} \right)$ is the value of the theoretical cross section \eqref{EQ2}-\eqref{EQ5} with $\sigma _{GDR} (\varepsilon _{i} )$ for model SLO or SMLO at gamma-ray energy $\varepsilon _{i}$, $\sigma _{\exp } \left(\varepsilon _{i} \right)$ is the measured value for the total photoabsorption cross section with uncertainty $\Delta \sigma \left(\varepsilon _{i} \right)$ at that energy, and
$N_{f}= N-N_{par}$ is the number of degrees of freedom for the data set fitted which is equal to the number $N$ of data points within the fitting interval minus the number $N_{par} $ of fitted parameters (3 parameters for each Lorentz-like curve).

If the EXFOR datafiles did not include experimental uncertainties, then they were taken into account according to Ref. \cite{PCG2011}.
Specifically, two different estimations of errors are adopted in absence of experimental uncertainties to check their impact on the determination of the GDR parameters: a 10\% constant error and an energy-dependent error. The former type of error is very often encountered in photoabsorption data files in the EXFOR database, while the latter energy dependence was chosen to simulate the statistical error that is inversely proportional to the counting rate which is maximum near the GDR. Hence, the energy-dependent relative uncertainties were assumed to take minimum values (10\%) near the GDR peaks and maximum values (50\%) on the GDR tails. For spherical nuclei, a triangular dependence on gamma-energy was assumed, while for deformed nuclei a trapezoidal dependence with the GDR peaks as the top corners of the trapezium.

For a given nuclide the data were fitted in an energy interval that was determined following the prescription of
Refs.~\cite{Ber1975,Ber1987,Diet1988,PCG2011,Chad2000,Var1999}. The mid-position was chosen near the peak of the photoabsorption cross section and the interval was placed within an energy range defined by the one-neutron and three-neutron separation energies, where the GDR strength is expected to be dominant. Adjustments to this interval were made in cases where there were too few experimental data points, in order to allow for a good fit to be obtained using a Lorentzian curve.

The minimization of the least-square deviation functional was performed by the CERN MINUIT package~\cite{Minuit}. The standard deviation of the parameters was estimated using the MINOS procedure of this code. The calculated mode was defined by the following sequence of commands: SEEK 1000, MIGRAD 10000 0.000001, IMPROVE 100, HESSE 1, MINOS 1.


\section{Discussion and Conclusion}

It should be noted that the energies $E_{r,j} $, widths $\Gamma _{r,j} $ and factors $s_{j} $ presented in Tables 1 and 2 are, in fact, the parameters of Lorentz-like curves (Lorentz parameters) representing the best
fit of the experimental photoabsorption cross sections in the intervals that hold peak energies for the SLO and SMLO models, respectively.

Different  studies mentioned in the previous section demonstrate
that the Lorentzian  parameters  can be considered as the GDR parameters or mean values of these parameters if the total photoabsorption cross-section is used in fitting and GDR excitation is dominant photoabsorption mechanism.

The accuracy of the description of GDR parameters by Lorentz parameters of the photoabsorption cross section data  depends on many factors.
Besides the well-known problems of the selection and verification of the experimental data and
estimating the contributions of emission cross sections of different particles to the total photoabsorption cross section, there are also ambiguities in the theoretical description of the
GDR component of the E1 photoabsorption cross section.
Namely, an unsolved problem with description of nuclear dissipation as well as the approximation of $\sigma_{GDR} $ by one- or two-component Lorentz-like curves \eqref{EQ5} near the beta-stability valley is, as a rule,
appropriate for rather heavy ($A \gtrsim 40$) spherical and axially deformed nuclei (155 $ \lesssim $ A $ \lesssim $ 190 or 225 $\lesssim$ A $\lesssim$ 250) for gamma-ray energies close to the GDR energy.

