($p, \mathrm{pn}$) reactions induced by 17-MeV protons on 12 different nuclei are studied by coincidence detection and energy measurements of the emitted neutron and proton. Probabilities of exciting various final states and of ($p, p^{\prime }\gamma$) reactions (i.e., no neutron emission) are measured as a function of the energy of the emitted particles, and attempts are made to explain the results with a model assuming that these are ($p, p^{\prime }$) reactions followed by neutron boil-off. There are many disagreements with the predictions of this model, and many inconsistencies between results from the different nuclei under this interpretation. It is shown that including contributions from ($p, n$) reactions followed by proton boil-off does little to improve the situation. The results might be explained if both particles are emitted in a direct reaction, although there is difficulty with the simplest such reaction, a single collision knockout, in that there is poor correlation between states excited in these reactions and in pickup reactions such as ($p, d$).

A new theory is presented for calculating the structure of finite nuclei from the nucleon-nucleon interaction. The essential features of the reaction matrix in finite nuclei are obtained from nuclear-matter theory through the local-density approximation. The resulting density- and energy-dependent effective interaction is justified in detail, and it is shown that the tensor force plays an important role in saturation. The effective interaction is cast into two different forms, one convenient for use in calculating matrix elements and the other specialized for a Hartree-Fock calculation in position space. The density-dependent Hartree-Fock equations are derived by variation of the ground-state expectation value of the energy, and in addition to the usual Hartree-Fock terms, one obtains rearrangement terms arising from the variation of the density appearing in the density-dependent interaction. The appropriate angular-momentum reduction for closed $j$-shell nuclei is performed. The need for modifying the effective interaction to account for higher-order corrections is discussed, and the constraints imposed on this modification by the properties of nuclear matter are examined. The results of this theory for ${\mathrm{O}}^{16}$, ${\mathrm{Ca}}^{40}$, ${\mathrm{Ca}}^{48}$, ${\mathrm{Zr}}^{90}$, and ${\mathrm{Pr}}^{208}$ are shown to yield very satisfactory agreement with experimental binding energies, single-particle energies, and electron scattering cross sections. The rearrangement terms in the density-dependent theory are demonstrated to have two essential effects on nuclear structure: a significant reduction in the central density of the nucleus, and a modification of the usual Hartree-Fock relation between single-particle energies and the binding energy. Equivalent local single-particle potentials are calculated and are shown to have significant state dependence.

The dynamics of nuclear distortion is studied for two spherical nuclei under the influence of their mutual Coulomb interactions. Both the quadrupole and the octupole degrees of freedom are considered. Realistic stiffness and effective-mass parameters are employed. It is found that the energy needed to bring the two nuclei into contact increases as a result of the distortions. However, in the most favorable case, the increase is only a few percent. This is much smaller than previous estimates using either the liquid-drop model or the adiabatic model.

Total elastic and inelastic scattering cross sections for fast neutrons are measured on ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ between 17 and 20.5 MeV in order to check the validity of standard optical-model parameters and to investigate the nature of resonant states in ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$. The region around 18 MeV is found to be free of isolated resonances, and good fits are obtained with standard parameters. A resonant state is apparent at an energy corresponding to 23 MeV in ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$, and indications of the spin and the structure of this state are obtained.

The reactions ${}_{}{}^6{}_{}{}^{}\mathrm{Li}(d, n){}_{}{}^7{}_{}{}^{}\mathrm{Be}$ (g.s.+0.431 MeV) and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(d, n){}_{}{}^{13}{}_{}{}^{}\mathrm{N}$ (g.s.) have been studied by recoil spectrometry at bombarding energies of 12, 15, and 17 MeV. The recoils were detected by a solid-state detector in coincidence with the neutrons detected by a plastic scintillator. Experimental absolute differential cross sections at the three bombarding energies are given for both reactions. Also given are the excitation functions over the energy region 12-17 MeV at about 60° recoil c.m. angle for both reactions, and for the reaction ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}(d, n){}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ (g.s.). The ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ reactions were analyzed in the distorted-wave Born approximation (DWBA), taking into account the effects of spin-orbit force, finite range, and nonlocality corrections. The agreement between the experimental and theoretical angular distributions is good for the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ reaction, and the agreement for the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ reaction is fair at 17 MeV. The excitation functions for the two reactions are relatively smooth. The experimental absolute differential cross sections for the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ reaction agree fairly well with the theoretical cross sections obtained by incorporating the spectroscopic factors from recent shell-model calculations. For the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ reaction, the spectroscopic factor extracted from the experimental cross section agrees well with the theoretical value at 17 MeV. The experimental cross sections at 12 and 15 MeV are higher than the theoretical estimates; some possible explanations are discussed. The ratios of the experimental to the theoretical cross sections as a function of bombarding energy follow the same trend as for the reaction ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(d, p){}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ (g.s.). An evaluation of the technique of recoil spectrometry for studying ($d, n$) and other nuclear reactions is given.

