A generalized approximation to seniority shell model, based on the number conserving quasiparticle theory, is presented which includes the cases where both neutrons and protons are present in the valence shells. The numerical calculations are carried out for even Zr isotopes. The results obtained compare well with the corresponding exact shell model results, demonstrating thereby the validity of the present approximation for this nuclear region.

NUCLEAR STRUCTURE Shell Model, Seniority Shell Model, Broken-Pair Approximation (BPA), Generalized BPA, Zr-isotopes

The recently suggested method of Bassichis and Strayer is compared with that of Révai and generalized for solving the $A$-body Schrödinger equation with $A>\mathrm{}1\mathrm{}$.

NUCLEAR STRUCTURE Schrödinger equation, separable potential, effective interaction in model space.

A simple method of imposing orthogonality constraints upon the relevant bound and continuum waves involved in the calculation of ($p$,${\pi }^{+}$) and other proton induced reactions is presented.

NUCLEAR REACTIONS Orthogonality relations for optical model and bound nuclear wave functions.

Electromagnetic corrections are calculated for electron capture to positron decay ratios. The effects are found to be finite but small. Particular application is made to the case of ${}_{}{}^{22}{}_{}{}^{}\mathrm{Na}$.

RADIOACTIVITY Calculated radiative corrections to $\frac{\epsilon }{{\beta }^{+}}$.

The transformation of scattering-matrix elements from a representation appropriate for particle channels to one that describes photon channels is rederived. Previous derivations have ignored an ambiguity in the relative phase of the vector potential for magnetic and electric multipole radiation. The resultant ambiguity in the $S$-matrix transformation seems to be a source of confusion about the relative phases of the various terms that contribute to the polarization of particles produced in photonuclear reactions.

NUCLEAR REACTIONS Transformation of $S$-matrix elements from particle to photon channels. Polarization of particles produced in photonuclear reactions.

Recurrence relations among all allowed radial matrix elements for Coulomb excitation are derived by making use of a first order matrix differential equation for the nonrelativistic point Coulomb radial wave functions. Explicit recurrence relations that involve a change by one unit of any one of the angular momentum labels are given for the cases of the point Coulomb matrix elements, the indefinite integral from some radius $R$ to infinity, and the point Coulomb matrix elements with retardation.

NUCLEAR REACTIONS Scattering theory, Coulomb excitation matrix elements.

The ${}_{}{}^{119,117}{}_{}{}^{}\mathrm{Sn}$($p$,$t$) reactions have been studied at $E_p=52\mathrm{}$ MeV. The angle integrated cross sections ($10°\le {\theta }_{\mathrm{c}.\mathrm{m}.\mathrm{}}\le 50°$) for $l=0\mathrm{} \mathrm{and} 2$ transfers have been compared with the corresponding ones in the neighboring even isotopes. About a 50% reduction in strength for g.s. ($l=0\mathrm{}$) transitions in odd isotopes has been observed. It is in agreement with the interpretation of Fleming et al. as due to a blocking effect. However, in contrast to the observation of Fleming et al., it is argued that such blocking may not be present for $l=2\mathrm{}$ transitions in these nuclei.

NUCLEAR REACTIONS ${}_{}{}^{119,117}{}_{}{}^{}\mathrm{Sn}$($p$,$t$) $E=52\mathrm{}$ MeV, measured $\sigma \left(\theta \right)$; enriched targets.

The recent ($d$,$p$) and ($\alpha$,${}_{}{}^3{}_{}{}^{}\mathrm{He}$) experiment on ${}_{}{}^{92,94}{}_{}{}^{}\mathrm{Zr}$ shows a large fragmentation of the $1h_{\frac{11}{2}}$ neutron single particle strength. This fragmentation has been explained in a semimicroscopic model which couples the neutron quasiparticle motion to the quadrupole and the octupole vibrations of the neighboring even-even core. The calculated results are in good agreement with the experimental data.

NUCLEAR STRUCTURE ${}_{}{}^{93,95}{}_{}{}^{}\mathrm{Zr}$; Calculated $\frac{{11}^{-}}{2}$ levels, $S$, Quasi-particle-phonon coupling

The maximum energy available for dissipation in the thermal-neutron induced fission of ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}$ has been determined on the basis of the calculated (static) potential energy and the experimental post-scission data. High dissipation is found to be incompatible with experiment.

RADIOACTIVITY, FISSION ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}$($n_{\mathrm{th}}$,$f$); calculated energy dissipation.

