The ${\beta }^{+}$–electron-capture decay of ${}_{}{}^{69}{}_{}{}^{}\mathrm{Se}$, produced via the ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$${(}^{32}$S, 2pn${)}^{69}$Se reaction, has been studied by β-delayed proton and γ-ray emissions using the recoil transport helium jet technique. The established decay scheme for ${}_{}{}^{69}{}_{}{}^{}\mathrm{Se}$ involves 13 up to now unreported γ emitting levels in ${}_{}{}^{69}{}_{}{}^{}\mathrm{As}$. The total proton branching ratio has been measured to be (4.5±1.0)×${10}^{\mathrm{-}4}$. The autocorrelation analysis of the delayed proton spectra indicates a level spacing in agreement with the back shifted Fermi gas model estimates. The Gamow-Teller beta strength distribution has been measured in 95% of the $Q_{\beta }$ window, up to 6.5 MeV excitation energy in ${}_{}{}^{69}{}_{}{}^{}\mathrm{As}$.

Beta-delayed proton decay was observed in ${}_{}{}^{148}{}_{}{}^{}\mathrm{Ho}$, ${}_{}{}^{150}{}_{}{}^{}\mathrm{Tm}$, and ${}_{}{}^{152}{}_{}{}^{}\mathrm{Lu}$ for the first time. Contrary to neighboring even-Z N=81 isotones, the proton spectra appear structureless and statistical in nature. Proton branching ratios for the high-spin isomers in these isotopes, based on the intensity of γ-ray transitions in the intermediate nuclei, are ($8_{\mathrm{-}2}^{+1\mathrm{}}$)×${10}^{\mathrm{-}4}$, (${1.2}_{\mathrm{-}0.4}^{+0.2\mathrm{}}$)×${10}^{\mathrm{-}2}$, and (1.5±0.7)×${10}^{\mathrm{-}1}$, respectively. The onset of proton emission in all three cases occurs at a proton to γ width ratio of about ${10}^{\mathrm{-}4}$. Protons were found to be in coincidence with x rays, γ rays, and positrons. Coincident K x rays served to identify the Z of the precursor, while the γ rays gave quantitative information about proton decay to excited states in the daughter nuclei. By comparing the final state branching ratios with statistical model calculations, it was concluded that ${}_{}{}^{148}{}_{}{}^{}\mathrm{Ho}$ and ${}_{}{}^{150}{}_{}{}^{}\mathrm{Tm}$ both have isomers with probable spin values of $1^{+}$ and $6^{\mathrm{-}}$. Statistical model calculations with ‘‘standard’’ prescriptions for level densities and γ widths, and with a reduced level density parameter are compared to experiment. To reproduce the shape of the proton spectrum it was necessary to assume Gaussian-shaped Gamow-Teller β strength functions centered near 8 MeV excitation energy. In the course of these experiments β-delayed proton emission in ${}_{}{}^{148}{}_{}{}^{}\mathrm{Er}$ was also identified.

The level structure of ${}_{}{}^{101}{}_{}{}^{}\mathrm{Y}$ has been studied through the β decay of ${}_{}{}^{101}{}_{}{}^{}\mathrm{Sr}$. Ninety-six γ rays are placed in a level scheme with 34 levels. The first 14 levels of ${}_{}{}^{101}{}_{}{}^{}\mathrm{Y}$ (below 1.1 MeV) are identified as members of the four rotational bands associated with the Nilsson orbitals (with bandhead energies in keV) (5/2[422] (0), (3/2[301] (510), (5/2[303] (666), and 1/2[301] (890). Above 1.2 MeV occur six low-spin (I≤(7/2) levels that have features expected for members of 1/2[431] and (3/2[431] bands, but it is not possible to make unambiguous assignments of all six levels to these two bands. The level energies and γ-decay patterns (both intraband and interband) are well reproduced by simple particle-rotor calculations consisting of single quasiparticles coupled to an axially symmetric core. As is the case for ${}_{}{}^{99}{}_{}{}^{}\mathrm{Y}$, the rotational structure of ${}_{}{}^{101}{}_{}{}^{}\mathrm{Y}$ indicates an axially symmetric deformation ε near the middle of the range of 0.3<ε<0.4. Similarities and differences between the bands observed in ${}_{}{}^{99}{}_{}{}^{}\mathrm{Y}$ and ${}_{}{}^{101}{}_{}{}^{}\mathrm{Y}$ are discussed and compared to model predictions.

