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## Vol. 19, No. 4 (1963)

##### Topics
###### CONTENT
1963, 96 (4): 205-214. doi: 10.7498/aps.19.205
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Nuclear interactions induced by cosmic ray high energy particles have been studied by means of a multiplate cloud chamber at 3185 meters above sea level with liquid scintillator as target material. From the analysis of 18 interactions induced by charged primaries it is found: (i) average primary energy E0=41±8Bev (by Castagnoli formula), (ii) average multiplicity of charged secondaries ns=4.9±0.3, (iii) with x=lgγctgθl the differential angular distribution dN/dx indicates some possibility of theexistence of double-humped shape. This angular distribution has been discussed tentatively along the lines of two-centered model.
1963, 96 (4): 215-224. doi: 10.7498/aps.19.215
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In this paper the differential equation of a helically invariant magnetic field is derived, and the method of simulating this type of field is analyzed in detail. It is shown that the original Wakefield's resistance network analogue may be simplified considerably. The method of simulating a helically invariant field with composite (azimu-thal) period of multiplicity is also given. A very simple resistance network has been constructed to verify the conclusions arrived at.
1963, 96 (4): 225-238. doi: 10.7498/aps.19.225
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1963, 96 (4): 239-248. doi: 10.7498/aps.19.239
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The time-depending formal theory of scattering, initiated by Lippmann and Schwinger is generalized to the case of multi-channel process.Ekstein has attempted to construct such a theory in 1956 and pointed out the orthogonality properties of the set of multi-channel outgoing (incoming) scattering states, which is very important for the establishment of scattering matrix, but it seems to him that the quite general starting point of the L-S formalism is not appreciated. In his work the simplicity of the L-S formalism is lost. He came to the conclusion that the scattering matrix can not be regarded as the matrix of a single linear operator, because he insisted to work in one single interaction representation for all the initial and final states. Thereby the concept of scattering matrix is confused.The present paper deals with the same generalization, but the simplicity of the L-S formalism is preserved. The explicit form of the scattering operator is given. The calculation of the various transition probability in the present case can be made in a similar way as in the original L-S theory.
1963, 96 (4): 249-258. doi: 10.7498/aps.19.249
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Utilizing a theorem from the variational principles, after transforming boundaries of a transmission line into simpler ones, we can find upper and lower bounds to the correct value of the characteristic impedance of the line, so that the lengthy calculation in the ordinary variational method is avoided. Impedances of the rectangular line with central cylindrical inner conductor, the trough line with the slab line as a special case and the multi-conductor cable are calculated.
1963, 96 (4): 259-267. doi: 10.7498/aps.19.259
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1963, 96 (4): 268-270. doi: 10.7498/aps.19.268
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1963, 96 (4): 271-272. doi: 10.7498/aps.19.271
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