Level structures up to 3000 keV in ${}_{}{}^{190}{}_{}{}^{}\mathrm{Os}$ and ${}_{}{}^{192}{}_{}{}^{}\mathrm{Os}$ have been studied using the ${}_{}{}^{191}{}_{}{}^{}\mathrm{Ir}$ and ${}_{}{}^{193}{}_{}{}^{}\mathrm{Ir}$ ($t$,$\alpha$) proton pickup reactions with 15 MeV tritons. The $\alpha$-particle spectra were obtained with the quadrupole-dipole-dipole-dipole magnetic spectrometer with peak widths of ∼11 keV (full width half maximum). This reaction strongly excites the $I,K^{\pi }=4,4^{+}$ levels at 1162 keV in ${}_{}{}^{190}{}_{}{}^{}\mathrm{Os}$ and at 1070 keV in ${}_{}{}^{192}{}_{}{}^{}\mathrm{Os}$, which were previously interpreted as two-phonon $\gamma$-vibrational states. The large two-quasiproton amplitude is reasonably explained by assuming single-phonon hexadecapole vibrations which involve the $\left\{\frac{5}{2} \mathrm{}\right[402], \frac{3}{2} \mathrm{}[402\left]\right\}$ configuration. Many two-quasiproton states are observed in the energy region 2000-3000 keV. The strongest peaks found at an excitation energy of ∼2600 keV in both ${}_{}{}^{190}{}_{}{}^{}\mathrm{Os}$ and ${}_{}{}^{192}{}_{}{}^{}\mathrm{Os}$ may be the remaining portions of the two-quasiproton ${\left\{\frac{5}{2} \mathrm{}\right[402], \frac{3}{2} \mathrm{}[402\left]\right\}}_{I,K^{\pi }=4,4^{+}}$ states.

NUCLEAR REACTIONS ${}_{}{}^{191,193}{}_{}{}^{}\mathrm{Ir}$($t$,$\alpha$) ${}_{}{}^{190,192}{}_{}{}^{}\mathrm{Os}$, $E_t=15\mathrm{}$ MeV: measured $\sigma \left(E_{\alpha }\right)$; enriched targets; analyses, DWBA including the ($t-\alpha -{\alpha }^{\prime }$) channel, the strong coupling model, RPA.

Excitation functions and angular distributions of the reactions ${}_{}{}^{28,30}{}_{}{}^{}\mathrm{Si}$($\alpha$,${\gamma }_0$) were used to study the distribution of $E2\mathrm{}$ strength in the energy regions 11-21 MeV of ${}_{}{}^{32,34}{}_{}{}^{}\mathrm{Si}$, as well as to probe the importance of isospin in the decay of the $E1$ giant resonance in these nuclei. It was found that the $E2\mathrm{}$ strength in the ($\gamma$, ${\alpha }_0$) channel is widely distributed and accounts for about 12% of the energy weighted isoscalar sum rule in each nucleus. Together with the $E2\mathrm{}$ strength observed in lower resonances, about 45% of the sum rule is accounted for in ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$ and 34% in ${}_{}{}^{34}{}_{}{}^{}\mathrm{S}$, where the measurements on the lower resonances are incomplete. The spreading of the $E2\mathrm{}$ strength can be attributed to the mixing of $n\mathrm{p}-n\mathrm{h}$ configurations into the basic 1p-1h excitations of the $E2\mathrm{}$ resonance, and the large $E2\mathrm{}$ strength is attributed to the presence of a direct or semidirect component in the ($\gamma$,${\alpha }_0$) process. A comparison of the $E1$ strengths in the ($\gamma$,${\alpha }_0$) channel of the giant dipole resonances in ${}_{}{}^{32,34}{}_{}{}^{}\mathrm{S}$ indicates that isospin conservation is important in these reactions. The relative weakness of the $E1$ ($\gamma$,${\alpha }_0$) strength in ${}_{}{}^{34}{}_{}{}^{}\mathrm{S}$ compared to the $E2\mathrm{}$ strength is attributed to the relative purity of the 1p-1h character of the $E1$ resonance as compared to that of the $E2\mathrm{}$ resonance.

NUCLEAR REACTIONS ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$($\alpha$,${\gamma }_0$), $E=5-16\mathrm{}$ MeV; ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}$($\alpha$,${\gamma }_0$), $E=4-15\mathrm{}$ MeV; measured $\sigma (E,E_{\gamma },{\ominus }_{\gamma })$. ${}_{}{}^{32,34}{}_{}{}^{}\mathrm{S}$ deduced $E1\mathrm{}$, $E2\mathrm{}$ strengths. Enriched targets.

