Bulletin of the American Physical Society
2005 2nd Joint Meeting of the Nuclear Physics Divisions of the APS and The Physical Society of Japan
Sunday–Thursday, September 18–22, 2005; Maui, Hawaii
Session CK: Nuclear Structure Theory |
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Sponsoring Units: DNP JPS Chair: Shalom Shlomo, Texas A&M University Room: Ritz-Carlton Hotel Maui |
Tuesday, September 20, 2005 2:00PM - 2:15PM |
CK.00001: Comparison of Potential Energy Surfaces for Fission and Fusion in Hartree-Fock and Macroscopic-Microscopic Models Ludovic Bonneau, Peter Moller In the macroscopic-microscopic model we calculate the nuclear potential energy versus five different shape coordinates for complete spaces, that is for all possible combinations of these shape coordinates, basically a 5-dimensional ``cube.'' Its structure, in particular saddle points and ridges are determined by use of a water immersion technique. In HF calculations the energies are calculated subject to a number of constraints, for example quadrupole moment and reflection asymmetry, but others are possible. In this approach it is less straightforward to locate saddle points and ridges, than in the other model. However, valleys and minima are fairly easily obtained. We discuss some of these important issues and what we have learned by comparing results of the two approaches. [Preview Abstract] |
Tuesday, September 20, 2005 2:15PM - 2:30PM |
CK.00002: The Nuclear Born--Oppenheimer Method and Nuclear Rotations Nouredine Zettili We want to discuss the application of the nuclear Born--Oppenheirmer (NBO) method to the study of nuclear rotations and collective motion. This application is illustrated on permanently deformed (non-spherical) nuclei that are axially-symmetric and even, but non-closed shell nuclei. We will focus, in particular, on the derivation of 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--a truly quantum mechanical description--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. In addition, 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. [Preview Abstract] |
Tuesday, September 20, 2005 2:30PM - 2:45PM |
CK.00003: Fission properties of superheavy nuclei and a limit of existence of nuclei Hiroyuki Koura We present a chart of nuclear decay modes for alpha decay, beta decay, proton emission, and spontaneous fission ranging from light nuclei to superheavy ones between neutron and proton drip lines with the use of a phenomenological atomic mass formula [1] to estimate decay rates of the above ones. The standard deviation of this mass formula from known masses is 0.67 MeV, and below 0.4 MeV from some separation energies. The WKB methods are applied to calculate decay rates without beta decay one, which is calculated with the gross theory. With these calculations, we find some regions of fissioning nuclei along the proton-drip line from $N\approx $130 to 160, around $Z\approx $108 and $N\approx $168, and from $Z\approx $100 and $N\approx $190 to heavier ones. The first one indicates a disappearance of proton emission in this region, the second one is qualitatively consistent with some recent experimental results in Dubna, and the third one indicates that a production of superheavy nuclei by the r-process nucleosynthesis in star is unexpected. We also calculate total half-lives in the ``island of stability for the superheavy nuclei'' and obtain an alpha-decay-dominant nucleus with the longest half-life on the beta-stability line in an order of 100 year with a certain ambiguity. We also estimate nuclei beyond the superheavy regions and will discuss the limit of existence of nuclei, which is given not by proton emission, but by fission. [1] H. Koura, et al., Prog. Theor. Phys. \textbf{113} (2005) 305. [Preview Abstract] |
Tuesday, September 20, 2005 2:45PM - 3:00PM |
CK.00004: The effect of Dirac sea and tensor coupling of omega meson in SU(2) chiral sigma model Setsuo Tamenaga, Akihiro Haga, Yoko Ogawa, Hiroshi Toki The chiral sigma model provides good saturation property for nuclear matter and produces the magic number 28 by pionic correlation in finite nuclei. However, the magic number appears at N=18 instead of N=20, which seems due to the incompressibility being too large (K=650[MeV]). We take the relativistic Hartree approximation (RHA) for the nucleon propagator with chiral symmetry. However this ordinary approach remains arbitrary and the total effective potential has the instability. We propose a new chiral symmetric renormalization (NCSR) method, which includes the higher-order counter terms of sigma and pi mesons. With this renormalization scheme, we can remove both arbitrariness and divergence, and obtain a stable potential. It is also known that the incompressibility decreases around 300[MeV] in SU(2) chiral sigma model with higher-order terms. In this model s-state level locates at a good place as we expect. However the effective mass (0.85M) is too large. Therefore it is impossible to produce the magic number 20 due to the small spin-orbit splitting of d- state despite of good incompressibility. We discuss the effect of Dirac sea (NCSR and Derivative expansion) and tensor coupling for omega meson in order to solve the problem at N=20. [Preview Abstract] |
