The two-step intranuclear-cascade evaporation model is used in the calculation of nucleon spectra, particle multiplicities, and radiochemical cross sections following stopped-${\pi }^{-}$ absorptions by complex nuclei. The nucleon spectra and particle multiplicities from the pion absorption by light elements are, in general, predicted quite well. The theoretical particle yields from the heavy elements are overestimated and the particle spectra are too soft. These discrepancies are attributed to an insufficient number of pion absorptions near the edge of the nucleus for the heavy elements in the theoretical model. The magnitudes of the theoretical radiochemical cross sections from slow-${\pi }^{-}$ absorption by iodine are in fair agreement with those from experiments, but the peak in the cross-section distribution versus isotope mass for some of the isotopes appears at lower mass values than the measured ones. This discrepancy is consistent with those above. The model does well in predicting the change-exchange cross section, but does poorly in estimating the double-charge-exchange cross section for pions with energies below 200 MeV. These cross sections represent about 1% or less of the total interaction cross section, and the theoretical model does not accurately reproduce such events, in general.

The production cross sections for Li, Be, and B fragments emitted in medium-energy proton and $\alpha$-particle reactions with the C, N, and O nuclei of a nuclear emulsion have been measured. The corresponding results for the $p$-induced and $\alpha$-induced reactions have been compared. Since helium abundance in the universe is about 10%, these reactions must be taken into account when considering the nucleosynthesis of Li, Be, and B.

Asymmetries and relative differential cross sections have been measured for elastic and inelastic scattering of 20.3-MeV polarized protons from light elements. The targets included ${\mathrm{C}}^{12}$, ${\mathrm{O}}^{16}$, ${\mathrm{Mg}}^{24}$, ${\mathrm{Mg}}^{25}$, ${\mathrm{Mg}}^{26}$, ${\mathrm{Al}}^{27}$, ${\mathrm{Si}}^{28}$, and ${\mathrm{Ca}}^{40}$. Significant differences have been observed in both the asymmetries and cross sections for transitions with a given angular momentum transfer. The shapes of the asymmetries for ${\mathrm{Al}}^{27}$ and ${\mathrm{Si}}^{28}$ show some disagreement with the weak-coupling model prediction. Coupled-channels and distorted-wave Born-approximation calculations (DWBA) have been performed for the first $2^{+}$ and $4^{+}$ states in ${\mathrm{Mg}}^{24}$ and ${\mathrm{Si}}^{28}$, with several types of deformed spin-orbit potential. In principle, it should be possible with a coupled-channel analysis to distinguish between vibrational and rotational models, and between positive and negative deformations. In fact, there are differences between the predictions of these models. However, none of them gives a good account of the $2^{+}$ and $4^{+}$ asymmetries in ${\mathrm{Mg}}^{24}$ and ${\mathrm{Si}}^{28}$, even when the full Thomas form of the spin-orbit potential is used. Microscopic- and macroscopic-model DWBA predictions of the $3_1^{-}$ and $5_1^{-}$ asymmetries in ${\mathrm{Ca}}^{40}$ yield fair agreement with the experimental data.

Angular distributions of 15.0-MeV deuterons scattered by ${\mathrm{F}}^{19}$ were measured between ${\theta }_{\mathrm{lab}}=18\mathrm{}° \mathrm{and} 85°$. Inelastic groups leaving ${\mathrm{F}}^{19}$ in its five lowest-lying excited states were observed using two position-sensitive detectors placed in the focal plane of a split-pole spectrometer. The elastic-scattering cross section was analyzed using an optical model. $B\left(E2\mathrm{}\right)\mathrm{}\downarrow$ values for the transitions from the $\frac{5}{2}$+(0.197-MeV) and the $\frac{3}{2}$+(1.56-MeV) states to the ground state were found to be 9±3 and 10±3 W.u. (single-particle units). They were calculated from the ${\beta }_2$ deformation parameter extracted from a distorted-wave Born-approximation (DWBA) analysis using a complex form factor derived from the optical-model analysis with a surface-absorption term. These results are in good agreement with results obtained from inelastic proton scattering and from Coulomb-excitation experiments. However, the $B\left(E3\mathrm{}\right)\mathrm{}\downarrow$ value for the ${\frac{5}{2}}^{-}\to {\frac{1}{2}}^{+}$ transition from the 1.35-MeV state was found to be 1.4±0.6 W.u. as compared to the upper limit of 3.8±0.6 W.u. from a ($p, p^{\prime }$) experiment, and to 12.0±4.0 and 7.6±1.3 W.u. from two different Coulomb-excitation experiments. The results are compared to various model predictions.

