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A general Dirac-Fock Computer Code, written by J. P. Desclaux,
becomes publicly available. It provides the radial algorithms
necessary for the correlation code.
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D. R. Beck, while in Greece, begins work on angular algorithms
needed to do relativistic correlation calculations. The presence
of open d or f shell electrons, which is fairly
typical in medium to high Z atoms, presents substantial
computational challenges, which we are continuing to overcome,
even at present.
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D. R. Beck (now at MTU) and C. A. Nicolaides calculate
relativistic and correlation effects separately for inner
electron binding energies of medium Z atoms.
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G. Aspromallis (a grad student/postdoc of C. A. Nicolaides and
D. R. Beck), C. A. Nicolaides, and D. R. Beck, compute the
lifetime of a long-lived Be−
state, which decays relativistically. Correlation and relativistic
effects are still treated separately. The lifetime prediction is
later confirmed experimentally.
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D. R. Beck publishes the methodology needed for a combined
relativistic and correlation treatment, and applies it to bound
states in Zn−. The formalism
used is that of Grant. At this stage, only energy differences for
bound states can be computed.
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D. R. Beck and Z. Cai (D. R. Beck’s first MTU Atomic
Physics student) publish electron affinities (EA) for
Mn−, Cr−, Fe−,
Co−, and
Ni− using the new methodology.
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D. R. Beck and Z. Cai extend the methodology to calculate
electric dipole (E1) transition probabilities for bound states
and apply it to transitions in Tl II.
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Z. Cai, D. R. Beck, and W. F. Perger extend the methodology
to resonances, and apply it to Hg I. The
key step is the creation of a radial continuum function algorithm,
implemented by W. F. Perger (EE faculty, MTU).
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D. R. Beck and D. Datta (the second atomic physics graduate
student) extend the methodology to calculate hyperfine structure
(HFS) and apply it to
Ag I, Sc II,
Y II, Ti I,
Ti II, Zr II,
Nb II, and La II.
The reason for the discrepancy between theory and experiment for
HFS of certain states is found and accounted for. Lifetimes for
two Nb II states were also obtained. During
this period, a procedure (REDUCE)
is inserted into the codes
which allows reductions of the number of basis functions by
factors from 3 to 100, allowing small (~350) energy matrices to be
used. This is an essential step in permitting calculations to be
done on complicated states.
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A modified version of an existing (Weber) large scale matrix
diagonalizer is inserted into the code by K. D. Dinov (the
third atomic physics graduate student) and D. R. Beck. This
allows energy matrices as large as 7000 to be treated. K. D.
Dinov also creates a program which simplifies construction of
the input data files enormously, and yields error-free data.
Previously, these multi-thousand line files took much
preparation time.
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K. D. Dinov, D. Datta and D. R. Beck publish EA’s for the
lanthanide elements Ce and Pr and the actinides
Th, U, and Pa in a series of papers. At
this time, none of these have been measured, and the calculations
are the first using p and d attachments for these atoms.
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S. M. O’Malley (4th atomic physics graduate student) and
D. R. Beck apply the methodology to Cs II
and Ba III (HFS) and Tb, Sb, Sn, and La
(EA’s). The results for Sb, Sn, and La are in good agreement
with contemporaneous measurements. The Sn work is our first
systematic inclusion of second order effects (triple and
quadruple excitations) which are important for greater accuracy
generally, and also in more complicated systems. This work
includes the first application of our magnetic dipole (M1) and
electric quadrupole (E2) transition probability algorithms.
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E. N. Avgoustoglou (Ph.D. Notre Dame) joins the group as a postdoc,
and using relativistic many body perturbation theory (RMBPT)
predicts EA’s for Ca, Sr, Ba, and Yb. His Yb work is the first
predicting (later confirmed) the non-existence of this negative
ion. RMBPT calculations are also done for resonance transitions
in Ne, Ar, Kr, and Xe; these serve as the theoretical standard.
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The methodology is applied by D. R. Beck to reduce theoretical
experimental discrepancies in energy differences for highly ionized
members of the 3d4
isoelectronic sequence.
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D. R. Beck extends the methodology to allow computation of Landé
g values, and publishes results (including lifetimes) for
Cs II.
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P. L. Norquist (5th atomic physics student) and D. R. Beck apply
the methodology to compute EA’s for Ru and Os. These predictions
are later found to be in good agreement with experiment. In order
to do the calculations, the REDUCE
algorithm is upgraded to handle
more complicated cases.
