We have completed a compilation of experimental results for the electric quadrupole transition probability B(E2)↑ between the $0^{+}$ ground state and the first $2^{+}$ state in even-even nuclei. The adopted B(E2)↑ values have been employed to test the various systematic, empirical, and theoretical relationships proposed by several authors (Grodzins, Bohr and Mottelson, Wang et al., Ross and Bhaduri, Patnaik et al., Hamamoto, Casten, Möller and Nix, and Kumar) on a global, local, or regional basis. These systematics offer methods for making reasonable predictions of unmeasured B(E2) values. For nuclei away from closed shells, the SU(3) limit of the intermediate boson approximation implies that the B(E2)↑ values are proportional to ($e_{\mathrm{p}{N}_{\mathrm{p}+e_{\mathrm{n}{N}_{\mathrm{n}{)}^2}}}}$, where $e_{\mathrm{p}(e_{\mathrm{n}}}$) is the proton (neutron) effective charge and $N_{\mathrm{p}}$ ($N_{\mathrm{n}}$) refers to the number of valence protons (neutrons). This proportionality is consistent with the observed behavior of B(E2)↑ vs $N_{\mathrm{p}{N}_{\mathrm{n}}}$. For deformed nuclei and the actinides, the B(E2)↑ values calculated in a schematic single-particle ‘‘SU(3)’’ simulation or large single-j simulation of major shells successfully reproduce not only the empirical variation of the B(E2)↑ values but also the observed saturation of these values when plotted against $N_{\mathrm{p}{N}_{\mathrm{n}}}$. .AE

We show that with a saturating interaction V=-${\mathit{V}}_0$exp(-${\mathrm{r}}^2$/${\mathrm{a}}^2$)+${\mathrm{t}}_3$δ(${\mathrm{r}}_1$-${\mathrm{r}}_2$)δ(${\mathrm{r}}_1$-${\mathrm{r}}_3$), whose parameters are chosen, for any given range a, to fit the ground state binding energy and radius of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, the excitation energy of the breathing mode state decreases as the range a increases. The same interaction is used to calculate the energy of the deformed intrinsic ‘‘four-particle excitation.’’ It is found that the energy of this state is low for the smallest value of a. As we change a, the volume is not conserved. Our results are compared with those of a Toronto group who performed a symplectic shell model calculation with a B1 interaction. Their conclusion, that the energy of the breathing mode state is low, is valid only when the range a is large. We obtain energies for the ‘‘four-particle excitation’’ which are higher than theirs when we constrain the volume to be constant, but lower than theirs when we remove that condition. Singularities and instabilities in the variational approach are discussed.

A method of attributing K quantum numbers to the bands of odd-odd nuclei in the interacting boson-fermion-fermion model is presented. In a particular demonstration case with a $j_1$=(3/2 proton and a $j_2$=(5/2 neutron coupled to the SU(3) boson core in the interacting boson-fermion-fermion model, we show explicitly the formation of the band pattern and transformation of the interacting boson-fermion-fermion model wave functions to the truncated-weak-coupling basis and to the K-representation basis, which leads to the identification of exact or approximate K quantum numbers. The same method gives analogous results for any combination $j_1$ and $j_2$ of proton and neutron orbitals.

Explicit construction of Dyson, Holstein-Primakoff, and Schwinger representations for random-phase approximation phonon operators is given within Lie algebraic framework. It is shown that these representations emerge as exact boson realizations of quadrupole collective algebra, but the enforcement of SU(6) symmetry involves important constraints embodied in definite nonlinear conditions imposed on random-phase approximation phonon amplitudes. The constructed Schwinger representation could be employed to provide alternative approach to the interacting boson model parameters, avoiding standard procedures of mapping the shell-model SD subspace into the sd boson space.

The isovector giant dipole resonances in certain rapidly rotating calcium isotopes wherein the bulk of the angular momentum is of an aligned nature are analyzed microscopically in the framework of the random phase approximation. The shape and deformation of the above nuclei at high spins are determined by the Mottelson-Nilsson method for rotating light nuclei. The allowed angular velocities for these deformations are obtained by the Fermi liquid drop model. The splitting of the resonance energies and the changes in the photoabsorption cross sections caused by rotation are studied in these nuclei by a simple schematic model of a rotating anisotropic harmonic oscillator which is justifiable in the case of the light nuclei considered. The results obtained show the general broadening of resonance widths in these light nuclei similar to that observed in the case of rare earth nuclei. The narrowing down of resonance widths in certain cases at higher angular momenta, suspected in lighter nuclei experimentally, is also theoretically observed and explained in the case of ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ as due to the shrinking effect of nuclear deformation at high spins.

The ${}_{}{}^{149}{}_{}{}^{}\mathrm{Sm}$(d${,}^3$He) reaction has been used to populate levels in ${}_{}{}^{148}{}_{}{}^{}\mathrm{Pm}$. Nineteen new excited states have been observed below 1 MeV excitation energy in ${}_{}{}^{148}{}_{}{}^{}\mathrm{Pm}$. The possible astrophysical implications of these results are discussed.

