Bound precision tests

In the case of the positronium spectrum the accuracy is on the MHz-level for most of the studied transitions (Is hyperfine splitting, Is — 2s interval, fine structure) [13] and the theory is slightly better than the experiment. The decay of positronium occurs as a result of the annihilation of the electron and the positron and its rate strongly depends on the properties of positronium as an atomic system and it also provides us with precise tests of bound state QED. Since the nuclear mass (of positronium) is the positron mass and me+ = me-, such tests with the positronium spectrum and decay rates allow one to check a specific sector of bound state QED which is not available with any other atomic systems. A few years ago the theoretical uncertainties were high with respect to the experimental ones, but after attempts of several groups [17,18,19,20] the theory became more accurate than the experiment. It seems that the challenge has been undertaken on the experimental side [13]. 

Fundamental physical constants are universal and their values are needed for different problems of physics and metrology, far beyond the study of simple atoms. That makes the precision physics of simple atoms a subject of a general physical interest. The determination of constants is a necessary and important part of most of the so-called precision test of the QED and bound state QED and that makes the precision physics of simple atoms an important field of a general interest. 

For all these reasons Ps is an ideal candidate for precision tests of bound state quantum electrodynamics (QED). 

Until now any precision test of bound state QED [2] was always realized in the way that only a final theoretical figure could be compared with some experimental result and no term of any theoretical expression could be tested separately. Any theoretical expression is a function of few parameters and one of them is the nuclear charge Z. However, there was no way to measure any function of Z. Only very few particular values of Z were available for precision experiments of the Lamb shift, fine and hyperfme structure. Now this has been changed dramatically. 

An important feature of the study of the g factor of a bound electron at Z = 20 — 30 is also the possibility to learn about higher-order two-loop corrections, which are one of the crucial problems of bound state QED theory. Below we discuss in detail the present status of theory and experiment. We consider a new opportunity to precisely test bound state QED and to accurately determine two fundamental constants the electron-to-proton mass ratio and the fine structure constant. 

Now let us discuss possible precision tests of bound state QED. First we need to discuss what experimental results have been available up-to-now [2] ... 

Concluding our consideration we would like to underline, that the study of the g factor of a bound electron [1] offers a new opportunity for us to precisely test bound state QED theory and to determine two important fundamental constants the fine structure constant a and the electron-to-proton mass ratio m/mp. The experiment can be performed at any Z with about the same accuracy [1] and one can expect new data at medium Z which will allow to verify the present ability to estimate unknown higher-order corrections (i. e. theoretical uncertainty) in both low-Z and high-Z calculations. 

QED can be considered to be one of the most precisely tested theories in physics at present. It provides an extremely accurate description of systems such as hydrogen and helium atoms, as well as for bound-leptonic systems, for example, positronium and muonium. Remarkable agreement between theory and experiment has been achieved with respect to the determination of the hyperfine structure and the Lamb shift. The same holds true for the electronic and muonic g-factors. The free-electron g-factor is determined at present as... 

Precise test of QED for the two lepton bound state and of the behavior of the muon as a heavy electron. 

In general, the calibration curve method is suitable for all samples where the test substance is not bound in complexes or when it can be liberated from complexes by suitable sample pretreatment. Otherwise, the compositions of the samples and of the standard solutions must be as similar as possible to obtain results with acceptable accuracy. In view of the ISE potential drift, the calibration must be repeated often (at least twice a day). As mentioned above, the precision of the determination is not particularly high with a common precision of the potential measureihent at a laboratory temperature of 1 mV the relative error is 4% for univalent and 8% for divalent ions [58], However, this often suffices for practical analytical purposes. An advantage is that the same precision... 

An advantage of the ASO method is that it can be used to simultaneously test samples for several different mutations by the use of multiple probes bound to a solid matrix. In practice, the success of this method relies on precisely establishing conditions for optimal oligonucleotide hybridization in order to ensure specific probe hybridization, and so multiplex ASO assays can be difficult to develop. Molecular diagnostic kits for use in genetic disorders based on ASO methods are available (14). 

