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 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.

196 Pt has been investigated with numerous (n,y) techniques. The structure of the lowspin positive-parity states below the pairing gap shows excellent agreement with the predictions of the 0(6) limit of the interacting boson approximation model of Arima and Iachello.The pure harmonic vibrator and the quadrupoledeformed rotor have long provided two elegant nuclear-structure symmetries or limiting cases. Though few nuclei attain the idealized extremes, these limits are useful in part because their simple energy-level and branching-ratio predictions offer a framework from which deviations, and thereby the forces or interactions that produce them, are more easily identified. A class of nuclei exists toward the end of major shells for which neither limit is applicable. These nuclei are characterized, for example, by low-lying 2 2 + states and missing or much higher-lying excited 0 + levels. (The triaxial-rotor model has sometimes been invoked for such cases, but with varying success.) Our purpose here is to summarize a third limiting symmetry, recently proposed, 1 which may characterize such nuclei and, in particular, to propose that 196 Pt may be an excellent empirical manifestation of it.Recently Iachello and Arima have developed an interacting-boson approximation (IBA) 1 " 3 model in which the Hamiltonian is written in terms of interactions between bosons which can occupy L = 0 and L = 2 (s and d) states. This model can be phrased in the group theoretical language of SU(6) in terms of which three natural limits arise for which analytical solutions are obtainable. These limits correspond to three subgroups of SU(6), namely SU(5), 2 SU(3), 3 and 0(G). 1 ' 3 The first two correspond to an (anharmonic) vibrator and the quadrupole-deformed rotor (with degener-ate "23 + " and "2 y + " levels), respectively. Many examples of nuclei close to these two limits are well known. The third limit and its application to 196 Pt is the subject of this Letter.In the 0(6) limit the energies of collective states are given by 1 E(V,T,J)=\A(N-U){N + G + 4)where N is the number of bosons, defined as half the sum of the number of protons plus the number of neutrons away from the nearest respective closed shells (for 196 Pt, iV = 6); a=N,N-2,N -4,...,0, and r = 0,l,... ,o\ J takes on the values 2 X, 2X-2, 2X-3, ..., X + l, X, where X is a nonnegative integer defined by X = r -3v A for y A = 0,l,2,... . An example of a level scheme with iV = 6 is shown in Fig. 1. Each level can be uniquely identified by the quantum numbersThe wave functions of the collective levels may be expanded 1 " 3 in basis states characterized by their spin, rf-boson number n d , and the numbers of pairs and triplets of bosons coupled to spin zero. In this representation, states with identical J and r but different a are composed of identical nonvanishing basis states whose amplitudes are distributed in different (orthogonal) ways. States differing only in r consist of basis states differing inn d . Electromagnetic transitions follow the E2 selection rules 1 Acr = 0, A...

The (d,p) neutron transfer and (d,d) elastic scattering reactions were measured in inverse kinematics using a radioactive ion beam of 132 Sn at 630 MeV. The elastic scattering data were taken in a region where Rutherford scattering dominated the reaction, and nuclear effects account for less than 8% of the elastic scattering cross section. The magnitude of the nuclear effects, in the angular range studied, was found to be independent of the optical potential used, allowing the transfer data to be normalized in a reliable manner. The neutron-transfer reaction populated a previously unmeasured state at 1363 keV, which is most likely the single-particle 3p 1/2 state expected above the N = 82 shell closure. The data were analyzed using finite-range adiabatic-wave calculations and the results compared with the previous analysis using the distorted-wave Born approximation. Angular distributions for the ground-and first-excited states are consistent with the previous tentative spin and parity assignments. Spectroscopic factors extracted from the differential cross sections are similar to those found for the one-neutron states beyond the benchmark doubly-magic nucleus 208 Pb.

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