Lifetimes of the $E2\mathrm{}$ transitions from the ½ + [631] state to the $\frac{5}{2}+\left[622\right]\mathrm{}$ state have been measured in several actinide nuclei using pulsed beam and delayed coincidence techniques. The ½ + [631] level was excited in ${}_{}{}^{239}{}_{}{}^{}\mathrm{U}$ and ${}_{}{}^{243}{}_{}{}^{}\mathrm{Pu}$ by the ($d, t$) reaction and in ${}_{}{}^{241}{}_{}{}^{}\mathrm{Pu}$ by the ($d, t$) reaction, and the subsequent $\gamma$-ray decay to the $\frac{5}{2}+\left[622\right]\mathrm{}$ level was observed between beam pulses. The corresponding $E2\mathrm{}$ transitions were observed in ${}_{}{}^{243}{}_{}{}^{}\mathrm{Cm}$ and ${}_{}{}^{245}{}_{}{}^{}\mathrm{Cm}$ from the radioactive decay of ${}_{}{}^{243}{}_{}{}^{}\mathrm{Bk}$ and ${}_{}{}^{245}{}_{}{}^{}\mathrm{Bk}$, respectively, and the lifetimes were determined from electron-photon delayed coincidence experiments. The half-lives from these measurements are: ${}_{}{}^{239}{}_{}{}^{}\mathrm{U}$ (0.78±0.04 μs); ${}_{}{}^{241}{}_{}{}^{}\mathrm{Pu}$ (0.88±0.05 μs); ${}_{}{}^{243}{}_{}{}^{}\mathrm{Pu}$ (0.33±0.03 μs); ${}_{}{}^{243}{}_{}{}^{}\mathrm{Cm}$ (1.08±0.03 μs); and ${}_{}{}^{245}{}_{}{}^{}\mathrm{Cm}$ (0.29±0.02 μs). Comparisons are made between the experimental transition probabilities and theoretical estimates. The differences between the transition rates in these nuclei are understood when pairing interactions are taken into account.

NUCLEAR REACTIONS ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}(d, p\gamma )$, $E_d=12\mathrm{}$ MeV; ${}_{}{}^{242}{}_{}{}^{}\mathrm{Pu}(d, p\gamma )$ and ${}_{}{}^{242}{}_{}{}^{}\mathrm{Pu}(d, t\gamma )$, $E_d=16\mathrm{}$ MeV; measured $t_{\frac{1}{2}}$ of 133.7-, 161.4-, and 384.0-keV levels in ${}_{}{}^{239}{}_{}{}^{}\mathrm{U}$, ${}_{}{}^{241}{}_{}{}^{}\mathrm{Pu}$, and ${}_{}{}^{243}{}_{}{}^{}\mathrm{Pu}$, respectively. Deduced $B\left(E2\mathrm{}\right)\mathrm{}$ values. Enriched targets.

RADIOACTIVITY ${}_{}{}^{243}{}_{}{}^{}\mathrm{Bk}$ [from ${}_{}{}^{241}{}_{}{}^{}\mathrm{Am}(\alpha , 2n)$] and ${}_{}{}^{245}{}_{}{}^{}\mathrm{Bk}$ [from ${}_{}{}^{243}{}_{}{}^{}\mathrm{Am}(\alpha , 2n)$]; measured $E_{\gamma }$, $E_{\mathrm{ce}}$, $t_{\frac{1}{2}}$ of 87.4-keV level in ${}_{}{}^{243}{}_{}{}^{}\mathrm{Cm}$ by $K$ x-ray-ce delayed coin; measured $t_{\frac{1}{2}}$ of 355.7-keV level in ${}_{}{}^{245}{}_{}{}^{}\mathrm{Cm}$ by $\gamma$-ce delayed coin. Deduced $B\left(E2\mathrm{}\right)\mathrm{}$ values. Mass-separated sources.

