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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...

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