A phenomenological, imaginary potential is incorporated into resonating-group calculations for the $p+\alpha$ system. The introduction of this potential allows, at energies above the reaction threshold of 18.35 MeV (c.m.), a more detailed comparison with experiment than was possible with previous resonating-group calculations. The calculations are compared with elastic scattering differential-cross-section data, polarization data, and spin-rotation-parameter data which exist between 23 and 75 MeV (c.m.). From this comparison it is concluded that a Majorana component whose strength varies with energy is very likely present in the imaginary potential.

A model-independent result for the $\beta -\gamma$ correlation in allowed $\beta$ decay is given, including all second-order-forbidden corrections. A suggested method for measurement of the firstclass contribution to the induced-tensor form factor is discussed.

The coherent scattering amplitude of tritium has been measured by a multiple-refraction method. A finely collimated beam of neutrons is passed through a powder alternately in vacuum and in a nonabsorbing fluid. The relative broadening of the neutron beam is determined by the coherent scattering amplitudes of the powder and the fluid. In this experiment, the powders were silicon and diamond, and the fluids were deuterium and tritium with densities up to 440 amagat. The coherent scattering amplitude of tritium was determined relative to deuterium using a value of $a_{\mathrm{D}}=+6.21\mathrm{}\pm 0.04$ F from our mirror measurements. The value obtained for tritium was $a_{\mathrm{T}}=+4.7\mathrm{}\pm 0.3$ F.

It should be noted that our value of $a_{\mathrm{D}}=+6.21\mathrm{}$ F is at variance with other measurements of $a_{\mathrm{D}}$. Using the accepted value of $a_{\mathrm{D}}=6.7\mathrm{}\pm 0.1$ F, the coherent scattering amplitude of tritium is $a_{\mathrm{T}}=5.0\mathrm{}\pm 0.3$ F.

The evaluation of the finite-range distorted-wave Born-approximation matrix elements is shown to be considerably simplified when one uses Eckart bound-state wave functions. The use of these wave functions to describe the stripping reaction ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^6{}_{}{}^{}\mathrm{Li},d){}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ is found to give reasonable aggrement with the experimental results. Also, the use of the Eckart interaction as a test of the various methods for the evaluation of matrix elements is demonstrated.

Optical-model analyses which include data far into the backward hemisphere for elastic scattering of complex projectiles at intermediate energies are found to produce optical potentials with many of the common ambiguities removed. This paper reports differential cross-section data with an extensive optical-model analysis for 59.8-MeV helions elastically scattered from ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$ and ${}_{}{}^{52}{}_{}{}^{}\mathrm{Cr}$. The data include scattering angles back to 166° for ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$ and to 149° for ${}_{}{}^{52}{}_{}{}^{}\mathrm{Cr}$. Optical-model fits to these data are satisfactory only with a surface-peaked absorption term and with a spin-orbit term included in the potential. The discrete or family ambiguity in the potential is removed, and continuous ambiguities are notably suppressed.

Properties of levels in ${}_{}{}^{54}{}_{}{}^{}\mathrm{Mn}$ have been studied using the reaction ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}(n,p\gamma ){}_{}{}^{54}{}_{}{}^{}\mathrm{Mn}$. These data alone were not sufficient to determine spin and parity assignments, but when correlated with data from prior experimental investigations of the ${}_{}{}^{54}{}_{}{}^{}\mathrm{Mn}$ nucleus, a set of unique $J^{\pi }$ assignments for the lowest five excited states was determined. These assignments are consistent with nearly all presently available experimental data and are in good agreement with shell-model calculations. The level excitation energies and $J^{\pi }$ values obtained are: ground state, $3^{+}$; 54.3 keV, $2^{+}$; 156.9 keV, $4^{+}$; 367.6 keV, $5^{+}$; 407.5 keV, $3^{+}$; and 839.0 keV, $4^{+}$. Transitions from higher-lying states were observed and possible $J^{\pi }$ values were obtained.

