We calculate the contribution to the nuclear energy density functional which arises from iterated pion-photon exchange between nucleons. In heavy nuclei, this novel charge-symmetry breaking interaction leads to an additional binding of each proton by about $0.2\text{MeV}$. Compared to that the analogous effect from irreducible pion-photon exchange is negligibly small. As a possible mechanism to resolve the Nolen-Schiffer anomaly we propose the iteration of one-photon exchange with an attractive short-range $NN$-interaction. The corresponding energy per proton reads $\overline{E}\left[{\rho }_p\right]=(2\alpha ∕15{\pi }^2)({\pi }^2-3+6\ln 2){\mathcal{A}}_{pp}{k}_p^2$ with ${\rho }_p=k_p^3∕3{\pi }^2$ the proton density and ${\mathcal{A}}_{pp}\approx 2\text{fm}$ an effective (in-medium) scattering length. Hints for such a value of ${\mathcal{A}}_{pp}$ come from phenomenological Skyrme forces and from the neutron matter equation of state.

The Kerman-Klein-Dönau-Frauendorf (KKDF) model is a linearized version of the nonlinear Kerman-Klein (equations of motion) formulation of the nuclear many-body problem. In practice, it is a generalization of the standard core-particle coupling model that, like the latter, provides a description of the spectroscopy of odd nuclei in terms of the corresponding properties of neighboring even nuclei and of single-particle properties, which are the input parameters of the model. A divers sample of recent applications attests to the usefulness of the model. In this paper, we first present a concise general review of the fundamental equations and properties of the KKDF model. We then derive a corresponding formalism for odd-odd nuclei with proton-neutron number $(Z,N)$ that relates their properties to those of the four neighboring even-even nuclei $(Z+1,N+1)$, $(Z-1,N+1)$, $(Z+1,N-1)$, and $(Z-1,N-1)$, all of which are required if one is to include both multipole and pairing forces. We treat these equations in two ways. In the first, we make essential use of the solutions of the neighboring odd nucleus problem, as obtained by the KKDF method. In the second, we relate the properties of the odd-odd nucleus directly to those of the even-even nuclei. For both choices, we derive equations of motion, normalization conditions, and an expression for transition amplitudes. We also resolve the problem of choosing the subspace of physical solutions that arises in an equation of motion approach that includes pairing interactions.

The PHENIX experiment at the Relativistic Heavy Ion Collider has measured charged hadron yields at midrapidity over a wide range of transverse momenta $\left(0.5<p_T<10\text{GeV}∕c\right)$ in $\text{Au}+\text{Au}$ collisions at $\sqrt{s_{NN}}=200\text{GeV}$. The data are compared to ${\pi }^0$ measurements from the same experiment. For both charged hadrons and neutral pions, the yields per nucleon-nucleon collision are significantly suppressed in central compared to peripheral and nucleon-nucleon collisions. The suppression sets in gradually and increases with increasing centrality of the collisions. Above $4–5\text{GeV}∕c$ in $p_T$, a constant and almost identical suppression of charged hadrons and ${\pi }^0$’s is observed. The $p_T$ spectra are compared to published spectra from $\text{Au}+\text{Au}$ at $\sqrt{s_{NN}}=130$ in terms of $x_T$ scaling. Central and peripheral ${\pi }^0$ as well as peripheral charged spectra exhibit the same $x_T$ scaling as observed in $p+p$ data.

We propose that the backbending phenomenon can be explained as a result of the disappearance of collective $\gamma$-vibrational mode in the rotating frame. Using a $\text{cranking}+\text{random}$ phase approximation approach for the modified Nilsson $\text{potential}+\text{monopole}$ pairing forces, we show that this mechanism is responsible for the backbending in ${}^{156}\mathrm{Dy}$ and ${}^{158}\mathrm{Er}$, and obtain a good agreement between theoretical and experimental results.

