Summary
The practical use of the new multiple scattering function, cos ηφ, introduced byLipkin (1)et al., was examined by comparing its theory with experiment. At the same time the mean absolute angle according to Molière’s scattering theory was compared with experiment for the second and third difference and the respective dispersions were determined experimentally. (The theoretical dispersion diverges in Molière’s theory.) A good agreement between theory and experiment was obtained in the cosine case, both for the mean value and the dispersions, as well as in the mean absolute angle case with cut-off. Writing the relative error ofpβ as\(D_{2.3} /\sqrt n \) (for the second and third differences, respectively) we have obtained in the cosine case: D2 = 0.976 and D3=1.36, and in the mean absolute angle case (with cut-off at (<∣ϕ∣>):D 2 = 0.97 andD 3 = 0.137. It is shown that, provided one restricts oneself to a certain class of estimates ofpβ, the above dispersion values are close to the minimum possible dispersion ofpβ. Also, an explanation is suggested for the known experimental fact that the ratio of the « scattering constants »K 3/E2is higher by a few percent than the expected value √3/2.
Riassunto
Confrontando la teoria con l’esperienza abbiamo esaminato l’uso pratico della nuova funzione di scattering multiplo cos η φ introdotta daLipkin (1)ei al. Contemporaneamente abbiamo confrontato con l’esperienza le differenze seconde e terze dell’angolo assoluto medio risultante dalla teoria dello scattering di Molière e determinato sperimentalmente le rispettive dispersioni. (Nella teoria di Molière la dispersione teorica diverge). Un buon accordo tra teoria ed esperienza si trova per il coseno, sia per il valor medio e le dispersioni sia per I’angolo assoluto medio con cut-off. Esprimendo l’errore relativo dipβ con\(D_{2.3} /\sqrt n \) (per le differenze seconde e terze rispettivamente) abbiamo ottenuto per la funzione coseno: D2 = 0.976 e D3=1.36, e per l’angolo assoluto medio (con cut-off a 4<∣ϕ∣> Si dimostra one, limitandosi a una determinata classe di valutazioni dipβ, i suddetti valori di dispersione sono vicini alla dispersione minima possibile dipβ. Si suggerisce anche una spiegazione del noto fatto sperimentale che il rapporto delle « costanti di scattering »K 3/K2è di qualcne percento maggiore del valore atteso √2/3.
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Bosendorff, S., Eisenberg, Y. Multiple scattering measurements in nuclear emulsions. Nuovo Cim 7, 23–38 (1958). https://doi.org/10.1007/BF02746879
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DOI: https://doi.org/10.1007/BF02746879