Three-body breakup spectra from a kinematically complete measurement of the $\mathrm{D}(p, 2p)n$ reaction have been analyzed to yield the cross section for the production of $d^{*}$, a quasiparticle consisting of a neutron and proton in a ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ configuration. An excitation function of the $\mathrm{D}(p, d^{*})p$ reaction is obtained for the proton bombarding energy range 9-13 MeV. In agreement with measurements and predictions of the ($p, d^{*}$) cross section on several nuclei, the $\mathrm{D}(p, d^{*})p$ cross section is about an order of magnitude less than the elastic $\mathrm{D}(p, d)p$ cross section. The $\mathrm{D}(p, d^{*})p$ excitation function shows a peak at the bombarding energy $E_p=10.25\mathrm{}$ MeV which coincides with a ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ excitation energy of 12.4 MeV. This peak might be interpreted as either a state in ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ or a threshold effect.

Since there exists considerable uncertainty in the short-range part of the real nucleon-nucleon interaction, any attempt at a rigorous derivation of the effective interaction is illusory. Rather, we have argued that requiring the effective interaction to conform to the real interaction in the long-range part is the furthest that one can meaningfully go in relating the two, and that the short-range part of the effective interaction should be chosen phenomenologically. Our earlier work is here extended to impose phenomenological constraints on the vector (spin-orbit) and tensor components of the effective interaction. The short-range phenomenological part of our effective interaction is to be chosen in such a way that the entire interaction satisfies the following conditions: (a) Nuclear matter is correctly saturated in first-order perturbation theory, with small second-order corrections. (b) The odd-state scattering parameters are fitted up to 300 MeV. (c) The low-energy singlet scattering parameters are fitted. (d) The low-energy triplet scattering parameters and the quadrupole moment of the deuteron are fitted. We find that it is never possible to satisfy more than three conditions simultaneously, and so arrive at four effective interactions, each of which is characterized by the violation of one of the above conditions. Two of these interactions are found to work well for both Hartree-Fock and spectroscopic calculations, and, hence, may be regarded as having some measure of universality.

The energy spectra of $\alpha$ particles were measured at 5° lab for the reaction ${}_{}{}^3{}_{}{}^{}\mathrm{He}({}_{}{}^3{}_{}{}^{}\mathrm{He}, \alpha )pp$ using a 20-MeV ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ beam; at 5° and 8° lab for the reaction ${}_{}{}^3{}_{}{}^{}\mathrm{He}(t, \alpha )np$; and at 5°, 8°, and 10° lab for the reaction ${}_{}{}^3{}_{}{}^{}\mathrm{H}(t, \alpha )nn$ using a 22-MeV triton beam. The 5° lab spectra corresponding to low relative energy in the unobserved two-nucleon system were well fitted with Watson-Migdal final-state-interaction theory for the following scattering lengths: $a_{\mathrm{pp}}=-7.52\mathrm{}\pm 0.22$ F, $a_{\mathrm{np}}=-21.5\mathrm{}\pm 2.3$ F, and $a_{\mathrm{nn}}=-16.96\mathrm{}\pm 0.51$ F. Analyzing the change-symmetric reactions with the comparison method and using the accepted value for $a_{\mathrm{pp}}$, we find $a_{\mathrm{nn}}=-18.11\mathrm{}\pm 0.75$ F. When compared with Coulomb-corrected values of $a_{\mathrm{pp}}$, these values of $a_{\mathrm{nn}}$ imply that nucleon-nucleon forces are charge-symmetric to better than 1%. In obtaining the scattering lengths, the effective range was fixed at $r_0=2.84\mathrm{}$ F. Allowing both the effective range and scattering length to vary in the fitting procedure for the $n-n$ final-state data, we find $a_{\mathrm{nn}}=-17.4\mathrm{}\pm 1.8$ F and ${\left(r_0\right)}_{\mathrm{nn}}=2.4\mathrm{}\pm 1.5$ F. If the $n-n$ scattering length is fixed at the value - 17.0 F, our data determine the effective range to be ${\left(r_0\right)}_{\mathrm{nn}}=2.75\mathrm{}\pm 0.35$ F.

