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<se *< *pl 297,21,240,13,4*
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Anders Lindgård
*qr*
1979-09-28
*rj*
*ns 1,2,Research Plan in Atomic Physics*
*ns 1,3,Atomic Transition Probabilities*
        -------------------------------*nl**np*
The Increasing need for basic atomic structure data especially
in astrophysics and controlled nuclear fusion research, makes
it attractive to look for simple semiempirical methods 
which can give a large number of resonably accurate lifetimes
for exited states in atomic ions and at a low cost.
*nl**np*
For simple ions like the important alkali-like ions the
recently developed and perfectioned numerical coulomb approximation
(Lindgård and Nielsen 1975; 1977) gives lifetimes and oscillatorstrengths
with an accuracy comparable with experiments and with ab-initio calculations.
Primary advantages of the numerical coulomb approximation are the ability of
obtaining good wavefunctions for highly exited states and the computation
speed. A single wavefunction is obtained in one sec (on the RC4000 computer) and

so is an oscillatorstrength. All the data for the alkali sequences as 
published (Lindgård and Nielsen, 1977) took less than 3 hours
for 11000 oscillatorstrengths. This data set has become a standard source
for oscillatorstrengths of the alkalisequences.
*nl**np*
For the Cu I sequence the numerical coulomb approximation has been combined
with recently developed extrapolation and interpolation methods to give
oscillatorstrengths for the lowest 20 states of all ions up to In XXI
(Curtis et. al., 1978; Lindgård et. al., 1979). Theese data are
of particular interest to fusion research, as strong lines from heavy
ions isolectronic with Cu I seem to be responsible for a large fraction
of the radiation loss in tokamaks.
*nl**np*
The numerical coulomb approximation was tried on 3-electron sions
of the Ga I and In I sequences (Andersen and Lindgård, 1977).
For the neutrals, which have nice regular rydberg series, the agreement
with experiment was execellent. For the isoelectronic ions some
of the computed results were clearly wrong. This is due to the increasing
degeneracy between the s-electrons and the p-electron of the same shell
when the charge increases toward the hydrogenic limit.
Terms with labels s!h2, which in the neutrals are far above
the first ionization limit, are in the ions in the lower
part of the bound spectrum, and they can introduce "configuration
mixing" i. e. a state can no longer be described by a wavefunction
for a single electron with a definite symmetry. However
it may possibly be described by a simple sum of single configuration
wavefunctions, provided the expansion coefficients can be derived,
preferably from experimental term values.
*nl**np*
Beam foil spectroscopy is the primary source for experimental lifetimes
in ions. It is therefore of importance for this work that they can
be relied on. However the interpretation of decaycurves is difficult
due to cascading processes from higher lying states. Multiexponential
fit often fails. By simulation studies using transition probabilities
computed in the numerical coulomb approximation, it is relatively
easy to determine the cascade contribution from all levels which are
resonably populated. Such studies are now being performed in Lund and
Copenhagen (Hultberg et. al., 1978).
*nl**np*
The work described above has taken place in close collaboration with
the University of Lund, Research Institute for Physics in Stockholm,
University of Århus and University of Copenhagen.
*ns 1,3,Research plan*
        -------------*nl**np*
The primary goal is to merge the numerical coulomb approximation
with other semiempirical methods for handling the configuration
mixing problem.
Several methods will be examined. The most promising  at
present is the Lu-Fano-Starace method (Starace, 1973; Crossley and
Richards, 1975). It has been used mainly for the analysis
of spectra, but a few computations has been done for Ne I and
some transitions in 3-electron systems. In the latter case the
use of the old Bates Damgaard method is probably responsible
for the often poor results. This problem has been taken
up with dr. Crossley, University of York and is supported
by a NATO research grant. The drawback of the Lu-Fano-Starace
method is the large number of parameters which must be determined
for even moderately complex cases. The available amount of experimental
energy levels may often not allow the use of this method. It is
therefore the intention to develop less elaborate methods with
only a few parameters, which still describe the features essential
for the calculation of oscillatorstrengts to be used when energy
levels are sparse.
*nl**np*
The sequences to be studied will primarily be of the two and three
electron types. The most important sequences are the Mg I and Be I
sequences. Energy level data here exist up to rather highly ionized
systems. The number of configurations which mix is small. Some
experimental lifetimes are known, allthough the material is sparse.
It however two important sequences to study in both astrophysics and
fusion research, as they cover some important highly ionized members
of the iron group. The goal is to compute nearly all lifetimes
for which energy level data exist with a 10% accuracy.
*nl**np*
Other two electron sequences to be studied are the Zn I and Cd I sequences.
Here unfortunately energy level data are rather sparse.
*nl**np*
For three electron system work is to be performed on the B I and Al I
sequences. The latter seem to be especially hard to do by ab-initio
methods, as some states cannot be resonably computed using the most
refined techniques (Froese Fisher, 1976). They are therefore
particularly challenging to do using semiempirical methods.
*nl**np*
The most important problem for semiempirical methods presents in
principle the ground state wavefunction. Allthough for the simple
alkalisequences it does not seem to be much of a problem, the
coulomb representation is bad for more complex systems
e. g. the C I sequence or for heavy ion systems where relativistic
effects are large. If time permits during the project, it would be
worth trying to use multiconfiguration Hartree-Fock wavefunctions
to represent the ground state and numerical coulomb wavefunctions
for the large number of exited states to compute oscillatorstrengths.
*nl**np*
The theoretical work described above should be performed in close
contact with the experimental groups in Lund, Stockholm, Århus and
Copenhagen. It is of great importance for this type of work to be
able to analyze the available experimental lifetimes and decay curves
jointly with the theoretical work. Further it is possible that this
work may require new measurements and remeasurements. It is a very
important issue how confident we can be in the numbers obtained theoretically
when they are going to be used in various fields of physics.
*ns 1,3,References*
*nl1*
Lindgård A. and Nielsen S. E.*nl*
J. Phys. B8 1183 (1975)
*nl2*
Lindgård A. and Nielsen S. E.*nl*
At. Data & Nucl. Data Tables 19 533 (1977)
*nl2*
Andersen T. and Lindgård A.*nl*
J. Phys. B10 2359 (1977)
*nl2*
Froese Fisher C.*nl*
Can. J. Phys. 54 740 (1976)
*nl2*
Starace A.*nl*
J. Phys. B6 76 (1973)
*nl2*
Crossley R. and Richards S.*nl*
Beam Foil Spectroscopy (Ed. Sellin and Pegg),*nl*
Plenum Press, New York, 1975 p.83
*nl2*
Curtis L.J. Lindgård A., Edlen B., Martinson I. and Nielsen S. E.*nl*
Phys. Scr. 16 72 (1977)
*nl2*
Lindgård A., Curtis L. J., Martinson I. and Nielsen S. E.*nl*
Phys. Scr. xx xxx (1979)
*nl2*
Hultberg S., Liljeby L., Lindgård A., Mannervik S., Nielsen S. E. and Veje E.*nl*
Phys. Lett. 69A 185 (1978)
*ef*
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