In the ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}$($t$,$p$) reaction at a bombarding energy of 15.0 MeV, excitation energies have been measured for 53 levels up to $E_x=11.5\mathrm{}$ MeV. Angular distributions for 29 levels below 8.8 MeV have been compared with distorted-wave Born approximation calculations in order to make $L$ (and hence $J^{\pi }$) assignments. Measured cross sections are compared with absolute predictions with distorted-wave Born approximation calculations that use two-nucleon transfer amplitudes from a full $\mathrm{sd}$-shell-basis shell-model calculation.

NUCLEAR REACTIONS ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}$($t$,$p$)${}_{}{}^{32}{}_{}{}^{}\mathrm{Si}$; $E=15\mathrm{}$ MeV; measured $\sigma (E_p,\theta )$, $\theta =7.5\mathrm{}°-105\mathrm{}°$. ${}_{}{}^{32}{}_{}{}^{}\mathrm{Si}$ levels. DWBA microscopic analysis.

The stucture of ${}_{}{}^{139}{}_{}{}^{}\mathrm{Pm}$ is investigated through the ${\beta }^{+}$ decay of ${}_{}{}^{139}{}_{}{}^{}\mathrm{Sm}_{}^g{}_{}{}^{}$, whose decay half-life is measured to be 2.57 ± 0.10 min. A level scheme comprising 33 excited states and all the observed 79 transitions is constructed based on information obtained from $\gamma$-ray, ${\beta }^{+}$, and internal conversion electron spectroscopic measurements. Using the deduced beta decay $log\mathrm{ft}$ values and transition multipolarities, $J^{\pi }$ assignments are made to states in ${}_{}{}^{139}{}_{}{}^{}\mathrm{Pm}$ and to the ground state of ${}_{}{}^{139}{}_{}{}^{}\mathrm{Sm}$. The ${\beta }^{+}$ end-point energy measurements give a total decay energy $Q_{\mathrm{EC}}=4.10\mathrm{}\pm 0.15$ MeV for ${}_{}{}^{139}{}_{}{}^{}\mathrm{Sm}_{}^g{}_{}{}^{}$. Systematics of low-lying states in the odd-A, $N=78\mathrm{}$ isotones are discussed.

RADIOACTIVITY ${}_{}{}^{139}{}_{}{}^{}\mathrm{Sm}$ from ${}_{}{}^{144}{}_{}{}^{}\mathrm{Sm}$($p$,$p5n$) and ($p$,$6n$) ${}_{}{}^{139}{}_{}{}^{}\mathrm{Eu}\to ({\beta }^{+},\mathrm{EC})$; measured $T_{\frac{1}{2}}$, $E_{\gamma }$, $I_{\gamma }$, $I_{\mathrm{ce}}$, $E_{\beta }^{+}$, $\gamma -\gamma$, ${\beta }^{+}-\gamma$ coin, deduced $Q_{\mathrm{EC}}$. ${}_{}{}^{139}{}_{}{}^{}\mathrm{Pm}$ deduced level, $J$,$\pi$,$log\mathrm{ft}$, ICC, $\gamma$-multipolarity. Enriched targets, Ge(Li), Si(Li), intrinsic Ge, magnetic spectrometers.

The theory of shakeoff of inner-shell electrons in $\beta$ decay is reexamined. A resolution of the discrepancy that exists between theory and experimental data is provided in the ${\beta }^{-}$ decay cases. This comes about by considering the many-body aspects of the problem, and evaluating the wave functions involved in the initial and final states more exactly. The results indicate that agreement between the $K$-electron ejection probabilities $P_K$ and recent experimental results produced by different techniques is generally restored.

RADIOACTIVITY $K$-vacancy creation in beta decay calculations.

Beta decay properties ($t_{\frac{1}{2}}$, ${\overline{E}}_{\beta }$, ${\overline{E}}_{\gamma }$, ${\overline{E}}_n$, and $P_n$) are calculated for fission product nuclei by a statistical model and are found to be in good agreement with experiment.

