Scissors Modes and Spin Excitations in Light Nuclei including ΔN\Delta N=2 excitations: Behaviour of 8Be^8Be and 10Be^{10}Be

Shell model calculations are performed for magnetic dipole excitations in $^8{Be}$ and $^{10}{Be}$ in which all valence configurations plus $2\hbar\omega$ excitations are allowed (large space). We study both the orbital and spin excitations. The results are compared with the `valence space only' calculations (small space). The cumulative energy weighted sums are calculated and compared for the $J=0^+$ $T$=0 to $J=1^+$ $T$=1 excitations in $^8{Be}$ and for $J=0^+$ $T$=1 to both $J=1^+$ $T$=1 and $J$=$1^+$ $T$=2 excitations in $^{10}{Be}$. We find for the $J=0^+$ $T$=1 to $J=1^+$ $T$=1 isovector {\underline {spin}} transitions in $^{10}{Be}$ that the summed strength in the {\underline {large}} space is less than in the {\underline {small}} space. We find that the high energy energy-weighted isovector orbital strength is smaller than the low energy strength for transitions in which the isospin is changed, but for $J=0^+$ $T$=1 to $J=1^+$ $T$=1 in $^{10}{Be}$ the high energy strength is larger. We find that the low lying orbital strength in $^{10}{Be}$ is anomalously small, when an attempt is made to correlate it with the $B(E2)$ strength to the lowest $2^+$ states. On the other hand a sum rule of Zheng and Zamick which concerns the total $B(E2)$ strength is reasonably satisfied in both $^8{Be}$ and $^{10}{Be}$. The Wigner supermultiplet scheme is a useful guide in analyzing shell model results. In $^{10}Be$ and with a $Q \cdot Q$ interaction the T=1 and T=2 scissors modes are degenerate, with the latter carrying 5/3 of the T=1 strength.Comment: 51 pages, latex, 9 figures available upon reques

Nuclear Breathing Mode in the Relativistic Mean Field Theory

The breathing-mode giant monopole resonance is studied within the framework of the relativistic mean-field (RMF) theory. Using a broad range of parameter sets, an analysis of constrained incompressibility and excitation energy of isoscalar monopole states in finite nuclei is performed. It is shown that the non-linear scalar self-interaction and the resulting surface properties influence the breathing-mode considerably. It is observed that dynamical surface properties respond differently in the RMF theory than in the Skyrme approach. A comparison is made with the incompressibility derived from the semi-infinite nuclear matter and with constrained nonrelativistic Skyrme Hartree-Fock calculaions.Comment: Latex (12 pages) and 3 figures (available upon request) J. Phys. G (in press

The BCS theory of q-deformed nucleon pairs - qBCS

We construct a coherent state of q-deformed zero coupled nucleon pairs distributed in several single-particle orbits. Using a variational approach, the set of equations of qBCS theory, to be solved self consistently for occupation probabilities, gap parameter Delta, and the chemical potential lambda, is obtained. Results for valence nucleons in nuclear degenerate sdg major shell show that the strongly coupled zero angular momentum nucleon pairs can be substituted by weakly coupled q-deformed zero angular momentum nucleon pairs. A study of Sn isotopes reveals a well defined universe of (G, q) values, for which qBCS converges. While the qBCS and BCS show similar results for Gap parameter Delta in Sn isotopes, the ground state energies are lower in qBCS. The pairing correlations in N nucleon system, increase with increasing q (for q real).Comment: 8 pages, REVTEX, 3 eps figure

The strength of nuclear shell effects at N=126 in the r-process region

We have investigated nuclear shell effects across the magic number N=126 in the region of the r-process path. Microscopic calculations have been performed using the relativistic Hartree-Bogoliubov approach within the framework of the RMF theory for isotopic chains of rare-earth nuclei in the r-process region. The Lagrangian model NL-SV1 with the inclusion of the vector self-coupling of omega meson has been employed. The RMF results show that the shell effects at N=126 remain strong and exhibit only a slight reduction in the strength in going from the r-process path to the neutron drip line. This is in striking contrast to a systematic weakening of the shell effects at N=82 in the r-process region predicted earlier in the similar approach. In comparison the shell effects with microscopic-macroscopic mass formulae show a near constancy of shell gaps leading to strong shell effects in the region of r-process path to the drip line. A recent analysis of solar-system r-process abundances in a prompt supernova explosion model using various mass formulae including the recently introduced mass tables based upon HFB approach shows that whilst mass formulae with weak shell effects at N=126 give rise to a spread and an overproduction of nuclides near the third abundance peak at A~190, mass tables with droplet models showing stronger shell effects are able to reproduce the abundance features near the third peak appropriately. In comparison, several analyses of the second r-process peak at A~130 have required weakened shell effects at N=82. Our predictions in the RMF theory with NL-SV1, which exhibit weaker shell effects at N=82 and stronger one at N=126 in the r-process region, support the conjecture that a different nature of the shell effects at the magic numbers may be at play in r-process nucleosynthesis of heavy nuclei.Comment: 14 pages, 8 figures; submitted to Physical Review C. Part of this work was presented at Nuclear Physics in Astrophysics II, 20th International Nuclear Physics Divisional Conference of the European Physical Society, at Debrecen, Hungary, May 16-20, 200

