The effects of intercluster antisymmetrization in ${}_{}{}^3{}_{}{}^{}\mathrm{He}$+$\alpha$ and $\alpha$+${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ systems are examined. The result indicates that the characteristic quantities of the Born-equivalent local potentials can be reliably employed to predict the relative importance of the various nucleon-exchange terms. Based on these quantities and by studying the cross section or phase-shift behavior, it is noted that many exchange terms are of only minor significance when the energy is high or when the absorption is strong. Furthermore, one finds that, at an energy higher than about 25 MeV/nucleon, the features of the cross-section angular-distribution curve, which has a distinct V shape, can be simply explained. Here our investigation shows that the contribution to the cross section in the decreasing part of the V-shaped curve comes essentially from the direct term and the one-exchange terms (mainly the knockon exchange term), while the contribution to the cross section in the increasing part of this curve comes essentially from the core-exchange terms.

NUCLEAR REACTIONS ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ ($\alpha , \alpha$) ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}(\alpha , \alpha )$. Effects of antisymmetrization with resonating-group method.

We prove here that by taking the zero range limit of conventional nonrelativistic three-particle theories and restricting the two-particle amplitude in this limit to have no singularities at negative energy other than bound state poles, we can derive unitary three-particle equations depending only on two-particle physical observables. Phenomenological extensions of this theory suitable for data analysis of systems with three-particle final states and two- and three-cluster reaction theories are briefly discussed. The extension of the theory to four-particle systems is sketched. Nonrelativistic and relativistic applications will be discussed in subsequent papers in this series.

NUCLEAR REACTIONS 3, 4 particle equations, generalized to $N$. Restricted to 2 particle observable input, no left hand cuts. Faddeev-Yakubovsky combinatorics.

A new connected kernel version of the Chandler-Gibson equations is derived. Both the new and the original versions of the Chandler-Gibson equations are then modified to incorporate identical particle symmetries. Both types of equations are written down in detail for two different six-body models of alpha-deuteron scattering. Various features of these equations are then compared.

NUCLEAR REACTIONS Connected kernel equations for distinguishable and identical particles; equations for alpha-deuteron scattering.

The ${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}({}_{}{}^3{}_{}{}^{}\mathrm{He}, d){}_{}{}^{198}{}_{}{}^{}\mathrm{Hg}$ reaction has been studied at $E_{3_{\mathrm{He}}}=50\mathrm{}$ MeV. Single-particle strengths for $s_{\frac{1}{2^{-}}}$ and $d_{\frac{3}{2}}$ proton transfer have been obtained for 15 levels. In total 24 levels have been identified. A comparison is made with the predictions of the supersymmetry model and of the Alaga model. At $E_x=2.45\mathrm{}$ MeV a state is found which has probably $J^{\pi }=1^{+}$ and carries nearly unfragmented the $s_{\frac{1}{2}}$ partial sum rule for $1^{+}$ states.

NUCLEAR REACTIONS ${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}({}_{}{}^3{}_{}{}^{}\mathrm{He}, d)$; $E_{3_{\mathrm{He}}}=50\mathrm{}$ MeV; deduced ${}_{}{}^{198}{}_{}{}^{}\mathrm{Hg}$ levels; measured $\sigma \left(\theta \right)$;DWBA analysis; deduced spectroscopic strengths; comparison with supersymmetry model and Alaga model.

It is shown that insertion of a deformation parameter ${\beta }_6$ in coupled channels calculations may be necessary for proper predictions of the neutron total cross sections (${\sigma }_T$) at incident energies below ∼700 keV. This is illustrated in the present work with the ${\sigma }_T$ measurements of Whalen et al. on the ${}_{}{}^{182,184,186}{}_{}{}^{}\mathrm{W}$ isotopes. In a previous report it has been established that these data could not be well reproduced using coupled channel calculations involving only ${\beta }_2$ and ${\beta }_4$ deformations. It is shown presently that this discrepancy can be removed if, provided that self-shielding corrections to these measurements are made, a small deformation parameter ${\beta }_6$ is considered in coupled channel analyses. As the W isotopes are lying at the rotational edge of the $A=190-200\mathrm{}$ transitional mass region, it is also emphasized that band mixing effects on the model predictions might be of some importance. These effects have been investigated for ${}_{}{}^{182,184,186}{}_{}{}^{}\mathrm{W}$ as well as for ${}_{}{}^{183}{}_{}{}^{}\mathrm{W}$ using realistic collective wave functions.

