The matrix elements which affect the shapes of the $\beta$ spectra and the $\beta -\gamma$ angular correlations are calculated for the ${}_{}{}^{20}{}_{}{}^{}\mathrm{F}$-${}_{}{}^{20}{}_{}{}^{}\mathrm{Na}$ mirror Gamow-Teller decays to the 1634 keV level of ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$. The dominant effects are due to the weak-magnetism and the axial-vector tensor form factors. Matrix elements relevant to the $\beta -\alpha$ correlations for other ${}_{}{}^{20}{}_{}{}^{}\mathrm{Na}$ decays are also evaluated, with similar conclusions.

RADIOACTIVITY ${}_{}{}^{20}{}_{}{}^{}\mathrm{F}$, ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$, ${}_{}{}^{20}{}_{}{}^{}\mathrm{Na}$, calculated $\beta$ decay form factors, $M1\mathrm{}$, $E2\mathrm{}$ matrix elements; predict $\beta$ spectrum shape, $\beta -\gamma$ and $\beta -\alpha$ angular correlations.

Lifetime measurements of the excited states of ${}_{}{}^{151}{}_{}{}^{}\mathrm{Sm}$ were carried out by delayed coincidence measurements between the $\beta$ spectrum of ${}_{}{}^{151}{}_{}{}^{}\mathrm{Pm}$ and the conversion lines that deexcite the levels in the self-comparison method, using a double-lens coincidence spectrometer. The mean lifetimes of the 344.9 keV and the 445.7 keV levels were determined as $\tau =13.4\mathrm{}\pm 3$ psec and 28.9 ± 4 psec, respectively. The spins of four states were determined from angular correlation measurements carried out for four cascades that deexcite the 344.9 keV state, utilizing two Ge(Li) detectors. The 27 $B\left(E1\mathrm{}\right)\mathrm{}$ and $B\left(M1\mathrm{}\right)\mathrm{}$ reduced transition probabilities deduced from the present work and from previous investigations were compared with the predictions of the Nilsson model.

RADIOACTIVITY ${}_{}{}^{151}{}_{}{}^{}\mathrm{Pm}$ [from ${}_{}{}^{150}{}_{}{}^{}\mathrm{Nd}$ $n,\gamma$]; measured $T_{\frac{1}{2}}$, $\beta$ ce ($t$) coin, $\gamma \gamma \left(\theta \right)$ coin, ${}_{}{}^{151}{}_{}{}^{}\mathrm{Sm}$ levels, deduced $J$, $B\left(E1\mathrm{}\right)\mathrm{}$, $B\left(M1\mathrm{}\right)\mathrm{}$. Enriched target.

The internal bremsstrahlung spectrum accompanying the nonunique second-forbidden $\beta$ decay in ${}_{}{}^{137}{}_{}{}^{}\mathrm{Cs}$ has been measured using the magnetic deflection technique. The internal bremsstrahlung data beyond 760 keV are investigated due to the presence of a 662 keV $\gamma$-ray line. The pileup effect is corrected for by graphical integration. The theoretical spectra of Knipp and Uhlenbeck, Bloch, Lewis and Ford, and Chang and Falkoff are folded with the response matrix of the detector system and compared with the experimental spectrum. The agreement between measurement and theory is poor throughout the energy range of the present investigation, though the experimental points are closer to the second-forbidden scalar theory of Chang and Falkoff.

RADIOACTIVITY ${}_{}{}^{137}{}_{}{}^{}\mathrm{Cs}$; measured IB spectrum; magnetic deflection method.

We calculate the single particle momentum distribution $n\left(q\right)\mathrm{}$ for a one-dimensional model with $\delta$ forces. There is a domain of $q$ for which $n\left(q\right)\mathrm{}$ has an exponential falloff, but after allowance is made for the nonsaturation in the model, that domain does not grow significantly with particle number. The relation of this result to large momentum scattering from the nucleus and to the Hartree approximation is briefly discussed.

NUCLEAR STRUCTURE Single particle momentum distribution in a one-dimensional model and its large momentum behavior.

A new truncation method for shell-model spaces is proposed, based on the proton-neutron correlations. The dominance of the quadrupole force in the $p-n$ interactions is established by the investigation of empirical matrix elements in the $\mathrm{pf}$ shell. A truncation scheme based on the quadrupole component of the $p-n$ interactions is applied to the $N=30\mathrm{}$ nuclei and compared with exact shell-model calculations. Satisfactory agreement between the two results suggests the wide validity of the present truncation method when applied to collective phenomena in nuclei. A relation between the shell model and the particle-vibration model is discussed.

