Lamb shift systems

Soon after the Schrodinger equation was introduced in 1926, several works appeared dealing with the fundamental problem of the nuclear motion in molecules. Very soon after, the relativistic equations were introduced for one-and two-electron systems. The experiments on the Lamb shift stimulated... 

As mentioned, most calculations we have done so far have concerned molecular systems. However, prior to development of the non-BO method for the diatomic systems, we performed some very accurate non-BO calculations of the electron affinities of H, D, and T [43]. The difference in the electron affinities of the three systems is a purely nonadiabatic effect resulting from different reduce masses of the pseudoelectron. The pseudoelectrons are the heaviest in the T/T system and the lightest in the H/H system. The calculated results and their comparison with the experimental results of Lineberger and coworkers [44] are shown in Table 1. The calculated results include the relativistic, relativistic recoil. Lamb shift, and finite nuclear size corrections labeled AEcorr calculated by Drake [45]. The agreement with the experiment for H and D is excellent. The 3.7-cm increase of the electron affinity in going from H to D is very well reproduced by the calculations. No experimental EA value is available for T. 

In the language of control theory, Tr[p(0)P] is a kinematic critical point [87] if Eq. (4.159) holds, since Tr[e p(0)e- P] = Tr[p(0)P] + Tr(7/[p(0),P]) + O(H ) for a small arbitrary system Hamiltonian H. Since we consider p in the interaction picture, Eq. (4.159) means that the score is insensitive (in first order) to a bath-induced unitary evolution (i.e., a generalized Lamb shift) [88]. The purpose of this assumption is only to simplify the expressions, but it is not essential. Physically, one may think of a fast auxiliary unitary transformation that is applied initially in order to diagonalize the initial state in the eigenbasis of P. 

As in the case of a hyperfine structure, there is a wealth of new experimental data on Lamb shift measurements of such exotic systems as lithium-like uranium U89+, again encouraging the relevant calculations [164-166],... 

In this section we consider a two-level system coupled to an environment which we treat as a quantum-mechanical system. We begin with a discussion of the Lamb shift and then show, in Subsection 3.3, how the results for the Lamb shift may be used to find the environment-induced correction to the Berry phase and the relaxation times. 

In this paper we have derived expressions for the environment-induced correction to the Berry phase, for a spin coupled to an environment. On one hand, we presented a simple quantum-mechanical derivation for the case when the environment is treated as a separate quantum system. On the other hand, we analyzed the case of a spin subject to a random classical field. The quantum-mechanical derivation provides a result which is insensitive to the antisymmetric part of the random-field correlations. In other words, the results for the Lamb shift and the Berry phase are insensitive to whether the different-time values of the random-field operator commute with each other or not. This observation gives rise to the expectation that for a random classical field, with the same noise power, one should obtain the same result. For the quantities at hand, our analysis outlined above involving classical randomly fluctuating fields has confirmed this expectation. 

Two years later, a detection system for Balmer-/ fluorescence was added to the 2S — 45/40 apparatus. Because of the better signal to noise ratio of that signal a remeasurement for both hydrogen and deuterium [23] resulted in improved values. By that time, the relative precision of the 15 Lamb shift already exceeded that of radio frequency measurements of the classic 2S—2P Lamb shift. 

Abstract. We present a review of the helium spectroscopy, related to transitions between 23S and 23P states around 1083 nm. A detailed description of our measurements, that have produced the most accurate value of the 23Po — 23Pi fine structure interval, is given. It could produce an accurate determination (34 ppb) of the fine structure constant a. Improvements in the experimental set up are presented. In particular, a new frequency reference of the laser system has been developed by frequency lock of a 1083 nm diode laser to iodine hyperfine transitions around its double of frequency. The laser frequency stability, at 1 s timescale, has been improved of, at least, two orders of magnitude, and even better for longer time scales. Simultaneous 3He —4 He spectroscopy, as well as absolute frequency measurements of 1083 nm helium transitions can be allowed by using the Li-locked laser as frequency standard. We discuss the implication of these measurements for a new determination of the isotope and 23 5 Lamb shifts. 

The simplest version of the atomic interferometer consists of two electrodes with the slits for passing the beam, separated with the variable gap L. For Lamb shift measurement corresponding interferometer is made of two two-electrode systems with longitudinal electric fields, mixing 2S and 2P-states. The systems were separated with a field-free gap of variable length L. This implies, that it is possible to write an exact expression for the probability W(L)e1,e2 of the yield I2P of 2P-atoms from the double system and determine, by processing the experimental dependence I2p(L), the Lamb shift value S. 

To overcome this limitation will require the measurement of the Lamb shift (the 2S-2P energy difference) in muonic hydrogen. Here the main QED contribution is vacuum polarization, for which calculations are now available at a precision level of 10-6 [11,12,13,14]. Because the effect of the finite proton size contributes as much as 2% to the pp Lamb shift, a precise measurement of the shift will provide an accurate value of the proton radius. The knowledge of the proton radius has intrinsic interest as a fundamental quantity, and is important in other measurements. A measurement of rp at 0.1% precision will permit QED calculations of bound systems to be compared with the ep experiments at a precision level of fewxlO-7 gaining an order of magnitude over the present limits. 

Abstract. CPT invariance is a fundamental property of quantum field theories in flat space-time. Principal consequences include the predictions that particles and their antiparticles have equal masses and lifetimes, and equal and opposite electric charges and magnetic moments. It also follows that the fine structure, hyperfine structure, and Lamb shifts of matter and antimatter bound systems should be identical. 

Our target is to develop a theory for the Lamb shift and the fine structure in these two atomic systems. Eventually we need to determine the 2s — 2pi/2 splitting in the helium ion (for comparison with the experiment [6]), difference of the Lamb shifts ER(2s) — ER(3s) in 4He+ (for the project [7]) and the 2p3/2 — 2s interval in hydrogen-like nitrogen. The difference mentioned is necessary [12,1] if one needs to compare the results of the Lamb shift (n = 2) measurement [6] and the 2s — 3s experiment. 

This paper describes the progress of a laser resonance experiment which aims to measure the Lamb shift in hydrogenic silicon with an accuracy that will allow it to test the two-loop binding corrections mentioned above. This in turn should allow the viability of calculable frequency standards, based on transitions in lower-Z one-electron systems such as hydrogen and He+, to be assessed. Following a review of some theoretical contributions to hydrogenic energy levels, the details of the laser resonance experiment are outlined. 

This work is supported by the UK National Measurement System (NMS) under the Foundation Programme project 4.2 Hydrogenic systems calculable frequency standards . The measurement of the 2S Lamb shift in Si13+ is also a key experiment in a five-year International Collaborative Research Project (ICORP) on Cold Trapped Ions between NPL, the University of Oxford and the Japan Science and Technology Corporation (JST). 

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