A variational perturbation theory based on the functional integral approach is formulated for many-particle systems. Using the variational action obtained through Jensen-Peierls’ inequality, a perturbative expansion scheme for the thermodynamic potential is established. A modified Wick’s theorem is obtained for the variational perturbation expansions. This theorem allows one to carry out systematic calculations of higher order terms without worrying about the double counting problem. A model numerical calculation was carried out on a nucleon gas system interacting through the Yukawa-type potential to test the efficiency of the present method.

The magnetic dipole moment of the $1^{+}$ ground state of the $T=1\mathrm{}$ nucleus ${}_{17}^{32}{\mathrm{Cl}}_{15}$ has been measured to be $\mu =1.114\mathrm{}\left(6\right)\mathrm{}{\mu }_N$ using conventional $\beta -\mathrm{NMR}$ spectroscopy. Polarized ${}^{32}\mathrm{Cl}$ nuclei were produced by fragmentation of a 100 MeV/nucleon ${}^{36}\mathrm{Ar}$ beam in a 642 $\mathrm{mg}/{\mathrm{cm}}^2$ ${}^{93}\mathrm{Nb}$ target, where the beam was incident on the target at an angle $2.5°$ to the normal beam axis. The desired ${}^{32}\mathrm{Cl}$ fragments were filtered from other fragmentation products using the A1200 fragment separator and implanted in a NaCl single crystal, maintained at room temperature, at the center of a $\beta -\mathrm{NMR}$ apparatus. The Larmor frequency was determined by measuring the $\beta$-decay asymmetry as a function of the applied radio-frequency field. Isoscalar and isovector moments for the $A=32,$ $T=1\mathrm{}$ isospin multiplet are extracted and compared with large-basis shell model calculations.

Quasielastic (p, n) reactions were studied at an incident proton energy of 35 MeV. Differential cross sections for isobaric analog $\Delta J^{\pi }{=0\mathrm{}}^{+}$ (Fermi-type) transitions and their angular distributions were measured in 27 $N>Z$ target nuclei ${}^7\mathrm{Li},$ ${}^9\mathrm{Be},$ ${}^{13,14}\mathrm{C},$ ${}^{15}\mathrm{N},$ ${}^{50}\mathrm{Cr},$ ${}^{54,56}\mathrm{Fe},$ ${}^{58,60,62,64}\mathrm{Ni},$ ${}^{70}\mathrm{Zn},$ ${}^{71}\mathrm{Ga},$ ${}^{92}\mathrm{Zr},$ ${}^{110,112,114,115}\mathrm{Cd},$ ${}^{116,118,120}\mathrm{Sn},$ ${}^{140}\mathrm{Ce},$ ${}^{172,174,176}\mathrm{Yb},$ and ${}^{208}\mathrm{Pb}.$ Pure $\Delta J^{\pi }{=0\mathrm{}}^{+}$ Fermi-type transitions were observed in 23 of them. As for the four light odd-A nuclei, contributions from mixed $\Delta J^{\pi }\ne 0^{+}$ components were evaluated by microscopic distorted-wave Born approximation (DWBA) calculations to subtract them from the raw data and extract pure Fermi-type transition strengths. Thus 27 $\Delta J^{\pi }{=0\mathrm{}}^{+}$ angular distributions were obtained, and fitted by macroscopic DWBA calculations with the Lane-model optical potential to derive systematically the isovector part of the potential. The best-fit parameters for each target are presented. The present results combined with our previous analysis on 13 other nuclei in the $17<~A<~48$ region cover almost the entire mass region. They were used to obtain A-dependent global parameters by least-squares fit.

The velocity dependence of the stopping power of swift protons in low-energy collisions is investigated. At low projectile energies the stopping is mainly due to nuclear stopping and charge exchange of the electron. The second mechanism dominates at $E_p>~200$ eV. A dynamical treatment of the charge exchange mechanism based on two-center electronic wave functions yields transparent results for the exchange probability. We predict that the stopping cross sections vary approximately as $v_p^{1.35}$ for projectile protons on hydrogen targets in the 1 keV energy region.

Superdeformed and highly deformed rotational bands were established in ${}^{65}\mathrm{Zn}$ using the ${}^{40}\mathrm{Ca}{(}^{29}\mathrm{Si}{,4p)}^{65}\mathrm{Zn}$ reaction, and averaged quadrupole moments were measured for two of these bands. The configurations of these bands were assigned based on Hartree-Fock calculations. One of the three bands exhibits at low $ħ\omega$ a rise in the $J^{\mathrm{}\left(2\right)\mathrm{}}$ dynamic moments of inertia that is similar to the alignment gain observed in ${}^{60}\mathrm{Zn}.$ A comparison of the rotational band configurations and their $J^{\mathrm{}\left(2\right)\mathrm{}}$ moments of inertia for light Zn isotopes suggests that the rise in $J^{\mathrm{}\left(2\right)\mathrm{}}$ is most likely caused by $\mathrm{np}$ interactions associated with the valence protons and neutrons occupying the $g_{9/2}$ intruder orbits.

