We discuss some isospin effects in nuclear strength distributions. We deal with the distribution, in energy, of the states of fixed isospin by considering essentially the centroid energies. In particular, we discuss the way in which the centroid energies for an excitation carrying a unit of isospin (isovector excitation) on a target $T$, split among the various available isospin channels. In these processes we may excite various $T+1\mathrm{}$, $T$, and $T-1\mathrm{}$ states. The energy separation between these three components is expressed both in terms of properties of the target state and of the interaction between the excitation and the target, and also in terms of measurable quantities; a method is given of analyzing data by means of target and interaction parameters. An important result has emerged from our analysis: The isospin geometry involved in these processes suggests parametrizing the theory with isoscalar, isovector, and isotensor effective potentials. Dipole (particle-hole) excitations and isovector excitations produced by adding or taking away two nucleons are carefully analyzed along these lines. A phenomenological lower limit for the isotensor potential significant in size and systematic, is found in the case of the dipole excitation. It is shown that an isotensor energy emerges naturally from a schematic model approach to the problem. Finally, we prove that the isotensor effective potential is basically a two-body potential and arises from second order effects when the interaction between the nucleons (nucleon holes) carrying the unit of isospin and the target is treated perturbatively.

NUCLEAR REACTIONS Isospin effects in excitations carrying a unit of isospin on $T>\mathrm{}\frac{1}{2}$ nuclei. Isotensor two-body potential introduced, connected with measurable quantities. Microscopic interpretation given.

The width $〈{\Gamma }_d〉$ of a doorway state, the escape width $〈{\Gamma }_d\uparrow 〉$, the damping width $〈{\Gamma }_d\downarrow 〉$, and the interaction $〈V_d〉$ which causes transitions from the doorway state to the more complicated states are discussed as a function of the ratio ($\frac{n_d}{n}$) between the numbers of the correlating and open channels. The results show that the widths $〈{\Gamma }_d〉$, $〈{\Gamma }_d\uparrow 〉$, $〈{\Gamma }_d\downarrow 〉$, and the interaction $〈V_d〉$ depend strongly on the square of this ratio.

NUCLEAR REACTIONS Discussed $〈{\Gamma }_d〉$, $〈{\Gamma }_d\uparrow 〉$, $〈{\Gamma }_d\downarrow 〉$, $〈V_d〉$.

The equivalence of the Hartree-Fock method and the folding model for the optical potential has been demonstrated using momentum-dependent modified $\delta$ interactions. The role of the rearrangement potential in the folding model is discussed. The importance of including hitherto neglected terms depending on the fourth power of the momentum has been discussed. The energy dependence of the optical potential obtained in this model agrees well with the phenomenological result.

NUCLEAR REACTIONS Calculated the single particle optical potential using momentum-dependent density-dependent $\delta$ interactions.

Cross sections for the production of mass 6 to 11 isobars from proton spallation of carbon targets have been measured at bombarding energies of 45, 55, 60, 65, 75, and 100 MeV. Isotopic cross sections for Li and Be have also been measured at 100 MeV. The excitation functions for these reactions have been used to test theories of Li, Be, and B nucleosynthesis. The measured abundance ratios ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$/${}_{}{}^{10}{}_{}{}^{}\mathrm{B}$ and B/Be can be reproduced using the experimental cross sections and astrophysical models which propose LiBeB synthesis in nuclear reactions well above the threshold energy. In order to obtain the natural ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$/${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, Li/Be, and Li/B abundance ratios, however, it is concluded that a substantial amount of ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ must be synthesized via some lower energy mechanism.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(p,\mathrm{HI})$; HI Mass numbers $A=6, 7, 9, 10, \mathrm{and} 11$; $E=45, 55, 60, 65, 75, 100$ MeV; HI Li and Be at 100 MeV; measured $\sigma$, $\sigma \left(\theta \right)$, and $\sigma \mathrm{}\left(E\right)\mathrm{}$; astrophysical implications of the data are discussed.

