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Il Nuovo Cimento (1955-1965)

, Volume 12, Issue 4, pp 327–355 | Cite as

Muon capture in certain light nuclei

  • A. Fujii
  • H. Primakoff
Article

Summary

The rates of the muon capture reactions: µ+ 2 3 He→ 1 3 +v, µ+ 3 6 Li→ 2 6 He+v, µ+ 6 12 C→ 5 12 B+v, with the daughter nuclei formed in their ground states, are calculated assuming ≪ universality ≫ between muon-bare nucleon and electron-bare nucleon coupling constants. The ≪ induced ≫ pseudoscalar interaction and the additional terms arising from the assumption of a ≪ conserved vector current ≫ are included in the muon-nucleon effective Hamiltonian. The ratios of the nuclear matrix elements for the muon captures and for the corresponding ß-decays are first estimated in an approximately ≪ model independent ≫ fashion using appropriate nuclear proton density distribution functions and then evaluated in more detail on the basis of variational trial wave functions for 2 3 He, 1 3 H, and of LS coupling andjj coupling shell model wave functions (with configuration mixing) for 3 6 Li, 2 6 He, and 6 12 C, 5 12 B, respectively. The calculated capture rate for µ+ 6 12 C → 5 12 B+v is in agreement with experiment — experiments however are not yet available in the other two cases.

Riassunto

Si calcolano le percentuali delle reazioni per cattura di muoni: µ§−+ 2 3 He → 1 3 H+v, µ+ 3 6 Li→ 2 6 He+v, µ+ 5 12 .C → 5 12 B + v, coi nuclei che ne derivano prodotti nei loro stati fondamentali assumendo 1’≪ universalitá ≫ tra le costanti d’accoppiamento muonenueleone nudo ed elettrone-nucleone nudo. L’interazione pseudoscalare ≪ indotta ≫ e i termini addizionali derivanti dall’assunzione di una ≪ corrente vettoriale conservata ≫ sono inclusi nell’Hamiltoniana effettiva muone-nucleone. I rapporti degli elementi della materia nucleare per le catture dei muoni e pei corrispondenti decadimenti ß si stimano dapprima in modo approssimato ≪ indipendentemente da modelli ≫ usando opportune funzioni di distribuzione della densità protonica nucleare e poi si calcolano più dettagliatamente sulla base di funzioni d’onda variazionali di prova per 2 3 He, 1 3 H, e funzioni d’onda d’accoppiamento LS ejj del modello a shell (con mistura di configurazioni) per 3 6 Li, 2 6 He e 6 12 C, 5 12 B rispettivamente. La percentuale di cattura calcolata per.π+ 6 12 C→ 5 12 B+v si accorda con l’esperienza; mancano, tuttavia le esperienze per gli altri due casi.

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Copyright information

© Società Italiana di Fisica 1959

Authors and Affiliations

  • A. Fujii
    • 1
  • H. Primakoff
    • 2
  1. 1.Department of PhysicsPurdue UniversityLafayette
  2. 2.Department of PhysiosWashington UniversitySt. Louis

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