NUCLEAR REACTIONS Neutron total and scattering cross sections. Tungsten isotopes. Statistical model calculations. Realistic collective models. Coupled channels analyses. Deduced ${\beta }_6$ deformation parameters. Calculated inelastic cross sections for ground state and vibrational band levels.

The masses of ${}_{}{}^{76}{}_{}{}^{}\mathrm{Kr}$ and ${}_{}{}^{74}{}_{}{}^{}\mathrm{Kr}$ were measured utilizing the ${}_{}{}^{78}{}_{}{}^{}\mathrm{Kr}$(${}_{}{}^4{}_{}{}^{}\mathrm{He}$, ${}_{}{}^6{}_{}{}^{}\mathrm{He}$) and ${}_{}{}^{78}{}_{}{}^{}\mathrm{Kr}$(${}_{}{}^4{}_{}{}^{}\mathrm{He}$, ${}_{}{}^8{}_{}{}^{}\mathrm{He}$) reactions. Mass excesses of -68971±13 and -62210±75 keV were obtained for ${}_{}{}^{76}{}_{}{}^{}\mathrm{Kr}$ and ${}_{}{}^{74}{}_{}{}^{}\mathrm{Kr}$, respectively, and found to compare favorably with some mass formulae predictions, but not with others. Speculations about shape differences in light krypton and rubidium isotopes are presented as they relate to various mass formulae.

NUCLEAR REACTIONS ${}_{}{}^4{}_{}{}^{}\mathrm{He}$+${}_{}{}^{78}{}_{}{}^{}\mathrm{Kr}$, $E_{\mathrm{lab}}=79.7\mathrm{} \mathrm{and} 102.7$ MeV; measured $E_{6_{\mathrm{He}}}$, $E_{8_{\mathrm{He}}}$; ${}_{}{}^{76}{}_{}{}^{}\mathrm{Kr}$, ${}_{}{}^{74}{}_{}{}^{}\mathrm{Kr}$ deduced $Q$, masses; magnetic spectrograph. Enriched gas targets.

The level structure of ${}_{}{}^{195}{}_{}{}^{}\mathrm{Pt}$ has been investigated via a study of the ${}_{}{}^{194}{}_{}{}^{}\mathrm{Pt}(n, \gamma ){}_{}{}^{195}{}_{}{}^{}\mathrm{Pt}$ reaction. Secondary $\gamma$ rays have been measured with curved crystal spectrometers and Ge(Li) detectors, and average resonance capture measurements have been performed to establish a complete set of low spin negative parity states below 1500 keV. The positive parity states reveal a decoupled band structure based on the ${\frac{13}{2}}^{+}$ isomer at 259 keV. The number of $J^{\pi }={\frac{1}{2}}^{-}, {\frac{3}{2}}^{-}$ states identified below 1 MeV, a total of 11, indicates that a simple Nilsson model description will not be adequate to describe the observed level scheme. The negative parity structure is discussed in the framework of the interacting boson fermion approximation in light of the recently proposed multi-$j$ supersymmetry predictions for this region.

NUCLEAR REACTIONS ${}_{}{}^{194}{}_{}{}^{}\mathrm{Pt}(n, \gamma )$, $E_n=\mathrm{th}, 2 \mathrm{KeV}, 24 \mathrm{KeV}$; measured $E_{\gamma }$, $I_{\gamma }$; ${}_{}{}^{195}{}_{}{}^{}\mathrm{Pt}$ deduced levels, $J$, $\pi$. Curved crystal spectrometers, Ge(Li) detectors, enriched targets. Comparison with predictions of multi-$j$ supersymmetry in interacting boson-fermion approximation.

The ($e, \alpha$) cross section for ${}_{}{}^{65}{}_{}{}^{}\mathrm{Cu}$ has been measured in the electron energy range 14-34 MeV. The results have been analyzed using the distorted-wave Born approximation $E1\mathrm{}$ and $E2\mathrm{}$ virtual photon spectra and the $E1\mathrm{}$ and $E2\mathrm{}$ components of the corresponding ($\gamma , \alpha$) cross section were obtained. To assess the accuracy of the virtual photon analysis, the ($e, 2n$) cross section for ${}_{}{}^{63}{}_{}{}^{}\mathrm{Cu}$ was also measured and the obtained ($\gamma , 2n$) cross section is compared with direct measurement of this cross section performed with annihilation gamma rays.

