Description of isospin mixing by a generator coordinate method

Background: Isospin mixing is an interesting feature of atomic nuclei that plays a crucial role in the astrophysical nuclear reactions. However, variational nuclear structure models cannot describe it in a straightforward manner.

Purpose: We propose a tractable method to describe isospin mixing within the framework of a generator coordinate method and demonstrate its usability.

Method: We generate basis wave functions by applying the Fermi transition operator to the wave functions of isobars. The superposition of these basis wave functions and variationally obtained wave functions quantitatively describes isospin mixing.

Results: We apply our method to ${}^{14}\mathrm{N}$ and show that it reasonably describes both $T=0$ and 1 states and their mixing. The energy spectrum and $E1$ transition strengths are compared with the experimental data.

Conclusion: The proposed method is effective in describing isospin mixing and is particularly useful for discussing of $\alpha$-capture reactions of $N=Z$ nuclei.

Figure 1

Energy curves for ${}^{14}\mathrm{N}$ and ${}^{14}\mathrm{C}$ as functions of the quadrupole deformation parameter $\beta$ obtained through the energy variation after parity projection.

Figure 2

Calculated and observed level scheme of ${}^{14}\mathrm{N}$ up to $J^{\pi }\le 3^{\pm }$. Black lines show the result of the present model, whereas blue lines show the results calculated using only the variationally obtained basis wave functions. The numbers in the figure indicate the amount of the $T=1$ component in percentage for the states with sizable isospin mixing.

Figure 3

Overlap functions of the $1_1^{+}, 0_1^{+}$, and $1_{1,2}^{-}$ states in the $J^{\pi }\otimes \nu \left(l_j\right)$ and $J^{\pi }\otimes \pi \left(l_j\right)$ channels. The phases of the overlap functions are arbitrarily chosen for presentation.