We have studied the contribution of the knockout-exchange mechanism to inelastic proton scattering the distorted-wave Born approximation (DWBA) as a function of two-body force range, orbital-angular-momentum transfer, incident-particle energy, and bound-particle energy and configuration. Several important features are revealed: (1) The exchange mechanism is found to be important for reasonable ranges (≈ 1 F) and for energies as high as 150 MeV; (2) the exchange-to-direct ratio is quite sensitive to the orbital-angular-momentum transfer $L$, and the exchange amplitude can exceed the direct for large $L$; (3) non-normal transfers [${\mathrm{}(-1\mathrm{})\mathrm{}}^L\ne {\mathrm{}(-1\mathrm{})\mathrm{}}^{\Delta \pi }$] are usually negligible but may become significant for high $L$, especially if no spin flip is involved; (4) both the magnitude and phase of the exchange amplitude relative to the direct are sensitive to the initial and final single-particle configurations, particularly to the radial quantum numbers; (5) in collective excitations constructive interference occurs among exchange amplitudes to a sufficient extent that the inclusion of exchange can double the cross section for $2^{+}$ states. Expressions for direct and exchange amplitudes are obtained in the zero-range limit of the PWBA which qualitatively explain the behavior observed in the numerical results. A new method is presented for estimating collective enhancement due to core polarization by using empirical $B\left(E2\mathrm{}\right)\mathrm{}$ values. Calculation of the absolute cross section for the $2^{+}$ excitation in ${}_{}{}^{118}{}_{}{}^{}\mathrm{Sn}(p, p^{\prime })$, including exchange and core polarization, yields a two-body effective interaction strength which agrees both with strengths derived from charge-exchange reactions and with those obtained from a semirealistic two-nucleon interaction.

The differential Coulomb-excitation probability for the 0.558-MeV $2^{+}$ excited state in ${\mathrm{Cd}}^{114}$ and for the 0.847-MeV $2^{+}$ excited state in ${\mathrm{Fe}}^{56}$ have been measured by Coulomb exciting with ${\mathrm{O}}^{16}$ ions of 25- and 30-MeV incident energy. Inelastically scattered ions were separated from ions scattered elastically by requiring a coincidence with a deexcitation $\gamma$ ray detected in a large scintillator placed close to the target. The differential excitation probability was interpreted in terms of the reorientation effect to yield the static electric quadrupole moments for the 0.558-MeV $2^{+}$ state in ${\mathrm{Cd}}^{114}$, $Q_{22}=-0.64\mathrm{}\pm 0.19\times {10}^{-24\mathrm{}}$ ${\mathrm{cm}}^2$, and for the 0.847-MeV $2^{+}$ state in ${\mathrm{Fe}}^{56}$, $Q_{22}=-0.345\mathrm{}\pm 0.054\times {10}^{-24\mathrm{}}$ ${\mathrm{cm}}^2$.