A generalization of the modified WKB method proposed by Good and by Rosen and Yennie as applied to the scattering problem is presented. In the formulation of this problem the main equation connects two parts, the solved part and the part to be solved. We consider not only the case where the radical wave function of the solved part has the form of the three-dimensional free-particle solution, as is done by the authors mentioned above, but also where it has the form given by an explicit solution with a known potential. The closer the resemblance between the potentials of the unsolved and the solved parts, the better the result is.

Angular correlations of $\gamma$ rays leading to states in ${}_{}{}^{39}{}_{}{}^{}\mathrm{Ca}$ at 2.47, 2.80, 3.03, 3.66, 3.95, and 4.02 MeV have been measured. The spins and parties of the first three excited states were found to be ${\mathrm{½}}^{+}$, ${\frac{7}{2}}^{-}$, and ${\frac{3}{2}}^{-}$, in agreement with previous work. The mixing ratio determined for the 2.80→g.s. transition implies 98% $M2\mathrm{}$, in disagreement with an earlier measurement. In conjunction with $l$-value assignments from distorted-wave Born-approximation analysis of charged-particle angular distributions, the present work assigns $J^{\pi }={\frac{9}{2}}^{-}$ for the 3.66-MeV state, ${\frac{3}{2}}^{-}$ for the 3.95-MeV state, and ${\mathrm{½}}^{+}$ for the 4.02-MeV state. Multipole mixing and branching ratios were extracted from the data.

The polarizations of protons from the ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}(d, p){}_{}{}^{29}{}_{}{}^{}\mathrm{Si}$ reactions leading to the ground state and the 1.28-, 2.03-, and 3.62-MeV excited states of ${}_{}{}^{29}{}_{}{}^{}\mathrm{Si}$ have been measured over the range of laboratory angles from 30° to 147° at a bombarding deuteron energy of 10.8 MeV. A scattering-chamber-polarimeter assembly employing solid-state detectors was used to allow the measurements on all groups to be made simultaneously. To provide additional data for theoretical comparisons, the differential cross sections for the same reactions and for the elastic scattering of deuterons from ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ have also been measured at the same bombarding energy. For the $l_n=0\mathrm{}$ ground-state reaction, the observed polarizations change rapidly from large negative to large positive values near the minima in the cross section at 50° and 90°. The 1.28-MeV excited-state reaction also shows large polarizations, but with no obvious relationship to variations in the cross section. Polarizations of protons corresponding to the 2.03- and 3.62-MeV excited states are smaller (between ±0.3) and appear to be uncorrelated with cross-section variations. Comparisons are made with published theoretical predictions where available.

The polarizations of protons from the reactions ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}(d, p){}_{}{}^{41}{}_{}{}^{}\mathrm{Ca}$ leading to the ground state and the 1.95-and 2.47-MeV excited states of ${}_{}{}^{41}{}_{}{}^{}\mathrm{Ca}$ have been measured at 13 angles between 30° and 148° in the laboratory system at a bombarding energy $E_d=10.8\mathrm{}$ MeV. A carbon polarimeter using solid-state detectors permitted the measurements for all three proton groups to be made simultaneously. The polarization results for the $l_n=3\mathrm{}$, $j_n=\frac{7}{2}$ ground-state reaction are in good agreement with previous measurements, but extend to larger angles. Shapes of the polarization angular distributions for protons from the $l_n=1\mathrm{}$, $j_n=\frac{3}{2}$ reactions exciting the 1.95- and 2.47-MeV states are very similar to each other except possibly near 100°. Comparisons are made with available theoretical predictions for these reactions.

The ${\mathrm{Ca}}^{48}({\mathrm{He}}^3, t){\mathrm{Sc}}^{48}$ reaction was studied with a magnetic spectrograph at a bombarding energy of 15 MeV. Energy levels of ${\mathrm{Sc}}^{48}$ were obtained and compared with the results of previous work. From consideration of cross sections, angular distributions, and previous spin and parity assignments, eight levels of ${\mathrm{Sc}}^{48}$ are tentatively assigned to the ($\pi {f_{\frac{7}{2}}}^1$) ($\nu {f_{\frac{7}{2}}}^{-1\mathrm{}}$) configuration—namely, those with $J^{\pi }=0^{+}$, $E_x=6.680\mathrm{}$; $1^{+}$, 2.525; $2^{+}$, 1.145; $3^{+}$, 0.624; $4^{+}$, 0.253; $5^{+}$, 0.133; $6^{+}$, 0; and $7^{+}$, 1.096 MeV. These states are populated roughly an order of magnitude more strongly than the other states in ${\mathrm{Sc}}^{48}$.

