Correlations and the relativistic structure of the nucleon self-energy

A key point of Dirac Brueckner Hartree Fock calculations for nuclear matter is to decompose the self energy of the nucleons into Lorentz scalar and vector components. A new method is introduced for this decomposition. It is based on the dependence of the single-particle energy on the small component in the Dirac spinors used to calculate the matrix elements of the underlying NN interaction. The resulting Dirac components of the self-energy depend on the momentum of the nucleons. At densities around and below the nuclear matter saturation density this momentum dependence is dominated by the non-locality of the Brueckner G matrix. At higher densities these correlation effects are suppressed and the momentum dependence due to the Fock exchange terms is getting more important. Differences between symmetric nuclear matter and neutron matter are discussed. Various versions of the Bonn potential are considered.Comment: 18 pages LaTeX, including 6 figure

Long-Term Variations in the Growth and Decay Rates of Sunspot Groups

Using the combined Greenwich (1874-1976) and Solar Optical Observatories Network (1977-2009) data on sunspot groups, we study the long-term variations in the mean daily rates of growth and decay of sunspot groups. We find that the minimum and the maximum values of the annually averaged daily mean growth rates are ~52% per day and ~183% per day, respectively, whereas the corresponding values of the annually averaged daily mean decay rates are ~21% per day and ~44% per day, respectively. The average value (over the period 1874-2009) of the growth rate is about 70% more than that of the decay rate. The growth and the decay rates vary by about 35% and 13%, respectively, on a 60-year time-scale. From the beginning of Cycle 23 the growth rate is substantially decreased and near the end (2007-2008) the growth rate is lowest in the past about 100 years.Comment: 1 table, 13 figures, accepted by Solar Physic

Relativistic Structure of the Nucleon Self-Energy in Asymmetric Nuclei

The Dirac structure of the nucleon self-energy in asymmetric nuclear matter cannot reliably be deduced from the momentum dependence of the single-particle energies. It is demonstrated that such attempts yield an isospin dependence with even a wrong sign. Relativistic studies of finite nuclei have been based on such studies of asymmetric nuclear matter. The effects of these isospin components on the results for finite nuclei are investigated.Comment: 9 pages, Latex 4 figures include

Higher spin quaternion waves in the Klein-Gordon theory

Electromagnetic interactions are discussed in the context of the Klein-Gordon fermion equation. The Mott scattering amplitude is derived in leading order perturbation theory and the result of the Dirac theory is reproduced except for an overall factor of sixteen. The discrepancy is not resolved as the study points into another direction. The vertex structures involved in the scattering calculations indicate the relevance of a modified Klein-Gordon equation, which takes into account the number of polarization states of the considered quantum field. In this equation the d'Alembertian is acting on quaternion-like plane waves, which can be generalized to representations of arbitrary spin. The method provides the same relation between mass and spin that has been found previously by Majorana, Gelfand, and Yaglom in infinite spin theories

Effective DBHF Method for Asymmetric Nuclear Matter and Finite Nuclei

A new decomposition of the Dirac structure of nucleon self-energies in the Dirac Brueckner-Hartree-Fock (DBHF) approach is adopted to investigate the equation of state for asymmetric nuclear matter. The effective coupling constants of $\sigma$, $\omega$, $\delta$ and $\rho$ mesons with a density dependence in the relativistic mean field approach are deduced by reproducing the nucleon self-energy resulting from the DBHF at each density for symmetric and asymmetric nuclear matter. With these couplings the properties of finite nuclei are investigated. The agreement of charge radii and binding energies of finite nuclei with the experimental data are improved simultaneously in comparison with the projection method. It seems that the properties of finite nuclei are sensitive to the scheme used for the DBHF self-energy extraction. We may conclude that the properties of the asymmetric nuclear matter and finite nuclei could be well described by the new decomposition approach of the G matrix.Comment: 16 pages, 5 figure

