A theoretical description of the first-forbidden β-decay transitions within Pyatov's restoration method

We describe the first-forbidden beta transitions by using Pyatov's restoration method within the framework of proton-neutron quasiparticle random phase approximation (pn-QRPA). A detailed formalism related to how to obtain the energies and wave functions of the first-forbidden excitations is clearly given in the present work. A comparison of the calculated results for various nuclei with the corresponding experimental data is given to demonstrate an application of the present approximation.