Angular distributions from the ${}_{}{}^{47}{}_{}{}^{}\mathrm{Ti}(d, {}_{}{}^3{}_{}{}^{}\mathrm{He}){}_{}{}^{46}{}_{}{}^{}\mathrm{Sc}$ and ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ti}(d, {}_{}{}^3{}_{}{}^{}\mathrm{He}){}_{}{}^{46}{}_{}{}^{}\mathrm{Sc}$ reactions have been measured with a deuteron beam energy of 17 MeV. The ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ particles were magnetically analyzed by position-sensitive counters and photographic emulsions mounted in an Enge split-pole spectrograph with typical experimental resolutions of 8-10 full width at half-maximum. With the use of distorted-wave Born-approximation calculations for $2s_{\frac{1}{2}}$, $1d_{\frac{3}{2}}$, $1f_{\frac{7}{2}}$, and $2p$ pickup, $l_p$ values and spectroscopic factors were deduced. The results verify a finite (≈ 0.2 protons) occupation in the $2p$ orbitals. In addition, the $1f_{\frac{7}{2}}$ orbit appears in slight excess and $1d_{\frac{3}{2}}$ is slightly deficient in its shell-model value of protons. By comparison with other studies in ${}_{}{}^{46}{}_{}{}^{}\mathrm{Sc}$, it is concluded that the similar average binding energies for $\pi f_{\frac{7}{2}}\nu {\left({f_{\frac{7}{2}}}^5\right)}_{\frac{7}{2}}$, $\pi f_{\frac{7}{2}}\nu {\left({f_{\frac{7}{2}}}^5\right)}_{\frac{5}{2}}$, and $\pi \left({d_{\frac{3}{2}}}^{-1\mathrm{}}\right){\left({f_{\frac{7}{2}}}^2\right)}_0\nu {\left({f_{\frac{7}{2}}}^5\right)}_{\frac{5}{2}}$ configurations are primarily responsible for the high level density and large configuration mixing in the 0-1-MeV excitation in ${}_{}{}^{46}{}_{}{}^{}\mathrm{Sc}$. In the 1-2-MeV region, the $\pi \left({s_{\frac{1}{2}}}^{-1\mathrm{}}\right){\left({f_{\frac{7}{2}}}^2\right)}_0\nu {\left({f_{\frac{7}{2}}}^5\right)}_{\frac{5}{2}}$, $\pi {d_{\frac{3}{2}}}^{-1\mathrm{}}{\left({f_{\frac{7}{2}}}^2\right)}_0\nu {\left({f_{\frac{7}{2}}}^5\right)}_{\frac{7}{2}}$, $\pi {d_{\frac{3}{2}}}^{-1\mathrm{}}{\left({f_{\frac{7}{2}}}^2\right)}_0\nu {d_{\frac{3}{2}}}^{-1\mathrm{}}{\left({f_{\frac{7}{2}}}^6\right)}_0$, and $\pi f_{\frac{7}{2}}\nu {\left({f_{\frac{7}{2}}}^4\right)}_{0}2p^1$ configurations dominate the spectrum.

The spin and multipolarity mixing ratios of five resonances and many bound states in ${\mathrm{Sc}}^{43}$ have been determined from angular-correlation and linear-polarization measurements. Unique spin assignments have been made for the following levels: 0.846 MeV ($\frac{5}{2}$), 0.856 MeV (½), 1.158 MeV ($\frac{3}{2}$), 1.179 MeV ($\frac{3}{2}$), 1.652 MeV ($\frac{5}{2}$), 1.963 MeV ($\frac{5}{2}$), 2.094 MeV ($\frac{3}{2}$), 2.143 MeV ($\frac{7}{2}$), and 2.580 MeV ($\frac{5}{2}$). In addition, limitations on the possible spin assignments have been made for the following levels: 1.885 MeV ($\frac{5}{2}, \frac{9}{2}$), 2.383 MeV ($\frac{3}{2}, \frac{7}{2}$), 2.986 MeV ($\frac{3}{2}, \frac{5}{2}$), 3.289 MeV 3.289 MeV ($\frac{3}{2}, \frac{5}{2}$), and 4.455 MeV ($\frac{5}{2}, \frac{9}{2}$). The parity of the 0.846-MeV level was found to be negative from linear-polarization measurements. These results, together with results due to other investigators, are discussed in terms of various nuclear models. It is shown that neither the shell model nor the cluster model can account for the observed properties of ${\mathrm{Sc}}^{43}$. The Coriolis-coupling model gives reasonable qualitative agreement, but quantitative agreement with experiment will require a modification of the model. Johnstone's model successfully accounts for the observed properties of all levels except for those levels identified as belonging to the $k^{\pi }={\frac{1}{2}}^{+}$ band. Specific experiments are suggested to determine the nature of these states.

