Employing the Yale and soft-core Reid free nucleon-nucleon potentials, the shell-model reaction matrix elements are calculated and tabulated for the Ni region. The matrix elements consist of the bare part and the renormalization effects due to the core polarization. The bare matrix elements are evaluated following the unitary-model approach of Shakin, Waghmare, Tomaselli, and Hull and the renormalization corrections are calculated in the same manner as by Kuo and Brown for a ${\mathrm{Ni}}^{56}$ core. As a test of these matrix elements, spherical shell-model spectra of ${\mathrm{Ni}}^{58}$, ${\mathrm{Cu}}^{58}$, ${\mathrm{Ni}}^{59}$, ${\mathrm{Cu}}^{59}$, ${\mathrm{Ni}}^{60}$, ${\mathrm{Zn}}^{60}$, and ${\mathrm{Cu}}^{60}$ are calculated. Quasiparticle calculations for the odd and even Ni isotopes are also performed. In general the calculated results are in good agreement with each other as well as with the observed data. It is concluded that different potentials which fit the same nucleon-nucleon scattering data give essentially the same results for effective-interaction and nuclear-structure calculations for the Ni region of the Periodic Table.

Employing the central Yukawa and Kuo-Brown renormalized matrix elements for the Hamada-Johnston interaction, self-consistent study of even Zn and Ge isotopes is made within the framework of Hartree-Fock (HF), Hartree-Fock-Bogoliubov (HFB), and spherical BCS approximations. It is found that both the interactions yield either oblate or spherical shapes for these isotopes except for ${\mathrm{Zn}}^{60}$ for which a prolate shape is favored. Isotopes having 20 neutrons outside the ${\mathrm{Ca}}^{40}$ core favor spherical BCS shapes. The agreement of the calculated binding energy per particle with the experimental ones is quite good. It is pointed out that for Zn isotopes, both the interactions do not exhibit the saturation in binding energy with the increase in neutron numbers which is observed experimentally. It is also found that for some of the solutions the HFB multipole moments acquire larger values as compared to the HF ones, though the cranking model moment of inertia is always decreased. The pickup strengths for neutrons and protons are also compared for the minimum energy solutions.

Angular distributions of deuterons from the ($p,d$) reaction (energy resolution ∼35 keV) on ${}_{}{}^{144}{}_{}{}^{}\mathrm{Sm}$ and ${}_{}{}^{142}{}_{}{}^{}\mathrm{Nd}$ at $E_p=35\mathrm{}$ MeV have been measured and compared with distorted-wave Born-approximation (DWBA) calculations. The DWBA calculations were performed both with and without the finite-range and nonlocality corrections. In some typical cases corrections were also included for the nuclear density dependence of the effective $\mathrm{pn}$ interaction. The DWBA cross sections for $l=5\mathrm{}$ show an enhanced sensitivity to the inclusion of these corrections. Calculations including both the nonlocality and finite-range corrections yield acceptable spectroscopic factors. Considerable fractionation of the $\left(2\mathrm{}{d}_{\frac{5}{2}}\right)_{\nu }^{}{}_{}{}^{-1\mathrm{}}$ and the $\left(1\mathrm{}{g}_{\frac{7}{2}}\right)_{\nu }^{}{}_{}{}^{-1\mathrm{}}$ states is observed. No measurable population of neutron states in the $82<N\le 126$ major shell was observed. The single-neutron-hole energies (in MeV) are as follows: $d_{\frac{3}{2}}$, 0.0; $s_{\frac{1}{2}}$, 0.45; $h_{\frac{11}{2}}$, 1.22; $d_{\frac{5}{2}}$, 1.52; and $g_{\frac{7}{2}}$, 2.12 for ${}_{}{}^{143}{}_{}{}^{}\mathrm{Sm}$; and $d_{\frac{3}{2}}$, 0.0; $s_{\frac{1}{2}}$, 0.43; $h_{\frac{11}{2}}$, 1.07; $d_{\frac{5}{2}}$, 1.47; and $g_{\frac{7}{2}}$, 2.20 for ${}_{}{}^{141}{}_{}{}^{}\mathrm{Nd}$. Data on the systematics of splitting and movement of these single-neutron-hole states as a function of the proton number ($Z$) in ${}_{}{}^{143}{}_{}{}^{}\mathrm{Sm}$, ${}_{}{}^{141}{}_{}{}^{}\mathrm{Nd}$, ${}_{}{}^{139}{}_{}{}^{}\mathrm{Ce}$, and ${}_{}{}^{137}{}_{}{}^{}\mathrm{Ba}$ shall be presented in a subsequent paper.

