Current state of the investigation of superallowed Fermi β decays

TLDR: In this paper, the authors analyzed the compatibility of the different estimates of the superallowed 0+-0+¯¯¯¯β transitions with the most recent surveys of experimental data and developed an alternative way of determining a limit for f¯¯¯¯s/f¯¯¯¯v using the phenomenological approach toδ¯¯¯¯c suggested by Wilkinson.

Abstract: Nuclear Structure: Superallowed Fermiβ transitions; derivation of the effective vector (G′v) and induced scalar (f s) coupling constants from experimental data. At the present time, the crucial point in a systematic study of superallowed 0+-0+ β transitions is the evaluation of the isospin impurity correctionδ c. In the literature,δ c is decomposed into two parts,δ c1 and δc2. Several estimates ofδ c1 have been published, while only one is available forδ c2. We analyze the compatibility of the different estimates ofδ c1 with the most recent surveys of experimental data. The simplest evaluation ofδ c1 reported some years ago by Damgaard is found to yield the most satisfactory ℱt values; these provide reliable values of the effective vector coupling constantG v [e.g.,G v=(1.41242+0.00023)×10−49 ergcm3]. These values are in excellent agreement with a recent valueG v=(1.41248+0.00044)×10−49 erg cm3 obtained by Wilkinson on the basis of a phenomenologic approach toδ c. Conversely, the most recent and detailed parentageexpansion approaches toδ c1 lead toℱt values which increase with Z, showing pronounced slopes. This fact might be due to a relative overestimation ofδ c1 for the lighter nuclei. Using the ℱt values calculated withδ c1 as reported by Damgaard, we evaluate the coupling constant for the induced scalar interaction following a procedure described in a previous paper. The mean of such values isf s/f v=(−0.17±0.80)×10−3. In addition, we develop an alternative way of determining a limit forf s/f v using the phenomenological approach toδ c suggested by Wilkinson. This new procedure yieldsf s/f v=(−0.16±0.87)×10−3, a result which is in excellent agreement with that obtained using the former method; both values are consistent with a value of zero, supporting the conserved vector current theory. The better accuracy of the experimental data makes it possible to reduce by a factor of two the limit established in a previous work.