A comparison among extended random phase approximation (RPA) theories is made by calculating the strength functions of double phonon states of isovector dipole and isoscalar quadrupole giant resonances in ${}^{40}\mathrm{Ca}$ using the small amplitude limit of the time-dependent density-matrix theory (STDDM). STDDM includes all the elements of one-body and two-body amplitudes and provides us with a quite general framework of extended RPA theories which consider the coupling of one-body amplitudes to two-body amplitudes. The results are compared with those obtained by using time-dependent versions of the second RPA (SRPA) and other extended RPA theories. It is found that SRPA overestimates collectivity of the isovector mode and underestimates that of the isoscalar mode. From a comparison between STDDM and other extended RPA theories, it is concluded that the inclusion of particle-hole–particle-hole amplitudes is necessary to obtain appropriate collectivity of double phonon states of giant resonances.

We have studied the ${}^2\mathrm{H}{(}^6\mathrm{Li},\alpha {)}^4\mathrm{He}$ two-body reaction by applying the “Trojan horse” method (THM) to the ${}^6\mathrm{Li}{(}^6\mathrm{Li},\alpha \alpha {)}^4\mathrm{He}$ three-body reaction. The astrophysical $S\left(E\right)\mathrm{}$ factor has been extracted in the energy range between 10–800 keV for the two cases of target and projectile quasifree break-up. We found good agreement between the two data sets leading an improved determination of the $S\left(E\right)\mathrm{}$ with $S\left(0\right)=16.9\mathrm{}\pm 0.5\hspace{0.5em}\mathrm{MeV}\mathrm{b}.$ Furthermore, the electron screening potential energy $U_e=320\mathrm{}\pm 50$ eV has been extracted in a model-independent way by comparing direct and THM data. This value is significantly higher than the value predicted by current theoretical models.

DWBA calculations are commonly used in the analysis of peripheral transfer reactions, to extract the asymptotic normalization coefficient (ANC). This quantity is uniquely related to the zero energy S-factor useful for astrophysical purposes. The aim of this work is to test the adequacy of the DWBA formalism. For a set of transfer reactions from which ANCs have been extracted, we perform full coupled channels calculations. We include the most relevant inelastic channels for both the entrance and exit partitions. The results show that the reactions ${}^{13}\mathrm{C}{(}^3\mathrm{He}{,d)}^{14}{\mathrm{N}}_{\mathrm{g}.\mathrm{s}.\mathrm{}}$ and ${}^{14}\mathrm{N}{(}^7\mathrm{Be}{,}^8\mathrm{B}{)}^{13}{\mathrm{C}}_{\mathrm{g}.\mathrm{s}.\mathrm{}}$ are free from coupling effects, even if some of the excited final-state channels are not. For ${}^{10}\mathrm{B}{(}^7\mathrm{Be}{,}^8\mathrm{B}{)}^9{\mathrm{Be}}_{\mathrm{g}.\mathrm{s}.\mathrm{}},$ the ANC should be extracted with caution. If the ${}^{10}\mathrm{B}$ and ${}^9\mathrm{Be}$ behave similarly in this reaction as in the ${}^9\mathrm{Be}{(}^3\mathrm{He}{,d)}^{10}\mathrm{B}$ case, couplings effects should not be neglected.

Parametric resonance in soft modes at the critical temperature ${(T}_c)$ in high-energy heavy ion collisions is studied in the case when the temperature (T) of the system is almost constant for a long time. By dividing the fields into three parts, a zero mode (condensate), soft modes, and hard modes, and assuming that the hard modes are in thermal equilibrium, we derive the equation of motion for soft modes at ${T=T}_c.$ Enhanced modes are extracted by comparing with the Mathieu equation for the condensate oscillating along the sigma axis at ${T=T}_c.$ It is found that the soft mode of $\pi$ fields at about 174 MeV is enhanced.

We show that the boost variable, the conjugate to the coordinate rapidity, which is associated with the center-of-mass motion, encodes the information about the finite size of colliding nuclei in a Lorentz-invariant way. The quasielastic forward color-changing scattering between the quantum boost states rapidly grows with the total energy of the collision and leads to an active breakdown of the color coherence at the earliest moments of the collision. The possible physical implications of this result are discussed.

