We propose a numerical algorithm to solve the time-dependent Hartree-Fock (TDHF) periodic orbits. Nuclear collective states can be determined from these periodic orbits through a requantization rule. We use the nucleus of ^4He with realistic nuclear forces as an example to illustrate the numerical algorithm. A RPA frequency of 27.654 MeV/h is extrapolated from the low energy periodic orbits, and a breathing mode of excitation energy 26.491 MeV is determined from the requantization rule for the ^4He nucleus.
[AC.02] New Methods and New Results in the Three-Nucleon Continuum including Three-Nucleon-Forces
D. Hüber (Los Alamos National Laboratory), H. Wita\l a (Jagiellonian University, Cracow), W. Glöckle, H. Kamada, A. Nogga (Ruhr-Universität Bochum)
We introduced a new single Faddeev equation(D. Hüber et al.), Acta Phys. Pol. B28 (1997) 1677 for the inclusion of a 3NF into the 3N continuum, leading to a significantly more efficient numerical algorithm. Another step forward is a new partial wave decomposition (PWD) for the 3NF(D. Hüber et al.), will appear in Few-Body Systems 22 (1997), which avoids an intractable numerical difficulty showing up in the PWD used up to now for partial waves with j>2. We applied the new PWD to the Tuscon-Melbourne (TM) 3NF. In order to get rid of the ambiguity in the cut-off parameter \Lambda in the strong form factors of the TM 3NF we fitted \Lambda to the experimental value of the triton binding energy for all modern, phase equivalent NN forces(A. Nogga et al.), will appear in Phys. Lett. B. With these 3N Hamiltonians we calculated the elastic Nd spin transfers K_y^y' and K_z^x' and compared them to recent nd(P. Hempen et al.), submitted for publication and pd(L. Sydow, et al.), submitted for publication measurements. These observables scale with the triton binding energy and agree well with the pd data, but lie somewhat below the nd data.
[AC.03] A microscopic calculation of inelastic proton-nucleus scattering
F. Sammarruca (University of Idaho), E.J. Stephenson (IUCF)
Using data for (\vecp,\vecp') spin-flip transitions, (such as the 4^- states(S.W. Wissink, in Spin and Isospin in Nucl.\ Int.)\ p.\ 253 (1991). in ^16O and the 6^- states(E.J. Stephenson et al.), Phys. Rev. Lett. 78, 1636 (1997). in ^28Si), we examine the DWIA predictions based on effective interactions derived from modern, high-precision free-space potentials (including Nijmegen,(V.G.J. Stoks et al.),\ Phys.\ Rev.\ C 49, 2950 (1994). Argonne AV18,(R.B. Wiringa et al.),\ Phys.\ Rev.\ C 51, 38 (1995). and CD-Bonn(R. Machleidt et al.),\ Phys.\ Rev.\ C 53, 1483 (1996).). Structure formfactors are chosen to match (e,e') scattering, and distortions are obtained from a microscopic optical model potential. Comparison with the data for combinations of polarization transfer observables offers a check on the magnitude of each tensor and spin-orbit squared amplitude. The effects of off-shell differences will be discussed. Agreement with data is not satisfactory. This establishes a reliable point of reference from which to explore medium effects within the context of a microscopic NN G-matrix, including possibilities beyond many-body mechanisms.
[AC.04] Rotations and Vibrations of Nuclei with a Davidson Potential
Chairul Bahri, David J. Rowe (Department of Physics, University of Toronto)
It is well known that for certain potentials (such as the Morse potential) the relative dynamics of a two-body system have algebraic solution. It has recently been shown that one such potential is the Davidson potential and has algebraic solutions both for diatomic molecules (in three dimensions) and for the liquid drop model of the nucleus (in five dimensions). The nuclear Davidson potential was introduced by Elliot et al. as a \gamma-independent potential and used by them to explore the relationship between the Wilets-Jean limit of the Bohr-Mottelson collective model and the O limit of the Interacting Boson Model. In this paper, we show that a many-nucleon Hamiltonian, which includes the many-nucleon kinetic energy, a harmonic oscillator shell model potential and a Davidson potential, has an Sp(3,R) dynamical symmetry and, as a consequence, is also amenable to numerical solution. Results will presented to show the range of solutions that can be obtained for different categories of representations.
[AC.05] \rho-exchange effects in coherent pion production.
P.A. Deutchman, F. Sammarruca (University of Idaho)
New theoretical calculations have been done for exclusive coherent pion production in nucleus-nucleus scattering. A theoretical test of the impact of rho-exchange has been assessed by doing comparative calulations of sensitive pion angular distributions with and without the rho-exchange term at incident nuclear energies of 100, 250 and 400MeV/nucleon. For the incident energies considered, the rho-exchange effect is a minor one.