NUCLEAR STRUCTURE ${}_{}{}^{54}{}_{}{}^{}\mathrm{Cr}$, ${}_{}{}^{55}{}_{}{}^{}\mathrm{Mn}$, ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$ calculated levels $J$, $\pi$. Monopole and quadrupole calculation.

We compute relativistic corrections to the triton binding energy ($B_T$) using an effective $s$-wave potential which yields, in the nonrelativistic case, $B_T=7.6\mathrm{}\pm 0.2$ MeV. In the framework of Vinogradov's formulation of the three-body problem in Lobachevsky space, we find $B_T=8.3\mathrm{}\pm 0.15$ MeV. We use two-body $t$ matrices that give the same two-body phase shifts and binding as the nonrelativistic $t$ matrices. Our results for relativistic corrections are substantially larger than those previously reported.

NUCLEAR STRUCTURE ${}_{}{}^3{}_{}{}^{}\mathrm{H}$; binding energy calculated with nonrelativistic and relativistic three-body theories; average $s$-wave potential.

The $K$ and $L$ transitions of muonic atoms of ${}_{}{}^{165}{}_{}{}^{}\mathrm{Ho}$ were measured. A modified Fermi distribution of three parameters was assumed for the charge distribution for purposes of the analysis. Correction for nuclear polarizations and extended space of the hydrogenlike atom were included in the calculation. It was possible to find a range of values for the half radius, the surface thickness, and the intrinsic quadrupole moment to give acceptable fits to the experimental data.

NUCLEAR STRUCTURE Energies of $K$ and $L$ transitions of muonic ${}_{}{}^{165}{}_{}{}^{}\mathrm{Ho}$ presented. Data fitted by three parameter modified Fermi distribution of electrical charge.

The second- and fourth-order mass moments of the even-neutron transition nuclei ${}_{}{}^{178-188}{}_{}{}^{}\mathrm{W}$, ${}_{}{}^{182-194}{}_{}{}^{}\mathrm{Os}$, ${}_{}{}^{187-195}{}_{}{}^{}\mathrm{Ir}$, ${}_{}{}^{186-198}{}_{}{}^{}\mathrm{Pt}$, ${}_{}{}^{191-199}{}_{}{}^{}\mathrm{Au}$, and ${}_{}{}^{194-206}{}_{}{}^{}\mathrm{Hg}$ have been calculated using a self-consistent version of the anisotropic oscillator model. A structural basis is found for possible asymmetric intrinsic nuclear shapes in the transition region, particularly in some of the Os and Pt nuclei and the Ir and Au nuclei nearest to even neighbors with large deformations. The calculations predict large negative fourth-order moments for this region.

NUCLEAR STRUCTURE Calculated $Q_{20}$, $Q_{22}$, $Q_{40}$, $Q_{42}$, $Q_{44}$, ${\beta }_2$, $\gamma$, and ${\beta }_4$ in anisotropic oscillator model for heavy transition nuclei.

We suggest that a recent $1^{+}$ spin-parity assignment to a group at $E_x=1.12\mathrm{}$ MeV in ${}_{}{}^{24}{}_{}{}^{}\mathrm{Al}$ is questionable. High-resolution ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$(${}_{}{}^3{}_{}{}^{}\mathrm{He}$, $t$)${}_{}{}^{24}{}_{}{}^{}\mathrm{Al}$ spectra indicate that the supposed single state is a doublet.

NUCLEAR REACTION: ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ (${}_{}{}^3{}_{}{}^{}\mathrm{He}$, $t$). ${}_{}{}^{24}{}_{}{}^{}\mathrm{Al}$ levels deduced.

The elementary particle approach to electron capture as formulated by McFarland and Repko is generalized to cover arbitrary allowed captures and to include weak magnetism and induced tensor form factors.

RADIOACTIVITY Elementary particle calculation of $e^{-}$ capture with second forbidden effects.

Fission probabilities of heavy (mass 245-251) actinides have been determined using previously described techniques. Empirical average $\frac{{\Gamma }_n}{{\Gamma }_f}$ values and fission barrier parameters deduced from statistical model fits to the results are compared with previous results for lighter mass actinides. Odd-$A$ Bk and Es nuclei exhibit a strong dip in $P_f$ above the neutron binding energy, followed by a gradual increase with increasing excitation energy. We are not able to reproduce this trend with statistical model calculations.

NUCLEAR REACTIONS, FISSION Measured fission probability in ${}_{}{}^{244-245}{}_{}{}^{}\mathrm{Am}$, ${}_{}{}^{245-249}{}_{}{}^{}\mathrm{Bk}$, and ${}_{}{}^{249-251}{}_{}{}^{}\mathrm{Es}$. Determined fission barrier heights.

Analysis of existing data suggests that two bands of dominant ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$-${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ character are indeed observed, up to fairly high excitation energy in ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$.

