Enhanced Sensitivity of Nuclear Binding Energies to Collective Structure

Abstract

We have studied calculated collective contributions to nuclear binding and separation energies and find that there is a deeper and much more sensitive link to nuclear structure than previously recognized or expected, especially near midshell in medium mass and heavy nuclei. As a consequence, measured masses may help understand the structure of well-deformed nuclei (e.g., intrinsic excitations). Conversely, future structure calculations must consider their implications for binding energies. Nuclear masses and binding energies reflect the sum of all nucleonic interactions. Those same interactions lead to shell structure and residual interactions and, hence, to nuclear structure in all its various forms. Therefore, it is obvious that masses and nuclear structure should be related. We will show in this Letter, however, a much more highly amplified interrelation than previously expected, especially in heavy deformed nuclei. A plot of two-neutron separation energies, as shown in Fig. 1 [1], illustrates aspects of the connection of masses and structure. These S 2n values are the energies required to remove the last two neutrons from the nucleus. One sees a sudden drop in S 2n after the N ¼ 82 major shell closure, reflecting the much lower binding of neutrons entering the next shell. Near N ¼ 90, the extra binding as deformation sets in results in a flattening of S 2n . Aside from exceptions such as this, however, the general trend in S 2n values is a series of parallel, more or less straight, lines. Careful inspection of Fig. 1, though, does show gentle curvatures to these S 2n lines whereas the Weizsäcker mass formula [2], and other approaches [3], suggest a linear behavior. Therefore, it is likely that these curvatures have their origin in certain collective effects [3].There have been a few attempts to calculate these contributions to S 2n in collective models, most notably the early interacting boson approximation (IBA) [4] model calculations of Sm isotopes [5], and in recent detailed studies [3,6,7] of several isotopic sequences. In particular, Ref.[6] analyzed transitional sequences of nuclei and noted that different fits, in roughly comparable agreement with the known data, differ significantly in binding and separation energies, concluding that it is important to treat binding energies and excitation spectra on an equal footing in the study of long chains of isotopes.It is the purpose of the present Letter to demonstrate a highly magnified, heretofore unexpected, sensitivity of binding energies to structure, to identify a large class of nuclei where this occurs, to understand why the effects are so large in these nuclei, and to demonstrate that the sensitivity is such that ground state binding energies (BEs) can even be used to assess their structure and intrinsic excitations. We will see, for example, that alternate calculations yielding collective states in deformed nuclei at excitation energies $1:3 MeV that differ in energy by only 200 keV, can lead to calculated separation energy differences of $4 MeV. Thi...

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