Fragmentation of the $M1\mathrm{}$ strength in ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ at energies near the ($\gamma , n$) threshold is studied. It is shown that the 2p-2h configuration can provide a mechanism for fragmenting the 1p-1h giant $M1\mathrm{}$ excitation; however, our results do not predict as much spreading of the $M1\mathrm{}$ strength as has been suggested by experiment. The 2p-2h mechanism is also unable to explain the large $M1\mathrm{}$ strength recently observed at 4.84 MeV in ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$.

NUCLEAR STRUCTURE ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$; calculated $1^{+}$ levels. Included 1p-1h, 2p-2h configurations.

The effort to isolate and study the dominant collective modes of a nuclear many-body system by generalized equations-of-motion methods (algebraic methods) confronts the inherent difficulty that such modes are correlated with each other and with noncollective modes by kinematic constraints traceable to the Pauli principle. This problem has previously been solved for simplified nuclear models. A solution is proposed for the general shell model problem of a number of interacting levels.

We report calculations on the contribution of the three-body potential $W$ to the energy of nuclear matter which include realistic correlations in all internucleon distances which are consistent with realistic two-body potentials ($V$) in the calculation of the dominant second order [$〈V\left(\frac{Q}{e}\right)W〉$] contribution to the binding energy. For the Reid soft core potential we get a binding energy contribution of 6 MeV/nucleon. This is to be compared with the binding energy of 1.7 MeV/nucleon obtained using hard core potentials. The latter result is consistent with the calculations of Loiseau, Nogami, and Ross. The physical reason for the large difference between the results obtained from hard core and soft core two-body potentials is clarified.

In a recent study of ($d, \alpha$) reactions on medium and heavy nuclei, DelVecchio and Daehnick employ a well-matching condition which limits the choice of the optical model potentials. It is shown that in the authors' derivation of the well-matching condition, they violate the post-prior equality necessary for distorted-wave transition amplitudes.

The sensitivity of many calculations in the distorted-wave-Born-approximation (DWBA) to optical model parameter ambiguities has led to the introduction of a well-matching condition which was discussed in a recent paper. The claim for the merit of this condition was based primarily on its success and consistent usefulness in standard DWBA calculations. A theoretical argument given for its plausibility is explained in greater detail. It is argued that the absence of restraints on optical model potentials may be expected to lead to poor results with the common DWBA approximations whereas the well-matching condition helps to insure the smallness of some generally neglected terms.

The droplet model mass equation of Myers and Swiatecki contains isospin-nonconserving contributions. When applied to the displacement energies between isobaric analog states, one obtained a hydrodynamical description of the Auerbach-Kahana-Weneser core polarization effect. The effect is not sufficient to explain the Coulomb-energy anomaly (Nolen-Schiffer anomaly) in light nuclei but is likely to contribute to the observed anomaly in heavy nuclei.

Odd-even differences in the elastic scattering of 48 MeV $\alpha$ particles by ${}_{}{}^{62,64}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{63,65}{}_{}{}^{}\mathrm{Cu}$, and ${}_{}{}^{64,66}{}_{}{}^{}\mathrm{Zn}$ are well accounted for, up to back angles, by core polarization.

NUCLEAR REACTIONS ${}_{}{}^{62,64}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{64,66}{}_{}{}^{}\mathrm{Zn}(\alpha , \alpha )$, ($\alpha , {\alpha }^{\prime }$), ${}_{}{}^{63,65}{}_{}{}^{}\mathrm{Cu}(\alpha , \alpha )$, $E=48\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$; $\theta =18-172\mathrm{}°$, enriched targets; ${}_{}{}^{63,65}{}_{}{}^{}\mathrm{Cu}$ core mixing deduced.

The ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}(\alpha , \alpha ){}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ excitation curve has been measured at 177.9° center of mass between 12.8 and 14.8 MeV incident energy with an energy resolution of 90 keV. Angular distributions taken at three resonance energies have been analyzed by a one-Regge-pole model: The $7^{-}$ spin of the 15.41 MeV level in ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ is confirmed and two new $6^{+}$ levels are found at 15.72 and 15.97 MeV in ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$.

