ATOMIC AND MOLECULAR PHYSICS AT THE
INTERFACE TO NUCLEAR AND PARTICLE PHYSICS
Introduction
Atomic physics is spectactular, not for the large scale of its
facilities, but rather for the precision achievable and the importance
of the information that can be obtained from experiments that are
literally "tabletop".
A close
collaboration between theory and experiment is a long-standing
characteristic of the Göteborg atomic physics group, as
emphasized already by the 1978 NFR evaluation of Swedish Atomic and
Molecular Physics. The combination of theory and experiment has made
atomic physics to a tool for extracting information e.g. about
nuclear parameters and about fundamental interactions less well known
than the Coulomb interaction, which dominates overwhelmingly in atoms.
An example is the study of the
parity non-conserving electroweak
interaction, which I think is one of the most important parts of my
work.
The tool of atomic physics is made even sharper, not only through the
experimental developments, but also throguh the development of
computers and through the development of methods to treat
many-electron systems also for heavy elements, where relativistic
effects play a very important role, and add formal and conceptual
challenges to those of numerical and computational character. Our
group has played a strong role in the development of methods to treat
relativistic many-body problems. QED as the fundamental theory
describing atomic systems, has been extremely successful. Modern
experiments provide critical tests in new regions of nuclear charge,
and thus keeps challenging the computationa and formal skills of
theorists, demanding accurate treatment of many-body effects, as well
as radiative corrections.
Throughout my career, I have been involved with calculations and
developments of methods to assist interpretation of experimental
results, usually in close collaboration with experimentalists in
Göteborg or abroad. In other cases, my work has given the first
quantative interpretation of experiments performed earlier, sometimes
as early as in the 1950s. My work has strong connections, not only
with experiments but also with nuclear and particle physics. The
formal aspects of the work lead to good contacts also with quantum
chemists. In 1994 I used these contacts to bring together researchers
from these different areas in a workshop centered around the
interpretation of experiments searching for violation of parity as
well as time reversal symmetry in diatomic molecules. A brief
report
from this workshop is available.
I think that my most important work has been in connection with the
study of parity non-conserving properties and I have written two reviews,
which present the field and put some of my other work into context.
The first review presents the studies of
parity non-conservation without accompanying
violation of time reversal symmetry (T). Here the task of matching
the increasing experimental accuracy poses a severe challenge.
By contrast, the
search for T violation in atoms has
given only upper limits. An atomic electric dipole moment could arise
through several
P and T violating mechanisms. The source of CP
violation, so far observed only in the decay of neutral K mesons,
remains obscure, and it is important to investigate as many
possibilities as possible. The calculation of these properties faces
fundamental problems connected to the relativistic formalism.
The ability to perform very accurate calculations is based
on earlier experience with non-relativistic calculations.
Parity Non-Conservation and Weak Interactions
The interest in atomic parity non-conservation stems from the
possibility to obtain the weak-interaction parameters at low energies
through combination of theoretical and experimental results.
After a discouraging and confusing start, the experiments have now
given results for several elements (Cs, Tl, Pb and Bi) which are in
good agreement with theoretical predictions based on atomic
calculations using the electron- nucleon interaction from the Standard
Model for electroweak interactions.
During 1978-81 I worked as a research associate in Seattle and Oxford
in groups where atomic parity non-conserving effects are being
studied. Since the PNC effects is strongly enhanced for heavy atoms
it is essential to use a relativistic procedure and I thus developed a
new set of computer programs. The need to treat two external
perturbations (the weak interaction and the interaction with the
electric dipole field from the photon) in addition to the Coulomb
interaction between the electrons makes already the one-particle
problem quite complicated. Single-particle effects have been included
to all orders in a procedure similar to the Random-Phase Approximation
or the Time-Dependent Hartree-Fock methods (but with a PNC operator in
the one-electron Hamiltonian), giving results in relatively good
agreement with experiments for Cs, Tl, Pb and Bi.
Also lowest-order correlation effects have now been included
using the relativistic pair program developed in our group.
