The generator coordinate method (GCM) is applied to the single-$j$ shell model with pure quadrupole-quadrupole interaction. The results of the GCM for the $j=15/2\mathrm{}$ and 19/2 shells are compared with the exact solutions in the shell model. As for the four-hole (or four-particle) systems, the GCM reproduces the shell model results exactly. The half-filled systems are found to exhibit the triaxial rigid rotorlike property against the expectation based on the mean-field theory. The spin-projected potential energy surface offers much more intuitive insight into the shell model spectra than the unprojected one.

The problem of the motion of the center of mass in nuclear many-body systems is revisited. In the first part of the work, the counterterms needed to fulfill the translational and Galilean invariances are solved through the exact albeit perturbative expansion underlying the random-phase approximation. Collective variables are introduced in the second part of the work. The inherent problems of overcounting and infrared divergencies are solved by means of the BRST invariance. Consistency between the two procedures is achieved by use of the same perturbative expansion. The formalism is applied to the calculation of matrix elements of some of the electroweak operators which are active in the $\left({\mu }^{-}{,e}^{-}\right)$ conversion process, to show the influence of center of mass effects upon transitions induced by vector terms of the weak current.

We derive the analog of the QCD low-energy theorems for the scalar and pseudoscalar gluonic correlators in nuclear matter. We find that the scalar correlations are depleted while the pseudoscalar correlations are enhanced to leading order in the nuclear matter density. We briefly discuss the consequences of these findings on the QCD spectrum.

In an effort to resolve the theoretical difficulties in explaining the total and partial decay rates and the ratio ${\Gamma }_n/{\Gamma }_p,$ a four-baryon point $\Lambda \overrightarrow{N}\mathrm{NN}$ interaction is suggested as a new model for the short-range part of the nonmesonic weak decay of hypernuclei in addition to the traditional one-pion-exchange model for the long-range part. It is shown that with any value of the axial vector coupling constant $g_A$ in the range $-0.1<~g_A<~0.3$ for the isoscalar weak current of nucleons, i.e., $p\left(n\right)\mathrm{}\to p\left(n\right)\mathrm{}$ transitions, the partial and the total nonmesonic decay rates ${\Gamma }_n,$ ${\Gamma }_p,$ and ${\Gamma }_{\mathrm{nm}}={\Gamma }_n+{\Gamma }_p$ and the ratios ${\Gamma }_n/{\Gamma }_p$ of ${}_{\Lambda }^4\mathrm{He},$ ${}_{\Lambda }^5\mathrm{He},$ and ${}_{\Lambda }^{12}\mathrm{C}$ are excellently fitted in the experimental data.

We present measurements of differential cross sections and the analyzing powers $A_y,$ ${\mathrm{iT}}_{11},$ $T_{20},$ $T_{21},$ and $T_{22}$ at $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=431.3\mathrm{}\mathrm{keV}.$ In addition, an excitation function of ${\mathrm{iT}}_{11}({\theta }_{\mathrm{c}.\mathrm{m}.\mathrm{}}=87.8\mathrm{}°)$ for $431.3<~E_{\mathrm{c}.\mathrm{m}.\mathrm{}}<~2000\mathrm{keV}$ is presented. These data are compared to calculations employing realistic nucleon-nucleon interactions, both with and without three-nucleon forces. Excellent agreement with the tensor analyzing powers and cross section is found, while the $A_y$ and ${\mathrm{iT}}_{11}$ data are found to be underpredicted by the calculations.

The one-body density matrix, momentum distribution, natural orbits, and quasihole states of ${}^{16}\mathrm{O}\mathrm{}$ and ${}^{40}\mathrm{Ca}\mathrm{}$ are analyzed in the framework of the correlated basis function theory using state-dependent correlations with central and tensor components. Fermi hypernetted chain integral equations and single operator chain approximation are employed to sum cluster diagrams at all orders. The optimal trial wave function is determined by means of the variational principle and the realistic Argonne $v_8^{\prime }$ two-nucleon and Urbana IX three-nucleon interactions. The correlated ${}^{16}\mathrm{O}$ momentum distribution is in good agreement with the variational Monte Carlo results and shows the well-known enhancement at large momentum values with respect to the independent-particle model. A similar behavior is found in ${}^{40}\mathrm{Ca}.$ The relative importance of the different types of correlations (mainly Jastrow and tensor) on the momentum distribution appears to be similar in the nuclei and in nuclear matter. Diagonalization of the density matrix provides the natural orbits and their occupation numbers. Correlations deplete the occupation number of the first natural orbital by more than $10\%.$ The orbitals following the first one result instead, occupied by a few percent, or less. The single particle overlap functions and the spectroscopic factors are computed in the correlated model for both nuclei and compared with previous estimates. Jastrow correlations lower the spectroscopic factors of the valence states by a few percent $(\sim 1–3\%)$ with respect to unity. An additional $\sim 8–12\%$ depletion is provided by spin-isospin tensor correlations. It is confirmed that a variational treatment of short-range correlations does not explain the spectroscopic factors extracted from ${(e,e}^{\prime }p)$ experiments. Such an approach corresponds to the zeroth order of the correlated basis function theory and two-hole one-particle perturbative corrections in the correlated basis are expected to provide most of the remaining strength, as in nuclear matter.

