A modification to an evaporation model employed in the analysis of isomer excitation functions is presented. Isomer excitation energies deduced from the modified model are shown to be in quantitative agreement with those obtained from a more sophisticated analysis.

Theoretical cross sections are presented for the excitation of the giant resonances in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ by electron neutrinos with energies $E_v=15\mathrm{}-75$ MeV. Although the excitation strengths of the individual giant-resonance levels are somewhat different for the two particle-hole models used (Lewis-Walecka-deForest's and Gillet's model), the total summed cross sections are similar.

1p1h amplitudes - usually being large - had been taken into account in the authors' paper. They vanish for self-consistent single-particle states and thus do not represent short-range correlations if the latter are defined as deviations from the self-consistent single-particle determinant.

Quadrupole resonance lines of $\beta$-unstable ${}_{}{}^{12}{}_{}{}^{}\mathrm{B}$ have been distinctly resolved in a single crystal of Be, and have behaved properly under field reversal and variation of the angle $\theta$ between crystal $c$ axis and external magnetic field.

Dyson's new $F$-statistic test for spurious or missing levels has been applied to recent ${\mathrm{Er}}^{166}$ data and other of our results. The $F$ test was shown to give good agreement with the ${\mathrm{Er}}^{166}$ total observed level set and our $l=0\mathrm{}$ population choices for ${\mathrm{Er}}^{168}$ and ${\mathrm{Er}}^{170}$, which were made before this test was known to us. The $F$ test involves the evaluation, at each resonance position $E_i$, of a parameter $F_i$, defined as $F_i\equiv \Sigma {j\ne i}^{}f\left(x_{\mathrm{ji}}\right)$, where $x_{\mathrm{ji}}=\frac{(E_j-E_i)}{L}$, and $j$ is summed over all resonances between ($E_i-L$) and ($E_i+L$), and $f\left(x\right)=\frac{1}{2}\ln \left\{\frac{[1+{(1-x^2)}^{\frac{1}{2}}]}{[1-{(1-x^2)}^{\frac{1}{2}}]}\right\}$ for $x<\mathrm{}1\mathrm{}$. The interval $L=M〈D〉$ is characterized by a properly chosen integer, $M$. Dyson finds that $〈F_i〉=n-\ln \mathrm{}\left(n\right)-0.656\mathrm{}$, with a standard deviation of ${\left[\ln \mathrm{}\right(n\left)\right]}^{\frac{1}{2}}$, where $n=\pi M$. If a spurious level is present, $〈F_i〉=n$, evaluated at the spurious level. Thus, a large positive fluctuation occurs at a spurious level, while a low value of $F_i$ results near a missed level. We have used the $F$ test and other statistical tests to see if sets of $l=0\mathrm{}$ resonances could be chosen for ${\mathrm{Th}}^{232}$ and ${\mathrm{U}}^{238}$ which agree with the Porter-Thomas (PT) distribution for ${\left({\Gamma }_n^0\right)}^{\frac{1}{2}}$ and all statistical level-ordering tests. For the ${\mathrm{Th}}^{232}$ and ${\mathrm{U}}^{238}$ we used our older data for ${\Gamma }_n^0$ values and for the positions of the stronger $s$ levels. Our more recent 1970 data for these isotopes were used to better establish the position of the weak levels. It should be emphasized that ≥80% of the final choice $s$ population is made of stronger $s$ levels having ${\Gamma }_n^0$ values too large to be $p$ levels. The only degree of freedom is for the $s$-level selection from the weaker $s+p$ levels observed. The number of weak "$s$" levels chosen is determined by the PT distribution and we attempt to fit (simultaneously) the Wigner nearest-neighbor spacing distribution, $\rho (S_j,S_{j+1\mathrm{}})\cong -0.27\mathrm{}$, the Dyson-Mehta $\Delta$ statistic, and the Dyson $F$ test. For both isotopes, good simultaneous fits were obtained. This result is highly unlikely unless the "true" $s$ population satisfied the tests, since ≥80% of the final choice involves nonweak $s$ levels.

