New information about levels in the transitional nucleus ${}_{}{}^{186}{}_{}{}^{}\mathrm{Os}$ is gained from a study of the decay of 15.8-h ${}_{}{}^{186}{}_{}{}^{}\mathrm{Ir}$. A significantly improved decay scheme was deduced from an extensive $\gamma -\gamma$ coincidence measurement. Spins and parities were determined for many levels from a nuclear orientation study; in several cases measured electron-conversion data were useful. Spins for the proposed members of a $\gamma$ band were confirmed, up to $I=6\mathrm{}$. In addition, detailed evidence for the existence of a $K=0\mathrm{}$ band, built upon the known $0^{+}$ level at 1061 keV, is presented ($2^{+}$, $4^{+}$, and $6^{+}$ members at 1209, 1461, and 1813 keV, respectively). Mixing ratios for interband transitions depopulating the members of both bands were determined from the nuclear orientation data, and are discussed. The deduced $E2\mathrm{}$ branching ratios are fairly well reproduced in a band-mixing calculation incorporating these bands. An absolute value of (2.8±0.3) ${\mathrm{\mu }}_{\mathit{N}}$ for the magnetic moment of ${}_{}{}^{186}{}_{}{}^{}\mathrm{Ir}$ is reported, and is discussed in terms of coupling of Nilsson states; the assignment $\left\{\frac{7}{2^{+}}\mathrm{}\right[404]\mathrm{}\pi ; \frac{3}{2^{-}}\mathrm{}[512\left]\mathrm{}\nu \right\}{5}^{-}$ is proposed. Results of a study of the ${}_{}{}^{186}{}_{}{}^{}\mathrm{W}(\alpha , 4n){}_{}{}^{186}{}_{}{}^{}\mathrm{Os}$ reaction, including $\gamma$, $\gamma -\gamma$, $\gamma \left(\theta \right)$, and $\gamma -t$ measurements, confirm the results of the decay study. In addition, two isomeric states were identified, at 1774 keV (8.1 ns) and at 2165-keV (5.3 ns). Side-feeding of negative parity levels was observed.

RADIOACTIVITY ${}_{}{}^{186}{}_{}{}^{}\mathrm{Ir}$ (15.8-h isomer); measured $I_{\gamma }\left(\theta \right)$ oriented nuclei; $\gamma -\gamma$ coin; ICC. ${}_{}{}^{186}{}_{}{}^{}\mathrm{Os}$ deduced levels; $J^{\pi }$, mixing ratios; band-mixing calculation. ${}_{}{}^{186}{}_{}{}^{}\mathrm{Ir}$ deduced magnetic moment, Nilsson assignment.

NUCLEAR REACTIONS ${}_{}{}^{186}{}_{}{}^{}\mathrm{W}(\alpha , 4n){}_{}{}^{186}{}_{}{}^{}\mathrm{Os}$, $E_{\alpha }=47\mathrm{}$ MeV; measured $E_{\gamma }$, $I_{\gamma }$, $\gamma -\gamma$ coin, $I_{\gamma }\left(\theta \right)$, $\gamma -t$; ${}_{}{}^{186}{}_{}{}^{}\mathrm{Os}$ deduced levels, $J^{\pi }$, $T_{\frac{1}{2}}$.

Calculations of the energy for two different nuclear matter models are carried out using Jastrow-Slater wave functions and an integral equation developed previously by Chakravarty and Woo. Even though the same variational parameters are used, our results differ significantly with those of Ceperley, Chester, and Kalos who employed a Monte Carlo technique. The discrepancy, mainly in the potential energy, is traced to short-range behavior of the pair correlation function. No satisfactory explanation can be offered at this time. Our integral equation is then subjected to a formal analysis for a weakly interacting Bose gas. It is shown to perform at least as well for boson systems as the Bogoliubov-Born-Green-Kirkwood-Yvon equation.