Angular distributions of 42-MeV $\alpha$ particles, elastically scattered from ${}_{}{}^{40,42,44,48}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{46,48,50}{}_{}{}^{}\mathrm{Ti}$, ${}_{}{}^{52}{}_{}{}^{}\mathrm{Cr}$, ${}_{}{}^{54,56}{}_{}{}^{}\mathrm{Fe}$, ${}_{}{}^{58,60,62}{}_{}{}^{}\mathrm{Ni}$ have been measured in the forward region with an absolute accuracy of ±0.1°; in particular, the locations of the minima near 35° (c.m. system) have been determined to within ±0.1°. The theoretical analysis has been done in three ways, using (a) the Fraunhofer model, (b) a direct parametrization of the scattering amplitude in terms of three parameters, and (c) a standard four-parameter optical model. Strong-absorption radii have been deduced from the critical angular momenta extracted from the scattering amplitudes. In addition, attempts have been made to determine, for the optical-model analysis, other sorts of strong-absorption radii that are more characteristic of the scattering than the usual midpoint radius of the potential. Our analyses indicate that the rate of increase of almost all such strong-absorption radii is smaller within the Ca and Ti isotopes than within the Fe and Ni isotopes, the radius of ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$ being anomalously small for all types of analysis.

The description of energy-averaged angular distributions for the ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}(\alpha , {\alpha }_0){}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ reaction from 5.5 to 17.5 MeV as the incoherent sum of an $l$-dependent-absorption optical-model cross section and a Hauser-Feshbach compound-elastic-scattering cross section is discussed. The parameters for both cross sections are determined throughout the energy range. Statistical-model calculations of the Hauser-Feshbach parameters $\rho$ and $\sigma$ are in good agreement with those extracted from the data. The compound-elastic-scattering cross sections obtained by analyzing the energy-averaged angular distributions are compared with those obtained in an Ericson fluctuation analysis of the fine-resolution excitation curves.

A general phenomenological theory is developed for the calculation of both elastic and inelastic transverse and longitudinal form factors for electron scattering from nuclei whose surfaces are deformed according to the expression $R+{\left(4\mathrm{}\pi \right)}^{\frac{1}{2}}{\Sigma }_{\mathrm{lm}}{\hat{a}}_{\mathrm{lm}}{Y}_{\mathrm{lm}}\left(\hat{\mathcal{r}}\right)$. Here, the ${\hat{a}}_{\mathrm{lm}}$ are operators in the nuclear Hilbert space, whose detailed dynamical character is left unspecified. The effects of deformation on the scattering, to any desired accuracy, are contained in reduced matrix elements of tensor products of the ${\hat{a}}_{\mathrm{lm}}$. These are then treated as phenomenological parameters whose values are to be fixed from an analysis of the scattering cross sections, particularly at high momentum transfer. All the static and transition multipole moments of the nucleus are thereby determined, at least in principle. The Helm model and its generalization to transverse scattering are obtained in the small-deformation limit. The theory is used to analyze the Coulomb elastic and inelastic (to the 1.3-MeV ${\frac{3}{2}}^{+}$ level) scattering of electrons from ${}_{}{}^{59}{}_{}{}^{}\mathrm{Co}$, as well as the magnetic elastic and inelastic scattering from ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}$. It is shown that the contribution of the deformation to elastic monopole scattering may be interpreted as due to an effective, oscillatory, spherically symmetric "modulating-charge" distribution, superimposed upon the more usual smeared uniform distribution. It is therefore suggested that the oscillations in the charge distribution which seem to be required in order to fit the high-energy elastic scattering from ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ and other nuclei may be due to deformations.