Bombardment of a thick germanium target with ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ ions of 32 to 36 MeV excited the 691-keV ($0_2^{+}$) and 834-keV ($2_1^{+}$) states of ${}_{}{}^{72}{}_{}{}^{}\mathrm{Ge}$. Observed yields of conversion electrons from the decay of these states were used to deduce $B(E2;0_2^{+}\to 2_1^{+})=1322\mathrm{}\pm 241 e^2{\mathrm{fm}}^4$. This result is compared with previous measurements where discrepancies have existed. An excitation function from 27 to 54 MeV was measured to indicate the energy region of pure Coulomb excitation of the $0_2^{+}$ state. The importance of exciting the $0_2^{+}$ state by transitions through higher-lying states including the giant dipole resonance is discussed.

Nuclear properties, such as ground-state energies, rms charge radii, and intrinsic quadrupole moments are calculated, using the Hartree-Fock method, for self-conjugate even-even $s-d$-shell nuclei. The internucleon interaction is a spin-independent $S$-state version of the Skyrme interaction. The density dependence of the $G$ matrix is simulated by a three-body repulsive $\delta$ interaction. The connection between the latter and a density-dependent two-body $\delta$ interaction is discussed in the Appendix.

Our results for binding energies and rms radii agree much better with experimental values than earlier calculations done by one of us (S.J.K.) using a different, density-independent, interaction. We also obtain generally better results for binding energies than the results of Zofka and Ripka and of Lassey and Volkov, and comparable results for rms radii.

The reaction ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}+{}_{}{}^{12}{}_{}{}^{}\mathrm{C}\to {\alpha }_1+{}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}_{}^{*}{}_{}{}^{}\to {\alpha }_2+{}_{}{}^{16}{}_{}{}^{}\mathrm{O}\mathrm{g}.\mathrm{s}.\mathrm{}$ was employed in the measurements of the spin of highly excited states in ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$. Coincidence angular correlations were obtained using two position-sensitive detectors. The spin and parity of four new levels were determined to be: $9^{-}$ (15.18 ± 0.04 MeV), $5^{-}$ (15.9 ± 0.04 MeV), $8^{+}$ (15.9 ± 0.04 MeV), and $7^{-}$ (18.10 ± 0.04 MeV). The two levels $5^{-}$ and $7^{-}$ may belong to the $K=0^{-}$ band of the (86) S${\mathrm{U}}_3$ symmetry arising from three-particle core excitation, while the $8^{+}$ level may be a member of the [220] "quartet" configuration. Results obtained from the ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}({}_{}{}^6{}_{}{}^{}\mathrm{Li},d){}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}({}_{}{}^7{}_{}{}^{}\mathrm{Li},t){}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ experiments are also presented and discussed.

The $\frac{M}{L}$ and $\frac{L}{K}$ orbital-electron-capture ratios in the decay of ${}_{}{}^{55}{}_{}{}^{}\mathrm{Fe}$ have been determined by introducing the radioactive compound ferrocene-${}_{}{}^{55}{}_{}{}^{}\mathrm{Fe}$ into a multiwire, wall-less anticoincidence proportional counter as part of the counting gas mixture. The results are $\frac{P_M}{P_L=0.157\mathrm{}\pm 0.003}$ and $\frac{P_L}{P_K}=0.117\mathrm{}\pm 0.001$ at $Z=26\mathrm{}$. These values are compared with various theoretical predictions and, together with previous experimental results on $\frac{M}{L}$ capture ratios at low $Z$, they demonstrate that of all the combinations of theoretical approaches, the Watson-Freeman wave functions with the exchange corrections of Vatai are the only ones which give good agreement with experiment at low $Z$. All other theoretical combinations lie considerably higher than experiment in the region below $Z=36\mathrm{}$.

The effective interactions between nucleons in the $s-d$ shells are investigated from an exact shell-model calculation via a least-squares fit of the experimental energy spectra of the normal-parity states in the ${}_{}{}^{18,19,20}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{18,19,20}{}_{}{}^{}\mathrm{F}$, and ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ nuclei. The effects of the $d_{\frac{3}{2}}$ single-particle orbit in shell-model calculations of light $s-d$-shell nuclei are discussed briefly. The two-body matrix elements are compared with those calculated by Kuo and by Arima et al.