NUCLEAR STRUCTURE Many-body variational calculation applied to nuclear matter model.

In the usual Bohr-Mottelson (Faessler-Greiner) treatment of the vibrations of permanently deformed nuclei with axially symmetric equilibrium shape the description of the $\gamma$ vibration is more complicated than that of the $\beta$ vibration: the coupling between the $\gamma$ vibration and the rotation about the approximate symmetry axis $z^{\prime }$ is not negligible in any reasonable zero-order approximation. We show that a simplification can be achieved if the $x^{\prime }$ and $y^{\prime }$ axes of the rotating frame are not chosen along principal quadrupole axes, but are left free as in the particle-plus-rotor model. For small vibrational amplitudes the Hamiltonian consists of uncoupled rotational, $\beta$- and $\gamma$-vibrational parts. The total vibrational part takes the form of a three-dimensional anisotropic harmonic oscillator with two equal eigenfrequencies, which is expected to be a convenient starting point for more exact calculations. In addition, this description may be more convenient to relate collective states to a microscopic picture.

NUCLEAR STRUCTURE Phonon discription of $\gamma$ vibrations, single-principal-axis frame.

The Brueckner $G$ matrix from the Reid soft-core potential is taken for the leading contribution of the effective two-proton interaction in the ${}_{}{}^{132}{}_{}{}^{}\mathrm{Sn}$ region. Phenomenological two-body pairing and multipole forces are added to adjust for all neglected effect. Two model spaces are selected; a small space ($0g_{\frac{7}{2}}, 1d_{\frac{5}{2}}$) and a large space ($0g_{\frac{7}{2}}, 1d_{\frac{5}{2}}, 0h_{\frac{11}{2}}, 2s_{\frac{1}{2}}, 2s_{\frac{1}{2}}$). For each space the strengths of the phenomenological terms are adjusted to fit the ${}_{}{}^{134}{}_{}{}^{}\mathrm{Te}$ spectrum. It is found that both of the total interactions have a high statistical correlation with the bare $G$ matrix. The total effective interactions are then used without further adjustment in shell model calculations to obtain good predictions for the spectra of ${}_{}{}^{135}{}_{}{}^{}\mathrm{I}$, ${}_{}{}^{136}{}_{}{}^{}\mathrm{Xe}$, and ${}_{}{}^{137}{}_{}{}^{}\mathrm{Cs}$.

NUCLEAR STRUCTURE Shell-model structure of ${}_{}{}^{132}{}_{}{}^{}\mathrm{Sn}$ core plus valence protons: shell-model effective interactions consisting of Brueckner reaction matrix plus phenomenological multipole corrections.

Level structures and level densities of nuclei consisting of a ${}_{}{}^{132}{}_{}{}^{}\mathrm{Sn}$ core plus as many as nine valence protons are calculated using a realistic effective interaction ($G$ matrix) plus previously determined correction terms. The correction terms were determined so that the total interaction, when used in shell-model calculations, gave a fit to the observed ${}_{}{}^{134}{}_{}{}^{}\mathrm{Te}$ spectrum. Recently developed trace reduction methods are employed to determine the energy moments of the level densities for each spin value. Comparisons between these moments and results of exact shell-model diagonalizations show excellent agreement. Level density comparisons demonstrate that the effect of the necessary correction terms on the spectra is small and decreases as the number of allowed orbits increases. This level density method is also used to investigate the effects of the Coulomb force on the multi-proton spectra.

NUCLEAR STRUCTURE Exact and statistical shell-model structure of ${}_{}{}^{132}{}_{}{}^{}\mathrm{Sn}$ core plus valence protons; shell-model effective interaction consisting of Brueckner reaction matrix plus phenomenological multipole corrections; level densities via moment expansions.