Tuesday, September 20, 2005 3:00PM - 3:15PM |
CK.00005: Refinement of Approximate Energy Expressions for Nuclear Matter by Taking into Account Tensor Correlations Kazunori Tanaka, Kazumasa Ebinuma, Masatoshi Takano Approximate energy expressions are refined for infinite zero-temperature nuclear matter by taking into account tensor correlations. They are explicitly expressed as functionals of spin-isospin-dependent radial distribution functions, tensor distribution functions and spin-orbit distribution functions, and can be used conveniently in the variational method. Before this refinement, nuclear matter energies calculated with this variational method were too low, possibly due to insufficiency of the expressions for the kinetic energy caused by noncentral correlations. Compared with the expectation values of the Hamiltonian, the two-body cluster terms are found to be included completely in the previous energy expressions, while the three-body cluster terms are not included sufficiently. Therefore, in this study, the main parts of the three-body-cluster kinetic-energy terms composed of the central and the tensor correlations are added to the previous expressions, as the first step of the refinement. The Euler-Lagrange equations are derived from the refined energy expressions and numerically solved for neutron matter with the AV18 potential. The results are considerably improved. [Preview Abstract] |
Tuesday, September 20, 2005 3:15PM - 3:30PM |
CK.00006: The Spin Cut-off Factor of Nuclear Level Density Aziz Behkami, Mehdi Soltani, Mehmet Kildir, Mehrdad Gholami Since detailed at high resolution $(n, \gamma)$ and transfer reaction data has become available, we have initiated a systematic investigation of the data in order to deduce the parameters involved in the model calculations, in particular the spin cut- off factor. It is difficult to determine experimentally the spin cut-off factor $\sigma$. We have attempted to obtain $\sigma$ near the ground state by fitting $f(J)$ to the experimental spin distribution for various nuclei with $ \chi^2=\sum_k\sum_{J_k}\{[n_k(J)-F_k(J)]^2/n_k(J)\}$ where $F_k=\sum_{J_k}n_k(J)/\sum_kf(J)$ and $n_k(J)$ being the number of levels of spin $J$ in nuclide $k$ which has the spin window $J_k^1$ and $J_k^2$. In addition the energy and mass dependence of the spin cut-off factor have been investigated using the microscopic model of BCS and reliable values for the spin cut- off factor which is often used in equilibrium decay calculations have been obtaind. The energy dependence of the effective moment of inertia determined from the deduced spin cut-off factor, $\sigma^2=(\Im_{eff}/\hbar^2)T$ for all nuclei under study will also be presented and discussed.\\\\ Work supported by the shiraz university research council through grant No. GR-Sc-52. [Preview Abstract] |
Tuesday, September 20, 2005 3:30PM - 3:45PM |
CK.00007: Zero-point energy corrections in self-consistent calculations with density-dependent forces Walid Younes Zero-point energy (ZPE) corrections appear naturally in the Gaussian-overlap approximation to the generator-coordinate method, and play a critical role in microscopic calculations of fission. These corrections are obtained through different prescriptions in the literature, and in a seminal paper by Girod and Grammaticos [1], a useful relationship was derived between ZPE corrections calculated with matrix elements of the angular-momentum operator and those of the multipole-moment operator. The derivation assumed a linearly-constrained Hamiltonian, and neglected re-arrangement terms arising from the density dependence of the effective interaction. Both methods of calculating ZPE corrections are commonly used in the literature, but the multipole-moment formalism provides a convenient framework for treating vibrational and rotational ZPE corrections on the same footing. In this talk, the results in [1] are generalized to the case of density-dependent interactions and quadratic constraints. The two methods of extracting ZPE corrections will be compared as a function of deformation for realistic calculations in heavy nuclei.\par \noindent [1] M. Girod and B. Grammaticos, Nucl. Phys. A330, 40 (1979). [Preview Abstract] |
Tuesday, September 20, 2005 3:45PM - 4:00PM |