We examine the feasibility of using the ${}_{}{}^2{}_{}{}^{}\mathrm{H}\mathrm{}(p,pp)n$ reaction as a means of extracting information about the short-range behavior of the nuclear force not obtainable from $N$-$N$ scattering experiments. To do this we use several separable potentials and examine the predicted cross section in various regions of phase space and for beam energies between 14 and 65 MeV. The questions that we address are likely to be insensitive to Coulomb effects. Both the form factor and the energy dependence of the potentials have been modified from the usual Yamaguchi form. The form of the energy dependence is chosen to obtain phase-shift equivalence for two different form factors while guaranteeing a unitary two-body scattering amplitude. The sensitivity of breakup results to the on-shell and off-shell aspects of the nuclear force is examined and discussed. Significant on-shell sensitivity occurs for breakup amplitudes in all states and for cross sections over all regions of phase space. Off-shell sensitivity appears only in the $S=\frac{1}{2}$, $L=0\mathrm{}$ breakup amplitudes, with all $S=\frac{3}{2}$ and all $L>\mathrm{}0\mathrm{}$ amplitudes exhibiting negligible off-shell dependence. This result leads to only a very small (≤5%) off-shell sensitivity for quasifree scattering. However, cross sections far from quasifree scattering, and in particular cross sections in the final-state interaction region of phase space, exhibit as much as a 50% variation for phase-shift-equivalent potentials. This sensitivity is small at low beam energy and increases with increasing energy. The energy dependence at negative energies of one potential is also altered to adjust the triton binding energy. This enables us to compare phase-shift-equivalent potentials differing off shell but predicting the same triton binding energy. The energy dependence of this potential is somewhat unconventional. Fixing of the triton binding energy reduces the off-shell sensitivity appreciably only for $E\lesssim 20$ MeV.

NUCLEAR REACTIONS ${}_{}{}^2{}_{}{}^{}\mathrm{H}\mathrm{}(p,pp)n$, $E=14.4, 23, 26, 30.3, 39.5, 44.9, 65$ MeV; Faddeev calculation $\sigma ({\theta }_1, {\theta }_2,E)$. Four potentials.

Using pulsed-beam neutron time-of-flight spectrometry relative differential cross sections for ${}_{}{}^7{}_{}{}^{}\mathrm{Li}(p,n_0){}_{}{}^7{}_{}{}^{}\mathrm{Be}$(g.s.) and ${}_{}{}^7{}_{}{}^{}\mathrm{Li}(p,n_1){}_{}{}^7{}_{}{}^{}\mathrm{Be}_{}^{*}{}_{}{}^{}$ (0.431 MeV) have been measured over the laboratory angular range 3.5° to 159° and from an incident bombarding energy of 4.2 to 26 MeV. These cross sections have been integrated over angle and at 5 MeV the resulting integral was normalized to the absolute measurement of Macklin and Gibbons in order to obtain absolute differential and total cross sections for each neutron group. At energies above 6 MeV the 3.5° cross section for each group decreases monotonically, reaching a minimum at about 12 MeV. Both cross sections then increase, the ground-state cross section approaching a center-of-mass value of 15 mb/sr at 26 MeV. The forward-angle ratio of $n_1$ to $n_0$ neutrons remains around 30% from 8 to 26 MeV, obtaining a maximum of about 35% at 26 MeV. The integrated cross sections, on the other hand, both decrease from 6 MeV to the maximum energy. Neutrons from states in ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$ at 4.55, 6.51, 7.19, and possibly 10.79 MeV as well as those from three-body breakup were also observed in this experiment.

NUCLEAR REACTIONS ${}_{}{}^7{}_{}{}^{}\mathrm{Li}\mathrm{}(p,n)E=4.2-26\mathrm{}$ MeV; measured $\sigma (E,\theta )$ to ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$ ground state and first excited state; $\theta =3.5\mathrm{}°-159\mathrm{}°$.