In a study of the ${}_{}{}^{53}{}_{}{}^{}\mathrm{Cr}(p, n\gamma ){}_{}{}^{53}{}_{}{}^{}\mathrm{Mn}$ reactions, levels of ${}_{}{}^{53}{}_{}{}^{}\mathrm{Mn}$ have been found at 377.5, 1288.4, 1440.1, and 1619.1 keV, with uncertainties of ±0.3 keV. The observation of $\gamma$-ray anisotropies and ($p, n$) cross-section ratios permits unique spin assignments to three of the levels. Analysis of the ($p, n$) cross-section ratios using the Hauser-Feshbach formalism is consistent with the results of earlier experiments for the two lower levels. The spins of the above levels are, in the order given above, $\frac{5}{2}$, $\frac{3}{2}$, $\frac{11}{2}$, and $\frac{9}{2}$. Mixing ratios for the 377.5- and 1619.1-keV transitions are measured to be -0.6±0.3 and -3.2±0.8, respectively.

Protons from the 90-in. cyclotron at Lawrence Radiation Laboratory (LRL)-Livermore have been scattered from enriched targets of ${}_{}{}^{70,72,74,76}{}_{}{}^{}\mathrm{Ge}$, with an over-all energy resolution (FWHM) of 70 keV. The incident proton energy was approximately 14.5 MeV, and angular distributions were obtained from 20° to 150°, in 10° intervals. The elastic-scattering results were analyzed using the optical model. Angular distributions were obtained for inelastic proton groups from seven levels in ${}_{}{}^{70}{}_{}{}^{}\mathrm{Ge}$, nine levels in ${}_{}{}^{72}{}_{}{}^{}\mathrm{Ge}$, eleven levels in ${}_{}{}^{74}{}_{}{}^{}\mathrm{Ge}$, and ten levels in ${}_{}{}^{76}{}_{}{}^{}\mathrm{Ge}$—all below 3.5-MeV excitation. These included scattering to the quadrupole and octupole one-phonon vibrational levels and scattering to the $0^{+}$, $2^{+}$, $4^{+}$ two-quadrupole-phonon triplet. The data were analyzed using a coupled-channel computer code and a vibrational model of the nucleus. Strengths to excited states (${\beta }_I$) and spins and parities of levels were determined and are compared with Coulomb-excitation decay studies and with other scattering experiments.

An exact numerical solution of the spin-dependent level-density problem for a spherical shell-model nucleus with realistic single-particle level spacings is used to investigate the validity of analytical expressions based on approximate treatments of the model. With parameters chosen by reference to the numerical values, at least one of the analytical expressions proposed in the literature results in adequate fits to these values. Fitted parameters for the region $Z=25\mathrm{} \mathrm{to} 59$ and $N=25\mathrm{} \mathrm{to} 91$ are presented, and their physical interpretation is discussed. The dependence of the parameters on the number of nucleons of either kind is strongly affected by the shell structure of the nucleus. The level-density parameter $a$ is not simply proportional to the mass number $A$, and the spin distribution parameter can not be represented by the rigid-body moment of inertia, nor by any other monotonic function of $A$. Both parameters vary smoothly across the major proton and neutron shells, and the contributions of the two types of nucleons are additive.

Angular-distribution measurements have been performed on the ${\mathrm{Ne}}^{22}(t, p){\mathrm{Ne}}^{24}$ reaction at $E_t=3.3\mathrm{}$ MeV. Formation of the ground and 4.76-MeV ${\mathrm{Ne}}^{24}$ states is characterized by $l=0\mathrm{}$ transfer, which establishes $J^{\pi }=0^{+}$ for these two states. The $J=2\mathrm{}$, 3.87-MeV state was observed to be formed via $l=2\mathrm{}$ transfer, and so even parity is indicated for this state. Proton-$\gamma$ angular-correlation experiments were carried out in method II geometry at $E_t=3.45\mathrm{} \mathrm{and} 3.33$ MeV. These results establish unambiguous $J=4\mathrm{} \mathrm{and} 2$ assignments for the respective 3.96- and 5.58-MeV levels of ${\mathrm{Ne}}^{24}$. The present experimental information on the static properties of ${\mathrm{Ne}}^{24}$ is shown to be consistent with a $j-j$ coupling-model representation involving pure twobody proton configurations. An intercomparison of the observed static properties associated with the low-lying levels of the even-$A$ neon isotopes is presented, and a remarkable similarity is shown to exist between the low-lying level structures of ${\mathrm{O}}^{18}$ and ${\mathrm{Ne}}^{24}$. It is concluded that $1d_{\frac{5}{2}}$ subshell closure effects underlie the ${\mathrm{Ne}}^{24}$ spectrum.

