Physical Review A

Angular-momentum-dependent Fano profiles in excited zinc atoms

Luka Pravica, D Cvejanović, Jim Williams, S. A. Napier

Published Mar 8, 2007• 22 citations

Abstract

The Fano-equivalent profiles of two negative-ion resonant states have been observed in the integrated Stokes parameters of 636.2 nm photons emitted from the $3{d}^{10}4s4{d\phantom{\rule{0.2em}{0ex}}}^{1}{D}_{2}$ state of zinc. These profiles reflect the effects of electron exchange and the spin-orbit interaction via the angular-momentum-dependent properties of the alignment and orientation Stokes parameters. The resonant states have energies of $10.98\ifmmode\pm\else\textpm\fi{}0.02\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ and $11.33\ifmmode\pm\else\textpm\fi{}0.02\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ and widths of $0.25\ifmmode\pm\else\textpm\fi{}0.03\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ and $0.33\ifmmode\pm\else\textpm\fi{}0.05\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, respectively, and are bound to an excited atomic state with a $3{d}^{9}$ core hole. The lower-energy resonance shows a strong spin-orbit interaction whereas the higher-energy resonance shows negligible spin-orbit interaction.

DOI: 10.1103/physreva.75.030701

Related papers

Topological angular momentum in electron exchange excitation of a single atom

Jim Williams, Luka Pravica, Sergey N. Samarin

Physical Review AFeb 6, 201211 citations

Spin-Orbit and Exchange Effects in Neon 3p States

Dehong Yu, P. A. Hayes, J. E. Furst +1 more

Physical Review LettersApr 7, 199714 citations

Spin exchange in the excitation of spin-polarized Na atoms by Ne+ -ion impact

Wolfgang Jitschin, S. Osimitsch, H Reihl +3 more

Physical Review ANov 1, 198619 citations

Indirect spin-orbit interaction in high- L Rydberg states with 2S1/2 cores

Erica L. Snow, R. A. Komara, M. A. Gearba +1 more

Physical Review AAug 29, 200316 citations

Spin-dependent effects in high-order above-threshold ionization: spin–orbit interaction and exchange effects

Dejan B. Milošević

Journal of Physics B Atomic Molecular and Optical PhysicsJul 6, 201715 citations

Effect of the spin-orbit interaction in photoionization Stark spectra of ml=1 excited rubidium atoms

J. M. Lecomte, Sylvain Liberman, Eliane Luc-Koenig +2 more

Physical Review AApr 1, 19846 citations

Physical Review A

Angular-momentum-dependent Fano profiles in excited zinc atoms

Luka Pravica, D Cvejanović, Jim Williams, S. A. Napier

Published Mar 8, 2007• 22 citations

Publisher

Abstract

The Fano-equivalent profiles of two negative-ion resonant states have been observed in the integrated Stokes parameters of 636.2 nm photons emitted from the

3{d}^{10}4s4{d\phantom{\rule{0.2em}{0ex}}}^{1}{D}_{2}

state of zinc. These profiles reflect the effects of electron exchange and the spin-orbit interaction via the angular-momentum-dependent properties of the alignment and orientation Stokes parameters. The resonant states have energies of

10.98\ifmmode\pm\else\textpm\fi{}0.02\phantom{\rule{0.3em}{0ex}}\mathrm{eV}

and

11.33\ifmmode\pm\else\textpm\fi{}0.02\phantom{\rule{0.3em}{0ex}}\mathrm{eV}

and widths of

0.25\ifmmode\pm\else\textpm\fi{}0.03\phantom{\rule{0.3em}{0ex}}\mathrm{eV}

and

0.33\ifmmode\pm\else\textpm\fi{}0.05\phantom{\rule{0.3em}{0ex}}\mathrm{eV}

, respectively, and are bound to an excited atomic state with a

3{d}^{9}

core hole. The lower-energy resonance shows a strong spin-orbit interaction whereas the higher-energy resonance shows negligible spin-orbit interaction.

