Bulletin of the American Physical Society
3rd Joint Meeting of the APS Division of Nuclear Physics and the Physical Society of Japan
Volume 54, Number 10
Tuesday–Saturday, October 13–17, 2009; Waikoloa, Hawaii
Session BM: Nuclear Theory I |
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Chair: Ionel Stetcu, University of Washington Room: Kings 1 |
Wednesday, October 14, 2009 7:00PM - 7:15PM |
BM.00001: Microscopic Calculation of Excitation Energies for Heavy Systems Sait Umar, Volker Oberacker The density-constrained-TDHF (DC-TDHF) theory is a fully microscopic theory for calculating heavy-ion interaction potentials and fusion cross sections below and above the fusion barrier. The only input into the theory is the effective interaction. The method is based on the TDHF evolution of the nuclear system, coupled with density-constrained Hartree-Fock calculations. This approach incorporates all of the dynamical entrance channel effects such as neck formation, particle transfer, internal excitations and dynamical deformation effects, and has been successfully applied to calculating above- and sub-barrier fusion cross-sections for a number of systems [1-3]. Here, we show that excitations energies of systems formed during heavy-ion collisions can also be microscopically calculated using this approach. Results will be presented for systems, $^{70}$Zn+$^{208}Pb$, $^{48}$Ca+$^{238}$U, and $^{96}$Zr+$^{132}$Sn.\\[4pt] [1] A.S. Umar and V.E. Oberacker, Phys. Rev. C 76, 014614 (2007). \par \noindent [2] A.S. Umar and V.E. Oberacker, Phys. Rev. C 77, 064605 (2008). \par \noindent [3] A.S. Umar and V.E. Oberacker, Eur. Phys. J. A 39, 243 (2009). [Preview Abstract] |
Wednesday, October 14, 2009 7:15PM - 7:30PM |
BM.00002: Coupling effects in the extraction of spectroscopic factors Filomena Nunes, Pierre Capel, Pawel Danielewicz Often one-nucleon spectroscopic factors for loosely-bound nuclei are extracted from peripheral reaction data. This is done under the assumption that, aside from the normalization, the one- nucleon overlap function for the reaction can be approximated in terms of a pure single-particle orbital. The latter can be expected to be valid when the spectroscopic approaches 1, but not necessarily otherwise. To test the validity of the single- particle assumption, we study the core+n system with coupling to excitation of the core. Interactions are fitted to reproduce a realistic nucleus (11Be). We also study an extreme-coupling toy- model, with only two states coupled through a surface delta force. Our results generally render support for the single- particle approximation in the extraction of the spectroscopic factor, even for small values of the factor. When the small values of the spectroscopic factor are combined, though, with a strong localization of the coupling, as in our toy model, deviations from the single particle form can become important. [Preview Abstract] |
Wednesday, October 14, 2009 7:30PM - 7:45PM |
BM.00003: Ensemble treatments of thermal pairing in nuclei Nguyen Quang Hung, Nguyen Dinh Dang A systematic comparison is conducted for pairing properties of finite systems at nonzero temperature as predicted by the exact solutions of the pairing problem embedded in three principal statistical ensembles, namely the grandcanonical ensemble, canonical ensemble and microcanonical ensemble, as well as the unprojected (FTBCS1+SCQRPA) and Lipkin-Nogami projected (FTLN1+SCQRPA) theories that include the quasiparticle number fluctuation and coupling to pair vibrations within the self-consistent quasiparticle random-phase approximation. The numerical calculations are performed for the pairing gap, total energy, heat capacity, entropy, and microcanonical temperature within the doubly-folded equidistant multilevel pairing model. The FTLN1+SCQRPA predictions are found to agree best with the exact grand-canonical results. In general, all approaches clearly show that the superfluid-normal phase transition is smoothed out in finite systems. A novel formula is suggested for extracting the empirical pairing gap in reasonable agreement with the exact canonical results. [Preview Abstract] |
Wednesday, October 14, 2009 7:45PM - 8:00PM |
BM.00004: Effective interactions between neutrons and protons in the intruder orbitals Naotaka Yoshinaga, Koji Higashiyama Effective interactions between neutrons and protons in the high-$j$ intruder orbitals in the medium mass nuclei are theoretically investigated using a simple collective model. In this model, a doubly-odd nucleus is described by one neutron in the 0$h_{11/2}$ orbital and one proton in the 0$g_{9/2}$ orbital, and the collective core representing the even-even part of the nucleus. The effective interactions between the neutrons and protons are written in terms of multipole interactions. The model reproduces well the energy levels of yrast and yrare bands including band head energies. It is found that the quadrupole neutron and proton interaction is dominant among other interactions, but octupole and hexadecapole interactions are important to reproduce band head energies. [Preview Abstract] |
Wednesday, October 14, 2009 8:00PM - 8:15PM |