The resonant-neutron-capture $\gamma$-ray spectra for 28 resonances below 600-eV neutron energy are measured in ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}(n,\gamma ){}_{}{}^{239}{}_{}{}^{}\mathrm{U}$ with improved neutron and $\gamma$-ray energy resolution to allow an accurate test of the predictions of the statistical model of neutron capture. No convincing departures from these predictions are observed. The variation over 23 $S$-wave neutron resonances of the $\gamma$-ray transition probabilities to 15 final states is consistent with the Porter-Thomas distribution for both $E1\mathrm{}$ and $M1\mathrm{}$ multipoles. There is also no statistically significant correlation between the different decay modes of the neutron resonances. A large correlation coefficient of + 0.81 is observed between the partial radiative widths of the 3991- and 3982- keV $\gamma$ rays. This result, however, is not in violation of statistical independence for a sample size of 15 $\gamma$ rays. The $E1\mathrm{}$ and $M1\mathrm{}$ $\gamma$-ray strength functions are (2.6 ± 0.4) × ${10}^{-3\mathrm{}}$ and (8.1 ± 1.6) × ${10}^{-3\mathrm{}}$, respectively, compared to 3 × ${10}^{-3\mathrm{}}$ and 4 × ${10}^{-3\mathrm{}}$ listed by Bartholomew as the median values of all nuclei. Three of the weaker resonances at 10.2, 89.5, and 263 eV are assigned to $P$-wave capture. The neutron binding energy is measured to be 4806.7 ± 2.0 keV, which is 5.0 keV higher than the previously accepted value. Previously unobserved $\gamma$-ray transitions are reported.

Internal-conversion coefficients, $\gamma$-ray intensities of weak $\gamma$ rays, and two $\gamma -\gamma$ directional correlations in the transitions of ${}_{}{}^{103}{}_{}{}^{}\mathrm{Rh}$, after the ${\beta }^{-}$ decay of ${}_{}{}^{103}{}_{}{}^{}\mathrm{Ru}$, were measured. The conversion coefficients are: ${\alpha }_K\mathrm{}\left(53\right)=2.47\mathrm{}\pm 0.14$, ${\alpha }_K\mathrm{}\left(444\right)=(6.4\mathrm{}\pm 2.7)\times {10}^{-3\mathrm{}}$, ${\alpha }_K\mathrm{}\left(497\right)=(4.4\mathrm{}\pm 0.4)\times {10}^{-3\mathrm{}}$, ${\alpha }_K\mathrm{}\left(557\right)=(3.7\mathrm{}\pm 0.7)\times {10}^{-3\mathrm{}}$, ${\alpha }_K\mathrm{}\left(610\right)=(2.7\mathrm{}\pm 0.3)\times {10}^{-3\mathrm{}}$, and $\frac{K}{L}+M+\left(497\right)=8.43\mathrm{}\pm 0.40$. The $\gamma -\gamma$ directional correlations of the 557-53 and 444-53-keV cascades were measured with a 33-${\mathrm{cm}}^3$ Ge(Li) detector and a 2 × 2-in. NaI(Tl) detector on an automatic cycling correlation apparatus. The results are $A_2(557\mathrm{}-53)=-0.130\pm 0.008$ and $A_2(444\mathrm{}-53)=-0.23\pm 0.02$. The data imply that the 444-keV transition is pure $E2\mathrm{}$ while the 53-keV transition is mixed $M1+E2\mathrm{}$ with $\delta \mathrm{}\left(53\right)=-0.13\mathrm{}\pm 0.03$. The data allow unambiguous spin and parity assignments of ${\frac{9}{2}}^{+}$, ${\frac{5}{2}}^{+}$, and ${\frac{7}{2}}^{+}$ for the 93-, 537-, and 650-keV levels, respectively. The above data imply that the 557-keV transition is a multipole mixed transition with $\delta \mathrm{}\left(557\right)=-0.32\mathrm{}\pm 0.03$.