$\gamma$ rays in the range from 150 to 1000 keV, following the spontaneous fission of ${}_{}{}^{252}{}_{}{}^{}\mathrm{Cf}$, are observed with a 20-${\mathrm{cm}}^3$ Ge(Li) detector [full width at half maximum (FWHM) 3.5 keV at 356 keV] in coincidence with $K$ x rays from the fission fragments, observed with a 0.14-${\mathrm{cm}}^3$ Ge(Li) detector (FWHM 350 eV at 31 keV). Twenty-one 1024-channel $\gamma$-ray spectra were accumulated and sorted by computer, corresponding to windows set on $K$ x rays from Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Sb, Te, I, Xe, Cs, Ba, La, Ce, Pr, Nd, Pm, Sm, and Eu. In conjunction with previous work, this data allowed both mass and charge assignments to be made for about 90 of the observed transitions. Relative yields for certain $\gamma$ rays in self-gated spectra, those for which both x ray and $\gamma$ ray originated from the same isotope, have been measured and compared with predictions based on previous work.

The reactions ${}_{}{}^{91,92,94}{}_{}{}^{}\mathrm{Zr}(\alpha ,t){}_{}{}^{92,93,95}{}_{}{}^{}\mathrm{Nb}$, ${}_{}{}^{90,91,92,94}{}_{}{}^{}\mathrm{Zr}(\alpha ,d){}_{}{}^{92,93,94,96}{}_{}{}^{}\mathrm{Nb}$, and ${}_{}{}^{92}{}_{}{}^{}\mathrm{Mo}(\alpha ,d){}_{}{}^{94}{}_{}{}^{}\mathrm{Tc}$ have been investigated with a 50-MeV $\alpha$-particle beam from the Berkeley 88-in. cyclotron. High-spin proton excited states observed in the ($\alpha ,t$) reaction, based on comparisons with (${}_{}{}^3{}_{}{}^{}\mathrm{He},d$) experiments on the same targets, include: ${}_{}{}^{92}{}_{}{}^{}\mathrm{Nb}$(≅5 MeV multiplet); ${}_{}{}^{93}{}_{}{}^{}\mathrm{Nb}$(1.08, 1.29, ≅4.5 MeV); and ${}_{}{}^{95}{}_{}{}^{}\mathrm{Nb}$(1.27, 1.65, 2.10 MeV). Two groups of strongly excited states appear in the ($\alpha ,d$) data. Members of the lower group [${}_{}{}^{92}{}_{}{}^{}\mathrm{Nb}$(g.s.), ${}_{}{}^{94}{}_{}{}^{}\mathrm{Nb}$(0.08 MeV), and ${}_{}{}^{96}{}_{}{}^{}\mathrm{Nb}$(0.23 MeV)] have been previously identified as being ${(\pi g_{\frac{9}{2}},\nu d_{\frac{5}{2}})}_{7^{+}}$ states. Based on the ${}_{}{}^{92}{}_{}{}^{}\mathrm{Mo}(\alpha ,d){}_{}{}^{94}{}_{}{}^{}\mathrm{Tc}$ results, the ${}_{}{}^{94}{}_{}{}^{}\mathrm{Tc}$ ground state can also be assigned $7^{+}$. The higher levels [${}_{}{}^{92}{}_{}{}^{}\mathrm{Nb}$(2.58 MeV), ${}_{}{}^{94}{}_{}{}^{}\mathrm{Nb}$-(2.42 MeV), ${}_{}{}^{96}{}_{}{}^{}\mathrm{Nb}$(2.38 MeV), and ${}_{}{}^{94}{}_{}{}^{}\mathrm{Tc}$(2.68 MeV)] are believed to be either ${(\pi g_{\frac{9}{2}},\nu g_{\frac{7}{2}})}_{8^{+}}$ or ${(\pi g_{\frac{9}{2}},\nu h_{\frac{11}{2}})}_{{10}^{-}}$ states based on the results of shell-model matrix-element calculations and the ($\alpha ,d$) structure factors of Glendenning.

On the basis of the macroscopic-microscopic method we have performed a new calculation of the nuclear potential energy of deformation for heavy and superheavy nuclei. Our primary emphasis has been to develop techniques that permit more accurate extrapolations both to the large deformations encountered in fission and heavy-ion reactions and to new regions of nuclei. With this purpose in mind, we specify the nuclear shape with five degrees of freedom, in terms of smoothly joined portions of three quadratic surfaces of revolution (e.g., two spheroids connected by a hyperboloidal neck). The single-particle potential is obtained by folding a Yukawa function with a uniform sharp-surface generating potential of appropriate shape. The parameters describing the potential are obtained from statistical (Thomas-Fermi) calculations that reproduce correctly the average trends throughout the Periodic Table of a variety of nuclear properties. To solve the Schrödinger equation for the single-particle energies and wave functions, we have used mainly an expansion of the wave function in a set of deformed harmonic-oscillator basis functions, but have also investigated a finite-difference method. Shell and pairing corrections are calculated from the single-particle energies by means of the methods developed by Strutinsky and added to the surface and Coulomb energies of the liquid-drop model to obtain the total potential energy of deformation.