NUCLEAR REACTION ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}(\alpha , \alpha )$, $E=12.8-14.8\mathrm{}$ MeV; measured $\sigma (E; 177.9°)$; measured $\sigma \left(\theta \right)$ at $E=13.08, 13.37, 13.53, 13.68, 13.89, \mathrm{and} 14.12$ MeV; one-Regge-pole model analysis; ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ levels deduced $J$, $\pi$.

A new energy-dependent-core model for attenuation effects in quasifree scattering is used to explain the difference in quasifree scattering cross sections for the two kinematically equivalent modes of deuteron breakup under proton bombardment.

NUCLEAR REACTIONS ${}_{}{}^2{}_{}{}^{}\mathrm{H}(p, pp)$, ($p, \mathrm{pn}$), $E=20-100\mathrm{}$ MeV; ${}_{}{}^4{}_{}{}^{}\mathrm{He}(p, pt)$, ($p, p{}_{}{}^3{}_{}{}^{}\mathrm{He}$), $E=47\mathrm{}$ MeV; calculated $\sigma$.

Regge-type representations are developed for the scattering amplitude of spin-one particles elastically scattered from nuclei. This work forms an addition to a recent paper by Shanta and Satpathy on the Regge-type representations.

For any conventional phenomenological nucleon-nucleon potential, we derive a relativistic two-body Hamiltonian. With this two-body Hamiltonian we construct an approximately relativistic many-body Hamiltonian that is used to find the lowest order relativistic corrections to the Brueckner theory of nuclear matter. These corrections are explicity presented as a sum of terms that are linear and quadratic functions of the nonrelativistic reaction matrix. Numerical results are obtained for the Reid soft core potential, the Ueda-Green potential, and several separable potentials. Due to extensive cancellations of the individual terms, the total correction is considerably smaller than that which would be expected from simple estimates. For the Reid potential the total correction to the energy per particle at saturation is only +0.22 MeV, and the change in the saturation density is negligible. The correction at saturation is also positive for all the other potentials considered.

The ${}_{}{}^{46,48}{}_{}{}^{}\mathrm{Ti}(d, {}_{}{}^6{}_{}{}^{}\mathrm{Li}){}_{}{}^{42,44}{}_{}{}^{}\mathrm{Ca}$ reactions to low-lying states have been studied at a bombarding energy of 28 MeV. Relative to the ground states, spectroscopic factors for the first excited $0^{+}$ and $2^{+}$ states are about 0.2. These results, and other work, indicate the need for components involving both 2 and 4 $sd$-shell holes for these nuclei.

NUCLEAR REACTIONS ${}_{}{}^{46,48}{}_{}{}^{}\mathrm{Ti}(d, {}_{}{}^6{}_{}{}^{}\mathrm{Li})$, $E=28\mathrm{}$ MeV; measured $\sigma (E_{{}_{}{}^6{}_{}{}^{}\mathrm{Li}}, \theta )$.

The neutron-proton scattering cross section at "zero energy" (${\sigma }_0$), which is an important experimental parameter in the analysis of low energy $np$ data, has been accurately redetermined by transmission measurements at 132 eV neutron energy on ${\mathrm{H}}_2$O, ${\mathrm{C}}_6$${\mathrm{H}}_6$, C${\mathrm{H}}_3$OH, and ${\mathrm{C}}_7$${\mathrm{H}}_8$. We obtain the total cross sections per molecule (132 eV) 44.731 ± 0.027, 151.40 ± 0.10, 90.37 ± 0.08, and 197.20 ± 0.34 b, respectively. To evaluate ${\sigma }_0$ we subtract the well-known cross sections of carbon and oxygen, and correct for the small contributions (<0.1%) of capture, molecular binding, effective range, and deuterium. Combining all known errors from the experimental and evaluation procedure, we find ${\sigma }_0=20.491\mathrm{}\pm 0.014$ b. This is 0.27%, or 2.4 standard errors, above the best previous measurement by Houk, and ∼0.6% above the mean of former data. Our result of ${\sigma }_0$ implies changes in the $np$ effective-range parameters towards higher values, by about twice the present standard errors in $a_s$, $a_t$, and $r_{0t}$ and 1 standard error in $r_{0s}$.

