We discuss methods used in mean-field theories to treat pairing correlations within the local density approximation. Pairing renormalization and regularization procedures are compared in spherical and deformed nuclei. Both prescriptions give fairly similar results, although the theoretical motivation, simplicity, and stability of the regularization procedure make it a method of choice for future applications.

Correlations among several nuclear matter properties are investigated in the Skyrme Hartree-Fock (SHF) and the relativistic mean field (RMF) models. The Skyrme parameters are related analytically to the isoscalar and isovector nuclear matter properties of the Hamiltonian density. Linear correlations are found among the isovector nuclear matter properties of the Hamiltonian density in both the SHF and the RMF models. We show analytically a singularity at the incompressibility $K_c=306$ MeV in correlations between the isovector nuclear matter properties and incompressibility with the SHF model, whereas there is no obvious singularity in those correlations with the RMF model. A linear correlation between the neutron skin thickness and the pressure of the neutron matter is given in terms of the ratio between the neutron and nuclear matter densities in the SHF model. We show that the neutron skin thickness gives crucial information about not only the neutron equation of state but also the isovector nuclear matter properties and the parametrization of the Skyrme interaction.

The ${}^{14}\mathrm{C}$(${}^{14}\mathrm{C}$, d) reaction at 22 MeV was used to study $T_z=2$ ${}^{26}\mathrm{Na}$. Charged particles were detected with a Si detector telescope at $0^{°}$, and γ transitions in coincidence were detected with an array of three Compton-suppressed “clover” detectors and seven Compton-suppressed single Ge crystals. The Deuteron-γ and $d\text{−}\gamma \text{−}\gamma$ coincidence data were analyzed to study the structure of ${}^{26}\mathrm{Na}$. New levels were found, and precise energies and γ-decay patterns were determined for many states previously observed in charge-exchange reactions. Candidates were observed for the $1^{+}$ state missing in β decay. Mixing ratios were determined for some γ transitions from angular distribution information. There is reasonable agreement with the model based on the universal $s\text{−}d$ shell (USD) interaction.

Back-to-back correlations of particle-antiparticle pairs are related to the in-medium mass-modification and squeezing of the quanta involved. They are predicted to appear when hot and dense hadronic matter is formed in high energy nucleus-nucleus collisions. The survival and magnitude of the back-to-back correlations (BBC) of boson-antiboson pairs generated by in-medium mass modifications are studied here in the case of a thermalized, finite-sized, spherically symmetric expanding medium. We show that the BBC signal indeed survives the finite-time emission, as well as the expansion and flow effects, with sufficient intensity to be observed at BNL Relativistic Heavy Ion Collider (RHIC).

In p-p collisions the average transverse momentum is known to be correlated with the multiplicity of produced particles. The correlation is shown to survive in a superposition model of nucleus-nucleus collisions. When properly parametrized, the correlation strength appears to be independent of the collision centrality—it is the same in p-p and central A-A collisions. However, the correlation is strongly suppressed by the centrality fluctuations.

The effects of mode-mode and isospin-isospin correlations on nonequilibrium chiral dynamics are investigated by using the method of the time-dependent variational approach with squeezed states as trial states. Our numerical simulations show that large domains of the disoriented chiral condensate (DCC) are formed because of the combined effect of the mode-mode and isospin-isospin correlations. Moreover, it is found that, when the mode-mode correlation is included, the DCC domain formation is accompanied by the amplification of the quantum fluctuation, which implies the squeezing of the state. However, neither the DCC domain formation nor the amplification of the quantum fluctuation is observed if only the isospin-isospin correlation is included. This suggests that the mode-mode coupling plays a key role in the DCC domain formation.

