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Concerning the success of the absorption method of investigating the high velocity limits of continuous β ray spectra

Published online by Cambridge University Press:  24 October 2008

N. Feather
N. Feather
Affiliation:
Fellow of Trinity College
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Extract

Experience has shown that simple absorption measurements lead to quite trustworthy estimates of the maximum energies represented in the continuous spectra of many β ray bodies. For the interpretation of these experiments the range-energy relation for homogeneous particles is apparently all that is necessary. In the present paper a detailed analysis is given of the various factors which conspire to this useful result. Analytical simplifications are possible when the energy distribution in question extends beyond about 7 × 105 electron volts energy. Under this limitation it is shown that the empirical result follows from the known form of the absorption curve for homogeneous particles and the most general considerations regarding the characteristics of such measuring instruments as are regularly employed. From the analysis in one case, however, it appears that, despite numerical agreement between the results of different methods of investigation, caution is still necessary in any statement concerning the absolute nature of the high energy limits of continuous β ray spectra.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 27 , Issue 3 , July 1931 , pp. 430 - 444
Copyright
Copyright © Cambridge Philosophical Society 1931

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References

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Feather, loc. cit.

** Gurney, Madgwick, loc. cit.

* It is a pleasure here to record my thanks to Professor K. F. Herzfeld, of the Johns Hopkins University, Baltimore, to whom I owe the first impetus to undertake an investigation such as the present one.

* It is assumed that, for the energies concerned, this represents a small fraction only of the complete range of the particles.

* No account has been taken of the relativity correction.

* The reason for this choice of energies (corresponding to r m = 7·5r 0) will be indicated below.

† Cf. Feather, , Phys. Rev., 35, p. 1559, 1930.CrossRefGoogle Scholar

* It is assumed that no attempt is being made to separate the different effects by means of a magnetic field.

* When the γ ray effect is considerable p decreases as the strength of source increases, and the definiteness of the end point is thereby enhanced.

* Recent experiments of Terroux (Proc. Roy. Soc., 131 A, p. 90, 1931Google Scholar) in the case of the primary β particles of radium E have been interpreted in terms of a roughly Maxwellian distribution in which 4 per cent, of the particles have energies greater than that corresponding to the previously accepted end point. In this connection it is interesting to remark that in the Maxwellian distribution which gives rise to curve E (fig. 3) particles of extrapolated range greater than 4·1 r 0 contribute 4 per cent, of the total number of particles. It is difficult to imagine conditions of measurement in which an effective absorption end point should appear in this region. Moreover, application of equation (3b) shows that even when there occurs in the energy distribution diagram a definite singularity or kink, formed by the junction of two linear portions of different slopes, then in the absorption curve for the complete radiation at the corresponding thickness the only discontinuity is to be found in the third differential coefficient of I(R). Contrary, therefore, to the assertion of Terroux (loc. cit. p. 97), no obvious singularity will be observed in this curve. At present we can only conclude that the results of absorption measurements and those obtained with the expansion chamber stand in complete disagreement.

† Schmidt, , Phys. Zeit., 8, p. 361, 1907.Google Scholar

‡ Loc. cit.