This approach is found to reproduce reasonably well the over-all trends of experimental fission-barrier heights of nuclei ranging from rare earths to actinides. The calculated fission barriers of actinide nuclei contain two peaks separated by a secondary minimum. The over-all variation in the relative heights of the two peaks agrees with experimental results, but the calculated first peak is somewhat low for thorium isotopes and somewhat high for curium isotopes. For the actinides the first saddle point is found to be symmetric in shape and the second saddle point asymmetric. The highest saddle point is asymmetric for ${}_{}{}^{226}{}_{}{}^{}\mathrm{Ra}$ and ${}_{}{}^{210}{}_{}{}^{}\mathrm{Po}$ and symmetric for ${}_{}{}^{188}{}_{}{}^{}\mathrm{Os}$. The fission barriers of superheavy nuclei near ${}_{}{}^{298}{}_{}{}^{}114$ are even higher than previously supposed. With respect to spontaneous fission, the island of superheavy nuclei is a mountain ridge extending from 114 protons to about 124 protons. The descent from the mountain down to the sea of instability is rather gentle for decreasing neutron numbers below 184, but is more rapid on the other three sides.

The statistic $\Lambda \mathrm{}\left(n\right)\mathrm{}$, previously defined for the purpose of comparing empirical distributions of energy-level spacings with theoretical distributions, is applied to the recently published series of neutron-capture levels observed in the even-$A$ erbium isotopes. When the empirical values of $\Lambda \mathrm{}\left(n\right)\mathrm{}$ in the energy range of the highest experimental resolution were averaged over all possible sets of $n$ successive spacings, the resulting value ${\Lambda }^{*}\mathrm{}\left(n\right)\mathrm{}$ is found to decrease sharply with increasing values of $n$. This decrease is consistent with that of the expectation value $〈\Lambda \mathrm{}\left(n\right)\mathrm{}〉$ calculated for Wigner's Gaussian orthogonal ensemble of real symmetric matrices.

We have studied the $\gamma$ rays emitted following the decay of 22.1-min ${}_{}{}^{141m}{}_{}{}^{}\mathrm{Sm}$ with Ge(Li) and NaI(Tl) detectors in various singles, coincidence, and anticoincidence configurations, including Ge(Li)-Ge(Li) two-dimensional "megachannel" coincidence experiments. Of the 47 $\gamma$ rays definitely established as belonging to ${}_{}{}^{141m}{}_{}{}^{}\mathrm{Sm}$ decay, all but six very weak ones have been placed in a consistent decay scheme. The energies in keV [and $J^{\pi }$ assignments] of the states in ${}_{}{}^{141}{}_{}{}^{}\mathrm{Pm}$ populated by the decay of ${}_{}{}^{141m}{}_{}{}^{}\mathrm{Sm}$ are 0 [${\frac{5}{2}}^{+}$], 196.6 [${\frac{7}{2}}^{+}$], 628.6 [${\frac{11}{2}}^{-}$], 804.5 [${\frac{11}{2}}^{+},{\frac{9}{2}}^{+}$], (837.1) [${\frac{9}{2}}^{+}$], 974.0 [${\frac{9}{2}}^{+}$], 1108.1 [${\frac{7}{2}}^{+},{\frac{9}{2}}^{+},\left({\frac{5}{2}}^{-}\right)$], 1167.2 [${\frac{13}{2}}^{-(+)\mathrm{}},{\frac{11}{2}}^{-(+)\mathrm{}},{\frac{9}{2}}^{-(+)\mathrm{}}$], 1313.2 [${\frac{13}{2}}^{-(+)\mathrm{}},{\frac{11}{2}}^{-(+)\mathrm{}},{\frac{9}{2}}^{-(+)\mathrm{}}$], 1414.8 [${\frac{11}{2}}^{-},{\frac{9}{2}}^{-}$], (1834.0) [${\frac{11}{2}}^{-},{\frac{9}{2}}^{-}$], 1983.1 [${\frac{9}{2}}^{-}$], 2063.5 [${\frac{11}{2}}^{-},{\frac{9}{2}}^{-}$], 2091.6 [${\frac{11}{2}}^{-},{\frac{9}{2}}^{-}$], 2119.0 [${\frac{11}{2}}^{-},{\frac{9}{2}}^{-}$], and 2702.4 [${\frac{13}{2}}^{-},{\frac{11}{2}}^{-},{\frac{9}{2}}^{-}$]. Less than 0.2% of the decay of ${\frac{11}{2}}^{-}$ ${}_{}{}^{141m}{}_{}{}^{}\mathrm{Sm}$ proceeds via an $M4\mathrm{}$ isomeric transition to 11.3-min ${\frac{3}{2}}^{+}$ ${}_{}{}^{141g}{}_{}{}^{}\mathrm{Sm}$. Two-thirds of the ${}_{}{}^{141m}{}_{}{}^{}\mathrm{Sm}$ electron-capture decay goes to the six (possibly seven) highest-lying states in ${}_{}{}^{141}{}_{}{}^{}\mathrm{Pm}$, another example analogous to ${}_{}{}^{139m}{}_{}{}^{}\mathrm{Nd}$ decay of the population of a well-defined three-quasiparticle multiplet by an $N=79\mathrm{}$ nuclide. In simple shell-model terms this can be written as ${\left(\pi d_{\frac{5}{2}}\right)}^2{\left(\nu d_{\frac{3}{2}}\right)}^{-2\mathrm{}}{\left(\nu h_{\frac{11}{2}}\right)}^{-1\mathrm{}}\to \left(\pi d_{\frac{5}{2}}\right){\left(\nu d_{\frac{3}{2}}\right)}^{-1\mathrm{}}{\left(\nu h_{\frac{11}{2}}\right)}^{-1\mathrm{}}$. Most of the remaining states can be characterized quite satisfactorily as specific single-particle and core-coupled states. The behavior of these states allows us to add considerably to the systematics of shell-model orbits and their occupations in this region below $N=82\mathrm{}$.

