Quadrupole Shape Distributions in Heavy Nuclei from Shell Model Monte Carlo

I will discuss recent results for quadrupole shape distributions in the laboratory frame in heavy nuclei. These calculations are carried out using the finite-temperature shell-model Monte Carlo method, in which we are able to extract the intrinsic nuclear deformation parameters $eta$ and $gamma$ without the need to invoke a symmetry-breaking mean-field approximation. This is accomplished with a Landau-like expansion of the logarithm of the shape probability distribution in terms of quadrupole invariants [1].

Recently, we have extended this method to different components of the quadrupole operator and to nuclei as heavy as the actinides. In particular, we show that distributions of different components of the quadrupole tensor operator give consistent and independent determinations of the quadrupole invariants. We have also shown directly that this Landau-like expansion is sufficiently accurate such that the distribution of one component of the quadrupole operator can be used to determine the distributions of the other components. Finally, I will discuss potential applications of these results to relativistic heavy-ion collisions.

[1] M.T. Mustonen, C.N. Gilbreth, Y. Alhassid, and G.F. Bertsch, Phys. Rev. C 98, 034317 (2018)