Relations Between Coefficients of Fractional Parentage

For each of the (9/2), (11/2) and (13/2) single j shells we have only one state with J=j V=3 for a five particle system. For four identical particles there can be more than one state of seniority four. We note some ``ratio'' relations for the coefficients of fractional parentage for the four and five identical particle systems

Weak Interaction Rate Coulomb Corrections in Big Bang Nucleosynthesis

We have applied a fully relativistic Coulomb wave correction to the weak reactions in the full Kawano/Wagoner Big Bang Nucleosynthesis (BBN) code. We have also added the zero temperature radiative correction. We find that using this higher accuracy Coulomb correction results in good agreement with previous work, giving only a modest 0.04 percent increase in helium mass fraction over correction prescriptions applied previously in BBN calculations. We have calculated the effect of these corrections on other light element abundance yields in BBN and we have studied these yields as functions of electron neutrino lepton number. This has allowed insights into the role of the Coulomb correction in the setting of the neutron-to-proton ratio during the BBN epoch. We find that the lepton capture processes' contributions to this ratio are only second order in the Coulomb correction.Comment: 8 pages, 3 figure

Investigation of Pygmy Dipole Resonances in the Tin Region

The evolution of the low-energy electromagnetic dipole response with the neutron excess is investigated along the Sn isotopic chain within an approach incorporating Hartree-Fock-Bogoljubov (HFB) and multi-phonon Quasiparticle-Phonon-Model (QPM) theory. General aspects of the relationship of nuclear skins and dipole sum rules are discussed. Neutron and proton transition densities serve to identify the Pygmy Dipole Resonance (PDR) as a generic mode of excitation. The PDR is distinct from the GDR by its own characteristic pattern given by a mixture of isoscalar and isovector components. Results for the $^{100}$Sn-$^{132}$Sn isotopes and the several N=82 isotones are presented. In the heavy Sn-isotopes the PDR excitations are closely related to the thickness of the neutron skin. Approaching $^{100}$Sn a gradual change from a neutron to a proton skin is found and the character of the PDR is changed correspondingly. A delicate balance between Coulomb and strong interaction effects is found. The fragmentation of the PDR strength in $^{124}$Sn is investigated by multi-phonon calculations. Recent measurements of the dipole response in $^{130,132}$Sn are well reproduced.Comment: 41 pages, 10 figures, PR

Fermion propagators in space-time

The one- and the two-particle propagators for an infinite non-interacting Fermi system are studied as functions of space-time coordinates. Their behaviour at the origin and in the asymptotic region is discussed, as is their scaling in the Fermi momentum. Both propagators are shown to have a divergence at equal times. The impact of the interaction among the fermions on their momentum distribution, on their pair correlation function and, hence, on the Coulomb sum rule is explored using a phenomenological model. Finally the problem of how the confinement is reflected in the momentum distribution of the system's constituents is briefly addressed.Comment: 26 pages, 9 figures, accepted for publication on Phys. Rev.

Ground State Properties of Many-Body Systems in the Two-Body Random Ensemble and Random Matrix Theory

We explore generic ground-state and low-energy statistical properties of many-body bosonic and fermionic one- and two-body random ensembles (TBRE) in the dense limit, and contrast them with Random Matrix Theory (RMT). Weak differences in distribution tails can be attributed to the regularity or chaoticity of the corresponding Hamiltonians rather than the particle statistics. We finally show the universality of the distribution of the angular momentum gap between the lowest energy levels in consecutive J-sectors for the four models considered.Comment: 12 pages, 5 figure