BM.00005: From UCOM potential to Shell-model and MCSM calculation Liu Lang, T. Otsuka, N. Shimizu The advent of realistic nucleon-nucleon (NN) potentials has created an opportunity to investigate nuclear structure starting from the first principle. In a simple approach, the many-body state is described in a subspace spanned by some trial states, e.g. Slater determinants. Those states cannot describe the strong short-range correlations induced by the realistic NN-potential. How to treat short-ranged repulsive core? 1) To adapt the Hamiltonian by replacing the interactoin with an effecive one. For example, the Brueckner G-Matrix formalism. 2)To introduce the short-range repulsive correlations into the many-body state. A Unitary Correlation Operator Method (UCOM) was Proposed by H. Feldmeier etc, which to a certain extend combines the advantages of the above methods. By using UCOM interaction, shell model and Monte Carlo Shell model calculation has been done with harmonic oscillator basis. Many shells should be mixed, in order to be ab-initio. [Preview Abstract] |
Wednesday, October 14, 2009 8:15PM - 8:30PM |
BM.00006: Tensor force in effective shell model interaction Naofumi Tsunoda, Takaharu Otsuka, Koshiro Tsukiyama Tensor force interaction in effective shell model interaction is investigated. It has been known in recent years that tensor force causes important effect on the structure of exotic nuclei, for example, neutron rich nuclei. Monopole part of the tensor force varies the effective single particle energy in the shell model calculation. In early studies on this subject, the tensor force in the shell model interaction has been taken, as a modeling, to be the bare NN potential generated by $\pi + \rho$ meson exchange potential. We propose a justification of this modeling by presenting the behavior of the tensor force in the effective interaction obtained from microscopic theory. We obtain effective interactions for shell model calculation in two steps. We first integrate out the high momentum part and obtain potential called $V_{lowk}$ defined in low momentum. With this potential, we then perform folded-diagram expansion which includes the effect caused by the truncation to a small model space, for example, the effect of the core-polarization. After obtaining an effective shell model interaction by such a microscopic theory, we decompose it to central, spin-orbit and tensor parts and analyze the basic robust properties of the tensor part. This study will suggest which tensor force should be appropriate for the calculations of nuclear structure. [Preview Abstract] |
Wednesday, October 14, 2009 8:30PM - 8:45PM |
BM.00007: Model space truncation in shell-model fits Calvin Johnson, George Bertsch The interacting shell model with fitted interactions has been a powerful predictive tool of nuclear structure theory, but there has been little study of the error associated with truncation of the shell model spaces. We present a model study of spectra in the $sd$-shell nuclei to address this question. Carrying out a truncation with a model Hamiltonian we find that the binding energies are strongly affected and the excitations less so, by an order of magnitude. We then refit the matrix elements of the two-particle interaction to compensate for the space truncation, and find that it is easy to capture 90\% of the binding energy shifts by refitting a few parameters. Numerically, the rms initial error associated with our Hamiltonian is 3.4 MeV and the remaining residual error is 0.16 MeV, to be compared with the 0.11 MeV residual error in the application to experimental data. [Preview Abstract] |
Wednesday, October 14, 2009 8:45PM - 9:00PM |
BM.00008: The effective three-body monopole interaction and ground-state energies in the $0p$-shell A.F. Lisetskiy, S.G. de Clark, B.R. Barrett, M.K.G. Kruse Following Refs. [1,2], we have earlier developed a valence cluster expansion to construct effective 2- and 3-body Hamiltonians for the $0p$-shell by performing No Core Shell Model (NCSM) calculations for $A=6$ and 7 nuclei and explicitly projecting the many-body Hamiltonians onto the $0\hbar\Omega$ space. These effective Hamiltonians can be separated into 0-, 1- and 2-body contributions(also 3-body for $A=7$), which can be used in standard shell model (SSM) calculations. In new studies we have derived the effective 3-body monopole Hamiltonian for the 0p-shell by performing $6\hbar\Omega$ NCSM calculations for $A=7-16$ nuclei and used it to investigate how the ground-state energies of these nuclei are affected, when it is included in the SSM calculations. \\[4pt] [1] P. Navr\'atil, M. Thoresen and B.R. Barrett, Phys. Rev. C {\bf 55}, R573 (1997). \\[0pt] [2] A. Lisetskiy, {\bf et al.}, Phys. Rev. C {\bf 78}, 044302 (2008). [Preview Abstract] |
Wednesday, October 14, 2009 9:00PM - 9:15PM |
BM.00009: Predominance of Prolate Nuclear Deformations Emerging from Many-Body Interactions Mihai Horoi, Vladimir Zelevinsky A new approach to the old problem of the predominance of prolate deformations among well deformed nuclei is proposed within the shell model framework. The parameter space is explored using the ensemble of random rotationally-invariant interactions. Subsets with rotational energy ratio $E(4^{+})/E(2^{+})$ and the rigid-rotor relation between the quadrupole moment $Q(2^{+})$ and the transition probability $B(E2;2^{+}\rightarrow 0^{+}))$ are found exhibiting prolate predominance. We identify matrix elements of the effective forces responsible for the predominance of prolate deformation. [Preview Abstract] |
Wednesday, October 14, 2009 9:15PM - 9:30PM |