The ${\mathrm{Si}}^{28}(d, t){\mathrm{Si}}^{27}$ reaction and the ${\mathrm{Si}}^{32}(d, t){\mathrm{Si}}^{31}$ and ${\mathrm{Ar}}^{36}(d, t){\mathrm{Ar}}^{35}$ reactions were studied at deuteron energies of 21.6 and 21.0 MeV, respectively. Angular distributions were obtained for triton groups from these ($d, t$) reactions leading to levels in the residual nuclei ${\mathrm{Si}}^{27}$, ${\mathrm{S}}^{31}$, and ${\mathrm{Ar}}^{35}$ with excitation energies up to approximately 3.5 MeV. Spectroscopic factors for the strong ($d, t$) transitions were extracted using now standard distorted-wave Born-approximation (DWBA) analyses. The ($d, t$) spectroscopic factors from this work are in reasonable agreement with previous neutron-pickup experimental data on ${\mathrm{Si}}^{28}$, ${\mathrm{S}}^{32}$, and ${\mathrm{Ar}}^{36}$, whenever the latter are available. Recent $2s-1d$ shell-model calculations are in reasonable accord with these data. In the particular case of the ${\mathrm{Ar}}^{36}(d, t){\mathrm{Ar}}^{35}$ data, it appears that the theoretical calculation which uses a "realistic" interaction derived from nucleon-nucleon scattering gives better agreement with these data than the theoretical calculation which uses a modified surface $\delta$ interaction.

$\gamma$-ray spectra following thermal- and resonant-neutron capture in copper have been studied using the Harwell electron linear accelerator and a lithium-drifted germanium detector. The energy resolution of the $\gamma$-ray spectrometer was about 14 keV over the neutron energy range from thermal to 2.7 keV. In addition to a thermal-neutron spectrum taken with a natural copper sample, the data include capture—$\gamma$-ray spectra for the 0.577-, 2.06-, and 2.66-keV resonances in ${}_{}{}^{63}{}_{}{}^{}\mathrm{Cu}(n, \gamma ){}_{}{}^{64}{}_{}{}^{}\mathrm{Cu}$, and the 0.229-keV resonance in ${}_{}{}^{65}{}_{}{}^{}\mathrm{Cu}(n, \gamma ){}_{}{}^{66}{}_{}{}^{}\mathrm{Cu}$. An analysis of the strengths of 91 assumed $E1\mathrm{}$ transitions in the ${}_{}{}^{63}{}_{}{}^{}\mathrm{Cu}(n, \gamma ){}_{}{}^{64}{}_{}{}^{}\mathrm{Cu}$ resonant data gave a best fit to a ${\chi }^2$ function with 1.0±0.2 degrees of freedom. The intensities of the four highest-energy transitions in the same reaction are observed to decrease by more than a factor of 6 as the neutron energy increases from thermal to 2.66 keV. A number of strong transitions approximately 3 MeV below the neutron binding energy is observed in the first resonance of both isotopes. Tentative spin assignments are given for the 0.229-keV resonance in ${}_{}{}^{65}{}_{}{}^{}\mathrm{Cu}$. If the resonance is due to capture of $s$-wave neutrons, the spin and parity are $2^{-}$. For capture of neutrons with higher partial waves, the spin is restricted to either 2 or 3 with the parity determined by the relative orbital angular momentum.