The ${}_{}{}^{46}{}_{}{}^{}\mathrm{Ti}$($p$,$p^{\prime }\gamma$),${}_{}{}^{46}{}_{}{}^{}\mathrm{Ti}$ reaction has been studied from $E_p=2.25\mathrm{} \mathrm{to} 3.10$ MeV with an overall energy resolution of about 350 eV. The magnitudes and relative signs of inelastic decay amplitudes were determined for the fine-structure resonances of a $\frac{3}{2^{-}}$ analog state in ${}_{}{}^{47}{}_{}{}^{}\mathrm{V}$. The relative sign of the decay amplitudes is constant for the fine-structure states, in agreement with both the theoretical prediction and the one previous measurement.

NUCLEAR REACTIONS ${}_{}{}^{46}{}_{}{}^{}\mathrm{Ti}$($p$,$p^{\prime }$); $E_p=2.25-3.10\mathrm{}$ MeV, enriched target, deduced resonance parameters ${\Gamma }_p$, ${\Gamma }_{p^{\prime }}(j^{\prime }=\frac{1}{2})$, ${\Gamma }_{p^{\prime }}(j^{\prime }=\frac{3}{2})$, ${\gamma }_{p^{\prime }}(j^{\prime }=\frac{1}{2}){\gamma }_{p^{\prime }}(j^{\prime }=\frac{3}{2})$, analog properties.

The ${}_{}{}^{41}{}_{}{}^{}\mathrm{Ca}$($d$,${}_{}{}^3{}_{}{}^{}\mathrm{He}$)${}_{}{}^{40}{}_{}{}^{}\mathrm{K}$ reaction has been studied at a bombarding energy of 20 MeV using a multigap magnetic spectrometer. Energy levels in ${}_{}{}^{40}{}_{}{}^{}\mathrm{K}$ up to 3 MeV excitation energy have been observed. All the levels coming from the [$1f_{\frac{7}{2^{-}}}{\left(1\mathrm{}{d}_{\frac{3}{2}}\right)}^{-1\mathrm{}}$] particle-hole configuration have been well resolved. Distorted wave analysis using exact finite range calculations have provided good values of the spectroscopic strengths for the observed particle-hole multiplets.

NUCLEAR REACTIONS ${}_{}{}^{41}{}_{}{}^{}\mathrm{Ca}$($d$,${}_{}{}^3{}_{}{}^{}\mathrm{He}$)${}_{}{}^{40}{}_{}{}^{}\mathrm{K}$, $E=20\mathrm{}$ MeV; measured $\sigma (E_{{}_{}{}^3{}_{}{}^{}\mathrm{He}},\theta )$ and spectroscopic factors. Enriched radioactive target.

The ($p$,$n$) reaction to ground- and excited-state analogs on ${}_{}{}^{144,148,150,152}{}_{}{}^{}\mathrm{Sm}$ is investigated at bombarding energies of 20.0, 24.5, and 26.0 MeV. Ground-state analog ($p$,$n$) angular distributions are measured at all three bombarding energies. Excited-analog $2^{+}$ and $3^{-}$ ($p$,$n$) angular distributions are obtained at 24.5 and 26.0 MeV. For ${}_{}{}^{152}{}_{}{}^{}\mathrm{Sm}$, the ground- and $2^{+}$ excited-analog neutron groups are not resolved, but an angular distribution for one $4^{+}$ excited-analog transition is obtained. Coupled-channel calculations indicate substantial three-step destructive interference which reduces the ground-analog cross sections and accounts substantially for the departure of these cross sections from a simple proportionality on neutron excess. A corresponding effect on the $2^{+}$ excited-analogs due to a set of four-step processes proceeding through one- and two-phonon states interfering destructively with the dominant two-step excited-analog mechanism is found.

NUCLEAR REACTIONS ${}_{}{}^{144,148,150,152}{}_{}{}^{}\mathrm{Sm}$($p$,$n$) $E=20, 24.5, 26$ MeV. Measured $\sigma \left(\theta \right)$ to ground- and excited-state analogs. Coupled-channel calculations including one- and two-phonon states.

