Measurements of the intensities of $K$ x rays in coincidence with fission were carried out in an experiment in which the energies of complementary fission fragment pairs and $K$ x rays were recorded event by event, using a multiparameter analyzer. Subsequent analysis of the data resulted in the determination of the x-ray intensities associated with intervals of fragment mass for each contributing element. Most probable charge and mass values for the emission of $K$ x rays were determined, and it was found that these most probable masses could be used to adequately define the $Z_p$ curve - without appreciable biasing due to details of nuclear structure. An examination of the effect of total kinetic energy on the x-ray distribution revealed a distinct enhancement of even-$Z$ $K$ x-ray contributions to the yields as the total kinetic energy increases. Apparent shifts in the values of most probable masses for the emission of $K$ x rays were also observed as a function of total kinetic energy.

The differences between various microscopic theories of isobaric analog resonances are exhibited. It is shown that the physical assumptions underlying the recent theory of Zaidi and Dyer are identical to those used in the formulation of Mekjian and MacDonald.

Proton elastic scattering data at 30.3 MeV are analyzed using the optical model recently developed by Greenlees, Pyle, and Tang. The present analysis differs from that given in the original paper in using a model-exact treatment of the spin-orbit and isospin terms of the potential. The quality of the fits obtained is insensitive to the detailed manner in which the potential is constructed and, in particular, to the choice of nucleon-nucleon force parameters. These parameters are therefore taken from an analysis of low-energy nucleon-nucleon scattering data, thus enabling the present analysis to give nuclear-neutron rms radii. The $n-p$ rms-radius difference is about zero for medium-weight elements and 0.1-0.2 F for heavy elements. Evidence is presented supporting the conclusion that the volume integral and the rms radius of the real central potential are the well-defined quantities which can be deduced from analyses of elastic proton scattering data.

The four-particle-four-hole state in ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and the corresponding states in the even-even, $N=Z$ nuclei of the $2s-1d$ shell have been investigated in the framework of the Hartree-Fock approximation. Detailed calculations were performed in each case to determine the most stable Hartree-Fock solution. By assuming a simple model, the excitation energies of the band heads were calculated showing that ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ is the last nucleus where a state analogous to the four-particle-four-hole state in ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ might be observed. Energy levels have been calculated in ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$, and ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ using a basis of good angular-momentum states. A comparison between the predicted and the observed energy spectrum has been shown. In ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, calculations have been performed both with phenomenological and realistic interactions and the results have been compared. The accuracy of the projected angular-momentum states from the twelve-particle-four-hole solution in ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ has been estimated and shows that the projected states in this case are close to the eigenstates. We have demonstrated that one of two $0^{+}$ states observed around 7 MeV in ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ is an eight-particle-four-hole state.

The nuclear polarization effect in muonic atoms is calculated for ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$. The nuclear intermediate states of ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ are collective particle-hole states calculated from realistic nucleon-nucleon forces. The total effect is an increase of binding of 6.0±0.6 keV for the $1s$ level, 1.9±0.2 keV for the $2p$ level, and 1.2±0.2 keV for the $2s$ level. We are able to set the uncertainties of the calculation at the relatively small values given above for the following reasons: The muonic intermediate states are treated exactly with the reference-spectrum method; the energies of nuclear intermediate states of $l>\mathrm{}2\mathrm{}$ turn out to be small compared with muonic intermediate state energies; the nuclear dipole states have been well studied experimentally and theoretically; and the nuclear monopole polarization calculated from the particle-hole states has been checked with a Thomas-Fermi theory which gives the observed surface thickness and the surface energy. Similar calculations for ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ give the correction to the $1s$ level as 0.2 keV. Henley and Cooper's closure approximation, which leads to a large correction of 58 keV to the ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ $1s$ level, is repeated with two of the following improvements: The intermediate muonic states in the continuum are treated properly, and the two-nucleon cross terms in the ground-state nucleus are included. The correction then comes down to 6 keV.