A reduction procedure for the construction of matrix equations applicable to direct nuclear reactions is described, where the direct channel Green's functions are used to simplify the many-particle problem. The Faddeev-type matrix equations are reduced to simpler forms so that the partial connectivity of the iteration kernels is maintained for those direct channels which are explicitly coupled. Auxiliary channels are then introduced to improve the connectivity property, while direct channel distortion potentials and simple channel projection operators are incorporated to facilitate the solution of the coupled equations. Using the reduction procedure, the multiple scattering equations of Watson are extended to include explicitly the rearrangement channels which are strongly coupled.

NUCLEAR REACTIONS Reduction of the Faddeev equations; coupled equations for direct interactions; auxiliary channels.

The energy spectra and angular distributions of photoprotons from the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(\gamma ,p){}_{}{}^{11}{}_{}{}^{}\mathrm{B}$ reaction have been measured at seven angles simultaneously, using 30 MeV bremsstrahlung. The giant dipole resonance peaks at 22.5 MeV, and reaches an absolute cross section value of 13.1 ± 0.8 mb. The anisotropy parameter $a_2$ from the Legendre polynomial expansion of the angular distributions has an average value of about -0.55 but shows some structure especially around 25 MeV. On the other hand, the asymmetry coefficient $a_1$ is always positive and rises slowly with energy. Discussion of all coefficients leads to the conclusion that, although the photonuclear absorption mechanism in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ leading to photoproton emission is dominated by the $E1$ component, a nonnegligible $E2\mathrm{}$ contribution (about 2%) might be present. A recent coupled-channel calculation by Birkholz satisfactorily describes our results.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(\gamma ,p)$, $E=16.0-30.0\mathrm{}$MeV, $\theta =37-143\mathrm{}°$; measured $\sigma (E,\theta )$; deduced $\sigma \mathrm{}\left(E\right)\mathrm{}$. Natural target.

The importance of including multistep inelastic processes in $\alpha$-particle-transfer reactions in light nuclei is discussed, and the necessity of using an exact-finite-range analysis of such reactions is emphasized. A formalism for the treatment of such reactions in an exact-finite-range Born approximation which includes inelastic effects to all orders is presented. An example from the ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$(${}_{}{}^3{}_{}{}^{}\mathrm{He}$, ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$)${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ reaction in which it is necessary to use this analysis in order to understand the experimental data is discussed.

NUCLEAR REACTIONS $\alpha$-transfer reactions, importance of multistep inelastic processes. Formalism for exact-finite-range coupled-channels analysis.

The (${}_{}{}^3{}_{}{}^{}\mathrm{He}$, ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$) reaction has been studied at a laboratory energy of 25.5 MeV for ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ targets and at energies of 25.5, 27.0, and 29.0 MeV for a ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ target. Angular distributions have been measured from ${\theta }_{\mathrm{lab}}=15\mathrm{}° \mathrm{to} 160°$ for transitions to low-lying states in the residual nuclei. The resulting angular distributions have been analyzed (1) using an exact-finite-range distorted-wave Born-approximation formalism including multistep processes and (2) using a Hauser-Feshbach compound-nuclear model. In general, the shapes of the forward angle (${}_{}{}^3{}_{}{}^{}\mathrm{He}$, ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$) data are well described by the finite-range distorted-wave Born-approximation and finite-range coupled-channels Born-approximation calculations. The magnitude of the measured transition to the 1.63-MeV ($2^{+}$) state in ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ is approximately 100 times larger than predicted by an ${\mathrm{SU}}_3$ theory for a simple one-step transition, and this transition is shown to be an example in which a finite-range coupled-channels Born-approximation analysis is required. Arguments concerning the direct nature of the reaction process populating these states are discussed, and spectroscopic information is extracted.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$(${}_{}{}^3{}_{}{}^{}\mathrm{He}$, ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$), $E_{\left({}_{}{}^3{}_{}{}^{}\mathrm{He}\right)}=25.5, 27.0, 29.0$ MeV, measured $\sigma (E,\theta )$ Hauser-Feshbach and finite-range CCBA analysis, spectroscopic factors.

The ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^7{}_{}{}^{}\mathrm{Li},t){}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}({}_{}{}^7{}_{}{}^{}\mathrm{Li},t){}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ reactions have been studied at a beam energy of 38 MeV. At this energy these reactions exhibit a high selectivity for populating α-particle cluster states. The angular distributions for these states have been analyzed using an exact-finite-range coupled-channels Born-approximation code incorporating final-state cluster wave functions derived from an α-core folded potential. The resulting $\alpha$-particle spectroscopic factors ($S_{\alpha }$) for the $0^{+}$, $2^{+}$, and $4^{+}$ members of the ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ ground state band are in good agreement with cluster model predictions. For the 7.12-MeV ($1^{-}$) state in ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, the spectroscopic factor ($S_{\alpha }\approx 0.20$) is consistent with other analyses but is uncertain by a factor of 2 due to the presence of significant compound-nuclear contributions to this transition. In general, for those states which are not selectively populated at forward angles the measured angular distributions are well described by a Hauser-Feshbach calculation. In particular it is shown that both the magnitude and shape of the angular distributions for the 11.10-MeV ($4^{+}$) state populated in the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^6{}_{}{}^{}\mathrm{Li},d){}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^7{}_{}{}^{}\mathrm{Li},t){}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ reactions can be well accounted for in terms of statistical compound-nuclear contributions. The elastic scattering of ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ ions from several light targets has also been studied and optical-model potentials derived.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}({}_{}{}^7{}_{}{}^{}\mathrm{Li},t)$, $E\left({}_{}{}^7{}_{}{}^{}\mathrm{Li}\right)=38\mathrm{}$ MeV, measured $\sigma (E,\theta )$, Hauser-Feshbach and finite-range CCBA analysis, spectroscopic factors.

A momentum space methodology is presented for calculating second order distorted wave Born approximation matrix elements without the use of the zero-range approximation. This methodology is applied to the sequential transfer term in ($p,t$) reactions. Examples are presented for ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}\mathrm{}(p,t)\mathrm{}{}_{}{}^{206}{}_{}{}^{}\mathrm{Pb}$ which show that: (1) finite-range effects can be large, (2) the shape of the calculated differential cross section can be strongly dependent on the contribution from a sequential transfer mechanism, and (3) the post-prior interchange usually used is probably the best realistic approximation.

NUCLEAR REACTIONS ($p$-$d$,$d$-$t$), finite range, momentum space techniques; ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}(p,t)E=35\mathrm{}$ MeV; calculated $\sigma \left(\theta \right)$; simultaneous plus sequential transfer, both finite range.

Differential cross sections for $\alpha$ particles elastically scattered from ${}_{}{}^{142,144,146,148,150}{}_{}{}^{}\mathrm{Nd}$ have been measured at six angles over the energy region 11-19 MeV. The cross sections were analyzed using the optical model, the incoming-wave boundary condition model, and the coupled-channels model. The radius at which the real nuclear potential is 2% of the Coulomb potential was found to be effectively independent of the ambiguities in the optical potential. In the coupled-channels analysis, the radius at which the spherically averaged real nuclear potential is 2% of the spherically averaged Coulomb potential is almost identical, for a given nucleus, to the corresponding quantity determined using the spherical optical model. The absolute increase in the "2% radius" over the neodymium isotopes is about 2 times larger than the increase in the charge distribution as observed in muonicatom and electron-scattering studies.

NUCLEAR REACTIONS ${}_{}{}^{142,144,146,148,150}{}_{}{}^{}\mathrm{Nd}(\alpha ,\alpha )$; $E=11-19\mathrm{}$ MeV; measured $\sigma (E,\theta )$. Deduced nuclear interaction size. Enriched targets.

The ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}({}_{}{}^3{}_{}{}^{}\mathrm{He},d){}_{}{}^{59}{}_{}{}^{}\mathrm{Cu}$ reaction has been studied at bombarding energies of 35 and 39 MeV. Excitation energies and angular distributions were measured for levels up to 9.2 MeV in excitation. Distorted-wave-Born-approximation calculations were performed using resonance form factors for the proton-unstable levels ($E_x\ge \sim 3.4$ MeV) in order to make $l$ assignments and to extract the spectroscopic factors. Twelve levels in ${}_{}{}^{59}{}_{}{}^{}\mathrm{Cu}$ are identified as possible analogs of states in ${}_{}{}^{59}{}_{}{}^{}\mathrm{Ni}$. A particle-core-coupling model is used to predict the properties of ${}_{}{}^{59}{}_{}{}^{}\mathrm{Cu}$ and fair agreement with the experiment is obtained.

NUCLEAR REACTIONS, NUCLEAR STRUCTURE ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}({}_{}{}^3{}_{}{}^{}\mathrm{He},d) E=35.0, 39.1$ MeV; measured $\sigma \left(\theta \right)$, ${}_{}{}^{59}{}_{}{}^{}\mathrm{Cu}$ levels, deduced $l$, $S$; identified analog states, calculated $J$, $\pi$, $S$, particle-core-coupling model.

The neutron states in ${}_{}{}^{195}{}_{}{}^{}\mathrm{Pt}$ have been studied using the ${}_{}{}^{194}{}_{}{}^{}\mathrm{Pt}(d,p){}_{}{}^{195}{}_{}{}^{}\mathrm{Pt}$ and ${}_{}{}^{196}{}_{}{}^{}\mathrm{Pt}(d,t){}_{}{}^{195}{}_{}{}^{}\mathrm{Pt}$ reactions and 12 and 13.5 MeV deuterons. Transfer $l$ values have been determined from angular distributions, and spectroscopic factors obtained by comparison with distorted wave Born approximation calculations. Many lower energy states are well explained by the Nilsson model assuming an oblate nuclear shape. These include the ${1/2}^{-}$[530], ${3/2}^{-}$[532], ${5/2}^{-}$[532], and decoupled ${1/2}^{+}$[600] bands, and more tentatively the ${3/2}^{-}$[541] and ${9/2}^{+}$[615] bands. Other low-lying states are well described by the Faessler-Greiner model using parameters consistent with the ${}_{}{}^{194}{}_{}{}^{}\mathrm{Pt}$ data. The Coriolis force is important in reproducing the large spectroscopic factors experimentally observed. The success of the Faessler-Greiner and Davydov models in explaining the experimental ${}_{}{}^{195}{}_{}{}^{}\mathrm{Pt}$ spectra is also compared.

NUCLEAR REACTIONS, NUCLEAR STRUCTURE ${}_{}{}^{194}{}_{}{}^{}\mathrm{Pt}\mathrm{}(d,p)\mathrm{}$, $E_d=12\mathrm{}$ MeV. ${}_{}{}^{196}{}_{}{}^{}\mathrm{Pt}\mathrm{}(d,t)\mathrm{}$, $E_d=13.5\mathrm{}$ MeV. Measured $\sigma (E_p,\theta )$, $\sigma (E_t,\theta )$, ${}_{}{}^{195}{}_{}{}^{}\mathrm{Pt}$ levels; deduced $l$, $S$; calculated $J$, $\pi$, $S$, rotation-vibration model. DWBA analysis, enriched targets.

