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- W2031037560 abstract "We consider a general reaction process in which two entrance-channel particles, the beam and target particles, interact off-resonance and produce two exit-channel particles. In the c.m. frame we derive a general expression relating the probability density of the exit-channel particles to that of the entrance-channel particles. Furthermore, we show that whenever the coherence length, ${w}_{B}$, of the beam particle is much larger than the coherence length, ${w}_{T}$, of the target particle, the wave function of each exit-channel particle may be expressed explicitly in terms of the wave function of the beam particle. We also derive expressions for the coherence time and coherence length of each exit-channel particle. In addition, whenever the speed of the target particle is much less than the speed ${v}_{i}$ (i=1,2) of an exit-channel particle, we show that a simple relationship exists between the coherence length, ${w}_{mathrm{ci}}$, of the exit-channel particle and the beam particle: ${w}_{mathrm{ci}}$=${v}_{i}$(${w}_{B}$/ensuremath{Vert}${mathrm{v}}_{B}$${mathrm{ensuremath{-}}mathrm{v}}_{T}$ensuremath{Vert}){1 ${mathrm{ensuremath{-}}[(mathrm{v}}_{mathrm{T}}$ensuremath{cdot}e${mathrm{^}}_{3}$)/ ${v}_{i}$](costheta')}, where the velocity of the beam particle is ${mathrm{v}}_{B}$ ${(mathrm{v}}_{B}$=${v}_{B}$e${^}_{3}$), and the velocity of the target particle is ${mathrm{v}}_{T}$ ${(mathrm{v}}_{T}$=${v}_{T}$e${^}_{3}$). The angle theta' is the spherical polar angular coordinate, measured with respect to the unit vector e${^}_{3}$, of the point at which the coherence length ${w}_{mathrm{ci}}$ is to be determined. The above relationship is applied in the case of photoionization of the hydrogen atom at low energies to obtain realistic estimates for the coherence lengths of the ionized electron and proton. The coherence length of the electron is shown to be of nearly macroscopic dimensions." @default.
- W2031037560 created "2016-06-24" @default.
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- W2031037560 date "1986-01-01" @default.
- W2031037560 modified "2023-09-27" @default.
- W2031037560 title "Effects of scattering on wave-packet structure" @default.
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- W2031037560 doi "https://doi.org/10.1103/physreva.33.131" @default.
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