NUCLEAR REACTIONS ${}_{}{}^{65}{}_{}{}^{}\mathrm{Cu}(e, \alpha )$ and ${}_{}{}^{63}{}_{}{}^{}\mathrm{Cu}(e, 2n)$. Measured ${\sigma }_{e,\alpha }\left(E_0\right)$ and ${\sigma }_{e,2n}\left(E_0\right)$. Deduced ${\sigma }_{\gamma ,\alpha }^{E1\mathrm{}}\mathrm{}\left(E\right)\mathrm{}$, ${\sigma }_{\gamma ,\alpha }^{E2\mathrm{}}\mathrm{}\left(E\right)\mathrm{}$, and ${\sigma }_{\gamma ,2n}^{E1\mathrm{}}\mathrm{}\left(E\right)\mathrm{}$.

Differential cross sections for proton elastic and inelastic scattering have been measured at $E_p=22.3\mathrm{}$ MeV for 14 nuclei with $92\le A\le 116$. The energy dependence has been studied between 10 and 35 MeV, considering also reaction cross sections at lower incident energies. The long standing sub-Coulomb optical model anomalies are thereby eliminated. Nuclear structure effects found in the analysis of elastic scattering are identified with strong couplings between ground and one-phonon states. These couplings are satisfactorily described by traditional collective models, using deformation parameters in agreement with those deduced from electromagnetic data. The transitions to weakly excited states require a more accurate spectroscopic description. Spectroscopic amplitudes taken from the interacting boson model are used. The radial dependence of transition densities is derived from optical model potentials.

NUCLEAR REACTIONS Proton scattering on ${}_{}{}^{92,94,96,98,100}{}_{}{}^{}\mathrm{Mo}$, ${}_{}{}^{102}{}_{}{}^{}\mathrm{Ru}$, ${}_{}{}^{104,106,108,110}{}_{}{}^{}\mathrm{Pd}$, and ${}_{}{}^{106,110,112,116}{}_{}{}^{}\mathrm{Cd}$; $E_p=22.3\mathrm{}$ MeV; on ${}_{}{}^{104}{}_{}{}^{}\mathrm{Pd}$ at $E_p=10.25, 12.1, 15.0, 17.3, 22.3, 30.2, \mathrm{and} 35.4$ MeV. Measured $\sigma \left(\theta \right)$; enriched targets. Optical model and coupled channels analyses. Collective vibrational model, coupling parameters. Interacting bosons approximation, form factors.

The ${}_{}{}^{195}{}_{}{}^{}\mathrm{Pt}(t, p){}_{}{}^{197}{}_{}{}^{}\mathrm{Pt}$ reaction has been measured with a 17 MeV triton beam. Excitation energies and angular distributions of states below 2.2 MeV have been obtained. Three sizable $L=0\mathrm{}$ transitions were observed to states below 1 MeV, in contrast to earlier $\mathrm{Pt}(t, p)$ and ($p, t$) reaction measurements where essentially all of the $L=0\mathrm{}$ strength was in the ground-state transition.

NUCLEAR REACTIONS ${}_{}{}^{195}{}_{}{}^{}\mathrm{Pt}(t, p)$, $E=17\mathrm{}$ MeV; enriched target; measured energy levels, $\sigma \left(\theta \right)$ in ${}_{}{}^{197}{}_{}{}^{}\mathrm{Pt}$; DWBA.

The proximity potential is applied to the coupled-channels analysis of the inelastic scattering of heavy ions. It is shown that a suitably chosen proximity potential accurately reproduces the effect of a folding-model interaction between spherical nuclei. The heavy-ion Woods-Saxon potential is then considered as the result of a folding procedure and presented as an optional form for a proximity type potential. An analysis of the collision between spherical and deformed nuclei shows that, while the proximity potential well reproduces the folding model for this system, the proximity and center-line potentials lead to the extraction of significantly different values of high-multipole deformations. Formulas appropriate to the proximity interaction between two deformed nuclei are also presented.

NUCLEAR REACTIONS ${}_{}{}^{152}{}_{}{}^{}\mathrm{Sm}$(${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$,${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$′)${}_{}{}^{152}{}_{}{}^{}\mathrm{Sm}$, calculated $\sigma (0^{+},2^{+},4^{+},6^{+})$ in coupled channels with deformed proximity potential; determined ${\beta }_6$.

Projectilelike reaction products from the ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$+${}_{}{}^{84}{}_{}{}^{}\mathrm{Kr}$ reaction were studied at a laboratory bombarding energy of 712 MeV. The fragments were identified by atomic number, and their kinetic energies and angular distributions were measured with solid-state $\Delta E-E$ telescopes. The angular distribution is found to be peaked at an angle slightly smaller than the grazing angle and the $Z$ distribution is peaked near $Z=36\mathrm{}$. Correlations of the experimental variables show that the angular and $Z$ distributions broaden drastically with kinetic energy dissipation in damped reactions. Various correlations between experimental observables, including the variance of the $Z$ distributions as a function of the reaction $Q$ value and the relationship between kinetic energy and reaction angle, are interpreted in terms of a classical dynamical model using a proximity one-body transport formalism.

