Session LM: Nuclear Theory IV

Spin- and Parity-Dependent Shell Model Nuclear Level Densities for Medium-Mass Nuclei

The spin- and parity-dependent nuclear level density (SPNLD), $\rho(E_{x},J,\pi)$, is an important element in the description of highly excited nuclei, and it is used to predict the nuclear reactions rates necessary for understanding the nucleosynthesis. Using the methods of statistical spectroscopy, we have developed a method for obtaining the SPNLD using the first two spin-projected moments of the Hamiltonian for each configuration of nucleons. We compare the results of this method with the results of the shell model, whose direct diagonalization approach quickly loses its feasibility, for nuclei in the pf model space and in the f5/2pg9/2 model space. Potential implications for reactions cross sections of nuclei in the rp-path will be discussed.   

Parallel on-the-fly configuration-interaction shell-model code

Configuration-interaction shell-model codes generally rely on computing and storing the full many-body Hamiltonian matrix, which while sparse, nonetheless push computational memory demands, especially when the number of basis states approach 10$^{8}$ and up. On-the-fly algorithms mitigate the memory burden by factorizing both the basis and the Hamiltonian. We describe BIGSTICK, an efficient on-the-fly code designed for large-scale parallel operation with both two- and three-body interactions. We present algorithm developments utilizing MPI, OPENMP, and hybrid schemes. Prepared by LLNL under Contract DE-AC52-07NA27344. Support from U.S. DOE/SC/NP (Work Proposal No. SCW0498) and U.S. DOE Grants DE-FG02-03ER41272 and DE-FC02-09ER41587 is acknowledged.   

Microscopic analysis of large amplitude collective dynamics in triaxial nuclear shapes

We have developed a microscopic theory of large amplitude collective motion that provides us with a collective Hamiltonian. The method is based on the adiabatic expansion of equations of the self-consistent collective coordinate method (Prog. Theor. Phys. {\bf 103}, 959 (2000)). In this approach, the canonical collective variables are self-consistently determined, and all the quantities in the collective Hamiltonian (mass parameters and potential) are also microscopically calculated. Quantizing the collective Hamiltonian, we can treat nuclear dynamics beyond the harmonic limit. We apply the method to the pairing-plus-quadrupole Hamiltonian to discuss properties of nuclear anharmonicity and shape mixing. Especially we stress importance of triaxial degrees of freedom in the shape coexistence phenomena.   

RPA calculations with Gaussian expansion method

The Gaussian expansion method (GEM) is applied to the calculations in the random-phase approximation (RPA). We adopt the mass-independent basis-set that has been tested in the mean-field calculations. The RPA results by the GEM are compared with those obtained by several other available methods in Ca isotopes, using a density-dependent contact interaction and the Woods-Saxon single-particle states. It is confirmed that energies, transition strengths and widths of their distribution are described by the GEM to good precision, for the $1^-$, $2^+$ and $3^-$ collective states. The GEM is then applied to the self-consistent RPA calculations with the finite-range Gogny D1S interaction. The spurious center-of-mass motion is well separated from the physical states in the $E1$ response, and the energy-weighted sum rules for the isoscalar transitions are fulfilled reasonably well.   

Nuclear Rotations and the Born--Oppenheimer Method

We want to discuss the study of nuclear rotations and collective motion within the context of the nuclear Born--Oppenheirmer (NBO) method--a truly quantum mechanical method. As an illustration, we apply the NBO method to study permanently deformed (non-spherical) nuclei; in particular, we study nuclei that are axially-symmetric and even, but with non-closed shells. In the presentation, we focus on the derivation of formal expressions for the energy and for the moment of inertia. Using trial functions in which the intrinsic structure is described in a mean-field approximation, we then show that the NBO formalism yields the Thouless-Valantin formula for the moment of inertia and that this moment of inertia increases with angular momentum, in agreement with experimental data. We show that the NBO formalism is well equipped to describe low-lying as well as high lying rotational states. Additionally, we establish a connection between the NBO method and the self-consistent Cranking (SCC) model, which is known to be successful in reproducing vast amounts of experimental data ranging from low-lying rotational states to high angular momentum states.   