A new semiempirical nuclear level density formula is proposed, which takes into account the influence of nuclear shell structure on level densities and the excitation energy dependence of shell effects. The ground state shell and pairing energies enter directly into this formula, which involves three mass-independent parameters characterizing the average single-particle level density near the Fermi level and the wavelength of shell oscillations. The present formulation is shown not only to give a good fit to the experimental data on neutron resonance spacings of spherical nuclei, but also to provide a reliable extrapolation to higher excitation energies. The present analysis has also brought out the need to include the dependence of level density parameter $a$ on the surface to volume ratio of nuclei. The analysis of the data for deformed nuclei with the present formulation does not indicate an enhancement of the level densities of the magnitude suggestive of a rotation degree of freedom completely decoupled from intrinsic degrees at the excitation energy equal to neutron binding energies.

NUCLEAR STRUCTURE Nuclear level densities, semiempirical formula, dependence on surface to volume ratio, shell effects, spherical, deformed nuclei.

Several new examples of electric dipole transitions to final isospin $\frac{3}{2}$ are calculated using the Fabre-Levinger formalism: (i) the Volkov potential (Serber exchange) gives an integrated cross section 4% higher than the O'Connell-Prats sum rule; (ii) the $V^x$ potential (zero force in odd-parity two-body states) gives a ${}_{}{}^3{}_{}{}^{}\mathrm{H}$ photoeffect cross section close to that found by Fabre and Levinger for ${}_{}{}^3{}_{}{}^{}\mathrm{He}$; (iii) transitions to an uncoupled grand orbital three are several percent of those to grand orbital one. Addition of the cross sections for uncoupled states gives poor agreement with the coupled calculation of Fang et al.; (iv) a $V^x$ potential (Wigner-Bartlett exchange) gives an integrated cross section 5% higher than the Thomas-Reiche-Kuhn value. We also calculate for final isospin ½, neglecting coupling to two-body breakup. The $V^x$ potential (zero force in odd-parity two-body states) gives an integrated cross section 23% higher than the O'Connell-Prats value. A Wigner-Bartlett mixture gives a 23% disagreement with the Thomas-Reiche-Kuhn sum rule. The calculated cross section (summed for both isospin states) has a higher and narrower peak than that measured by Gorbonov (summed for two-body and three-body breakup).

NUCLEAR REACTIONS photodisintegration of trinucleon; hyperspherical harmonics.

The eigenvalue equation to the Faddeev kernel is analytically continued on to nonphysical sheets adjacent to the real energy axis of the physical sheet. The position of the pole of the three-body $S$ matrix corresponding to the deepest three-body bound state is calculated as a function of the two-body interaction strength. In a three-neutron model of pure ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ interaction and spectator angular momentum $\lambda =1\mathrm{}$ favored by the shell model, the very pattern of the pole trajectory rules out the possibility of a low-energy resonance.

NUCLEAR STRUCTURE Analytical continuation of Faddeev kernel to nonphysical energy sheets. Calculated three-neutron $S$-matrix pole trajectory.

The results of time-dependent Hartree-Fock calculations in two and three dimensions are compared for ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ + ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ at $E_{\mathrm{lab}}=278\mathrm{}$ MeV. The primary difference is the large fusion cross section calculated in three dimensions which is not present in two dimensions. Energy loss, scattering angle, and orbits are compared for a variety of impact parameters.

NUCLEAR REACTIONS ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}({}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}, x)$ in time dependent Hartree-Fock approximation. Comparison, two and three dimensions.