Recent studies of the $\Lambda (1520)$ resonance within chiral unitary theory with coupled channels find the resonance as a dynamically generated state from the interaction of the decuplet of baryons and the octet of mesons, essentially a quasibound state of $\pi {\Sigma }^{*}(1385)$ in this case, although the coupling of the $\Lambda (1520)$ to the $\overline{K}N$ and $\pi \Sigma$ makes this picture only approximate. The $\pi {\Sigma }^{*}(1385)$ decay channel of the $\Lambda (1520)$ is forbidden in free space for the nominal mass of the ${\Sigma }^{*}(1385)$, but the coupling of the π to ph components in the nuclear medium opens new decay channels of the $\Lambda (1520)$ in the nucleus and produces a much larger width. Together with medium modifications of the $\overline{K}N$ and $\pi \Sigma$ decay channels, the final width of the $\Lambda (1520)$ at nuclear matter density is more than five times bigger than the free one. We perform the calculations by dressing simultaneously the $\Lambda (1520)$ and the ${\Sigma }^{*}(1385)$ resonances, finding moderate changes in the mass but substantial ones in the width of both resonances.

The isotopic composition of lutetium has been measured with high precision using a thermal ionization mass spectrometer whose linearity was verified by measuring an isotopically certified reference material for potassium prepared by the National Institute of Standards and Technology (NIST 985). The abundance sensitivity of the mass spectrometer for the measured ion beams of ${\mathrm{Lu}}^{+}$ was examined to ensure the absence of tailing effects and interfering ion beams. The isotope fractionation of the measured ${}^{176}\mathrm{Lu}$/${}^{175}\mathrm{Lu}$ ratio was estimated with reference to the isotope fractionation of ytterbium (whose isotopes are in the same mass region as lutetium), which was recently measured in this laboratory using gravimetrically prepared solutions of the enriched isotopes ${}^{171}\mathrm{Yb}$ and ${}^{176}\mathrm{Yb}$. This is the first reported publication in which the measured isotope ratio of Lu has been corrected for isotope fractionation. An accurate determination of the abundance of ${}^{176}\mathrm{Lu}$ is required because of the importance of this isotope in cosmochronometry, cosmothermometry, and s-process branching studies. An accurate abundance of ${}^{176}\mathrm{Lu}$ is also required as it is the parent nuclide of the ${}^{176}\mathrm{Lu}$/${}^{176}\mathrm{Hf}$ geochronometer. The measured isotopic composition of Lu, corrected for isotope fractionation, is ${}^{176}\mathrm{Lu}$/${}^{175}\mathrm{Lu}$ = 0.026680 ± 0.000013, which gives isotope abundances for ${}^{175}\mathrm{Lu}$ of 97.4013 ± 0.0012% and of ${}^{176}\mathrm{Lu}$ of 2.5987 ± 0.0012%. The isotope abundances and relative atomic masses of the two isotopes give an atomic weight of 174.9668 ± 0.0001, which is in good agreement with the present Standard Atomic Weight $A_r$(Lu) = 174.967 ± 0.001, but with improved accuracy. An accurate assessment of the ${}^{176}\mathrm{Lu}$/${}^{175}\mathrm{Lu}$ ratio is important in order to calculate the Solar System abundances of ${}^{175}\mathrm{Lu}$ and ${}^{176}\mathrm{Lu}$ for astrophysical evaluations. The experimentally determined Solar System abundances for ${}^{175}\mathrm{Lu}$ and ${}^{176}\mathrm{Lu}$ of 0.0347918 ± 0.0000004 and 0.0009282 ± 0.0000004, respectively (as compared to silicon equals ${10}^6$ atoms), should now be used for these purposes. This determination of the isotopic composition of Lu also demonstrates that the presently accepted half-life of ${}^{176}\mathrm{Lu}$ needs to be reevaluated.

