We analyze the occurrence of dynamically equivalent Hamiltonians in the parameter space of general many-body interactions for quantum systems, particularly those that conserve the total number of particles. As an illustration of the general framework, the appearance of parameter symmetries in the interacting boson model 1 and their absence in the Ginocchio ${\mathrm{SO}}_8$ fermionic model are discussed.

The energy spectrum for high energy $\gamma$ rays ${(E}_{\gamma }>~10$ MeV) from the process $p\overrightarrow{p}\gamma \gamma X$ emitted at $90°$ in the laboratory frame has been measured at an energy below the pion production threshold, namely, at 216 MeV. The resulting photon energy spectrum extracted from $\gamma -\gamma$ coincidence events consists of a narrow peak at a photon energy of about 24 MeV and a relatively broad peak in the energy range of $50-70$ MeV. The statistical significances for the narrow and broad peaks are $5.3\sigma$ and 3.5σ, respectively. This behavior of the photon energy spectrum is interpreted as a signature of the exotic dibaryon resonance $d_1^{\star }$ with a mass of about 1956 MeV, which is assumed to be formed in the radiative process $p\overrightarrow{p}\gamma d_1^{\star }$ followed by its electromagnetic decay via the $d_1^{\star }\to \mathrm{pp}\gamma$ mode. The experimental spectrum is compared with those obtained by means of Monte Carlo simulations.

Interband $B\left(E2\mathrm{}\right)\mathrm{}$ transition strengths between different normal parity bands in ${}^{163}\mathrm{Dy}$ and ${}^{165}\mathrm{Er}$ are described using the pseudo-SU(3) model. The Hamiltonian includes Nilsson single-particle energies, quadrupole-quadrupole and pairing interactions with fixed, parametrized strengths, and three extra rotor terms used to fine tune the energy spectra. In addition to interband transitions, the energy spectra and the ground state intraband B(E2) strengths are reported. The results show the pseudo-SU(3) shell model to be a powerful microscopic theory for a description of the normal parity sector in heavy deformed odd-$A$ nuclei.

The shape of the measured barrier distribution for the ${}^{34}\mathrm{S}{+}^{168}\mathrm{Er}$ reaction is analyzed using the coupled-channels description. The ${}^{168}\mathrm{Er}$ nucleus is a good candidate to test current fusion models description of deformation since it has a large quadrupole deformation with an insignificant hexadecapole deformation. Coupling to weaker channels, the $2_1^{+}$ state in ${}^{34}\mathrm{S},$ the $3_1^{-}$ state in ${}^{168}\mathrm{Er},$ and the pair neutron transfer channel, all were found to have little influence on the barrier distribution. A successful description of the barrier distribution was only obtained after the hexacontatetrapole deformation term in ${}^{168}\mathrm{Er}\hspace{0.5em}\left({\beta }_6^T\right)$ was included in the coupling scheme. However, a positive value for ${\beta }_6^T$ was needed where the macroscopic-microscopic model predicts a negative one.

Shell-model results for the electric quadrupole $\mathrm{}\left(E2\mathrm{}\right),$ magnetic dipole $\mathrm{}\left(M1\mathrm{}\right),$ and Gamow-Teller transition strength sums and occupation numbers are calculated using different valence spaces and compared to the embedded Gaussian orthogonal ensemble (EGOE) predictions. It is shown that transition strength sums can be considered as a new statistic able to distinguish between regular and chaotic motion. Moreover it is established that the EGOE (but not the GOE) provides the good description of the shell-model strength sums in the chaotic domain. To get this result we have studied the behavior of strength sums in order to chaos transitions generated by means of a family of Hamiltonians $H\left(\lambda \right)=h\left(1\right)+\lambda V\left(2\right),$ built from realistic one- and two-body interactions.

The origin of the dominance of prolate shapes over oblate ones of the ground states of atomic nuclei is investigated with the Nilsson-Strutinsky method. The number of prolate nuclei among all the deformed even-even nuclei is calculated as a function of the strengths of the spin-orbit and the $l^2$ terms of the Nilsson potential. The latter simulates a square-well-like radial profile of the mean potential. The proportion of prolate nuclei is 86% with the standard strengths corresponding to the actual atomic nuclei. By weakening the spin-orbit potential, the proportion oscillates strongly, having a local minimum value of 42% with about half of the standard strength and a local maximum value of 79% without the spin-orbit potential.

Analyzing powers $A_{\mathrm{xx}}\left(\theta \right),$ $A_{\mathrm{yy}}\left(\theta \right),$ $A_{\mathrm{zz}}\left(\theta \right),$ and $A_y^d\left(\theta \right)$ of the $\mathrm{H}\left(\overrightarrow{d}{,}^3\mathrm{He}\right)\gamma$ reaction were measured at $E_d=17.5\mathrm{}\hspace{0.5em}\mathrm{MeV}.$ A hydrogen gas target sealed with thin carbon foils was used and the angular distribution of ${}^3\mathrm{He}$ recoils was observed to measure the analyzing powers. High-statistics data were obtained over a wide c.m. angular range. The results are compared with recent Faddeev calculations based on the realistic two body potential with and without three-nucleon force incorporated.

