Journal of Physics B Atomic Molecular and Optical Physics

Correlation in the ground state of Li-, Na-and K-

Birte L. Christensen-Dalsgaard

Published Jul 28, 1988• 15 citations

Abstract

The ground-state wavefunctions for Li - , Na - and K - are calculated using the hyperspherical method. They are analysed and compared with the ground state as well as the first 1 S resonance in H - to reveal the effect of correlation. In order to perform a quantitative comparison an absolute measure of angular and radial correlation based on statistical methods is used and its relevance to characterise correlation in the ground states is discussed.

DOI: 10.1088/0953-4075/21/14/007

Related papers

Hyperspherical Calculations on Electron Affinity and Geometry for Li − and Na −

Han Hui-Li, Xianzhou Zhang, Ting-Yun Shi

Chinese Physics LettersDec 1, 20072 citations

Electron Correlations Observed Through Intensity Interferometry: Study of Model Initial State Wave Functions

Bernold Feuerstein, Michael Schulz, R. Moshammer +1 more

Physica ScriptaJan 1, 20018 citations

Ground-state properties of weakly bound helium-alkali trimers

Petar Stipanović, Leandra Vranješ Markić, Darko Zarić +1 more

The Journal of Chemical PhysicsJan 4, 20178 citations

H− and He in a uniform magnetic field: Ground-state wave functions, energies, and binding energies for fields below 109 G

Chang‐Hwan Park, Anthony F. Strace

Physical Review AFeb 1, 198440 citations

H- and He in a uniform magnetic field: Ground-state wave functions, energies, and binding energies for fields below 109 G

Chang‐Hwan Park, Anthony F. Starace

Feb 1, 19840 citations

Long-range interactions between excited helium and alkali-metal atoms

J. Y. Zhang, Li-Yan Tang, T.-Y. Shi +2 more

Physical Review ADec 3, 201210 citations

Journal of Physics B Atomic Molecular and Optical Physics

Correlation in the ground state of Li-, Na-and K-

Birte L. Christensen-Dalsgaard

Published Jul 28, 1988• 15 citations

Publisher

Abstract

DOI: 10.1088/0953-4075/21/14/007

Related papers

Hyperspherical Calculations on Electron Affinity and Geometry for Li − and Na −

Han Hui-Li, Xianzhou Zhang, Ting-Yun Shi

Using a model potential to describe the interaction between the core and the valence electron, we perform hyperspherical calculations for electron affinity and geometry of the weakly bound Li − and Na − systems. In our calculation, channel functions are expanded in terms of B-splines. Using the special properties of B-splines, we make the knot distributions more precisely, characterizing the behaviour of channel functions. This improves the convergence greatly. Our results are in good agreement with the other theoretical and experimental values.Using a model potential to describe the interaction between the core and the valence electron, we perform hyperspherical calculations for electron affinity and geometry of the weakly bound Li − and Na − systems. In our calculation, channel functions are expanded in terms of B-splines. Using the special properties of B-splines, we make the knot distributions more precisely, characterizing the behaviour of channel functions. This improves the convergence greatly. Our results are in good agreement with the other theoretical and experimental values.

Chinese Physics LettersDec 1, 20072 citations

Electron Correlations Observed Through Intensity Interferometry: Study of Model Initial State Wave Functions

Bernold Feuerstein, Michael Schulz, R. Moshammer +1 more

Recently, a new method of analysing electron correlations based on intensity interferometry has been applied to double ionization of He and Ne by fast ion impact [1]. The data reveal sensitively correlation effects while they appear to be very insensitive to the collision dynamics. In order to analyse the role of the initial state electron correlation a statistically defined correlation function based on intensity interferometry was calculated for the ground state of He. In a comparative study of model wave functions we demonstrate that correlation can be considered from a statistical point of view which offers a new tool to study correlation effects in many-particle systems.Recently, a new method of analysing electron correlations based on intensity interferometry has been applied to double ionization of He and Ne by fast ion impact [1]. The data reveal sensitively correlation effects while they appear to be very insensitive to the collision dynamics. In order to analyse the role of the initial state electron correlation a statistically defined correlation function based on intensity interferometry was calculated for the ground state of He. In a comparative study of model wave functions we demonstrate that correlation can be considered from a statistical point of view which offers a new tool to study correlation effects in many-particle systems.

