The $2\nu2\beta$ decay of $^{150}$Nd to the first excited 740.5 keV $0^{+}_{1}$ level of $^{150}$Sm was measured over 5.845 yr with the help of a four-crystal low-background HPGe $\gamma$ spectrometry system in the underground low-background laboratory STELLA of LNGS-INFN. A 2.381 kg highly purified Nd-containing sample was employed as the decay source. The expected de-excitation gamma-quanta of the $0^{+}_{1}$ level with energies 334.0 keV and 406.5 keV were observed both in one-dimensional spectrum and in coincidence data resulting in the half-life $T_{1/2}=[0.83^{+0.18}_{-0.13}\mathrm{(stat)}^{+0.16}_{-0.19}\mathrm{(syst)}]\times 10^{20}$ yr. Interpreting an excess of the 334.0-keV peak area as an indication of the $2\beta$ decay of $^{150}$Nd to the 334.0 keV $2^+_1$ excited level of $^{150}$Sm with a half-life of $T_{1/2}=[1.5^{+2.3}_{-0.6}\mathrm{(stat)}\pm 0.4\mathrm{(syst)}]\times10^{20}$ yr, the $2\nu2\beta$ half-life of $^{150}$Nd for the transition to the 0$^{+}_{1}$ level is $T_{1/2}=[1.03^{+0.35}_{-0.22}\mathrm{(stat)}^{+0.16}_{-0.19}\mathrm{(syst)}]\times 10^{20}$ yr, in agreement with the previous experiments. Both half-life values reasonably agree with the theoretical calculations in the framework of proton-neutron QRPA with isospin restoration combined with like nucleon QRPA for description of excited states in the final nuclei. For $2\nu2\beta$ and $0\nu2\beta$ transitions of $^{150}$Nd and $^{148}$Nd to several excited levels of $^{150}$Sm and $^{148}$Sm, limits were set at level of $T_{1/2}>10^{20}-10^{21}$ yr.

The most sensitive direct neutrino mass searches today are based on measurement of the endpoint of the beta spectrum of tritium to infer limits on the mass of the unobserved recoiling neutrino. To avoid the smearing associated with the distribution of molecular final states in the T-He molecule, the next generation of these experiments will need to employ atomic (T) rather than molecular (T$_{2}$) tritium sources. Following production, atomic T can be trapped in gravitational and / or magnetic bottles for beta spectrum experiments, if and only if it can first be cooled to millikelvin temperatures. Accomplishing this cooling presents substantial technological challenges. The Project 8 collaboration is developing a technique based on magnetic evaporative cooling along a beamline (MECB) for the purpose of cooling T to feed a magneto-gravitational trap that also serves as a cyclotron radiation emission spectroscope. Initial tests of the approach are planned in a pathfinder apparatus using atomic Li. This paper presents a method for analyzing the dynamics of the MECB technique, and applies these calculations to the design of systems for cooling and slowing of atomic Li and T. A scheme is outlined that could provide a current of T at the millikelvin temperatures required for the Project 8 neutrino mass search.

We address the problem of evaluating neutron-transfer induced breakup cross sections caused by the Borromean nucleus $^{9}$Be, using the reaction $^{197}$Au($^{9}$Be,$^{8}$Be)$^{198}$Au as a test case. This reaction was recently measured over a wide range of incident energies around the Coulomb barrier. To deal with the high density of $^{198}$Au states that can be potentially populated in this reaction, we employ the Ichimura, Austern, Vicent model, in which the spectrum of physical states for this system is replaced by the solutions of a complex n+$^{197}$Au potential, accounting effectively for the fragmentation of single-particle states into physical states. Furthermore, to account for the unbound nature of the emitted $^{8}$Be system, we employ a three-body model of $^{9}$Be. The calculated stripping cross sections are found to be in good agreement with existing data over a wide range of incident energies. The importance of taking into account the energy spread of the single-particle strength of the outgoing $^{8}$Be and the target-like residual nucleus is discussed.