Neutrons and charged light and intermediate-mass products from the ${}^{197}\mathrm{Au}{+}^{86}\mathrm{Kr}$ reaction at $E_{\mathrm{lab}}/A=35\mathrm{}\hspace{0.5em}\mathrm{MeV}$ were measured with $4\pi$ angular coverage, in coincidence with projectilelike (PLFs) and targetlike fragments (TLFs). The characteristics of PLF and TLF yields and their correlation with neutron, light-charged particles, and intermediate-mass fragments (IMFs) are consistent with a scenario where essentially all collisions proceed through a dissipative stage. It is found that the damping of the available kinetic energy into thermal excitation is essentially incomplete, with no positive evidence for complete damping. Slow, massive reaction products are observed with significant yields. These products, termed also heavy residues, are identified as TLF evaporation residues and as TLF fission fragments. The TLF fission mode is seen to fade away in favor of TLF evaporation residue production for excitation energies above 3–4 MeV/nucleon. The suppression of the TLF fission can be traced to the dynamical IMF production process which reduces considerably the sizes of the primary reaction fragments and, hence, their fissility.

Lifetimes of some 20 high-spin states in ${}^{101}\mathrm{Ag}$ in the range between 0.2 and 200 ps have been measured using various Doppler shift techniques. The states have been populated in the reaction ${}^{58}\mathrm{Ni}{(}^{50}\mathrm{Cr},\alpha 3p)$ at 200–205 MeV beam energy and their decays observed by means of the GASP array. For many states, the problem of their unknown side-feeding times has been circumvented by using the DDCM and NGTB $\gamma \gamma$-coincidence methods. A total of some 60 reduced transition strengths or limits of them has been deduced. Moderately enhanced electric quadrupole transitions (up to 30 W.u.) have been derived as well as rather strong stretched magnetic dipole transitions within the negative parity yrast sequence (0.2–0.7) W.u. An attempt has been made to interpret the level energies and electromagnetic transitions within the interacting boson fermion plus broken pair model.

The neutrinoless double-beta-decay $(0\mathrm{}\nu \beta \beta$ decay) transition to the first excited $0^{+}$ collective final state is examined for $A=76,$ 82, 100, and 136 nuclei by assuming light and heavy Majorana neutrino exchange mechanisms as well as the trilinear R-parity violating contributions. Realistic calculations of nuclear matrix elements have been performed within the renormalized quasiparticle random phase approximation. Transitions to the first excited two-quadrupole phonon $0^{+}$ state are described within a boson expansion formalism and alternatively by using the operator recoupling method. We present the sensitivity parameters to different lepton number violating signals, which can be used in planning the $0\nu \beta \beta$-decay experiments. The half-life of $0\nu \beta \beta$ decay to the first excited state $0_1^{+}$ is by a factor of 10–100 larger than that of the transition to the ground state, $0_{\mathrm{g}.\mathrm{s}.\mathrm{}}^{+}.$

We compute the photon asymmetry $B_{\gamma }$ for near threshold parity-violating (PV) pion photoproduction through subleading order. We show that subleading contributions involve a new combination of PV couplings not included in previous analyses of hadronic PV. We argue that existing constraints on the leading order contribution to $B_{\gamma }$—obtained from the PV $\gamma$-decay of ${}^{18}\mathrm{F}$—suggest that the impact of the subleading contributions may be more significant than expected from naturalness arguments.

We identify the $J^{\pi }{=2\mathrm{}}_3^{+}$ state of ${}^{96}\mathrm{Ru}$ as the proton-neutron mixed-symmetry $2_{\mathrm{ms}}^{+}$ state of this nucleus. This identification is based on the measurement of the transition strengths ${B(M1,2\mathrm{}}_3^{+}\to 2_1^{+})=0.78\mathrm{}(23)\mathrm{}\hspace{0.5em}{\mu }_N^2$ and ${B(E2;2\mathrm{}}_3^{+}\to 0_1^{+})=1.6\mathrm{}(3)\mathrm{}$ W.u. These transition strengths were obtained from the Coulomb excitation yield for the population of the $2_3^{+}$ state relative to the yield of the $2_1^{+}$ state with known $E2\mathrm{}$ excitation strength. The Coulomb excitation was done in inverse kinematics using the reaction ${}^{\mathrm{nat}}\mathrm{C}{(}^{96}\mathrm{Ru}{,}^{96}{\mathrm{Ru}}^{\star })$ at 280 MeV. This work demonstrates the accessibility of the isovector quadrupole excitation in the valence shell using experiments with an accelerated beam of the nuclei of interest.

