Abstract:
We extend the quark mean field model to the study of $\Lambda$ hypernuclei. Without adjusting parameters, the properties of $\Lambda$ hypernuclei can be described reasonably well. The small spin-orbit splittings for $\Lambda$ in hypernuclei are achieved, while the $\Lambda$ single particle energies in the present model are slightly underestimated as compared with the experimental values. About 3% deviation from the quark model prediction for the $\omega-\Lambda$ couplings is required in order to reproduce the experimental single particle energies.

Abstract:
The study of hypernuclei in the quark mean-field model are extended from single-$\Lambda$ hypernuclei to double-$\Lambda$ hypernuclei as well as $\Xi$ hypernuclei (double strangeness nuclei), with a broken SU(3) symmetry for the quark confinement potential. The strength of the potential for $u,d$ quarks is constrained by the properties of finite nuclei, while the one for $s$ quark is fixed by the single $\Lambda$-nucleus potential at the nuclear saturation density, which has a slightly different value. Compared to our previous work, we find that the introduction of such symmetry breaking improves efficiently the description of the single $\Lambda$ energies for a wide range of mass region, which demonstrates the importance of this effect on the hypernuclei study. Predictions for double-$\Lambda$ hypernuclei and $\Xi$ hypernuclei are then made, confronting with a few available experiential double-$\Lambda$ hypernuclei data and other model calculations. The consistency of our results with the available double-$\Lambda$ hypernucleus is found to be surprisingly good. Also, there is generally a bound state for $\Xi^0$ hypernuclei with both light and heavy core nuclei in our model.

Abstract:
We study the properties of the $\Theta^+$ in nuclear matter and $\Theta^+$ hypernuclei within the quark mean-field (QMF) model, which has been successfully used for the description of ordinary nuclei and $\Lambda$ hypernuclei. With the assumption that the non-strange mesons couple only to the $u$ and $d$ quarks inside baryons, a sizable attractive potential of the $\Theta^+$ in nuclear matter is achieved as a consequence of the cancellation between the attractive scalar potential and the repulsive vector potential. We investigate the $\Theta^+$ single-particle energies in light, medium, and heavy nuclei. More bound states are obtained in $\Theta^+$ hypernuclei in comparison with those in $\Lambda$ hypernuclei.

Abstract:
The Relativistic Hartree Bogoliubov model in coordinate space, with finite range pairing interaction, is applied to the description of $\Lambda$-hypernuclei with a large neutron excess. The addition of the $\Lambda$ hyperon to Ne isotopes with neutron halo can shift the neutron drip by stabilizing an otherwise unbound core nucleus. The additional binding of the halo neutrons to the core originates from the increase in magnitude of the spin-orbit term. Although the $\Lambda$ produces only a fractional change in the central mean-field potential, through a purely relativistic effect it increases the spin-orbit term which binds the outermost neutrons.

Abstract:
The shapes of light normal nuclei and $\Lambda$ hypernuclei are investigated in the $(\beta, \gamma)$ deformation plane by using a newly developed constrained relativistic mean field (RMF) model. As examples, the results of some C, Mg, and Si nuclei are presented and discussed in details. We found that for normal nuclei the present RMF calculations and previous Skyrme-Hartree-Fock models predict similar trends of the shape evolution with the neutron number increasing. But some quantitative aspects from these two approaches, such as the depth of the minimum and the softness in the $\gamma$ direction, differ a lot for several nuclei. For $\Lambda$ hypernuclei, in most cases, the addition of a $\Lambda$ hyperon alters slightly the location of the ground state minimum towards the direction of smaller $\beta$ and softer $\gamma$ in the potential energy surface $E \sim (\beta, \gamma)$. There are three exceptions, namely, $^{13}_\Lambda$C, $^{23}_\Lambda$C, and $^{31}_\Lambda$Si in which the polarization effect of the additional $\Lambda$ is so strong that the shapes of these three hypernuclei are drastically different from their corresponding core nuclei.

Abstract:
We present an overview of a fully covariant formulation for describing the production of strangeness -1 and -2 hypernuclei using probes of different kinds. This theory is based on an effective Lagrangian picture and it focuses on production amplitudes that are described via creation, propagation and decay into relevant channel of intermediate baryonic resonance states in the initial collision of the projectile with one of the target nucleons. The bound state nucleon and hyperon wave functions are obtained by solving the Dirac equation with appropriate scalar and vector potentials. Specific examples are discussed for reactions which are of interest to current and future experiments on the hypernuclear production.

Abstract:
We study the binding energies, radii, single-particle energies, spin-orbit potential and density profile for multi-strange hypernuclei in the range of light mass to superheavy region within the relativistic mean field (RMF) theory. The stability of multi-strange hypernuclei as a function of introduced hyperons ($\Lambda$ and $\Sigma$) is investigated. The neutron, lambda and sigma mean potentials are presented for light to superheavy hypernuclei. The inclusion of hyperons affects the nucleon, lambda and sigma spin-orbit potentials significantly. The bubble structure of nuclei and corresponding hypernuclei is studied. The nucleon and lambda halo structure are also investigated. A large class of bound multi-strange systems formed from the combination of nucleons and hyperons (n, p, $\Lambda$, $\Sigma^+$ and n, p, $\Lambda$, $\Sigma^-$) is suggested in the region of superheavy hypernuclei which might be stable against the strong decay. These multi-strange systems might be produced in heavy-ion reactions.

Abstract:
We study the properties of double-$\Lambda$ hypernuclei in the relativistic mean-field theory, which has been successfully used for the description of stable and unstable nuclei. With the meson-hyperon couplings determined by the experimental binding energies of single-$\Lambda$ hypernuclei, we present a self-consistent calculation of double-$\Lambda$ hypernuclei in the relativistic mean-field theory, and discuss the influence of hyperons on the nuclear core. The contribution of two mesons with dominant strange quark components (scalar $\sigma^*$ and vector $\phi$) to the $\Lambda\Lambda$ binding energy of double-$\Lambda$ hypernuclei is examined.

Abstract:
We shortly illustrate how the field-theoretic approach to critical phenomena takes place in the more complete Wilson theory of renormalization and qualitatively discuss its domain of validity. By the way, we suggest that the differential renormalization functions (like the beta-function) of the perturbative scalar theory in four dimensions should be Borel summable provided they are calculated within a minimal subtraction scheme.

Abstract:
Theoretical estimations of production cross sections of light $\Lambda$ and $\Sigma$ hypernuclei in $(e,e'K^{+})$ reactions at around CEBAF energies are given. Because of dominant spin-flip amplitudes and large momentum transfers, unnatural parity states and stretched states of hypernuclei are favorably excited. They are compared with quasifree hyperon productions.