Avoided-level -crossing

Figure 9.41 Potential energy curves for the two lowest electronic states of Nal showing avoided level crossing and the effect of excitation with a femtosecond laser pulse. (Reproduced, with permission, from Rose, T. S., Rosker, M. J. and Zewail, A. H., J. Chem. Phys., 91, 7415, 1989)...

Jz = — 6 substrates are brought to resonance at p0H = 0T, thus giving rise to an avoided level crossing which allows QTM to occur (down) [9, 216]. (b) A close view of the hysteresis loop with steps corresponding to the four avoided level crossings [216, 217],... 

Fig. 6.19 Ionization rates for the (12,6,3,2) level of Na in the region of the crossing with the rapidly ionizing (14,0,11,2) level. The levels are specified as (n, i, 2>M). The solid line is a theoretical curve. The dashed line is calculated neglecting another avoided level crossing...

As shown by Fig. 15.8(a), if the system is initially in state A it traverses two avoided level crossings to reach the final state B, and there are two possible paths to go from A to B. Whether the transition amplitudes for these two paths add... 

Figure 6 shows the effect of these avoided level crossings can be seen in hysteresis loop measurements. When the applied field is near an avoided level crossing, the magnetization relaxes faster, yielding steps separated by plateaus. As the temperature is lowered, there is a decrease in the transition rate due to reduced thermal-assisted tunneling. 

Here, m and rrC are the quantum numbers of the avoided level crossing, denote the tunnel splitting between the levels (Fig. 7), dHJdt is the constant field sweep rate, g 2, /uB is the Bohr magneton, and h is Planck s constant. 

Figure 7. Detail of the energy level diagram near an avoided level crossing, m and m are the quantum numbers of the energy level. Pm m- is the Landau-Zener tunnel probability when sweeping the applied field from the left to the right over the anticrossing. The greater the gap A and the slower the sweeping rate, the higher is the tunnel rate, Eq. (2).

Muonium-substituted free radicals contain the muon as a polarized spin label which allows its detection either by the transverse field muon spin rotation (TF-pSR) technique or by longitudinal field avoided-level-crossing muon spin resonance (ALC-pSR) [4]. 

Figure 10. SR spectra of the radicals formed by Mu addition to liquid 6,6 -dimethylfiilvene. Transverse field muon spin rotation spectrum (upper, with lines for the radicals a and b, and for muons in diam netic environment D), and longitudinal field avoided level crossing spectrum (lower), simulation and experimental data based on the structures in the inset with proton coupling constants given in Gauss (adapted fi om [43] with permission of The Royal Society of Chemistry).

Avoided-level crossing muon spin resonance (ALC-p.SR), a derivative of the NMR technique, can be applied to systems in which adsoAed flee radicals are formed by loss of H [94Schl]. When bombarded with highly-polarized positive mirons (p., these radicals can combine with muonittm... 

ALC-pSR Avoided-level crossing mnon spin resonance... 

There are still other means to carry out p.SR experiments. Most notably among them is the so-called (Avoided) Level Crossing Resonance (LCR or ALC, Kreitzman 1986, Kieft 1986, Heming et al. 1986, Krefl and Kreitzman 1992, Leon 1994). In this review we will... 

ALC- J,SR avoided-level-crossing muon spin resonance ( jLCR)... 

An approximate value of the hyperfine coupling constant and hence the type of radical formed can be deduced using repolarization curves. These are plots of the initial amplitude of the muon relaxation signal, which increases as the hyperfine interaction is decoupled by an applied magnetic field. However, these estimates can be distorted by anisotropic terms and motional effects and more accurate values of the hyperfine coupling constants would be given by TF- xSR (transverse field) and ALC- xSR (avoided level crossing) measurements. 

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