This PhD report presents a study of radiative neutron capture reaction of the ¹⁷³Lu to determine the (n,γ) cross section. Contrary to stable nuclei for which a huge amount of data is available, there is a real lack of information for radioactive nuclei. The first part of this PhD focuses on the presentation of different formalisms involved in cross section calculations and on the use of TALYS code based on these models. TALYS allowed us to evaluate the (n,γ) cross section on ¹⁷³Lu with data from the capture reaction on the ¹⁷⁵Lu. In a second step, the (n,γ) cross section on ¹⁷³Lu was measured at the LANSCE facility with the 4π detector DANCE. This experience turned out to be a real challenge for both the target production of ¹⁷³Lu and for obtaining data due to the high radioactivity of this isotope. Interesting informations have been extracted such as the total capture yield, the identification and the characterization of new resonances, the determination of parameters like average spacing, neutron and γ widths and the value of the density function. All these new informations enabled us to reconstruct the (n,γ) cross section on ¹⁷³Lu up to 200 eV. We could then estimate a correction for the cross section evaluated by TALYS in order to obtain a new evaluation. The third part of this PhD deals with getting additionnal information on the ¹⁷³Lu(n,γ)¹⁷⁴Lu reaction by using the surrogate method. Firstly, this technique has been tested on a well-known reaction : ¹⁷⁵Lu(n,γ)¹⁷⁶Lu with the reaction ¹⁷⁴Yb(³He,p)¹⁷⁶Lu. Secondly, we studied the ¹⁷³Lu(n,γ)¹⁷⁴Lu reaction with the ¹⁷⁴Yb(³He,t)¹⁷⁴Lu reaction. The γ decay probability in different ways have been measured and compared with a TALYS calculation. This comparison showed large discrepancies between the transfer reactions and the reactions induced by neutrons. Then our investigation was focused on the spin distribution of the formed compound nucleus. It has been extracted thanks to a fit of the measured γ decay probability. This distribution has shown (³He,X) reactions populate much higher spins than observed in (n,γ) reactions. The measurement of the γ transitions intensities ratios also corroborates this result even if the mean value of the populated spins seem to be lower. This experiment clearly demonstrated a reaction induced by a ³He beam could not to be substituted to a (n,γ) reaction. Throughout this document, we have shown by different aspects on one hand, how it can be difficult to extract information on unstable nuclei such as ¹⁷³Lu and on the other hand that both experimental and theoretical challenges still remain for the future.