A modified Zimányi-Moszkowski model for finite nuclei is investigated in this paper. The improvement on the Zimányi-Moszkowski (ZM) model is achieved by including a tensor force. It shows that in the ZM model the spin-orbit splittings of finite nuclei can be improved by the inclusion of a tensor coupling. Furthermore, the tensor force is generally attractive in the interior of nuclei and repulsive in the surface region. As a result, nucleons become more tightly bound in the deep-lying states, and more loosely bound in the states close to the Fermi surface, when the tensor force is included.

We calculate the formation cross sections of transactinides (superheavy elements), as well as heavy actinides (No and Lr), which have been or might be obtained in fusion reactions with the evaporation of only one neutron. We use both more realistic fusion barrier and survival probability of the compound nucleus in comparison with the original phenomenological model [Phys. Rev. C 59, 2634 (1999)] that prompted the Berkeley experiment on the synthesis of a new superheavy element 118 [Phys. Rev. Lett. 83, 1104 (1999)]. Calculations are performed for asymmetric and symmetric target-projectile combinations and for reactions with stable and radioactive-ion beams. The formation cross sections measured at GSI-Darmstadt for transactinides and heavy actinides, as well as that for superheavy element 118 reported by the LBNL-Berkeley group, are reproduced within a factor of 2.4, on average. Based on the obtained relatively large cross sections, we predict that optimal reactions with stable beams for the synthesis of so far unobserved superheavy elements 119, 120, and 121 are ${}^{209}\mathrm{Bi}{(}^{86}\mathrm{Kr},\hspace{0.5em}{1n)}^{294}119,{\hspace{0.5em}}^{208}\mathrm{Pb}{(}^{88}\mathrm{Sr},\hspace{0.5em}{1n)}^{295}120,$ and ${}^{209}\mathrm{Bi}{(}^{88}\mathrm{Sr},\hspace{0.5em}{1n)}^{296}121,$ respectively. This is because of the magic of both the target and the projectile that leads to larger Q value and, consequently, lower effective fusion barrier with larger transmission probability. The same effect is responsible for relatively large cross sections predicted for the symmetric reactions ${}^{136}\mathrm{Xe}{(}^{124}\mathrm{Sn},\hspace{0.5em}{1n)}^{259}\mathrm{Rf},{\hspace{0.5em}}^{136}\mathrm{Xe}{(}^{136}\mathrm{Xe},\hspace{0.5em}{1n)}^{271}\mathrm{Hs}{,}^{138}\mathrm{Ba}{(}^{136}\mathrm{Xe},\hspace{0.5em}{1n)}^{273}110,$ and ${}^{140}\mathrm{Ce}{(}^{136}\mathrm{Xe},\hspace{0.5em}{1n)}^{275}112.$ Although shell effects in the magic nuclei ${}^{124}\mathrm{Sn},{\hspace{0.5em}}^{136}\mathrm{Xe},{\hspace{0.5em}}^{138}\mathrm{Ba},$ and ${}^{140}\mathrm{Ce}$ are not as strong as in ${}^{208}\mathrm{Pb}$ and ${}^{209}\mathrm{Bi},$ they act on both the target and the projectile and lead to the prediction of measurable cross sections.

A stack of annular detectors made of high purity germanium and a magnet spectrograph were used to measure $p\overrightarrow{p}d{\pi }^{+}$ differential cross sections at a beam momentum of $850\mathrm{MeV}/c$ over a large angular range. A total cross section of $\sigma =0.2301\mathrm{}\pm 0.0036\left(\mathrm{stat}\right)\pm 0.0230\mathrm{}\left(\mathrm{syst}\right)\mathrm{}$ mb and an anisotropy $A_2{/A}_0=0.856\mathrm{}\pm 0.016$ were deduced. These values follow fits to low energy data. From the present $A_2$ value it is found that the pionic p-wave amplitude $a_0$ is larger than assumed so far.

