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The multi-scattering model for calculations of positron spatial distribution in the multilayer stacks, useful for conventional positron measurements
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10.1063/1.4818578
/content/aip/journal/jap/114/7/10.1063/1.4818578
http://aip.metastore.ingenta.com/content/aip/journal/jap/114/7/10.1063/1.4818578

Figures

Image of FIG. 1.
FIG. 1.

The cross section of the stack consisting of five different foils in which the positron point source is located in the middle of the third foil. Each foil is described by parameters such as positron absorption coefficient α, the positron backscattering coefficient and its thickness . The stack is the subject of consideration of the MSM, see text.

Image of FIG. 2.
FIG. 2.

The simplified path of positrons: they travel in the third and the adjoining foils in the stack. This allows us to calculate the fractions of positrons transmitted from the third layer, where the source is located, to the surrounding layers. The functions (), ( , , ), and ( , , ) are described in detail in the text. In the schema, some of the variables of these functions were omitted, and also a new function was introduced as , where (, α) is the transmittance function: Eq. (6) .

Image of FIG. 3.
FIG. 3.

The simplified path of positrons which travel in the foils located far from the source. This allows us to calculate the fraction of positrons transmitted and reflected positrons fraction from the layer 4, see Fig. 1 to the surrounding layers. For this layer, the positron source is located on the interface between the layers 3 and 4, and positrons are moving toward the layer 5. The functions (x,α), ( , , ), and ( , , ) are described in detail in the text. In this figure, some of the variables of these functions were omitted, and also initial positron source contribution equal to one was assumed. The correct amount of reflected and transmitted positrons should be further determined by multiplying them by the T factor, see text.

Image of FIG. 4.
FIG. 4.

The comparison of two implantation profiles of positrons emitted from Na isotope into the symmetrical stack of foils around the source, one simulated by the MC method and one calculated using the LYS-1 program. In (a), the stack consists of the two aluminum plates, which surround the source, see the top. In (b), the stack consists of the Al foil of thickness of 60 m and Ag foil of thickness of 40 m enclosed by the Al plates, see the top of the figure. The positron implantation profile obtained from MC simulations using GEANT4 code is represented by the solid gray line. The dashed black line represents the implantation profile obtained using the MSM implemented in the LYS-1 program described in the text.

Image of FIG. 5.
FIG. 5.

Intensities of the source and sample components evaluated from the positron lifetime spectra measured for non-symmetrical stack as a function of thicknesses of the Al foil which adjoin the source. The solid and dashed lines present the dependences obtained using the MSM with different parameters, see in text. In (a) the experimental and theoretical results for the stack with the Ag foil and two Al plates are presented, and in (b) for the stack containing the magnesium plate on one side. The cross sections of the stack are given in the insets.

Image of FIG. 6.
FIG. 6.

Intensities of the source and sample components evaluated from the positron lifetime spectra measured for non-symmetrical stacks as a function of thicknesses of the Al foil which adjoin the source. The solid and dashed lines present the dependences obtained using the MSM with different parameters, see in text. In (a) the experimental and theoretical results for the stack with Au foil and two Al plates are presented, and in (b) for the stack containing the magnesium plate on one side. The cross sections of the stack are given in the insets.

Image of FIG. 7.
FIG. 7.

Intensities of the source and sample components evaluated from the positron lifetime spectra measured for symmetrical stacks as a function of thicknesses of the Al foil which adjoin the source. The stacks consist foils or plates with different materials, i.e., Au (a), Fe (b), Ag (c), and Si (d) The solid lines present the obtained from MSM dependences with adjusted parameters, see in text. The cross sections of the stack are given in the insets.

Image of FIG. 8.
FIG. 8.

Intensities of the Au (a) and Ag (b) foils components evaluated from the positron lifetime spectra measured for symmetrical stacks as a function of their thickness, see the inset. These foils where separated from the positron source by the aluminum foil of thickness equal to 30, 38, and 53 m. The solid lines present the results obtained from the MSM with adjusted parameters, see in text.

Image of FIG. 9.
FIG. 9.

The positron implantation profile measured using the DSIP method for the stack consisted of the Al plate, positron source, 60  m thick Al foil, 40 m thick Ag foil and Al plate, see the top of the figure. The dashed gray line represents the profile obtained for such a stack from the LYS-1 program, and the solid, black line represents the same profile convoluted with the spatial resolution function, see text.

Tables

Generic image for table
Table I.

The values of the linear absorption and backscattering coefficients (in the adjoined source layer and the other layers) obtained from MSM by manually adjusting procedure.

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/content/aip/journal/jap/114/7/10.1063/1.4818578
2013-08-21
2014-04-25
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: The multi-scattering model for calculations of positron spatial distribution in the multilayer stacks, useful for conventional positron measurements
http://aip.metastore.ingenta.com/content/aip/journal/jap/114/7/10.1063/1.4818578
10.1063/1.4818578
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