Half-lives $T_{1/2}$ of states in ${}^{95,97}\mathrm{Sr}$, ${}^{97,100,104}\mathrm{Zr}$, ${}^{106}\mathrm{Mo}$, and ${}^{148}\mathrm{Ce}$, which decay by delayed γ transitions, were determined by using a new time-gated triple γ coincidence method. Transition energy dependent effects such as time walks, time jitters, amplitude walks, and possible timing fluctuations of Ge detectors that contribute to the width of the time window were taken into consideration by comparing prompt and delayed cascades with similar transition energies. It is shown that the normalized triple γ coincidence counts of two prompt cascades with similar transition energies are similar. Also, it is observed that the real triple γ coincidence counts in the prompt cascades change systematically with the widths of the coincidence time window and the transition energies. Half-lives of states in ${}^{100,104}\mathrm{Zr}$ were measured for the first time. The half-lives of states in the delayed cascades were determined by using the prompt cascades with transition energies similar to those in delayed cascades. The half-life of the 2${}^{+}$ state in ${}^{104}\mathrm{Zr}$ is measured to be 2.0(3) ns. The B(E2$;2^{+}\to 0^{+}$)($e^2{b}^2$) value and quadrupole deformation ${\beta }_2$ are 0.40(6) ($e^2{b}^2$) and 0.47(7), respectively. ${}^{104}\mathrm{Zr}$ has the most deformed 2${}^{+}$ state among medium and heavy even-even nuclei, except for ${}^{102}\mathrm{Sr}$. This method is only approximately valid, but it is believed to be generally within 10% of the true value.

The Hartree-Fock-Bogoliubov (HFB) equation for deformed nuclei in a simplified model is solved in coordinate space with correct asymptotic boundary conditions, in order to study the pair correlation in nuclei close to the neutron drip line. The eigenphase formalism is applied, when the upper components of HFB radial wave functions are continuum wave functions. Calculated occupation probabilities of various Nilsson orbits in the HFB ground state vary smoothly from the region of the upper components being bound wave functions to that of those being continuum wave functions. It is shown that weakly-bound or resonance-like ${\Omega }^{\pi }=1/2^{+}$ Nilsson orbits contribute little to the occupation probability of the HFB ground state, while the contribution by the orbits with a large value of Ω, of which the smallest possible orbital-angular-momentum is neither 0 nor 1, may be approximately estimated using the BCS formula.

Results from the study of the β decays of ${}^{40,42}\mathrm{S}$ and ${}^{43}\mathrm{Cl}$, produced in the fragmentation of a 70-MeV/nucleon ${}^{48}\mathrm{Ca}$ beam, are presented. The half-lives for ${}^{42}\mathrm{S}$ and ${}^{43}\mathrm{Cl}$ have been measured to be $1.03\pm 0.03$ s and $3.13\pm 0.09$ s, respectively. On the basis of γ-ray singles and $\gamma \gamma$ coincidence data, decay schemes for each of these decays have been established. Only subtle changes in low-energy nuclear structure, including switching of the order of the $2^{-}$ and $3^{-}$ states in the odd-odd Cl isotopes, were observed when passing the midpoint of the $\nu f_{7/2}$ subshell. These results agree well with previous shell-model calculations using restricted model spaces suggesting that deformation and shell-breaking effects in the midshell region are small. However, excitations across the $N=20$ shell gap are important to explain the low-lying positive parity states.

High resolution spectra from fast proton radiative capture in ${}^{208}\mathrm{Pb}$ are presented for three energies of the incident protons: 14.8, 15.7, and 16.9 MeV. The collected spectra were analyzed with emphasis on the region of capture to unbound states in order to search for possible structure and to study the competition between two basically different phenomena: the statistical process versus the fluctuation effects in radiative capture to unbound final states. In the energy region of incoming protons considered in our experiment, the statistical processes modeled with a Hauser-Feshbach calculation dominate. The spectra of primary γ rays, coincident with the low energy one from the decay of the $f_{7/2}$ single-particle state, show a prominent structure which is predominantly of $g_{9/2}$ character. The calculations of continuum spectra based on the extended direct-semidirect model and the Hauser-Feshbach statistical approach successfully reproduce the experimental data.