The effective interactions of the nucleons in the upper $s-d$ shell are studied in a truncated shell-model calculation by a least-squares fit to the experimental energy levels of the normal-parity states in the nuclei ${}_{}{}^{36}{}_{}{}^{}\mathrm{S}$, ${}_{}{}^{36,37}{}_{}{}^{}\mathrm{Cl}$, ${}_{}{}^{37,38}{}_{}{}^{}\mathrm{K}$, and ${}_{}{}^{36,38}{}_{}{}^{}\mathrm{Ar}$. The resulting effective interactions and two-body matrix elements are discussed briefly.

The scission configuration is described by two interacting fragments in a single-particle model with pairing correlations and studied as function of two parameters. One parameter is the distance between the fragment centers of mass and the other parameter is the mass ratio of the two fragments. The scission-point region can be conveniently studied in this molecular model, particularly because extensive knowledge about the fragment structure is incorporated. Level schemes, equilibrium deformations of the fragments, total energies, and charge distributions are studied for the compound systems ${}_{}{}^{240}{}_{}{}^{}\mathrm{Pu}$ and ${}_{}{}^{242}{}_{}{}^{}\mathrm{Pu}$. The scission configurations are characterized by an approximate cancellation of the attractive nuclear force and the repulsive Coulomb force between the fragment. The proton numbers of the fragments turn out to be a rather good quantum number at scission. The results support the existence of a potential barrier at the scission point (scission barrier). It is shown that the calculated energies of the scission configurations can account for the asymmetry in the fragment-mass yield with its maximum at the heavy-fragment mass $A_1\approx 140$. The decrease of the total energy for $A_1\approx 140$ is due to single-particle states which have a small angular momentum component along the symmetry axis and — because of their prolate density distribution — give large contributions to the binding energy between the fragments. The 50-proton shell closure has its greatest influence on the scission configuration around $A_1=130\mathrm{}$, whereas the 82-neutron shell closure is most effective around $A_1=135\mathrm{}$.

Spin assignments have been made for 47 neutron resonances in the target nuclei ${\mathrm{Nd}}^{143}$ and ${\mathrm{Nd}}^{145}$ by two independent methods: measurement of coincidences between cascade capture $\gamma$ rays, and measurement of the ratio of low-energy $\gamma$-ray intensities. A new method for analyzing data of this type is introduced which enables us to assign a probability of correctness to each spin measurement. The use of an energy window rather than an integral bias level for the coincidence experiment improves the separation of the two spin groups. The $s$-wave strength function does not appear to be spin-dependent. The distribution of the spin values is consistent with a $2J+1$ level-density dependence.

The measured intensities of intraband cascading transitions in the ground-state bands of 21 high-yield even-even fission products have been analyzed by two methods to determine the magnitude of the intrinsic angular momentum of the primary products formed in the spontaneous fission of ${}_{}{}^{252}{}_{}{}^{}\mathrm{Cf}$. The first method was to quantitatively compare the intensities of the intraband transitions observed in fission with those reported in the literature for in-beam (particle, $\mathrm{xn}$) reactions for which the primary angular-momentum distribution was determined by optical-model calculations. The second method was based on a simple statistical-model analysis of the angular momentum distribution throughout the neutron evaporation and the pre-ground-state-band $\gamma$-ray transition phases of the deexcitation process. The two methods gave reasonably similar results, with the former method yielding a somewhat larger primary angular momentum for the fragments. The general conclusions from the statistical-model analysis are that: (1) The average angular momentum of the products is $\overline{l}\approx (7\mathrm{}\pm 2)\hslash$; (2) the heavy fission products have $\approx 20\%$ greater angular momentum than the light products; (3) the more symmetric the mass division the lower the initial angular momentum; and (4) there are only small changes in angular momentum [$\sim \mathrm{}(1-2)\mathrm{}\hslash$] with changes in fragment kinetic energy. An important feature of these results is that the fragment angular momentum does not correlate with the number of neutrons evaporated by the fragment. Additional measurements have been made to study the angular distribution of individual prompt $\gamma$ rays. In all observed cases the $2^{+}\to 0^{+}$ ground-state transitions were forward-peaked with respect to the fission axis, and this is consistent with the assumption that the angular momentum is aligned in a plane perpendicular to the direction of fission. The results are discussed in terms of a quasistatistical model in which the neck width at scission is approximately constant.