The β-γ angular correlations for the decay of ${}_{}{}^{20}{}_{}{}^{}\mathrm{Na}$ and ${}_{}{}^{20}{}_{}{}^{}\mathrm{F}$ to the 1.633 MeV state of ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ have been measured using a twenty-detector system of cylindrical symmetry. ${}_{}{}^{20}{}_{}{}^{}\mathrm{Na}$ was produced by the ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$(p,n${)}^{20}$Na reaction using a 19 MeV proton beam, and ${}_{}{}^{20}{}_{}{}^{}\mathrm{F}$ was produced by the reaction ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$(d,p${)}^{20}$F using ${\mathrm{SF}}_6$ gas and 4 MeV deuterons. The activated gasses were continuously transferred, through a thin capillary, from the target cell into the source cell in the center of the correlation apparatus. Two γ detectors and 16 β detector telescopes allowed for the simultaneous measurements of β-γ coincidences at 0°, 25°, 45°, 65°, 90°, 115°, 135°, 155°, and 180°, and at their symmetric counterparts with respect to the 0°–180° direction. The β-γ correlation was also measured for the first-forbidden ${\beta }^{\mathrm{-}}$ decay of ${}_{}{}^{124}{}_{}{}^{}\mathrm{Sb}$, in order to confirm the computed attenuation in measured anisotropy caused by the finite geometry of the detectors and the source cell. The correlation function is denoted by ${\mathit{W}}_{\pm }$(${\mathrm{\theta }}_{\mathrm{\beta }\mathrm{-}\gamma }$)=1+${\mathrm{\alpha }}_{\pm }$(E)(pE${)}^2$${\cos }^2$${\mathrm{\theta }}_{\mathrm{\beta }\mathrm{-}\gamma }$. The ° subscripts refer to electron or positron decay, p is the beta momentum, and E is the beta total energy in MeV. The present result for ${}_{}{}^{20}{}_{}{}^{}\mathrm{Na}$(β-γ) correlation is ${\mathrm{\alpha }}_{\mathrm{-}}$(E)=(-4.45±0.31)×${10}^{\mathrm{-}3}$E+(1.87±0.42)×${10}^{\mathrm{-}4}$${\mathit{E}}^2$. The least squares fit to the energy dependence for ${}_{}{}^{20}{}_{}{}^{}\mathrm{F}$ was performed by assuming the quadratic energy dependence measured for ${}_{}{}^{20}{}_{}{}^{}\mathrm{Na}$, and the linear term in ${\alpha }_{+}$(E) yielded ${\mathrm{\alpha }}_{+}$(E)=(0.08±0.16)×${10}^{\mathrm{-}3}$E.

First and second class induced pseudotensor form factors ($d_{\mathrm{I}}$ and $d_{\mathrm{II}}$) were evaluated by combining the linear energy dependences and yielded $d_{\mathrm{II}/\mathrm{Ac}=\mathrm{-}1.1\pm 0.7}$ and $d_{\mathrm{I}/\mathrm{Ac}=11.3\mathrm{}\pm 0.7}$. The 1977 Calaprice calculations for the value of the second-forbidden axial vector form factor $j_2$ were used. Assuming the Calaprice prediction for $j_2$, $j_3$ could be deduced from the quadratic term of the energy dependence of the asymmetry. We obtained $j_3$=-(19.5±3.0)×${10}^4$. We conclude that the angular correlations in mass 20 are close to and may be in agreement with expectations based on conserved vector current theory. Our best value for second class axial currents, $d_{\mathrm{II}/\mathrm{Ac}=\mathrm{-}1.1\pm 0.7}$, is at the level of 10% of the weak magnetism term; however, the statistical error given and the large uncertainty in $j_2$, derived from shell model wave functions, preclude a more definite statement regarding the existence of second class currents.

Data on the nuclear equation of state from a number of different sources, from nuclei, high energy nuclear collisions, supernova, and neutron stars are analyzed. The current situation concerning supernova simulations is critically appraised. It is found that simulations that have achieved a prompt ejection do so with an equation of state that is too soft to support the measured masses of several known neutron stars. It is concluded that supernova explosions have not been proven to provide a significant constraint on the nuclear equation of state. Additionally it is concluded that the theoretical bias used to interpret data on neutron star masses as if they belonged to a population all having the same mass (of 1.4$M_{\odot }$) is unjustified. Evidence from the various nuclear data and neutron star masses favor a high compression modulus, K≊300 MeV. No definitive statement can be made about the equation of state at higher density, save that the neutron star equation of state must be moderately stiff to accommodate neutron stars of mass ≊1.85$M_{\odot }$.

The low-energy spectroscopy of odd-A nuclei in the mass region A∼219–229 is modeled by coupling states of a deformed shell model including octupole deformation to a reflection-asymmetric rotor core. Theory and experiment are compared for the nuclei in which data are available: ${}_{}{}^{219}{}_{}{}^{}$,221,223,225Rn, ${}_{}{}^{221}{}_{}{}^{}$,223,225,227Fr, ${}_{}{}^{219,221,223,225,227}{}_{}{}^{}\mathrm{Ra}$, ${}_{}{}^{219,223,225,227,229}{}_{}{}^{}\mathrm{Ac}$ ${}_{}{}^{221,223,225,227,229}{}_{}{}^{}\mathrm{Th}$, and ${}_{}{}^{229}{}_{}{}^{}\mathrm{Pa}$. Overall agreement requires an octupole deformation ${\beta }_3$∼0.1. The results throughout the region are synthesized to evaluate the model.

