Positrons enter a material, slow down, and annihilate with an electron in the ‘electron sea’. The lifetime is typically very short ~100 ps. Some materials have ‘voids’ in the sea of electrons, and positrons that stop in the ‘voids’ have longer lifetimes (~ 200+ ps). Decay curves may therefore have multiple components.
Fig *. Information contained in a decay-time measurement.
The lifetime of the slow component is related to the nature of the ‘void’ and the strength of the slow component is related to the relative number of ‘voids’.
Suppose electrons in a material are classified as either conduction
electrons or core/valence electrons. Since positrons are positively charged
they will avoid the nuclei and thereby avoid the regions where the core
electrons live. Most e+ annihilations therefore occur with the conduction
Conduction electrons have momentum and this additional momentum adds & subtracts from the equal & opposite 511-511’s from the annihilation process itself. The broadening of the 511 line is determined by the range of momenta in the conduction band. The Fermi momentum (and Fermi energy) can be extracted from the distribution.
Positron interactions with the core/valence electrons are ~ 103 less apparent than those discussed above. The core electrons are fast moving and therefore the energy spread of the 511-511s is much greater.
Fig *. Shape of the 511-keV annihilation line.
Studying the properties of low-lying nuclear states reveals much information about the behavior of nuclear matter. In the heavier nuclei where many nucleons are involved, it is not possible to keep track of the orbital motion of "hundreds" of individual particles and one is forced to use almost exclusively the collective model description. The collective model treats the nucleus as a fluid undergoing vibrations and rotations.
As in any system, the nuclear fluid will oscillate in it's normal modes. (In what shapes do bubbles blown from a soap-bubble wand oscillate?)
But in fact, the nucleus is composed of neutron and protons -- distinguishable particles, so the nucleus should be considered as a mixture of two separate fluids. These two fluids do not necessarily have to oscillate in phase. These exotic oscillations are commonly referred to as mixed-symmetry states or isovector states.
As is the case in many systems undergoing oscillations, it is becoming apparent that the actual motion of the nucleus is not in pure normal modes. The extent of the fragmentation of isovector vibrations has not been measured in spherical nuclei.
Present research concentrates on the Tellurium nuclei -- there are 7 stable nuclei. The mid-shell nuclei 120Te and 122Te are clearly dominated by vibrational characteristics. The heavier nuclei such as 130Te are clearly dominated by the particle orbital structure. By studying the whole range of tellurium nuclei, one should gain some insight into the evolution of these structures and perhaps those aspects of the nuclear force which control the balance.
Most of the measurements are done at the University of Kentucky Nuclear Structure Laboratory. Isotopically enriched samples are hung in a neutron beam which was produced by use of the Van de Graaff accelerator. Most of our experiments focus on things that can be learned by measuring the gamma ray reaction products.
Occasionally the required reactions cannot be performed with the Univ Ky accelerator, and we have traveled to the Swiss nuclear physics lab: the Paul Scherrer Institut. There we utilized beams made from one of their cyclotrons.
There are a few measurements which remain to be done on the tellurium isotopes, and we have also traveled to the Nuclear Structure Lab at the University of Cologne, Germany. --- no pictures yet..
Chemical and accelerator-based elemental analysis techniques are used to determine the chemical composition of materials. Chemical techniques are time consuming and require much handling of the sample. Chemical techniques also destroy the sample, and this is a great disadvantage for rare materials. The popularity of accelerator-based techniques such as PIXE (proton induced X-ray emission) is currently growing rapidly because the sample remains intact and undamaged. Both these techniques determine elemental compositions of samples.
In some instances, it is useful to also know the isotopic composition of materials. Any variations in isotopic abundance which deviates from "standard" abundances may be due to 1) a sensitivity of chemical reaction rates to the isotopic mass of the reactants, 2) sensitivity of physical processes (transport, crystallization, etc) to the isotopic composition, or 3) differences in radiation environment.
The ground work for this project was laid during the Spring 1993 semester with SP490 research student 1/C Matt LaBonte. We wish to compare the isotopic composition of elements found in meteorites to the "standard" isotopic composition of elements found on Earth. The use of meteorites is unique because it allows one to search for variations throughout the solar system and from different depths (core/mantle) inside their parent planetary body. We are focusing on a particular class of meteorites, the carbonaeous chondrites, because they are thought to contain large amounts of primitive material predating the formation of the solar system (~4 billion years old). Such primitive material has the potential providing a window to the early solar system and contains a radiation record of the distant past.