BM.00010: Mean-field derivation of the Interacting Boson Model for deformed nuclei Kosuke Nomura, Lu Guo, Noritaka Shimizu, Takaharu Otsuka We propose a new scheme to determine a Hamiltonian of the Interacting Boson Model (IBM) microscopically, starting from the mean-field model with Skyrme-type interactions [PRL101, 142501 (2008)]. The multi-fermion dynamics of surface deformation and the effects of nuclear forces are simulated by bosonic degrees of freedom. By comparing the potential energy surface of the mean-field model with that of the IBM, the parameters of the IBM Hamiltonian can be obtained as functions of $N$ and $Z$. One of the merits is being able to compute levels and wave functions of excited states precisely. By this method, existing cases of dynamical symmetries of the IBM and the critical-points of the quantum shape-phase transitions can be reproduced. Moreover, intriguing spectroscopic properties, e.g., unexpectedly large region of the E(5) symmetry, are predicted for experimentally unknown heavy exotic nuclei such as osmium and tungsten isotopes with $N>$126. Finally, we would like to discuss more precise analysis on excited spectra of well-deformed samarium nuclei by making a minor correction for the present mapping procedure. The strategy and the preliminary results will be presented. [Preview Abstract] |
Wednesday, October 14, 2009 9:30PM - 9:45PM |
BM.00011: Systematics in the structure of low-lying, non-yrast band-head configurations of strongly deformed nuclei Gabriela Popa Strongly deformed nuclei show interesting paterns in the energy spectrum above around 1 MeV. An empirical investigation of the trends in the properties of the non-yrast $K^\pi=2^+_\gamma$ and $K^\pi=0^+_2$ bandhead configurations in nuclei that are related to one another through the addition or removal of alpha-particle-like structures, reveals their complex and changing behavior in contrast to the smooth behavior of the yrast states. A systematic application of the pseudo-SU(3) model for such a sequence of deformed nuclei from the rare earth region leads to an accurate and unified description of not only yrast, but non-yrast collective bands. The onset of deformation as manifested through the position of the excited bandheads in the spectra is understood and interpreted by using a realistic model Hamiltonian in conjunction with a microscopic distribution of the eigenstates across allowed proton and neutron strong- coupled SU(3) configurations. [Preview Abstract] |
Wednesday, October 14, 2009 9:45PM - 10:00PM |
BM.00012: Comment on top-on-top mechanism in triaxial strongly deformed even mass nuclei Kosai Tanabe, Kazuko Sugawara-Tanabe We have derived the algebraic solution to the particle-rotor model with high $j$ nucleon coupled to a triaxially deformed core, $H=H_{\rm rot} +H_{\rm sp}$. The rotating core top with ${\vec R}={\vec I}-{\vec j}$ and the single-particle top with ${\vec j}$, are strongly correlating each other. We call this mechanism as top-on-top mechanism, where the Coriolis term, ${\vec I}\cdot{\vec j}$ in $H_{\rm rot}$, is explicitly taken into account, giving a big difference from the wobbling model. The algebraic solution to the top-on-top mechanism clarifies not only the energy level scheme, but also gives the approximate selection rules in the strength of transitions among bands. If the single-particle angular momentum $j$ is assumed to be the sum of two angular momenta as $j=j_1 +j_2$ and the value of integer $j$ keeps constant over some range of $I$, then the algebraic solution is easily extended to the even-even nucleus with alignment of integer $j$. Although several candidates of TSD bands are observed in Hf isotopes, no linking transitions between (0,0) and (1,0) are found. The rough estimation of the transition rates give a factor of $(\frac{I-j}{I})^3$ both in $B(E2)$ and $B(M1)$ values for the transitions with $\Delta I=1$ among the favored (0,0) and the unfavored (1,0) bands. The value of $I-j$ is smaller for even-$A$ case than odd-$A$ case, which makes the observation of the other partner band difficult. [Preview Abstract] |
Wednesday, October 14, 2009 10:00PM - 10:15PM |
BM.00013: BCS-BEC transition in finite systems Nguyen Dinh Dang, Nguyen Quang Hung, Peter Schuck The BCS-BEC (Bose-Einstein condensation) transition is studied in finite systems by using an exactly solvable multilevel pairing model as well as a realistic single-particle spectrum for $^{20}$O nucleus. The predictions obtained within~the selfconsistent quasiparticle RPA~that includes the effects due to quantal and thermal fluctuations are discussed along with those given by the BCS theory and exact solutions.~They show a~smooth BCS-BEC transition in the qualitative behavior of the chemical potential as a function of the pairing interaction parameter $G$. The BEC is achieved at $G = G_{c}$\textit{(BEC)}, where the chemical potential reaches the bottom of the single-particle spectrum, and continues to decrease as $G $becomes larger than $ G_{c}$\textit{(BEC)}. The critical temperature $T_{c}$\textit{(BEC) }of the BCS-BEC transition in the strong coupling regime is deducted, at which the entropy of the system reaches the limit of the free bose gas. The effect due to the angular momentum on the BCS-BEC transition is also discussed. [Preview Abstract] |
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