Gross Theory of β-Decay and Its Application to the Fermi Matrix Element

Abstract

663The gross theory of nuclear j3-decay proposed by Takahashi and Yamada is reinvestigated. A revised model for treating the even-odd mass difference is set up and is applied to the calculation of the squared Fermi matrix elements. The results for the superallowed transitions agree well with those expected from the isospin formalism except for the transitions from odd-odd to even-even nuclei. The isospin-forbidden Fermi transitions are also studied. The results are consistent with the existence of the gross structure in the Fermi transitions.If the isospin is conserved and as far as the conserved vector current (CVC) theory 5 l is valid, 6 l the Fermi transition should obey the selection rule iJT= 0 (T: total isospin). The strength of the conventional Fermi matrix element is exhausted by the analog state to which the /1-decay cannot occur energetically in heavier nuclei. In this paper, we assume the CVC. Then, in the usual /1transitions feeding the states other than the analog state, only the isospin impurities in the wave functions contribute to the Fermi parts of the transitions. Conversely, the isospin impurity can be evaluated from the small Fermi matrix elements. Such an idea was first applied to the o-1 --0 l-Fermi transition by Alford and French in the case of 66 Ga decay . 7 l A fuller discussion of the role of the isospin in the {1-decay is given in the review article by Bloom. 8 l·*l On the experimental side, it has become possible to separate the Fermi matrix element in the allowed transition of mixed type by measurements of the /1-r (CP=--= circularly polarized) correlation. A rather large amount of data have been accumulated till now.Theoretical calculations of the isospin-forbidden Fermi matrix elements were *' Quite recently, Blin-Stoyle's review article 47 > appeared. at Purdue University Libraries ADMN on May 31, 2015 http://ptp.oxfordjournals.org/ Downloaded from (2) where --E is the decay energy. The integrand I Afli' (E) 1 2 is the average of the squared Fermi matrix elements around E multiplied by the final level density.* 1 *l Such a quantity as this is sometimes called the "strength function ".1 4 ) at Purdue University Libraries ADMN on May 31, 2015 http://ptp.oxfordjournals.org/ Downloaded frombecause the relevant single-particle operator r;~;or r;~;+ necessarily transforms a proton to a neutron or vice versa leaving the amplitude unchanged as a whole.Other properties of DF (E, c.) are also inferred from sum rules. In Eq.(3), c; 1 and 8 0 (E) are respectively the upper and lower limits of the "single-nucleon en-

Analysis of Electron and Antineutrino Energy Spectra from Fissile Samples under Irradiation based on Gross Theory of Beta-decay

“…Here E e and Eν are the kinetic energies of the electron and the antineutrino. In order to calculate I e i (E e ) and I¯ν i (Eν), we applied the Gross Theory of beta decay first developed by Takahashi, Koyama and Yamada [1][2][3] and then improved by Kondoh and Tachibana et al [4,5]. The details of these calculations related to eqs.…”

“…The details of these calculations related to eqs. (1) and (2) are given elsewhere [6]. The decay constants λ i and the decay chains were taken from JENDL FP Decay Data File 2011 along with the fission yields from JENDL Fission Yield Data File 2011 [7].…”

Analysis of reactor-neutrino spectra fully based on gross theory of beta-decay emphasizing the special role of odd-odd FP nuclides

“…The point is how to obtain the antineutrino spectra, Iν e i (Eν e ), for each individual nuclide i. In order to calculate Iν e i (Eν e ), we applied the gross theory of beta decay first developed by Takahashi, Koyama and Yamada [15][16][17] and then improved by Kondoh, Tachibana et al [10][11][12]. We call this as GT2 after 'generation 2' of the gross theory.…”

Improvement to the gross theory of β decay by inclusion of change in parity

“…The gross theory is based on the sum rule of the β-decay strength function and treats the transitions to all the final nuclear levels in a statistical manner. It has been successful in describing β decay for the entire range of nuclear masses [1][2][3][4][5][6][7]. The results obtained by the gross theory provide a guide for experiments on β decay, especially for newly measured nuclear data, such as very-neutron-rich nuclei, and for purely theoretical nuclei that are extremely different from known nuclei.…”