The possible $0^{-}$ →$0^{+}$ ground-state pair decay of the ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ 10.95- MeV $0^{-}$ state was reinvestigated using the ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}(p, \alpha ){}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ reaction at $E_p=5.4-5.7\mathrm{}$ MeV and a magnetic pair spectrometer. A previously reported pair peak of 3.84 MeV due to the 10.952→7.117-MeV transition was not observed. The data indicate a much smaller relative population of the 10.95-MeV state in this reaction than reported previously and this places doubt on the upper limit derived earlier for the $0^{-}$ →$0^{+}$ ground-state pair decay. In a test of the ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}({}_{}{}^3{}_{}{}^{}\mathrm{He}, p){}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ reaction at $E_{{}_{}{}^3{}_{}{}^{}\mathrm{He}}=4\mathrm{}$ MeV the yield was too low to study the 10.95-MeV state. Using the ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}(d, p){}_{}{}^{14}{}_{}{}^{}\mathrm{C}$ reaction at $E_d=4.5\mathrm{}$ MeV the $0^{-}$ →$0^{+}$ ground-state branch from the 6.90-MeV $0^{-}$ state of ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$ was found to be<1.1 × ${10}^{-4\mathrm{}}$ via pair decay. The corresponding lifetime limit, $\tau {(0^{-}\to 0^{+})}_{e^{+}{e}^{-}}>3\mathrm{}\times {10}^{-10\mathrm{}}$ sec, is not considered significant. It is concluded that a sensitive search for M0 pair transitions remains to be made.

NUCLEAR STRUCTURE ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$: measured ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}(p, \alpha )$ and ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}(d, p)$ pair spectra; previous results on ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ 10.95-MeV $\tau {\mathrm{}\left(M0\mathrm{}\right)\mathrm{}}_{e^{+}{e}^{-}}$ not confirmed; deduced lower limit on ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$ 6.90-MeV $\tau {\mathrm{}\left(M0\mathrm{}\right)\mathrm{}}_{e^{+}{e}^{-}}$.

Recent results indicate that terms in the optical potential nonlinear in the matter density $\rho$ are important in $\pi$-nucleus scattering. It does not seem possible to identify these terms with a single physical effect. In particular, the contribution to the real part of the optical potential due to true meson absorption may be of the same order as that of the Lorentz-Lorenz effect.

NUCLEAR REACTIONS $\pi$-nucleus scattering, two-nucleon correlations, meson absorption.

Measurements of the total nuclear cross section for the reaction ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}(p, 2pn){}_{}{}^{38}{}_{}{}^{}\mathrm{K}$ in an energy range of 20-160 MeV are presented as a function of the mean proton energy in the target.

NUCLEAR REACTIONS ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}(p, 2pn)$; $E_p=20-160\mathrm{}$ MeV; presents measured values for the total nuclear cross section.

An analytic function of energy is fitted to the available $S$, $P$, and $D$ wave $\pi N$ phase shifts of various goups below 400 MeV. This global average, which reproduces well most of the experiment cross sections, is anticipated to be useful in pion-nucleus and pion-nucleon interaction calculations.

NUCLEAR REACTIONS ${\pi }^{\pm }N$; 0-400 MeV; analytic function fitted to tabulated phase shifts.

The half-life of ${}_{}{}^{57}{}_{}{}^{}\mathrm{Mn}$ has been measured to be 87±2 s.

RADIOACTIVITY ${}_{}{}^{57,58}{}_{}{}^{}\mathrm{Mn}$; measured $T_{\frac{1}{2}}$.

Excited states and associated resonance widths in the ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ system for $J^{\pi }=4^{-}, 5^{-}, 5^{+}, \mathrm{and} 6^{+}$ are calculated within the framework of the generalized $R$-matrix methodology of Lane and Robson. All calculated levels lie well above the known resonances in the ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ system. The effect of the Coulomb interaction on the ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ continuum wave functions is also discussed.

NUCLEAR STRUCTURE Calculated $J^{\pi }=4^{-}, 5^{-}, 5^{+}, \mathrm{and} 6^{+}$ resonance positions and associated widths in the ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ system. All states lie above 55 MeV excitation.

A six band rotation-particle coupling calculation is done for the $\frac{11}{2^{-}}$ states in ${}_{}{}^{147}{}_{}{}^{}\mathrm{Sm}$. An entirely different distribution of the band energies is found as compared with the recently reported results from (${}_{}{}^3{}_{}{}^{}\mathrm{He}$, $\alpha$) reactions.