The neutron capture cross section of the unstable $s$-process branching nucleus ${}^{185}\mathrm{W}$ has been derived from experimental data of the inverse ${}^{186}\mathrm{W}\left(\gamma ,n\right){}^{185}\mathrm{W}$ photodisintegration taken with monochromatic photon beams from laser Compton scattering. The result of $\sigma =553\pm 60\text{mb}$ at $kT=30\text{keV}$ leads to a relatively high effective neutron density in the classical $s$ process of $N_n=4.7\times {10}^8{\text{cm}}^{-3}$. A realistic model for the $s$ process in thermally pulsing asymptotic giant branch stars overestimates the abundance of ${}^{186}\mathrm{Os}$ significantly because of the relatively small neutron capture cross section of ${}^{185}\mathrm{W}$.

Excited levels in ${}^{69}\mathrm{Se}$ have been studied using the ${}^{40}\mathrm{Ca}\left({}^{32}\text{S},2pn\right){}^{69}\mathrm{Se}$ reaction at 95- and $105\text{−}\text{MeV}$ beam energy. $\gamma$ rays have been detected with the EUROBALL spectrometer operated in conjunction with the neutron wall and the charged-particle detector array EUCLIDES. New level sequences with positive and negative parities have been identified from $n\text{−}\gamma \gamma$ and $n\text{−}\gamma \gamma \gamma$ coincidences. Spins have been assigned to many of the levels on the basis of angular distribution and directional correlation measurements. Excitation energies of the positive-parity yrast band and the branching ratios of its decay are compared with the predictions of the rigid triaxial rotor plus particle model.

Lifetime measurements in ${}^{154}\mathrm{Gd}$ were performed by means of the recoil distance Doppler-shift method. Excited states of ${}^{154}\mathrm{Gd}$ were populated via Coulomb excitation with a ${}^{32}\mathrm{S}$ beam at $110\text{MeV}$ delivered by the FN tandem accelerator of the University of Cologne. The determined transition probabilities as well as the low-spin level scheme of ${}^{154}\mathrm{Gd}$ demonstrate a good agreement with the predictions of the critical point symmetry X(5). Comparison of specific experimental observables for the $N=90$ rare earth isotones with the calculations of the X(5) model clearly show that ${}^{154}\mathrm{Gd}$ is one of the good examples of the realization of the X(5) dynamical symmetry. In addition, the experimental data are compared to fits in the framework of the IBA and the general collective model.

The effective interaction GXPF1 for shell-model calculations in the full $pf$ shell is tested in detail from various viewpoints such as binding energies, electromagnetic moments and transitions, and excitation spectra. The semimagic structure is successfully described for $N$ or $Z=28$ nuclei, ${}^{53}\mathrm{Mn}$, ${}^{54}\mathrm{Fe}$, ${}^{55}\mathrm{Co}$, and ${}^{56,57,58,59}\mathrm{Ni}$, suggesting the existence of significant core excitations in low-lying nonyrast states as well as in high spin yrast states. The results of $N=Z$ odd-odd nuclei, ${}^{54}\mathrm{Co}$ and ${}^{58}\mathrm{Cu}$, also confirm the reliability of GXPF1 interaction in the isospin dependent properties. Studies of shape coexistence suggest an advantage of Monte Carlo shell model over conventional calculations in cases where full-space calculations still remain too large to be practical.

A method is proposed for constructing fully antisymmetric $A$-body hyperspherical harmonics with well-defined orthogonal symmetry. These hyperspherical harmonics are obtained by diagonalizing the matrix of the second Casimir operator for the orthogonal group, calculated in the hyperspherical basis constructed with the help of the Slater determinants of the oscillator translation-invariant shell model. The introduction of orthogonal symmetry has computational benefits and also provides a physical insight into collective modes of motion of atomic nuclei. Numerical applications have been performed for ${}^{3–5,7}\mathrm{H}$ and ${}^{4–10}\mathrm{He}$.

The mass and isotope dependence of limiting temperatures for hot nuclei are investigated. The predicted mass dependence of limiting temperatures is in good agreement with data derived from the caloric curve data. The predicted isotope distribution of limiting temperatures appears to be a parabolic shape and its centroid is not located at the isotope on the $\beta$-stability line $\left(T=0\right)$ but at neutron-rich side. Our study shows that the mass and isotope dependence of limiting temperatures depend on the interaction and the form of surface tension and its isospin dependence sensitively.