NUCLEAR REACTIONS ${}_{}{}^1{}_{}{}^{}\mathrm{H}(n, n)$, $E=132\mathrm{}$ eV; measured ${\sigma }_T$. Cobalt-resonance neutron beam, targets ${\mathrm{H}}_2$O, ${\mathrm{C}}_6$${\mathrm{H}}_6$, C${\mathrm{H}}_3$OH, ${\mathrm{C}}_7$${\mathrm{H}}_8$.

As part of a program utilizing the fusion-evaporation reaction to study high-spin states in $A\simeq 40$ nuclei, linear polarization measurements were made on the $\gamma$ rays emitted following fusion of the six projectile-target combinations: ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ + ${}_{}{}^{26}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ + ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ + ${}_{}{}^{26}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ + ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$, ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$ + ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$, and ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$ + ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$. All beam energies were 40 MeV except the last, which was 45 MeV. The linear polarization of about 50 $\gamma$ rays from the highly aligned states were measured in each experiment using a two-crystal Ge(Li) Compton polarimeter. The results are tabulated. As an example of the application of these results, the polarization data in conjunction with previous $\gamma -\gamma$ coincidence and $\gamma$-ray angular distribution measurements suggest $E2\mathrm{}$ character for the $\gamma$ cascades between the ${}_{}{}^{41}{}_{}{}^{}\mathrm{K}$ levels at 4983, 4275, 2762, and 1294 keV and thus support the spin-parity sequence $\frac{19}{2^{-}}$, $\frac{15}{2^{-}}$, $\frac{11}{2^{-}}$, and $\frac{7}{2^{-}}$ for these states. Applications to the spectroscopy of other levels in ${}_{}{}^{41}{}_{}{}^{}\mathrm{K}$, ${}_{}{}^{41}{}_{}{}^{}\mathrm{Ca}$, and ${}_{}{}^{39}{}_{}{}^{}\mathrm{K}$ are discussed.

NUCLEAR REACTIONS (HI, $\mathrm{xn}$, $\mathrm{yp}$, $z\alpha$) studies for $A\sim 40$ nuclei, ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$, ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$ projectiles, ${}_{}{}^{24,26}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$, ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ targets, $E=40-45\mathrm{}$ MeV; measured $P(E_{\gamma }, 90°)$, deduced $\Lambda$ for transitions, and $J^{\pi }$, $\delta$ for high-spin states in ${}_{}{}^{39,41}{}_{}{}^{}\mathrm{K}$ and ${}_{}{}^{41}{}_{}{}^{}\mathrm{Ca}$.

A potential model with forbidden states for describing the nucleon-nucleon interaction in the inner region is suggested. Forbidden states in the $N-N$ system may occur due to the composite structure of nucleons as a consequence of the Pauli exclusion principle. A consistent description of singlet even phase shifts at energies up to 400 MeV has been obtained. The generalization of Levinson's theorem taking forbidden states into account permits a new interesting interpretation of the phase-shift analysis data at higher energies and as a result gives a "smooth matching" of the low-energy phase shifts with the asymptotic region $E\gtrsim 10$ GeV. The loop which the wave function has in the inner region provides a considerable contribution to the deuteron form factor at great momentum transfers. A comparison is made with the repulsive core model. Possible consequences for the three- and many-nucleon systems are discussed.

NUCLEAR REACTIONS $N$ $(N, N)N$, potential model with forbidden states, ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ phase shift to 400 MeV.