The ${}^{34,35}\mathrm{Al}$ $\beta$ decays have been studied at the CERN online mass separator ISOLDE by β-γ, β-γ-γ, and $\beta -n-\gamma$ measurements in order to corroborate the low-level description of ${}^{34}\mathrm{Si}$ and to obtain the first information on the level structure of the $N=21\mathrm{}$ isotope ${}^{35}\mathrm{Si}.$ Earlier observed $\gamma$ lines in ${}^{34}\mathrm{Al}$ decay were confirmed and new $\gamma$ transitions following both $\beta$ decay and $\beta -\mathrm{d}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{y}\mathrm{e}\mathrm{d}$ neutron emission have been established. The first level scheme of ${}^{35}\mathrm{Si}$ includes three excited states at 910, 974, and 2168 keV. Indication is found for $J^{\pi }{=(3/2)\mathrm{}}^{-}$ and ${\mathrm{}(3/2)\mathrm{}}^{+}$ for the first two excited states, respectively. Beta-decay half-life of $T_{1/2}=38.6\mathrm{}\left(4\right)\mathrm{}\hspace{0.5em}\mathrm{ms}$ and $\beta -\mathrm{d}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{y}\mathrm{e}\mathrm{d}$ neutron branching value $P_n=41\mathrm{}\left(13\right)\%$ were measured unambiguously. The significance of the single-particle energy determination at $N=21,$ $Z=14\mathrm{}$ for assessing the effective interaction in $\mathrm{sd}-\mathrm{fp}$ shell-model calculations is discussed and illustrated by predictions for different neutron-rich isotopes.

With the supersymmetry scheme including many-body interactions, a parametrization of the excitation energy of superdeformed (SD) states is proposed. The identical SD bands with $\Delta I=4\mathrm{}$ bifurcation, ${}^{149}\mathrm{Gd}\mathrm{}\left(1\right)\mathrm{}{-}^{148}\mathrm{Gd}\mathrm{}\left(6\right)\mathrm{}{-}^{148}\mathrm{Eu}\mathrm{}\left(1\right),$ are investigated. Quantitatively good results are obtained. The result shows that the parametrization can describe the identical SD bands and the $\Delta I=4\mathrm{}$ bifurcation simultaneously. It suggests that the $\Delta I=4\mathrm{}$ bifurcation in the SD bands may have a bearing on a perturbation exhibiting the $\mathrm{SO}\mathrm{}\left(5\right)\mathrm{}$ [or $\mathrm{SU}\mathrm{}\left(5\right)\mathrm{}]$ symmetry in the mean field and the identical bands may be interrelated with the supersymmetry.

We discuss the nonmesonic decay of deformed p-shell hypernuclei. The Nilsson model with angular momentum projection is employed in order to take into account the deformation effects. The nonmesonic decay rate and the intrinsic $\Lambda$ asymmetry parameter decrease as a function of the deformation parameter, while the ratio of the neutron- to proton-induced decay rates increases. We find that the deformation effects change these observables by about 10% for ${}_{\Lambda }^9\mathrm{Be}$ from the spherical limit.

In the framework of the Glauber approximation, using a simple suggested approach for the three-body force effect and taking into account $D-\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{e}$ and phase variation effects, $p-,$ $\overline{p}-,$ and ${\pi }^{-}-d$ elastic scattering differential cross sections at different energies are calculated. In general, one or two effects only from the three used effects are not enough to obtain a good fit with the data. Thus, with the $D-\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{e}$ effect as a principal correction, the three-body force effect plays a role in the scattering process. The reality of the three-body force effect with a small contribution can be accepted to obtain a good fit with the experimental data.

$J/\Psi$ dissociation in collisions with nucleons is studied within a boson-exchange model and the energy dependence of the dissociation cross section is calculated from the threshold for ${\Lambda }_c\overline{D}$ production to high energies. We illustrate the agreement of our results with calculations based on short-distance QCD and Regge theory. The compatibility between our calculations and the data on $J/\Psi$ photoproduction on a nucleon is discussed. We evaluate the elastic $J/\Psi +N$ cross section using a dispersion relation and demonstrate the overall agreement with the predictions from QCD sum rules. Our results are compatible with the phenomenological dissociation cross section evaluated from the experimental data on $J/\Psi$ production from $\gamma +A,$ $p+A,$ and $A+A$ collisions.