The simultaneous observation of ($p, t$) and ($p$, ${}_{}{}^3{}_{}{}^{}\mathrm{He}$) reactions has led to the location and identification of the lowest-energy ($0^{+}$) $T=2\mathrm{}$ states in ${}_{}{}^{28}{}_{}{}^{}\mathrm{Al}$, ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$, ${}_{}{}^{32}{}_{}{}^{}\mathrm{P}$, ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$, ${}_{}{}^{36}{}_{}{}^{}\mathrm{Cl}$, ${}_{}{}^{36}{}_{}{}^{}\mathrm{Ar}$, ${}_{}{}^{40}{}_{}{}^{}\mathrm{K}$, and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, as well as the ($0^{+}$) $T=3\mathrm{}$ states in ${}_{}{}^{38}{}_{}{}^{}\mathrm{Cl}$ and ${}_{}{}^{38}{}_{}{}^{}\mathrm{Ar}$. The energies of these states are used to predict the masses of six neutron-deficient nuclei: ${}_{}{}^{28}{}_{}{}^{}\mathrm{S}$, ${}_{}{}^{32}{}_{}{}^{}\mathrm{Ar}$, ${}_{}{}^{36}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{38}{}_{}{}^{}\mathrm{Sc}$, ${}_{}{}^{38}{}_{}{}^{}\mathrm{Ti}$, and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ti}$. In addition, the ($p, t$) cross section for production of each analog state relative to the cross section for producing the ground state in the same nucleus is compared with calculations which assume a simple shell model. Good agreement is obtained.

Cross sections have been measured for elastic and inelastic scattering of 42-MeV $\alpha$ particles by ${}_{}{}^{25}{}_{}{}^{}\mathrm{Mg}$ in the range $\theta \left(\mathrm{lab}\right)=10\mathrm{}°-60\mathrm{}°$. Six inelastic $\alpha$ groups were identified at the following measured $-Q$ values: 1.59, 1.94, 2.55, 2.75 (doublet), 3.400 (doublet), and 4.05 MeV. The cross sections are analyzed in terms of the distorted-wave Born-approximation version of the extended optical model and the smoothed Fraunhofer inelastic diffraction model. A general discussion is given of the transition strengths of odd-mass nuclei within the context of the strong-coupling rotational model or modifications thereof, and application is made to the present results. The main conclusions are: Inelastic scattering within the ground-state band supports the rotational model in its simplest form. Comparison of the elastic cross sections from ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{25}{}_{}{}^{}\mathrm{Mg}$, and ${}_{}{}^{26}{}_{}{}^{}\mathrm{Mg}$ indicates the presence of a quadrupole contribution to the elastic cross section from ${}_{}{}^{25}{}_{}{}^{}\mathrm{Mg}$, consistent with the strong-coupling prediction. The $\lambda =2\mathrm{}$ single-nucleon contribution to transitions into the lowest $K={\frac{1}{2}}^{+}$ band appears to be very small. The excitation corresponding to the known level at 4.057 MeV suggests that this level arises from coupling a $\gamma$ vibration to the ground-state band. The second $K={\frac{1}{2}}^{+}$ band may have the same origin, although other evidence indicates that there is at least a sizable admixture of a single-nucleon orbital to this band.

Total neutron cross sections and elastic and inelastic neutron-scattering cross sections of vanadium are experimentally studied. Total neutron cross sections are determined with good resolution (≳1 keV) from 0.1 to 1.45 MeV. Differential elastic and inelastic scattering angular distributions are measured at incident-neutron energy intervals of ≲10 keV and with resolutions of ∼20 keV from 0.3 to 1.5 MeV. The inelastic excitation of states at 330±10 and 926±10 keV is observed. The experimental results are interpreted in terms of the optical model and statistical concepts inclusive of resonance-width fluctuations. The observed intermediate structure is discussed in the context of strongly overlapping resonances, distributions in resonance widths and spacing, and an intermediate optical model.

