We discuss the tangible consequences of the existence of Pauli forbidden states of relative motion of two nuclei for the nucleus-nucleus interaction. The ranges of the influence of the Pauli forbidden states are tabulated for the systems ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$-${}_{}{}^{12,13,14}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$-${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{12,14}{}_{}{}^{}\mathrm{C}$-${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$-${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, $\alpha$-${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$, and $\alpha$-${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$.

NUCLEAR REACTIONS Influence of Pauli forbidden states on the nucleus-nucleus interaction.

The differential muon-capture rate $\frac{d\Gamma }{d{E}_T}$ is obtained for the reaction ${\mu }^{-}+{}_{}{}^6{}_{}{}^{}\mathrm{Li}\to {}_{}{}^3{}_{}{}^{}\mathrm{H}+{}_{}{}^3{}_{}{}^{}\mathrm{H}+{\nu }_{\mu }$ over the allowed range of $E_T$, the tritium energy, for two assumptions concerning the behavior of $F_A$, the axial current form factor, in the timelike region; analytic continuation from the spacelike region and mirror behavior, $F_A(q^2, \mathrm{timelike})=F_A(q^2, \mathrm{spacelike})$. The values of $\frac{d\Gamma }{d{E}_T}$ under these two assumptions are found to vary substantially in the timelike region as a function of the mass $M_A$ in the dipole fit to $F_A$. Values of $\frac{d\Gamma }{d{E}_T}$ are given for ${M_A}^2=2\mathrm{}{m_{\pi }}^2$, $4.95{m_{\pi }}^2$, and $8{m_{\pi }}^2$.

NUCLEAR REACTIONS Muon capture ${}_{}{}^6{}_{}{}^{}\mathrm{Li}({\mu }^{-}, {\nu }_{\mu }){}_{}{}^3{}_{}{}^{}\mathrm{H}{}_{}{}^3{}_{}{}^{}\mathrm{H}$, $\Gamma$, $\frac{d\Gamma }{d{E}_T}$ calculated for two assumptions concerning the axial current form factor behavior in timelike region.

Elastic scattering angular distribution and 180° c.m. excitation function are rather well reproduced just above the Coulomb barrier by a heavy-ion nuclear potential having a repulsive core at short distances and a very strong attractive behavior at the nuclear surface. An important prediction of this potential, a precipitous drop in differential cross section at 180°, is verified experimentally.

NUCLEAR REACTIONS Prediction and observation of a simultaneous minimum in the backward angular distribution and excitation function for mass-asymmetric heavy-ion elastic scattering; signal for a molecular resonance.

The coefficients of Fourier-Bessel expansion of charge distribution in ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ are determined from the single proton wave functions derived from two sets of optimized Woods-Saxon potentials. The set of potentials optimized with respect to the observed single particle states in ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ give excellent agreement with the model independent analysis of the charge distribution. But the potentials obtained from core-polarization corrected single particle states give very poor charge distribution.

NUCLEAR STRUCTURE ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ charge distribution. Deduced effect of core polarization.

Measurements on the newly discovered $1^{+}$ state at $E_x=5.845\mathrm{}$ MeV in ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ provide an opportunity to examine the spin dependence in the nuclear effective Hamiltonian. The data require a somewhat weaker spin-orbit splitting than given by conventional Hamiltonians. The isoscalar spin-dependent residual interaction, which was poorly determined by previous data, is found to be much weaker than the isovector spin-dependent interaction, as predicted by Brueckner theory.

NUCLEAR STRUCTURE Simple shell model, spin parameters in the Hamiltonian for ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$.

The theory of nuclear beta decay induced by intense electromagnetic fields as previously presented is applied to a much broader range of physical variables. The most important intensity domain is found to occur at lower values than had previously been estimated. Furthermore, electromagnetic field "retardation terms," previously pointed out as potentially important but unevaluated, are found to be significant contributors to the overall transition probability. A treatment of the entire problem in "electric field" gauge, instead of the original Coulomb gauge, gives identical results.

RADIOACTIVITY Intense-field-induced $\beta$ decay. $\beta$ decay forbiddenness removal.