The analysis of muonic x-ray spectra in deformed nuclei was carried out in the past by diagonalizing the electric quadrupole interaction between the spin doublets ($2p_{\frac{3}{2}}, 2p_{\frac{1}{2}}$), ($3d_{\frac{5}{2}}, 3d_{\frac{3}{2}}$) and the lowest rotational band of the nucleus. With the present experimental accuracy, this procedure is no longer adequate. To take into account the muonic and nuclear states not included in the diagonalization, we renormalize the electric quadrupole interaction by virtual excitations into those states. We find that the renormalization correction amounts to a few percent of the quadrupole matrix elements. This explains the systematic tendency for the intrinsic quadrupole moments obtained from the traditional analysis to be a few percent larger than the values deduced from Coulomb excitation experiments. We also find that the inclusion of the renormalization corrections has a very significant effect on the parameters of the charge distribution and the intensity ratios of the hyperfine multiplets.

Precise measurements, using a stable high-resolution Ge(Li) spectrometer, have been made of the $K(2p-1s)\mathrm{}$ and $L(3d-2p)\mathrm{}$ muonic x-ray spectra for nine deformed even-even nuclei: ${}_{}{}^{150}{}_{}{}^{}\mathrm{Nd}$, ${}_{}{}^{152}{}_{}{}^{}\mathrm{Sm}$, ${}_{}{}^{162}{}_{}{}^{}\mathrm{Dy}$, ${}_{}{}^{164}{}_{}{}^{}\mathrm{Dy}$, ${}_{}{}^{168}{}_{}{}^{}\mathrm{Er}$, ${}_{}{}^{170}{}_{}{}^{}\mathrm{Er}$, ${}_{}{}^{182}{}_{}{}^{}\mathrm{W}$, ${}_{}{}^{184}{}_{}{}^{}\mathrm{W}$, and ${}_{}{}^{186}{}_{}{}^{}\mathrm{W}$. From these measurements, parameters describing the nuclear charge distribution have been determined. Nuclear-polarization corrections have been included in the analysis. The accuracy of the determination of the parameters of the nuclear charge distribution is limited by theoretical rather than experimental uncertainties. Isotope shifts have been determined and compared with optical and electronic x-ray results.

Isotope shifts in the muonic spectra of ${}_{20}{}^{40}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{44}{}_{}{}^{}\mathrm{Ca}$; ${}_{24}{}^{50}{}_{}{}^{}\mathrm{Cr}$, ${}_{}{}^{52}{}_{}{}^{}\mathrm{Cr}$, ${}_{}{}^{53}{}_{}{}^{}\mathrm{Cr}$, ${}_{}{}^{54}{}_{}{}^{}\mathrm{Cr}$; ${}_{29}{}^{63}{}_{}{}^{}\mathrm{Cu}$, ${}_{}{}^{65}{}_{}{}^{}\mathrm{Cu}$; ${}_{42}{}^{92}{}_{}{}^{}\mathrm{Mo}$, ${}_{}{}^{95}{}_{}{}^{}\mathrm{Mo}$, ${}_{}{}^{96}{}_{}{}^{}\mathrm{Mo}$, ${}_{}{}^{97}{}_{}{}^{}\mathrm{Mo}$; ${}_{50}{}^{116}{}_{}{}^{}\mathrm{Sn}$, ${}_{}{}^{117}{}_{}{}^{}\mathrm{Sn}$, ${}_{}{}^{118}{}_{}{}^{}\mathrm{Sn}$, ${}_{}{}^{119}{}_{}{}^{}\mathrm{Sn}$, ${}_{}{}^{120}{}_{}{}^{}\mathrm{Sn}$, ${}_{}{}^{122}{}_{}{}^{}\mathrm{Sn}$, ${}_{}{}^{124}{}_{}{}^{}\mathrm{Sn}$; ${}_{60}{}^{142}{}_{}{}^{}\mathrm{Nd}$, ${}_{}{}^{143}{}_{}{}^{}\mathrm{Nd}$, ${}_{}{}^{144}{}_{}{}^{}\mathrm{Nd}$, ${}_{}{}^{145}{}_{}{}^{}\mathrm{Nd}$, ${}_{}{}^{146}{}_{}{}^{}\mathrm{Nd}$, ${}_{}{}^{148}{}_{}{}^{}\mathrm{Nd}$, and ${}_{}{}^{150}{}_{}{}^{}\mathrm{Nd}$ have been measured using a stable high-resolution Ge(Li) spectrometer system. The results are compared with values calculated for assumed nuclear charge distributions. In the case of the Nd isotopes, the half-density radius and the skin thickness have been determined from the measured $K$ and $L$ x-ray energies. An interesting shell-closing effect has been observed among the Cr isotopes. The muonic isotope shifts have been used to extract specific-mass shifts from optical measurements. We find that, even in Nd, these specific-mass shifts are very large, and not at all negligible in the analysis of optical results. The isotope shifts in Sn follow favorably the theoretically predicted general trend. The great reduction of the isotope shift between ${}_{}{}^{122-124}{}_{}{}^{}\mathrm{Sn}$ as reported in an optical investigation was not found in the muonic case. Lastly, a comparison has been made between the muonic results and recent electronic x-ray measurements. These were found to be in reasonable agreement.

