We have measured the scattering angle dependence of cross sections for ionization in p+H2 collisions for a fixed projectile energy loss. Depending on the projectile coherence, interference due to indistinguishable diffraction of the projectile from the two atomic centers was either present or absent in the data. This shows that, due to the fundamentals of quantum mechanics, the preparation of the beam must be included in theoretical calculations. The results have far-reaching implications on formal atomic scattering theory because this critical aspect has been overlooked for several decades.
We consider the cross section for a scattering reaction averaged over a statistical ensemble of incident beam wave packets. We generalize a result known from neutron diffraction that static experiments involving stationary scattering via conservative interactions and steady beam currents cannot distinguish the wave-packet nature of the incident beam. Thus we interpret the results of recent experiments on the loss of interference effects in proton scattering from molecular hydrogen as due to the weak collimation of the incident beam rather than alterations to beam wave packets.
In the study of collision processes, a series of conditions is usually assumed. One of them is that the beam of projectiles is coherent in lengths greater than those of the targets against which it strikes. However, recent experimental results and theoretical analyzes have shown that this assumption can not only fail, but that it is possible to manipulate the coherence length experimentally to go from a coherent situation to an incoherent one. The most conspicuous and studied manifestation of such loss of coherence is the disappearance of interference effects. However, in the present work we show that a strong decrease can also occur in the magnitude of the cross section, not only differential but also total, due to an atomic concealment effect.
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,
wB, of the beam particle is much larger than the coherence length,
wT, 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
vi (i=1,2) of an exit-channel particle, we show that a simple relationship exists between the coherence length,
wci, of the exit-channel particle and the beam particle:
wci=
vi(
wB/\ensuremath{\Vert}
vB${\mathrm{\ensuremath{-}}\mathrm{v}}_{T}$\ensuremath{\Vert}){1 ${\mathrm{\ensuremath{-}}[(\mathrm{v}}_{\mathrm{T}}$\ensuremath{\cdot}e${\mathrm{^}}_{3}$)/
vi](costheta')}, where the velocity of the beam particle is
vB (vB=
vBe${^}_{3}$), and the velocity of the target particle is
vT (vT=
vTe${^}_{3}$). 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
wci 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.
Bragg diffraction divides a Bose-Einstein condensate into two overlapping components, moving with respect to each other with high momentum. Elastic collisions between atoms from distinct wave packets can significantly deplete the condensate. Recently, Zi\ifmmode \acute{n}\else \'{n}\fi{} et al. [Phys. Rev. Lett. 94, 200401 (2005)] introduced a model of two counterpropagating atomic Gaussian wave packets incorporating the dynamics of the incoherent scattering processes. Here we study the properties of this model in detail, including the nature of the transition from spontaneous to stimulated scattering. Within the first-order approximation, we derive analytical expressions for the density matrix and anomalous density that provide excellent insight into correlation properties of scattered atoms.