Physica ScriptaJan 1, 20018 citations

Ground-state properties of weakly bound helium-alkali trimers

Petar Stipanović, Leandra Vranješ Markić, Darko Zarić +1 more

Weakly bound triatomic molecules consisting of two helium atoms and one alkali metal atom are studied by means of the diffusion Monte Carlo method. We determined the stability of 4He2A, 4He3HeA, and 3He2A, where A is one of the alkali atoms Li, Na, K, Rb, or Cs. Some of the trimers with 3He are predicted to be self-bound for the first time, but this is observed to be dependent on the He–A interaction potential model. In addition to the ground-state energy of the trimers, we determined their density, radial, and angular distributions. Many of them are spatially very extended, which qualifies them as quantum halo states.Weakly bound triatomic molecules consisting of two helium atoms and one alkali metal atom are studied by means of the diffusion Monte Carlo method. We determined the stability of 4He2A, 4He3HeA, and 3He2A, where A is one of the alkali atoms Li, Na, K, Rb, or Cs. Some of the trimers with 3He are predicted to be self-bound for the first time, but this is observed to be dependent on the He–A interaction potential model. In addition to the ground-state energy of the trimers, we determined their density, radial, and angular distributions. Many of them are spatially very extended, which qualifies them as quantum halo states.

The Journal of Chemical PhysicsJan 4, 20178 citations

H− and He in a uniform magnetic field: Ground-state wave functions, energies, and binding energies for fields below 109 G

Chang‐Hwan Park, Anthony F. Strace

Wave functions, energies, and binding energies for the lowest singlet states of ${\mathrm{H}}^{\ensuremath{-}}$ and He in uniform magnetic fields $B<{10}^{9}$ G are calculated using an adiabatic approximation in hyperspherical coordinates. In computing the angular part of the wave functions, a coupled expansion in one-electron oblate spheroidal angle functions is used. In addition to contracting the two-electron wave function radially, the magnetic field is found to distort the angular part of the wave function mainly by reducing the $\mathrm{ss}^{1}S$ character of the state and replacing it with an $\mathrm{sd}^{1}D$ character. Results for energies and binding energies are comparable with those obtained in variational calculations. In order to compute the binding energies of ${\mathrm{H}}^{\ensuremath{-}}$ and He we have also calculated the binding energies of the ground states of H and ${\mathrm{He}}^{+}$ in uniform magnetic fields $B<{10}^{9}$ G using the adiabatic oblate-spheroidal-coordinate method of Starace and Webster.Wave functions, energies, and binding energies for the lowest singlet states of ${\mathrm{H}}^{\ensuremath{-}}$ and He in uniform magnetic fields $B<{10}^{9}$ G are calculated using an adiabatic approximation in hyperspherical coordinates. In computing the angular part of the wave functions, a coupled expansion in one-electron oblate spheroidal angle functions is used. In addition to contracting the two-electron wave function radially, the magnetic field is found to distort the angular part of the wave function mainly by reducing the $\mathrm{ss}^{1}S$ character of the state and replacing it with an $\mathrm{sd}^{1}D$ character. Results for energies and binding energies are comparable with those obtained in variational calculations. In order to compute the binding energies of ${\mathrm{H}}^{\ensuremath{-}}$ and He we have also calculated the binding energies of the ground states of H and ${\mathrm{He}}^{+}$ in uniform magnetic fields $B<{10}^{9}$ G using the adiabatic oblate-spheroidal-coordinate method of Starace and Webster.

Physical Review AFeb 1, 198440 citations

H- and He in a uniform magnetic field: Ground-state wave functions, energies, and binding energies for fields below 109 G

Chang‐Hwan Park, Anthony F. Starace

Wave functions, energies, and binding energies for the lowest singlet states of H- and He in uniform magnetic fields B<109 G are calculated using an adiabatic approximation in hyperspherical coordinates. In computing the angular part of the wave functions, a coupled expansion in one-electron oblate spheroidal angle functions is used. In addition to contracting the two-electron wave function radially, the magnetic field is found to distort the angular part of the wave function mainly by reducing the ss1S character of the state and replacing it with an sd 1D character. Results for energies and binding energies are comparable with those obtained in variational calculations. In order to compute the binding energies of H- and He we have also calculated the binding energies of the ground states of H and He+ in uniform magnetic fields B<109 G using the adiabatic oblate-spheroidal-coordinate method of Starace and Webster.Wave functions, energies, and binding energies for the lowest singlet states of H- and He in uniform magnetic fields B<109 G are calculated using an adiabatic approximation in hyperspherical coordinates. In computing the angular part of the wave functions, a coupled expansion in one-electron oblate spheroidal angle functions is used. In addition to contracting the two-electron wave function radially, the magnetic field is found to distort the angular part of the wave function mainly by reducing the ss1S character of the state and replacing it with an sd 1D character. Results for energies and binding energies are comparable with those obtained in variational calculations. In order to compute the binding energies of H- and He we have also calculated the binding energies of the ground states of H and He+ in uniform magnetic fields B<109 G using the adiabatic oblate-spheroidal-coordinate method of Starace and Webster.