DOI: 10.1103/physreva.75.030701

Related papers

Topological angular momentum in electron exchange excitation of a single atom

Jim Williams, Luka Pravica, Sergey N. Samarin

In a single free two-valence-electron atom, the motion of the electron spin is a consequence of quantum statistics and the Pauli exclusion principle. Subsequently, during an electron impact exchange excitation from a ${}^{1}{S}_{0}\phantom{\rule{0.16em}{0ex}}{M}_{S}=0$ to a ${}^{3}{S}_{1}\phantom{\rule{0.16em}{0ex}}{M}_{S}=0$ state, the electron spin is ``parallel transported'' around a closed path with a geometrical Berry phase of \ensuremath{\pi} radians creating an aligned exchange spin angular momentum. This alignment is observed via the Stokes parameter ${P}_{2}$ of the photon decay into a ${}^{3}P$ state. The geometric phase is in addition to the dynamic phase. Measurements from zinc and mercury atoms in different laboratories show the effect close to the excitation threshold where there are no competing excitation processes. Similar effects are expected in other atomic and molecular quantum scattering processes where comparable geometrical or topological paths exist. Electron quantum scattering theories use antisymmetrized wave functions but none include this geometrical exchange angular momentum.In a single free two-valence-electron atom, the motion of the electron spin is a consequence of quantum statistics and the Pauli exclusion principle. Subsequently, during an electron impact exchange excitation from a ${}^{1}{S}_{0}\phantom{\rule{0.16em}{0ex}}{M}_{S}=0$ to a ${}^{3}{S}_{1}\phantom{\rule{0.16em}{0ex}}{M}_{S}=0$ state, the electron spin is ``parallel transported'' around a closed path with a geometrical Berry phase of \ensuremath{\pi} radians creating an aligned exchange spin angular momentum. This alignment is observed via the Stokes parameter ${P}_{2}$ of the photon decay into a ${}^{3}P$ state. The geometric phase is in addition to the dynamic phase. Measurements from zinc and mercury atoms in different laboratories show the effect close to the excitation threshold where there are no competing excitation processes. Similar effects are expected in other atomic and molecular quantum scattering processes where comparable geometrical or topological paths exist. Electron quantum scattering theories use antisymmetrized wave functions but none include this geometrical exchange angular momentum.

Physical Review AFeb 6, 201211 citations

Spin-Orbit and Exchange Effects in Neon 3p States

Dehong Yu, P. A. Hayes, J. E. Furst +1 more

Spin-orbit and exchange effects are separately identified through the measurement of integrated Stokes parameters ${P}_{2}$ and ${P}_{3}$ for the decay radiation from spin-polarized electron impact excited states. The observations are made for the radiations from the transitions ${3p}^{\ensuremath{'}}[\frac{1}{2}{]}_{1}\ensuremath{\rightarrow}{3s}^{\ensuremath{'}}[\frac{1}{2}{]}_{0}$ (616.4 nm) and $3p[\frac{1}{2}{]}_{1}\ensuremath{\rightarrow}3s[\frac{3}{2}{]}_{2}$ (703.3 nm) in neon just above threshold.Spin-orbit and exchange effects are separately identified through the measurement of integrated Stokes parameters ${P}_{2}$ and ${P}_{3}$ for the decay radiation from spin-polarized electron impact excited states. The observations are made for the radiations from the transitions ${3p}^{\ensuremath{'}}[\frac{1}{2}{]}_{1}\ensuremath{\rightarrow}{3s}^{\ensuremath{'}}[\frac{1}{2}{]}_{0}$ (616.4 nm) and $3p[\frac{1}{2}{]}_{1}\ensuremath{\rightarrow}3s[\frac{3}{2}{]}_{2}$ (703.3 nm) in neon just above threshold.

