Bulletin of the American Physical Society
2009 APS April Meeting
Volume 54, Number 4
Saturday–Tuesday, May 2–5, 2009; Denver, Colorado
Session C10: Nuclear Theory II: Structure and Reactions |
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Sponsoring Units: DNP Chair: James Shepard, University of Colorado Room: Governor's Square 10 |
Saturday, May 2, 2009 1:30PM - 1:42PM |
C10.00001: Auxiliary Field Variational Monte Carlo method: an efficient variational method for nuclear computational theory Mohamed Bouadani Realizing efficient and accurate calculation of hadronic properties requires a realistic wave-function which correlated basis function theory offer. In spite of the complex nuclear interaction that hinders advances in diagrammatic techniques, elaborated computational methods like Green function Monte Carlo have had important successes but are limited to small size nuclei with $A\leq 12$ and pure neutron matter with $N \leq 14$. A novel approach will be described based on auxiliary fields method to circumvent the many-body state dependence of the leading two-body operators in the Hamiltonian. This Auxiliary Fields Variational Monte Carlo, AFVMC, method has been successively implemented for the sampling of the Jastrow form wave-functions with the dominant $v_6$ type operators with a computational scaling as $\leq A^4$. Results show good agreement with other methods. First variational calculations for twenty neutron drop, ${}^{20}n$, and some mid-size nuclei like Oxygen-16 will be shown. This AFVMC calculation show a reasonable possibility of a pioneered Path-Integral calculation for nuclear matter. [Preview Abstract] |
Saturday, May 2, 2009 1:42PM - 1:54PM |
C10.00002: Effective operators in the p-shell from {\em ab-initio} approach M.K.G. Kruse, A.F. Lisetskiy, B.R. Barrett, P. Navr\'atil$^{\ddagger}$, I. Stetcu$^{*}$, J.P. Vary$^{**}$ The {\em ab initio} no-core shell model (NCSM) is a powerful many-body technique to perform fundamental microscopic studies of the structure of light nuclei. Extension to heavier nuclei can be realized by employing the importance truncation scheme or the valence cluster expansion (VCE) approach. The VCE procedure allows to create many-body renormalized effective interaction for the standard shell model (SSM) with a core and consequently to reduce drastically the computational effort necessary to calculate the low-lying states. On the other hand, one can also create a similar SSM effective operator for radii and an electromagnetic operator, like E2 and M1. The properties of such operators, for example in terms of renormalization of proton and neutron charges as a function of model space size are not clearly understood. We employ the VCE procedure for creating E2, M1 and Gamow-Teller operators in the p-shell, using $^5$Li, $^5$He and $^6$Li NCSM results, and show how these operators depend on one- and two-body contributions. \vspace*{0.05in} \noindent $^{\dagger}$Supported in part by NSF grant PHY-0555396; $^{\ddagger}$ Prepared by LLNL under contract No. DE-AC52-07NA27344 $^{*}$ Supported in part by DOE No. DE-AC52-06NA25396 $^{**}$ Supported in part by DOE grant DE-FG02-87ER40371 [Preview Abstract] |
Saturday, May 2, 2009 1:54PM - 2:06PM |
C10.00003: Exact Pairing in a Deformed Hartree-Fock Basis Roman Senkov, B. Alex Brown, Vladimir Zelevinsky, George Bertsch, Yuan Lung Luo A new theoretical approach is presented that combines the Hartree-Fock variational scheme with the exact solution of the pairing problem in the finite orbital space. Using this formulation in the $sd$ and $pf$ model spaces an examples, we show that the exact pairing significantly improves the results for the ground state energies. [Preview Abstract] |
Saturday, May 2, 2009 2:06PM - 2:18PM |
C10.00004: Magnetic Moments and Symmetries for even-even Argon Isotopes Larry Zamick, Shadow Robinson, Yitzhak Sharon In a single-j-shell calculation the spectra, g factors, and B(E2)'s of $^{40}$Ar and $^{44}$Ar are identical. Thus, deviations from this equivalence in the experimental data are due to configuration mixing. We do large-scale shell model calculations for the even-even Argon isotopes with the two interactions WBT and SDPF. The calculated g factors of the 2$_1^+$ states from A=38 to A=46 are, respectively, with WBT (.308,-.197,-.095,-.022,.100) and with SDPF (.319,-.228,-.084,-.040,.513). The two interactions agree very well except for $^{46}$Ar. For this nucleus the probability in the 2$_1^+$ wave function of the configuration where the neutrons form a closed f$_{7/2}$ shell, but a proton is excited from s$_{1/2}$ to d$_{3/2}$, is 2.5\% with WBT but 21.8\% with SDPF. This difference may be related to the rapid change with N of the J=(3/2)$^+$ - J=(1/2)$^+$ splittings in the odd-A Potassium isotopes. The respective calculated splittings from A=41 to A=49 in keV are with WBT (1106,1109,871,507,729) and with SDPF (854,672,345,-320,78), while the experimental ones are (980,561,474,-360,200). We see a crossover at A=47 which is given correctly by SDPF but not by WBT. This could help explain the large difference in the g(2$_1^+$) factors for $^{46}$Ar with these two interactions. It will be interesting to see what the experimental results will be. [Preview Abstract] |
