Beta-ray Spectra, I

Takebe, Hisao

doi:10.1143/ptp.12.561

Cited by 11 publications

(5 citation statements)

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“…For details see eqs. (11) and the following explanations. Table 1 as percentages of the main terms for a few particular cases.…”

Section: C Normalization Of the Inner Waye Functionsmentioning

confidence: 96%

“…This is a generalization of Fermi's method for allowed ·decay.ll We call this approximation the K-U approximation hereafter. Several papers 11 ·which appeared thenceforth are based on this K-U approximation. K-U also proposed a further approximation which was supposed to be valid for light elements 31 • We ;particularly call the latter approximation the K-U low-Z approximation.…”

Section: Z Matumoto and M Yamadamentioning

confidence: 99%

“…It should be noted that no approximation is used in this procedure. The electron wave function is not replaced by its surface value divided by r 11 (1 1 : magnitude of orbital angular momentum) as is usually done. Therefore, our theory fully takes into account the effect of j3-decay from inside of the nucleus.…”

Section: Ik (R) Is Not Much Different From Unity and Ik(r)-h For Z~omentioning

confidence: 99%

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Formulas in the Fermi Theory of Beta-Decay, I

Matumoto¹,

Yamada²

1958

Prog. Theor. Phys.

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28511-spectra are calculated by assuming the Fermi theory. All the effects due to the finiteness of the nuclear size are taken into account in an analytical form, and the screening effect by atomic electrons are included as additional factors though their values are not given explicitly. In ~ 2 the electron wave functions are calculated and in e 3 they are applied to get the correction factors for 11-spectra. The mixed type interaction consisting of scalar, tensor and pseudoscalar is especially examined. in detail. The final formulas are similar to those for light nuclei of Konopinski and Uhlenbeck. There is a difference, however, which lies in the fact that several "effective nuclear radii " are used in our formulas instead of the usual nuclear radius. Special attention is paid to the errors in our formulas, which seem to be inevitable from the practical view-point, and also to the insensitivity of the 11-spectra to the nuclear charge distribution. § I. IntroductionThe tJ-decay interaction first proposed by Fermill is a sum of products of the fourspinor field operators for the proton, neutron, electron and neutrino.The theory with.the above mentioned characteristics was extended afterwards to include all the possibilities. within the restriction of invariance under the proper and improper Lorentz transformations. This theory, which has been called "the Fermi theory of j3-decay ", is not onlysimple but also very powerful. There seemed to be no evidence of contradiction in it,. until recently the surprising experiment by Wu et ai.~l has revealed that the parity is. not conserved in the f9-decay. Although the original Fermi theory had to be abandoned in this respect, it is easy to extend it to explain the parity violation, still keeping the form of a sum of products of the four spinor field operators. Therefore, we still call this generalized theory the Fermi theory. Besides the Fermi theory a number of varieties.were proposed on the theory of tJ-decay but they either failed to explain experiments orwere too peculiar to be accepted widely. The Fermi theory is the ruling theory at present,. although we cannot neglect other theories which may be successful too. * On leave of absence from University of Tokyo. at Uniwersytet Warszawski Biblioteka Uniwersytecka on March 21, 2015 http://ptp.oxfordjournals.org/ Downloaded from at Uniwersytet Warszawski Biblioteka Uniwersytecka on March 21, 2015 http://ptp.oxfordjournals.org/ Downloaded from 2A. Unnormalized electron waye function inside the nucleus Eqs. (1) have suitable forms for obtainning the inner wave functions. The unnormalized (regular) solution of eqs. ( 1) is obtained by putting d1 = 0, d2 = 1 (these values are chosen only for convenience) for tc < b, and d 1 = 1, d 2 = 0 for tc > 0. The nuclear radius p is 0.01 to 0.02 in our unit for most nuclei, though the definition is somewhat ambiguous. The electron energy W is usually less than 10. V(r) is of the order of aZjp, and aZ is less than unity. If we regard W and aZ as of the order of unity, and r as of the order...

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“…For details see eqs. (11) and the following explanations. Table 1 as percentages of the main terms for a few particular cases.…”

Section: C Normalization Of the Inner Waye Functionsmentioning

confidence: 96%

Section: Z Matumoto and M Yamadamentioning

confidence: 99%

Section: Ik (R) Is Not Much Different From Unity and Ik(r)-h For Z~omentioning

confidence: 99%

See 1 more Smart Citation

Formulas in the Fermi Theory of Beta-Decay, I

Matumoto¹,

Yamada²

1958

Prog. Theor. Phys.

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“…[21][22][23] Several attempts have also been made to take into account the effects of finite nuclear size. 24 In the present work we assume point nuclear charge.…”

Section: A Theoretical Formulationmentioning

confidence: 99%

Beta-Gamma Directional Correlation inRe186

et al. 1956

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“…1 In I we have taken the factors '~f~U,f) as unknown parameters. In (16) we consider the integrals R:~:(K. K'), or 21'"• 1 (K, K'), ~6 (1(, K'), (£'"· 6 (K, K') and ~"· 6 (K, K'), as the parameters.…”

mentioning

confidence: 99%