RADIOACTIVITY Rb, Sr, I, Xe; calculated $T_{\frac{1}{2}}$, ${\overline{E}}_{\beta }$, ${\overline{E}}_{\gamma }$, ${\overline{E}}_n$, $P_n$; compared to experiment.

The $\frac{\epsilon }{{\beta }^{+}}$ decay of 23.0-min ${}_{}{}^{145}{}_{}{}^{}\mathrm{Gd}$ has been thoroughly studied with Ge(Li) and plastic scintillator detectors. A total of 326 $\gamma$ rays deexciting 136 levels in ${}_{}{}^{145}{}_{}{}^{}\mathrm{Eu}$ have been placed by this work. The available decay energy, $Q_{\epsilon }=5.07\mathrm{}\pm 0.06$ MeV, was measured by $\beta -\gamma$ coincidence techniques. $\frac{\epsilon }{{\beta }^{+}}$-decay branching ratios have been measured for several transitions, and a long standing anomaly in those ratios has been resolved by the new $Q_{\epsilon }$ value and the discovery of additional electron-capture decay. We have investigated the $\beta$-strength function for ${}_{}{}^{145}{}_{}{}^{}\mathrm{Gd}$ and discovered pronounced structure with resonances at 1042, 1819, 2584, and 4500 keV. The 1042-keV resonance is proposed to result from a ${\left(\pi d_{\frac{3}{2}}\right)}^2{\left(\nu s_{\frac{1}{2}}\right)}^{-1\mathrm{}}\to {\left(\pi d_{\frac{3}{2}}\right)}^1\beta$ transition, the 1919- and 2584-keV resonances from ${\left(\pi d_{\frac{5}{2}}\right)}^2\to {\left[\right(\pi d_{\frac{5}{2}})\otimes 2^{+}]}_{1,2}$ decays, and the very strong 4500-keV resonance from the ${\left(\pi h_{\frac{11}{2}}\right)}^2\to \left(\pi h_{\frac{11}{2}}\right)\otimes (\nu h_{\frac{9}{2}}+\nu f_{\frac{7}{2}}+\dots )$ transition across the shell closure.

RADIOACTIVITY ${}_{}{}^{145}{}_{}{}^{}\mathrm{Gd}$; measured $E_{\gamma }$, $\gamma -\gamma$ coin, $E_{\beta }$, $\beta -\gamma$ coin, $Q$, $t_{\frac{1}{2}}$, $x-\gamma$ coin, ${\gamma }^{\pm }-\gamma$ coin; deduced $\frac{\epsilon }{{\beta }^{+}}$ ratios, $log\mathrm{ft}$, $\beta$-strength function, missing continuum decay intensity. ${}_{}{}^{145}{}_{}{}^{}\mathrm{Eu}$; deduced levels, $J$, $\pi$; calculated level energies with shell model, weak-coupling model.

We delineate the conditions of interaction and density in extended Bose systems under which the single permanent of plane waves yielding the lowest energy expectation value deviates from the zero-momentum condensate. A potential $v\left(r\right)\mathrm{}$ independent of relative orbital angular momentum $L$ does not favor abnormal occupation at any density, provided its Fourier transform is non-negative. However, abnormal occupation can occur for simple reasonable choices of $v\left(r\right)\mathrm{}$, in particular, a repulsive square barrier. Considering $L$-dependent interactions, truncation of the partial wave expansion of the potential will ordinarily promote abnormal occupation in some density region. Several specific examples of abnormal momentum distributions are studied, and numerical results are given for potentials relevant to alpha-particle matter and liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$.

NUCLEAR STRUCTURE Infinite alpha matter, Hartree-Fock method, abnormal occupation of plane wave orbitals.