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S. M. O’Malley computes EA’s for
Ce− and Lu− in anticipation of a
measurement, and E1 transition probabilities for
Fe V in order to test some newly published
results. The purchase of new memory (1 GB), allows the matrix
size to be increased to 20k, and still reside in memory. The
increased size is first used for Fe V.
Shortly thereafter, P. L. Norquist and D. R. Beck complete a
calculation for Ta II E1 oscillator strengths
using the new code. A modification is made to the transition
probability code allowing all optical transitions for the same
initial and final state
J’s to be done at once, which speeds up the
Ta II calculations by a factor of 70.
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M. G. Tews (6th atomic physics graduate student), W. F. Perger,
D. R. Beck, and P. L. Norquist calculate the lifetime of a very
long-lived Ba− state, which
decays by relativistic autoionization. W. F. Perger’s radial
continuum program is modified by M. G. Tews and W. F. Perger,
and D. R. Beck and P. L. Norquist begin to thoroughly automate
and extend the programs used by Z. Cai for Hg I
resonances. When completed, the program will be a fully
relativistic generalization of the code used by G. Aspromallis
for the Be− lifetimes.
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S. M. O’Malley and D. R. Beck finish calculations for E1
transitions in Tc I. The configurations are
so complicated, that REDUCE
must be heavily modified. Application
to Fe II is made in 2004 by D. R. Beck.
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D. E. Woon and D. R. Beck speculate that atomic anions
possessing several bound states may form anion hydrides with
more than one bound state. This is indeed the case for
SiH− and
GeH−.
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D. R. Beck and others extend the work to the more complicated
rare earth ions, specifically energy differences of
4f11
Er IV which is associated with an important
lasing transition within a GaN host. Later (2006) calculations
are done by D. R. Beck for 4f7
Gd IV which is important in
PbF2:Gd scintillators. Accuracies
of ~1000 cm−1 can be achieved.
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L. Pan (7th atomic physics student) and D. R. Beck complete
calculations on isoelectronic Zr III,
Nb IV, and Mo V,
repositioning the 5s2
Nb IV level, and obtaining the first
ab initio f values. In Mo V,
4p54d3 levels are
found to be relatively low-lying. Their treatment is made difficult
because more core-valence (core-core) correlation must be included. The
simpler Mo VI species, for which there are
some observations (sometimes conflicting) is also examined.
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Several of the Rare Earth EA’s measured by J. S. Thompson and
V. T. Davis are larger than our theoretical predictions. For
Tm− and Eu− long lived excited states
may be what is observed (neutral atoms left in excited states).
For Ce−, the discrepancy seems
to be associated with the ~26 bound
Ce− states which complicate
interpretation of the observations, as indicated by the
photoionization cross sections calculated by S. M. O’Malley
and D. R. Beck.
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L. Pan and D. R. Beck calculate the 1s ionization potential
(IP) and excitation energies in Krn+
and Brn+ (n=0, 1, 2).
These are needed for synchrotron studies. Relaxation, correlation,
QED effects, and continuum shift effects must be included. Theory
and experiment agree to ~1 eV for the 1s IP of
Kr I. The remaining discrepancy may arise in
part from missing QED effects.
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S. M. O’Malley, L. Pan, and D. R. Beck make substantial
improvements in obtaining photodetachment cross sections of rare
earth anions with the addition of the following: (1) extensive
shell scripts and codes that prepare data and manage runs, (2)
extensive reduction of
4fn couplings
with little loss with the subsequent large reduction in basis size
(and number of determinants in some cases), (3) better correlated
final state functions including the effect of resonances and
partial inclusion of interchannel correlation using the Fano and
Mies theory, and (4) a systematic attempt to identify,
a priori, which are the important photodetachment channels.
Initial application is to the Nd− and
Hf− anions.
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S. M. O’Malley develops a generalized angular momentum
addition program, allowing efficient and systematic preparation
of input data with JLS term restrictions on subgroups of
electrons. S. M. O’Malley and D. R. Beck initially use the
methodology to restrict the 4f4 and
4f3 subgroups
of Nd and Nd− each to a
single term (5I and
4I, respectively). Basis sizes
are limited by this procedure nearly on par with
REDUCE without
its complications of second order correlation losses due to the
reference selection issues.
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S. M. O’Malley expands and automates the angular momentum
addition program and its methodology, allowing for the selection
of secondary LS terms and decreasing data preparation time
considerably.
S. M. O’Malley and D. R. Beck apply the methodology to the
entire lanthanide row, including 6p attachments to all
4fn6s2 and
4fm5d6s2
ground states (m≡n−1) and 6s
attachments to open-s excited thresholds. These are the first
ab initio EA calculations for Pm−
through Er−.
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