5. Recent HRIBF Research - Approaching Neutron-Rich Nuclei Using the
Shell Model Monte Carlo Approach in a Proton-Neutron
(D. J. Dean, Spokesperson)
The Shell model Monte Carlo (SMMC) method  was developed as an alternative to direct diagonalization in order to study low-energy nuclear properties. It was successfully applied to nuclear problems where large model spaces made diagonalization impractical. One calculates the thermal canonical expectation values of observables of few-body operators by representing the imaginary-time many-body evolution operator as a superposition of one-body propagators in fluctuating auxiliary fields. Thus, one recasts the Hamiltonian diagonalization problem as a stochastic integration problem.
Cem Ozen, a University of Tennessee Depeartment of Physics and Astronomy graduate student, working with David Dean, recently developed an SMMC approach in the pn-formalism where isospin is explicitly broken. This implementation of SMMCpn enables one to treat shell-model Hamiltonians that are not isospin invariant in the model space, or for which different model spaces are used for protons and neutrons. The method presented in this work is general and may be used for realistic Hamiltonians, as well those of a more schematic variety. Formulation of the method, technical implementation, and initial results constitute Cem's Ph.D. thesis and are reported in a Phys. Rev. C submission .
As a first novel application of the new implementation, we performed SMMCpn calculations for the even-even 90-104Zr and 92-106Mo isotopic chains using a realistic effective interaction  derived with many-body perturbation theory techniques for the 1p1/20g9/2 proton and 1d2s0g7/20h11/2 neutron model spaces. Initial experimental studies  indicated that nuclei in this region have very large deformations, and that the transition from spherical shapes to highly deformed shapes occurs abruptly: 96Zr is rather spherical, while 100-104Zr nuclei are well deformed with a quadrupole deformation parameter of &beta2=0.35 . Furthermore, the spherical-to-deformed transition is more abrupt in the Zr isotopes than in the nearby elements Mo, Ru, and Pd. Generator-coordinate mean-field calculations in this region  are able to reproduce the shape transitions with particular Skyrme interactions. The region also exhibits significant shape-coexistence phenomena .
Shown in Fig.5-1 are calculations of the ground-state masses for the Zr isotope chain relative to the 88Sr core. Note that a very simple modification of the monopole part of the interaction (one that does not change the excitation spectrum) yields a reasonable description of masses along the isotope chains. Further work will be performed to understand the nuclear deformations in this region. Although nuclei above A=94 show significant deformation with this realistic interaction, there is still a factor of two difference between theory and experiment. We will investigate the origin of this problem in future work.
S.E. Koonin, D.J. Dean, and K. Langanke, Phys. Reps. 278, 2 (1997)
 C. Ozen and D.J. Dean, submitted to Phys. Rev. C (2005).
 A. Holt et al., Phys. Rev. C 61, 064318 (2000).
 E. Cheifetz et al., Phys. Rev. Lett. 25, 38 (1970).
 M. A. C. Hotchkis et al., Phys. Rev. Lett. 64, 3123 (1990).
 J. Skalski et al., Nucl. Phys. A559, 221 (1993).
 P.-G. Reinhard et al., Phys. Rev. C 60, 014316 (1999); J.L. Wood et al., Phys. Rep. 215, 101 (1992).