A method for measuring neutron-charged-particle coincidences from the 14.4-MeV neutron-induced reaction has been developed. The $n+d\to p+n+n$ reaction has been studied by the coincidence detection of the outgoing proton and neutron. The cross section has been measured as a function of five independent kinematic variables. A contribution of neutron-proton quasifree scattering has been observed. The cross section for ${\ominus }_n={\ominus }_p=30\mathrm{}°$ is found to be $\sigma =37.5\mathrm{}\pm 5.8$ mb/${\mathrm{sr}}^2$. This result is in fair agreement with the data for proton-proton quasifree scattering from the $p+d\to p+p+n$ reaction. The possibility of obtaining a proper $a_{\mathrm{nn}}$ value is discussed.

Proton recoil spectra from $n-p$ elastic scattering were measured with a counter telescope for an incident neutron energy of 24.0 MeV at mean lab proton recoil angles of 8°, 17°, 31°, and 45°, corresponding to c.m. neutron scattering angles of 164°, 146°, 118°, and 89°. The ratio $\frac{\sigma \left(164\mathrm{}°\right)}{\sigma \left(89\mathrm{}°\right)}$ was 1.134±0.016, where the error quoted is based on counting statistics. In order to obtain a differential cross section, the c.m. relative angular distribution was normalized to a total cross section of 397.2 mb using an $A(1+B{cos}^2\theta )$ fit. This gave $A=30.1\mathrm{}\pm 0.3$ mb/sr and $B=0.146\mathrm{}\pm 0.017$.

The activation cross sections for 18 ($n, p$), ($n, \alpha$), and ($n, 2n$) reactions have been measured with 14.8-MeV neutrons. The radioactivity measurements were carried out with a Ge(Li) detector. The cross sections measured, in millibarns, are ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}(n, p){}_{}{}^{27}{}_{}{}^{}\mathrm{Mg}$, 73±5; ${}_{}{}^{85}{}_{}{}^{}\mathrm{Rb}(n, 2n){}_{}{}^{84m}{}_{}{}^{}\mathrm{Rb}$, 714±50; ${}_{}{}^{85}{}_{}{}^{}\mathrm{Rb}(n, 2n){}_{}{}^{84g}{}_{}{}^{}\mathrm{Rb}$, 621±75; ${}_{}{}^{85}{}_{}{}^{}\mathrm{Rb}(n, p){}_{}{}^{85m}{}_{}{}^{}\mathrm{Kr}$, 6±1; ${}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}(n, 2n){}_{}{}^{86m}{}_{}{}^{}\mathrm{Rb}$, 584±40; ${}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}(n, 2n){}_{}{}^{86g}{}_{}{}^{}\mathrm{Rb}$, 833±60; ${}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}(n, p){}_{}{}^{87}{}_{}{}^{}\mathrm{Kr}$, 7±1; ${}_{}{}^{84}{}_{}{}^{}\mathrm{Sr}(n, 2n){}_{}{}^{83}{}_{}{}^{}\mathrm{Sr}$, 395±75; ${}_{}{}^{86}{}_{}{}^{}\mathrm{Sr}(n, 2n){}_{}{}^{85m}{}_{}{}^{}\mathrm{Sr}$, 360±30; ${}_{}{}^{86}{}_{}{}^{}\mathrm{Sr}(n, p){}_{}{}^{86m}{}_{}{}^{}\mathrm{Rb}$, 9±1; ${}_{}{}^{88}{}_{}{}^{}\mathrm{Sr}(n, 2n){}_{}{}^{87m}{}_{}{}^{}\mathrm{Sr}$, 344±30; ${}_{}{}^{88}{}_{}{}^{}\mathrm{Sr}(n, p){}_{}{}^{88}{}_{}{}^{}\mathrm{Rb}$, 20±2; ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}(n, 2n){}_{}{}^{89m}{}_{}{}^{}\mathrm{Zr}$, 143±15; ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}(n, 2n){}_{}{}^{89g}{}_{}{}^{}\mathrm{Zr}$, 342±25; ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}(n, p){}_{}{}^{90m}{}_{}{}^{}\mathrm{Y}$, 13±1; ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}(n, \alpha ){}_{}{}^{87m}{}_{}{}^{}\mathrm{Sr}$, 4.6±0.5; ${}_{}{}^{93}{}_{}{}^{}\mathrm{Nb}(n, 2n){}_{}{}^{92m}{}_{}{}^{}\mathrm{Nb}$, 455±25; and ${}_{}{}^{93}{}_{}{}^{}\mathrm{Nb}(n, \alpha ){}_{}{}^{90m}{}_{}{}^{}\mathrm{Y}$, 5.8±0.5. The measured cross sectons are compared with those calculated by evaporation theory. The ($n, 2n$) measured cross sections agree well with the calculated values but the agreement between calculated and measured values for ($n, p$) reactions is poor.

