Atomic nuclei have a shell structure in which nuclei with 'magic numbers' of neutrons and protons are analogous to the noble gases in atomic physics. Only ten nuclei with the standard magic numbers of both neutrons and protons have so far been observed. The nuclear shell model is founded on the precept that neutrons and protons can move as independent particles in orbitals with discrete quantum numbers, subject to a mean field generated by all the other nucleons. Knowledge of the properties of single-particle states outside nuclear shell closures in exotic nuclei is important for a fundamental understanding of nuclear structure and nucleosynthesis (for example the r-process, which is responsible for the production of about half of the heavy elements). However, as a result of their short lifetimes, there is a paucity of knowledge about the nature of single-particle states outside exotic doubly magic nuclei. Here we measure the single-particle character of the levels in (133)Sn that lie outside the double shell closure present at the short-lived nucleus (132)Sn. We use an inverse kinematics technique that involves the transfer of a single nucleon to the nucleus. The purity of the measured single-particle states clearly illustrates the magic nature of (132)Sn.

The best examples of halo nuclei, exotic systems with a diffuse nuclear cloud surrounding a tightlybound 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 Be, the spectroscopic factors for the two bound states remain poorly constrained. In the present work, the 10 Be(d,p) reaction has been used in inverse kinematics at four beam energies to study the structure of 11 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 a n j = 2s 1/2 state coupled to the ground state of 10 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. Nuclear halos are a phenomenon associated with certain weakly-bound nuclei, in which a tail of dilute nuclear matter is distributed around a tightly bound core [1][2][3]. This effect is only possible for bound states with no strong Coulomb or centrifugal barrier, and which lie close to a particle-emission threshold. Though excited-state halos exist, the number of well-studied halo states is predominantly limited to a handful of light, weakly-bound nuclei which exhibit the phenomenon in their ground state.The neutron-rich nucleus 11 Be is a brilliant example of this phenomenon, with halo structures in both of its bound states, and light enough to be modeled with an ab initio approach. It is well documented that the 1/2 + ground state and 1/2 − first excited state in 11 Be are inverted with respect to level ordering predicted from a naïve shell model. There has been considerable theoretical effort toward reproducing this level inversion in a systematic manner, while maintaining the standard ordering in the nearby nuclide 13 C, where the 1/2 + state lies over 3 MeV above the 1/2 − ground state. A Variational Shell Model approach [4] and models which vary the singleparticle energies via vibrational [5] and rotational [6] core couplings reproduce this level inversion in a systematic manner. Common to the success of these models is the inclusion of core excitation. Ab initio No-Core Shell Model calculations [7] have been unable to reproduce this level inversion though a significant drop in the energy of the 1/2 + state in 11 Be is reported with increasing model space. In all of these models, the wave functions for the 11 Be halo states show a considerable overlap with a valence neutron coupled to an excited 10 Be(2 + ) core, in addition to the naïve n⊗ 10 Be(0 + gs ) component. Despite decades of study, the extent of this mixing is not well understood, with both structure calculations and the interpretation of experimental results ranging from a few...

The breaking of the N=8 shell-model magic number in the 12Be ground state has been determined to include significant occupancy of the intruder d-wave orbital. This is in marked contrast with all other N=8 isotones, both more and less exotic than 12Be. The occupancies of the [FORMULA: SEE TEXT]orbital and the [FORMULA: SEE TEXT], intruder orbital were deduced from a measurement of neutron removal from a high-energy 12Be beam leading to bound and unbound states in 11Be.

The extraction of detailed nuclear structure information from transfer reactions requires reliable, well-normalized data as well as optical potentials and a theoretical framework demonstrated to work well in the relevant mass and beam energy ranges. It is rare that the theoretical ingredients can be tested well for exotic nuclei owing to the paucity of data. The halo nucleus 11 Be has been examined through the 10 Be(d,p) reaction in inverse kinematics at equivalent deuteron energies of 12, 15, 18, and 21.4 MeV. Elastic scattering of 10 Be on protons was used to select optical potentials for the analysis of the transfer data. Additionally, data from the elastic and inelastic scattering of 10 Be on deuterons was used to fit optical potentials at the four measured energies. Transfers to the two bound states and the first resonance in 11 Be were analyzed using the Finite Range ADiabatic Wave Approximation (FR-ADWA). Consistent values of the spectroscopic factor of both the ground and first excited states were extracted from the four measurements, with average values of 0.71(5) and 0.62(4) respectively. The calculations for transfer to the first resonance were found to be sensitive to the size of the energy bin used and therefore could not be used to extract a spectroscopic factor.

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