engleski

Interference effects in Compton profiles of molecules: The examples of $H_{;2};$ and $H_{;2};^{;+};$

There has been considerable interest recently in Young-type interference effects in the processes of photoeffect and charged particle scattering from diatomic molecules. These interference effects manifest themselves usually in an oscillatory structure of the energy dependence of the ratio of a cross section obtained (experimentally or theoretically) for a process on a diatomic molecule to the corresponding cross section for the process on a free atom. We will discuss Young-type interference effects on the Compton profile (CP) $J(p_{;z};)$ of H$_{;2};$ and H$_{;2};^{;+};$. The Compton profile can be defined in terms of the electron momentum density (EMD) $\rho ({;\bf p};)$ of atomic electrons, where $\rho ({;\bf p};)=\vert \Psi({;\bf p};)\vert^2$ and $\Psi({;\bf p};)$ is the Fourier transform of the coordinate space electron wave function. The importance of the CP is in the fact that both impulse approximation doubly differential cross sections (DDCS), for scattering of photons in the region of the Compton peak and for scattering of electrons in the binary encounter region, are products of a simple kinematic factor $F_{;K};$ (depending on the process) and the CP of the system. A good picture of these effects can already be obtained for the simple H$_{;2};^{;+};$ molecule with wave function $\Psi({;\bf R};, {;\bf r};)$, where ${;\bf R};$ is the relative position of the nuclei and ${;\bf r};$ is the position of the electron. The Fourier transform $\Psi({;\bf R};, {;\bf p};)$, of this two center electron wave function (for which $\left\vert\Psi\right\vert^{;2};$ integrated over ${;\bf R};$ gives the EMD $\rho ({;\bf p};)$), contains $\cos({;\bf p};\cdot {;\bf R};)$ terms. These terms, after summation over all orientations, lead to $\sin(pR_{;0};)/pR_{;0};$ terms in the EMD, where $R_{;0};$ is the average distance between the nuclei, which are characteristic of Young-type interference. These oscillatory terms are then also reflected in the CP $J(p_{;z};)$. The result is that the ratio of the molecular CP to the atomic CP shows oscillations as a function of $p_{;z};$. We discuss the effects of these interferences on the Compton profiles of molecules. We also analyze existing experimental results on H$_{;2};$ and show that these Young-type interference effects are present in the data if the ratio is examined.

Compton scattering; Impulse approximation; Compton profile; hydrogen molecule; interference

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