Borggreen and Hyde recently reported the discovery of three new $\alpha$-emitting osmium isotopes, ${}_{}{}^{172}{}_{}{}^{}\mathrm{Os}$, ${}_{}{}^{173}{}_{}{}^{}\mathrm{Os}$, and ${}_{}{}^{174}{}_{}{}^{}\mathrm{Os}$. The present study deals with a search for osmium nuclides with $A<\mathrm{}172\mathrm{}$. These osmium isotopes were produced by bombarding ${}_{}{}^{156}{}_{}{}^{}\mathrm{Dy}$ with the 160-MeV ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}_{}^{6+}{}_{}{}^{}$ beam from the Oak Ridge isochronous cyclotron. With the use of $\alpha$ spectroscopy and the helium gas-jet technique, two new $\alpha$ groups were observed. Their mass assignments and decay characteristics are as follows: (1) ${}_{}{}^{170}{}_{}{}^{}\mathrm{Os}$, $E_{\alpha }=5.40\mathrm{}\pm 0.01$ MeV, $T_{\frac{1}{2}}=7.1\mathrm{}\pm 0.5$ sec; and (2) ${}_{}{}^{171}{}_{}{}^{}\mathrm{Os}$, $E_{\alpha }=5.24\mathrm{}\pm 0.01$ MeV, $T_{\frac{1}{2}}=8.2\mathrm{}\pm 0.8$ sec.

The angular distribution of $\alpha$ particles emitted in the spontaneous fission of ${}_{}{}^{252}{}_{}{}^{}\mathrm{Cf}$ has been determined with respect to the light fragments and with respect to the heavy fragments. The full width at half maximum (FWHM) for the angular distribution of $\alpha$ particles is 23.5°-distinctly narrower than has been reported in the literature. The FWHM for the angular distribution of $\alpha$ particles emitted in coincidence with all the fragments is 37.5°. Trajectory and Monte Carlo calculations were done to find a set of initial parameters that give rise to an angular distribution and energy spectrum of $\alpha$ particles in agreement with experiment. The parameters so obtained were: $D$ is the interfragment distance at scission (21.5×${10}^{-13\mathrm{}}$ cm); $t$ is the time of emission of $\alpha$ particle (0.4×${10}^{-21\mathrm{}}$ sec); $E_0$ is the average initial energy of $\alpha$ particle at scission (2 MeV); $\sigma$ is the standard deviation in the initial position of $\alpha$ particle (2.5×${10}^{-13\mathrm{}}$ cm). These parameters are contradictory to predictions of the statistical model. Furthermore, we have found that parameters given by the statistical model at fission lead to a calculated energy spectrum that is not in agreement with experiment.

