By exploiting Coulomb dissociation of high-energy radioactive beams of the neutron-rich nuclei [129][130][131][132]134 Sb, their dipole-strength distributions have been measured. A sizable fraction of "pygmy" dipole strength, energetically located below the giant dipole resonance, is observed in all of these nuclei. A comparison with available pygmy resonance data in stable nuclei ( 208 Pb and N = 82 isotones) indicates a trend of strength increasing with the proton-to-neutron asymmetry. On theoretical grounds, employing the RQRPA approach, a one-to-one correlation is found between the pygmy strength and parameters describing the density dependence of the nuclear symmetry energy, and in turn with the thicknesses of the neutron skins. On this basis, by using the experimental pygmy strength, parameters of the nuclear symmetry energy (a 4 = 32.0 ± 1.8 MeV and p o = 2.3 ± 0.8 MeV/fm 3 ) are deduced as well as neutron-skin thicknesses R n − R p of 0.24 ± 0.04 fm for 132 Sn and of 0.18 ± 0.035 fm for 208 Pb, both doubly magic nuclei. Astrophysical implications with regard to neutron stars are briefly addressed.The neutron root-mean-square (rms) radii of nuclei are fundamental quantities which are difficult to measure in a model-free way [1] and are, therefore, known only for few cases and with relatively poor accuracy [2][3][4]. This fact is particularly cumbersome since neutron rms radii belong to the few laboratory data that can be used to constrain the isospin-asymmetric part of the equation of state of nuclear matter [5][6][7], which in turn is closely related, e.g., to the radii of such exotic objects as neutron stars. Neutron skins in heavy nuclei and the crust of neutron stars are both built from neutron-rich nuclear matter and one-to-one correlations were drawn between neutron-skin thicknesses in nuclei [8][9][10] and specific properties of neutron stars. In a recent paper, Piekarewicz [11] pointed out that the experimentally observed "pygmy" dipole (E1) strength [12] might play an equivalent role as the neutron rms radius in constraining the nuclear symmetry energy. Excess neutrons forming the skin give rise to pygmy dipole transitions at excitation energies below the giant dipole resonance; to which extent such transitions represent a collective vibration of excess neutrons against an isospinsymmetric core is theoretically under discussion yet [13][14][15][16].Experimental evidence for pygmy dipole resonances (PDR) is still rather scarce. In an earlier paper [12], we reported on low-lying E1 strength observed in the exotic nuclei 130,132 Sn exhausting a few percent of the energy-weighted ThomasReiche-Kuhn (TRK) sum rule. Stable N = 82 isotones and 208 Pb investigated in (γ, γ ) reactions [17-19] display a concentration of dipole strength below the neutron-separation threshold, absorbing, however, a much smaller fraction of the TRK sum rule.In the first part of this Rapid Communication we present new experimental data for the unstable isotopes 129,131 Sn and 133,134 Sb obtained from the same measurement as in...

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...

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