas atom playing a decisive role. The cross sections of l-changing collisions of the Rydberg atoms with the rare-gas atoms are evaluated for small angular momentum changes. They are compared with experimental data available at present, under the assumption that there is no selection rule for the distribution over the final angular momentum states of the Rydberg atom, and are found to be consistent with experimental findings. The relation between this approach and some others is examined. The possibility of learning about low-energy electron-rare-gas collisions from refined experimental data on the title processes is briefly discussed.
For $20\ensuremath{\le}n\ensuremath{\le}45$, two types of quasielastic state-changing-collisional (QESCC) processes, i.e., (i) lll-changing and (ii) nnn-and lll-changing processes, have been theoretically investigated based on the free-electron model in which an excited Rydberg electron behaves as if it were "free" and slow with its interaction with a rare-gas atom playing a decisive role. It is shown that a parameter ${u}_{min}[=\frac{\ensuremath{\nu}{\ensuremath{\nu}}^{\ensuremath{'}}\ensuremath{\Delta}E{a}_{0}}{(\ensuremath{\hbar}V)}]$ is quite useful for characterizing both of these QESCC processes in a unified way where $\ensuremath{\nu}(\ensuremath{\simeq}{\ensuremath{\nu}}^{\ensuremath{'}})$ is an effective principal quantum number of the initial (final) state, $\ensuremath{\Delta}E$ is an energy defect, and VVV is a relative velocity. It is theoretically found that higher-angular-momentum states are dominantly populated in the final channel of these QESCC processes with $1<{u}_{min}\ensuremath{\lesssim}\ensuremath{\nu}$ such as in the nnn- and lll-changing collision of Rb∗∗(ns)+He{\mathrm{Rb}}^{**}(\mathrm{ns})+\mathrm{He}Rb∗∗(ns)+He. This is in contrast with the uniform distribution over the final angular-momentum states for the usual lll-changing processes, i.e., ${u}_{min}\ensuremath{\lesssim}1$. The calculated cross sections of these QESCC processes with $1<{u}_{min}\ensuremath{\lesssim}\ensuremath{\nu}$ are found to be in reasonable agreement with experimental findings available at present.
In the present work very-high-n Rydberg-atoms (nsim100−nsim400)(n \\sim 100 - n \\sim 400)(nsim100−nsim400) are used to probe electron-molecule collisions at ultra-low electron energies. Based on the essentially-free-electron model, for sufficiently high n, Rydberg atom-molecule collisions can be described in terms of a binary interaction between the target molecule and the essentially-free Rydberg electron. Since the average kinetic energy of the Rydberg electron is ultra-low rm(sim85mueV−sim1.4meV),\\rm({\\sim}85\\mu eV - {\\sim}1.4meV),rm(sim85mueV−sim1.4meV), analysis of the very-high-n Rydberg-atom collision data can provide information on electron-molecule scattering at electron energies corresponding to electron temperatures of only $\\sim111\\sp\\circ$K, which are far below those accessible using any alternate approach.\nRate constants for destruction of very-high-n Rydberg atoms in collisions with various target molecules have been measured. This study focuses on Rydberg electron transfer to an electron-attaching molecule which results in negative ion formation via the reactions rmK(itnp/)+XYtoKsp++(XY)sp−∗ortoKsp++Xsp−+Yeqno(1)\\rm K({\\it np\\/}) + XY \\to K\\sp+ + (XY)\\sp{-*}\\ or\\ \\to K\\sp+ + X\\sp- + Y\\eqno(1)rmK(itnp/)+XYtoKsp++(XY)sp−∗ortoKsp++Xsp−+Yeqno(1)and on rotational energy transfer from polar molecules which leads to Rydberg atom ionization rmK(itnp/)+XY(itJ/)toKsp++itesp−+XY(itJ/−1)eqno(2)\\rm K({\\it np\\/}) + XY({\\it J\\/}) \\to K\\sp+ + {\\it e}\\sp- + XY({\\it J\\/}-1)\\eqno(2)rmK(itnp/)+XY(itJ/)toKsp++itesp−+XY(itJ/−1)eqno(2)\nThe n dependence of the rate constants for Rydberg-atom destruction depends on the reactions involved. In reaction (1) the rate constant is independent of n whereas in reaction (2) it increases nearly linearly with n. When both reactions are possible, the measured n dependence can be explained in terms of contributions from each process.\nThe essentially-free-electron model suggests that the n dependence of the rate constants for Rydberg-atom destruction reflects the energy dependence of the cross sections of the corresponding free electron-molecule collision processes which are $$\\eqalignno{&e\\sp- + \\rm XY \\to (XY)\\sp{-*}\\ or\\ \\to X\\sp- + Y&(1\\sp\\prime)\\cr &e\\sp- + \\rm XY({\\it J\\/}) \\to {\\it e}\\sp- + XY({\\it J\\/}-1)&(2\\sp\\prime)\\cr}$$Analysis of the data therefore provides the behavior of cross sections for these processes at ultra-low electron energies.
Collisions of Rydberg atoms with other atoms may induce changes in the electronic orbital angular momentum of the Rydberg state. A theory is presented that expresses the cross section for this process in terms of the sss-wave amplitude for low-energy-electron scattering from the other atom. In its most accurate form, the theory requires a convolution of the electron-scattering amplitude and the initial momentum-space wave function of the Rydberg state. However, an approximate analytic solution is derived in which the lll-mixing cross section at a particular nnn is written as the electron-scattering cross section at the mean electronic kinetic energy of the Rydberg state, multiplied by a scaling function that depends only on nnn. The analytic solution clearly exhibits the asymptotic scaling behavior of the cross sections. Collisions of Na(nd)+He\mathrm{Na}(\mathrm{nd})+\mathrm{He}Na(nd)+He, Ne, and Ar are treated as specific examples.
State changing of high-Rydberg atoms by collisions with rare-gas atoms have been theoretically investigated using the free-electron model. The non-selective character of transitions arising from the short range of the interaction between the high-Rydberg atoms and the rare-gas atoms is found to be strongly modified in the following two cases. First, for the high-Rydberg atoms in the circular states with | m |= l ≃ n , it has been found that transitions take place overwhelmingly between the circular states. This propensity rule originates from a highly anisotropic electron-density distribution of the initial circular states. Second, for the high-Rydberg states with large quantum defects (modulo 1), suppression of the yield of the lower angular momentum states have been observed. This cancels out the fair enhancement of the production of the high-Rydberg states with small | m | seen for the hydrogenic case with small quantum defects. It leads to the m distribution of the final states apparently proportional to their statistical weight.