Quark Masses: An Environmental Impact Statement

We investigate worlds that lie on a slice through the parameter space of the Standard Model over which quark masses vary. We allow as many as three quarks to participate in nuclei, while fixing the mass of the electron and the average mass of the lightest baryon flavor multiplet. We classify as "congenial" worlds that satisfy the environmental constraint that the quark masses allow for stable nuclei with charges one, six, and eight, making organic chemistry possible. Whether a congenial world actually produces observers depends on a multitude of historical contingencies, beginning with primordial nucleosynthesis, which we do not explore. Such constraints may be independently superimposed on our results. Environmental constraints such as the ones we study may be combined with information about the a priori distribution of quark masses over the landscape of possible universes to determine whether the measured values of the quark masses are determined environmentally, but our analysis is independent of such an anthropic approach. We estimate baryon masses as functions of quark masses and nuclear masses as functions of baryon masses. We check for the stability of nuclei against fission, strong particle emission, and weak nucleon emission. For two light quarks with charges 2/3 and -1/3, we find a band of congeniality roughly 29 MeV wide in their mass difference. We also find another, less robust region of congeniality with one light, charge -1/3 quark, and two heavier, approximately degenerate charge -1/3 and 2/3 quarks. No other assignment of light quark charges yields congenial worlds with two baryons participating in nuclei. We identify and discuss the region in quark-mass space where nuclei would be made from three or more baryon species.Comment: 40 pages, 16 figures (in color), 4 tables. See paper for a more detailed abstract. v4: Cleaning up minor typo

A Microscopic T-Violating Optical Potential: Implications for Neutron-Transmission Experiments

We derive a T-violating P-conserving optical potential for neutron-nucleus scattering, starting from a uniquely determined two-body $\rho$-exchange interaction with the same symmetry. We then obtain limits on the T-violating $\rho$-nucleon coupling $\overline{g}_{\rho}$ from neutron-transmission experiments in $^{165}$Ho. The limits may soon compete with those from measurements of atomic electric-dipole moments.Comment: 8 pages, 2 uuencoded figures in separate files (replaces version sent earlier in the day with figures attached), in RevTeX 3, submitted to PR

Isospin dependence of nuclear matter symmetry energy coefficients

Generalized symmetry energy coefficients of asymmetric nuclear matter are obtained as screening functions. The dependence of the isospin symmetry energy coefficient on the neutron proton (n-p) asymmetry may be determined unless by a constant (exponent) $Z$ which depend on microscopic properties. The dependence of the generalized symmetry energy coefficients with Skyrme forces on the n-p asymmetry and on the density, only from .5 up to 1.5 $\rho_0$, are investigated in the isospin and scalar channels. The use of Skyrme-type effective forces allows us to obtain analytical expressions for these parameters as well as their dependences on the neutron-proton (n-p) asymmetry, density and even temperature. Whereas the density dependence of these coefficients obtained with Skyrme forces is not necessarily realistic the dependence on the n-p asymmetry exhibit a more consistent behaviour. The isospin symmetry energy coefficient (s.e.c.) increases as the n-p asymmetry acquires higher values whereas the isoscalar s.e.c. decreases. Some consequences for the Supernovae mechanism are discussed.Comment: 17 pages (latex) plus four figures in two eps files. To be published in Nucl. Phys.

Global Study of Nuclear Structure Functions

We present the results of a phenomenological study of unpolarized nuclear structure functions for a wide kinematical region of x and Q^2. As a basis of our phenomenology we develop a model which takes into account a number of different nuclear effects including nuclear shadowing, Fermi motion and binding, nuclear pion excess and off-shell correction to bound nucleon structure functions. Within this approach we perform a statistical analysis of available data on the ratio of the nuclear structure functions F_2 for different nuclei in the range from the deuteron to the lead. We express the off-shell effect and the effective scattering amplitude describing nuclear shadowing in terms of few parameters which are common to all nuclei and have a clear physical interpretation. The parameters are then extracted from statistical analysis of data. As a result, we obtain an excellent overall agreement between our calculations and data in the entire kinematical region of x and Q^2. We discuss a number of applications of our model which include the calculation of the deuteron structure functions, nuclear valence and sea quark distributions and nuclear structure functions for neutrino charged-current scattering.Comment: 67 pages, 18 figures (v3: updated text and references, a new section with discussion about relation between off-shell effect and modification of the nucleon size in nuclei, accepted for publication in Nucl. Phys. A

Center-of-mass motion and cross-channel coupling in time-dependent Hartree-Fock theory

We provide a discussion of issues related to the center-of-mass motion and cross-channel coupling in applications of the time-dependent Hartree-Fock (TDHF) theory to heavy-ion collisions. We find that the entrance channel dynamics of a heavy-ion collision as described by TDHF does not seem to be significantly influenced by these effects, whereas the long-time evolution may be less reliable.Comment: 4 pages, 4 figure