The $\gamma \overrightarrow{p}\gamma {\pi }^{0}p$ reaction in the $\Delta \mathrm{}\left(1232\right)\mathrm{}$-resonance region is investigated as a method to access the ${\Delta }^{+}\mathrm{}\left(1232\right)\mathrm{}$ magnetic dipole moment. The calculations are performed within the context of an effective Lagrangian model containing both the $\Delta$-resonant mechanism and a background of nonresonant contributions to the $\gamma \overrightarrow{p}\gamma {\pi }^{0}p$ reaction. Results are shown both for existing and forthcoming $\gamma \overrightarrow{p}\gamma {\pi }^{0}p$ experiments. In particular, the sensitivity of unpolarized cross sections and photon asymmetries to the ${\Delta }^{+}$ magnetic dipole moment is displayed for those forthcoming data.

$\beta$-decay properties of proton-rich odd-$A$ and even-even krypton isotopes are studied in the framework of a deformed self-consistent Hartree-Fock calculation with density-dependent Skyrme forces, including pairing correlations between like nucleons in BCS approximation. Residual spin-isospin interactions are consistently included in the particle-hole and particle-particle channels and treated in the quasiparticle random phase approximation. The similarities and differences in the treatment of even-even and odd-$A$ nuclei are stressed. Comparison to available experimental information is shown for Gamow-Teller strength distributions, summed strengths, and half-lives. The dependence of these observables on deformation is particularly emphasized in a search for signatures of the shape of the parent nucleus.

We test the charge-radius predictions of two modern mass formulas. Comparing with the charge-radius data for the 523 nuclei listed in the compilation of Nadjakov et al. [At. Data Nucl. Data Tables 56, 133 (1994)] it has been found that the finite-range droplet model mass formula leads to an rms deviation of 0.045 fm. The corresponding quantity for the Skyrme-Hartree-Fock mass formula HFBCS-1 is 0.024 fm.

The production and survival of ${}^{180}\mathrm{Ta}$ in stars presents a nuclear structure and astrophysics puzzle. From earlier work in the laboratory, photon scattering from the $9^{-},$ 75 keV isomeric state has been shown to result in eventual de-excitation to the relatively short-lived $1^{+}$ ground state, through intermediate states whose character is uncertain. It is suggested here that the lowest observed photon resonances match the energies of known states in the rotational band based on the recently assigned $K^{\pi }{=5\mathrm{}}^{+}$ state at 592 keV, states which are accessible by $E1\mathrm{}$ excitation from the $9^{-}$ isomer. Analysis of the previously observed resonance strengths and the known in-band properties implies $\gamma$-ray $E1\mathrm{}$ transition probabilities which are stronger than expected given the nominal K forbiddenness. Predicted widths for “back”-decay to the $9^{-}$ isomer and its rotational band are calculated and shown to be significant. Their observation would have implications for the proposed associations and mixing effects above the yrast line.

We investigate the origin of the regular features observed in numerical studies of the interacting boson model with random interactions, in particular the dominance of $L=0\mathrm{}$ ground states and the occurrence of vibrational and rotational band structures. It is shown that all of these properties can be interpreted and explained in terms of a Hartree-Bose mean-field analysis, in which different regions of the parameter space are associated with geometric shapes. The same conclusions hold for the vibron model.

The 9.17 MeV excited state of ${}^{14}\mathrm{N}$ has been populated using the sharp resonance at 1.75 MeV in the ${}^{13}\mathrm{C}(p,\gamma {)}^{14}\mathrm{N}$ reaction, and the energies of four sequential $\gamma$ rays deexciting the state to ground have been measured on a scale derived from the known energies of ${}^{56}\mathrm{Co}$ lines. An excitation energy of 9171.540(38) keV is determined, and the energies of two other states are found to be 6445.967(26) and 3947.904(17) keV.

