Background The nuclear structure of the cluster bands in $^{20}$Ne presents a challenge for different theoretical approaches. It is especially difficult to explain the broad 0$^+$, 2$^+$ states at 9 MeV excitation energy. Simultaneously, it is important to obtain more reliable experimental data for these levels in order to quantitatively assess the theoretical framework. Purpose To obtain new data on $^{20}$Ne $alpha$ cluster structure. Method Thick target inverse kinematics technique was used to study the $^{16}$O+$alpha$ resonance elastic scattering and the data were analyzed using an textit{R} matrix approach. The $^{20}$Ne spectrum, the cluster and nucleon spectroscopic factors were calculated using cluster-nucleon configuration interaction model (CNCIM). Results We determined the parameters of the broad resonances in textsuperscript{20}Ne: 0$^+$ level at 8.77 $pm$ 0.150 MeV with a width of 750 (+500/-220) keV; 2$^+$ level at 8.75 $pm$ 0.100 MeV with the width of 695 $pm$ 120 keV; the width of 9.48 MeV level of 65 $pm$ 20 keV and showed that 9.19 MeV, 2$^+$ level (if exists) should have width $leq$ 10 keV. The detailed comparison of the theoretical CNCIM predictions with the experimental data on cluster states was made. Conclusions Our experimental results by the TTIK method generally confirm the adopted data on $alpha$ cluster levels in $^{20}$Ne. The CNCIM gives a good description of the $^{20}$Ne positive parity states up to an excitation energy of $sim$ 7 MeV, predicting reasonably well the excitation energy of the states and their cluster and single particle properties. At higher excitations, the qualitative disagreement with the experimentally observed structure is evident, especially for broad resonances.
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