Hartree-Fock+BCS calculations of 15 even nuclei within and around the actinide region have been performed with the Skyrme SIII effective force. A careful optimization of the two parameters of the truncated expansion basis has been made for each nucleus. The iterative process has been carried out as far as to yield an excellent numerical convergence of quadrupole $Q_2$ and hexadecapole $Q_4$ moments (better than 0.1% for $Q_2$ and 1% for $Q_4$).Total binding energies have been reproduced up to ∼2 MeV. Charge radii have been found in agreement with experimental data to ∼1%, whereas the error on $Q_2$ and $Q_4$ moments (for $A\le 240$) were less than 5% and 25%, respectively. Single particle Hartree-Fock energy spectra are discussed and will be compared with experimental data in a subsequent paper. Finally, the deformation energy curves of two nuclei (${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$ and ${}_{}{}^{240}{}_{}{}^{}\mathrm{Pu}$) are displayed.

NUCLEAR STRUCTURE 15 heavy even nuclei from ${}_{}{}^{224}{}_{}{}^{}\mathrm{Ra}$ to ${}_{}{}^{260}{}_{}{}^{}104$ studied within Hartree-Fock+BCS using Skyrme SIII force. Binding energies, charge radii, quadrupole and hexadecapole moments, single particle energies calculated. Numerical convergence assessed.

Spectroscopic properties of 23 odd nuclei within and around the actinide region have been calculated according to a rotor plus quasiparticle approximation where the quasiparticle states have been extracted from self-consistent calculations discussed in a previous paper. The phenomenological parameters are only six force parameters fitted once for all to nuclear saturation properties, neutron and proton pairing gaps uniquely given by odd-even mass differences, and experimental ground band energies of neighboring nuclei. Excluding thus any elusive ad hoc parameter adjustment, this approach has successfully reproduced most of the experimentally confirmed rotational bands for both odd-neutron (thorium, uranium, and plutonium) and odd-proton (actinium, protactinium, neptunium, and americium) isotopes, assessing thus the validity of the whole approach and, in particular, the relevance of the self-consistent deformed mean fields yielded by the Skyrme $S\mathrm{III}$ effective force. Many bands previously assigned to be of a particle-vibration nature have not been found in our calculations. Their nonrotational character is thus confirmed. Reduced transition probabilities and static moments for $E2$ and $M1$ electromagnetic modes have been evaluated. Calculated magnetic and electric quadrupole moments have been shown to reproduce very well available data. Absolute intraband and interband $E2$ and $M1$ reduced transition probabilities have also been found in very good agreement with experimental results.

NUCLEAR STRUCTURE 23 heavy odd nuclei from ${}_{}{}^{229}{}_{}{}^{}\mathrm{Th}$, ${}_{}{}^{229}{}_{}{}^{}\mathrm{Ac}$ to ${}_{}{}^{241}{}_{}{}^{}\mathrm{Am}$, ${}_{}{}^{241}{}_{}{}^{}\mathrm{Pu}$ studied within rotor plus quasiparticle approximation. Quasiparticle states issued from Hartree-Fock plus BCS calculations using Skyrme $S\mathrm{III}$ force. Nuclear spectra, $E2$ and $M1$ moments and transition probabilities calculated.

The eikonal pole approximation to the multiple scattering Watson series is introduced and explored. For noncommuting potentials this approximation naturally defines the ordering of the $z$ coordinates of the scatterers and for commuting potentials leads to the Glauber multiple scattering series. It is shown that the cancellations in the Watson expansion which produce the usual form of Glauber theory are between the infinite series of reflection terms and the off-pole contribution of nonreflective ones. This generalizes the earlier result on cancellations for a two-particle target to targets of arbitrary size.

NUCLEAR REACTIONS Multiple scattering, derivation of Glauber high energy approximation from Watson series, commuting and non-commuting potentials.

The classical Hamiltonian of the interacting boson model is defined and expressed in terms of the conventional quadrupole variables. This is used in the analyses of the dynamics in the various limits of the model. The purpose is to determine the range and the features of the collective phenomena which the interacting boson model is capable of describing. In the commonly used version of the interacting boson model with one type of the $s$ and $d$ bosons and quartic interactions, this capability has certain limitations and the model should be used with care. A more sophisticated version of the interacting boson model with neutron and proton bosons is not discussed.