An intense source of ${}^{37}\mathrm{Ar}$ was produced by the $(n,\alpha )$ reaction on ${}^{40}\mathrm{Ca}$ by irradiating 330 kg of calcium oxide in the fast neutron breeder reactor at Zarechny, Russia. The ${}^{37}\mathrm{Ar}$ was released from the solid target by dissolution in acid, collected from this solution, purified, sealed into a small source, and brought to the Baksan Neutrino Observatory where it was used to irradiate 13 tonnes of gallium metal in the Russian-American gallium solar neutrino experiment SAGE. Ten exposures of the gallium to the source, whose initial strength was $409\pm 2$kCi, were carried out during the period April to September 2004. The ${}^{71}\mathrm{Ge}$ produced by the reaction ${}^{71}\mathrm{Ga}({\nu }_e,e^{-}){}^{71}\mathrm{Ge}$ was extracted, purified, and counted. The measured production rate was $11.0_{-0.9}^{+1.0}\text{(stat)}\pm 0.6\text{(syst)}$ atoms of ${}^{71}\mathrm{Ge}$/d, which is $0.{79}_{-0.10}^{+0.09}$ of the theoretically calculated production rate. When all neutrino source experiments with gallium are considered together, there is an indication the theoretical cross section has been overestimated.

The squares of neutron asymptotic normalization coefficient (ANC) for ${}^{27}\mathrm{Mg}$ → ${}^{26}\mathrm{Mg}$ + n are extracted to be 44.0 ± 5.3, 3.40 ± 0.32 and 0.90 ± 0.08 fm${}^{-1}$ from the angular distributions of the ${}^{26}\mathrm{Mg}$($d,p$)${}^{27}\mathrm{Mg}$ reaction leading to the ground, first, and second excited states of ${}^{27}\mathrm{Mg}$, respectively, based on distorted wave Born approximation (DWBA) analysis. According to charge symmetry of mirror nuclei, the square of proton ANC for ${}^{27}\mathrm{P}$ → ${}^{26}\mathrm{Si}$ + p is determined to be 1840 ± 240 fm${}^{-1}$ and then utilized to calculate the astrophysical S-factor and rate for the direct capture into the ${}^{27}\mathrm{P}$ ground state. In addition, the proton widths for the first and second excited states in ${}^{27}\mathrm{P}$ are derived to be 1.30 ± 0.12 × 10${}^{-8}$ and 1.79 ± 0.15 × 10${}^{-5}$ MeV from the neutron ANCs and used to compute the contribution of the resonant captures. Furthermore, we have also presented the total astrophysical ${}^{26}\mathrm{Si}$($p,\gamma$)${}^{27}\mathrm{P}$ reaction rate.

A three-fluid hydrodynamic model for simulating relativistic heavy-ion collisions is introduced. Along with two baryon-rich fluids, the new model considers the time-delayed evolution of a third, baryon-free (i.e., with zero net baryonic charge) fluid of newly produced particles. Its evolution is delayed because of a formation time τ, during which the baryon-free fluid neither thermalizes nor interacts with the baryon-rich fluids. After the formation it starts to interact with the baryon-rich fluids and quickly gets thermalized. Within this model with pure hadronic equation of state, a systematic analysis of various observables at incident energies between few and about 160A GeV has been done as well as a comparison with results of transport models. We have succeeded in reasonably reproducing a great body of experimental data in the incident energy range of $E_{\mathrm{lab}}\simeq$ (1–160)A GeV. The list includes proton and pion rapidity distributions, proton transverse-mass spectra, rapidity distributions of Λ and $\overline{\Lambda }$ hyperons, elliptic flow of protons and pions (with the exception of proton $v_2$ at 40A GeV), multiplicities of pions, positive kaons, ϕ mesons, hyperons, and antihyperons, including multistrange particles. This agreement is achieved on the expense of substantial enhancement of the interflow friction as compared to that estimated proceeding from hadronic free cross sections. However, we have also found out certain problems. The calculated yield of $K^{-}$ is approximately higher than that in the experiment by a factor of 1.5. We have also failed to describe directed transverse flow of protons and pion at $E_{\mathrm{lab}}\ge 40A$ GeV. This failure apparently indicates that the used EOS is too hard and thereby leaves room for a phase transition.

