A two-particle space correlation function is derived from the single-particle momentum distribution of the emission source. A signal of a first-order phase transition is obtained from this correlation function if density fluctuations are large.

Within the framework of a phenomenological hydrodynamical model, the relationship of the freeze-out temperature parameter $T_f$ and the transverse flow velocity $v_{\perp }$ is discussed. It is found that the experimental single-particle distributions are not very sensitive to the exact form of the assumed velocity profile, but that there is a definite anticorrelation between $T_f$ and the average $v_{\perp }.$

The coupled $\eta N$,$\pi N$ system is described by a $K$-matrix method. The parameters in this model are adjusted to get an optimal fit to $\pi N\to \pi N$, $\pi N\to \eta N,$ and $\gamma N\to \eta N$ data in an energy range of about 100 MeV each side of the $\eta$ threshold. In the notation $T^{-1}$+${\mathrm{iq}}_{\eta }=1/a+$($r_0/2\mathrm{}$)$q_{\eta }^2{+sq}_{\eta }^4$, $q_{\eta }$ being the momentum in the$\eta N$ center of mass, the resulting effective range parameters for$\eta N$ scattering are found to be$a$ (fm) =0.75(4)$+i0.27\mathrm{}\left(3\right),$ $r_0$ (fm) =–1.50(13)-$i$0.24(4), and$s$ (fm${}^3)$ =–0.10(2)-$i$0.01(1).

Low-rank separable potentials greatly simplify perturbation-theory based many-body computations and are especially useful in finite temperature and nonequilibrium nuclear matter studies. With local potentials such calculations become very lengthy. In this paper, we present a first version of a separable potential constructed directly from available empirical nucleon-nucleon phase shifts ${(E}_{\mathrm{lab}}<$1.6 GeV), and established deuteron properties, via nonrelativistic inverse scattering. In our approach, the on-shell and off-shell properties of the potential can be independently varied: the on-shell scattering data are exactly fitted by construction while physically motivated off-shell features can be systematically included. This advantage is illustrated by the application of the procedure in the ${}^3{S}_1{-}^3{D}_1$ channel, where the deuteron wave function serves as off-shell input at the binding energy. The simplest potential thus constructed in this channel has rank 4. The deuteron wave function is nevertheless empirically undetermined at high momenta, prompting us to adopt as well as construct several model wave functions that all fit the low momentum deuteron data while allowing variations at high momenta. The effects of these off-shell variations on predicted nuclear matter properties are discussed. No off-shell information is included in the other channels, leading to potentials of rank either 1 or 2. With this simple model potential we perform standard Brueckner nuclear matter ground state calculations and compare the results with Machleidt’s using Bonn OBEP. The agreement is good in the $S$ channels and in the singlet $D_2$ channel. Other channels show larger discrepancies, the most significant of which coming from the ${}^3{P}_1$ and ${}^3{D}_1$ channels. These results are explained by the off-shell behavior of our model potential as compared to the Bonn OBEP. Further off-shell input, empirical and/or theoretical, will be explored in future improved versions of the model.

We have studied the ionic charge state dependence of the nuclear lifetime of the 35.5-keV first excited state of ${}^{125}$Te. We found for the 47${}^{+}$ and 48${}^{+}$ ions, 400 and 670 % variations with respect to the neutral-atom half-life (1.49 ns). These unusually large effects are due to the energetic blocking of the $K$-shell internal conversion as the charge state increases past ${47}^{+}$. For the ${46}^{+}$, we suggest a new internal conversion mode without any electron emission into the energy continuum.

The first excited state of ${}^{17}$Ne has been populated via relativistic Coulomb excitation with a radioactive beam of ${}^{17}$Ne on a ${}^{197}$Au target and the subsequent $\gamma$-ray decay has been observed. This $\frac{3}{2}$${}^{-}$ state is bound with respect to proton emission but unbound to two-proton decay. The measured $\gamma$-ray yield accounts for ${43}_{-14}^{+19\mathrm{}}$% of the predicted yield from an excitation cross section of $28$ mb. It is unlikely that the missing cross section can be attributed to two-proton emission because the lifetime of this branch would have to be a factor 1700 smaller than predicted by standard barrier penetration calculations.

The $\gamma$ decays of high spin states in ${}^{77}$Rb populated in the reaction ${}^{40}$Ca${(}^{40}$Ca,$3p)$${}^{77}$Rb were studied with the EUROGAM I $\gamma$-ray spectrometer at Daresbury Laboratory, in conjunction with the recoil mass separator. The data were used to extend or establish three positive parity and five negative parity bands in ${}^{77}$Rb. Level lifetimes and sidefeeding times were then measured with the NORDBALL $\gamma$-ray spectrometer, using the Doppler shift attenuation method. A very detailed level scheme including many weakly populated states was established and the bands were observed over large spin ranges. The deduced lifetimes demonstrate the high collectivity of the excited states and are consistent with their having large prolate deformations. The structures of the bands and their crossings are discussed in relation to the large shell gap at prolate deformation ${\beta }_2\approx 0.4$.