($p, \mathrm{pn}$) reactions induced by 17-MeV protons on 12 different nuclei are studied by coincidence detection and energy measurements of the emitted neutron and proton. Probabilities of exciting various final states and of ($p, p^{\prime }\gamma$) reactions (i.e., no neutron emission) are measured as a function of the energy of the emitted particles, and attempts are made to explain the results with a model assuming that these are ($p, p^{\prime }$) reactions followed by neutron boil-off. There are many disagreements with the predictions of this model, and many inconsistencies between results from the different nuclei under this interpretation. It is shown that including contributions from ($p, n$) reactions followed by proton boil-off does little to improve the situation. The results might be explained if both particles are emitted in a direct reaction, although there is difficulty with the simplest such reaction, a single collision knockout, in that there is poor correlation between states excited in these reactions and in pickup reactions such as ($p, d$).

A new theory is presented for calculating the structure of finite nuclei from the nucleon-nucleon interaction. The essential features of the reaction matrix in finite nuclei are obtained from nuclear-matter theory through the local-density approximation. The resulting density- and energy-dependent effective interaction is justified in detail, and it is shown that the tensor force plays an important role in saturation. The effective interaction is cast into two different forms, one convenient for use in calculating matrix elements and the other specialized for a Hartree-Fock calculation in position space. The density-dependent Hartree-Fock equations are derived by variation of the ground-state expectation value of the energy, and in addition to the usual Hartree-Fock terms, one obtains rearrangement terms arising from the variation of the density appearing in the density-dependent interaction. The appropriate angular-momentum reduction for closed $j$-shell nuclei is performed. The need for modifying the effective interaction to account for higher-order corrections is discussed, and the constraints imposed on this modification by the properties of nuclear matter are examined. The results of this theory for ${\mathrm{O}}^{16}$, ${\mathrm{Ca}}^{40}$, ${\mathrm{Ca}}^{48}$, ${\mathrm{Zr}}^{90}$, and ${\mathrm{Pr}}^{208}$ are shown to yield very satisfactory agreement with experimental binding energies, single-particle energies, and electron scattering cross sections. The rearrangement terms in the density-dependent theory are demonstrated to have two essential effects on nuclear structure: a significant reduction in the central density of the nucleus, and a modification of the usual Hartree-Fock relation between single-particle energies and the binding energy. Equivalent local single-particle potentials are calculated and are shown to have significant state dependence.