Feb 1, 19840 citations

Long-range interactions between excited helium and alkali-metal atoms

J. Y. Zhang, Li-Yan Tang, T.-Y. Shi +2 more

The dispersion coefficients for the long-range interaction of the first four excited states of He, i.e., He(2 ${}^{1,3}\phantom{\rule{-0.16em}{0ex}}$ $S$ ) and He(2 ${}^{1,3}$ $P$ ), with the low-lying states of the alkali-metal atoms Li, Na, K, and Rb are calculated by summing over the reduced matrix elements of the multipole transition operators. For the interaction between He and Li the uncertainty of the calculations is 0.1--0.5 $%$ . For interactions with other alkali-metal atoms the uncertainty is 1--3 $%$ in the coefficient ${C}_{5}$ , 1--5 $%$ in the coefficient ${C}_{6}$ , and 1--10 $%$ in the coefficients ${C}_{8}$ and ${C}_{10}$ . The dispersion coefficients ${C}_{n}$ for the interaction of He(2 ${}^{1,3}\phantom{\rule{-0.16em}{0ex}}$ $S$ ) and He(2 ${}^{1,3}$ $P$ ) with the ground-state alkali-metal atoms and for the interaction of He(2 ${}^{1,3}\phantom{\rule{-0.16em}{0ex}}$ $S$ ) with the alkali-metal atoms in their first ${}^{2}$ $P$ states are presented in this Brief Report. The coefficients for other pairs of atomic states are listed in the Supplemental Material.The dispersion coefficients for the long-range interaction of the first four excited states of He, i.e., He(2 ${}^{1,3}\phantom{\rule{-0.16em}{0ex}}$$S$) and He(2 ${}^{1,3}$$P$), with the low-lying states of the alkali-metal atoms Li, Na, K, and Rb are calculated by summing over the reduced matrix elements of the multipole transition operators. For the interaction between He and Li the uncertainty of the calculations is 0.1--0.5$%$. For interactions with other alkali-metal atoms the uncertainty is 1--3$%$ in the coefficient ${C}_{5}$, 1--5$%$ in the coefficient ${C}_{6}$, and 1--10$%$ in the coefficients ${C}_{8}$ and ${C}_{10}$. The dispersion coefficients ${C}_{n}$ for the interaction of He(2 ${}^{1,3}\phantom{\rule{-0.16em}{0ex}}$$S$) and He(2 ${}^{1,3}$$P$) with the ground-state alkali-metal atoms and for the interaction of He(2 ${}^{1,3}\phantom{\rule{-0.16em}{0ex}}$$S$) with the alkali-metal atoms in their first ${}^{2}$$P$ states are presented in this Brief Report. The coefficients for other pairs of atomic states are listed in the Supplemental Material.

Physical Review ADec 3, 201210 citations

Wave functions, energies, and binding energies for the lowest singlet states of ${\mathrm{H}}^{\ensuremath{-}}$ and He in uniform magnetic fields

B<{10}^{9}

G are calculated using an adiabatic approximation in hyperspherical coordinates. In computing the angular part of the wave functions, a coupled expansion in one-electron oblate spheroidal angle functions is used. In addition to contracting the two-electron wave function radially, the magnetic field is found to distort the angular part of the wave function mainly by reducing the

\mathrm{ss}^{1}S

character of the state and replacing it with an

\mathrm{sd}^{1}D

character. Results for energies and binding energies are comparable with those obtained in variational calculations. In order to compute the binding energies of ${\mathrm{H}}^{\ensuremath{-}}$ and He we have also calculated the binding energies of the ground states of H and

{\mathrm{He}}^{+}

in uniform magnetic fields

B<{10}^{9}

G using the adiabatic oblate-spheroidal-coordinate method of Starace and Webster.

The dispersion coefficients for the long-range interaction of the first four excited states of He, i.e., He(2

{}^{1,3}\phantom{\rule{-0.16em}{0ex}}

S

) and He(2

{}^{1,3}

P

), with the low-lying states of the alkali-metal atoms Li, Na, K, and Rb are calculated by summing over the reduced matrix elements of the multipole transition operators. For the interaction between He and Li the uncertainty of the calculations is 0.1--0.5

%

. For interactions with other alkali-metal atoms the uncertainty is 1--3

%

in the coefficient

{C}_{5}

, 1--5

%

in the coefficient

{C}_{6}

, and 1--10

%

in the coefficients

{C}_{8}

and

{C}_{10}

. The dispersion coefficients

{C}_{n}

for the interaction of He(2

{}^{1,3}\phantom{\rule{-0.16em}{0ex}}

S

) and He(2

{}^{1,3}

P

) with the ground-state alkali-metal atoms and for the interaction of He(2

{}^{1,3}\phantom{\rule{-0.16em}{0ex}}

S

) with the alkali-metal atoms in their first

{}^{2}

P

states are presented in this Brief Report. The coefficients for other pairs of atomic states are listed in the Supplemental Material.