NUCLEAR STRUCTURE Rotation-particle calculation for $1h_{\frac{11}{2}}$ neutron-hole states in ${}_{}{}^{147}{}_{}{}^{}\mathrm{Sm}$.

Measurements of cross sections and analyzing powers are examined for polarized proton capture on ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}$, ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$, ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$, ${}_{}{}^{58}{}_{}{}^{}\mathrm{Fe}$, ${}_{}{}^{59}{}_{}{}^{}\mathrm{Co}$, and ${}_{}{}^{88}{}_{}{}^{}\mathrm{Sr}$ at energies which cover the giant dipole resonance region. These data are used to extract the relative amplitudes and phases of the contributing $E1\mathrm{}$ $T$-matrix elements. A typical result exhibits two solutions. Calculations using the direct (or a direct-semidirect) capture model appear to provide a means for choosing the physical solution.

NUCLEAR REACTIONS: ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}(\overrightarrow{p}, {\gamma }_0)$, ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}(\overrightarrow{p}, {\gamma }_0)$, ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}(\overrightarrow{p}, {\gamma }_0)$, ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}(\overrightarrow{p}, {\gamma }_0)$, ${}_{}{}^{58}{}_{}{}^{}\mathrm{Fe}(\overrightarrow{p}, {\gamma }_0)$, ${}_{}{}^{59}{}_{}{}^{}\mathrm{Co}(\overrightarrow{p}, {\gamma }_0)$, ${}_{}{}^{88}{}_{}{}^{}\mathrm{Sr}(\overrightarrow{p}, {\gamma }_0)$; measured $\sigma \left(\theta \right)$ and $A\left(\theta \right)$ over energy region of the giant dipole resonance. Deduced $T$-matrix amplitudes and phases. Compare results to direct-semidirect model calculations.

The determination of reduced normalizations by measuring ($d, p$) reactions in the energy region of sub-Coulomb and quasi-Coulomb stripping with an experimental accuracy which has not been attained in former investigations allows reasonable comparisons with corresponding reduced normalizations of analog states obtained by elastic proton scattering via isobaric analog resonances. This comparison includes 38 states with known spins and parities formed by adding a further nucleon to the nuclei ${}_{}{}^{124}{}_{}{}^{}\mathrm{Sn}$, ${}_{}{}^{130}{}_{}{}^{}\mathrm{Te}$, ${}_{}{}^{138}{}_{}{}^{}\mathrm{Ba}$, ${}_{}{}^{140}{}_{}{}^{}\mathrm{Ce}$, ${}_{}{}^{142}{}_{}{}^{}\mathrm{Nd}$, and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$. The reduced normalizations of the proton analog states are based on the experimental partial widths given by other authors and on own calculations according to two different shell model theories of isobaric analog resonances. The uncertainties still remaining in the theoretical description of some effects inherent in the direct reaction mechanism of transfer reactions as well as in the shell model reaction theoreis do not permit a unique decision concerning the validity of the different theoretical approaches in determining the decay widths of single particle states.

NUCLEAR REACTIONS ${}_{}{}^{124}{}_{}{}^{}\mathrm{Sn}$, ${}_{}{}^{130}{}_{}{}^{}\mathrm{Te}$, ${}_{}{}^{138}{}_{}{}^{}\mathrm{Ba}$, ${}_{}{}^{140}{}_{}{}^{}\mathrm{Ce}$, ${}_{}{}^{142}{}_{}{}^{}\mathrm{Nd}$, ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}(d, p)$,, ($p, p$) calculated reduced normalizations of 38 parent and analog states, respectively, based on experimental data as well as on DWBA and two shell model reaction approaches; comparison and discussion of results.