NUCLEAR STRUCTURE ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$; proposed a new scheme of highly excited rotational bands.

The lifetime of 2.21 ns previously attributed to the 5147 keV level in ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$ is assigned to the 4504 keV level and an upper limit of 1 ns is established for the lifetime of the 5147 keV level.

NUCLEAR REACTIONS ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$ ($p,p^{\prime }\gamma$), $E=28\mathrm{}$ MeV; $\gamma -\gamma$ coin; measured pulsed beam electronic timing; deduced ${\tau }_m$. Enriched target, Ge(Li) detectors.

The familiar pairing-plus-quadrupole interaction is found to have (in some standard applications) the unacceptable property that the excitation energy of the first excited $2^{+}$ state increases with the strength of the quadrupole interaction. A modified pairing-plus-quadrupole interaction which does not suffer from this pathology is proposed and tested.

NUCLEAR STRUCTURE Improved version of pairing-plus-quadrupole model.

A ${}_{}{}^{180}{}_{}{}^{}\mathrm{W}$ target (enriched to 92.6%) was bombarded with ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ ions to produce 28-sec ${}_{}{}^{186}{}_{}{}^{}\mathrm{T}1\mathrm{}$. In a previous experiment this nuclide had been produced with a less favorable target-projectile combination, i.e., ${}_{}{}^{182}{}_{}{}^{}\mathrm{W}$ + ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$. The 5.641-MeV $\alpha$-particle group assigned to ${}_{}{}^{186}{}_{}{}^{}\mathrm{T}1\mathrm{}$ at that time was not observed in the present study; it is apparently associated with ${}_{}{}^{185}{}_{}{}^{}\mathrm{Hg}$ $\alpha$ decay.

RADIOACTIVITY ${}_{}{}^{186}{}_{}{}^{}\mathrm{T}1\mathrm{}$; measured $T_{\frac{1}{2}}$, $E_{\gamma }$, $I_{\gamma }$, $E_{\alpha }$, $I_{\alpha }$. Enriched (92.6%) ${}_{}{}^{180}{}_{}{}^{}\mathrm{W}$ target.

Using bremsstrahlung, the resonance fluorescence yield has been measured for the 1.836-MeV $2_1^{+}$ level in ${}_{}{}^{88}{}_{}{}^{}\mathrm{Sr}$. The observed yield corresponds to a level width $\Gamma =2.94\mathrm{}\pm 0.15$ meV.

NUCLEAR REACTIONS ${}_{}{}^{88}{}_{}{}^{}\mathrm{Sr}$ ($\gamma ,\gamma$), bremsstrahlung $2.0<~E_e<~2.31$ MeV; measured $\sigma \left(96\mathrm{}°\right)$ and $\sigma \left(126\mathrm{}°\right)$, deduced $\Gamma \mathrm{}\left(1.836\right)\mathrm{}$. Natural target.

The excitation function for the reaction ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$($d,2n$) ${}_{}{}^{232}{}_{}{}^{}\mathrm{Pa}$ has been reinvestigated in the energy range 10-26 MeV, using a different technique, to check the earlier report of the existence of two maxima in the excitation function. The present results, while confirming the first maximum, have not shown any indication of a second peak. The shape of the present excitation function generally agrees with that predicted by the hybrid model. On this basis, the mechanism of the reaction could be explained in terms of the usual evaporation and preequilibrium decay of the compound system.

NUCLEAR REACTIONS ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$ ($d,2n$), $E=10-26\mathrm{}$ MeV, measured $\sigma \mathrm{}\left(E\right)\mathrm{}$, foil stack technique, $\gamma$ counting method.

Angular distributions of the analyzing power and differential cross section for ${}_{}{}^3{}_{}{}^{}\mathrm{He}(\overrightarrow{t}, t){}_{}{}^3{}_{}{}^{}\mathrm{He}$ elastic scattering are reported for triton bombarding energies of 9.02, 11.00, 13.02, 15.02, 16.00, and 17.02 MeV, over a c.m. angular range from 25° to 155°. Excitation functions for the analyzing power are presented for the energy range 14.42-17.22 MeV. Problems in the phase-shift analysis of the data are discussed.

NUCLEAR REACTIONS ${}_{}{}^3{}_{}{}^{}\mathrm{He}(\overrightarrow{t}, t)$, $E_t=9.02, 11.00, 13.02, 15.02, 16.00, 17.02$ MeV. Measured $A_y\left(\theta \right)$, $\theta =25\mathrm{}°-155\mathrm{}°$; $A_y\mathrm{}\left(E\right)\mathrm{}$, $E=14.42-17.22\mathrm{}$ MeV; $\sigma \left(\theta \right)$, $\theta =30\mathrm{}°-150\mathrm{}°$.