With a combined theoretical and experimental accuracy of around one
percent these investigations would test the radiative corrections to
the weak interactions which is an indirect probe of physics at a very
high energy scale, normally probed only with extremely large
accelerators. Recent experiments for Pb (Meekhof et al. Phys.
Rev. Lett. 71 3442 1993) and Tl (?) (ICAP-14, Abstract 1D-3, and ?).
has reached this accuracy. For Cs, where ,the
theoretical value is most accurate, a significant improvement is
expected to the 2% result by Noecker et al (Phys. Rev. Lett. 61
310-3 1988). This is the system where the theoretical accuracy is
largest:. In 1990, several researchers calculating PNC effects met at
a workshop on Coupled-Cluster Theory which resulted in a joint
review
paper (coordinated by our group) which discusses and compares the
different approaches as well as the implications of the results for
PNC in Cs. Future experimental developments are expected to lead to
increased accuracy not only for Cs, but also for the other heavy
atoms, such as, Tl, Pb and Bi.
For the more complex atoms the interactions between the valence
electrons, and also the core-valence interactions, are much larger
than for the alkali atoms. To treat these systems, we plan a
development of the coupled-cluster program in order to use more
general potentials and wavefunctions as starting points. The study of
PNC in several different atoms is important, since it leads to an
independent confirmation of the results and thereby increases the
reliability of the weak interaction parameters extracted from the
atomic physics experiments.
Another current line of PNC research is the study of sequences of
isotopes of an element, such as Sm and Cs, in order to establish the
neutron number dependence of the result. To interpret these data with
sufficient accuracy, more detailed knowledge of the nuclear
distributions is needed. The isotope shift measurements in the Cs
chain will provide helpful information, in particular when combined
with accurate theoretical isotope shift parameters, as discussed
below.
Related Publications ,
The presence of an EDM in an atom or elementary particle would imply a
simultaneous violation of symmetry under parity (P) and time (T)
reversal, and limits on EDMs can impose restrictions e.g. on
supersymmetric gauge theories. Experimental results (Vold et al.Phys.
Rev. Lett. 51 2229 1984, and Lamoureaux et al. Phys. Rev. Lett.
57 3125 1986, Jacobs et al. Phys. Rev. Lett. 71 3782 1993) have
established very low upper limits for the electric dipole moment in Xe
and Hg. The limit for Xe has been used to set an upper limit for a
possible P and T violating electron-nucleon interaction and we
have also performed a calculation relating an atomic EDM to a possible
electron EDM in order to obtain limits for the electron EDM. For the
closed shell ground state of Xe and Hg, the interaction with the
nuclear magnetic moment is necessary to enable the electron EDM to
cause an atomic EDM, thereby making the atomic EDM a few orders of
magnitude smaller than the electronic one. The situation is quite
different for the alkalis, where the atomic EDM are a few orders of
magnitude larger than the electronic EDM. A number of groups are
working to establish lower experimental limits for the the EDMs of
one-valence systems the lowest limit today is derived from recent
experiments on Cs and Tl and we have performed calculations also for
these systems and are working on the inclusion of correlation
effects . A possibly much more sensitive test may be provided by
polar molecules and in 1994, I therefore organized an ESF
workshop workshop in Oxford to
bring together experimentalists, particle
physicists and quantum chemists in discussing such possibilities.
Isotope shifts are small energy differences between different isotopes
of an element and arises from different sources: The normal mass
shift (NMS) is due to the reduced mass of the electrons, the specific
mass shift (SMS) is caused by a correlation of the electronic momenta
due to the motion of the nucleus with its finite (non-infinite) mass,
and the volume or field shift is due to the finite (non-zero) size of
the nucleus. For a long time it was believed that meaningful ab
initio calculations of the SMS were out of reach However, in 1981, I
initiated and performed in collaboration with Sten Salomonson a
calculation of all lowest order correlation contributions using the
above- mentioned pair program. This gave a relatively satisfactory
agreement with experiment, especially when "Brueckner orbitals", which
include certain correlation effects directly in the orbitals, were
used in the evaluation. This work marked a breakthrough and
stimulated other groups to take up the challenge of the SMS. Similar
calculations have now been performed also in the relativistic
framework. However, higher-order correlation effects are not
negligible and I am now developing a computer program for the
evaluation of the SMS using relativistic coupled-cluster
wavefunctions.
