Barkas effect

Hygroelastic Effects. When hygroscopic materials such as wood are restrained from swelling freely they not only exert a swelling pressure but also come to a lower moisture content than if unrestrained. The reverse effect also holds true wood restrained from shrinking exhibits a higher equilibrium moisture content than if unrestrained. This is the hygroelastic effect, sometimes called the Barkas effect because Barkas was the first to treat it quantitatively (26). 

In the case of light ions, this approach has been applied to calculate the energy loss for the following systems (i) helium ions in aluminum targets [37], and (ii) protons and antiprotons in various solids [38] (with particular evaluation of the Barkas effect). In all these cases the agreement with experimental results was very good. 

Stopping power vs. relative momentum, py = p/Mc, for muons in copper. The solid curve indicates the total stopping power, the dash-dotted and dashed lines the Bethe-Bloch equation with and without density effect correction. The vertical bands separate the validity regions of various approximations indicated in the figure. The dotted line denoted with p. indicates the Barkas effect. In the Bethe-Bloch region the stopping power scales with the particle mass and Z/A of the medium... 

The Barkas effect, which makes the stopping power for negative and positive particles different in matter, can also be included there as a term zLiiP ) it makes the energy loss for a slow negative particle lower than for a positive one under identical conditions due to polarization of the medium. This effect is studied in detail at the Antiproton Decelerator at CERN (Moeller et al. 2002). 

The Barkas term. The leading correction term to the first Bom result gives rise to the Barkas effect and has been the center of much attention during the last decades. The theoretical efforts... 

The theoretical literature on the Barkas-Andersen effect is extensive. The present discussion focuses on the role of quantal V5. classical arguments. 

Traditionally the effect is incorporated into stopping theory via expansion in powers of Zj. As pointed out by Lindhard [21], there are two independent dimensionless parameters containing Zj, namely, the Bohr parameter k (equation (17)) and the Barkas parameter... 

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].

Clever schemes have been developed to treat the Barkas-Andersen effect for light ions in an electron gas ([27,34] and others) in what is called the nonlinear quantum regime. While there is little doubt that there must be a lower velocity limit for the validity of Bohr-like stopping theory, a reliable estimate of this limit does not seem available, nor is there a demonstration of where and in what manner quantum mechanics is an indispensable feature. 

Moreover, estimates for an electron gas can hardly be representative for insulating materials. There have been speculations on the relevance of promotion effects [35], but theoretical estimates of the Barkas-Andersen effect in insulating solid materials have been performed only on the basis of classical theory so far... 

Finally, just as thermophoresis has as a limit thermal diffusion- in dilute gas mixtures, so one would expect a thermophoretic effect on particles suspended in dense gases and liquids, whose limit would be thermal diffusion of mixtures in these media. The photophoretic effect may have been observed by BARKAS [2.145] in aqueous solutions of colloids. More recently, McNAB and MEISEN [2.146] have reported experimental evidence of thermophoresis in liquids for 1.011 and 0.79 ym spheres in water and n-hexane. They report that their data for the thermophoretic velocity are described by an empirical equation... 

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