The ${(}^3\mathrm{He},t)$ charge-exchange reaction has been studied at ${E(}^3\mathrm{He})=450\mathrm{}\mathrm{MeV}$ and angles near $0°$ on targets of ${}^{90}\mathrm{Zr}$ and ${}^{208}\mathrm{Pb}.$ Fragmentation of the Gamow-Teller (GT) strength into separate components of the particle-hole type has been observed. The distribution of the GT strength in ${}^{90}\mathrm{Nb}$ and in ${}^{208}\mathrm{Bi}$ has been calculated within the continuum quasiparticle random phase approximation and continuum-random-phase approximation approaches, respectively. These components, especially in ${}^{208}\mathrm{Pb},$ could be related with the direct, core polarization, and back-spin-flip Gamow-Teller strength.

The $K\overline{K}$ low-energy elastic scattering and bound states are studied on the basis of the quark potential model which is composed of the t-channel one-gluon exchange potential and the s-channel one-gluon exchange potential as well as the linear confining potential. In the study, an effective $K\overline{K}$ interaction potential is derived by means of the resonating group method. Use of this potential to evaluate $K\overline{K}$ elastic scattering phase shifts leads to a result which is in reasonable argreement with the experiment. The calculation of the bound states by employing the same potential gives support to the explanation that the exotic meson states $f_0\mathrm{}\left(980\right)\mathrm{}$ and $a_0\mathrm{}\left(980\right)\mathrm{}$ can possibly be viewed as the $K\overline{K}$ molecules. Moreover, the exotic states $f_1\mathrm{}\left(1420\right),$ $f_J\mathrm{}\left(1710\right),$ and $f_J\mathrm{}\left(2220\right)\mathrm{}$ may presumably be interpreted as the excited states of the $K\overline{K}$ molecules when we take $J=2\mathrm{}$ for $f_J\mathrm{}\left(1710\right)\mathrm{}$ and $J=4\mathrm{}$ for $f_J\mathrm{}\left(2220\right),$ respectively.

The lifetime of the 21.8-keV ${(5\mathrm{}}^{+})$ state in ${}^{98}\mathrm{Tc}$ has been measured to be 3.5(9) ns by direct timing methods, using a ${\mathrm{BaF}}_2$ scintillator and a low-energy photon spectrometer. This state is of interest because it is expected to decay partially by bound internal conversion when the charge state of the technetium ion is 20 or greater.

The Crystal Ball (CB) Collaboration at Brookhaven National Laboratory has recently presented results regarding a study of the ${\pi }^{-}\overrightarrow{A}{\pi }^0{\pi }^0{A}^{\prime }$ reaction on H, D, C, Al, and Cu, using a nearly $4\pi$ detector. Similar results, but for the ${\pi }^{+}\overrightarrow{A}{\pi }^{+}{\pi }^{\pm }{A}^{\prime }$ reaction on ${}^2\mathrm{H},$ ${}^{12}\mathrm{C},$ ${}^{40}\mathrm{Ca},$ and ${}^{208}\mathrm{Pb},$ have been published earlier by the CHAOS Collaboration at TRIUMF. In this Brief Report a comparison of the results of the two measurements is made, which shows that the CHAOS and CB data share relevant common features. In particular, the increase in strength as a function of A seen in the near-threshold ${\pi }^{+}{\pi }^{-}$ invariant mass spectra reported by the CHAOS group is also seen in the ${\pi }^0{\pi }^0$ CB data, when the results from the two groups are compared in a way which accounts for the different acceptances of the two experiments.

Excited isomeric states $I^{\pi }{=20\mathrm{}}^{+}$ have been identified for the first time in odd-odd ${}^{190,192}\mathrm{Au}$ nuclei. Two independent measurements of their half-lives were performed, using the recoil shadow anisotropy method with the Eurogam-II data, and using the time distribution of K-electron lines from the Orsay electron-spectrometer data. Half-lives of $7.0\pm 0.3$ and $5.4\pm 0.3$ ns were obtained for these isomers in ${}^{190}\mathrm{Au}$ and ${}^{192}\mathrm{Au},$ respectively, by the latter measurements. The $\pi h_{11/2}^{-1}\otimes \nu i_{13/2}^{-2}{h}_{9/2}^{-1}$ configuration was assigned to these isomeric states. A shape transition towards highly triaxial deformation with $\gamma \sim -90°$ is suggested by total Routhian surface calculations, which could be the cause for their relatively hindered decay.