Previous theoretical studies of the disappearance of directed transverse flow showed a dual dependence on the equation of state (EOS) and the in-medium cross section $\left({\sigma }_{\mathrm{nn}}\right)$ for light systems. Also, the balance energy was shown to increase as a function of the impact parameter. However, Boltzmann-Uehling-Uhlenbeck (BUU) model calculations show that the dependence on ${\sigma }_{\mathrm{nn}}$ weakens for heavy systems such as Au+Au, and data presented here show that the impact parameter dependence nearly vanishes for Au+Au. Therefore, the EOS parameter K can be isolated using the balance energy, and BUU calculations show good agreement for a soft EOS. The reduction in ${\sigma }_{\mathrm{nn}}$ is then investigated using the experimental mass dependence of the balance energy.

The self-consistent quasiparticle random phase approximation (SCQRPA) within the O(5) model in the coupled proton-neutron representation is analyzed. The exact vacuum wave function is used to compute all involved matrix elements. A stability analysis of the stationary points is performed. A phase transition from the uncoupled to the coupled stable proton-neutron regime beyond the QRPA breakdown value of the particle-particle strength is evidenced. The excitation energies are close to the lowest stable exact eigenvalues given by the diagonalization procedure for all cases. The conditions for which the Ikeda sum rule is fulfilled for all values of the particle-particle strength are pointed out.

Surface localization of the initial target-projectile interaction has been investigated for incident protons and neutrons at bombarding energies of 14–100 MeV within the framework of the exciton preequilibrium model. Incident neutrons, at least at energies up to around 30 MeV, show a greater amount of surface peaking than do incident protons as judged by the effective well depth available to the hole degree of freedom created. With this difference included, exciton model calculations can describe the energy spectra in all four $\mathrm{}(N,N)\mathrm{}$ reaction channels with a consistent set of model input. To aid in this study, the excitation of strong spectroscopic collective states was included in the calculations. The addition of giant resonance state excitation has a small but helpful effect. There is a need for additional data, especially for incident neutrons above 26 MeV.

In this Rapid Communication we present results from the analysis of the isotopic yields of fragments emitted in two selected reactions: the decay of the quasiprojectile in Au+Au peripheral collisions at 35 MeV/nucleon, and the disassembly of the unique source formed in Xe+Cu central reactions at 30 MeV/nucleon. We find that the relative yields of neutron-rich isotopes increase with the excitation energy of the emitting sources. In the framework of a statistical multifragmentation model which reproduces fairly well the experimental observables, such behavior can be explained with the increase of the $N/Z$ ratio of the hot primary fragments. This corresponds to the statistical evolution of the fragmentation mechanism as a function of the excitation energy, from the decay into few small fragments with a heavy residue to complete multifragmentation.

Excited states in ${}^{110}\mathrm{I}$ have been identified for the first time using the $\alpha \mathrm{pn}$ evaporation channel from the ${}^{58}\mathrm{Ni}{+}^{58}\mathrm{Ni}$ reaction at a beam energy of 250 MeV. The experiment was carried out using GAMMASPHERE coupled to the MICROBALL charged-particle detector array and an array of 15 neutron detectors. Two collective structures were observed with the yrast band built on the $\pi h_{11/2}\otimes \nu h_{11/2}$ configuration. Comparisons of the yrast-band energies with the excitation energies of the yrast states in even ${}_{52}\mathrm{Te}$ and in odd ${}_{52}\mathrm{Te}$ and ${}_{53}\mathrm{I}$ isotopes for $A\sim 110$ were analyzed, revealing different responses of the underlying cores to the valence $\pi h_{11/2}$ and $\nu h_{11/2}$ orbitals. It is concluded that the neutron $h_{11/2}$ valence orbital has a larger influence than that of the proton $h_{11/2}$ valence orbital.

High spin states in the $N=79\mathrm{}$ ${}^{137}\mathrm{Ce}$ nucleus have been studied with the reaction ${}^{124}\mathrm{Sn}{(}^{18}\mathrm{O}{,5n)}^{137}\mathrm{Ce}$ at beam energy 78 MeV. The level scheme has been expanded with spin up to $\frac{43}{2}ħ.$ At low spins, the yrast collective structure built on the $\nu h_{11/2}^{-1}\times 2^{+}$ multiplet shows a transitional shape with $\gamma =30.8\mathrm{}°$ according to calculations of the triaxial rotor-plus-particle model. The configurations for several high spin states have been discussed from a systematical comparison with neighboring nuclei. A collective band built on $I=33/2\mathrm{}$ level has been observed for the first time. This band has an oblate shape with $\gamma =-60°$ and most probably originates from the five-quasiparticle $\nu s_{1/2}\otimes [\nu h_{11/2}{]}^2\otimes \pi g_{7/2}\otimes \pi h_{11/2}$ configuration.

