The $\beta$-decay half-lives of 110 neutron-rich isotopes of the elements from ${}_{37}\mathrm{Rb}$ to ${}_{50}\mathrm{Sn}$ were measured at the Radioactive Isotope Beam Factory. The 40 new half-lives follow robust systematics and highlight the persistence of shell effects. The new data have direct implications for $r$-process calculations and reinforce the notion that the second ($A\approx 130$) and the rare-earth-element ($A\approx 160$) abundance peaks may result from the freeze-out of an $(n,\gamma )\rightleftarrows (\gamma ,n)$ equilibrium. In such an equilibrium, the new half-lives are important factors determining the abundance of rare-earth elements, and allow for a more reliable discussion of the $r$ process universality. It is anticipated that universality may not extend to the elements Sn, Sb, I, and Cs, making the detection of these elements in metal-poor stars of the utmost importance to determine the exact conditions of individual $r$-process events.

Spectroscopic factors have been extracted for proton-rich ${}^{34}\mathrm{Ar}$ and neutron-rich ${}^{46}\mathrm{Ar}$ using the ($p$, $d$) neutron transfer reaction. The experimental results show little reduction of the ground state neutron spectroscopic factor of the proton-rich nucleus ${}^{34}\mathrm{Ar}$ compared to that of ${}^{46}\mathrm{Ar}$. The results suggest that correlations, which generally reduce such spectroscopic factors, do not depend strongly on the neutron-proton asymmetry of the nucleus in this isotopic region as was reported in knockout reactions. The present results are consistent with results from systematic studies of transfer reactions but inconsistent with the trends observed in knockout reaction measurements.

The best examples of halo nuclei, exotic systems with a diffuse nuclear cloud surrounding a tightly bound core, are found in the light, neutron-rich region, where the halo neutrons experience only weak binding and a weak, or no, potential barrier. Modern direct-reaction measurement techniques provide powerful probes of the structure of exotic nuclei. Despite more than four decades of these studies on the benchmark one-neutron halo nucleus ${}^{11}\mathrm{Be}$, the spectroscopic factors for the two bound states remain poorly constrained. In the present work, the ${}^{10}\mathrm{Be}(d,\text{}p)$ reaction has been used in inverse kinematics at four beam energies to study the structure of ${}^{11}\mathrm{Be}$. The spectroscopic factors extracted using the adiabatic model were found to be consistent across the four measurements and were largely insensitive to the optical potential used. The extracted spectroscopic factor for a neutron in an $n\ell j=2s_{1/2}$ state coupled to the ground state of ${}^{10}\mathrm{Be}$ is 0.71(5). For the first excited state at 0.32 MeV, a spectroscopic factor of 0.62(4) is found for the halo neutron in a $1p_{1/2}$ state.

The $\beta$-decay half-lives of 94 neutron-rich nuclei ${}^{144-151}\mathrm{Cs}$, ${}^{146-154}\mathrm{Ba}$, ${}^{148-156}\mathrm{La}$, ${}^{150-158}\mathrm{Ce}$, ${}^{153-160}\mathrm{Pr}$, ${}^{156-162}\mathrm{Nd}$, ${}^{159-163}\mathrm{Pm}$, ${}^{160-166}\mathrm{Sm}$, ${}^{161-168}\mathrm{Eu}$, ${}^{165-170}\mathrm{Gd}$, ${}^{166-172}\mathrm{Tb}$, ${}^{169-173}\mathrm{Dy}$, ${}^{172-175}\mathrm{Ho}$, and two isomeric states ${}^{174m}\mathrm{Er}$, ${}^{172m}\mathrm{Dy}$ were measured at the Radioactive Isotope Beam Factory, providing a new experimental basis to test theoretical models. Strikingly large drops of $\beta$-decay half-lives are observed at neutron-number $N=97$ for ${}_{58}\mathrm{Ce}$, ${}_{59}\mathrm{Pr}$, ${}_{60}\mathrm{Nd}$, and ${}_{62}\mathrm{Sm}$, and $N=105$ for ${}_{63}\mathrm{Eu}$, ${}_{64}\mathrm{Gd}$, ${}_{65}\mathrm{Tb}$, and ${}_{66}\mathrm{Dy}$. Features in the data mirror the interplay between pairing effects and microscopic structure. $r$-process network calculations performed for a range of mass models and astrophysical conditions show that the 57 half-lives measured for the first time play an important role in shaping the abundance pattern of rare-earth elements in the solar system.

The level structures of the very neutron-rich nuclei ${}^{128}\mathrm{Pd}$ and ${}^{126}\mathrm{Pd}$ have been investigated for the first time. In the $r$-process waiting-point nucleus ${}^{128}\mathrm{Pd}$, a new isomer with a half-life of $5.8(8)\mu \mathrm{s}$ is proposed to have a spin and parity of $8^{+}$ and is associated with a maximally aligned configuration arising from the $g_{9/2}$ proton subshell with seniority $\upsilon =2$. For ${}^{126}\mathrm{Pd}$, two new isomers have been identified with half-lives of 0.33(4) and $0.44(3)\mu \mathrm{s}$. The yrast $2^{+}$ energy is much higher in ${}^{128}\mathrm{Pd}$ than in ${}^{126}\mathrm{Pd}$, while the level sequence below the $8^{+}$ isomer in ${}^{128}\mathrm{Pd}$ is similar to that in the $N=82$ isotone ${}^{130}\mathrm{Cd}$. The electric quadrupole transition that depopulates the $8^{+}$ isomer in ${}^{128}\mathrm{Pd}$ is more hindered than the corresponding transition in ${}^{130}\mathrm{Cd}$, as expected in the seniority scheme for a semimagic, spherical nucleus. These experimental findings indicate that the shell closure at the neutron number $N=82$ is fairly robust in the neutron-rich Pd isotopes.