The impurity effect of hyperon on atomic nuclei has received a renewed interest in nuclear physics since the first experimental observation of appreciable reduction of $E2$ transition strength in low-lying states of hypernucleus $^{7}_Lambda$Li. Many
more data on low-lying states of $Lambda$ hypernuclei will be measured soon for $sd$-shell nuclei, providing good opportunities to study the $Lambda$ impurity effect on nuclear low-energy excitations. We carry out a quantitative analysis of $Lambda$ hyperon impurity effect on the low-lying states of $sd$-shell nuclei at the beyond-mean-field level based on a relativistic point-coupling energy density functional (EDF), considering that the $Lambda$ hyperon is injected into the lowest positive-parity ($Lambda_s$) and negative-parity ($Lambda_p$) states. We adopt a triaxially deformed relativistic mean-field (RMF) approach for hypernuclei and calculate the $Lambda$ binding energies of hypernuclei as well as the potential energy surfaces (PESs) in $(beta, gamma)$ deformation plane. We also calculate the PESs for the $Lambda$ hypernuclei with good quantum numbers using a microscopic particle rotor model (PRM) with the same relativistic EDF. The triaxially deformed RMF approach is further applied in order to determine the parameters of a five-dimensional collective Hamiltonian (5DCH) for the collective excitations of triaxially deformed core nuclei. Taking $^{25,27}_{Lambda}$Mg and $^{31}_{Lambda}$Si as examples, we analyse the impurity effects of $Lambda_s$ and $Lambda_p$ on the low-lying states of the core nuclei...
We derive new constraints on the mass of the Milky Ways dark matter halo, based on a set of halo stars from SDSS as kinematic tracers. Our sample comprises 2401 rigorously selected Blue Horizontal-Branch (BHB) halo stars drawn from SDSS DR-6. To inte
rpret these distributions, we compare them to matched mock observations drawn from two different cosmological galaxy formation simulations designed to resemble the Milky Way, which we presume to have an appropriate orbital distribution of halo stars. We then determine which value of $rm V_{cir}(r)$ brings the observed distribution into agreement with the corresponding distributions from the simulations. This procedure results in an estimate of the Milky Ways circular velocity curve to $sim 60$ kpc, which is found to be slightly falling from the adopted value of $rm 220 km s^{-1}$ at the Suns location, and implies M$(<60 rm kpc) = 4.0pm 0.7times 10^{11}$M$_odot$. The radial dependence of $rm V_{cir}(r)$, derived in statistically independent bins, is found to be consistent with the expectations from an NFW dark matter halo with the established stellar mass components at its center. If we assume an NFW halo profile of characteristic concentration holds, we can use the observations to estimate the virial mass of the Milky Ways dark matter halo, M$_{rm vir}=1.0^{+0.3}_{-0.2} times 10^{12}$M$_odot$, which is lower than many previous estimates. This estimate implies that nearly 40% of the baryons within the virial radius of the Milky Ways dark matter halo reside in the stellar components of our Galaxy. A value for M$_{rm vir}$ of only $sim 1times10^{12}$M$_odot$ also (re-)opens the question of whether all of the Milky Ways satellite galaxies are on bound orbits.
