The meaning of a particular form of cluster wave functions, which have been used in a previous paper to describe the ground-state rotational band of ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$, is discussed.

The effect of a class of residual potentials in the Hamiltonian and nucleon-nucleon correlation on calculations in the independent-particle shell-model wave function of ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ has been investigated. A method has been developed to give minimum energies of various states of a nuclear system with a somewhat realistic Hamiltonian and wave function. The results on energy calculations are in good agreement with the observed data. The $E2$ transition rate and other relevant observables pertaining to this transition using this wave function and several others have been calculated. Comparison of the results of these calculations with experimental data and other theoretical predictions shows a definite preference for the correlated wave function of ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ developed here. The method is convenient for application to other nuclear systems.

For the elastic scattering of ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ + ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, excitation functions at c.m. angles of 60, 70, 80, and 90° have been studied in the c.m. energy range 5-17 MeV, and angular distributions have been measured at c.m. energies of 6, 10, and 14 MeV. The excitation functions are relatively featureless, with a broad gross-structure peak at 90° centered around 13 MeV. Good fits to individual angular distributions are obtained with the optical model and, except for the highest energies studied, parametrized phase-shift calculations. These calculations, however, do not correctly reproduce the energy dependence of the data. The single most outstanding conclusion from the present analysis is that ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ + ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ is dominated by absorption, and this dominance leads to scattering behavior very different from that found for other heavy ions.

The $p+{\mathrm{He}}^3$ and $n+{\mathrm{H}}^3$ systems are considered with the resonating-group method in the one-channel approximation. A purely central nucleon-nucleon potential which has different ranges in the singlet and triplet states is employed. The internal wave function of the three-nucleon cluster is a sum of two Gaussian functions, with its parameters adjusted to reproduce quite well the properties of the cluster. From the results obtained it is found that the agreement with experiment is quite satisfactory, although in the very low-energy region, detailed fit is not obtained, which is most probably due to the omission of the specific distortion effect in our calculation. An effective interaction between the clusters is also constructed. From this effective interaction it is concluded that the requirement of antisymmetry for the total wave function is very important. In particular, it creates an odd-even feature, wherein the effective potentials in the odd-$l$ and even-$l$ states are quite different.

Polarized ${}_{}{}^{13}{}_{}{}^{}\mathrm{B}$ nuclei have been produced through the ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}\mathrm{}(t,p)\mathrm{}{}_{}{}^{13}{}_{}{}^{}\mathrm{B}$ reaction using the 3.5-MeV Van de Graaff accelerator at Brookhaven National Laboratory. The recoiling nuclei were stopped in Au, Pd, and Pt foils, and the effective dipole moments of ${}_{}{}^{13}{}_{}{}^{}\mathrm{B}$ in these metals were measured by a resonant depolarization technique. From earlier measurements of the spin-lattice relaxation times of ${}_{}{}^{12}{}_{}{}^{}\mathrm{B}$ in the same metals, the magnetic effects of the stopping foils were estimated. Using a common enhancement factor for the three metals, the ${}_{}{}^{13}{}_{}{}^{}\mathrm{B}$ magnetic dipole moment was found to be $\mu ({}_{}{}^{13}{}_{}{}^{}\mathrm{B}=+3.17712\mathrm{}(51)\mathrm{}{\mu }_N$, the plus sign being inferred from the Schmidt limits for odd-proton spin $\frac{3}{2}$ nuclei.

A variational method that involves solution of inhomogeneous linear equations is used to calculate the wave function and binding energy of the triton. Cohen and Willis's classification of the triton wave function is employed. Internal wave functions are expanded in terms of polynomials of the interparticle distances up to 170 terms. A binding energy of -6.7 MeV is obtained for the unmodified Hamada-Johnston potential. Due to the simplicity of our variational wave function, all the matrix elements are evaluated analytically in terms of the exponential integrals. With the aid of recurrence relations, the computing time has been reduced to a minimum.

Many investigators have studied the scattering of low-energy nucleons by light nuclei using a single-particle effective potential which is derived from a many-nucleon Hamiltonian under the assumption that the contribution to the scattering by virtual excitations of the target nucleus can be neglected. In addition, they have approximated the ground-state wave functions of the target nuclei by crude variational wave functions, thus introducing an unknown error into the results of the scattering calculation. In this paper we investigate that error for the specific case of neutron-triton scattering. To do this we derive three approximate effective potentials which differ from each other and from the exact single-particle effective potential by the same order in the error of the approximate triton wave function. The difference between the phase shifts calculated with the approximate potentials gives an indication of the uncertainty in the calculations, and as the approximate triton wave function is improved the difference decreases. Our work shows that previous calculations involve large errors which may be reduced by improving the approximate target wave function.