The reactions ${}_{}{}^{114}{}_{}{}^{}\mathrm{Cd}$($p$,$p^{\prime }$) and ${}_{}{}^{114}{}_{}{}^{}\mathrm{Cd}$($p$,$p^{\prime }\gamma$) have been studied for polarized and unpolarized protons at a bombarding energy of 11 MeV. Differential and double differential cross sections as well as analyzing powers, correlation asymmetries, and the spin flip probability have been measured by use of a multidetector arrangement consisting of 11 silicon surface barrier detectors and two Ge(Li) detectors. The experimental data have been analyzed in terms of coupled channels on the basis of a harmonic vibrator and a rigid symmetric rotator model. The correlation data are found to be more sensitive to the models used and the sign of the quadrupole deformation than differential cross sections and analyzing powers. Considering the correlation data, the rotator model with oblate deformation must be ruled out for ${}_{}{}^{114}{}_{}{}^{}\mathrm{Cd}$. The best description of the experiment is obtained by the harmonic vibrator model. Compound nucleus contributions can be neglected.

NUCLEAR REACTIONS ${}_{}{}^{114}{}_{}{}^{}\mathrm{Cd}$($p$,$p^{\prime }$), ${}_{}{}^{114}{}_{}{}^{}\mathrm{Cd}$($p$,$p^{\prime }\gamma$), $E=11\mathrm{}$ MeV; polarized and unpolarized protons; measured analyzing powers, inplane $p_1\gamma$-correlations and spin flip probability. Coupled channels analyses; enriched target.

Deformation effects in differential cross sections for neutron scattering from ${}_{}{}^{142,144,146,148,150}{}_{}{}^{}\mathrm{Nd}$ have been studied at an incident energy of 7 MeV, where measurements and calculations of total cross sections show maximum differences for different deformations. Differential cross sections were obtained for elastic scattering and inelastic scattering to the first $2^{+}$ states of the five isotopes. The experimental cross sections are compared to the predictions of surface excitation models using coupled-channels calculations. The parameters of the model are adjusted to fit low energy scattering properties and total cross sections for incident energies from 0.7 to 14 MeV as well as the present data. The large set of data tightly constrains all parameters, including the quadrupole deformation parameters. These are compared to those obtained using other probes of the nuclear surface.

NUCLEAR REACTIONS ${}_{}{}^{142,144,146,148,150}{}_{}{}^{}\mathrm{Nd}$($n$,$n$), ($n$,$n^{\prime }$), $E_n=7.0\mathrm{}$ MeV measured $\sigma (E_n,\theta )$; $\theta =20-160\mathrm{}°$; $\Delta \theta =5\mathrm{}°$. Enriched targets. Deduced coupled-channels optical potential parameters, quadrupole deformation parameters.

Cross sections for the production of long-lived radioactive isotopes by proton induced reactions on iron, cobalt, and tungsten are reported for proton energies less than or equal to 63 MeV. Data are compared with previous experiments and theoretical predictions. Estimates of neutron flux in the region near the end of the proton range are made.

NUCLEAR REACTIONS 63 MeV protons on natural Fe, Co, and W. Measured $\sigma \mathrm{}\left(E\right)\mathrm{}$ for ${}_{}{}^{48}{}_{}{}^{}\mathrm{V}$, ${}_{}{}^{51}{}_{}{}^{}\mathrm{Cr}$, ${}_{}{}^{52,54}{}_{}{}^{}\mathrm{Mn}$, ${}_{}{}^{56,57,58}{}_{}{}^{}\mathrm{Co}$, ${}_{}{}^{183,184}{}_{}{}^{}\mathrm{Re}$.

The photoneutron cross section of ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ was observed using a very high resolution time-of-flight spectrometer. The cross sections were observed in the photoneutron energy range 16 to 1000 keV and at reaction angles of 90° and 135°. The deduced ground-state radiative widths were calibrated to the well-known ${}_{}{}^2{}_{}{}^{}\mathrm{H}$($\gamma$,$n$)${}_{}{}^1{}_{}{}^{}\mathrm{H}$ reaction cross section. The 7.99-MeV resonance, previously believed to be an $M1$ excitation, is shown to be an $E1$ resonance. Current progress in the search for the collective $M1$ resonance in ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ is reviewed. In addition, recent theoretical predictions of the properties of the giant $M1$ resonance are reviewed. Finally, the present high resolution observations in conjunction with previous photoneutron polarization measurements were employed in order to deduce the $s-d$-wave admixtures for eight $E1$ excitations.

NUCLEAR REACTIONS ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$($\gamma$,$n$)${}_{}{}^{207}{}_{}{}^{}\mathrm{Pb}$, $E_{\mathrm{exc}}=7.4-8.4\mathrm{}$ MeV, observed $\sigma \left(\theta \right)$, $\theta =90\mathrm{}°, 135°$; deduced ${\Gamma }_{\gamma 0}$, $J^{\pi }$.