Angular distributions of 26 $\gamma$ rays in ${}_{}{}^{182}{}_{}{}^{}\mathrm{W}$ have been measured following the $\beta$ decay of ${}_{}{}^{182}{}_{}{}^{}\mathrm{Ta}$ oriented at low temperatures in iron. Triple multipole mixing ($E1+M2+E3\mathrm{}$) of the 1189-keV $\gamma$ radiation was inferred by comparison of the present results with those of $\gamma -\gamma$ directional correlations and internal-conversion measurements; values deduced for the mixing ratios of the 1189-keV radiation were $\delta \left(\frac{M2\mathrm{}}{E1\mathrm{}}\right)=+0.49\mathrm{}\pm 0.03$ and $\delta \left(\frac{E3\mathrm{}}{E1\mathrm{}}\right)=-0.64\mathrm{}\pm 0.05$. $\frac{E2\mathrm{}}{M1\mathrm{}}$ multipole mixing ratios deduced for other $\gamma$ transitions were (energies in keV): $\delta \mathrm{}\left(85\right)=+0.30\mathrm{}\pm 0.02$; $\delta \mathrm{}\left(114\right)=+0.31\mathrm{}\pm 0.02$; $\delta \mathrm{}\left(179\right)=+{0.92}_{-0.07\mathrm{}}^{+0.13\mathrm{}}$; $\delta \mathrm{}\left(1002\right)=-\left({8.9}_{-1.8\mathrm{}}^{+2.1\mathrm{}}\right)$; $\delta \mathrm{}\left(1121\right)=+{21}_{-6\mathrm{}}^{+19\mathrm{}}$; $\delta \mathrm{}\left(1157\right)=-\left({7.6}_{-4.8\mathrm{}}^{+\infty }\right)$; $\delta \mathrm{}\left(1231\right)=-\left({60}_{-20\mathrm{}}^{+100\mathrm{}}\right)$. The $\frac{M2\mathrm{}}{E1\mathrm{}}$ mixing ratios deduced were $\delta \mathrm{}\left(222\right)=+0.007\mathrm{}\pm 0.005$; $\delta \mathrm{}\left(1274\right)=+0.42\mathrm{}\pm 0.04$. The $\frac{E3\mathrm{}}{M2\mathrm{}}$ mixing ratio of the 960-keV transition was deduced to be $-3.6\mathrm{}\le \delta \mathrm{}\left(960\right)\mathrm{}\le +0.3\mathrm{}$. The allowed $\beta$ transition populating the 1374-keV level was determined to be (38 ± 23)% Fermi ($L=0\mathrm{}$) and 62 ∓ 23)% Gamow-Teller ($L=1\mathrm{}$). In the first-forbidden $\beta$ transition populating the 1443-keV level, probably all, but at least half, of the $\beta$ transitions carry one unit of angular momentum, with the remainder carrying two units. The hyperfine splitting of ${}_{}{}^{182}{}_{}{}^{}\mathrm{Ta}$ in iron was found to be 21 ± 2 mK, corresponding to a ${}_{}{}^{182}{}_{}{}^{}\mathrm{Ta}$ ground-state magnetic moment of $2.6\pm 0.2{\mu }_N$. Measurements of the parity-nonconserving 0-180° (forward-backward) asymmetry of the 1189-keV $\gamma$-ray angular distribution indicated an asymmetry of (-2.8 ± 1.7) × ${10}^{-4\mathrm{}}$; vanishing asymmetries were found for the 222-, 1121-, and 1274-keV $\gamma$ rays. These results would seem to be in reasonable agreement with the vanishing circular polarization of the ${}_{}{}^{182}{}_{}{}^{}\mathrm{W}$ $\gamma$ rays measured elsewhere.