NUCLEAR STRUCTURE Interacting bosons, classical IBM Hamiltonian in quadrupole variables, phenomenological content of the IBM and its limitations.

The nuclear properties of the low lying states of even isotopes of Ca, Ti, Cr, and Fe are calculated in the framework of the broken pair approximation. The broken pair approximation configuration space for an even number of identical valence nucleons includes all the seniority ($\nu$) two components while for nonidentical (even-even) valence nucleons, it contains all configurations with $\nu \le 4$ except $\nu =4\mathrm{}$ proton components and $\nu =4\mathrm{}$ neutron components. The calculations have been carried out with a ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ core using two different sets of realistic interaction matrix elements: (i) the set reported by Kuo and Brown and its modified version due to McGrory; and (ii) a set of Tabakin interaction matrix elements which includes the second order Born term and core polarization effects. The effect of the truncation of the valence space has been examined in detail. The calculated energy spectra, quadrupole moments for the first $2^{+}$ states, and $E2$ transition rates, compare well with the corresponding shell model results (wherever available) as well as with the experiment.

NUCLEAR STRUCTURE Shell model, number conserving shell model, broken pair approximation, energy spectra, $E2$ transition rates, quadrupole moment, Ca, Ti, Cr, and Fe even isotopes.

A detailed study of the transition between the SU(5) and O(6) limit of the interacting boson model (IBA-1) has been performed in a schematic way. A comparison of the experimental excitation energies and $E2$ transition probabilities for neutron-rich Ru and Pd isotopes with this calculation shows that this mass region is well described in terms of this phase transition.

NUCLEAR STRUCTURE Transition between the SU(5) and O(6) limit of IBA-1, energy levels, $B\left(E2\right)$, comparison with experimental data for ${}_{}{}^{98-110}{}_{}{}^{}\mathrm{Ru}$, ${}_{}{}^{110-114}{}_{}{}^{}\mathrm{Pd}$.

Coulomb form factors for the $0_{\mathrm{gnd}}^{+}$→$2^{+}$ transitions in the even-even $1f_{\frac{7}{2}}$-shell nuclei are studied in terms of the shell model within the $f_{\frac{7}{2}}^n+f_{\frac{7}{2}}^{n-1\mathrm{}}{p}_{\frac{3}{2}}$ configurations and with the effective interactions. It is shown that the characteristics of the $C2$ form factors in the higher-momentum-transfer region, not explained by the simple $f_{\frac{7}{2}}^n$ model, can be interpreted by the mixing of the one-particle excitations into the $p_{\frac{3}{2}}$ orbit in the shell-model wave functions. $E2$ transition strengths and $Q$ moments are also discussed in connection with the $C2$ form factors.

NUCLEAR STRUCTURE ${}_{}{}^{42,44,46,48}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{46,48,50}{}_{}{}^{}\mathrm{Ti}$, ${}_{}{}^{50,52}{}_{}{}^{}\mathrm{Cr}$, ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$; calculated $C2$ form factors for inelastic electron scattering, $B\left(E2\right)$ transition strengths and $Q$ moments. Shell model within the $f_{\frac{7}{2}}^n+f_{\frac{7}{2}}^{n-1\mathrm{}}{p}_{\frac{3}{2}}$ configurations with effective interactions.

With the aid of an on-line isotope separator the decay of ${}_{}{}^{147}{}_{}{}^{}\mathrm{Dy}$ to levels in ${}_{}{}^{147}{}_{}{}^{}\mathrm{Tb}$ was investigated in a series of heavy-ion bombardments of rare earth targets. These data allow us to identify the $s_{\frac{1}{2}}$, $d_{\frac{3}{2}}$, $d_{\frac{5}{2}}$, and $g_{\frac{7}{2}}$ proton orbitals in ${}_{}{}^{147}{}_{}{}^{}\mathrm{Tb}$, a nucleus with one proton beyond the ${}_{64}{}^{146}{}_{}{}^{}\mathrm{Gd}_{82}^{}{}_{}{}^{}$ core.

