5. Recent HRIBF Research - Approaching Neutron-Rich Nuclei Using the
Shell Model Monte Carlo Approach in a Proton-Neutron
Formalism The Shell model Monte Carlo (SMMC) method [1] 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 [2].
As a first novel application of the new implementation, we performed
SMMCpn calculations for the even-even ^{90-104}Zr and
^{92-106}Mo isotopic chains using a realistic effective
interaction [3] derived with many-body perturbation theory techniques
for the 1p_{1/2}0g_{9/2 }proton and
1d2s0g_{7/2}0h_{11/2} neutron model spaces. Initial
experimental studies [4] indicated that nuclei in this region have
very large deformations, and that the transition from spherical shapes
to highly deformed shapes occurs abruptly: ^{96}Zr is rather
spherical, while ^{100-104}Zr nuclei are well deformed with a
quadrupole deformation parameter of &beta_{2}=0.35 [5].
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 [6] are able to reproduce the
shape transitions with particular Skyrme interactions. The region also
exhibits significant shape-coexistence phenomena
[7].
Shown in Fig.5-1 are calculations of the
ground-state masses for the Zr isotope chain relative to the
^{88}Sr 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.
[1]
S.E. Koonin, D.J. Dean, and K. Langanke, Phys. Reps. 278, 2 (1997) |