[AC.06] Faddeev calculations for ømega-meson and d' 0^-,\,\pi NN resonance
Z. Papp (Hungarian Academy of Sciences, Debrecen), M. Sander, H.V. von Geramb (University of Hamburg, Germany)
We study the performance of recently developed inversion potentials of SAID phase shifts for nucleon--nucleon, meson--nucleon and meson--meson systems in rigourous Faddeev calculations. The ømega is based upon the L=1, T=1 \pi\pi interaction which describes the \rho-meson. An attempt with our inversion potential predicted (H. Garcilazo, private communication), 1997 a \piNN 0^-, T=0 configuration as resonance at 2018 MeV and a width of 1.75 MeV. It is associated with the experimentally observed resonance at 2065 MeV known as d' (R. Bilger, H. Clement, M. Schepkin, Phys.Rev.Lett. 72, 2972 (1994)). We can confirm largely this result and show further that slightly different fits of the S_11 \pi N phase shift yield inversion potentials which can fit the experimental d' value with a width below 5 MeV. We conjecture for d' to be essentially a molecular three body system composed of colour singlet meson and nucleons. Contrary to the d' configuartion, predict inversion potentials a highly bound ømega. As suppossed, this confirms that the ømega--meson is not a three pion--molecule but a genuine QCD colour singlet configuration. A systematic variation of the L=1, T=1 \pi\pi interaction enligthens the \rho and ømega differences.
[AC.07] Nuclear Matter Calculations with N-N Inversion Potentials
F.A. Brieva, H.F. Arellano (Universidad de Chile), M. Sander, H.V. von Geramb (University of Hamburg)
Nucleon-Nucleon potentials constructed from Arndt's phase shifts SM94 and SM95 using inversion techniques are used to investigate infinite nuclear matter properties. Based on a Brueckner-Hartree-Fock approach, our calculations show that binding energy per nucleon is sensitive to the phase shift behaviour above pion threshold. The main uncertainty comes from the coupled ^3S_1-^3D_1 state. This finding may question the accuracy of now standard N-N potentials, determined in the 0-300 MeV range, for microscopic calculations.
[AC.08] Observables of NN elastic scattering from the solitary boson exchange potential OSBEP.
Lutz Jäde, H.V. von Geramb (University of Hamburg, Germany)
Using the one solitary boson exchange potential OSBEP(L. Jäde and H.V. von Geramb, Phys.Rev. C55, 57 (1997)) we calculate neutron-proton and proton--proton observables for energies below pion threshold. This model uses selfinteracting mesons with its motivation based upon QCD Lagrangians. An essential result is the replacement of commonly used phenomenological form factors by normalized meson fields which imply finite selfenergy diagrams. Furthermore, the NN data support an empirical scaling law between the pion and other meson fields, with the implication that half the number of free parameters, used in Bonn--B, suffice. The complete SAID set of np and pp observable have been sampled. In comparison with Paris, Nijmegen and Bonn--B potentials, OSBEP reproduces NN observables with similar \chi^2 values.
[AC.09] \pi\pi, K\pi and \pi N potential scattering and a prediction of a narrow \sigma meson resonance.
H.V. von Geramb, M. Sander (University of Hamburg, Germany)
Low energy scattering and bound state properties of the \pi N, \pi\pi and K\pi systems are studied as coupled channel problems using inversion potentials of phase shift data. In a first step we apply the potential model to explain recent measurements of pionic hydrogen shift and width. Secondly, predictions of the model for pionium lifetime and shift confirm a well known and widely used effective range expression. Thirdly, as extension of this confirmation, we predict an unexpected medium effect of the pionium lifetime which shortens by several orders of magnitude. The \sigma meson shows a narrow resonance structure as a function of the medium modified mass with the implication of being essentially energy independent. Similarly, we see this medium resonance effect realized for the K\pi system. To support our findings we present also results for the \rho meson and the \Delta(1232) resonance.
[AC.10] Total reaction cross sections for 20 to 100 MeV deuterons from a microscopic model
R.E. Warner (Oberlin College)
Recent extensive measurements of total reaction cross sections for 38, 65, and 97 MeV deuterons on targets from ^9Be to ^208Pb were fitted with microscopic model calculations. Using accepted 2- and 3-parameter Fermi matter distributions, zero-range nucleon-nucleon forces, and eikonal orbits for the projectile, reasonable fits were obtained when the impact parameter was corrected for Coulomb force effects. Correcting the orbit for nuclear force effects worsened the fits somewhat, as did the use of finite-range nuclear forces; we argue however that it is redundant to make both of these corrections. The results were nearly independent of whether a Hulthen, Gartenhaus, or gaussian form factor was used for the deuteron matter distribution. An attempt to fit older d+Pb measurements near 25 MeV indicates either a failure of the model at low energies or a need for remeasurement of these data.
[AC.11] P--matrix analyses of NN, \pi N, \pi\pi and K\pi potentials.
H.V. von Geramb, M. Sander, H. Labes (University of Hamburg, Germany)
Phase shift analyses of elastic channel two body scattering are used as input to generate nonrelativistic and relativistic Gelfand-Levitan-Marchenko inversion potentials. A comprehensive list of such potentials is used to study P-matrix properties along the spirit of Jaffe and Low to identify exotic and nonexotic intrinsic excitation modes. The inversion potentials are bridging S-- and P--matrix radial domains. Furthermore, they facilitate computation of radial wave functions, evaluations in the complex energy domain and off-shell. To solidify our conclusions we made also comparisons with separabel and other potential models. Of particular interest and mostly new are the results for the L=0 \pi N,\pi\pi and K\pi channels regarding their short range interaction and associated resonance features.