The multiphonon method based on $K^{\pi }$${=0\mathrm{}}^{\mathrm{-}}$ and $K^{\pi }$${=0\mathrm{}}^{+}$ phonons is applied to heavy mass deformed even nuclei, such as Th, U, and Pu isotopes. Special emphasis is put on the location and properties of the ‘‘two phonon’’ states. Relative to an harmonic situation, the calculated energy spectra are systematically dilated. The octupole vibrations with $K^{\pi }$${=0\mathrm{}}^{\mathrm{-}}$ present larger anharmonicities than the vibrations $K^{\pi }$${=0\mathrm{}}^{+}$ which, in these nuclei, are found to be mainly of pairing nature. The two modes appear to be weakly coupled. The ‘‘two phonon’’ states are predicted to have an energy of about 1.7 to 2.0 MeV and keep some collective character through their electromagnetic transitions to the ‘‘one phonon’’ states. These conclusions are at variance with those of the quasiparticle phonon nuclear model of Soloviev et al.

The analytical wave functions for the ${\mathrm{SO}}_7$, ${\mathrm{SU}}_3$, and ${\mathrm{SU}}_2$×${\mathrm{SO}}_3$ limits of the fermion dynamic symmetry model are constructed. These wave functions along with the already known wave functions for the ${\mathrm{SU}}_2$×${\mathrm{SO}}_5$ and ${\mathrm{SO}}_6$ limits of fermion dynamic symmetry model are cast into such a form that their relation with the wave functions of the interacting boson model are vivid and transparent. According to the correspondence relation, the intrinsic wave functions for the interacting boson model ${\mathrm{SU}}_3$ limit are constructed from its fermion counterpart and analytic expressions are given for the ${\mathrm{SU}}_6$⊃${\mathrm{SU}}_3$ isoscalar factors. The correlation between the D pair abundance in the ground states and the interaction strength is discussed.

To take systematic account of thermal correlation effect on the mean field, the thermal random phase approximation formalism is extended based on the thermofield dynamics scheme. The random phase approximation phonon operator is expressed in terms of the thermofield dynamics quasiparticle operators with a tilde as well as those without a tilde, and the increase of the dimensionality of variational parameter manifold enables us to derive the extended thermal random phase approximation equation from deeper minimum of grand potential. It is shown that the extended thermal random phase approximation equation is justified also from viewpoint of time-dependent formalism. The method of constrained variation applied to the first extended thermal random phase approximation can be straightforwardly generalized to the second, or higher extended thermal random phase approximation. Extended expressions are given also for the stability condition of thermal Hartree-Fock-Bogoliubov approximation and the energy-weighted sum rule.

Muonic transition energies between low-lying states in ${\mu }^{\mathrm{-}}$${\mathrm{-}}^{208}$Pb have been measured in a precision experiment using a Compton suppression spectrometer. Nuclear charge parameters and nuclear polarization corrections have been adjusted to the data. In particular, experimental correlations between the nuclear polarization corrections of the lower muonic levels have been established. A set of nuclear charge parameters reproducing all the experimental transition energies can only be obtained by assuming an inversion in magnitude of the nuclear polarization corrections not only for the 2p states, but also for the two 3p states. Such a result is unexplained by present theoretical models, but corroborates the findings of a recent experiment concerning the 2p states in ${\mu }^{\mathrm{-}}$${\mathrm{-}}^{90}$Zr. Using our best-fit parameters, a ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ rms radius of 〈$r^2$${〉}^{1/2}$=5.5031(11) fm has been obtained.

We present the detailed results of calculations of excitation-energy spectra, quadrupole and magnetic moments, and B(E2) and B(M1) values for the odd-odd ${}_{}{}^{180}{}_{}{}^{}$,182,184Re isotopes in the framework of the interacting-boson-fermion-fermion approximation model. Also, calculations are presented for both positive- and negative-parity excitations in the nearby odd-mass Re and Os nuclides and for collective states in the even-even Os core nuclides. The calculated results are compared with experimental data.

Impulse approximation and isovector pion-exchange current contributions to the trinucleon magnetic moments are calculated using wave functions generated from solutions of the configuration-space form of the Faddeev equations for the Reid soft core, Argonne ${\mathrm{V}}_{14}$, and super-soft-core C nucleon-nucleon force models and the Tucson-Melbourne or Brazilian three-nucleon force models. Numerical results for solutions with two-body partial waves having j≤4 (up to 34 channels) are reported. Agreement between theory and experiment appears reasonable for these nonrelativistic Hamiltonians which are restricted to one-pion exchange currents.