It is shown that the absolute normalization of $\gamma$-ray yields ($I_{\gamma }$) for transitions among levels in ${}_{}{}^{225}{}_{}{}^{}\mathrm{Ra}$ following $\alpha$ decay of ${}_{}{}^{229}{}_{}{}^{}\mathrm{Th}$ reported by Rattan et al. should be increased by at least 22%. Disagreements of reported values of $I_{\gamma }$ with those in a recent report are discussed but not resolved.

RADIOACTIVITY ${}_{}{}^{229}{}_{}{}^{}\mathrm{Th}$; properties of transitions among levels of ${}_{}{}^{225}{}_{}{}^{}\mathrm{Ra}$.

The low-energy logarithmic derivative of the $S$ factor for ${}_{}{}^7{}_{}{}^{}\mathrm{Be}(\mathrm{p}, \gamma ){}_{}{}^8{}_{}{}^{}\mathrm{B}$ calculated by Williams and Koonin using only asymptotic wave functions differs from that obtained with a potential model. It is suggested that this is due at least in part to an inappropriate choice of nuclear phase shift in the former calculation.

NUCLEAR REACTIONS ${}_{}{}^7{}_{}{}^{}\mathrm{Be}(\mathrm{p}, \gamma ){}_{}{}^8{}_{}{}^{}\mathrm{B}$, $E<\mathrm{}100\mathrm{}$ keV, extrapolated $S$.

The analyzing power $A_y\left(\theta \right)$ and differential cross section $\sigma \left(\theta \right)$ have been measured for elastic scattering of 10-MeV neutrons from ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$. These data were analyzed with a spherical optical model which has a real spin-orbit potential with either a three-parameter conventional form or a one-parameter semimicroscopic form. The predictions with both spin-orbit potentials reproduce the data equally well, suggesting that fewer free parameters can be used in spherical optical model calculations. Including an imaginary spin-orbit term $W_{\mathrm{SO}}\mathrm{}\left(r\right)\mathrm{}$ in the optical potential greatly improves the fits to the $A_y\left(\theta \right)$ measurements and establishes the need for $W_{\mathrm{SO}}\mathrm{}\left(r\right)\mathrm{}\ne 0$ in the n + ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ potential.

NUCLEAR REACTIONS ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$(n, n); $E=10\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$, $A_y\left(\theta \right)$; deduced complex spin-orbit potential; spherical optical model calculations.

The two-potential formalism for long-range forces is generalized to coupled channels. Assuming the short-range potential to be separable we treat the proton-proton interaction in the coupled partial waves ${}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}-{}_{}{}^3{}_{}{}^{}F_2^{}{}_{}{}^{}$. We derive the corresponding Coulomb-modified nuclear transition matrices in closed analytic form and calculate the Coulomb distortion of the phase shifts and of the mixing parameter. The separable parametrization proposed for the p-p interaction in ${}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}-{}_{}{}^3{}_{}{}^{}F_2^{}{}_{}{}^{}$ yields an accurate fit to the experimental data available for these channels. The potential completes the description of the N-N interaction by the Graz-II separable model.

NUCLEAR REACTIONS Coupled-channel problem with long-range forces; p-p interaction in ${}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}-{}_{}{}^3{}_{}{}^{}F_2^{}{}_{}{}^{}$; separable potential proposed; rigorous treatment of Coulomb distortion; closed analytic formulas for transition matrices.

Excitation of strength peaked at 12.0 MeV is observed in ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ and ${}_{}{}^{206}{}_{}{}^{}\mathrm{Pb}$ via the inelastic scattering of 200 MeV protons. Based upon angular distribution measurements in ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ we interpret the strength as an isoscalar $2\hslash \omega$, $L=4\mathrm{}$, excitation.

NUCLEAR REACTIONS ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$, ${}_{}{}^{206}{}_{}{}^{}\mathrm{Pb}$ (p,p'), $R_p=200\mathrm{}$ MeV; measured $E_x$, $\sigma \left(\theta \right)$ for giant resonances; deduced, $E_R$, ${\Gamma }_R$, $B\left(E4\mathrm{}\right)\mathrm{}$.