Mean lifetimes of 22 bound levels and upper lifetime limits of four more levels in ${}^{32}$P below an excitation energy of 6.4 MeV were deduced from the Doppler-shift attenuation of $\gamma$ rays produced in the inverse reaction ${}^2$H${(}^{31}$P$,p\gamma )$. Of these 26 levels, the lifetimes of six levels are reported here for the first time. The low-lying portion of the level scheme, the level lifetimes, and the $\gamma$-ray branchings and reduced transition probabilities have been compared with shell-model predictions. The overall agreement is reasonably good.

By using on-line mass separation of residues from heavy-ion-induced fusion-evaporation reactions, we studied the ${\beta }^{+}$/EC decay of the neutron-deficient isotopes ${}^{107}$Sb and ${}^{108}$Sb. A search for direct proton decay of ${}^{105}$Sb did not yield a conclusive result. The experimental $\beta$-decay half-lives of ${}^{104-108}$Sb are discussed with reference to results obtained from quasiparticle random-phase approximations, while the ${}^{108}$Sb${\to }^{108}$Sn and ${}^{107}$Sb${\to }^{107}$Sn level schemes are interpreted in comparison with shell model predictions.

Excitations in ${}^{192}$Po have been studied via in-beam $\gamma$-ray spectroscopy following the ${}^{164}$Er + 164 MeV ${}^{32}$S reaction. The experiment was performed at the ATLAS facility using ten Compton-suppressed Ge detectors and the Fragment Mass Analyzer. The $\alpha$ decay of ${}^{192}$Po has been used to identify prompt $\gamma$-ray transitions by means of the recoil decay tagging technique. The first three excited states of ${}^{192}$Po were established. The particle-core model has been successfully used to model these excitations and the quasiparticle random phase approximation has been applied to extract microscopic wave functions of the 2${}_1^{+}$ states.

Previous computations of the potential landscape with the shapes parametrized in terms of Cassini ovaloids are extended to collective dynamics at finite excitations. Taking fission as the most demanding example of large scale collective motion, transport coefficients are evaluated along a fission path. We concentrate on those for average motion, namely, stiffness $C$, friction $\gamma$, and inertia $M$. Their expressions are formulated within a locally harmonic approximation and with the help of linear response theory. Different approximations are examined and comparisons are made with both previous studies, which involved different descriptions of single-particle dynamics, and macroscopic models. Special attention is paid to an appropriate definition of the deformation of the nuclear density and its relation to that of the single-particle potential. For temperatures above 3 MeV the inertia agrees with that of irrotational flow to less than a factor of 2, but shows larger deviations below, in particular in its dependence on the shape. Also, friction exhibits large fluctuations along the fission path for small excitations. They get smoothed out above 3–4 MeV where $\gamma$ attains values in the range of the wall formula. For $T>~2$ MeV the inverse relaxation time $\beta =\gamma /M$ turns out to be rather insensitive to the shape and increases with $T$.

The coherent state model is extended to negative parity states. Thus three positive (ground, beta, and gamma) and three negative parity bands are projected out from three orthogonal states exhibiting both quadrupole and octupole deformations. An effective Hamiltonian acting on the space of projected states is constructed. For illustration, the numerical application is confined to the ground and $K^{\pi }{=0\mathrm{}}^{-}$ bands. In a certain range of deformations these bands show a “shell” structure. Good agreement with experimental data in ${}^{218,220,226}$Ra is obtained for energy levels and $E1\mathrm{}$ transition probabilities. Specific features like the interleaved structure, the low energy of the state $1^{-}$, and strong $E1\mathrm{}$ transitions are well described.

A method that generalizes the definition of identical bands was established. More than 100 available superdeformed bands were analyzed by means of the method and the number of identical bands as a function of criteria is presented. It is found that the quantization of incremental alignments depends very sensitively on the tolerance of the criterion for identical bands. The relation between the particle-rotor model and the present method is given.

The $\sigma$-$\omega$ model of nuclei is studied at leading order in the $1/N$ expansion thereby introducing the self-consistent Hartree approximation, the Dirac sea corrections and the one fermion loop meson self-energies in a unified way. For simplicity, the Dirac sea is further treated within a semiclassical expansion to all orders. The well-known Landau pole vacuum instability appearing in this kind of theory is removed by means of a scheme recently proposed in this context. The effect of such a removal on the low momentum effective parameters of the model, relevant to describe nuclear matter, finite nuclei, and $\mathrm{NN}$ force, is analyzed. The one fermion loop meson self-energies are found to have a sizeable contribution to these parameters. However, such contribution turns out to come mostly from the Landau poles and is thus spurious. We conclude that the fermionic loop can only be introduced consistently in the $\sigma$-$\omega$ nuclear model if the Landau pole problem is dealt with properly. We comment on the possibility of a nonperturbative formulation of the model.