The radiations associated with the decay of 11.4-min ${}_{}{}^{152}{}_{}{}^{}\mathrm{Nd}$ and its 4.1-min ${}_{}{}^{152}{}_{}{}^{}\mathrm{Pm}$ daughter have been studied with Ge(Li), NaI(Tl), and anthracene detectors in both singles and coincidence configurations. A tentative decay scheme for ${}_{}{}^{152}{}_{}{}^{}\mathrm{Nd}$ involving allowed $\beta$ decay to the 4.1-min isomer of ${}_{}{}^{152}{}_{}{}^{}\mathrm{Pm}$ ($1^{+}$) ($logft=4.8\mathrm{}$) and to an excited $1^{+}$ level 294.6-keV higher ($logft=4.2\mathrm{}$) is presented. The 4.1-min level undergoes $\beta$ decay to 10 levels in ${}_{}{}^{152}{}_{}{}^{}\mathrm{Sm}$ which have been previously established in decay studies of ${}_{}{}^{152}{}_{}{}^{}\mathrm{Eu}$, and from Coulomb excitation and reaction studies. A new level in ${}_{}{}^{152}{}_{}{}^{}\mathrm{Sm}$ has been placed at ≅1081 keV. The total $\beta$-decay energy is nearly the same as the measured $\beta$ end-point energy, 3.6 ± 0.2 MeV.

Evidence is presented for the existence of two previously unreported high-spin isomers of ${}_{}{}^{152}{}_{}{}^{}\mathrm{Pm}$ having half-lives of 7.5 ± 1.0 min and ≅18 min. A decay scheme is proposed for the 7.5-min isomer ($4^{\pm }$) of ${}_{}{}^{152}{}_{}{}^{}\mathrm{Pm}$ including 16 known ${}_{}{}^{152}{}_{}{}^{}\mathrm{Sm}$ levels and new levels at 1081, 1804, and possibly 1941 keV. At least 40% of the $\beta$ transitions decay to the 1804-keV level with a $log\mathrm{ft}$ of ≅5.7 which suggests hindered allowed or first-forbidden decay. The observation of a 1.8-MeV $\beta$ group in coincidence with an intense 1437-keV $\gamma$ transition which deexcites the 1804-keV level establishes the total $\beta$-decay energy for 7.5-min ${}_{}{}^{152}{}_{}{}^{}\mathrm{Pm}$ as 3.6 ± 0.1 MeV. The ≅18-min isomer (≥$6^{\pm }$) of ${}_{}{}^{152}{}_{}{}^{}\mathrm{Pm}$ appears to populate a new level at 2172 keV and possibly the 1941-keV level in ${}_{}{}^{152}{}_{}{}^{}\mathrm{Sm}$.

The excitation energy of the first excited state of ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ was measured with inelastic deuteron scattering using the energy of $\alpha$ particles from ${}_{}{}^{210}{}_{}{}^{}\mathrm{Po}$ as a standard. The result is 1368.2 ± 0.5 keV. The average of recent measurements of the energy of $\gamma$ rays emitted by this state gives an excitation energy of 1368.67 keV based on the electron rest-mass energy. Thus the widely used polonium calibration energy is found to be consistent with the $\gamma$-ray energy standard to within 0.04%.

