The complex scaling method (CSM) is a useful similarity transformation of the Schrodinger equation, in which bound-state spectra are not changed but continuum spectra are separated into resonant and non-resonant continuum ones. Because the asymptotic
wave functions of the separated resonant states are regularized by the CSM, many-body resonances can be obtained by solving an eigenvalue problem with the $L^2$ basis functions. Applying this method to a system consisting of a core and valence nucleons, we investigate many-body resonant states in weakly bound nuclei very far from the stability lines. Non-resonant continuum states are also obtained with the discretized eigenvalues on the rotated branch cuts. Using these complex eigenvalues and eigenstates in CSM, we construct the extended completeness relations and Greens functions to calculate strength functions and breakup cross sections. Various kinds of theoretical calculations and comparisons with experimental data are presented.
We perform a detailed comparison of results of the Gamow Shell Model (GSM) and the Gaussian Expansion Method (GEM) supplemented by the complex scaling (CS) method for the same translationally-invariant cluster-orbital shell model (COSM) Hamiltonian.
As a benchmark test, we calculate the ground state $0^{+}$ and the first excited state $2^{+}$ of mirror nuclei $^{6}$He and $^{6}$Be in the model space consisting of two valence nucleons in $p$-shell outside of a $^{4}$He core. We find a good overall agreement of results obtained in these two different approaches, also for many-body resonances.
We provide a method to correct the observed azimuthal anisotropy in heavy-ion collisions for the event plane resolution in a wide centrality bin. This new procedure is especially useful for rare particles, such as Omega baryons and J/psi mesons, whic
h are difficult to measure in small intervals of centrality. Based on a Monte Carlo calculation with simulated v_2 and multiplicity, we show that some of the commonly used methods have a bias of up to 15%.
We report selected results from STAR collaboration at RHIC, focusing on jet-hadron and jet-like correlations, quarkonium suppression and collectivity, di-electron spectrum in both p+p and Au+Au, and higher moments of net-protons as well as azimuthal anisotropy from RHIC Beam Energy Scan program.
Predictions of elliptic flow ($v_2$) and nuclear modification factor ($R_{AA}$) are provided as a function of centrality in U + U collisions at $sqrt{s_{_{NN}}}$ = 200 GeV. Since the $^{238}$U nucleus is naturally deformed, one could adjust the prope
rties of the fireball, density and duration of the hot and dense system, for example, in high energy nuclear collisions by carefully selecting the colliding geometry. Within our Monte Carlo Glauber based approach, the $v_2$ with respect to the reaction plane $v_2^{RP}$ in U + U collisions is consistent with that in Au + Au collisions, while the $v_2$ with respect to the participant plane $v_2^{PP}$ increases $sim$30-60% at top 10% centrality which is attributed to the larger participant eccentricity at most central U + U collisions. The suppression of $R_{AA}$ increases and reaches $sim$0.1 at most central U + U collisions that is by a factor of 2 more suppression compared to the central Au + Au collisions due to large size and deformation of Uranium nucleus.
One of the most striking results is the large elliptic flow ($v_2$) at RHIC. Detailed mass and transverse momentum dependence of elliptic flow are well described by ideal hydrodynamic calculations for $p_{mathrm{T}} < $ 1 GeV/c, and by parton coalesc
ence/recombination picture for $p_{mathrm{T}} = 2 - 6$ GeV/c. The systematic error on $v_2$ is dominated by so-called non-flow effects, which is the correlation not originated from reaction plane. It is crucial to understand and reduce the systematic error from non-flow effects in order to understand the underlying collision dynamics. In this paper, we present the centrality dependence of $v_2$ with respect to the first harmonic event plane at ZDC-SMD ($v_2${ZDC-SMD}) in Au + Au collisions at $sqrt{s_{NN}}$ = 200 GeV. Large rapidity gap ($|Deltaeta| > 6$) between midrapidity and the ZDC could enable us to minimize possible non-flow contributions. We compare the results of $v_2${ZDC-SMD} with $v_2${BBC}, which is measured by event plane determined at $|eta| = 3.1 - 3.9$. Possible non-flow contributions in those results will be discussed.
