Binary stopping theory

Figure 2 shows the stopping force of argon gas on protons. Experimental data are compared to two predictions of binary stopping theory to be discussed below, excluding and including shell correction, respectively. The difference is seen to be substantial. 

Fig. 3. Barkas-Andersen effect predicted by binary stopping theory. Plotted are stopping numbers for singly charged Ar, Li, and H ions and for their anti-ions in Si. Also shown are the respective ion/anti-ion ratios. From Ref. [23].

While more than a handful theoretical schemes are available to nonpermrba-tively evaluate the Barkas-Andersen correction quantum mechanically, binary stopping theory developed recently [32] fulfills the task on the basis of the Bohr stopping model the only quantum feature added is the inverse-Bloch correction (18) which does not differentiate between particle and antiparticle. Figure 4 demonstrates that with regard to comparison with experimental antiproton stopping data, classical theory is fully competitive with various quantum theories. 

The essential point in binary stopping theory is the avoidance of an expansion of T p) in powers of Zi this is achieved by mapping the Bohr model on a binary-collision problem involving a screened interaction potential, following a suggestion by Lindhard [21] but with an additional term that generates exact equivalence in the limit of distant collisions. The theory has been implemented in the PASS code [33] which allows incorporation of several features that were either unknown or of no interest at Bohr s time. 

Fig. 2. Stopping cross section for hydrogen in argon. Calculated from binary theory with and without shell correction. Experimental data from numerous laboratories compiled in Ref. [6].

Laradji and Here [72] have simulated the dynamics of phase separation in binary blends in the presence of nanorods the simulations predicted that rods would dramatically slow down, and possibly stop, the phase separation, leading to the stabilization of a single-phase morphology. Still, it is not clear whether this morphology is a simple homogeneous structure or, more likely, a complicated phase like a microemulsion. Similarly, there have been some experimental studies [50] suggesting that nanoplatelets could lead to microemulsion-like behavior, when platelets occupy interfaces between A-rich and B-rich domains and stabilize them. At present, to our knowledge, there is no satisfactory theory to describe this behavior, and more research is needed. 

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