We are exploring various techniques for extracting the desired abundance information. First, we are using the PIXE technique to determine the elemental composition of the sample. Nuclear reaction techniques are required to extract the isotopic information. We are considering neutron activation (with the assistance of Prof Nelson, NAOME), inelastic neutron scattering, and proton capture. Each technique has its merits and draw-backs. The neutron activation technique must battle the orders-of-magnitude variation in neutron capture cross sections between neighboring nuclei, but is not confined to a particular region of the Periodic Table. The proton capture technique probably does not suffer from order-of-magnitude variation in capture, but is confined to elements lighter than ~ Zinc. The inelastic neutron scattering technique, does not suffer from either of these effects, and may be the most promising.
In either case, isotopes are identified by their unique gamma ray de-excitation signatures. The intensity of the g-rays will be unfolded to yield composition of the sample. The ultimate goal would be to develop a portable method for making such measurements -- using a PuBe or AmBe neutron source.
There are many rules governing how a physical system evolves: conservation of energy, conservation of momentum, conservation of angular momentum, etc. Given this collection of rules, one could examine all systems and extract "philosophical" fundamental principles which are embodied in all the rules. One arrives at three fundamental symmetries. Parity symmetry is invariance of the rules with respect to the choice of a left- or right-handed coordinate system. Time-reversal symmetry, deals with an invariance of the rules with respect to forward-backward flow of time. Charge conjugation symmetry involves an invariance with respect to the interchange of particles with antiparticles. A violation of any of the three symmetries requires a revision of the rules of physics.
Parity violation (PV) was first observed in 1957 in the b-decay measurements of C.S. Wu, and has since been observed in many nuclear and elementary particle reactions. The existance of parity violation was explained on a fundamental level by the Weak Interaction. Typically the strength of Weak Interaction is only ~10-7 the strength of "normal" interactions. However in nucleon scattering on heavy nuclei, the nuclear structure and dynamics serves to amplify the Weak Interaction to produce ~ 5 % effects upon observables. Large parity violation effects have been seen at resonances in the nuclei: 81Br, 111Cd, 117Sn, 139La, 232Th,and 238U.
Time-reversal violation (TRV) has never been directly observed, but is implied only in the decay of two particular elementary particles -- the neutral kaons. This isolated case makes it difficult to draw any direct conclusions about time-reversal symmetry. Time-reversal violation effects are thought to be extremely small (Å10-15 or less of the "normal" interactions), and some mechanism to enhance the signal is required.
Experiments are under development at Los Alamos National Laboratory, the Joint Institute of Nuclear Research, Dubna (USSR), and the KEK Laboratory (Japan). These experiments seek to gain a good understanding of parity violation before beginning the search for the much weaker time-reversal effects. Obviously there are experimental problems that must be overcome to do the measurements. There are also problems to consider in analyzing the data to extract the parity violation matrix elements. I have focused on the analysis problems over the past ~7 years.
Details of the PV kinematic enhancement were the focus of a series of papers in 1987, 1988, 1989, and 1993. S- and P-wave scattering amplitudes enter coherently to produce the observable effect in the cross sections. It was shown that the enhancements are sensitive to the amplitudes of the individual partial waves that contribute, and that in certain situations the effect reaches extremes. The interference effect is not always constructive -- in special cases the observable effects will vanish identically regardless of whether parity is violated or conserved.
Trident Scholar Paul Larsen investigated systematic difficulties associated with the neutron beam propagating through the target. Results are summarized in a paper published in Zeitschrift fur Physik. The lesson was clear: one always needs to know the resonance parameters well to extract a reliable value of the PNC matrix element. The importance of the detailed resonance spectroscopy was also indicated in the sensitivity of the PNC observables to experimental errors such as improper spin reversal. The sensitivity to incorrect spin reversal changes more than an order of magnitude depending on the resonance parameters. Depolarization effects also can be important. Since the details of the depolarization process depend not only on the characteristics of the target material, but also on the details of the specific sample, we simply note that depolarization can be included in the present approach.
Similar or related effects with sensitive dependence on the resonance parameters may be crucial in proposed time reversal invariance tests which utilize a polarized neutron beam and a polarized target. Effects such as acquired polarization and depolarization should be considered in depth for these experiments. Our results show that explicit inclusion of actual resonance parameters and detailed calculation of the dependance of experimental observables on these parameters provides additional insight into symmetry-breaking measurements. How to perform similar calculations for time-reversal violation experiments is not clear. Proper treatment of spin precession in the individual magnetic domains of the target is a major concern.
These calculations are closely tied to the status of the experiments at Los Alamos, Dubna, and KEK. Funding for future experiments at Dubna and Los Alamos looks bleak at present, but the KEK Laboratory in Japan is taking up the slack by starting construction on TRV apparatus. Experimental groups in the US and FSU are transfering their support to the KEK Laboratory. Experiments at KEK will come online in a few years. As the TRV experiments progress, it will be necessary to examine similar effects which will occur there.