The $\beta$ decay of ${\mathrm{Ta}}^{186}$ to the levels in ${\mathrm{W}}^{186}$ has been studied using scintillation and Ge(Li) spectrometers. The sources of ${\mathrm{Ta}}^{186}$ were obtained by the ${\mathrm{W}}^{186}(n, p){\mathrm{Ta}}^{186}$ reaction on enriched as well as on natural samples of tungsten with 14.8-MeV neutrons. The half-life of ${\mathrm{Ta}}^{186}$ has been measured as 10.5±0.5 min. $\gamma$ rays which have been assigned to the decay of ${\mathrm{Ta}}^{186}$ are 94, 122.5, 183.5, 198, 214, 274.2, 291, 295, 308, 314, 322, 341.5, 411, 418, 424, 440, 458, 462, 510, 536, 567, 583.5, 605, 615.5, 637, 656, 708, 726, 736.5, 738, 753.3, 755, 758, 785, 799, 829.5, 846, 870, 884, 891.5, 921, 925, 952, 1014, 1027.5, 1080, 1111, 1124.5, 1151.5, 1173, 1211.5, 1247, 1274, 1438, and 1486 keV. The study of the $\beta$ spectrum, using an anthracene scintillation spectrometer, showed the existence of four $\beta$ groups with the end-point energies of 3.10±0.15(5%), 2.50±0.10(32%), 2.20±0.10(49%), and 1.5±0.2 (14%) MeV. The $\beta -\gamma$ and $\gamma -\gamma$ coincidence studies have been made, and a level scheme of ${\mathrm{W}}^{186}$ is proposed with levels at 122.5, 396.7, 738, 859, 921, 952, 1046, 1150, 1247, 1274, 1464, 1589, 1608, 1660, and 2032 keV. The results are discussed in the light of the unified model.

Measurements have been made of the independent fission yields of several iodine isotopes in thermal-neutron-induced fission of ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}$. These yields were obtained by isolation of iodine-fission products at early times after fission by a new, fast radiochemical procedure. The fractional cumulative fission yield and half-life of ${}_{}{}^{135}{}_{}{}^{}\mathrm{Te}$ were also determined from the experimental results. Fission yields measured are: ${}_{}{}^{131}{}_{}{}^{}\mathrm{I}$, (4.2±0.4)×${10}^{-3\mathrm{}}$% independent; ${}_{}{}^{132}{}_{}{}^{}\mathrm{I}$, (1.74±0.11)×${10}^{-2\mathrm{}}$% independent; ${}_{}{}^{133}{}_{}{}^{}\mathrm{I}$, 0.176±0.009% independent; ${}_{}{}^{134}{}_{}{}^{}\mathrm{I}$, 0.90±0.08% independent; ${}_{}{}^{135}{}_{}{}^{}\mathrm{I}$, 0.44±0.07 fractional independent; ${}_{}{}^{135}{}_{}{}^{}\mathrm{Te}$, 0.52±0.07 fractional cumulative. The half-life of ${}_{}{}^{135}{}_{}{}^{}\mathrm{Te}$ was determined to be 11.2±2.6 sec.

The mean life of the 343-keV state in ${}_{}{}^{111}{}_{}{}^{}\mathrm{Cd}$ is measured, using the delayed coincidence method, employing a $\beta -\gamma$ coincidence arrangement, with plastic crystals and the centroid shift technique. A value of 85±17 psec is obtained for the mean life. This is in complete disagreement with the previous Coulomb-excitation results, and is in agreement with that of the resonance scattering experiment. The transition probabilities $T\left(E2\mathrm{}\right)\mathrm{}$ and $T\left(M1\mathrm{}\right)\mathrm{}$ are estimated, using the present value of the mean life and the available values of the conversion coefficient, mixing and branching ratios. An $E2\mathrm{}$ enhancement of 7.5±2 and $M1\mathrm{}$ hindrance of 129±33 over the single-particle estimates are noted. The theoretical values estimated using the wave functions of Kisslinger and Sorensen as well as those of Barnes are found to be unsuitable for the estimation of the transition probabilities. The experimental values are therefore employed to obtain phenomenological wave functions for the ground and the 343-keV states. The resultant wave functions show dominant $d_{\frac{5}{2}}$ plus phonon contributions in both the ground and the 343-keV state.

The proposed method for measuring the spin of $S$-wave neutron resonances is based on the detailed properties of the low-energy capture $\gamma$-ray spectrum. Measurements on nuclei with resonances of known spin show that this method gives reliable spin assignments. It is also applied to unassigned resonances in ${}_{}{}^{167}{}_{}{}^{}\mathrm{Er}$ and ${}_{}{}^{187,189}{}_{}{}^{}\mathrm{Os}$.