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.

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

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

S-matrix approach to equation of state of nuclear matter

We calculate the equation of state of nuclear matter based on the general analysis of the grand canonical partition function in the $S$-matrix framework. In addition to the low mass stable particles and their two-body scattering channels considered earlier, the calculation includes systematically all the higher mass particles and their exited states as well as the scattering channels formed by any number of these species. We estimate the latter contribution by resonances in all the channels. The resulting model-independent virial series for pressure gets substantial contribution from the heavy particles and the channels containing them. The series converges for larger values of baryon density than found earlier.Comment: Version to appear in PRC, Rapid Communication

Projected multicluster model with Jastrow and linear state dependent correlations for 12≤A≤1612 \leq A \leq 16 nuclei

Variational wave functions based on a Margenau-Brink cluster model with short range and state dependent correlations, and angular momentum projection are obtained for some nuclei with $12 \leq A \leq 16$. The calculations have been carried out starting from the nucleon-nucleon interaction by using the Variational Monte Carlo method. The configuration used consists of three alpha clusters located at the apexes of an equilateral triangle, and an additional cluster, not necessarily of alpha type, forming a tetrahedron. This cluster is located at the top of its height. Short-range and state dependent correlations are included by means of a central Jastrow factor and a linear operatorial correlation factor respectively. Angular momentum projection is performed by using the Peierls-Yoccoz operators. Optimal structures are obtained for all the nuclei studied. Some aspects of our methodology have been tested by comparing with previous calculations carried out without short range correlations. The binding energy, the root mean square radius, and the one- and two-body densities are reported. The effects of correlations on both the energy and the nucleon distribution are analyzed systematically.Comment: 19 pages, 6 figure