Physical Review LettersApr 7, 199714 citations

Spin exchange in the excitation of spin-polarized Na atoms by Ne+ -ion impact

Wolfgang Jitschin, S. Osimitsch, H Reihl +3 more

The 3s-3p excitation of spin-polarized Na atoms by ${\mathrm{Ne}}^{+}$ ions has been studied for impact energies ${E}_{\mathrm{lab}=200}$ eV to 6 keV, i.e., in the adiabatic regime. The total excitation cross section and the three Stokes polarization parameters of the fluorescence light have been measured. The linear polarization of the light shows a preferential excitation of the \ensuremath{\Vert} ${m}_{l}$ \ensuremath{\Vert}=1 magnetic substates. The circular polarization probes the spin orientation of the excited 3p state. At the highest impact energies investigated the experimental data are compatible with conservation of spin orientation during the collision. With decreasing impact energy, the spin polarization of the final 3p state becomes smaller than the spin polarization of the initial 3s state. This apparent spin depolarization is attributed to the exchange interaction between the Na valence electron and the unfilled ${\mathrm{Ne}}^{+}$ 2 ${p}^{5}$ core in the quasimolecule formed during the collision.The 3s-3p excitation of spin-polarized Na atoms by ${\mathrm{Ne}}^{+}$ ions has been studied for impact energies ${E}_{\mathrm{lab}=200}$ eV to 6 keV, i.e., in the adiabatic regime. The total excitation cross section and the three Stokes polarization parameters of the fluorescence light have been measured. The linear polarization of the light shows a preferential excitation of the \ensuremath{\Vert}${m}_{l}$\ensuremath{\Vert}=1 magnetic substates. The circular polarization probes the spin orientation of the excited 3p state. At the highest impact energies investigated the experimental data are compatible with conservation of spin orientation during the collision. With decreasing impact energy, the spin polarization of the final 3p state becomes smaller than the spin polarization of the initial 3s state. This apparent spin depolarization is attributed to the exchange interaction between the Na valence electron and the unfilled ${\mathrm{Ne}}^{+}$ 2${p}^{5}$ core in the quasimolecule formed during the collision.

Physical Review ANov 1, 198619 citations

Indirect spin-orbit interaction in high- L Rydberg states with 2S1/2 cores

Erica L. Snow, R. A. Komara, M. A. Gearba +1 more

In high- $L$ Rydberg states, where exchange interactions are of negligible size, spin-orbit interactions are expected to determine the energy differences between states of different spin orientations. This is well studied in the case of helium, where it results in a fourfold splitting of each high- $L$ term, coming from the two electrons' spin-orbit interactions. A similar structure might be expected in heavier Rydberg states, whose core ion is a ${}^{2}{S}_{1/2}$ state. However, observations in barium Rydberg states and recent observations in Rydberg states of ${\mathrm{Si}}^{2+}$ reveal significant deviations from this expectation. Both can be explained as an indirect effect of spin-orbit interactions in virtual excitations of the core ion. A perturbative treatment predicts an indirect spin-orbit interaction for the Rydberg state proportional to the inverse sixth power of the Rydberg electron's radial coordinate. The significance of this term, relative to the direct magnetic interactions, varies by more than six orders of magnitude between the three systems studied, helium, ${\mathrm{Si}}^{2+},$ and barium.In high-$L$ Rydberg states, where exchange interactions are of negligible size, spin-orbit interactions are expected to determine the energy differences between states of different spin orientations. This is well studied in the case of helium, where it results in a fourfold splitting of each high-$L$ term, coming from the two electrons' spin-orbit interactions. A similar structure might be expected in heavier Rydberg states, whose core ion is a ${}^{2}{S}_{1/2}$ state. However, observations in barium Rydberg states and recent observations in Rydberg states of ${\mathrm{Si}}^{2+}$ reveal significant deviations from this expectation. Both can be explained as an indirect effect of spin-orbit interactions in virtual excitations of the core ion. A perturbative treatment predicts an indirect spin-orbit interaction for the Rydberg state proportional to the inverse sixth power of the Rydberg electron's radial coordinate. The significance of this term, relative to the direct magnetic interactions, varies by more than six orders of magnitude between the three systems studied, helium, ${\mathrm{Si}}^{2+},$ and barium.

