Mass Measurements of Exotic Nuclei for Tests of Nuclear Models and Mass Equations or Formulae

The mass of a nucleus is one of its fundamental properties together with its charge, size and electromagnetic moments. It reflects the total binding energy of the nucleus and contains information about the constituents of the nucleus and the forces that bind them together. It thus provides a means to study the fundamental nucleon-nucleon interaction.

Complete theories of nuclear matter have so far been mainly applied to nuclear binding energies and equilibrium densities. Considerable effort has been devoted to the further development of such theories [17] in order to treat the varying density and finite geometry of nuclei. Although detailed mass predictions are still beyond the scope of such theories, an increase in the number of nuclides with known masses over a wide area of the chart of the nuclides would provide a broad view, upon which trends can be established, that can guide the formulation of such theories. The interim solution has been the formulation of many semi-empirical mass formulae.

A good theory would be based on a few, physically well-founded, assumptions, have predictive power and provide physical insight. The main approaches for the formulation of mass models may be roughly divided into three groups: macroscopic, microscopic and the hybrid macroscopic-microscopic. An excellent summary of the current state of these approaches may be found in [18]. The droplet model of the nucleus, first formulated by Weiz\E4cker and latter improved by others (see for e.g. [19]) is elegant in its simplicity and a good example of a macroscopic mass formula. It produces an rms deviation of 3.02 MeV, when fitted to a broad range of nuclei. Not surprisingly, the theory does not reproduce the effect of phenomena like shell closures where the predictions may deviate from the data by as much as 3 times this value. To reproduce these essential features, it is necessary to undertake calculations that include the interactions between the particles in the nucleus: the so called microscopic theories (see for e.g. [20]) or a combination of these two approaches, macroscopic-microscopic theories [21]).

Relative theoretical predictions of various mass models and/or formulae with respect to one model for Cs isotopes.

Such approaches are more satisfying in that they provide more physical insight into the nuclear system and make it possible to test the physical assumptions that are incorporated in them. For example, consider the more fundamental approach which is based on Hartree-Fock calculations with a phenomenological effective interaction such as one of the Skyrme interactions [20] with the pairing corrections provided by a BCS approach (HFBCS-1). Such calculations can provide good predictions: the rms error for the 1888 measured nuclei with Z,N \B3 8 is 0.738 MeV [18]. These calculations rely on parameters of interaction, which are determined by agreement with existing data and may be improved if additional data on the masses of doubly magic and spherical nuclei were available for the parameter fit.

Currently, such data are available on 7 of the 9 doubly magic nuclei known to exist and the remaining two, ⁷⁸Ni and ¹⁰⁰Sn, are candidates for measurements at TITAN (⁷⁸Ni with UC-target inside a plasma source). The masses of these nuclei and other radioactive spherical nuclei would be an asset to future Hartree-Fock calculations.

Recently, a hybrid, high-speed, version of the Hartree-Fock method has been formulated [21]. This so called ETFSI approach calculates the macroscopic part of the binding energy in the extended Thomas-Fermi (ETF) approximation, and the shell correction using the Strutinsky theorem in its integral form (SI) [18, 22]. This technique produces a fit with known masses with rms error of 0.738 MeV.

In contrast, to the HF approach described above, the effective force parameters are obtained from a fit to all known masses. New mass values far from stability are essential for the improvement in the quality of the predictions of mass formulae. This is because the data from stable (and close to stability) nuclides have been incorporated into the fits and the theories reproduce these values. However, the predictions of various approaches for nuclides outside this set often disagree by considerable amounts. It has been noted that new data have the effect of improving the predictions for nuclides near them in subsequent iterations. The predictions often provide the only information we have for remote nuclei and allow us to determine the limits of stability against nucleon emission and the variation in shell strength in regions of extreme proton and neutron number. They also play a crucial role in understanding the process of nucleosynthesis by providing reaction energies along the astrophysical r and rp process paths.

It is not possible to single out individual cases for measurement, from purely nuclear physics motivations. The addition of a large number of mass measurements, as far away from the region of stability as possible, to a precision of 10^-6 to 10^-7 is essential for the testing and improvement of these theories. The wide range of nuclei that can be produced at the ISAC facility coupled with the proposed system provides a unique opportunity to extend our knowledge of the atomic masses of exotic nuclei and improve the theories of atomic mass.