\}. \nonumber\\
 &&
 \end{aligned}$$ Thus, a seven dimensional minimization is performed using the gradient method. For odd systems, the additional minimization over configurations is performed at every step of the gradient procedure. Considered configurations consist of the odd particle occupying one of the levels close to the Fermi level and the rest of the particles forming a paired BCS state on the remaining levels. Ten states above and ten states below the Fermi level have been blocked and energy minimized over these configurations.

The main problem in a search for saddle points is that, since they are neither minima nor maxima, one has to know energy on a multidimensional grid of deformations (the often used and much simpler method of minimization with imposed constraints may produce invalid results [@Moller2009; @Dubray; @IIbarriers; @Schunck]. To find saddles on a grid we used the Imaginary Water Flow (IWF) technique. This conceptually simple and at the same time very efficient (from a numerical point of view) method was widely used and discussed before [@Luc91; @Mam98; @Hayes00; @Moeler04; @Moller2009; @IIbarriers]. The number of numerically tractable deformation parameters $\{\beta_{\lambda \mu}\}$ is practically limited. More than five-dimensional grids, keeping in mind a subsequent interpolation, are intractable in 