The numerical solutions of nonlocal and local Boltzmann kinetic equations for the simulation of central heavy ion reactions are parametrized in terms of time-dependent thermodynamical variables in the Fermi liquid sense. This allows one to discuss dynamical trajectories in phase space. The nonequilibrium state is characterized by nonisobaric, nonisochoric, etc., conditions, shortly called isonothing conditions. Therefore a combination of thermodynamical observables is constructed which allows one to locate instabilities and points of possible phase transition in a dynamical sense. We find two different mechanisms of instability, a short time surface-dominated instability and later a spinodal-dominated volume instability. The latter one occurs only if the incident energies do not exceed significantly the Fermi energy and might be attributed to spinodal decomposition. In contrast the fast surface explosion occurs far outside the spinodal region and pertains also in the cases where the system develops too fast to suffer a spinodal decomposition and where the system approaches equilibrium outside the spinodal region.

$R$-matrix formulas are used to derive information about levels of ${}^8\mathrm{Be}$ and reactions involving ${}^8\mathrm{Be}.$ Data from the ${}^4\mathrm{He}(\alpha {,p)}^7\mathrm{Li},$ ${}^4\mathrm{He}(\alpha {,n)}^7\mathrm{Be},$ and ${}^7\mathrm{Li}(p,\alpha {)}^4\mathrm{He}$ reactions and from $\alpha +\alpha$ elastic scattering are fitted, and a value obtained for the zero-energy S factor for ${}^7\mathrm{Li}(p,\alpha {)}^4\mathrm{He}:$ $S\left(0\right)=58\mathrm{}$ keV b. Recent measurements and analyses of the ${}^7\mathrm{Li}(d,\alpha \alpha )n$ and ${}^7\mathrm{Li}(p,{\gamma }_0{)}^8\mathrm{Be}$ reactions, and calculations concerned with low-lying intruder states in ${}^8\mathrm{Be},$ are discussed with reference to R-matrix fits.

We calculate the multiparticle Bose-Einstein correlations of pions and kaons produced by a surface hadronization of quark-gluon plasma droplets with initial baryon densities of 0.5 and $0{\mathrm{fm}}^{-3}.$ For a finite initial baryon density, the multiparticle correlations of $K^{+}$ are weaker than those of $\pi ,$ and the average multiparticle correlation intensities of $K^{-}$ decrease greatly with the increase of the number of the droplets, $N_d.$ For zero initial baryon density the differences between the average multiparticle correlation intensities of $K^{+}$ and $\pi$ become obvious with increasing $N_d.$

The angular momentum distribution of the compound nucleus is a fundamental characteristic of the reaction dynamics and can provide insight into reactions involving neutron- or proton-rich projectiles. Specifically, following the fusion of ${}^6\mathrm{He}$ with ${}^{209}\mathrm{Bi}$ (at center-of-mass energies of 18 to 27 MeV), ${}^{212}\mathrm{At}$ is formed by the evaporation of three neutrons from the compound nucleus. The decay process leaves the residual ${}^{212}\mathrm{At}$ in either the ground state ${(J}^{\pi }{=1\mathrm{}}^{-},$ $T_{1/2}=314\mathrm{}$ ms) or a metastable state ${(J}^{\pi }{=9\mathrm{}}^{-},$ $T_{1/2}=119\mathrm{}$ ms). The ratio of the number of residual ${}^{212m}\mathrm{At}$ to the total number of ${}^{212}\mathrm{At}$ residual nuclei is sensitive to the original momentum distribution of the compound nucleus. The measured isomer ratio is consistent with that predicted by standard models. This agreement is observed even at the lower energies where the measured three neutron evaporation cross section is greatly enhanced compared to model calculations. While the inclusion of coupling to the neutron-transfer channels improves the agreement with the observed cross-section data somewhat, the predicted isomer ratio then diverges from the measured ratio.

We compare results for the $D_{13}\mathrm{}\left(1520\right)\mathrm{}$ photon-decay amplitudes determined in analyses of $\eta$- and pion-photoproduction data. The ratio of helicity amplitudes ${(A}_{3/2}{/A}_{1/2}),$ determined from $\eta$-photoproduction data, is quite different from that determined in previous analyses of pion-photoproduction data. We consider how strongly the existing pion-photoproduction data constrain both this ratio and the individual photon-decay amplitudes.