The ${}_{}{}^{63}{}_{}{}^{}\mathrm{Cu}(p, n)$ analog and excited analog differential cross sections have been measured at bombarding energies of 16, 19, and 22 MeV. Analogs of excited states populated by the ($p, n$) reaction in medium mass odd-$A$ nuclei have not been previously reported. Coupled-channel calculations for the ($p, n$) reaction to the ${\frac{5}{2}}^{-}$ and ${\frac{7}{2}}^{-}$ excited analog states give differential cross sections at 19 and 22 MeV in excellent agreement with measurements. At 16 MeV, the measured ${\frac{5}{2}}^{-}$, ${\frac{7}{2}}^{-}$, and ${\mathrm{½}}^{-}$ cross sections are higher than calculations at the middle angles, perhaps reflecting the contribution from preequilibrium processes. At 16 and 19 MeV the ${\mathrm{½}}^{-}$ angular distribution shapes suggest some spin-flip contribution. The calculated cross section for the ${\mathrm{½}}^{-}$ state is too high at 22 MeV. As in even-$A$ nuclei a two-step mechanism is mainly responsible for the population of excited analog states in ${}_{}{}^{63}{}_{}{}^{}\mathrm{Cu}(p, n)$.

NUCLEAR REACTIONS ${}_{}{}^{63}{}_{}{}^{}\mathrm{Cu}(p, n)$ $E=16, 19, \mathrm{and} 22$ MeV; ${}_{}{}^{64}{}_{}{}^{}\mathrm{Zn}(p, n)$ $E=22\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$ for ground-state analog and excited-state analog transitions. Isotopically separated targets. Measurements are compared with coupled-channel calculations.

Simple concepts which can be directly applied to measurements of resonances and the accompanying continua have been studied. Pickup reaction spectra leading to hole states in the continuum were found to give an understanding of the excitation energy dependence of resonance damping and the concurrent rise of "background" continuum states. When these hole resonances are parametrized in terms of the shell model, they can be used to predict the energy dependence of the damping of more complex resonances, such as collective particle-hole excitations in the inelastic scattering spectra. Furthermore, it is proposed that part of the background continuum in pickup spectra is the semidirect excitation of the 2h-1p states, the density of which determines both the nuclear damping width and the continuum cross section.

NUCLEAR REACTIONS ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}({}_{}{}^3{}_{}{}^{}\mathrm{He}, \alpha )$, $E=75\mathrm{}$ MeV, ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}(p, d)$, $E=62\mathrm{}$ MeV; calculated continuum cross sections in a direct reaction.

Cross sections for the reactions (${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$, $4n$) and (${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$, $5n$) induced on ${}_{}{}^{141}{}_{}{}^{}\mathrm{Pr}$ and ${}_{}{}^{142}{}_{}{}^{}\mathrm{Nd}$ were determined by detecting the $\alpha$ decay of the products ${}_{}{}^{151,150}{}_{}{}^{}\mathrm{Dy}$ and ${}_{}{}^{152,151}{}_{}{}^{}\mathrm{Ho}$, respectively. The experimental technique consisted of a direct recoil catch measurement combined with one using a gas-jet-capillary system. With recently determined $\alpha$-decay branching ratios counting rates were converted into absolute cross sections. Reasonable agreement was found between these experimental data and results obtained from statistical-model calculations.

NUCLEAR REACTIONS ${}_{}{}^{141}{}_{}{}^{}\mathrm{Pr}({}_{}{}^{14}{}_{}{}^{}\mathrm{N}, 4n)$, (${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$, $5n$), measured $\sigma$ at 92 MeV; ${}_{}{}^{142}{}_{}{}^{}\mathrm{Nd}({}_{}{}^{14}{}_{}{}^{}\mathrm{N}, 4n)$, (${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$, $5n$), measured $\sigma$ at 73 and 79 MeV, deduced $\sigma \mathrm{}\left(E\right)\mathrm{}$ for $E=58-98\mathrm{}$ MeV.