The nucleus of ${}^{173}\mathrm{Ta}$ was populated using the reaction ${}^{159}\mathrm{Tb}{(}^{18}\mathrm{O}{,4n)}^{173}\mathrm{Ta}$ at a beam energy of 84 MeV. Lifetime measurements in the bands built on two Nilsson configurations $\pi h_{9/2}\left[541\right]{1/2}^{-}$ and $\pi g_{7/2}\left[404\right]{7/2}^{+}$ were performed using the recoil-distance Doppler shift method. The measured lifetimes were used to extract the reduced transition probabilities $B\left(E2\mathrm{}\right).$ Microscopic Hartree-Fock theory with the angular momentum projection was used for calculating the reduced transition probabilities. The $Q_t$ values obtained from the measured $B\left(E2\mathrm{}\right)\mathrm{}$ values show a larger collectivity for the $h_{9/2}$ band as compared to the $g_{7/2}$ band. Cranked Hartree-Fock Bogoliubov calculations were used for calculating the quasiparticle Routhians. The experimental results in conjunction with the cranking calculations also explain the experimental band-crossing delays associated with the $i_{13/2}$ neutron alignment in the ${}^{173}\mathrm{Ta}$ nucleus.

The ${}^{12}\mathrm{C}(\overrightarrow{\gamma },pp)$ and ${}^{12}\mathrm{C}(\overrightarrow{\gamma },pn)$ reactions have been studied for $E_{\gamma }=160\mathrm{}-350$ MeV using linearly polarized photons from the Glasgow tagged photon spectrometer at the Mainz microtron MAMI. Both reaction channels show a negative photon asymmetry $\Sigma$ for missing energies $E_m$ below 70 MeV, where direct emission nucleon pairs is expected. A strong peak at low $E_m$ is observed in ${\Sigma }_{(\gamma ,pp)},$ but not in ${\Sigma }_{(\gamma ,pn)}.$ Further differences between the two reaction channels are observed in the $E_{\gamma }$ dependence of $\Sigma$ and in the angular distributions of differential cross sections for photons polarized parallel, or perpendicular, to the reaction plane. Theoretical calculations using an unfactorized distorted wave treatment of direct two-nucleon emission do not agree with the magnitude of the photon asymmetry or the angular dependence of the differential cross sections for either channel. For $E_m>70\mathrm{}$ MeV and $E_{\gamma }>250\mathrm{}$ MeV, $\Sigma$ has a substantial negative value which is similar for both reaction channels. This is attributed to two-step reactions following initial quasifree pion production.