Elastic and inelastic scattering of 15-MeV protons, accelerated by the 90-in. cyclotron at Lawrence Radiation Laboratory, Livermore, from isotopically enriched targets of ${}_{}{}^{92,94,96,98,100}{}_{}{}^{}\mathrm{Mo}$ were studied with an over-all resolution of 50 keV (full width at half maximum). The experimental angular distributions were analyzed using a coupled-channel calculation. The collective vibrational model was employed to describe the states of the nucleus. Fifty angular distributions of scattered particles were measured and all but three were fitted with theoretical curves. The results for ${}_{}{}^{92}{}_{}{}^{}\mathrm{Mo}$, which has a closed neutron shell associated with the magic number $N=50\mathrm{}$, are discussed separately. All the inelastic scattering to levels in ${}_{}{}^{92}{}_{}{}^{}\mathrm{Mo}$ were fitted with single-step processes. The other even-mass isotopes of molybdenum were analyzed first by considering the main quadrupole and octupole vibrational states and then considering the states that can be described as possible mixtures of one- and two-quadrupole phonons. A high degree of single-phonon admixture was found to be present. Finally the weaker states were considered with the simple $0^{+}-I^{\pi }$ coupling scheme. Electromagnetic transition rates inferred from the deformabilities deduced in the present experiment. The results are compared with other experiments.

Our improved approach combining the renormalized Fermi-gas model (RGM) with the use of an average collective potential energy surface (PES) has been used to estimate the energy release in prompt fission phenomena from fission of excited nuclei. The role of excess excitation $\Delta U_I$ on top of the fission barrier, under several assumed constraints, is discussed. The partition of $\Delta U_I$ into the conjugate prompt fragments has been calculated from a simple RGM saturation condition. The practical limits of $\Delta U_I$ have been discussed from the viewpoint of the statistical model of nuclear reactions. The number of evaporated neutrons from the prompt fragments ${\nu }_F$ has been estimated from LeCouteur and Lang's approximation using Wing and Varley's neutron binding-energy tables. Fairly satisfactory agreement for the number ${\nu }_F$ has been obtained with the experimental work on fission of ${}_{}{}^{230}{}_{}{}^{}\mathrm{Th}$ by 25.7- and 29.5- MeV ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ ions and of ${}_{}{}^{226}{}_{}{}^{}\mathrm{Ra}$ by 13.0-MeV protons. A linear relationship of the average number of prompt neutrons $\overline{\nu }$ with $\Delta U_I$ is predicted from our model.

Most of the experiments to date which have indicated the presence of a parity-nonconversing component to the nuclear force have used $\beta$ decays to populate states which in turn decay electromagnetically. This report analyzes the degree to which parity nonconservation, present in the $\beta$ decay, affects the experimentally observed circular polarization of the electromagnetic radiation. A background contribution is found which has no monochromatic component, provided the electromagnetic and $\beta$-decay interactions are time-reversal invariant. A crude estimate of the effect of this background on specific experiments indicates that it should be much smaller than presently observed effects. A second more elaborate estimate comparing this background effect with the effect expected using theories of the parity-nonconserving forces confirms this.

Results of $\beta -\gamma$ directional-correlation measurements in the nonunique first-forbidden $\beta$ decay of the ground states of several odd-odd nuclei (${\mathrm{Sb}}^{124}$, ${\mathrm{Eu}}^{152}$, ${\mathrm{Re}}^{186}$, ${\mathrm{Tm}}^{170}$, ${\mathrm{Rb}}^{84}$) to the first $2^{+}$ levels in the even-even daughter nuclei are presented. These measurements were made as a function of the $\beta$-ray energy using a small shaped-field magnetic spectrometer. The results, in combination with all other available experimental data on each $\beta$ transition, have been analyzed to obtain the nuclear matrix element parameters. The analysis is based on the theoretical expressions given by Morita and Morita using exact electron radial wave functions which include finite nuclear size corrections. In addition, we have analyzed all available experimental data for the nonunique first-forbidden $\beta$ decay of ${\mathrm{Re}}^{188}$ and ${\mathrm{Rb}}^{86}$. A unique set of parameters was found for ${\mathrm{Re}}^{186}$, ${\mathrm{Re}}^{188}$, and ${\mathrm{Tm}}^{170}$ although the set for ${\mathrm{Tm}}^{170}$ suffers from a lack of adequate experimental information. For ${\mathrm{Rb}}^{86}$, the matrix element sets depend on whether the shape of the $\beta$ spectrum is statistical or not. For ${\mathrm{Rb}}^{84}$, five distinct sets of parameters were found which fit all available data equally well. For both ${\mathrm{Sb}}^{124}$ and ${\mathrm{Eu}}^{152}$, two sets of parameters were found that fit the data equally well; however, it is shown that a measurement of the $\beta$-circularly-polarized $\gamma$ correlation as a function of energy can eliminate one set in each case. Appropriate discussions based on nuclear models are given.