A new short-lived isomer of ${}_{}{}^{150}{}_{}{}^{}\mathrm{Tb}$ has been identified. The mass assignment was confirmed by excitation functions and cross bombardments. The 5.8 ± 0.2-min activity is probably a $9^{+}$ state ($\pi h_{\frac{11}{2}}\nu f_{\frac{7}{2}}$) and decays chiefly to an ($8^{+}$) state at 2554.4 keV in ${}_{}{}^{150}{}_{}{}^{}\mathrm{Gd}$ with a $log\mathrm{ft}$ value of 4.1. No isomeric transition to the 3.1-h ${}_{}{}^{150}{}_{}{}^{}\mathrm{Tb}$ was observed. The $\gamma$-ray spectrum was investigated with Ge(Li) detectors. The 19 $\gamma$ rays observed were assigned to 10 excited levels (in keV) at 638.05, $2^{+}$; 1134.35, $3^{-}$; 1288.4, ($4^{+}$); 1700.9, ($5^{-}$); 1936.8, ($6^{+}$); 2116.1, ($6^{+}$); 2211.2, ($7^{-}$); 2392.5; 2554.4, ($8^{+}$); and 2906.0. The energy spacing of the positive-parity states in ${}_{}{}^{150}{}_{}{}^{}\mathrm{Gd}$ suggests a close correspondence to a vibrator model although low-spin members of multiplets corresponding to multiphonon states are not observed. The quasiband representation of Sakai appears also to be a useful way of interpreting these states. Three negative-parity states form a sequence which may correspond to a combination of octupole and quadrupole phonons or an octupole quasiband.

As two conflicting values have been given for the half-lives of both ${}_{}{}^{20}{}_{}{}^{}\mathrm{Na}$ and ${}_{}{}^{36}{}_{}{}^{}\mathrm{K}$, we have carefully measured them with a "pneumatic-shuttle" system. We find $T_{\frac{1}{2}}=446\mathrm{}\pm 8$ msec for ${}_{}{}^{20}{}_{}{}^{}\mathrm{Na}$ and $T_{\frac{1}{2}}=343\mathrm{}\pm 28$ msec for ${}_{}{}^{36}{}_{}{}^{}\mathrm{K}$. In addition, and as a check against systematic errors, the half-lives of ${}_{}{}^{28}{}_{}{}^{}\mathrm{P}$, ${}_{}{}^{32}{}_{}{}^{}\mathrm{Cl}$, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Sc}$, and ${}_{}{}^{64}{}_{}{}^{}\mathrm{Ga}$ were measured.

Numerical evaluation of the entropy of a system of fermions moving in a model single-particle level scheme has been carried out, and the results compared with the analytical expression derived by Kahn and Rosenzweig. It is shown that in the asymptotic high-energy limit, the total additive correction to the excitation energy, and not merely a part of it, is equal to the ground-state shell correction.

An investigation is made of the effects of two-step processes on both the ($t,d$) and ($d,p$) reactions on ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, leading to the ${\frac{3}{2}}^{+}$ 2.02-MeV state in ${}_{}{}^{41}{}_{}{}^{}\mathrm{Ca}$. The particular process considered is that in which the $3^{-}$ collective state in ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ is excited first and then the stripping follows. The effects were found weak for both the ($t,d$) and ($d,p$) reactions.

Microscopic expressions are obtained for the coefficients in the angular momentum expansion $E_I=a_2\left(\frac{1}{2}I\right)+a_4{\left(\frac{1}{2}I\right)}^2+\cdots$ of the energies of quasirotational members of quadrupole vibrational bands. Some limitations on the applicability of perturbation treatments of anharmonic corrections to the random-phase approximation are noted.