Excitation functions and angular distributions for the reaction ${}_{}{}^{54}{}_{}{}^{}\mathrm{Cr}(p, \alpha ){}_{}{}^{51}{}_{}{}^{}\mathrm{V}$ have been measured between 6.5 and 20.0 MeV for the ground state and the first two excited states in ${}_{}{}^{51}{}_{}{}^{}\mathrm{V}$ at 0.32 and 0.92 MeV, with spins ${\frac{7}{2}}^{-}$, ${\frac{5}{2}}^{-}$, and ${\frac{3}{2}}^{-}$, respectively. From the angular distributions and the excitation functions, a compound nuclear mechanism is supported for the population of the ${\frac{5}{2}}^{-}$ and ${\frac{3}{2}}^{-}$ levels. At higher bombarding energies there is evidence that a simple pickup mechanism dominates for producing the ${\frac{7}{2}}^{-}$ level. From the fluctuation analysis of the excitation functions for the ${\frac{5}{2}}^{-}$ and ${\frac{3}{2}}^{-}$ levels, the decay width of the compound nucleus ${}_{}{}^{55}{}_{}{}^{}\mathrm{Mn}$ was obtained as a function of energy. From the differential cross sections and decay widths, the level density of ${}_{}{}^{55}{}_{}{}^{}\mathrm{Mn}$ was deduced at excitation energies between 15 and 23 MeV. The results were combined with low-energy level-density data previously obtained with a magnetic spectrograph. These results, when compared with similar data for even-even ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$, show that the energy shift required to match level densities for odd and even nuclei is the same at low and high excitation energies. The energy dependence of the level density cannot be reproduced over the whole energy range with level-density expressions employing conventional odd-even corrections. The same conclusion is supported by statistical-model calculations of the excitation functions.

A Ge(Li) detector and the reaction ${\mathrm{Si}}^{30}(d, p){\mathrm{Si}}^{31}$ with $E_d=2-4\mathrm{}$ MeV are used in the coincidence version of the Doppler-shift attenuation method to obtain the following information concerning the mean lives of some low-lying states in ${\mathrm{Si}}^{31}$: $\tau \left(0.75\mathrm{} \mathrm{MeV}\right)=\left({{7.2}_{-1.8\mathrm{}}}^{+2.6\mathrm{}}\right)\times {10}^{-13\mathrm{}}$ sec, $\tau \left(1.69\mathrm{} \mathrm{MeV}\right)=(7.4\mathrm{}\pm 2.3)\times {10}^{-13\mathrm{}}$ sec, $\tau \left(2.32\mathrm{} \mathrm{MeV}\right)<\mathrm{}3\mathrm{}\times {10}^{-13\mathrm{}}$ sec, $\tau \left(3.14\mathrm{} \mathrm{MeV}\right)=\left({{5.0}_{-2.6\mathrm{}}}^{+2.2\mathrm{}}\right)\times {10}^{-13\mathrm{}}$ sec, $\tau \left(3.53\mathrm{} \mathrm{MeV}\right)<\mathrm{}3.7\mathrm{}\times {10}^{-14\mathrm{}}$ sec. From these results, the reduced matrix elements for electromagnetic transitions among some of these states are obtained. A comparison is made between these reduced matrix elements and those predicted by the extreme single-particle model, the Nilsson rotational model, and the shell model with configuration mixing in the $2s_{\frac{1}{2}}$ and $1d_{\frac{3}{2}}$ shells. Our results indicate a value of $\left|\eta \right|={{2.8}_{-0.4\mathrm{}}}^{+0.5\mathrm{}}$ for the Nilsson deformation parameter for ${\mathrm{Si}}^{31}$. A value of 752±1 keV was obtained for the excitation energy of the 0.75-MeV state.

The $\gamma$ decays of the two lowest $T=\frac{3}{2}$ states in ${\mathrm{Na}}^{21}$ at 8.97 and 9.22 MeV were studied as resonances in the ${\mathrm{Ne}}^{20}(p, \gamma )$ reaction by use of a gas cell and a 30-cc Ge(Li) detector. For the lower resonance, we find three branches: to the ${\frac{3}{2}}^{+}$ ground state (11%), to the ${\frac{5}{2}}^{+}$ first excited state (50%), and to the ${\frac{7}{2}}^{+}$ second excited state (39%). These results imply that $J={\frac{5}{2}}^{+}$ for the $T=\frac{3}{2}$ state. On the simple rotational model, transitions from states of the $K=\frac{1}{2}$ (Nilsson orbit #6) band are possible only to the ground-state $K=\frac{3}{2}$ (#7) band. A $J={\frac{5}{2}}^{+}$, $K=\frac{1}{2}$ assignment for the lowest $T=\frac{3}{2}$ state fits the observed branching ratios. The second resonance decays predominantly to the ground state, and there is at most a 9% branch to the ${\mathrm{½}}^{+}$ state at 2.41 MeV. The second resonance is assigned $J={\frac{1}{2}}^{+}$, $K=\frac{1}{2}$. If the 2.41-MeV state is $K=\frac{1}{2}$ (#9), no transition to it is expected. On both resonances, transitions to higher excited states are obscured by background.