## 3 Results and Discussion
According to the theory [12], the \(2D\)-\(3D\) crossover should happen when  
\[\mathrm{T}_{0}=\mathrm{T}_{c}\{1+2[\xi_{c}(0)/\mathrm{d}]^{2}\}, \tag{4}\]  
where it is assumed that \(\alpha=1/2\), i.e., the following:  
\[\rho(\text{T})=\text{AT}^{-1}+\text{BT} \tag{1}\]0  
Having determined the value of \(\varepsilon_{0}\) and applying the literature data on the dependence of \(T_{c}\) and interplanar spacing on \(\delta\)[31], it was feasible to calculate the value \(\xi_{c}(0)\). In Figure 5 are shown the \(\Delta\sigma_{ab}(T)\) dependencies in \(\mathrm{ln}\Delta\sigma(\mathrm{ln}\varepsilon)\) coordinates for different \(r\) values, experimentally derived from the following relation:  
\[\rho(\text{T})=\text{AT}^{-1}+\text{BT} \tag{1}\]1  
before and after irradiation. With a temperature range between \(T_{c}\) and \(\leq 1.1T_{c}\) (depending upon the oxygen concentration), these dependencies were adequately approximated by straight lines with a slope angle of \(\alpha_{1}\approx-0.5\), thus indicating a three-dimensional character of fluctuation superconductivity in this temperature regime. by increasing the T, the rate of decrease in \(\Delta\sigma\) increased significantly (\(\alpha_{2}\approx-1\)). This is an indication of a change in the dimensionality of fluctuation conductivity (FC). This change corresponds to a \(2D\)-\(3D\) crossover. Notably, in previous studies of the FC in \(\mathrm{YBa_{2}Cu_{3}O_{7-8}}\) HTSC systems of various compositions using the Kouvel-Fisher method [4,6,10], a whole chain of crossovers was repeatedly recorded, and this was interpreted as a sequence of transitions of \(1D\)-\(2D\), \(2D\)-\(3D\) and \(3D\)-critical fluctuations and intermediate types between them. Taking into account these results, we considered the following picture of superconducting pairing in HTSC. Fluctuation pairs, nucleated inside the CuO\({}_{2}\) planes at \(T\leq T^{*}\)  
\[\rho(\text{T})=\text{AT}^{-1}+\text{BT} \tag{1}\]2 (**a**). Dependencies \(\mathrm{ln}\Delta\sigma(\mathrm{T})\) on \(\mathrm{ln}\varepsilon\) for fluences 0 (circles) and \(55.7\times 10^{18}\) e/cm\({}^{2}\) (squares) and \(79.2\times 10^{18}\) e/cm\({}^{2}\) (inset (a)). The inset (b) shows the dependencies of \(\xi_{c}(0)\) on \(\Phi\). (**b**). Temperature dependencies of excess conductivity in the \(ab\)-plane for \(Y_{1-2}\mathrm{Pr_{2}Ba_{2}Cu_{3}O_{7-8}}\) single crystals in \(\mathrm{ln}\Delta\sigma\)-\(\mathrm{ln}\varepsilon\) coordinates. Inset (a) shows the dependence for z = 0.48. Inset (b) shows the dependencies of \(\xi_{c}(0)\) on z. The curves’ numbering is consistent with \[\rho(\text{T})=\text{AT}^{-1}+\text{BT} \tag{1}\]3  
led to an increase in _nsc_. Since at \(T>>T_{c}\) the values of _nsc_ and especially the \(\xi_{c}(T)\) are very small, there is likely to be no interaction between the pairs. The corresponding electronic state of the fluctuation pairs can be considered as 0-D, which is not represented by the existing FC theories. At \(T\leq T_{2D}\), fluctuation pairs begin to overlap, but still only within the CuO\({}_{2}\) planes, forming a \(2D\) electronic state, which was described by the Mackie-Thompson regime (MT) contribution of the Hikami-Larkin (HL) theory [14]. At \(T\leq T_{3D}\), the increasing \(\xi_{c}(T)\) becomes greater than \(d\) and connects the conducting planes by paired tunnel interactions of Josephson type. Now, the fluctuation pairs interact through the whole volume of the superconductor and form a \(3D\) electronic state, which is well described by the \(3D\) contribution of the Aslamazov-Larkin (AL) theory [12]. In fact, only now is the system entirely ready to complete the transition to the superconducting state. Note that for the In\(\Delta\)s(Ine) dependences obtained at maximum irradiation fluences (F = 7.92 and 8.63 \(\times\) 10\({}^{19}\) e/cm\({}^{2}\)), a non-monotonic progression of the curves was observed, which may have indicated an additional crossover at temperatures e \(\geq\) e\({}_{0}\) with a sharp decrease in slope, \(\alpha\).