Feshbach resonances series

Infinite series of Feshbach resonances due to the Coulomb tail... 

Photoionization of neutral atoms and molecules and electron-ion collisions, for example, are rich in infinite Rydberg series of Feshbach resonances. On the other hand, only a finite number of Feshbach (and possibly shape) resonances occur in electron-neutral collisions and photodetachment of an electron attached to a neutral species, with an exception of the following cases. 

According to Eq. (81) with /S = 6, the three a values for H in Figure 4.14 are —3.708, 2.000, and 9.708. Thus, the asymptotically lowest hyperspherical potential supports an infinite series of Feshbach resonances in the nonrelativistic approximation, although only three lowest members remain as resonances after corrections for the relativistic and radiative effects [80, 82], as was mentioned in Section 3.1.2. Only the lowest member is indicated in the figure by a horizontal line. This resonance is supported by the diabatic potential with A = — 1 connecting from the lowest curve for large p to the middle curve for small p. 

Figure 4.15 Hyperspherical potentials without the adiabatic correction term for Hef P0) converging to the asymptotic limits e + He+(n = 4,5,6). Each potential supports an infinite Rydberg series of Feshbach resonances. Some of them exhibit typical cases of inter-series overlapping resonances illustrated in Figures 4.9 and 4.10. Figure from Ref. [69].

Ho also computed series of high-lying Feshbach-type resonances converging to the TV = 3,..,9 hydrogen threshols (133). Several tens of resonances were reported. Chen (134) applied a basis set of B-spline functions within the saddle-point complex rotation method to compute parameters of twelve and low lying Feshbach resonances. 

Here, all the three particles are assumed to have a unit charge. The value of j3 is 6 for H with an infinitely heavy nucleus and is 8 for Ps. With the values of a from these analytic formulas, and hence f, Eq. (80) played an essential role in the analysis of the Feshbach series of resonances in muonic... 

For more accurate estimation, complex-rotation calculations [80] and coupled-channel calculations [81, 82] with the correct relativistic and radiative splitting AE taken into account reveal that, for H Feshbach series below the H(n = 2) threshold, the number vmax of resonances for the 1Se series is 4 (and the same for the system e+H) [81], vmax = 3 for the 1P° series [80,82], and vmax = 4 for the 3P° series [82], The relativistic effects also mix different LS states. This affects the resonance positions only slightly, but the components... 

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