Speaker
Description
Neutrino capture cross-section, which depend on the incident-neutrino energy $E_{\nu}$, has the form:
$\sigma(E_{\nu}) = \frac{(G_F g_A)^2}{\pi c^3 \hbar^4} \int_{0}^{W - Q} W p_e F(Z, A, W) S(x) dx$
where $S(E)$ is the charge-exchange strength function, $G_F / (\hbar c)^3 = 1.1663787(6) \times 10^{-5}$ $GeV^{-2}$ is the weak coupling constant, $g_A = - 1.2723$ is the axial-vector constant and $F(Z, A, W)$ is the Fermi-function, which takes into account the Coulomb interaction between beta-particle and the daughter nucleus. The change in the Fermi-function is practically proportional to the change in the cross-section. Since the founding work of Fermi [1] which presented the Fermi-function for point-like nucleus there have been many works describing corrections to the Fermi-function including finite nuclear size, charge distribution, screening etc. One can see a good review of different types of them in [2].
In this work we present the influence of finite nuclear size, screening etc. corrections to the Fermi-function and consequently to cross-section as an example of the $^{127}$I [3]. Particular attention is paid to the dependence of Fermi-function on the nuclear charge radius $R_C$ . Recent experimental results of isotopic dependence of the charge radii for K, Cu, Sn together with theoretical calculations based on the self-consistent theory of finite Fermi-systems with the Fayans density functional was taken into account [4], [5].
- E. Fermi, Z.Phys. 88, 161–177(1934).
- L. Hayen, et al., Rev.Mod.Phys. 90, 015008 (2018).
- Yu. S. Lutostansky, G. A. Koroteev, N.V. Klochkova, A.P. Osipenko, V.N. Tikhonov, and A.N. Fazliakhmetov, JETP Lett. 111, 603 (2020).
- E. E. Saperstein and S. V. Tolokonnikov, Phys. Atom. Nuclei 79, 1030–1066 (2016)
- I. N. Borzov and S. V. Tolokonnikov, Phys. Atom. Nuclei 83, 828–840 (2020).