RADIOACTIVITY ${}_{}{}^{147}{}_{}{}^{}\mathrm{Dy}$, measured $E_{\gamma }$, $I_{\gamma }$, $\gamma \gamma$ coinc; ${}_{}{}^{147}{}_{}{}^{}\mathrm{Tb}$ deduced levels, $J^{\pi }$.

The decay rate of $1^{+}$ ${}_{}{}^{90}{}_{}{}^{}\mathrm{Nb}_{}^m{}_{}{}^{}$ is observed via $E3$ conversion electrons to investigate if this $1^{+}$ isomer is populated by another isometric transition of extremely low energy. Such a transition could be of interest for perturbation studies, but has not been found.

NUCLEAR REACTIONS ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$($p$,$n$), $E=7.8\mathrm{}$ MeV; ${}_{}{}^{90}{}_{}{}^{}\mathrm{Nb}$ detected conversion electrons; measured $T_{\frac{1}{2}}$.

It is shown that the "extended time-dependent Hartree-Fock approximation" cannot be applied to two isolated crossings if a Markov approximation is employed. In a collision of two nucleons in a time varying single particle potential, energy is not conserved; the collision may be off shell by a few MeV.

NUCLEAR REACTIONS Heavy ion reactions, fusion, extended time-dependent Hartree-Fock approximation.

The 10.2 MeV state in ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$ has been confirmed to be $J^{\pi }=1^{+}$ by ($p$,$p^{\prime }$) and ($\alpha$, ${\alpha }^{\prime }$) experiments. The state was strongly excited by the ($p$,$p^{\prime }$) reaction at $E_p=65\mathrm{}$ MeV. Differential cross sections of the state are compared with a microscopic distorted-wave Born approximation calculation based on a shell model. The calculation overestimates the cross sections by a factor of 4.

NUCLEAR REACTIONS ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$($p$,$p^{\prime }$), $E=65\mathrm{}$ MeV, ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$($\alpha$,${\alpha }^{\prime }$), $E=70\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$; $J^{\pi }=1^{+}$ assigned for the 10.2 MeV level. Enriched target. DWBA analysis.

Low-lying one-particle, two-hole (1p-2h) intruder bands which coexist with hole states are established in ${}_{}{}^{83}{}_{}{}^{}\mathrm{Se}$ ($N=49\mathrm{}$) and are shown to exhibit properties similar to those of known intruder bands in odd-proton In ($Z=49\mathrm{}$) nuclei. Systematics of ($N=49\mathrm{}$) nuclei show that ${}_{}{}^{83}{}_{}{}^{}\mathrm{Se}$ ($Z=34\mathrm{}$) has the lowest-lying 1p-2h intruder state rather than midshell ${}_{}{}^{89}{}_{}{}^{}\mathrm{Zr}$ ($Z=40\mathrm{}$) as would be expected by comparing with the In isotopes. We discuss the well established occurrence of intruder bands in odd-proton nuclei in contrast to the paucity of such bands in odd-neutron nuclei, and suggest that the $Z=40\mathrm{}$ and 64 subshell closures inhibit the core collectivity necessary for the lowering of particle states and formation of intruder bands in odd-neutron nuclei.

RADIOACTIVITY ${}_{}{}^{83}{}_{}{}^{}\mathrm{As}$ decay measured $E_{\gamma }$, $I_{\gamma }$, $t_{\frac{1}{2}}$, ${}_{}{}^{83}{}_{}{}^{}\mathrm{Se}$ deduced levels, $J^{\pi }$. Ge(Li) detectors.

NUCLEAR STRUCTURE Coexistence in odd-neutron nuclei.