Information has been obtained on the mass distribution and kinetic energy release for fission of ${}_{}{}^{226}{}_{}{}^{}\mathrm{Ra}$ induced by protons and deuterons at moderate bombarding energies (<20 MeV). The mass distribution, which is triple peaked, has previously been interpreted in terms of two separate fission "modes": a single symmetric peak, characteristic of symmetric fission, associated with higher excitation energies; and a double-peaked distribution, characteristic of asymmetric fission, associated with lower excitation energies. It is shown that by a proper choice of proton and deuteron bombarding energies, and by a proper weighting of their respective mass-yield curves, the mass distribution for the fission of a single species, ${}_{}{}^{228}{}_{}{}^{}\mathrm{Ac}$, can be determined for a single excitation energy. At excitation energies near 25 MeV this mass distribution for ${}_{}{}^{228}{}_{}{}^{}\mathrm{Ac}$ is shown to be a single symmetric peak, in agreement with the hypothesis of two fission components. It is shown further that the measured kinetic energy distributions can also be interpreted in terms of the two-component hypothesis.

The effect of $Y_{40}$ deformation on the $\Delta N=2\mathrm{}$ orbital crossing is found to yield the observed splitting of the levels.

Directional-correlation measurements have been performed with two high-resolution and high-efficiency Ge(Li) counters on several $\gamma$ rays in coincidence with the 244.66-keV transition which deexcites the 366.44-keV ($4^{+}$) state to the 121.78-keV ($2^{+}$) level in ${}_{}{}^{152}{}_{}{}^{}\mathrm{Sm}$. It was determined that the 1005.15-keV transition deexciting the $4^{+}$ level of the $\gamma$ band to the $4^{+}$ level of the ground-state rotational band has (${93.3}_{-4.5\mathrm{}}^{+3.5\mathrm{}}$)% $E2\mathrm{}$ mixing. Furthermore, the existence of a new level in ${}_{}{}^{152}{}_{}{}^{}\mathrm{Sm}$ at 1681.5 keV has been established.

The most accurate nucleon-nucleon scattering experiments below 10 MeV are now consistent with the following values and uncertainties for the ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ scattering lengths and effective ranges:

$a_{\mathrm{pp}}^c=-7.823\mathrm{}\pm 0.01F$

$r_{\mathrm{pp}}^c=2.794\mathrm{}\pm 0.015F$

$a_{\mathrm{nn}}=-17\mathrm{}\pm 1F$

$r_{\mathrm{nn}}=2.84\mathrm{}\pm 0.03F$

$a_{\mathrm{np}}=-23.715\mathrm{}\pm 0.015F$

$r_{\mathrm{np}}=2.73\mathrm{}\pm 0.03F$

Unless strong theoretical arguments can be advanced that all charge-dependent corrections to the parameters can be calculated accurately enough to prove that the values $a_{\mathrm{nn}}$, $r_{\mathrm{nn}}$, or $r_{\mathrm{np}}$ must be moved outside these limits, or strong experimental reasons given to believe that experiments leading to these results were significantly in error, it is argued that new calculations or experiments aimed at changing these values are likely to fail. This argument is supported by an analysis of the latest $p-p$ experiments of Jarmie, Jett, Detch, and Hutson at 9.918 MeV, which reconfirm the one-pion-exchange shape effect and give $G_{{\pi }^{0}p}^2=15.3\mathrm{}\pm 2.4$ for the pion-nucleon coupling constant.