The event-by-event reconstruction procedure and related uncertainties involved in the derivation of excitation energy and source-size distributions are investigated for GeV hadron-induced reactions. The analysis is performed for the $5.0–14.6\mathrm{GeV}/c$ proton-, ${\pi }^{-}$ and antiproton-induced reactions on ${}^{197}\mathrm{Au},$ measured with the Indiana silicon sphere charged-particle detector array at the Brookhaven AGS accelerator. The relative contributions of the three major components of the excitation-energy calorimetry: charged-particle kinetic-energy sums, neutrons, and Q values from reconstructed events, are found to be relatively constant for excitation energies above about 500 MeV. Effects on the results imposed by various assumptions necessary to account for experimental factors are examined and a corresponding deconvolution of the excitation-energy distribution is performed. The major uncertainties in the calorimetry are found to be (1) separation of nonequilibrium and thermal-like charged particles, and (2) the unmeasured neutron component. The self-consistency of the procedure is tested via comparisons with the SMM and SIMON codes for the disintegration of hot nuclei.

The relation between excitation energy and reaction observables has been examined for $(6.0\mathrm{}–14.6)-\mathrm{GeV}/c$ protons, (5.0–9.2)-GeV ${\pi }^{-},$ and $8.0-\mathrm{GeV}/c$ antiprotons incident on a ${}^{197}\mathrm{Au}$ target. Relative to proton and ${\pi }^{-}$ beams, $8.0-\mathrm{GeV}/c$ antiprotons are found to be the most effective projectile for depositing high excitation energies in the targetlike residue. For protons and ${\pi }^{-}$ the excitation-energy distributions are nearly identical and appear to be independent of beam momentum above $6–8\mathrm{GeV}/c.\mathrm{}$ It is found that total measured charge, total thermal energy, and total charged-particle multiplicity scale most directly with excitation energy, whereas IMF multiplicity and total transverse energy exhibit large fluctuations. Correlations of the observed fragment multiplicity, charge, and kinetic-energy distributions with excitation energy indicate a transition in the reaction observables near $E^{*}/A\approx 4–6\mathrm{MeV}.$ These experimental signals are consistent with a multifragmentation mechanism that becomes the dominant deexcitation mode above in the range $E^{*}/A\sim 4–6\mathrm{MeV}.$

Three-body correlations in the dissociation of two-neutron halo nuclei are explored using a technique based on intensity interferometry and Dalitz plots. This approach provides for the combined treatment of both the $n-n$ and core-$n$ interactions in the exit channel. As an example, the breakup of ${}^{14}\mathrm{Be}$ into ${}^{12}\mathrm{Be}+n+n$ by Pb and C targets has been analyzed and the halo $n-n$ separation extracted. Evidence for a finite delay between the emission of the neutrons in the reaction on the C target was observed and is attributed to ${}^{13}\mathrm{Be}$ resonances populated in sequential breakup.

The ${}^{229}\mathrm{Th}$ nucleus is known to have a ${3/2}^{+}$ level at $3.5\pm 1.0\hspace{0.5em}\mathrm{eV}$ above the ${5/2}^{+}$ ground state. In a hydrogenlike ${}^{229}{\mathrm{Th}}^{89+}$ ion these two levels are predicted to mix due to the high magnetic field produced at the nucleus by the $1s$ electron. This paper gives a theoretical analysis of the time evolution of the ${}^{229}{\mathrm{Th}}^{89+}$ hydrogenlike system after its formation in a fast collision process. In particular, nuclear-spin mixing oscillations are considered and the oscillation frequency is estimated to be about ${10}^{15}\hspace{0.5em}{\mathrm{s}}^{-1}.$ The time dependence of population of the hyperfine structure levels is determined. Considerations are extended to other ions of ${}^{229}\mathrm{Th}$ with the last electron in a higher s state. Consequences of different energy of the isomer are examined. A possible way to confront these predictions with experiment is briefly outlined.