# Single and Triple Differential Cross Sections for DoublePhotoionization of H- Page: 1 of 12

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Single and Triple Differential Cross Sections for Double Photoionization of H

F. L. Yip,1 D. A. Horner,2 C. W. McCurdy,3,4 and T. N. Rescigno4

'Department of Chemistry, University of California, Berkeley, CA 94720

2Los Alamos National Laboratory, Theoretical Division, Los Alamos NM 87545

3Departments of Applied Science and Chemistry, University of California, Davis, CA 95616

4Lawrence Berkeley National Laboratory, Chemical Sciences, Berkeley, CA 94720

(Dated: February 15, 2007)

The hydride anion H- would not be bound in the absence of electron correlation. Electron

correlation drives the double photoionization process and, thus should impact double photoionization

results most strongly for H-. We present fully differential cross sections for the three-body breakup

of H- by single photon absorption. The absolute triple-differential and single-differential cross

sections were yielded by ab initio calculations making use of exterior complex scaling within a

discrete variable representation partial wave basis. Results calculated at photon energies of 18eV

and 30eV are compared with reported cross sections for helium calculated at 20eV above the double

ionization threshold. These comparisons show a clear signature of initial state correlation that

differentiate the He and H- cases.I. INTRODUCTION

Recent experimental investigations have focused on

double photoionization (DPI) of two-electron atoms [1

7] and molecules [8 11] as a sensitive probe of the corre-

lated motion of electrons. The DPI problem is interesting

from both experimental and theoretical viewpoints be-

cause the process by which an atom or molecule absorbs

a photon of sufficient energy to eject two electrons into

the continuum necessarily depends on electron correla-

tion. Since the optical absorbtion is described by a sum of

one-body dipole operators, any theoretical approach that

treats the electrons in an independent particle model will

produce inaccurate results for the amplitudes connect-

ing the initial and final states. Such considerations have

been previously addressed using different theoretical ap-

proaches for both atomic [12 25] and molecular [26 29]

two-electron targets, with varying degrees of electron cor-

relation being included in the initial and/or final states.

In addition to providing a fingerprint of correlated elec-

tronic motion, double photoionization problems repre-

sent an ambitious theoretical challenge because of the

difficulty in applying the correct boundary conditions

when two electrons enter the continuum. Since the pio-

neering theoretical work of the 1960s [30 32] to describe

the correct asymptotic form of the wavefunction and the

accompanying double ejection amplitude, numerous ef-

forts have been applied to the more general three-body

Coulomb breakup problem, including the use of anzatz

wavefunctions [12 14], convergent close-coupling (CCC)

methods [15 18], adapted R-matrix techniques [19, 20],

time dependent close coupling (TDCC) methods [21 23],

complex basis functions [24], and finally the method of

exterior complex scaling (ECS) [25, 33, 34]. In addition

to ensuring that the calculated wavefunctions maintain

the proper boundary conditions for three-body breakup,

each method requires a proper means to extract the phys-

ically relevant amplitude associated with the two-electron

outgoing wave to produce cross sections that can be com-

pared with experiment.The canonical system for both double photoionization

experimental investigations and theoretical calculations

is the helium atom. This case represents a three-body

Coulomb problem where electron repulsion represents a

significant contribution to the energetics of the system.

Theoretical treatments of helium DPI also benefit from

atomic selection rules that restrict the overall final state

produced from ground state 1S helium to 'P symmetry,

thereby restricting the number of coupled angular mo-

mentum contributions that must be considered in any

partial wave expansion of the total wavefunction.

Analogous to the helium case is double photoioniza-

tion of the isoelectronic hydride anion H-. Indeed, from

a theoretical point of view, DPI of H- is more interesting

because of the greater importance of electron repulsion

relative to the Coulomb attraction of the electrons to the

nucleus when Z 1. Thus, the atomic properties of H-

are more sensitive to electron correlation effects when

compared to helium. This can be most easily demon-

strated by simply comparing the results of a Hartree-

Fock calculation of the He and H- ground state energies.

Whereas in the case of helium the ground state correla-

tion energy is a few percent of the exact total energy, the

Hartree-Fock energy of the hydride anion is above that of

a is hydrogen atom and free electron by 0.33eV [35, 36].

The fact that an independent electron treatment yields

increasingly more significant contributions to the exact

energy of atoms as the nuclear charge Z increases indi-

cates that the electron correlation effects should be most

important in the prototypical case of H-.

Numerous theoretical approaches have been applied

to double photoionization of H-, dating back to a

multichannel J-matrix calculation by Broad and Rein-

hardt [37]. Since then, the problem has been treated by

model calculations [38, 39], variationally [40], R-matrix

methods [41], convergent close-coupling [42], time depen-

dent close-coupling [43], and most recently by wavepacket

propagation [44]. The application of these various meth-

ods have yielded absolute total cross sections for DPI of

H- as well as ratios of single ionization to double ioniza-

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Yip, Frank L.; Horner, Daniel A.; McCurdy, C. William & Rescigno,Thomas N. Single and Triple Differential Cross Sections for DoublePhotoionization of H-, article, February 15, 2007; United States. (digital.library.unt.edu/ark:/67531/metadc896689/m1/1/: accessed November 19, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.