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.
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 , 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 . Since then, the problem has been treated by
model calculations [38, 39], variationally , R-matrix
methods , convergent close-coupling , time depen-
dent close-coupling , and most recently by wavepacket
propagation . 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 January 17, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.