The spectra of low-lying states of ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}$ have been studied using the reactions ${}_{}{}^{233}{}_{}{}^{}\mathrm{U}\mathrm{}(t,p)\mathrm{}{}_{}{}^{235}{}_{}{}^{}\mathrm{U}$, ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}(d,d^{\prime }){}_{}{}^{235}{}_{}{}^{}\mathrm{U}$, ${}_{}{}^{234}{}_{}{}^{}\mathrm{U}\mathrm{}(d,p)\mathrm{}{}_{}{}^{235}{}_{}{}^{}\mathrm{U}$, ${}_{}{}^{236}{}_{}{}^{}\mathrm{U}\mathrm{}(d,t)\mathrm{}{}_{}{}^{235}{}_{}{}^{}\mathrm{U}$, and ${}_{}{}^{234}{}_{}{}^{}\mathrm{U}(n,\gamma ){}_{}{}^{235}{}_{}{}^{}\mathrm{U}$. Using intensity ratios and angular distributions from the charged-particle reactions, primary $\gamma$-ray excitations, patterns of $\gamma$-ray deexcitations, and rotational-band systematics, 80% of the levels observed up to 1500 keV have been assigned to 23 individual rotational bands. Some of the rotational bands can be associated with expected single-particle excitations, but in many cases it is shown that the single-particle strength is fragmented, giving rise to several rotational bands with similar properties. Mechanisms for this fragmentation are discussed and the distribution of single-particle strength over the states observed is examined and compared with theoretical predictions. The neutron binding energy for ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}$ is determined to be 5297.6 ± 0.5 keV.

Measurements made with Ge(Li) detectors are reported for $\gamma$-ray transition energies and intensities observed following the $\beta$ decay of the neutron-rich nuclei ${}_{}{}^{92}{}_{}{}^{}\mathrm{Kr}$, ${}_{}{}^{92}{}_{}{}^{}\mathrm{Rb}$, and ${}_{}{}^{92}{}_{}{}^{}\mathrm{Sr}$. These nuclides are members of the isobaric decay chain for $A=92\mathrm{}$ beginning with ${}_{}{}^{92}{}_{}{}^{}\mathrm{Kr}$, which was obtained using the on-line isotope-separator system TRISTAN developed for the study of gaseous fission-product activities. Level schemes have been constructed for ${}_{}{}^{92}{}_{}{}^{}\mathrm{Rb}$, ${}_{}{}^{92}{}_{}{}^{}\mathrm{Sr}$, and ${}_{}{}^{92}{}_{}{}^{}\mathrm{Y}$ with the aid of Ge(Li)-Ge(Li) coincidence results. Some of the energy levels found are considered from a shell-model approach.

The decays of the $9^{-}$ isomers, ${}_{}{}^{202m}{}_{}{}^{}\mathrm{Pb}$ and ${}_{}{}^{204m}{}_{}{}^{}\mathrm{Pb}$, have been investigated using Ge(Li) detectors in a variety of singles and coincidence configurations. Improved conversion coefficients were obtained for two of the transitions following the decay of ${}_{}{}^{204m}{}_{}{}^{}\mathrm{Pb}$, but no new, weak transitions were seen. Considerable improvement and enlargement of the ${}_{}{}^{202m}{}_{}{}^{}\mathrm{Pb}$ decay scheme was possible. We have been able to make unambiguous multipolarity assignments for 15 of the 18 transitions following its decay and to place all 18 in a consistent decay scheme. States in ${}_{}{}^{202}{}_{}{}^{}\mathrm{Pb}$ were established (following the 90.5% isomeric-transition decay) at 0 ($J^{\pi }=0^{+}$), 960.70 ($2^{+}$), and 1382.82 ($4^{+}$), 1623.1 ($4^{+}$), 1915.2 ($4^{+}$), 2040.3 ($5^{-}$), and 2169.8 keV ($9^{-}$). Those in ${}_{}{}^{202}{}_{}{}^{}\mathrm{Tl}$ (following the 9.5% electron-capture decay) lie at 0 ($2^{-}$), 490.47 ($4^{-}$), 950.19 ($7^{+}$), 1098.7 ($6^{+}$, $7^{+}$, $8^{+}$), 1340.1 ($8^{+}$), 1552.1 ($8^{+}$ [$9^{+}$]), and 1675.6 keV ($9^{+}$, $8^{+}$). Interpretation is made concerning the nature of the states in ${}_{}{}^{202}{}_{}{}^{}\mathrm{Pb}$ and even-even Pb isotopes and also in ${}_{}{}^{202}{}_{}{}^{}\mathrm{Tl}$ and odd-odd Tl isotopes on the basis of the simple shell-model plus pairing forces.