Abstract
The influence of perturbative interactions is discussed in the frame-work of time-dependent perturbation theory. A characteristic time (to be calledrelaxation time), during which a given initial state of the system will be depleted, is defined. In case this relaxation time is smaller than the collision time of the process, the usual adiabatic perturbation treatment becomes vague. In this sense, the usefulness of various approaches to the problem, such as those based on two-center Dirac wave functions or Hartree-Fock states can be quantitatively investigated. Calculations based on two-center Dirac wave functions and a restricted quasimolecular configuration for the electronic system in U-U collisions, reveal that the electron-electron interactions can be safely neglected for the inner-shell electronic states. A prescription is given to obtain more reliable transition probabilities when the adiabatic perturbation treatment fails. It is shown that unitarity is recovered in such a prescription.
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References
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This may not always be allowed in intermediate quasimolecules due to the complicated level crossing mechanism
Strictly speeking Equation (10) should not be written as a series. However, as an exact value forξ cannot be indicated, we leave it like that for flexibility in choosing some appropriate value
Such calculations are being presently done by W. Betz, Inst. Theoret. Phys., Univers. Frankfurt, W. Germany
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This procedure is well known, when discussing natural line broadening effects
This follows from the mathematical observation, that {Vm0(t)· e iωm0(t)} is a function whose t-dependence varies randomly in sign as eitherm ort are changed. Becauset andt′ inΦ(t, t′) are continuous variables, this randomness will generally constraint to approximately equalt′ in Φ(t, t′), so thatΦ(t, t′) is of appreciable size only in a strip in thet-t′)-plane with a maximum around t=t′
If the matrix-elements Vnm do not depend on time and if the phasesw mn (t) are of the form wmn(t)=amn·t, then one would have\(\tilde \Phi \)(<) =(<) =Φ(0) ·δ(τ) (Φ-is some average value). Such a form leads directly to the usual Weisskopf & Wigner forme −γt of line broadining
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Betz, W., Heiligenthal, G., Müller, B., Oberacker, V., Reinhardt, J., Schäfer, W., Soff, G., Greiner, W.: Int. Summer School on Nucl. Phys.; Predeal, Romania (1976) Betz, W., Heiligenthal, G., Müller, B., Soff, G., Greiner, W.: to be published
Betz, W.: Diplom a thesis (1976), Inst. Theoret. Phys., Univers. of Frankfurt, W. Germany
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We thank W. Betz for help in the computer calculations.
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Rihan, T.H., Aly, N.S., Merzbacher, E. et al. Relaxation times in intermediate quasi-molecules. Z Physik A 285, 397–403 (1978). https://doi.org/10.1007/BF01813240
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DOI: https://doi.org/10.1007/BF01813240