In-plane and out-of-plane correlations of light charged particles and neutrons emitted in the ${}^{35}\mathrm{Cl}\left(260\text{MeV}\right)+{}^{24}\mathrm{Mg}$ complete fusion reaction have been measured to investigate deformation and angular momentum effects upon the decay of ${}^{59}\mathrm{Cu}$ compound nucleus. An array of $21{\text{BaF}}_2$ crystals has been used to identify the light charged particles $\left(Z⩽4\right)$ and neutrons emitted in coincidence with heavy fragments $\left(Z⩾5\right)$ detected in six ionization chamber telescopes. Coincident energy spectra and angular distributions of neutrons, protons, and $\alpha$-particles have been described by the statistical-model calculations with nuclear level densities tuned to take account of deformation effects in the emitters. This spin-dependent approach suggests the onset of large nuclear deformation in ${}^{59}\mathrm{Cu}$ at high spin. This conclusion is consistent with the recent observation of a superdeformed band in the ${}^{59}\mathrm{Cu}$ nucleus.

The centrality dependence of transverse momentum distributions and yields for ${\pi }^{\pm },K^{\pm },p$, and $\overline{p}$ in $\text{Au}+\text{Au}$ collisions at $\sqrt{s_{NN}}=200\text{GeV}$ at midrapidity are measured by the PHENIX experiment at the Relativistic Heavy Ion Collider. We observe a clear particle mass dependence of the shapes of transverse momentum spectra in central collisions below $\sim 2\text{GeV}∕c$ in $p_T$. Both mean transverse momenta and particle yields per participant pair increase from peripheral to midcentral and saturate at the most central collisions for all particle species. We also measure particle ratios of ${\pi }^{-}∕{\pi }^{+}$, $K^{-}∕K^{+}$, $\overline{p}∕p$, $K∕\pi$, $p∕\pi$, and $\overline{p}∕\pi$ as a function of $p_T$ and collision centrality. The ratios of equal mass particle yields are independent of $p_T$ and centrality within the experimental uncertainties. In central collisions at intermediate transverse momenta $\sim 1.5–4.5\text{GeV}∕c$, proton and antiproton yields constitute a significant fraction of the charged hadron production and show a scaling behavior different from that of pions.

The electromagnetic and axial form factors of the nucleon and its lowest positive parity excitations, the $\Delta \left(1232\right)$ and the $N\left(1440\right)$, are calculated with constituent-quark models that are specified by simple algebraic representations of the mass-operator eigenstates. Poincaré covariant current operators are generated by the dynamics from single-quark currents that are covariant under a kinematic subgroup. The dependence of the calculated form factors on the choice of kinematics and on the gross features of the wave functions is illustrated for instant-form, point-form, and front-form kinematics. A simple algebraic form of the orbital ground state wave function, which depends on two parameters, allows a fair description of all the form factors over the empirically accessible range, although with widely different choices of the parameters, which determine the range and shape of the orbital wave function. The neutron electric form factor requires additional features, for instance the presence of mixed-symmetry $S$-state component with $1–2\%$ probability in the ground state wave function. Instant- and front-form kinematics demand a spatially extended wave function, whereas in point-form kinematics the form factors may be described with a quite compact wave function.

We have recently performed a relativistic $O\left(q^4\right)$ chiral expansion of the two-pion exchange $NN$ potential, and here we explore its configuration space content. Interactions are determined by three families of diagrams, two of which involve just $g_A$ and $f_{\pi }$, whereas the third one depends on empirical coefficients fixed by subthreshold $\pi N$ data. In this sense, the calculation has no adjusted parameters and gives rise to predictions, which are tested against phenomenological potentials. The dynamical structure of the eight leading nonrelativistic components of the interaction is investigated and, in most cases, found to be clearly dominated by a well defined class of diagrams. In particular, the central isovector and spin-orbit, spin-spin, and tensor isoscalar terms are almost completely fixed by just $g_A$ and $f_{\pi }$. The convergence of the chiral series in powers of the ratio (pion mass∕nucleon mass) is studied as a function of the internucleon distance and, for $r>1\text{fm}$, found to be adequate for most components of the potential. An important exception is the dominant central isoscalar term, where the convergence is evident only for $r>2.5\text{fm}.$ Finally, we compare the spatial behavior of the functions that enter the relativistic and heavy baryon formulations of the interaction and find that, in the region of physical interest, they differ by about $5\%$.