Strong resonant scattering of bremsstrahlung by a level in ${}_{}{}^{144}{}_{}{}^{}\mathrm{Sm}$ at 3.225-MeV excitation energy has been observed. Angular distribution and linear polarization measurements have led to a $1^{-}$ assignment for this level. From a self-absorption study, a value ${\Gamma }_0=220\mathrm{}\pm 30$ meV has been obtained for the partial radiative width of the ground-state transition. For the known $1^{-}$ states in ${}_{}{}^{150}{}_{}{}^{}\mathrm{Sm}$ (1.166 MeV) and ${}_{}{}^{154}{}_{}{}^{}\mathrm{Sm}$ (0.921 MeV), partial widths ${\Gamma }_0\mathrm{}\left(1.166\right)=(5.4\mathrm{}\pm 0.4)$ meV, and ${\Gamma }_0\mathrm{}\left(0.921\right)=(7.4\mathrm{}\pm 1.0)$ meV were measured. Combining the results of bremsstrahlung measurements with those of previous resonance fluorescence experiments utilizing high-speed rotation of radioisotopes, a width ${\Gamma }_0=(3.1\mathrm{}\pm 0.4)$ meV was arrived at for the ground-state transition from the 1.465-MeV $1^{-}$ state in ${}_{}{}^{148}{}_{}{}^{}\mathrm{Sm}$. The excitation energies of the $1^{-}$ states studied in the even Sm isotopes below $N=89\mathrm{}$ are fairly close to the sums [$E\left(2_1^{+}\right)+E\left(3_1^{-}\right)$]. The $B\left(E1\right)\text{'}\mathrm{s}$ initially decrease as one moves away from the deformed region. While this is not unexpected, the reversal of this trend near and at the magic neutron number $N=82\mathrm{}$, as evidenced by the large $B\left(E1\right)$ observed in ${}_{}{}^{144}{}_{}{}^{}\mathrm{Sm}$ and the behavior of the $B\left(E1\right)\text{'}\mathrm{s}$ in ${}_{}{}^{142,144}{}_{}{}^{}\mathrm{N}\mathrm{d},$ is somewhat surprising.

NUCLEAR REACTIONS ${}_{}{}^{144,148,150,154}{}_{}{}^{}\mathrm{Sm}(\gamma ,\gamma )$; bremsstrahlung $E=1.2-3.8\mathrm{}$ MeV; measured $\sigma \left(96\mathrm{}°\right)$ and $\sigma \left(126\mathrm{}°\right)$, LP; deduced $J$, $\pi$, $\Gamma$. Enriched ${}_{}{}^{144}{}_{}{}^{}\mathrm{Sm}$ and ${}_{}{}^{150}{}_{}{}^{}\mathrm{Sm}$ targets.

Excitation functions for $\alpha +{}_{}{}^{40,44}{}_{}{}^{}\mathrm{Ca}$ elastic scattering have been measured with bombarding energies in the range of 20-27 MeV in 50-keV steps at several angles between 150 and 175°. For ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ excitation functions were also taken in 10-keV steps over a limited interval. Statistical fluctuations were observed in all the excitation functions and were found to be generally stronger for ${}_{}{}^{44}{}_{}{}^{}\mathrm{Ca}$ than for ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$. An analysis of the fluctuations yields a relative compound contribution of about 2% for ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ and greater than about 5% for ${}_{}{}^{44}{}_{}{}^{}\mathrm{Ca}$. The backward enhancement in $\alpha +{}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ scattering, observed by many previous workers, is shown to arise primarily from a direct contribution and not from a fluctuating compound one.

NUCLEAR SCATTERING ${}_{}{}^{40,44}{}_{}{}^{}\mathrm{Ca}(\alpha ,\alpha )$, $E=20-26\mathrm{}$ MeV measured $\sigma (\theta ,E)$, $\theta >150\mathrm{}°$, $\Delta E=50\mathrm{}$ keV, $\Delta \theta =5\mathrm{}°$. Fluctuation analysis: deduced compound and direct components.