On Ratios of B(E2)'s

We have conducted a wide survey of the ratio B(E2; 4+to2+ ) / B(E2; 2+ to zero+ ) throughout the periodic table. In the rotational model this ratio is 10/7 and in the vibrational model it is 2/1(stimulated emission) There are considerable deviations from this for magic or semi-magic nuclei e.g. for 86Kr (N=50) the ratio is close to zero. But what is more surprising is that there are large deviations for other nuclei as well, which will be systematically shown. Theoretical discussions for some of these deviations will be given.   

Operator Evolution Using SRG Flow Equations for Few-Body Systems

The Similarity Renormalization Group (SRG) flow equations are a series of unitary transformations which can be used to to achieve different patterns of decoupling in a Hamiltonian. An SRG transformation applied to internucleon interactions leads to greatly improved convergence properties while preserving observables. Not only does it provide a way to consistently evolve many-body potentials, but also other operators.\footnote{S.K. Bogner, R.J. Furnstahl, and R.J. Perry, Phys. Rev. C 75 (2007) 061001.} Here, a method to implement SRG evolved few-body operators is applied to both model and realistic calculations. Properties of the corresponding observables are explored for both long- and short- range operators. Methods to improve their convergence in a truncated model space are also considered.   

Fission of heavy $\Lambda$ hypernuclei with the Skyrme-Hartree-Fock approach

It has been shown that the shape of a few deformed nuclei change toward spherical when a $\Lambda$ particle is added to them. This is caused because the interaction between a $\Lambda$ particle and a nucleon is attractive. This fact has motivated us to investigate the influence of $\Lambda$ particle on the fission of heavy nuclei. In this talk, we will discuss the fission-related phenomena of heavy $\Lambda$ hypernuclei with the constraint Skyrme-Hartree-Fock+BCS (SHF+BCS) method. We employ a Skyrme-type interaction for the $\Lambda N$ interaction and assume adiabaticity, that is, the $\Lambda$ particle is assumed to be in the lowest state at all deformations. We will show that the fission barrier heights increase by about 200 keV by adding a $\Lambda$ particle. Our result confirms that the $\Lambda$ particle is stuck to the heavier fission fragment, which is consistent with the experimental result of CERN. We will also discuss the deformation of heavy $\Lambda$ hypernuclei and the $\Lambda$ particle motion inside the core nuclei.   

Microscopic description of fission-fragment properties

The development of a microscopic theory of fission remains one of the greatest challenges in nuclear physics. At the same time, recent advances in theoretical tools and computational power are bringing the goal of a predictive microscopic theory of fission within reach. In this talk, I will discuss the quantitative definition of scission, and the identification of scission configurations within the framework of Hartree-Fock-Bogoliubov (HFB) formalism with the Gogny effective interaction. I will present fission-fragment properties (shapes, kinetic and excitation energies) for low-energy fission of $^{240}$Pu, obtained using static HFB calculations and discuss the prospects for future work within a time-dependent treatment of fission.   

The role of pions on finite nuclei with relativistic chiral mean field model

We present a relativistic chiral mean field (RCMF) model, which is a method for proper treatment of pion-exchange interaction in the nuclear-many body problem. There the term of the pionic correlation is expressed in 2-particle 2-hole (2p-2h) states with particle-hole having pionic quantum number $J^{\pi} = 0^{1}, 1^{+}, 2^{-}, 3^{+}$,...to describe the full strength of the pionic correlation in the intermediate- and long-ranged region (r $>$ 0.5 fm). We include further the effect of the short-range repulsion in terms of the unitary correlation operator method (UCOM) for the central part of the pion-exchange interaction. We apply this model to $^{4}$He, $^{12}$C, and $^{16}$O nuclei. Pion plays an important role on the formation of the jj-magic shell structure by the Pauli-blocking mechanism of the pion- exchange interaction. The lowest pionic quantum number, $J^{\pi} = 0^{-}$, is the dominant component for construction of the surface structure. We also discuss chiral symmetry in finite nuclei in the linear sigma model.