Particle-$\gamma$ Spectroscopy of $^{13}$C($^{134}$Te,$^{12}$C)$^{135}$Te and $^{9}$Be($^{134}$Te,$^8$Be)$^{135}$Te: One-Neutron Transfer Study of Z=52, N=83 and the $\nu$i$_{13/2}$ State

A HPGe and CsI array (CLARION+HYBALL @ HRIBF) is used to study the $^{13}$C($^{134}$Te,$^{12}$C)$^{135}$Te and $^9$Be($^{134}$Te,$^8$Be)$^{135}$Te direct reactions by particle-$\gamma$ coincidence measurements. The particle-$\gamma$ technique has several advantages (particularly in inverse kinematics) which include the following: can determine decay paths by particle-$\gamma$-$\gamma$, can determine high-precision level energies, can determine multipolarities of transitions by particle-$\gamma$ angular correlations, and can infer cross sections. The use of one-neutron transfer into Z=52, N=83 is employed to gain selectivity to the single-particle neutron states outside of the N=82 shell closure. Results are presented for $^{135}$Te(Z=52,N=83); particularly, results are presented for the new $\nu$i$_{13/2}$ single-particle state at 2107 keV.