CK.00008: Cluster Variational Calculations of the Equation of State for Infinite Nuclear Matter Hiroaki Kanzawa, Kazunori Tanaka, Masatoshi Takano We report variational calculations of the equation of state (EOS) for neutron matter and symmetric nuclear at zero temperature. We assume the Jastrow-type wave functions with spin-isospin-dependent central, tensor and spin-orbit correlation functions. With the two-body cluster approximation, the energies per nucleon are expressed in the terms of the correlation functions. Since the obtained saturation point of symmetric nuclear matter is not in good agreement with the empirical one, additional three-body nuclear forces are necessary. In this study, therefore, we evaluate the three-body potential energies with the UrbanaIX potential, energies are determined so as to reproduce the empirical saturation point of symmetric nuclear matter. Finally, we extend the above calculations for asymmetric nuclear matter. [Preview Abstract] |
Tuesday, September 20, 2005 4:00PM - 4:15PM |
CK.00009: The study of the effect of the tensor force using the charge- and parity-projected Hartree-Fock method Satoru Sugimoto, Kiyomi Ikeda, Hiroshi Toki The tensor force is very important in nuclear structure. It is known that the tensor force plays the decisive role in the binding mechanism of nuclei. Recently we proposed the mean- field-type framework which can take into account the correlation induced by the tensor force by introducing single- particle states with parity and charge mixings. Because the total wave function made from such single-particle states does not have good parity and a charge number, the parity and charge projections are performed. By taking a variation of the total energy calculated with the projected wave function with respect to a single-particle state, we obtain a Hartree-Fock-like equation, the charge- and parity-projected Hartree-Fock (CPPHF) equation. We applied the CPPHF equation to the alpha particle and found that the finite tensor correlation energy is obtained with our method. We applied the CPPHF method to oxygen isotopes and studied the effect of the tensor force on the binding energy. We also calculated the 1-partice and 1-hole states in this region to study the effect of the tensor correlation on single-particle ls splitting. [Preview Abstract] |
Tuesday, September 20, 2005 4:15PM - 4:30PM |
CK.00010: The elusive 1st excited state in 229Th Peter Moller, Anna C. Hayes Several different approaches have been proposed and implemented to find the 1st excited state in 229Th which from systematics and other considerations has been postulated to be located just a few eV above the ground state. One possibility is to populate states in 229Th and study the alpha-decays from the gs and isomer to 225Ra and observe the different alpha-decay half-lives and associated decay energies. Another intriguing possibility is to study the beta decay from 229Ac into 229Th and observe the beta-decays to both the isomer and the gs of Th229. We summarize briefly the current experimental status and review the different theoretical issues associated with interpreting the different approaches. [Preview Abstract] |
Tuesday, September 20, 2005 4:30PM - 4:45PM |
CK.00011: Testing the predictive power of nuclear-structure models against new experimental data Peter Moller Nuclear masses are of paramount importance in studies and modeling of nuclear reactions since the reaction $Q$ values can be obtained from the masses involved. Reliable mass models are of paramount importance to provide masses to nuclear data bases for nuclei for which no experimental masses are available. A key question is: {\it Are the masses calculated for nuclei in unknown regions reliable?}. We argue that when evaluating mass models one needs in addition to address 1) if the basis of the model is sound, 2) if it is general enough to provide additional nuclear structure quantities, not just nuclear masses, and 3) if the model is global so that it is possible to calculate these properties for any or almost any nucleus with proton number $Z$ and neutron number $N$. Using the above starting points we comment on several different mass models that are currently in use, in particular we compare the model deviations from measured masses in the Audi 2003 evaluations and to $\alpha$-decay energies from the heaviest elements and discuss the different physics of the models. [Preview Abstract] |
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CK.00012: Global Studies of Axial Shape Asymmetry of the Nuclear Ground State Peter Moller, Ragnar Bengtsson In the macroscopic-microscopic model we have calculated potential energy surfaces versus $\epsilon_2$, $\epsilon_4$, and the axial asymmetry shape coordinate $\gamma$ for more than 7000 nuclei throughout the nuclear chart. Minima and the saddle points between them are studied with a water immersion technique. We discuss where we calculate that nuclei are axially deformed in their ground state and study the consequences when this effect is incorporated in the model for nuclear masses. [Preview Abstract] |
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