The cross sections for the production of ${}_{}{}^{11}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$ by protons from a ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ target has been measured at energies from 5-24 MeV for ${}_{}{}^{11}{}_{}{}^{}\mathrm{C}$ and 13-42 MeV for ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$. A sharp rise above the thresholds for the ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}(p,\alpha )$ and ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}(p,2\mathrm{}\alpha )$ reactions was observed, with maxima, respectively, around 200 and 45 mb.

Measurements of the angular distribution and polarization of neutrons from the reaction ${}_{}{}^3{}_{}{}^{}\mathrm{H}({}_{}{}^3{}_{}{}^{}\mathrm{He},n){}_{}{}^5{}_{}{}^{}\mathrm{Li}$ have been made for mean ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ bombarding energies of 2.70 and 3.55 MeV. Polarizations were measured using a ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ gas scintillator, and cross sections were determined using a liquid scintillator employing pulse-shape discrimination. Contributions from the three-body breakup channel ${}_{}{}^3{}_{}{}^{}\mathrm{H}({}_{}{}^3{}_{}{}^{}\mathrm{He},np){}_{}{}^4{}_{}{}^{}\mathrm{He}$ were removed by assuming these neutrons to be unpolarized and to have a statistical energy distribution in the high-energy portion of the neutron spectrum. The angular distribution of neutrons from the reaction ${}_{}{}^3{}_{}{}^{}\mathrm{H}({}_{}{}^3{}_{}{}^{}\mathrm{He},n){}_{}{}^5{}_{}{}^{}\mathrm{Li}$ exhibits a broad peak in the vicinity of ${\theta }_{\mathrm{c}.\mathrm{m}.\mathrm{}}={45}^{\circ }$. The neutron polarization was found to be negative at all angles investigated, and reaches a minimum value of -0.30 at ${\theta }_{\mathrm{c}.\mathrm{m}.\mathrm{}}={125}^{\circ }$, $E_{3\mathrm{He}}=2.7\mathrm{}$ MeV. Excitation functions for the cross section were measured at laboratory angles of 0 and 40° for ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ energies between 0.7 and 3.8 MeV. The reaction data can be reproduced qualitatively with a simple two-nucleon-transfer distorted-wave Born-approximation calculation, but the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-${}_{}{}^3{}_{}{}^{}\mathrm{H}$ potential parameters used do not reproduce published elastic scattering data at somewhat higher energy.

Within the context of the impulse approximation we analyze the reaction ${\mu }^{-}+{\mathrm{Li}}^6\to {\mathrm{H}}^3+{\mathrm{H}}^3+\nu$ using the current-current theory of weak interactions and an $\alpha -d$ model of ${\mathrm{Li}}^6$ fitted to the binding energy and charge radius of ${\mathrm{Li}}^6$. The model is tested by considering the channel ${\mu }^{-}+{\mathrm{Li}}^6\to {\mathrm{He}}^6+\nu$. Within the limitations of our stated approximations, total rates are estimated for these two modes and the combined triton distribution given for the ditriton channel.

Differential cross sections for ${\mathrm{Li}}^{6,7}$ + ${\mathrm{Li}}^{6,7}$ + ${\mathrm{Be}}^9$ nuclear reactions leading to low-lying residual-nucleus states have been measured over the energy range from 4-14 MeV. In the ${\mathrm{Li}}^7({\mathrm{Li}}^7,\alpha ){\mathrm{Be}}^{10}\mathrm{}\left(3.37\right)\mathrm{}$ case, the energy range was extended to 2.1 and 21 MeV. Striking enhancement and weakening of cross sections for formation of the 0.72-MeV state in ${\mathrm{B}}^{10}$ can be attributed to cluster structure of lithium nuclei. Resonance-like peaks are observed in some yields. Their general character is consistent with an extended-structure interpretation of the reaction mechanism.

An analysis of available data, with emphasis on the ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}\mathrm{}(d,p)\mathrm{}$ and ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}\mathrm{}(p,x)\mathrm{}$ reactions, indicates that the analogs of the first seven ${}_{}{}^{12}{}_{}{}^{}\mathrm{B}$ states can be identified in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$. Neutron reduced widths ${{\gamma }_{\lambda n}}^2$ for the first six states in ${}_{}{}^{12}{}_{}{}^{}\mathrm{B}$ are calculated from spectroscopic factors which were extracted from the ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}\mathrm{}(d,p)\mathrm{}$ data by use of a distored-wave Born approximation analysis. Proton reduced widths ${{\gamma }_{\lambda p}}^2$ of the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ analog states are deduced from observed widths by use of an $R$-matrix formulation. It is found that the analog relationship $\frac{{{\gamma }_{\lambda n}}^2}{2{{\gamma }_{\lambda p}}^2}=1\mathrm{}$ is satisfied to within ∼30% for all of the observed pairs of states, except for the pair corresponding to the ${}_{}{}^{12}{}_{}{}^{}\mathrm{B}$ first excited state. The possibility that this discrepancy is due to experimental error is discussed.