The nuclear shell effects near the r-process path in the relativistic Hartree-Bogoliubov theory

We have investigated the evolution of the shell structure of nuclei in going from the r-process path to the neutron drip line within the framework of the Relativistic Hartree-Bogoliubov (RHB) theory. By introducing the quartic self-coupling of $\omega$ meson in the RHB theory in addition to the non-linear scalar coupling of $\sigma$ meson, we reproduce the available data on the shell effects about the waiting-point nucleus $^{80}$Zn. With this approach, it is shown that the shell effects at N=82 in the inaccessible region of the r-process path become milder as compared to the Lagrangian with the scalar self-coupling only. However, the shell effects remain stronger as compared to the quenching exhibited by the HFB+SkP approach. It is also shown that in reaching out to the extreme point at the neutron drip line, a terminal situation arises where the shell structure at the magic number is washed out significantly.Comment: 18 pages (revtex), 8 ps figures, to appear in Phys. Rev.

Phenomenology of the minimal supersymmetric U(1)B−L×U(1)RU(1)_{B-L}\times U(1)_R extension of the standard model

We discuss the minimal supersymmetric $U(1)_{B-L}\times U(1)_R$ extension of the standard model. Gauge couplings unify as in the MSSM, even if the scale of $U(1)_{B-L}\times U(1)_R$ breaking is as low as order TeV and the model can be embedded into an SO(10) grand unified theory. The phenomenology of the model differs in some important aspects from the MSSM, leading potentially to rich phenomenology at the LHC. It predicts more light Higgs states and the mostly left CP-even Higgs has a mass reaching easily 125 GeV, with no constraints on the SUSY spectrum. Right sneutrinos can be the lightest supersymmetric particle, changing all dark matter constraints on SUSY parameter space. The model has seven neutralinos and squark/gluino decay chains involve more complicated cascades than in the MSSM. We also discuss briefly low-energy and accelerator constraints on the model, where the most important limits come from recent $Z'$ searches at the LHC and upper limits on lepton flavour violation.Comment: 46 pages, 11 figure

Gradient Clogging in Depth Filtration

We investigate clogging in depth filtration, in which a dirty fluid is ``cleaned'' by the trapping of dirt particles within the pore space during flow through a porous medium. This leads to a gradient percolation process which exhibits a power law distribution for the density of trapped particles at downstream distance x from the input. To achieve a non-pathological clogging (percolation) threshold, the system length L should scale no faster than a power of ln w, where w is the width. Non-trivial behavior for the permeability arises only in this extreme anisotropic geometry.Comment: 4 pages, 3 figures, RevTe

Bound State Solutions of Klein-Gordon Equation with the Kratzer Potential

The relativistic problem of spinless particle subject to a Kratzer potential is analyzed. Bound state solutions for the s-wave are found by separating the Klein-Gordon equation in two parts, unlike the similar works in the literature, which provides one to see explicitly the relativistic contributions, if any, to the solution in the non-relativistic limit.Comment: 6 page

Electronic screening and damping in magnetars

We calculate the screening of the ion-ion potential due to electrons in the presence of a large background magnetic field, at densities of relevance to neutron star crusts. Using the standard approach to incorporate electron screening through the one-loop polarization function, we show that the magnetic field produces important corrections both at short and long distances. In extreme fields, realized in highly magnetized neutron stars called magnetars, electrons occupy only the lowest Landau levels in the relatively low density region of the crust. Here our results show that the screening length for Coulomb interactions between ions can be smaller than the inter-ion spacing. More interestingly, we find that the screening is anisotropic and the screened potential between two static charges exhibits long range Friedel oscillations parallel to the magnetic field. This long-range oscillatory behavior is likely to affect the lattice structure of ions, and can possibly create rod-like structures in the magnetar crusts. We also calculate the imaginary part of the electron polarization function which determines the spectrum of electron-hole excitations and plays a role in damping lattice phonon excitations. We demonstrate that even for modest magnetic fields this damping is highly anisotropic and will likely lead to anisotropic phonon heat transport in the outer neutron star crust.Comment: 14 pages, 5 Figure

Uncertainties In Direct Neutron Capture Calculations Due To Nuclear Structure Models

The prediction of cross sections for nuclei far off stability is crucial in the field of nuclear astrophysics. For spherical nuclei close to the dripline the statistical model (Hauser-Feshbach) approach is not applicable and direct contributions may dominate the cross sections. For neutron-rich, even-even Sn targets, we compare the resulting neutron capture cross sections when consistently taking the input for the direct capture calculations from three different microscopic models. The results underline the sensitivity of cross sections calculated in the direct model to nuclear structure models which can lead to high uncertainties when lacking experimental information.Comment: 4 pages, using espcrc1.sty, Proc. Intl. Conf. "Nuclei in the Cosmos IV", Univ. Notre Dame 1996, Nucl. Phys. A, in press. A postscript version can also be obtained from http://quasar.physik.unibas.ch/research.htm