Excited states in ${}^{210}\mathrm{Ra}$ and ${}^{209}\mathrm{Ra}$ were populated using the ${}^{184}\mathrm{W}\left({}^{30}\mathrm{Si},xn\right)$ reaction at $148\text{MeV}$ beam energy. Fusion evaporation recoils were selected using the gas-filled spectrometer, SASSYER. Prompt $\gamma$ rays were detected using Compton-suppressed Ge detectors from the YRAST Ball array surrounding the target. Delayed $\gamma$ rays, following isomeric decays, were detected at the focal plane of SASSYER with a smaller array of Ge detectors. The decay energy and lifetime for the $8^{+}{\left(\pi h_{9∕2}\right)}^n$ isomer of ${}^{210}\mathrm{Ra}$ were determined; values for the yrast $B\left(E2;8^{+}\to 6^{+}\right)$ in ${}^{210}\mathrm{Ra}$ and neighboring nuclei are interpreted within the seniority scheme. This isomer was also used to select $\gamma$-rays deexciting levels above the isomeric state in ${}^{210}\mathrm{Ra}$. In addition, transitions in ${}^{209}\mathrm{Ra}$ were identified for the first time. Two high-spin isomers are suggested to exist in this isotope.

The spherical Hartree-Fock approximation is applied to the ab initio no-core shell model, with a realistic effective nucleon-nucleon interaction in order to investigate the range of its utility. Hartree-Fock results for binding energies, one-body density distributions, and occupation probabilities are compared with results from exact diagonalization in similar model spaces. We show that this mean-field approximation, especially with second-order corrections, is able to provide some useful approximations for ${}^4\mathrm{He}$ and ${}^{16}\mathrm{O}$. We also explore the physical insights provided by the Hartree-Fock results for single-particle properties such as spin-orbit splittings. We find single-particle state ordering consistent with the phenomenological shell model.

We use chiral perturbation theory to compute the effective nucleon propagator in an expansion about low density in the chiral limit. We neglect four-nucleon interactions and focus on pion exchange. Evaluating the nucleon self-energy on its mass shell to leading order, we show that the effective nucleon mass increases by a small amount. We discuss the relevance of our results to the structure of compact stars.

A systematic study of correlations in the chart of nuclear masses calculated using the finite range droplet model of Möller et al. is presented. It is shown that the differences between the calculated and measured masses have a well defined oscillatory component as function of the proton and neutron numbers, which can be removed with an appropriate fit, concentrating the error distribution on a single peak around zero. The presence of this regular residual correlations suggests that the Strutinsky method of including microscopic fluctuations in nuclear masses could be improved.

It is shown that due to Coulomb interaction additional fusion reactions can happen in extra channels in solid state environment (e.g., in crystalline Pd) partly filled with deuterons. In the process that may be called solid state internal conversion, the total reaction energy is taken off by an accelerated charged particle (e.g., electron) and by the fused nucleus. The phenomenon is demonstrated on the $p+d\to {}^3\text{He}$ reaction. Formula for the nuclear reaction constant of the processes is presented. Its value for the $p+d+\left(e\right)\to {}^3\text{He}+\left(e\right)$ and the $p+d+\left(d\right)\to {}^3\text{He}+\left(d\right)$ reactions is calculated.

The $3N$ forces due to $\pi \text{−}\rho ,\pi \text{−}\sigma$, and $\pi \text{−}\omega$ exchanges following from the nucleon Born diagrams and diagrams with an intermediate $N^{*}\left(1440\right)$ are reanalyzed. The cancellation between $\pi \text{−}\sigma$ and $\pi \text{−}\omega$ forces is rather sensitive to the values of the coupling constants and to the form of the $\pi NN$ vertex. Experimental uncertainties in the parameters of the Tucson-Melbourne $\pi \text{−}\pi$ potential are assessed. They lead to uncertainties in theoretical predictions of the triton binding energy of about $\pm 0.4\text{MeV}$. The low-energy limit of $\pi \text{−}\sigma$ and $\pi \text{−}\omega$ potentials is performed. It defines the coupling constants of effective contact $\pi NNNN$ vertices, which are compared with the corresponding contact vertices of chiral perturbation theory.