In the region $E_{\mathrm{p}<2\mathrm{}}$ MeV, where two isobaric analog states with $J^{\pi }$${=(5/2\mathrm{}}^{\mathrm{-}}$ and ${(7/2\mathrm{}}^{\mathrm{-}}$ are expected, only three l=3 resonances have been found, at $E_{\mathrm{p}=1.204\mathrm{}}$, 1.451, and 1.513 MeV, all with $J^{\pi }$${=(5/2\mathrm{}}^{\mathrm{-}}$. .AE

Differential cross sections are presented for pion elastic and inelastic scattering from ${}_{}{}^{48}{}_{}{}^{}$,50Ti, ${}_{}{}^{52}{}_{}{}^{}\mathrm{Cr}$, and ${}_{}{}^{54}{}_{}{}^{}$,56Fe at $T_{\pi }$=180 MeV to the $0^{+}$, $5^{\mathrm{-}}$, and higher lying $2^{+}$, $3^{\mathrm{-}}$, and $4^{+}$ states. Inelastic-scattering data were analyzed using distorted-wave impulse-approximation calculations with collective-model transition densities. Matrix elements for most of the transitions have been extracted.

It is proposed that a measurement of the ratio of the charged pion asymmetries for the Δ(1232) resonance with a polarized electron beam on a polarized ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ target provides a sensitive test of the presence of Δ components in the ground state of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$. In the absence of final-state interactions and nonresonant contributions, it is estimated in a simple quasielastic scattering picture that the ratio of charged pion asymmetries would change by a factor of 2 for a 2% probability to find a Δ in the ground state of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$.

The ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$(α,2α${)}^{16}$O reaction at 140 MeV incident energy is analyzed in the framework of the distorted-wave impulse approximation. The bound state α wave functions in ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ are generated using the orthogonal condition model. The predicted results agree with the experimental data. They are also in rough accord with the results obtained with the Woods-Saxon α wave function.

Neutron and proton Gamow resonances are evaluated in ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ and they are used together with bound states as single-particle representation to calculate random phase approximation particle-hole excitations. A good account of the escape width corresponding to the particle-hole giant resonances is obtained.

Using the multiple scattering model for ultrarelativistic nuclear collisions, we have calculated the cross section of photons from the decay of neutral pions that are produced in the collision between two heavy ions at energies to be available in the heavy-ion collider. We have found that photons with low energies and at forward angles do not constitute an appreciable background to the bremsstrahlung photons due to the deacceleration of the nuclei. The bremsstrahlung photon can therefore serve as a probe of the nuclear stopping power in ultrarelativistic heavy-ion collisions.

I suggest that the anomaly at I${=6\mathrm{}}^{+}$ in the ground-state band of ${}_{}{}^{172}{}_{}{}^{}\mathrm{Os}$ results from the increase from two to three in the difference in nucleon number of the revolving cluster when I increases to I+2, and that the yrast cusp at I${=16\mathrm{}}^{+}$ corresponds to the change in structure from one revolving cluster to two revolving clusters. Values of the electric quadrupole moment are predicted.

By stressing the application of boson mapping techniques to the truncated collective branch of nuclear excitations, the usefulness of two recently developed methods for the treatment of spurious states are compared. It is shown why the identification proposed by Geyer et al. is superior to the use of the ‘‘Majorana’’ operator S as proposed by Park.

Studies of ${\pi }^{+}$/${\pi }^{\mathrm{-}}$ inelastic excitation of the giant quadrupole resonance in ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ have been interpreted as implying a quadrupole matrix element ratio for neutron to proton excitations of $M_{\mathrm{n}/M_{\mathrm{p}=3.8\mathrm{}}}$, and a reduced electric transition rate of B(E2)↑=1010±600 $e^2$${\mathrm{fm}}^4$. These values are in strong disagreement with the results of a large body of inelastic light-ion scattering data as well as recent electron scattering results, all of which are consistent with a predominantly isoscalar character for this resonance. A similar situation prevails for the scattering of 400-MeV ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and 1428-MeV ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$ ions where Coulomb excitation is important, and the inelastic cross sections are very sensitive to B(E2)↑ as well as the hadronic interaction strength. Studies of the photon decay of the giant quadrupole resonance are also in good agreement with random phase approximation calculations that imply a predominantly isoscalar character; this agreement would be destroyed if the interpretation of the pion experiment were correct.

Tacik et al. have studied the (π,3p) reaction seeking to find a clear signature of quasielastic π+p scattering followed by absorption of the pion on a nucleon pair. Their negative result reflects the importance of off-shell effects which arise from the small mass and short mean free path of the pion.

The energy-dependent, semiempirical, surface transparency factor of Kox et al. is accurately represented by a simple analytical expression. Total reaction cross sections obtained using this parametrization agree with Kox’s predictions to within four percent.

High resolution inelastic electron scattering measurements on ${}_{}{}^{140}{}_{}{}^{}\mathrm{Ce}$ have led to the identification of a $J^{\pi }$${=12\mathrm{}}^{\mathrm{-}}$ state at 6.31 MeV. This transition has only 8% of the calculated single-particle strength. The absence of strong transverse excitations is interpreted as evidence for fragmentation of the single-particle strength.

A previous proposal for a mixed-symmetry $1^{+}$ state in the O(6) nucleus ${}_{}{}^{134}{}_{}{}^{}\mathrm{Ba}$ is not supported by inelastic neutron scattering spectroscopic measurements. Instead it is suggested that the 2029- and 2088-keV levels share the properties of the lowest mixed-symmetry $2^{+}$ state of the neutron-proton interacting boson model.