The $T$ matrix half off the energy shell can be expressed in terms of the on-shell $T$ matrix and the difference between the full scattering wave function and the phase-shifted free wave function. This representation allows one to investigate variations in the half-shell $T$ matrix by means of a parametrization of the scattering wave function in the interaction region. Most of our knowledge of the physical constraints on that wave function may then be included. In particular we have studied the arbitrariness remaining in the half-shell $T$ matrix given the following constraints: (1) The on-shell $T$ matrix is given; (2) a specific local potential acts beyond a certain radius; and (3) the wave function is suppressed at short distances. We construct models of the ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ two-nucleon half-shell $T$ matrix. In a simple one-parameter model satisfying these constraints, the range of variation of the near off-shell behavior is displayed.

The bound state of three $\alpha$ particles is considered. For the $\alpha$-cluster model, we consider the Coulomb Green's function in the nucleus ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$. The calculated binding energy of the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ nucleus is consistent with previous calculations.

The features of the kernel function in the nonlocal $n+\alpha$ interaction, derived with the resonating-group method, which uses a totally antisymmetric wave function and a nucleon-nucleon potential, is studied. This kernel function is made up of three terms, corresponding to knockout, heavy-particle-pickup, and nucleon-rearrangement processes. In the medium- and high-energy regions, the knockout process contributes mainly in the forward directions, while the heavy-particle-pickup and nucleon-rearangement processes contribute mainly in the backward directions. In particular, it is found that these latter two processes are almost entirely responsible for the occurrence of large backward-angle cross sections in the $n+\alpha$ problem. An equivalent local potential between the neutron and the $\alpha$ particle is also constructed, which, in the Born approximation, yields the same results as does the resonating-group calculation. This equivalent local potential has an explicit energy dependence and a significant amount of Majorana space-exchange component. Finally, approximation methods are proposed which contain the essential features of the antisymmetization procedure and yet could be used to consider such more complicated problems as the scattering of nucleons by medium- and heavy-weight nuclei.

Linear-polarization and angular-distribution measurements have been made on the three transitions from the 1.459-MeV level in ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$ using inelastic proton scattering. The mixing ratios were determined to be $-0.1<{\delta }_{\frac{M2\mathrm{}}{E1\mathrm{}}}<0.0\mathrm{}$ for the 1.459→ 0.197-MeV transition, $0.30<\mathrm{}{\delta }_{\frac{E2\mathrm{}}{M1\mathrm{}}}<0.38\mathrm{}$ for the 1.459→ 0.110-MeV transition, and $\left|{\delta }_{\frac{M2\mathrm{}}{E1\mathrm{}}}\right|<\mathrm{}0.06\mathrm{}$ for the 1.459→ 0-MeV transition. The results indicate that the level in question cannot be explained as a $p_{\frac{1}{2}}$ proton hole coupled to the pure ground-state rotational band as has been accepted in the past.

The three-body reaction ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}\mathrm{}(p,pn)\mathrm{}{}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ has been studied experimentally in a kinematically complete experiment. $p-n$ coincidence events were measured for several bombarding energies between 7.9 and 12.5 MeV using associated time-of-flight techniques, pulse-shape discrimination for the neutron-detection system, and a silicon surface-barrier detector for the charged particles. Only in the region of 12.5-MeV bombarding energy is there an indication of sequential decay via "singlet deuteron" formation. Higher energies were not attainable with the available equipment, and at lower energies sequential decay through levels in ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{13}{}_{}{}^{}\mathrm{N}$ was relatively strong and obstructed the observation of possible contributions from $p-n$ final-state interactions. An upper limit is assigned to the two-body ($p,d^{*}$) cross section.