Physical Review AAug 29, 200316 citations

Spin-dependent effects in high-order above-threshold ionization: spin–orbit interaction and exchange effects

Dejan B. Milošević

Abstract Spin-dependent effects in atomic processes can be caused by the spin–orbit interaction or/and by the requirement that the wave function of identical electrons is antisymmetric. Such effects are usually neglected in strong-field physics. We show two examples, supported by theoretical results and numerical calculations, in which these effects are important. The first one is based on strong-field ionization of Xe atoms by a bicircular field. The corresponding momentum distribution of spin-polarized electrons emitted in the above-threshold ionization process exhibits wavelength-dependent fast oscillations. For longer wavelengths and small electron emission angle there is a wide photoelectron kinetic energy region in which the spin asymmetry parameter changes continuously from large positive to large negative values. In addition, the emission time of such electrons in high-order above-threshold ionization is determined on the attosecond time scale. The second process considered is high-order above-threshold ionization of excited Li + ions. We have found that in this case, even in the absence of spin–orbit coupling, the photoelectron momentum distribution strongly depends on the initial spin state. In the singlet state we have characteristic minima, which are caused by the destructive interference of the direct and exchange rescattering amplitudes. Such minima are absent in the triplet state.Abstract Spin-dependent effects in atomic processes can be caused by the spin–orbit interaction or/and by the requirement that the wave function of identical electrons is antisymmetric. Such effects are usually neglected in strong-field physics. We show two examples, supported by theoretical results and numerical calculations, in which these effects are important. The first one is based on strong-field ionization of Xe atoms by a bicircular field. The corresponding momentum distribution of spin-polarized electrons emitted in the above-threshold ionization process exhibits wavelength-dependent fast oscillations. For longer wavelengths and small electron emission angle there is a wide photoelectron kinetic energy region in which the spin asymmetry parameter changes continuously from large positive to large negative values. In addition, the emission time of such electrons in high-order above-threshold ionization is determined on the attosecond time scale. The second process considered is high-order above-threshold ionization of excited Li + ions. We have found that in this case, even in the absence of spin–orbit coupling, the photoelectron momentum distribution strongly depends on the initial spin state. In the singlet state we have characteristic minima, which are caused by the destructive interference of the direct and exchange rescattering amplitudes. Such minima are absent in the triplet state.

Journal of Physics B Atomic Molecular and Optical PhysicsJul 6, 201715 citations

Effect of the spin-orbit interaction in photoionization Stark spectra of ml=1 excited rubidium atoms

J. M. Lecomte, Sylvain Liberman, Eliane Luc-Koenig +2 more

Experimental results on the photoionization spectra of excited rubidium atoms in a well-defined ${m}_{l}=1$ state in the presence of an electric field are reported. Spectra corresponding to a definite polarization of the ionizing light exhibit characteristic resonances which are ascribed either to the non-Coulombic part of the central potential or to the spin-orbit interaction. The different line profiles are interpreted as being due to interferences between discrete states and continua, the observed structures depending directly on the density of oscillator strengths and not simply on the density of continuum states.Experimental results on the photoionization spectra of excited rubidium atoms in a well-defined ${m}_{l}=1$ state in the presence of an electric field are reported. Spectra corresponding to a definite polarization of the ionizing light exhibit characteristic resonances which are ascribed either to the non-Coulombic part of the central potential or to the spin-orbit interaction. The different line profiles are interpreted as being due to interferences between discrete states and continua, the observed structures depending directly on the density of oscillator strengths and not simply on the density of continuum states.

Physical Review AApr 1, 19846 citations

The Fano-equivalent profiles of two negative-ion resonant states have been observed in the integrated Stokes parameters of 636.2 nm photons emitted from the

3{d}^{10}4s4{d\phantom{\rule{0.2em}{0ex}}}^{1}{D}_{2}

10.98\ifmmode\pm\else\textpm\fi{}0.02\phantom{\rule{0.3em}{0ex}}\mathrm{eV}

and

11.33\ifmmode\pm\else\textpm\fi{}0.02\phantom{\rule{0.3em}{0ex}}\mathrm{eV}

and widths of

0.25\ifmmode\pm\else\textpm\fi{}0.03\phantom{\rule{0.3em}{0ex}}\mathrm{eV}

and

0.33\ifmmode\pm\else\textpm\fi{}0.05\phantom{\rule{0.3em}{0ex}}\mathrm{eV}

, respectively, and are bound to an excited atomic state with a

3{d}^{9}

core hole. The lower-energy resonance shows a strong spin-orbit interaction whereas the higher-energy resonance shows negligible spin-orbit interaction.