The dynamics of nuclear distortion is studied for two spherical nuclei under the influence of their mutual Coulomb interactions. Both the quadrupole and the octupole degrees of freedom are considered. Realistic stiffness and effective-mass parameters are employed. It is found that the energy needed to bring the two nuclei into contact increases as a result of the distortions. However, in the most favorable case, the increase is only a few percent. This is much smaller than previous estimates using either the liquid-drop model or the adiabatic model.

Total elastic and inelastic scattering cross sections for fast neutrons are measured on ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ between 17 and 20.5 MeV in order to check the validity of standard optical-model parameters and to investigate the nature of resonant states in ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$. The region around 18 MeV is found to be free of isolated resonances, and good fits are obtained with standard parameters. A resonant state is apparent at an energy corresponding to 23 MeV in ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$, and indications of the spin and the structure of this state are obtained.

The reactions ${}_{}{}^6{}_{}{}^{}\mathrm{Li}(d, n){}_{}{}^7{}_{}{}^{}\mathrm{Be}$ (g.s.+0.431 MeV) and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(d, n){}_{}{}^{13}{}_{}{}^{}\mathrm{N}$ (g.s.) have been studied by recoil spectrometry at bombarding energies of 12, 15, and 17 MeV. The recoils were detected by a solid-state detector in coincidence with the neutrons detected by a plastic scintillator. Experimental absolute differential cross sections at the three bombarding energies are given for both reactions. Also given are the excitation functions over the energy region 12-17 MeV at about 60° recoil c.m. angle for both reactions, and for the reaction ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}(d, n){}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ (g.s.). The ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ reactions were analyzed in the distorted-wave Born approximation (DWBA), taking into account the effects of spin-orbit force, finite range, and nonlocality corrections. The agreement between the experimental and theoretical angular distributions is good for the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ reaction, and the agreement for the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ reaction is fair at 17 MeV. The excitation functions for the two reactions are relatively smooth. The experimental absolute differential cross sections for the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ reaction agree fairly well with the theoretical cross sections obtained by incorporating the spectroscopic factors from recent shell-model calculations. For the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ reaction, the spectroscopic factor extracted from the experimental cross section agrees well with the theoretical value at 17 MeV. The experimental cross sections at 12 and 15 MeV are higher than the theoretical estimates; some possible explanations are discussed. The ratios of the experimental to the theoretical cross sections as a function of bombarding energy follow the same trend as for the reaction ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(d, p){}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ (g.s.). An evaluation of the technique of recoil spectrometry for studying ($d, n$) and other nuclear reactions is given.

Three-body breakup spectra from a kinematically complete measurement of the $\mathrm{D}(p, 2p)n$ reaction have been analyzed to yield the cross section for the production of $d^{*}$, a quasiparticle consisting of a neutron and proton in a ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ configuration. An excitation function of the $\mathrm{D}(p, d^{*})p$ reaction is obtained for the proton bombarding energy range 9-13 MeV. In agreement with measurements and predictions of the ($p, d^{*}$) cross section on several nuclei, the $\mathrm{D}(p, d^{*})p$ cross section is about an order of magnitude less than the elastic $\mathrm{D}(p, d)p$ cross section. The $\mathrm{D}(p, d^{*})p$ excitation function shows a peak at the bombarding energy $E_p=10.25\mathrm{}$ MeV which coincides with a ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ excitation energy of 12.4 MeV. This peak might be interpreted as either a state in ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ or a threshold effect.

Since there exists considerable uncertainty in the short-range part of the real nucleon-nucleon interaction, any attempt at a rigorous derivation of the effective interaction is illusory. Rather, we have argued that requiring the effective interaction to conform to the real interaction in the long-range part is the furthest that one can meaningfully go in relating the two, and that the short-range part of the effective interaction should be chosen phenomenologically. Our earlier work is here extended to impose phenomenological constraints on the vector (spin-orbit) and tensor components of the effective interaction. The short-range phenomenological part of our effective interaction is to be chosen in such a way that the entire interaction satisfies the following conditions: (a) Nuclear matter is correctly saturated in first-order perturbation theory, with small second-order corrections. (b) The odd-state scattering parameters are fitted up to 300 MeV. (c) The low-energy singlet scattering parameters are fitted. (d) The low-energy triplet scattering parameters and the quadrupole moment of the deuteron are fitted. We find that it is never possible to satisfy more than three conditions simultaneously, and so arrive at four effective interactions, each of which is characterized by the violation of one of the above conditions. Two of these interactions are found to work well for both Hartree-Fock and spectroscopic calculations, and, hence, may be regarded as having some measure of universality.