The soft-rotator model was applied to understand the collective nuclear structure, electromagnetic transition, and the nucleon (both neutron and proton) interaction data of ${}^{58}\mathrm{Ni}$ in a consistent manner. It was found that the model could describe the collective level structure of ${}^{58}\mathrm{Ni},$ which does not exhibit the typical rotational or harmonic vibrational structure, up to excitation energy of 4.5 MeV modestly. The nucleon interaction data were described up to 150 MeV reasonably well by the coupled-channels method with a coupling scheme constructed consistent to the nuclear structure of ${}^{58}\mathrm{Ni}.$

An analysis of the experiment of the Erlangen group on the density distribution measurement for the reaction ${\pi }^{-}\overrightarrow{p}{\pi }^{-}{\pi }^{+}n$ at the Paul Scherrer Institute accelerator is presented. Revised data were used to determine the reaction amplitude parameters including ππ scattering lengths. It is shown that the amplitude $a_0^{I=2\mathrm{}}$ can only be extracted with large uncertainties from these data, while $a_0^{I=0\mathrm{}}$ and three other scattering lengths are obtained with rather good statistical accuracy. However, the available experimental data do not allow one to make a good choice between several solutions which essentially increases the theoretical uncertainties of the ππ scattering lengths obtained. It is shown that the location of detectors in this experiment was not optimal for selecting the one pion exchange (OPE) graph effects.

The method of lowest-order constrained variational calculations, which predicts semiempirical data for nuclear matter reasonably well, is used to calculate the equation of state of $\beta$-stable matter at finite temperature. The Reid soft-core potential, with and without $N-\Delta$ interactions, as well as the ${\mathrm{UV}}_{14}$ potential which fit the $N-N$ scattering data, are considered in the nuclear many-body Hamiltonian. In the total Hamiltonian, the electron and muon are treated relativistically at given temperature and density, in order to neutralize the fluid electrically and stabilize it against $\beta$ decay. The calculation is performed for a wide range of baryon densities and temperatures which are of interest in astrophysics. The free energy, entropy, proton abundance, etc., of nuclear $\beta$-stable matter are calculated. It is shown that by increasing the temperature, the maximum proton abundance is pushed towards lower densities while the maximum itself increases as the temperature is increased. The proton fraction is not sufficient to produce any gas-liquid phase transition. Finally, we obtain an overall agreement with other many-body techniques, which are available only at zero temperature.

A new phase of a ${}^{116}\mathrm{Cd}$ double β decay experiment is in progress in the Solotvina Underground Laboratory. Four enriched ${}^{116}{\mathrm{CdWO}}_4$ scintillators with total mass of 339 g are used in a setup, whose active shield is made of 15 natural ${\mathrm{CdWO}}_4$ crystals (20.6 kg). The background rate in the energy interval 2.5–3.2 MeV is 0.03 counts/yr kg keV. The half-life for 2ν2β decay of ${}^{116}\mathrm{Cd}$ is measured as $T_{1/2}\left(2\mathrm{}\nu \right)=2.6\mathrm{}\pm 0.1\left(\mathrm{stat}{)}_{-0.4}^{+0.7\mathrm{}}\right(\mathrm{syst})\times {10}^{19}$ yr. The $T_{1/2}$ limits for neutrinoless 2β decay of ${}^{116}\mathrm{Cd}$ are set at $T_{1/2}>~0.7\left(2.5\right)\mathrm{}\times {10}^{23}$ yr at 90%(68%) C.L. for transition to ground state of ${}^{116}\mathrm{Sn},$ while for decays to the first $2_1^{+}$ and second $0_1^{+}$ excited levels of ${}^{116}\mathrm{Sn}$ at $T_{1/2}>~1.3\left(4.8\right)\mathrm{}\times {10}^{22}$ yr and $>~0.7\left(2.4\right)\mathrm{}\times {10}^{22}$ yr with 90%(68%) C.L., respectively. For 0ν2β decay with emission of one or two Majorons, the limits are $T_{1/2}\left(0\mathrm{}\nu M1\right)>~3.7\left(5.8\right)\mathrm{}\times {10}^{21}$ yr and $T_{1/2}\left(0\mathrm{}\nu M2\right)>~5.9\left(9.4\right)\mathrm{}\times {10}^{20}$ yr at 90%(68%) C.L. Restrictions on the value of the neutrino mass, right-handed admixtures in the weak interaction, and the neutrino-Majoron coupling constant are derived as $m_{\nu }<~2.6\left(1.4\right)\mathrm{}$ eV, $\eta <~3.9\times {10}^{-8},$ $\lambda <~3.4\times {10}^{-6},$ and $g_M<~12\left(9.5\right)\mathrm{}\times {10}^{-5}$ at 90%(68%) C.L., respectively.