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A recent sensitivity study has shown that the $^{35}$K$(p,\gamma)^{36}$Careaction is one of the ten $(p,\gamma)$ reaction rates that could significantlyimpact the shape of the calculated X-ray burst light curve. In this work, wepropose to reinvestigate the $^{35}$K$(p,\gamma)^{36}$Ca reaction rate, as wellas related uncertainties, by determining the energies and decay branchingratios of $^{36}$Ca levels, within the Gamow window, in the 0.5 to 2 GK X-rayburst temperature range. These properties were studied using the one neutronpick-up transfer reaction $^{37}$Ca$(p,d)^{36}$Ca in inverse kinematics using aradioactive beam of $^{37}$Ca at 48 MeV nucleon$^{-1}$. The experimentperformed at GANIL, used the liquid Hydrogen target CRYPTA, the MUST2 detectorarray for the detection of the light charged particles and a zero degreedetection system for the outgoing heavy ions. The atomic mass of $^{36}$Ca isconfirmed and new resonances have been proposed together with their protondecay branching ratios. This spectroscopic information, used in combinationwith recent theoretical predictions for the $\gamma$-width, were used tocalculate the $^{35}$K$(p,\gamma)^{36}$Ca reaction rate. The recommended rateof the present work was obtain within a uncertainty factor of 2 at 1 sigma.This is consistent, with the previous estimate in the X-ray burst temperaturerange. A large increase of the reaction rate was found at higher temperaturesdue to two newly discovered resonances. The $^{35}$K$(p,\gamma)^{36}$Cathermonuclear reaction rate is now well constrained by the present work in abroad range of temperatures. Our results show that the$^{35}$K$(p,\gamma)^{36}$Ca reaction does not affect the shape of the X-rayburst light curve, and that it can be removed from the list of the fewinfluential proton radiative captures reactions having a strong impact on thelight curve.

Evaluation of the $^{35}$K($p$,$\gamma$)$^{36}$Ca reaction rate using the $^{37}$Ca($p$,$d$)$^{36}$Ca transfer reaction