passing through the point ${\bf r}_i$, correspondingly. Neglecting the quasiparticle tunneling between the vortex cores the wave function can be found as a superposition of two states localized at different vortices and having close energies: $\varepsilon_{v1}=-\omega[\mu-(k_F a/2)\sin\theta_p]$ and $\varepsilon_{v2}=-\omega[\mu+(k_F a/2)\sin\theta_p]$. The transformation of the quasiclassical spectrum occurs due to the overlapping of the corresponding wave functions and can be analysed using a standard quantum mechanical approach describing a two–level system[@LL-III], which yields the secular equation $$\label{secularVV}
  (\varepsilon-\varepsilon_{v1})(\varepsilon-\varepsilon_{v2})
  =(\delta\varepsilon)^2\,,$$ and the resulting splitting of isoenergetic lines near the degeneracy point in the $\mu-\theta$ plane ($\theta_p=0$ for our case) $$\label{orbit1}
  \omega\mu=-\varepsilon\pm\sqrt{\omega^2(k_F a/2)^2\theta_p^2
  +(\delta\varepsilon)^2}\,.$$ The tunneling of quasiparticles between the vortex cores is determined by the exponentially small overlapping of wave functions localized near the cores and results in the splitting of the energy levels: $\delta\varepsilon\sim\Delta_0\exp(-a/\xi)$. Thus, the estimate for the splitting $\delta\mu\simeq\delta\varepsilon/\omega$ of isoenergetic lines in the $(\mu,\theta_p)$–plane reads (see Eq. (\[orbit1\])): $$\label{delta-mu}
  \delta \mu(a)\sim k_F\xi\exp\left(-\frac{a}{\xi}\right)\,.$$

In the case of a vortex-antivortex pair the non-interacting states localized at different vortices have the energies $\varepsilon_v=-\omega[\mu+(k_F a/2)\sin\theta_p]$ and $\varepsilon_{av}=\omega[\mu-(k_F a/2)\sin\theta_p]$. Taking into account the overlapping of the corresponding wave functions states we obtain the secular equation (\[secularVV\]) with $\varepsilon_{v1}=\varepsilon_v$ and $\varepsilon_{v2}=\varepsilon_{av}$. Therefore, the quasiclassical 