The mean lifetime of the first excited state of ${}_{}{}^{11}{}_{}{}^{}\mathrm{Be}$ at 0.32 MeV has been measured by the Doppler-shift-attenuation method. The result 0.18±0.06 psec corresponds to a very strong $E1$ transition, 0.33 W.u. This value is in very good agreement with a simple harmonic-oscillator picture of the $2s_{\frac{1}{2}}\to 1p_{\frac{1}{2}}$ transition which gives 0.32 W.u. However, the agreement is probably fortuitous, since the same model fails for the analogous transition in ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$, which is an order of magnitude too slow. No simple model relieves this discrepancy. The energy of the state in ${}_{}{}^{11}{}_{}{}^{}\mathrm{Be}$ is found to be 319.8±0.2 keV.

The ground-state masses of ${}_{}{}^9{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{13}{}_{}{}^{}\mathrm{O}$, and ${}_{}{}^{21}{}_{}{}^{}\mathrm{Mg}$ have been determined through measurement of the $Q$ values of the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(${}_{}{}^3{}_{}{}^{}\mathrm{He}$, ${}_{}{}^6{}_{}{}^{}\mathrm{He}$)${}_{}{}^9{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$(${}_{}{}^3{}_{}{}^{}\mathrm{He}$, ${}_{}{}^6{}_{}{}^{}\mathrm{He}$)${}_{}{}^{13}{}_{}{}^{}\mathrm{O}$, and ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$(${}_{}{}^3{}_{}{}^{}\mathrm{He}$, ${}_{}{}^6{}_{}{}^{}\mathrm{He}$)${}_{}{}^{21}{}_{}{}^{}\mathrm{Mg}$ reactions. The measurements were made with 68-70-MeV ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ beams using a split-pole magnetic spectrograph. A new method for obtaining a precise calibration for the beam analyzer and magnetic spectrograph at these high bombarding energies is presented.

The mass excess of ${}_{}{}^9{}_{}{}^{}\mathrm{C}$ has been measured as 28.911 ± 0.009 MeV, that of ${}_{}{}^{13}{}_{}{}^{}\mathrm{O}$ as 23.103 ± 0.014 MeV, and that of ${}_{}{}^{21}{}_{}{}^{}\mathrm{Mg}$ as 10.912 ± 0.018 MeV. These nuclei represent the $T_z=-\frac{3}{2}$ members of the $T=\frac{3}{2}$ quartets for $A=9, 13, \mathrm{and} 21$, respectively.

The present results show excellent agreement with a quadratic isobaric-multiplet mass equation for $A=13\mathrm{}$ and $A=21\mathrm{}$, but there is some indication that a small cubic term is required for the $A=9\mathrm{}$ multiplet.

A general class of exactly soluble three-level models is presented for an $N$-fermion system. Assuming a monopole-monopole interaction among the fermions allows one to express the model Hamiltonian in terms of the generators of the $S{U}_3$ group. A specialized version of this class of models is adapted for the study of mixing two collective states of opposite parity, analogous to the mixing of giant-dipole-resonance and surface quadrupole vibrations in nuclei. Exact results of the model are studied as a function of interaction parameters and compared with approximations including up to three-particle-three-hole excitations. It is shown that in the model many-particle-many-hole states play an important role in the mixing of collective states and cannot be properly neglected. The implications of this result for the study of actual nuclei is discussed.

The various phenomenological potential form factors which describe the elastic scattering of $\alpha$ particles from a given target nucleus are similar at large radii. It is shown that reasonably accurate limits can be placed on both the magnitude and falloff rate of the potential in this surface region close to the maximum of the Coulomb barrier. This surface-region potential is found to be well reproduced by a simple folding of the nuclear-matter distribution with a two-body potential which fits free nucleon-$\alpha$ scattering.

The mean lifetimes of nine levels in ${}_{}{}^{39}{}_{}{}^{}\mathrm{K}$ up to 4.12 MeV in excitation have been measured by the Doppler-shift-attenuation method. The levels were populated by the ${}_{}{}^{39}{}_{}{}^{}\mathrm{K}(p,p^{\prime }\gamma ){}_{}{}^{39}{}_{}{}^{}\mathrm{K}$ reaction at proton energies of 6.47 and 6.67 MeV. $\gamma$ rays were detected in a 30-${\mathrm{cm}}^3$ coaxial Ge(Li) detector at 30 and 135° to the beam direction in coincidence with protons scattered between 164-174°. Transition strengths have been calculated for the first four excited states, and the results are compared with predictions of the weak-coupling model and a phonon-hole coupling model. The weak-coupling model is shown to underestimate $E2$, $M2$, and $E3$ strengths, while the phonon-hole coupling model predicts enhanced $E3$ strengths.