The problem was overcome with the use of mildly fixed microtubules [10] in which the paclitaxel binding site is unaltered, while protected from cold and dilution depolymerisation and a paclitaxel molecule bound to a fluorescent probe (either fluorescein or difluorofluorescein) [8], The fluorescent derivatives of paclitaxel were then tested to check that they compete with taxoids for the same site, with the same 1 1 stoichiometry producing the same celular effects as paclitaxel and docetaxel, thus it can be assumed that they bind for the same site [9], Using these stabilized microtubules, it is possible to determine precisely the binding constant of the fluorescent taxoid which was found to be of the order of 108 M at 25°C. 

Further, the validation of a model needs the definition of the criterion for establishing that a model has been validated. How well should a model predict effects precisely, and what are the bounds between which one calls a model (sufficiently) valid It also needs the definition of the context against which a model is to be considered valid. For example, validation of the SSD model has generally been based on whether the so-called hazardous concentration for 5% of the species (HC5) is a concentration that is conservative (sufficiently protective) compared to the no-effect concentration in multispecies mesocosm or field tests. In that sense, the model has performed well for both aquatic and terrestrial systems (e.g., Emans et al. 1993 Okkerman et al. 1993 Posthuma et al. 1998 Versteeg et al. 1999 van den Brink... 

Microbial tests based on reverse mutation are specific, because a unique mutation must undergo precise reversion.423 This may be a limitation, in that only one genetic end point is monitored, although little empirical evidence supports this criticism. A prokaryotic or eukaryotic cell apparently uses a number of pathways at the same time to cope with adducts that cure covalently bound to DMA. 

Perhaps a problem more important for applications is to eliminate the nuclear effects and to test the bound state QED precisely or use the bound state QED for the determination of some fundamental physical constants. There are a few ways to manage this problem [11] and to expand the accuracy of the tests of bound state QED beyond a level of our knowledge of the nuclear structure effects. 

The fine structure constant a can be determined with the help of several methods. The most accurate test of QED involves the anomalous magnetic moment of the electron [40] and provides the most accurate way to determine a value for the fine structure constant. Recent progress in calculations of the helium fine structure has allowed one to expect that the comparison of experiment [23,24] and ongoing theoretical prediction [23] will provide us with a precise value of a. Since the values of the fundamental constants and, in particular, of the fine structure constant, can be reached in a number of different ways it is necessary to compare them. Some experiments can be correlated and the comparison is not trivial. A procedure to find the most precise value is called the adjustment of fundamental constants [39]. A more important target of the adjustment is to check the consistency of different precision experiments and to check if e.g. the bound state QED agrees with the electrical standards and solid state physics. 

Abstract. Muonium is a hydrogen-like system which in many respects may be viewed as an ideal atom. Due to the close confinement of the bound state of the two pointlike leptons it can serve as a test object for Quantum Electrodynamics. The nature of the muon as a heavy copy of the electron can be verified. Furthermore, searches for additional, yet unknown interactions between leptons can be carried out. Recently completed experimental projects cover the ground state hyperfine structure, the ls-2s energy interval, a search for spontaneous conversion of muonium into antimuonium and a test of CPT and Lorentz invariance. Precision experiments allow the extraction of accurate values for the electromagnetic fine structure constant, the muon magnetic moment and the muon mass. Most stringent limits on speculative models beyond the standard theory have been set. 

We will review here experimental tests of quantum electrodynamics (QED) and relativistic bound-state formalism in the positron-electron (e+,e ) system, positronium (Ps). Ps is an attractive atom for such tests because it is purely leptonic (i.e. without the complicating effects of nuclear structure as in normal atoms), and because the e and e+ are antiparticles, and thus the unique effects of annihilation (decay into photons) on the real and imaginary (related to decay) energy levels of Ps can be tested to high precision. In addition, positronium constitutes an equal-mass, two-body system in which recoil effects are very important. 

---