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7 pags., 5 figs., 2 tabs., The single-particle properties of Mg29 have been investigated via a measurement of the Mg28(d,p)Mg29 reaction, in inverse kinematics, using the ISOLDE Solenoidal Spectrometer. The negative-parity intruder states from the fp shell have been identified and used to benchmark modern shell-model calculations. The systematic data on the single-particle centroids along the N=17 isotones show good agreement with shell-model predictions in describing the observed trends from stability toward O25. However, there is also evidence that the effect of the finite geometry of the nuclear potential is playing a role on the behavior of the p orbitals near the particle-emission threshold., This work wassupported by the U.K. Science and Technology Facilities Council [Grants No. ST/P004598/1, No. ST/N002563/1, No. ST/M00161X/1 (Liverpool), No. ST/P004423/1 (Manchester), No. ST/P005314/1 (Surrey), the ISOL-SRS Grant (Daresbury), No. ST/R004056/1 (Ernest Rutherford Fellowship - Gaffney), and No. ST/T004797/1 (Ernest Rutherford Fellowship - Sharp)], the U.S. Department of Energy, Office of Science, Office of Nuclear Physics, under Contracts No. DE-AC02-06CH11357 (ANL) and No. DE-SC-0014552 (UConn), the European Union’s Horizon 2020 Framework research and innovation program under Grant Agreement No. 654002 (ENSAR2), the Marie Skłodowska-Curie Grant Agreement No. 665779, the Research Foundation Flanders (FWO, Belgium), the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC Grant Agreement No. 617156, and the Spanish Ministry of Science and Innovation under Grants No. PGC2018-095640- B-I00“ELEGANT” and No. PID2019-104390GB-I00. This research used targets provided by the Center for Accelerator Target Science at Argonne National Laboratory. The FSU shell-model calculations were performed using the computational facility of the nuclear physics theory group, Florida State University, supported by grants from the U.S. Department of Energy, Office of Science (DE-SC-0009883 (FSU).

Nucleon-transfer sum rules have been assessed via a consistent reanalysis of cross-section data from neutron-adding ($d$,$p$) and -removing ($d$,$t$) reactions on well-deformed isotopes of Gd, Dy, Er, Yb, and W, with $92\leq N\leq108$, studied at the Niels Bohr Institute in the 1960s and 1970s. These are complemented by new measurements of cross sections using the ($d$,$p$), ($d$,$t$), and ($p$,$d$) reactions on a subset of these nuclei. The sum rules, defined in a Nilsson-model framework, are remarkably consistent. A single overall normalization is used in the analysis, which appears to be sensitive to assumptions about the reaction mechanism, and in the case of sums using the ($d$,$t$) reaction, differs from values determined from reactions on spherical systems., 7 pages, 4 figures

The pairing properties of the neutrinoless double-$\beta$ decay candidate $^{116}$Cd have been investigated. Measurements of the two-neutron removal reactions on isotopes of $^{114,116}$Cd have been made in order to identify 0$^+$ strength in the residual nuclei up to $\approx$3 MeV. No significant $L=0$ strength has been found in excited states indicating that the Bardeen-Cooper-Schrieffer (BCS) approximation is a reasonable basis to describe the neutrons in the ground state. This approximation avoids complications in calculations of double-$\beta$ decay matrix elements that use the quasiparticle random-phase approximation (QRPA) techniques. However this is not the case for the protons, where pair vibrations are prevalent and the BCS approximation is no longer valid, complicating the use of traditional QRPA techniques for this system as a whole.