We present a detailed study of chemical freeze-out in p-p, C-C, Si-Si, and Pb-Pb collisions at beam momenta of 158A GeV as well as Pb-Pb collisions at beam momenta of 20A, 30A, 40A, and 80A GeV. By analyzing hadronic multiplicities within the statistical hadronization model, we studied the parameters of the source as a function of the number of participating nucleons and the beam energy. We observe a nice smooth behavior of temperature, baryon chemical potential, and strangeness under-saturation parameter as a function of energy and nucleus size. Interpolating formulas are provided which allow us to predict the chemical freeze-out parameters in central collisions at center-of-mass energies $\sqrt{s}{}_{\mathit{NN}}\gtrsim 4.5$ GeV and for any colliding ions. Specific discrepancies between data and the model emerge in particle ratios in Pb-Pb collisions at beam energies between 20A and 40A GeV which cannot be accounted for in the considered model schemes.

The recent high-precision data for the reaction $\gamma p\to p{\eta }^{\prime }$ at photon energies in the range 1.5–2.3 GeV obtained by the CLAS Collaboration at the Jefferson Laboratory have been analyzed within an extended version of the photoproduction model developed previously by the authors based on a relativistic meson-exchange model of hadronic interactions [Phys. Rev. C 69, 065212 (2004)]. The ${\eta }^{\prime }$ photoproduction can be described quite well over the entire energy range of available data by considering $S_{11},P_{11},P_{13}$, and $D_{13}$ resonances, in addition to the t-channel mesonic currents. The observed angular distribution is due to the interference between the t-channel and the nucleon s- and u-channel resonance contributions. The $j=3/2$ resonances are required to reproduce some of the details of the measured angular distribution. For the resonances considered, our analysis yields mass values compatible with those advocated by the Particle Data Group. We emphasize, however, that cross-section data alone are unable to pin down the resonance parameters and it is shown that the beam and/or target asymmetries impose more stringent constraints on these parameter values. It is found that the nucleonic current is relatively small and that the $\mathit{NN}{\eta }^{\prime }$ coupling constant is not expected to be much larger than 2.

The $E2/M1$ ratio (EMR) of the Δ(1232) is extracted from the world data in pion photoproduction by means of an effective Lagrangian approach (ELA). This quantity has been derived within a crossing symmetric, gauge invariant, and chiral symmetric Lagrangian model which also contains a consistent modern treatment of the Δ(1232) resonance. The bare $s$-channel Δ(1232) contribution is well isolated and final state interactions (FSI) are effectively taken into account fulfilling Watson's theorem. The obtained EMR value, EMR $=(-1.30\pm 0.52)$%, is in good agreement with the latest lattice QCD calculations [Phys. Rev. Lett. 94, 021601 (2005)] and disagrees with results of current quark model calculations.

The polarization of ${}^{34}\mathrm{Al}$ fragments, produced by single neutron pickup from a ${}^9\mathrm{Be}$ target by a ${}^{36}\mathrm{S}$ projectile at 77.5 MeV/nucleon, have been observed at GANIL via the detection of resonantly destroyed β-asymmetry. The reaction-induced polarization is deduced using a tentative spin/parity assignment for the ${}^{34}\mathrm{Al}$ ground state. A positive polarization was measured near the peak of the ${}^{34}\mathrm{Al}$ yield curve. A kinematical model based on the spectator-participant model for projectile fragmentation reactions has been extended in order to take into account the features of pickup reactions, i.e., the picked-up nucleon having an average momentum equal to the Fermi momentum and aligned along the incident beam direction. The trend-line in the observed spin-orientation is very well reproduced by this model.