We have also used many-body theory to evaluate also the electronic
factor for the field isotope shift and found that higher-order
contributions to this effect are significantly different from
corresponding contributions to the contact hyperfine interaction.
This leads to errors in the semi-empirical procedure commonly used to
extract the electronic factor. In the light of these theoretical
results we have reanalysed experimental data available for
long chains of isotopes from experiments e.g. at CERN and GSI. In
this way more reliable values for the changes d in the nuclear
charge radii, of importance for nuclear physics, could be obtained.
Related publications. ,
Hyperfine structure calculations often serve as a useful assessment of
the accuracy of the atomic wavefunctions used to extract other
properites, since it can usually be measured very accurately, and the
nuclear magnetic moment can be determined independently. Recently, I
extended these calculations to include also the effect of the
distribution of the nuclear magnetic moment, known as "hyperfine
anomaly" or the
"Bohr-Weisskopf effect". The distribution of nuclear
magnetization has been found to be important in recent investigations
at GSI of hydrogen-like Bi, with the purpose of testing QED
corrections (Klaft et al Phys. Rev. Lett. 73 2425, 1994). However,
there are many older experimental results available for several
different elements. In recent work, I was able to give a
quantitative interpretation in terms of changes in the magnetic radius
between 203Tl and 205Tl, based on experiments performed in the 1950s.
This change was found to be significantly larger than the
corresponding change in the charge radius. This difference may have
implications for the interpretation of experiments searching for P and
T violation. The results obtained should also provide a useful
calibration for nuclear theory. In a recent project work, Martin
Gustafsson examined in detail the effect of different charge
distributions on the hyperfine structure, and implemented
possibilities to use directly the results from scattering experiments
studying nuclear charge distributions. The studies of the
Bohr-Weisskopf effect will continue for other systems of experimental
interest, e.g., in connection with experiments performed at ISOLDE for
Cs isotopes.(Henry Stroke, Curt Ekström and others)
Related publications on
hyperfine structure and on
Magnetic moment distributions.
Pair correlation is essential for the studies of all properties
discussed above. By means of iterative numerical solution of the
"pair equation", pair correlatin can be treated to all orders within
the "coupled-cluster approach". This was implemented in a non-
relativistic program as part of my thesis work. The more
recent calculations have focused on heavy atoms, where relativistic
effects are essential. The ability to perform accurate calculations
for heavy atoms has developed rapidly in recent years. Also
relativistic pair correlation effects can now be treated within the
coupled-cluster approach. Fundamental questions in connection with
the relativistic electron-electron interaction are much better
understood and methods have been developed to treat the Breit and
Coulomb interactions together. The numerical accuracy is very
good, as demonstrated e.g. in our recent paper studying the 1s2p
states for helium-like systems. Here, the ability to handle a
more general model space enabled us to obtain accurate results also
for low Z, where earlier attempts to apply relativistic perturbation
theory had failed. The high numerical accuracy is essential for
critical comparisons of quantum-electrodynamic (QED) effects with
experimental data. Accurate wavefunctions for heavy atoms also makes
it possible to obtain quantitative results for other properties, as
discussed above.
Related publications on
Pair Correlation ,
Formal developments and calculations of
various atomic properties .
Formal developments are likely to include the incorporation of quantum
electrodynamic (QED) effects in the coupled cluster approach. We
expect that a combination of "multi- configuration" methods and
perturbation theory will give accurate results also for more complex
atoms and will pursue development in this direction. The powerful
methods already developed in our group enable accurate calculations
for different properties and systems. In the near future, we expect
more applications to oscillator strengths in alkali atoms, where
recent accurate experiments make possible a critical comparison.
Negative ions show unusually large correlation effects, and are
therefore of special theoretical interest. It is also one of the main
directions of the experimental part of the group, and we foresee
continued fruitful collaboration.
Research Programme, A-M Mårtensson-Pendrill
Ann-Marie.Pendrill@fy.chalmers.se
http://fy.chalmers.se/~f3aamp/research