Results of relativistic and nonrelativistic impulse approximation calculations are compared for p+${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ elastic scattering observables between 181 and 1040 MeV. At 400 MeV and above, the relativistic approach is superior, especially with regard to spin observables. Below 400 MeV, neither calculation agrees well with experiment.

NUCLEAR REACTIONS Energy dependence of the relativistic impulse approximation, Dirac phenomenology, invariant nucleon-nucleon amplitudes, nucleon-nucleus elastic scattering, $E_{\mathrm{p}}=181-1040\mathrm{}$ MeV.

Differential cross-section and analyzing-power angular distributions have been measured for the elastic scattering of 159.4 MeV protons on ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ and for the inelastic transitions to the 2.31-MeV and 3.95-MeV states. Elastic-scattering data for $\overrightarrow{\mathrm{p}}$+${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and inelastic data for the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(\overrightarrow{\mathrm{p}}, {\mathrm{p}}^{\prime }){}_{}{}^{12}{}_{}{}^{}\mathrm{C}\left(4.44\mathrm{} \mathrm{MeV}\right)$ reaction have also been obtained at the same energy as a normalization check. The ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}(\overrightarrow{\mathrm{p}}, {\mathrm{p}}^{\prime }){}_{}{}^{14}{}_{}{}^{}\mathrm{N}\left(2.31\mathrm{} \mathrm{MeV}\right)$ transition has been analyzed in the distorted-wave impulse approximation. This transition has long been regarded as a favorable test for the tensor component of the effective nucleon-nucleon interaction. Calculations employing wave functions that provide the necessary cancellation of the $L=0\mathrm{}$ central-interaction transition strength do not provide a good description of the differential cross-section angular distribution. It is suggested that more complicated reaction mechanisms, e.g., (p,d)(d,p′) contributions, may be needed to describe this transition.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(\overrightarrow{\mathrm{p}}, \mathrm{p})$, ($\overrightarrow{\mathrm{p}}, {\mathrm{p}}^{\prime }$), $E_x=4.44\mathrm{}$ MeV; ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}(\overrightarrow{\mathrm{p}}, \mathrm{p})$, ($\overrightarrow{\mathrm{p}}, {\mathrm{p}}^{\prime }$), $E_x=2.31, 3.95$ MeV; $E_{\mathrm{p}}=159.4\mathrm{}$ MeV. Measured $\sigma \left(\theta \right)$, $A_y\left(\theta \right)$, ${\theta }_{\mathrm{lab}}=7.5\mathrm{}°-45\mathrm{}°$. DWIA analysis of 2.31-MeV transition.

The reaction ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$(t,p) has been used to locate 1p-2h and 2p-3h states in ${}_{}{}^{15}{}_{}{}^{}\mathrm{C}$. Results for the negative-parity levels are in good agreement with expectations for ${\mathrm{}\left(\mathrm{sd}\right)\mathrm{}}^2$ $L=0, 2, \mathrm{and} 4$ transfers as given by ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$(t,p)${}_{}{}^{16}{}_{}{}^{}\mathrm{C}$.

NUCLEAR REACTIONS ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$(t,p)${}_{}{}^{15}{}_{}{}^{}\mathrm{C}$; $E=18\mathrm{}$ MeV; measured $\sigma (E_{\mathrm{p}}, \theta )$, $\theta =3.75-86.25\mathrm{}°$ (lab) ${}_{}{}^{15}{}_{}{}^{}\mathrm{C}$ levels, $L$, $J^{\pi }$, comparison with ${}_{}{}^{16}{}_{}{}^{}\mathrm{C}$.

It is shown that within the multistep compound theory the use of matrix elements calculated with a density dependent two-body residual interaction of the Yukawa form makes possible reproduction of the experimental data of multistep compound reactions with an interaction strength $V_0$ which turns out to be consistent with the one used in the analysis of multistep direct processes.

NUCLEAR REACTIONS Statistical multistep compound and direct analysis, deduced two-body residual interaction strength.