Calculations of the trinucleon S- and D-wave asymptotic normalization constants, with and without Coulomb effects, are extended to include all two-body partial waves up to j≤4 (34 three-body channels). Wave functions were generated with configuration-space, Faddeev-type equations for Hamiltonians based upon the two-body forces of Reid and the Argonne group, plus the Tucson-Melbourne and Brazilian model three-body forces. Comparison with previously published results is made. Results for $C_S$, $C_D$, η, and $D_2$ are interpolated as a function of binding to extract best estimates for ${}_{}{}^3{}_{}{}^{}\mathrm{H}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$. In agreement with our earlier (j<=1) calculations, we find that Coulomb effects increase the S-wave asymptotic normalization of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ by less than 1% over that of ${}_{}{}^3{}_{}{}^{}\mathrm{H}$ and that Coulomb effects decrease the D-wave asymptotic normalization of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ relative to that of ${}_{}{}^3{}_{}{}^{}\mathrm{H}$ by about 6%. The distorted-wave Born approximation D-wave parameter $D_2^C$ for ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ is almost identical to $D_2$ for ${}_{}{}^3{}_{}{}^{}\mathrm{H}$. Finally, we predict the ratio of the the D-wave to S-wave asymptotic normalization constants to be η${(}^3$H)≃0.046 and ${\eta }^C$${(}^3$He)≃0.043. .AE

The configuration-space Faddeev equations for the trinucleon ground states are solved for the Paris, Nijmegen, and (coordinate-space version) Bonn potentials, both with and without a Coulomb interaction. These momentum-dependent forces are structurally identical, but have different functional forms parametrizing their radial dependence. Our triton binding energies agree with some previous results for the Paris potential and with all previous Bonn results, and our new Nijmegen solutions exhibit binding commensurate with all other ‘‘realistic’’ potentials except the Bonn. Other model properties are also calculated, including such observables as the rms radii, asymptotic normalization constants, and charge densities.

The concepts of internal transformation brackets and quasi-Euler angles are introduced in this paper. With their help, the transformation brackets of hyperspherical harmonics of four-body systems with arbitrary masses can be expressed by those of three-body systems.

The electromagnetic decays of low-spin states of ${}_{}{}^{198}{}_{}{}^{}\mathrm{Pt}$ have been investigated by detecting γ rays and internal conversion electrons following inelastic proton scattering at $E_{\mathrm{p}=12.3\mathrm{}}$ MeV. The γ-ray decay of the 914-keV $0^{+}$ state is confirmed, branching ratios for other states have been measured, and a newly observed level at 2603 keV is suggested as a possible core excited octupole state.

The thin, triple-foil transient field technique has been used to measure the g factors of the first excited $2^{+}$ states of the even-even ${}_{}{}^{122\mathrm{-}130}{}_{}{}^{}\mathrm{Te}$ isotopes. The general trend of the measured g factors is similar to that seen for other even-even isotopic sequences in this mass region; however, the g factor of ${}_{}{}^{126}{}_{}{}^{}\mathrm{Te}$ is measured to be significantly greater than the value reported in a recent experiment.

The levels of ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$ have been studied by inelastic proton scattering at $E_{\mathrm{p}}$=65 MeV. The fine structure of the low-energy octupole resonance in ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$ has been observed. An octupole strength of ∼18% of the energy-weighted sum rule is obtained for the fragmented $3^{\mathrm{-}}$ states at $E_x$<12 MeV. This sum rule strength is consistent with a simple shell model estimate.

We have measured the cross section of the ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$${(}^6$Li${,}^8$He${)}^{25}$Si reaction. At a scattering angle of 5.5° and a beam energy of 92.5 MeV, we find the laboratory cross section to populate the ${}_{}{}^{25}{}_{}{}^{}\mathrm{Si}$ ground state doublet to be 3.6±1.0 nb/sr and the cross section to populate the 0.82 MeV second excited state to be ≊200 pb/sr. We also measured the ${(}^6$Li${,}^8$He) reaction for ${}_{}{}^{64}{}_{}{}^{}\mathrm{Zn}$ and ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ targets. We find yields of ≊250 pb/sr and <300 pb/sr, respectively. This experiment represents the first observation of the ${(}^6$Li${,}^8$He) exotic nuclear reaction.

The excitation function of the 15.11 MeV ($1^{+}$,T=1) state in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ has been measured by using the (π,π’γ) angular correlation technique. By this method, the background can be suppressed substantially. The relative cross section ratio of the 15.11 MeV ($1^{+}$,T=1) and the 12.71 MeV ($1^{+}$,T=0) state as a function of the pion incident energy is found to show a resonancelike behavior in the region of the Δ resonance, in agreement with previous measurements of Morris et al.