The energy spectra of $\alpha$ particles were measured at 5° lab for the reaction ${}_{}{}^3{}_{}{}^{}\mathrm{He}({}_{}{}^3{}_{}{}^{}\mathrm{He}, \alpha )pp$ using a 20-MeV ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ beam; at 5° and 8° lab for the reaction ${}_{}{}^3{}_{}{}^{}\mathrm{He}(t, \alpha )np$; and at 5°, 8°, and 10° lab for the reaction ${}_{}{}^3{}_{}{}^{}\mathrm{H}(t, \alpha )nn$ using a 22-MeV triton beam. The 5° lab spectra corresponding to low relative energy in the unobserved two-nucleon system were well fitted with Watson-Migdal final-state-interaction theory for the following scattering lengths: $a_{\mathrm{pp}}=-7.52\mathrm{}\pm 0.22$ F, $a_{\mathrm{np}}=-21.5\mathrm{}\pm 2.3$ F, and $a_{\mathrm{nn}}=-16.96\mathrm{}\pm 0.51$ F. Analyzing the change-symmetric reactions with the comparison method and using the accepted value for $a_{\mathrm{pp}}$, we find $a_{\mathrm{nn}}=-18.11\mathrm{}\pm 0.75$ F. When compared with Coulomb-corrected values of $a_{\mathrm{pp}}$, these values of $a_{\mathrm{nn}}$ imply that nucleon-nucleon forces are charge-symmetric to better than 1%. In obtaining the scattering lengths, the effective range was fixed at $r_0=2.84\mathrm{}$ F. Allowing both the effective range and scattering length to vary in the fitting procedure for the $n-n$ final-state data, we find $a_{\mathrm{nn}}=-17.4\mathrm{}\pm 1.8$ F and ${\left(r_0\right)}_{\mathrm{nn}}=2.4\mathrm{}\pm 1.5$ F. If the $n-n$ scattering length is fixed at the value - 17.0 F, our data determine the effective range to be ${\left(r_0\right)}_{\mathrm{nn}}=2.75\mathrm{}\pm 0.35$ F.

We have studied the contribution of the knockout-exchange mechanism to inelastic proton scattering the distorted-wave Born approximation (DWBA) as a function of two-body force range, orbital-angular-momentum transfer, incident-particle energy, and bound-particle energy and configuration. Several important features are revealed: (1) The exchange mechanism is found to be important for reasonable ranges (≈ 1 F) and for energies as high as 150 MeV; (2) the exchange-to-direct ratio is quite sensitive to the orbital-angular-momentum transfer $L$, and the exchange amplitude can exceed the direct for large $L$; (3) non-normal transfers [${\mathrm{}(-1\mathrm{})\mathrm{}}^L\ne {\mathrm{}(-1\mathrm{})\mathrm{}}^{\Delta \pi }$] are usually negligible but may become significant for high $L$, especially if no spin flip is involved; (4) both the magnitude and phase of the exchange amplitude relative to the direct are sensitive to the initial and final single-particle configurations, particularly to the radial quantum numbers; (5) in collective excitations constructive interference occurs among exchange amplitudes to a sufficient extent that the inclusion of exchange can double the cross section for $2^{+}$ states. Expressions for direct and exchange amplitudes are obtained in the zero-range limit of the PWBA which qualitatively explain the behavior observed in the numerical results. A new method is presented for estimating collective enhancement due to core polarization by using empirical $B\left(E2\mathrm{}\right)\mathrm{}$ values. Calculation of the absolute cross section for the $2^{+}$ excitation in ${}_{}{}^{118}{}_{}{}^{}\mathrm{Sn}(p, p^{\prime })$, including exchange and core polarization, yields a two-body effective interaction strength which agrees both with strengths derived from charge-exchange reactions and with those obtained from a semirealistic two-nucleon interaction.