We consider the three flavor Nambu–Jona-Lasinio model with the ’t Hooft interaction incorporating the $\mathrm{U}{\mathrm{}\left(1\right)\mathrm{}}_{\mathrm{A}}$ anomaly. In order to set the coupling strength of the ’t Hooft term, we employ the topological susceptibility $\chi$ instead of the ${\eta }^{\prime }$ meson mass. The value for $\chi$ is taken from lattice simulations. We also calculate $\chi$ at finite temperature within the model. Comparing it with the lattice data, we extract information about the behavior of the $\mathrm{U}{\mathrm{}\left(1\right)\mathrm{}}_{\mathrm{A}}$ anomaly at finite temperature. We conclude that within the present framework, the effective restoration of the $\mathrm{U}{\mathrm{}\left(1\right)\mathrm{}}_{\mathrm{A}}$ symmetry does not necessarily take place even at high temperature where the chiral symmetry is restored.

Interplay of collective and single-particle degrees of freedom is a common phenomenon in strongly correlated many-body systems. Despite many successful efforts in the study of superdeformed nuclei, there is still unexplored physics that can be best understood only through the nuclear magnetic properties. We point out that study of the gyromagnetic factor $(g$ factor) may open a unique opportunity for understanding superdeformed structure. Our calculations suggest that investigation of the g-factor dependence on spin and particle number can provide important information on single-particle structure and its interplay with collective motion in the superdeformed mass-190 nuclei. Modern experimental techniques combined with the new generation of sensitive detectors should be capable of testing our predictions.

The ground state half-lives of the gold isotope ${}^{196}\mathrm{Au},$ the mercury isotopes ${}^{195,197,203}\mathrm{Hg},$ the lead isotope ${}^{203}\mathrm{Pb},$ and the half-lives of two isomers in ${}^{199}\mathrm{Hg}$ and ${}^{204}\mathrm{Pb}$ have been measured with high precision using the photoactivation technique. The $\gamma$-ray activity was counted over several half-lives with high-purity germanium detectors. The measured half-lives are: $T_{1/2}{(}^{196}\mathrm{Au})=6.1669\mathrm{}\pm 0.0006$ d; $T_{1/2}{(}^{195}\mathrm{Hg})=10.53\mathrm{}\pm 0.03$ h; $T_{1/2}{(}^{197}\mathrm{Hg})=64.94\mathrm{}\pm 0.07$ h; $T_{1/2}{(}^{203}\mathrm{Hg})=46.6\mathrm{}\pm 0.1$ d; $T_{1/2}{(}^{204}\mathrm{Pb})=51.95\mathrm{}\pm 0.01$ h; $T_{1/2}{(}^{199m}\mathrm{Hg})=42.67\mathrm{}\pm 0.09$ min; $T_{1/2}{(}^{204m}\mathrm{Pb})=1.14\mathrm{}\pm 0.04$ h.

The $N=21\mathrm{}$ nucleus ${}^{34}\mathrm{Al},$ located at the boundary of the island of inversion, was studied via intermediate-energy Coulomb excitation. A $\gamma$ ray with an energy of $657\pm 9\hspace{0.5em}\mathrm{keV}$ has been observed in ${}^{34}\mathrm{Al}$ and its production cross section has been measured. This $\gamma$ ray may connect states which are members of the low-lying neutron $d_{5/2}{-f}_{7/2}$ multiplet.

We calculate in (two-loop) chiral perturbation theory the local $\mathrm{NN}$ potentials generated by the three-pion exchange diagrams with one insertion from the second order chiral effective pion-nucleon Lagrangian proportional to the low-energy constants $c_{1,2,3,4}.$ The resulting isoscalar central potential vanishes identically. In most cases these $3\pi$-exchange potentials are larger than the ones generated by the diagrams involving only leading order vertices due to the large values of $c_{3,4}$ (which mainly represent virtual $\Delta$ excitation). A similar feature has been observed for the chiral $2\pi$ exchange. We also give suitable (double-integral) representations for the spin-spin and tensor potentials generated by the leading-order diagrams proportional to $g_A^6$ involving four nucleon propagators. In these cases the Cutkosky rule cannot be used to calculate the spectral functions in the infinite nucleon mass limit since the corresponding mass spectra start with a nonvanishing value at the $3\pi$ threshold. Altogether, one finds that chiral $3\pi$ exchange leads to small corrections in the region $r>~1.4\mathrm{fm}$ where $1\pi$ and chiral $2\pi$ exchange alone provide a very good strong $\mathrm{NN}$ force as shown in a recent analysis of the low-energy $\mathrm{pp}$-scattering database.