The angular distributions of cross sections and analyzing powers have been measured for the ${}_{}{}^{54,56,58}{}_{}{}^{}\mathrm{Fe}(\overrightarrow{p},{\gamma }_0)$ reactions throughout the giant dipole resonance regions of ${}_{}{}^{55,57,59}{}_{}{}^{}\mathrm{Co}$. In addition, the 90° yield curve has been measured for the ${}_{}{}^{58}{}_{}{}^{}\mathrm{Fe}(p,{\gamma }_0){}_{}{}^{59}{}_{}{}^{}\mathrm{Co}$ reaction for $E_p$ from 5.0 to 16.0 MeV in 100 keV steps. The data are analyzed to deduce the amplitudes and phases of the $T$ matrix elements involved. The preferred solution indicates that the major change occurring in crossing the giant dipole resonance occurs in the relative phase between the $d_{\frac{5}{2}}$ and $g_{\frac{9}{2}}$ amplitudes. The implications of these results are discussed vis $\stackrel{`}{a}$ vis the isospin splitting of the giant dipole resonance.

NUCLEAR REACTIONS ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}(\overrightarrow{p},{\gamma }_0)$, ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}(\overrightarrow{p},{\gamma }_0)$, ${}_{}{}^{58}{}_{}{}^{}\mathrm{Fe}(\overrightarrow{p},{\gamma }_0)$; measured $\sigma \left(\theta \right)$ and $A\left(\theta \right)$, $E_p=8.0-15.0\mathrm{}$ MeV, $E_p=8.0-14.5\mathrm{}$ MeV, and $E_p=7.6-15.0\mathrm{}$ MeV, respectively. ${}_{}{}^{58}{}_{}{}^{}\mathrm{Fe}(p,{\gamma }_0)$ measured $\sigma \left(90\mathrm{}°\right)$, $E_p=5.0-16.0\mathrm{}$ MeV. Deduced $T$-matrix amplitudes and phases in all three cases. Discussed isospin splitting.

The ${}_{}{}^{89}{}_{}{}^{}\mathrm{Y}(p,t){}_{}{}^{87}{}_{}{}^{}\mathrm{Y}$ and ${}_{}{}^{88}{}_{}{}^{}\mathrm{Sr}\mathrm{}(p,t)\mathrm{}{}_{}{}^{86}{}_{}{}^{}\mathrm{Sr}$ reactions were studied at 42 MeV proton energy, using a quadrupole-dipole-dipole-dipole spectrograph. Comparison of excitation energies, ($p,t$) cross-section strengths, and angular distribution shapes indicates that basic features of the core-coupling model apply to these nuclei. However, mixing of single-particle states with the core-coupled states is evident. The ($p,t$) cross-section strength summed over the ${}_{}{}^{87}{}_{}{}^{}\mathrm{Y}$ multiplet is found with few exceptions to be nearly a constant multiple of the ($p,t$) strength of the associated ${}_{}{}^{86}{}_{}{}^{}\mathrm{Sr}$ state.

NUCLEAR REACTIONS ${}_{}{}^{88}{}_{}{}^{}\mathrm{Sr}$, ${}_{}{}^{89}{}_{}{}^{}\mathrm{Y}\mathrm{}(p,t)\mathrm{}$, $E=42\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$ and level energies; DWBA analysis, deduced $L$, $J^{\pi }$. Resolution 12 keV for ${}_{}{}^{86}{}_{}{}^{}\mathrm{Sr}$ levels and 17 keV for ${}_{}{}^{87}{}_{}{}^{}\mathrm{Y}$ levels. Enriched targets. Core-coupling model.

Calculations of energy spectra of neutrons emitted from ($p,n$) reactions were performed on the basis of the pre-equilibrium exciton model. The results were compared with several experiments, covering the range from $A=27\mathrm{}$ to $A=208\mathrm{}$ of target masses, and from 17.6 to 63.8 MeV of incident proton energy. Within the limits of accuracy of both calculations and experimental data, the theoretical previsions were found adequate, and provided reasonable evaluations of the yields of pre-equilibrium neutron emissions.

NUCLEAR REACTIONS ($p,n$) for $18<\mathrm{}{E}_p<64\mathrm{}$ MeV. Calculated neutron energy spectra with pre-equilibrium statistical model.