Narrowing of the neutron sd-pf shell gap in $^{29}$Na

The wave-function composition for the low-lying states in $^{29}$Na was explored by measuring their electromagnetic properties using the Coulomb-excitation technique. A beam of $^{29}$Na$^{5+}$ ions, postaccelerated to 70~MeV, bombarded a $^{110}$Pd target with a rate of up to 600 particles per second, in the first physics experiment using the {\small ISAC-II} facility at {\small TRIUMF}. Six segmented clover detectors of the {\small TIGRESS} $\gamma$-ray spectrometer were used to detect deexcitation $\gamma$ rays in coincidence with scattered or recoiling charged particles in the segmented silicon detector, {\small BAMBINO}. A preliminary reduced transition matrix element $| \langle \frac{5}{2}^{+}_{1} ||E2|| \frac{3}{2}^{+}_{\rm gs} \rangle | = 0.229(20)$~$e$b was derived for $^{29}$Na from the measured $\gamma$-ray yields for both projectile and target. This first-time measured value is consistent with the most recent Monte Carlo shell-model calculation (MCSM) of Utsuno {\it et al.}, predicted to be 0.232~$e$b, indicating an approximately equal admixture of both $sd$ and $pf$ components in the wave function, and also providing evidence for the narrowing of the $sd$-$pf$ shell gap from $\sim 6$~MeV for stable nuclei to $\sim 3$~MeV for $^{29}$Na.