The ${}_{}{}^{70,72,74,76}{}_{}{}^{}\mathrm{Ge}(d, {}_{}{}^3{}_{}{}^{}\mathrm{He}){}_{}{}^{69,71,73,75}{}_{}{}^{}\mathrm{Ga}$ reactions have been studied at 26 MeV with 15-keV resolution full width at half maximum using a tandem accelerator and split pole magnetic spectrometer. The spectroscopic factors are determined for 15 levels in ${}_{}{}^{69}{}_{}{}^{}\mathrm{Ga}$ and 11 levels in each of the 3 other Ga isotopes. Level schemes are proposed for the practically unknown ${}_{}{}^{73}{}_{}{}^{}\mathrm{Ga}$ and ${}_{}{}^{75}{}_{}{}^{}\mathrm{Ga}$. Anomalies in the occupation numbers are observed between $Z=31\mathrm{} \mathrm{and} 32$ and between $N=40\mathrm{} \mathrm{and} 42$, this last one corresponding to the structural transition observed recently in a comparison of the ($p, t$) and ($t, p$) reactions. These anomalies could be related to changes in the nuclear shape.

NUCLEAR REACTIONS ${}_{}{}^{70,72,74,76}{}_{}{}^{}\mathrm{Ge}(d, {}_{}{}^3{}_{}{}^{}\mathrm{He})$, $E=26\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$;; ${}_{}{}^{69}{}_{}{}^{}\mathrm{Ga}$, ${}_{}{}^{71}{}_{}{}^{}\mathrm{Ga}$, ${}_{}{}^{73}{}_{}{}^{}\mathrm{Ga}$, ${}_{}{}^{75}{}_{}{}^{}\mathrm{Ga}$ deduced levels, $E$, $l$, $j$ $\pi$, $C^{2}S$; deduced Ge ground-state proton occupation numbers.

A ${}_{}{}^2{}_{}{}^{}\mathrm{He}$ detection system has been developed and used to investigate the ($\alpha$, ${}_{}{}^2{}_{}{}^{}\mathrm{He}$) reaction at bombarding energies of 55 and 65 MeV on targets of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$, ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$, ${}_{}{}^{22}{}_{}{}^{}\mathrm{Ne}$, ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{26}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$, ${}_{}{}^{29}{}_{}{}^{}\mathrm{Si}$, ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$, ${}_{}{}^{36}{}_{}{}^{}\mathrm{Ar}$, ${}_{}{}^{38}{}_{}{}^{}\mathrm{Ar}$, and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$. Preferential population of two-neutron states with dominant ${{\left(d_{\frac{5}{2}}\right)}^2}_4$, ${\left(d_{\frac{3}{2}}{f}_{\frac{7}{2}}\right)}_5$, and ${{\left(f_{\frac{7}{2}}\right)}^2}_6$ character was observed. A linear $A$ dependence of the binding energies of the $J^{\pi }=5^{-} \mathrm{and} 6^{+}$ states was obtained. This systematic behavior is well described by the Bansal-French model, using the parameters $a=-0.30\mathrm{}$ MeV and $b=2.6\mathrm{}$ MeV. Simple shell-model calculations for the $2n$ configurations are in good agreement with the experimental data.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$, ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$, ${}_{}{}^{22}{}_{}{}^{}\mathrm{Ne}$, ${}_{}{}^{26}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$, ${}_{}{}^{29}{}_{}{}^{}\mathrm{Si}$, ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$, ${}_{}{}^{36}{}_{}{}^{}\mathrm{Ar}$, ${}_{}{}^{38}{}_{}{}^{}\mathrm{Ar}(\alpha , {}_{}{}^2{}_{}{}^{}\mathrm{He})$, $E=65\mathrm{}$ MeV and ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}(\alpha , {}_{}{}^2{}_{}{}^{}\mathrm{He})$, $E=55\mathrm{}$ MeV. Measured $\sigma (E_f, \theta )$, deduced $E_x$ and $J^{\pi }$ systematics.