We examine isovector and isoscalar neutron-proton correlations in an exactly solvable model based on the algebra SO(8). We look particularly closely at Gamow-Teller strength and double $\beta$ decay, both to isolate the effects of the two kinds of pairing and to test two approximation schemes: the renormalized neutron-proton quasiparticle random phase approximation (QRPA) and generalized BCS theory. When isoscalar pairing correlations become strong enough a phase transition occurs and the dependence of the Gamow-Teller ${\beta }^{+}$ strength on isospin changes in a dramatic and unfamiliar way, actually increasing as neutrons are added to an $N=Z$ core. Renormalization eliminates the well-known instabilities that plague the QRPA as the phase transition is approached, but only by unnaturally suppressing the isoscalar correlations. Generalized BCS theory, on the other hand, reproduces the Gamow-Teller strength more accurately in the isoscalar phase than in the usual isovector phase, even though its predictions for energies are equally good everywhere. It also mixes $T=0\mathrm{}$ and $T=1\mathrm{}$ pairing, but only on the isoscalar side of the phase transition.

A method is proposed and tested for the analysis of the so-called $\Delta I=2\mathrm{}$ staggering observed in nuclear rotational bands. We examine six superdeformed (SD) bands in five nuclei, among which only the SD bands $a$ and $e$ of the nucleus ${}^{149}$Gd seem to exhibit such staggering. However, we emphasize that the presence of a staggering may not necessarily imply the occurrence of a bifurcation. The mechanism which leads to the staggering in question is still to be clarified. It is shown that a similar staggering seen in normally deformed bands is a manifestation of band crossings.

Collective gyromagnetic ratios $g_R,$ microscopically calculated from Hartree-Fock plus BCS calculations using the ${\mathrm{SkM}}^{*}$ force, are found to be very different from the rough $Z/A$ estimates. It is pointed out that the latter disagree with the spectroscopic data in normally deformed states of even-even nuclei. The consequences of taking into account microscopic values of $g_R$ on the spectroscopic properties of odd superdeformed $A=190\mathrm{}$ nuclei are discussed. Quenching factors, for proton and neutron $g_s$ ratios, are tentatively proposed. Single-particle assignments postulated by experimentalists for the available data are confirmed by our consistent approach.

The intensities of primary γ-ray transitions following thermal and average resonance neutron capture have been found to display a dependence on the final-state $K$ quantum number. The apparent $K$-hindrance effect is significantly stronger in the thermal than in the average resonance case. After thermal neutron capture, the intensity distributions indicate that the “$K$-allowed” transitions are associated with a higher number of degrees of freedom than the “$K$-forbidden” transitions. Possible explanations for the observed phenomena are discussed.

The most consistently useful simple model for the study of odd deformed nuclei, the particle-rotor model (strong-coupling limit of the core-particle coupling model) has nevertheless been beset by a long-standing problem: It is necessary in many cases to introduce an ad hoc parameter that reduces the size of the Coriolis interaction coupling the collective and single-particle motions. Of the numerous suggestions put forward for the origin of this supplementary interaction, none of those actually tested by calculations has been accepted as the solution of the problem. In this paper we seek a solution for the difficulty within the framework of a general formalism that starts from the spherical shell model and is capable of treating an arbitrary linear combination of multipole and pairing forces. With the restriction of the interaction to the familiar sum of a quadrupole multipole force and a monopole pairing force, we have previously studied a semimicroscopic version of the formalism whose framework is nevertheless more comprehensive than any previously applied to the problem. We obtained solutions for low-lying bands of several strongly deformed odd rare-earth nuclei and found good agreement with experiment, except for an exaggerated staggering of levels for $K=$$\frac{1}{2}$ bands, which can be understood as a manifestation of the Coriolis attenuation problem. We argue that within the formalism utilized, the only way to improve the physics is to add interactions to the model Hamiltonian. We verify that by adding a magnetic dipole interaction of essentially fixed strength, we can fit the $K=$$\frac{1}{2}$ bands without destroying the agreement with other bands. In addition we show that our solution also fits ${}^{163}$Er, a classic test case of Coriolis attenuation that we had not previously studied. 

The damping mechanisms of the $\Delta$(1232) resonance in nuclei are studied by analyzing the quasifree decay reactions ${}^{12}$C$({\pi }^{+},{\pi }^{+}{p)}^{11}$B and ${}^{12}$C${(}^3$He,$t{\pi }^{+}{p)}^{11}$B and the $2p$ emission reactions ${}^{12}$C$({\pi }^{+}{,pp)}^{10}$B and ${}^{12}$C${(}^3$He,${tpp)}^{10}$B. The coincidence cross sections are calculated within the framework of the isobar-hole model. It is found that the $2p$ emission process induced by the decay of the $\Delta$ resonance in the nucleus can be consistently described by a $\pi +\rho {+g}^{\prime }$ model for the $\Delta +N\to N+N$ decay interaction.