Saturday, May 2, 2009 2:18PM - 2:30PM |
C10.00005: Effective interactions for sd-shell space from {\em ab-initio} approach A.F. Lisetskiy, M.K.G. Kruse, B.R. Barrett, P. Navratil, I. Stetcu, J.P. Vary Insight gained from projected No Core Shell Model calculations in the p-shell [1] can now be utilized to obtain information about and to derive effective Standard Shell Model (SSM) single particle energies (SPEs) and two-body matrix elements (TBMEs) for heavier nuclei. Here we report on a NCSM investigation in $2 \hbar \Omega$, $4 \hbar \Omega$ and $6 \hbar \Omega$ model spaces for $A=17,18$ in order to determine effective interactions for the sd-shell employing valence cluster expansion method. The validity range of the two-body valence cluster truncation is demonstrated by SSM results for binding energies and spectra of $A \ge 19$ nuclei. [1]~A.~F.~Lisetskiy, B.~R.~Barrett, M.~K.~G.~Kruse, P.~Navr\'atil, I.~Stetcu, and J.~P.~Vary, Phys. Rev. C 78, 044302 (2008). $^{\dagger}$Supported in part by NSF grant PHY-0555396; $^{\ddagger}$ Prepared by LLNL under contract No. DE-AC52-07NA27344; $^{*}$ Supported in part by DOE No. DE-AC52-06NA25396; $^{**}$ Supported in part by DOE grant DE-FG02-87ER40371. [Preview Abstract] |
Saturday, May 2, 2009 2:30PM - 2:42PM |
C10.00006: A no-potential approach to nucleon final-state interaction in inclusive electron-nucleus quasielastic scattering L.C. Liu The nucleon-nucleus final-state interaction (FSI) has been customarily calculated through the use of a nucleon-nucleus potential, either relativistic or nonrelativistic. When the nucleon scattering wave function generated by the potential in the final state is not orthogonal to the nucleon bound-state wave function in the initial state, calculations will overestimate cross sections at small momentum transfers. More generally, the orthogonality is lost whenever theoretical description is restricted to a model space that includes only a limited number of open channels in an inclusive reaction. Using the unitarity equation satisfied by the nucleon scattering wave functions, a theory [1] has been developed to express the FSI contributions in terms of experimentally measured nuclear form factors, avoiding completely the use of any potential and, therefore, the associated potential-model dependence of the calculation. The calculated longitudinal response function for $^{12}$C(e,e')X reaction at q=300 MeV/c will be shown as an example of the application of the new approach. \\[3pt] Ref.[1]: Lon-chang (L.C.) Liu, ``Pauli blocking and final-state interaction in electron-nucleus quasielastic scattering,'' to be published in Physical Review C. [Preview Abstract] |
Saturday, May 2, 2009 2:42PM - 2:54PM |
C10.00007: Calculation of Nuclear Level Densities Near the Drip Lines Shaleen Shukla Nuclear Level Densities are crucial inputs in the study of many physical processes spanning from Astrophysics to Nuclear Medicine. We focus on Nuclear Level Densities for nuclei that exist away from the valley of stability. The efforts to make these nuclei theoretically accessible involve a variety of theoretical and computational tools. Effective potentials and regular Quantum mechanical methods have been used to compute the single particle excitation energies of a neutron or a proton inside a nucleus. These single particle energy levels are then used as inputs in rigorous many-body calculations that formulate the nucleus as a gas of fermions. Our results show that nuclei near the drip lines can indeed be studied using the methods described here at least for 40 $\le $ A$\le $100. [Preview Abstract] |
Saturday, May 2, 2009 2:54PM - 3:06PM |
C10.00008: Energy functional for the three-level Lipkin model Michael Bertolli, Thomas Papenbrock We compute the energy functional of a three-level Lipkin model via a Legrendre transform and compare exact numerical results with analytical solutions obtained from the random phase approximation (RPA). Except for the region of the phase transition, the RPA solutions perform very well. We also study the case of three non-degenerate levels and again find that the RPA solution agrees well with the exact numerical result. For this case, the analytical results give us insight into the form of the energy functional in the presence of symmetry-breaking one-body potentials. [Preview Abstract] |
Saturday, May 2, 2009 3:06PM - 3:18PM |
C10.00009: Law of Radioactive Decay and Motion of Emitted Decay Particle Stewart Brekke All bodies are in a state of no motion, linear, vibratory or rotational motion singly or in some combination. Therefore, if a particle is emitted from a decaying nucleus, it will move linearly, rotate, vibrate or have no motion singly or in some combination. If k is a vibrational force constant, $x_0$ the amplitude of vibratation, $1/2I\omega^2$ the kinetic energy of rotation and $1/2mv^2$ the linear kinetic energy, P is parent nucleus, D is daughter nucleus and p is the emitted decay particle the equation for this law is $M_Pc^2 + 1/2M_Pv_P^2 +1/2I\omega_P^2 + {1/2k_Px_P}_0^2 = M_Dc^2 + 1/2M_Dv_D^2 +1/2I\omega^2_D + 1/2k_Dx_{0_D^2} + m_pc^2 + 1/2m_pv_p^2 + 1/2I\omega_p^2 + {1/2k_px_0}_p^2$. [Preview Abstract] |
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