A phenomenological equation of state for isospin asymmetric nuclear matter

A phenomenological momentum-independent (MID) model is constructed to describe the equation of state (EOS) for isospin asymmetric nuclear matter, especially the density dependence of the nuclear symmetry energy $E_{\text{\textrm{sym}}}(\rho)$. This model can reasonably describe the general properties of the EOS for symmetric nuclear matter and the symmetry energy predicted by both the sophisticated isospin and momentum dependent MDI model and the Skyrme-Hartree-Fock approach. We find that there exists a nicely linear correlation between $K_{\mathrm{sym}}$ and $L$ as well as between $J_{0}/K_{0}$ and $K_{0}$, where $L$ and $K_{\mathrm{sym}}$ represent, respectively, the slope and curvature parameters of the symmetry energy at the normal nuclear density $\rho_{0}$ while $K_{0}$ and $J_{0}$ are, respectively, the incompressibility and the third-order derivative parameter of symmetric nuclear matter at $\rho_{0}$. These correlations together with the empirical constraints on $K_{0}$, $L$ and $E_{\text{\textrm{sym}}}(\rho_{0})$ lead to an estimation of -477 MeV $\leq K_{\mathrm{sat,2}}\leq -241$ MeV for the second-order isospin asymmetry expansion coefficient for the incompressibility of asymmetric nuclear matter at the saturation point.Comment: 9 pages, 4 figures, contribution to Special Topic on Large-Scale Scientific Facilities (LSSF) in Science in China Series G: Physics, Mechanics & Astronom

Quaiselastic scattering from relativistic bound nucleons: Transverse-Longitudinal response

Predictions for electron induced proton knockout from the $p_{1/2}$ and $p_{3/2}$ shells in $^{16}$O are presented using various approximations for the relativistic nucleonic current. Results for the differential cross section, transverse-longitudinal response ($R_{TL}$) and left-right asymmetry $A_{TL}$ are compared at $|Q^2|=0.8$ (GeV/c)$^2$ corresponding to TJNAF experiment 89-003. We show that there are important dynamical and kinematical relativistic effects which can be tested by experiment.Comment: 10 pages, including 2 figures. Removed preliminary experimental data from the figure

Search for Short-Term Periodicities in the Sun's Surface Rotation: A Revisit

The power spectral analyses of the Sun's surface equatorial rotation rate determined from the Mt. Wilson daily Doppler velocity measurements during the period 3 December 1985 to 5 March 2007 suggests the existence of 7.6 year, 2.8 year, 1.47 year, 245 day, 182 day and 158 day periodicities in the surface equatorial rotation rate during the period before 1996. However, there is no variation of any kind in the more accurately measured data during the period after 1995. That is, the aforementioned periodicities in the data during the period before the year 1996 may be artifacts of the uncertainties of those data due to the frequent changes in the instrumentation of the Mt. Wilson spectrograph. On the other hand, the temporal behavior of most of the activity phenomena during cycles 22 (1986-1996) and 23 (after 1997) is considerably different. Therefore, the presence of the aforementioned short-term periodicities during the last cycle and absence of them in the current cycle may, in principle, be real temporal behavior of the solar rotation during these cycles.Comment: 11 pages, 6 figures, accepted for publication in Solar Physic

Scalar and vector decomposition of the nucleon self-energy in the relativistic Brueckner approach

We investigate the momentum dependence of the nucleon self-energy in nuclear matter. We apply the relativistic Brueckner-Hartree-Fock approach and adopt the Bonn A potential. A strong momentum dependence of the scalar and vector self-energy components can be observed when a commonly used pseudo-vector choice for the covariant representation of the T-matrix is applied. This momentum dependence is dominated by the pion exchange. We discuss the problems of this choice and its relations to on-shell ambiguities of the T-matrix representation. Starting from a complete pseudo-vector representation of the T-matrix, which reproduces correctly the pseudo-vector pion-exchange contributions at the Hartree-Fock level, we observe a much weaker momentum dependence of the self-energy. This fixes the range of the inherent uncertainty in the determination of the scalar and vector self-energy components. Comparing to other work, we find that extracting the self-energy components by a fit to the single particle potential leads to even more ambiguous results.Comment: 35 pages RevTex, 7 PS figures, replaced by a revised and extended versio