Decay width

Gurvitz SA, Kalbermann G (1987) Decay width and the shift of a quasistationary state. Phys Rev Lett 59 262... 

Therefore, the contribution of the diagram with u>—p mixing (FIG.7) is negligible with respect to the contribution of the diagram with 0 — p mixing (FIG.6). Thus,the decay width of the 0 — W7r° decay mainly is defined by the diagram with [Pg.294]

Above Tc, Eqs. (22) and (24) yield rather smooth functions of T except the region t 1. The fluctuation region is rather wide since Cy Cy even at T essentially larger then Tc. The appearance of an extra channel of the diquark decay width, beyond the Hartree approximation does not... 

Secondly, the cross section reflects the nature of the dependence of the partial widths on the intermolecular distance R. As expected from Eq. (20), is small for large R and increases gradually with decrease in R. On the other hand, Fgx in its empirical form (Eq. (17)) is extremely small at large distances and increases sharply near the repulsive wall. Therefore, the de-excitation probability due to Penning ionization is determined by the dipole-dipole part of the decay width in collisions with large impact parameter, whereas the probability for Penning ionization is already almost unity by the single contribution... 

Figure 14 Interaction potential and autoionization decay width employed and determined in the...

The prediction of a heavy boson has received preliminary empirical support [92,96] from an anomaly in Z decay widths that points toward the existence of Z bosons with a mass of 812 GeV 1 33j [92,96] within the SO(l) grand unified field model, and a Higgs mechanism of 145 GeV4gj3. This suggests that a new massive neutral boson has been detected. Analysis of the hadronic peak cross sections obtained at LEP [96] implies a small amount of missing invisible width in Z decays. The effective number of massless neutrinos is 2.985 0.008, which is below the prediction of 3 by the standard model of electroweak interactions. The weak charge Qw in atomic parity violation can be interpreted as a measurement of the S parameter. This indicates a new Qw = 72.06 0.44, which is found to be above the standard model pre-... 

Some of the earliest applications of MQDT dealt with vibrational and rotational autoionization in H2 [21-25]. One concept that emerged from these studies is that of complex resonances [26], which are characterized by a broad resonant distribution of photoionization intensity with an associated rather sharp fine structure. These complex resonances cannot be characterized by a single decay width they are the typical result of a multichannel situation where several closed and open channels are mutually coupled. The photoionization spectrum of H2 affords a considerable number of such complex resonances. 

Focusing on comparisons to measurable quantities, the relative probability of a reaction (exit) channel can be written as the ratio of the cross section for that channel, (r to the total reaction cross section, 07. The ratios are labeled as the relative decay widths, T, in a notation that is, unfortunately, easy to confuse with the number of states discussed above. The sum of the decay widths is the total width of the state and can be used to calculate the lifetime of the excited state. Thus,... 

N. Yabusaki, M. Hirano, K. Kato, M. Sakai, Y. Matsuda, Masses and OZI-allowed decay widths of T states in a coupled channel model, Prog. Theo. Phys. 106 (2001) 389. 

The Fano-ADC technique outlined above can be generalized to the case of multiply ionized systems. Full description of the effect of the additional vacancies requires, of course, an ab initio approach that explicitly takes into account multiple ionization. In the case of a single additional charge, the ADC scheme for doubly ionized states would be appropriate. Such a scheme was developed by Schirmer and Barth [31]. The extended second-order ADC technique for double ionization [31] treats explicitly the two-hole (2h) and the three-hole one-particle (3hlp) excitation classes up to the second and first orders, respectively. Fano-ADC(2)x for decay widths of doubly ionized states embedded into triple ionization continua has been developed in Ref. [32]. 

Figure 6.2 Auger decay width of (2p n) Mg+-H+ as a function of the Mg-proton distance, R.z is Mg-proton axis. Diamonds and solid line Fano-ADC(2)x calculation with atomic orbital basis centered both on Mg and on the proton circles and long-dashed line Fano-ADC(2)x calculation with atomic orbital basis centered only on Mg stars and short-dashed line Fano-ADC(2)x calculation for (2p 1) Mg+ alone, with atomic orbital basis centered both on Mg and at the distance R along the z-axis, showing the so-called basis set superposition error (BSSE) triangles and dashed-dotted line Fano-ADC(2)x calculation with atomic orbital basis centered on Mg only, with the 3s orbital of Mg being frozen at its shape at R = 6.5A. The inset shows the low-r part of the plot on logarithmic scale. See Ref. [35] for the details of the computation.

Table 6.3 Fano-ADC total and partial Auger decay widths (in meV) for doubly ionized Ne atom...

Table 6.4 Comparison of the Fano-ADC results with the available theoretical and experimental values for the K-LL Auger decay widths in CH4, NH3, and H2O molecules...

The decay widths are in meV, citations are given in square brackets. Experimental value for ammonia is lacking because of the vibrational broadening in the Auger electron spectrum of ammonia [65], See Ref. [44] for the details of the Fano-ADC computation. 

Some qualitative understanding of the CICD can be gained by means of Wentzel-type theory that treats the initial and final states of the decay as single Slater determinants taking electronic repulsion responsible for the transitions as a perturbation. The collective decay of two inner-shell vacancies (see Figure 6.6) is a three-electron transition mediated by two-electron interaction. Thus, the process is forbidden in the first-order perturbation theory, and its rate cannot be calculated by the first-order expressions, such as (1). Going to the second-order perturbation theory, the expression for the collective decay width can be written as... 

Proceeding with the large-R analysis of the ionization matrix element, (f V i), we find that at large Kr2-X separations it decreases as 1/R r2 x. As a result, the contribution of the two-electron recombination - ionization pathway to the decay width depends on the cluster geometry as l/-R r Kr Kr2-x-Since the decomposition of the (Kr+)2X cluster along the Kr+-Kr+ coordinate automatically means elongation of the Kr2-X distance as well, the power law exponents are effectively summed, resulting in the l/R Kr dependence. A detailed analysis shows that this type of power law is characteristic of all the possible decay pathways. 

Quantitative results for the collective interatomic decay in (4s-1,4s-1) (Kr+)2Ar have been obtained in Ref. [54] using Fano-ADC theory. The results for T as a function of the Kr-Kr distance (at R][ 2 Ar = 3.3A [54]) are shown in Figure 6.7a. At the equilibrium Kr-Kr distance (R = 4.0A [54]), the collective decay width reaches 1.9 meV for triplet and 2.0 meV for singlet doubly ionized states, which corresponds to lifetimes around 300 fs. The predicted lifetime is five orders of magnitude shorter than the one of the... 

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