Furthermore, additional physical effects should also be taken into account for the correct description of the photoabsorption in nuclei. The nuclear responses of the low-lying states
(two-phonon states, pygmy dipole resonance) to the E1 field have an impact on the photoabsorption at the low-energy wing of the GDR. The isospin splitting, the neutron excess and the
triaxial deformation can affect the shape of the photoabsorption cross section near the GDR and lead to the splitting of the GDR. For medium-mass to heavy nuclei, these effects can be described effectively by
an additional  broadening of the shape-line. But in some situations, isospin splitting and  triaxiality of the nuclear shape have to be considered explicitly in the formulas \cite{Gard1984,Bow1981,ABL1988,AB1990,Jung2008,GJM2014}.

From the tables 1,2  it can be seen that these uncertainties for GDR energy $E_{r} $ do not exceed
$\thicksim$ 10\%. The values of width $\Gamma _{r} $ and the factors $\; s_{j} $ are much more sensitive to the shape of the theoretical curve and their systematic uncertainties can be rather significant.
The difference in the magnitude of the parameters obtained from fitting within SLO and SMLO models can
be considered as the systematic uncertainty due to ambiguity of the theoretical description
of complex mechanism of the GDR relaxation which as yet studied.
However, the overall consistency between different sets of parameters for the
same nucleus in each table are, as a rule, rather good, while the variation of these parameters can be attributed to systematic uncertainties affecting both measurements and the theoretical approach.

The set of the Lorentzian parameters in the first line  (first entry) for each nuclide was determined using, as a rule, the closest experimental data to the total photoabsorption cross sections near GDR and corresponds to minimal least-square deviation in comparison with other entries. Therefore, the quantities in the first entries are the recommended GDR parameters and are used in all our calculations presented below.

The quality of the description of the experimental photonuclear cross sections by the different models is
considered  by means of  the ratio of the least-square deviations (Eq.\eqref{EQ14}) for models SMLO and SLO,
$Rc_i = \chi_{\rm{smlo}}^2 / \chi_{\rm{slo}}^2$, in different intervals ($\Delta \varepsilon_{i}$).
The lower index $i$ indicates  the comparison interval: $i=f$  stands for fitting intervals $\Delta \varepsilon_{f}$ =  $\varepsilon_{min}\leq \varepsilon_{\gamma} \leq \varepsilon_{max}$ from the Tables 1,2 ; $i=l$ for intervals of the GDR left tail $\Delta \varepsilon_{l}$ = $\varepsilon_{0} \leq \varepsilon_{\gamma} \leq  E_{r,1}$   and $i=m$ for whole intervals with the experimental data $ \Delta \varepsilon_{m}$ = $\varepsilon_{0}\leq \varepsilon_{\gamma} \leq 30$ MeV with the energy  $\varepsilon_{0}$ of the first experimental data-point.

The factors $Rc_i$ are indicated in the Graphs and are collected in the Table A.
This table  gives the ratios of the arithmetic means of least-square values of models SMLO to SLO  $<\chi_{\rm{smlo}}^2> / <\chi_{\rm{slo}}^2>$  in different gamma-ray intervals  and for different sets of nuclei.
Here,  the isotopes from the mass-ranges 150 $ \leq $A$ \leq $ 190 and 220 $ \leq$ A $\leq$ 253 are named as axially deformed nuclei. The parameters $\beta $  of effective quadrupole deformation of nuclear surface were taken from file "deflib.dat" packed in "gamma-strength-analytic.tgz", section GAMMA on http://www-nds.iaea.org/RIPL-2/. Nuclei with $\beta < 0.1$ were assumed to be spherical.

\begin{table}[htbp]
\noindent
\caption{ \footnotesize{The ratio of arithmetical means of least-square deviations  for SMLO and SLO models $<\chi^2(SMLO)>/<\chi^2(SLO)>$ }}
\label{tabl1}
\small{
\begin{center}
\begin{tabular}[c]{|c|c|c|c|}
  \hline
  Intervals
     & \multicolumn{3}{|c|}{Nuclei}\\ \cline{2-4}
     & Spherical & Spherical+Axially deformed & All\\ \cline{2-4}
  \hline
  $\Delta \varepsilon _f$
        & 0.96 & 1.11 & 1.09 \\ \cline{2-4}
  \hline
    $\Delta \varepsilon _l$
        & 0.71 & 0.73 & 0.76 \\ \cline{2