We report new high-precision measurements of $p(\overrightarrow{\gamma },\gamma ),$ $p(\overrightarrow{\gamma },{\pi }^0)$ and $p(\overrightarrow{\gamma },{\pi }^{+})$ cross section and beam asymmetry angular distributions for photon beam energies in the range from 213 MeV to 333 MeV. The cross sections for all three channels are locked together with a small common systematic scale uncertainty of 2%. A large overdetermination of kinematic parameters was used to achieve the first complete separation of the Compton scattering and ${\pi }^0$-production channels. This has also allowed all detector efficiencies for the $p(\overrightarrow{\gamma },\gamma )$ and $p(\overrightarrow{\gamma },{\pi }^0)$ channels to be measured directly from the data itself without resorting to simulations. The new Compton results are approximately 30% higher than previous Bonn data near the peak of the $\Delta$ resonance, resolving a long-standing unitarity puzzle. However, our $p(\overrightarrow{\gamma },{\pi }^0)$ and $p(\overrightarrow{\gamma },{\pi }^{+})$ cross sections are also about 10% higher than both earlier Bonn data and recent Mainz measurements, while our $p(\overrightarrow{\gamma },{\pi }^{+})$ cross sections are in good agreement with results from Tokyo. Our polarization asymmetry data are of the highest precision yet available and have considerable impact upon multipole analyses. These new data have been combined with other polarization ratios in a simultaneous analysis of both Compton scattering and $\pi$ production, with Compton scattering providing two new constraints on the photopion amplitude. This analysis has improved the accuracy in the $E2/M1\mathrm{}$ mixing ratio for the $\overrightarrow{N}\Delta$ transition, $EMR=-[3.07\pm 0.26(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}+\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})\pm 0.24(\mathrm{model}\left)\right]\mathrm{}(\%),$ and the corresponding $\overrightarrow{N}\Delta$ transverse helicity amplitudes, $A_{1/2}=-[135.7\pm 1.3(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}+\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})\pm 3.7(\mathrm{model}\left)\right]{(10\mathrm{}}^{-3}{\mathrm{GeV}}^{-1/2})$ and $A_{3/2}=-[266.9\pm 1.6(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}+\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})\pm 7.8(\mathrm{model}\left)\right]{(10\mathrm{}}^{-3}{\mathrm{GeV}}^{-1/2}).\mathrm{}$ From these we deduce an oblate spectroscopic deformation for the ${\Delta }^{+}.$ The same simultaneous analysis has been used to extract the proton dipole polarizabilities, $\overline{\alpha }-\overline{\beta }=+[10.39\pm 1.77(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}+\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}{)}_{-1.87}^{+1.02\mathrm{}}\left(\mathrm{model}\right)\left]{(10\mathrm{}}^{-4}{\mathrm{fm}}^3\right)$ in agreement with previous low energy measurements, and $\overline{\alpha }+\overline{\beta }=+[13.25\pm 0.86(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}+\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}{)}_{-0.58}^{+0.23\mathrm{}}\left(\mathrm{model}\right)\left]{(10\mathrm{}}^{-4}{\mathrm{fm}}^3\right)$ in agreement with recent evaluations of the Baldin sum rule. Our simultaneous analysis has also provided the first determination of the proton spin polarizabilities, ${\gamma }_{\pi }=-[27.23\pm 2.27(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}+\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}{)}_{-2.10}^{+2.24\mathrm{}}\left(\mathrm{model}\right)\left]{(10\mathrm{}}^{-4}{\mathrm{fm}}^4\right),$ ${\gamma }_0=-[1.55$$\pm 0.15(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}+\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}{)}_{-0.03}^{+0.03\mathrm{}}(\mathrm{model}\left)\right]{(10\mathrm{}}^{-4}{\mathrm{fm}}^4),$ ${\gamma }_{13}=+[3.94\pm 0.53(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}+\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}{)}_{-0.18}^{+0.20\mathrm{}}\left(\mathrm{model}\right)\left]{(10\mathrm{}}^{-4}{\mathrm{fm}}^4\right),$ and ${\gamma }_{14}=-[2.20\pm 0.27(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}+\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}{)}_{-0.09}^{+0.05\mathrm{}}\left(\mathrm{model}\right)\left]{(10\mathrm{}}^{-4}{\mathrm{fm}}^4\right).\mathrm{}$ The extracted value of the backward spin polarizability, ${\gamma }_{\pi },$ is considerably different from other analyses and this has been instrumental in bringing the value of $\overline{\alpha }-\overline{\beta }$ extracted from high energy data into agreement with low energy experiments.

The structure of the ${}^{147}\mathrm{Eu}$ nucleus has been studied via the ${}^{124}{\mathrm{S}\mathrm{n}(}^{28}\mathrm{Si},p4n)$ fusion-evaporation reaction at 125 MeV beam energy. The yrast level scheme has been extended up to 10 MeV and spin near 55/2. Up to the highest spins the levels are interpreted in terms of specific multinucleon excitations involving up to seven quasiparticles. Parameter free shell model calculations for three or five nucleons, or for three nucleons and an octupole phonon, are in good agreement with experiment for all the states observed here below 4.2 MeV, and also with the above-yrast levels known from earlier $\mathrm{}(p,2n)\mathrm{}$ experiments.

A broad excited state was observed in ${}^6\mathrm{He}$ with energy $E_x=5\mathrm{}\pm 1$ MeV and width $\Gamma =3\mathrm{}\pm 1$ MeV, following the reaction ${}^7\mathrm{Li}(\gamma {,p)}^6\mathrm{He}.$ The state is consistent with a number of broad resonances predicted by recent cluster model calculations. The well-established reaction mechanism, combined with a simple and transparent analysis procedure confers considerable validity to this observation.

Branch points in the complex plane are responsible for avoided level crossings in closed and open quantum systems. They create not only an exchange of the wave functions but also a mixing of the states of a quantum system at high level density. The influence of branch points in the complex plane on the low-lying states of the system is small.

The interplay between spectator and participant matter in heavy-ion collisions is investigated in the context of a microscopic transport model. Transport simulations show that flow patterns for the participant matter are strongly influenced by the presence of the nearby spectator matter. However, the influence is mutual. During the explosion of the participant zone, the spectator matter acquires a transverse momentum $〈P^x/A〉$ that shows sensitivity to the nuclear incompressibility and to the momentum dependence of the nuclear mean field (MF). An observed change in the net average momentum per nucleon, $\Delta |〈\mathbf{P}/A〉|,$ can be associated with the momentum dependence of the MF. For a momentum-dependent MF and a low impact parameter in a heavy system, the spectators may emerge faster than in the initial state, accelerated by the violent participant explosion. The average excitation energy and the mass of the spectators, in contrast to the momentum, show little sensitivity to the nuclear equation of state.