{}^{1}{S}_{0}\phantom{\rule{0.16em}{0ex}}{M}_{S}=0

to a

{}^{3}{S}_{1}\phantom{\rule{0.16em}{0ex}}{M}_{S}=0

state, the electron spin is ``parallel transported'' around a closed path with a geometrical Berry phase of \ensuremath{\pi} radians creating an aligned exchange spin angular momentum. This alignment is observed via the Stokes parameter

{P}_{2}

of the photon decay into a

{}^{3}P

state. The geometric phase is in addition to the dynamic phase. Measurements from zinc and mercury atoms in different laboratories show the effect close to the excitation threshold where there are no competing excitation processes. Similar effects are expected in other atomic and molecular quantum scattering processes where comparable geometrical or topological paths exist. Electron quantum scattering theories use antisymmetrized wave functions but none include this geometrical exchange angular momentum.

Spin-orbit and exchange effects are separately identified through the measurement of integrated Stokes parameters

{P}_{2}

and

{P}_{3}

for the decay radiation from spin-polarized electron impact excited states. The observations are made for the radiations from the transitions ${3p}^{\ensuremath{'}}[\frac{1}{2}{]}_{1}\ensuremath{\rightarrow}{3s}^{\ensuremath{'}}[\frac{1}{2}{]}_{0}$ (616.4 nm) and $3p[\frac{1}{2}{]}_{1}\ensuremath{\rightarrow}3s[\frac{3}{2}{]}_{2}$ (703.3 nm) in neon just above threshold.

The 3s-3p excitation of spin-polarized Na atoms by

{\mathrm{Ne}}^{+}

ions has been studied for impact energies

{E}_{\mathrm{lab}=200}

eV to 6 keV, i.e., in the adiabatic regime. The total excitation cross section and the three Stokes polarization parameters of the fluorescence light have been measured. The linear polarization of the light shows a preferential excitation of the \ensuremath{\Vert}

{m}_{l}

\ensuremath{\Vert}=1 magnetic substates. The circular polarization probes the spin orientation of the excited 3p state. At the highest impact energies investigated the experimental data are compatible with conservation of spin orientation during the collision. With decreasing impact energy, the spin polarization of the final 3p state becomes smaller than the spin polarization of the initial 3s state. This apparent spin depolarization is attributed to the exchange interaction between the Na valence electron and the unfilled

{\mathrm{Ne}}^{+}

{p}^{5}

core in the quasimolecule formed during the collision.

In high-

L

Rydberg states, where exchange interactions are of negligible size, spin-orbit interactions are expected to determine the energy differences between states of different spin orientations. This is well studied in the case of helium, where it results in a fourfold splitting of each high-

L

term, coming from the two electrons' spin-orbit interactions. A similar structure might be expected in heavier Rydberg states, whose core ion is a

{}^{2}{S}_{1/2}

state. However, observations in barium Rydberg states and recent observations in Rydberg states of

{\mathrm{Si}}^{2+}

reveal significant deviations from this expectation. Both can be explained as an indirect effect of spin-orbit interactions in virtual excitations of the core ion. A perturbative treatment predicts an indirect spin-orbit interaction for the Rydberg state proportional to the inverse sixth power of the Rydberg electron's radial coordinate. The significance of this term, relative to the direct magnetic interactions, varies by more than six orders of magnitude between the three systems studied, helium,

{\mathrm{Si}}^{2+},

and barium.

Experimental results on the photoionization spectra of excited rubidium atoms in a well-defined

{m}_{l}=1

state in the presence of an electric field are reported. Spectra corresponding to a definite polarization of the ionizing light exhibit characteristic resonances which are ascribed either to the non-Coulombic part of the central potential or to the spin-orbit interaction. The different line profiles are interpreted as being due to interferences between discrete states and continua, the observed structures depending directly on the density of oscillator strengths and not simply on the density of continuum states.