Physical Review A

Triply excited P2 and D2 resonance of He−

Kwong T. Chung

Published Oct 1, 1980• 31 citations

Abstract

The $^{2}P$ ($2s2s2p$) and $^{2}D$ ($2s2p2p$) resonance structure observed in the electron-helium scattering experiments has been investigated using a saddle-point technique. For $^{2}P$ we obtain for the energy --- 0.796 93 a.u. with an 82-term wave function. This agrees well with the experimental result. In the past, the $^{2}D$ structure was thought to be a Feshbach resonance. In this calculation, we show that the $2s2p$ $^{3}P$ target is repulsive to the third $p$ electron in the sense that the variational energy of the ${\mathrm{He}}^{\ensuremath{-}}$ system is monotonically increased as the $p$ electron approaches the target. Hence, the Feshbach resonance cannot be formed for this state. Some comments will be made concerning earlier theoretical calculations in the literature.

DOI: 10.1103/physreva.22.1341

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Physical Review A

Triply excited P2 and D2 resonance of He−

Kwong T. Chung

Published Oct 1, 1980• 31 citations

Publisher

Abstract

The

^{2}P

(

2s2s2p

) and

^{2}D

(

2s2p2p

) resonance structure observed in the electron-helium scattering experiments has been investigated using a saddle-point technique. For

^{2}P

we obtain for the energy --- 0.796 93 a.u. with an 82-term wave function. This agrees well with the experimental result. In the past, the

^{2}D

structure was thought to be a Feshbach resonance. In this calculation, we show that the

2s2p

^{3}P

target is repulsive to the third

p

electron in the sense that the variational energy of the

{\mathrm{He}}^{\ensuremath{-}}

system is monotonically increased as the

p

electron approaches the target. Hence, the Feshbach resonance cannot be formed for this state. Some comments will be made concerning earlier theoretical calculations in the literature.

DOI: 10.1103/physreva.22.1341

Related papers

1s2s2pP2 resonance of He−

Kwong T. Chung

By using a saddle-point technique, the $1s2s2p^{2}P$ resonance of ${\mathrm{He}}^{\ensuremath{-}}$ is found to be a Feshbach resonance. It is formed by the strong coupling of [ $(1s2s)^{1}S$ , $2p$ ] and [ $(1s2p)^{1}P$ , $3d$ ] configurations. By using a seven-partial-wave 54-term wave function and neglecting the open channels, the energy is -2.149 045 a.u. This is higher than the -2.175 23 a.u. $(1s2s)^{3}S$ threshold, but significantly below the -2.145 97 a.u. $(1s2s)^{1}S$ threshold. A quasi-projection-operator method is also carried out. Using the same wave function, the energy is -2.150 54 a.u. These results generally agree with that of experiment.By using a saddle-point technique, the $1s2s2p^{2}P$ resonance of ${\mathrm{He}}^{\ensuremath{-}}$ is found to be a Feshbach resonance. It is formed by the strong coupling of [$(1s2s)^{1}S$,$2p$] and [$(1s2p)^{1}P$,$3d$] configurations. By using a seven-partial-wave 54-term wave function and neglecting the open channels, the energy is -2.149 045 a.u. This is higher than the -2.175 23 a.u. $(1s2s)^{3}S$ threshold, but significantly below the -2.145 97 a.u. $(1s2s)^{1}S$ threshold. A quasi-projection-operator method is also carried out. Using the same wave function, the energy is -2.150 54 a.u. These results generally agree with that of experiment.

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Timothy M. F. Hirsch, Daniel Cocks, Sean S. Hodgman

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A. L. Sinfailam, ROBERT K. NESBET

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Physical Review ADec 1, 1972113 citations

The

^{2}P

(

2s2s2p

) and

^{2}D

(

2s2p2p

) resonance structure observed in the electron-helium scattering experiments has been investigated using a saddle-point technique. For

^{2}P

we obtain for the energy --- 0.796 93 a.u. with an 82-term wave function. This agrees well with the experimental result. In the past, the

^{2}D

structure was thought to be a Feshbach resonance. In this calculation, we show that the

2s2p

^{3}P

target is repulsive to the third

p

electron in the sense that the variational energy of the

{\mathrm{He}}^{\ensuremath{-}}

system is monotonically increased as the

p

electron approaches the target. Hence, the Feshbach resonance cannot be formed for this state. Some comments will be made concerning earlier theoretical calculations in the literature.

By using a saddle-point technique, the

1s2s2p^{2}P

resonance of ${\mathrm{He}}^{\ensuremath{-}}$ is found to be a Feshbach resonance. It is formed by the strong coupling of [

(1s2s)^{1}S

2p

] and [

(1s2p)^{1}P

3d

] configurations. By using a seven-partial-wave 54-term wave function and neglecting the open channels, the energy is -2.149 045 a.u. This is higher than the -2.175 23 a.u.

(1s2s)^{3}S

threshold, but significantly below the -2.145 97 a.u.

(1s2s)^{1}S

threshold. A quasi-projection-operator method is also carried out. Using the same wave function, the energy is -2.150 54 a.u. These results generally agree with that of experiment.

Low-energy positron scattering from singlet and triplet metastable He(

1s2s

) is investigated using the

R

-matrix propagation method in hyperspherical coordinates. Elastic and positronium-formation cross sections are reported, and near-threshold resonance structures are analyzed in terms of eigenphase sums and the time-delay matrix. For the triplet target, the calculated cross sections are in agreement with available convergent-close-coupling results and display the expected threshold behavior. Beyond the known

S

-wave features, Feshbach resonance series in higher partial waves extending up to highly excited atomic thresholds are systematically identified. The time-delay matrix further uncovers hidden resonances that produce obvious structures in the positronium-formation cross sections.

Helium atoms in the metastable

2^{3}S_{1}

state (

{\mathrm{He}}^{*}

) have unique advantages for ultracold atomic experiments. However, there is no known accessible Feshbach resonance in

{\mathrm{He}}^{*}

which could be used to manipulate the scattering length and hence unlock several new experimental possibilities. Previous experimental and theoretical studies for

{\mathrm{He}}^{*}

have produced contradictory results. We aimed to resolve this discrepancy with a theoretical search for Feshbach resonances, using a close-coupled model of

{\mathrm{He}}^{*}

collisions in the presence of an external magnetic field. Several resonances were detected and the existing literature discrepancy was resolved. Although none of the resonances identified are readily experimentally usable, an interesting non-Feshbach scattering length variation with magnetic field was observed in heteronuclear collisions, at field strengths that are experimentally accessible.

s

p

d

, and

f

waves are presented. The width of the

^{2}S

closed-channel resonance below the

n=2

threshold is found to be 0.015 eV, in comparison with the 0.015-0.020-eV estimates of Andrick and Ehrhardt from experiment and the 0.01-eV estimate of Simpson and Fano.