Collectivity, Chaos, and Computers

Two important pieces of nuclear structure are many-body collective deformations and single-particle spin-orbit splitting. The former can be well-described microscopically by simple SU(3) irreps, but the latter mixes SU(3) irreps, which presents a challenge for large-scale, ab initio calculations on fast modern computers. Nonetheless, SU(3)-like phenomenology remains even in the face of strong mixing. The robustness of band structure is reminiscent of robust, pairing collec-tivity that arises from random two-body interactions. The goal of nuclear structure theory is to understand experimental spectra, but what do we mean by understand ? There are two routes to understanding. One is the brute force, extreme reductionism of ab initio computations 1 : one starts from bare nucleon-nucleon scattering data and eventually computes many-body binding energies , spectra, transition rates, etc. This is of course very appealing to physicists, and I believe such ab initio calculations are among the most important nuclear structure results of the past decade, but it has the very obvious danger of getting lost in the numerical details. Furthermore, brute-force calculations are limited by available computing power. The alternate is back-of-the-envelope reasoning: simple, primarily analytic models that are easy to intuit. Algebraic models are prime examples 2,3. The danger here is that the simple picture may not accurately represent the microscopic physics. Ideally, one would like to combine these two: perform microscopically detailed ab initio calculations built upon basis state constructed from algebraic models. Such a hybrid approach would certainly allow one greater insight into the microscopic calculation, and would, one hopes, be much