Formulation of $s$-wave zero-energy Faddeev-type scattering equations including a Coulomb interaction is discussed. Numerical solutions of these equations for the $s$-wave NN potential models of Malfliet and Tjon are obtained using spline techniques. Kohn variational estimates are presented and comparison is made to previously published results. Our quartet pd scattering lengths are larger than others previously obtained, and our pd doublet results are smaller than the corresponding nd results, and thus in contrast to the experimental values. An explication of this feature is presented in terms of a model two-body problem. Perturbation theory for the Coulomb corrections to the scattering length is developed and confirms the Kohn estimates.

NUCLEAR REACTIONS ${}_{}{}^2{}_{}{}^{}\mathrm{H}$(p,p)${}_{}{}^2{}_{}{}^{}\mathrm{H}$, $E=0\mathrm{}$ MeV, p-d $s$-wave scattering lengths, configuration space Faddeev calculations.

The total neutron cross sections of the helium isotopes were measured in the energy range from 1.5 to 40 MeV. A continuous energy neutron source was used in connection with a 190 m long flight path and high resolution time-of-flight techniques. The energy resolution achieved enabled us to improve considerably the parameters of the narrow ${\frac{3}{2}}^{+}$ resonance in the n+${}_{}{}^4{}_{}{}^{}\mathrm{He}$ system. The position of the resonance was found to be 22 133±10 keV, with a total width of 76±12 keV and a neutron width of 37±5 keV. This agrees well with previous analyses, which yield ${\Gamma }_{\mathrm{n}}\sim \frac{1}{2}\Gamma$. Absolute values for the cross sections were determined with an overall error smaller than 3%. Comparison with older data shows agreement within the total errors. Our data are 4% to 5% higher than the most recent data set; however, in the case of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, the data are still below the predictions from an $R$-matrix analysis. It was pointed out recently that a slight disagreement exists between the total neutron cross section of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ and the sum of the partial n-${}_{}{}^3{}_{}{}^{}\mathrm{He}$ cross sections. This discrepancy is removed by our new data.

NUCLEAR REACTIONS Measured $\sigma \left(E_{\mathrm{n}}\right)$ for ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, 1.5-40 MeV, high resolution TOF techniques, high pressure gas samples, four-nucleon system, ${}_{}{}^5{}_{}{}^{}\mathrm{He}$ level parameters.

We present a new formalism which systematically accounts for nucleon compositeness in nuclear scattering amplitudes, consistent with quantum chromodynamics and covariance. Reduced gauge-invariant nuclear amplitudes are defined which have elementary quantum chromodynamic scaling properties. The procedure is applied to the photodisintegration and electrodisintegration of the deuteron as a test of nuclear chromodynamics and as a method to isolate contributions of dibaryon resonances.

NUCLEAR REACTIONS Treatment of nucleon compositeness; general formalism developed. Applied to $\mathrm{d}(\gamma , \mathrm{p})\mathrm{n}$, d(e,p)n, $E\gtrsim 1$ GeV; calculated $\sigma \left(\theta \right)$, background to dibaryon resonances. Compared $\sigma \left(\theta \right)$ with available data.

Accurate differential cross sections have been measured at 90° for the reaction ${}_{}{}^3{}_{}{}^{}\mathrm{H}(\mathrm{p}, {\gamma }_0){}_{}{}^4{}_{}{}^{}\mathrm{He}$ at $E_{\mathrm{p}}=8.34\mathrm{} \mathrm{and} 13.6$ MeV. Previously published results for both ${}_{}{}^3{}_{}{}^{}\mathrm{H}(\mathrm{p}, {\gamma }_0){}_{}{}^4{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^4{}_{}{}^{}\mathrm{He}(\gamma , {\mathrm{p}}_0){}_{}{}^3{}_{}{}^{}\mathrm{H}$ are reviewed and compared with the present data. The theoretical implications of the results are briefly discussed.

NUCLEAR REACTIONS ${}_{}{}^3{}_{}{}^{}\mathrm{H}(\mathrm{p}, {\gamma }_0){}_{}{}^4{}_{}{}^{}\mathrm{He}$, $E_{\mathrm{p}}=8.34\mathrm{} \mathrm{and} 13.60$ MeV, measured $\sigma \left(\theta \right)$ at 90°.