Employing ${\mathrm{Ca}}^{48}$ as the core and the reaction matrix elements of Kuo and Brown for the residual interaction among the three valence protons, the nuclear energy levels of ${\mathrm{V}}^{51}$ are calculated within the spherical shell-model framework. All the $0f-1p$ configurations are included. The wave functions obtained on diagonalizing the Hamiltonian matrices are used to calculate the transition rates and spectroscopic factors for the reaction ${\mathrm{Ti}}^{50}({\mathrm{He}}^3,d){\mathrm{V}}^{51}$. Good agreement with experiments is found suggesting that it is not necessary to include deformation in ${\mathrm{V}}^{51}$ as in the papers of Scholz and Malik. The consequences of mixing effective interaction matrix elements of Lips and McEllistrem and realistic Kuo-Brown matrix elements are studied and it is pointed out that such a mixture does not yield a successful effective interaction model. Our results are further supported by similar calculations on ${\mathrm{Cr}}^{52}$.

Magnetic $\beta$-ray spectrometer studies at 0.05% momentum resolution with isotope-separator-prepared samples have revealed structure below the $K$ conversion lines of the 122- and 136- keV (${\mathrm{Fe}}^{57}$) and the 661-keV (${\mathrm{Ba}}^{137}$) transitions. This structure consists of an abrupt rise below the $K$ conversion line (in atomic number $Z$) at an energy displacement approximately equal to the $L_3$ binding in the ($Z+1\mathrm{}$) neutral atom, and a continuum extending to lower energies. These continua are interpreted as the spectra complementary to the (unobserved; energy near zero) $L$ -shakeoff spectra; i.e., the sum of ejected $K$- and $L$-electron energies equals a constant. The double-vacancy binding energy for $K{L}_3$ is ${7905}_{-10\mathrm{}}^{+20\mathrm{}}$ eV for Fe and 43.01±0.03 keV for Ba. The sum of $\mathrm{KL}$ shakeoff from all three $L$ subshells compared with the $K$ line is $\Sigma \frac{\mathrm{KL}}{K}=9\mathrm{}\times {10}^{-3\mathrm{}}$ for Fe and 1×${10}^{-3\mathrm{}}$ for Ba (both with uncertainties estimated at ∼50%), in good agreement with self-consistent-field overlap integrals for shakeoff in ${\beta }^{-}$ decay if one takes the effective charge change for $L$ electrons during $K$ conversion as ∼0.85 times that for ${\beta }^{-}$ decay. The spectrum shape of the $\mathrm{KL}$ continua, in the main, confirms the predictions of the nonrelativistic calculations which have been made for $\beta$-decay processes, but some discrepancies are suggested. For the less probable $K$ shakeoff accompanying $K$ conversion, preliminary values for intensities of the continua with respect to the $K$ line are $\frac{\mathrm{KK}}{K}$ between (0.4-2)×${10}^{-4\mathrm{}}$ for Fe, and $\frac{\mathrm{KK}}{K}<2\mathrm{}\times {10}^{-4\mathrm{}}$ for Ba. No $M_1$ or $M_{2,3}$ shakeoff was obvious on the $K$ line of the 14-keV transition in ${\mathrm{Fe}}^{57}$.

Seven excited levels of ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$ have been populated by the ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}(p,p^{\prime })$ reaction and studied with $\gamma -\gamma$ and $p^{\prime }-\gamma$ angular-correlation techniques. Spin-parity assignments are: 1461 keV, $2^{+}$; 2121 keV, $0^{+}$; 2524 keV, $2^{+}$; 2892 keV, ${\mathrm{}\left(4\right)\mathrm{}}^{+}$; 3207 keV, $2^{+}$ or $1^{\pm }$; 3507 keV, $2^{+}$ or $1^{+}$; 3681 keV, $3^{-}$. Multipole amplitude mixing ratios are: $2524\to 1461$-keV transition, $\delta \left(\frac{E2\mathrm{}}{M1\mathrm{}}\right)=+0.24\mathrm{}$; $3207\to 1461$-keV transition, if $2^{+}\to 2^{+}$, $\delta \left(\frac{E2\mathrm{}}{M1\mathrm{}}\right)=-0.20\mathrm{}$, and if $1^{\pm }\to 2^{+}$, $\delta =0\mathrm{}$. $\gamma$-ray branching ratios for the second to seventh excited levels have been measured. These results, together with lifetimes previously determined by others, are used to calculate $B\mathrm{}\left(E2\mathrm{}\right)\mathrm{}$ and $B\mathrm{}\left(M1\mathrm{}\right)\mathrm{}$ values which are compared with those of similar levels in ${}_{}{}^{42}{}_{}{}^{}\mathrm{Ca}$.