NUCLEAR REACTIONS ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$(${}_{}{}^{84}{}_{}{}^{}\mathrm{Kr}$,HI); $E_{\mathrm{lab}}=712\mathrm{}$ MeV; measured $\sigma (\theta , E, Z)$; damped reaction; extracted moments of element distributions and centroids of angular distributions as a function of $Q$ value; comparison with dynamical calculations employing proximity one-body transport model.

First and second moments of the projectilelike fragment distributions in the $\mathrm{NZ}$ plane have been measured for the reactions of ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$ with ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$ at 315 and 461 MeV, with ${}_{}{}^{64}{}_{}{}^{}\mathrm{Ni}$ at 464 MeV, and with ${}_{}{}^{122}{}_{}{}^{}\mathrm{Sn}$ at 320 and 460 MeV bombarding energy. Results are compared as a function of energy loss to predictions of theoretical transport calculations which include effects of the deexcitation of the excited fragments by particle evaporation. Comparisons involve no adjusted parameters. Theoretical and experimental results for second moments are in good agreement for all cases. First moments agree well with theory for ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$ and ${}_{}{}^{64}{}_{}{}^{}\mathrm{Ni}$ cases, but for ${}_{}{}^{122}{}_{}{}^{}\mathrm{Sn}$ the experimental data show a drift toward higher masses that is less rapid than predicted. It is concluded that a theory employing statistical single nucleon exchange as the dominant mechanism in energy damping can generally reproduce the results of these experiments.

NUCLEAR REACTIONS Heavy ions. Measured isotopic distributions versus energy loss for ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$ + ${}_{}{}^{58,64}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{122}{}_{}{}^{}\mathrm{Sn}$. Compare to predictions from transport theory.

We develop a simple model for the average $S$ matrix that describes heavy ion direct processes in the presence of absorption due to compound nucleus formation. The fluctuation cross sections and the fusion cross section are then derived for deformed heavy ion systems where multiple Coulomb excitation is important. The modifications in the conventional expressions for these cross sections, due to multiple Coulomb excitation, are discussed. Applications are made to the systems ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$+${}_{}{}^{148,150,152}{}_{}{}^{}\mathrm{Sm}$.

NUCLEAR REACTIONS Coulomb excitation effect on heavy-ion compound and fusion processes are studied.

The cross sections of 15 products produced in the relativistic heavy-ion reactions of 211 and 377 MeV/nucleon ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ ions with Cu were measured using activation techniques. The isobaric mass yield curves measured in this study compare well with previous results of relativistic heavy-ion- and proton-induced Cu spallation after taking into account the increased absolute total reaction cross section of ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$. The target fragmentation yields resulting from peripheral collisions were compared with abrasion-ablation model calculations. Central collision processes were examined by comparing light mass ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$ yields.

NUCLEAR REACTIONS Cu(${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$, spallation), $E=4.22\mathrm{} \mathrm{and} 7.54$ GeV. Measured absolute $\sigma (A, z)$ 15 products, deduced mass yield. Natural targets Ge(Li) $\gamma$-ray spectroscopy.

Resonancelike structures have been seen in the excitation functions for fusion in light "$\alpha$-particle" nuclei, with spacings of about 5 MeV and widths of about 2 MeV. These have been reported in systems as heavy as ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$+${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, but were not found in ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$+${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$. A search for similar structure was made for the ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$+${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ system, in steps of 350 keV from $40 \mathrm{MeV}\le E_{\mathrm{lab}}\left({}_{}{}^{16}{}_{}{}^{}\mathrm{O}\right)\lesssim 51 \mathrm{MeV}$, by observing the $\gamma$-ray yields of specific residues. While there is evidence for weak structure in the yields of some residues, cross-correlation analysis indicates that no correlated structure exists at the statistical accuracy of the present data (≲5%).

NUCLEAR REACTIONS ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ + ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, $E_{\mathrm{lab}}=40-51\mathrm{}$ MeV; measured ${\sigma }_{\mathrm{fusion}}\mathrm{}\left(E\right)\mathrm{}$ of residues; correlation analysis of data.

Excitation functions for the yields of ten residual nuclides from the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$+${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ reaction have been measured over the range $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=5.25-20.0\mathrm{}$ MeV in steps of 125 keV, using $\gamma$-ray techniques. Nearly all of the reaction channels, including those with light-particle evaporation, showed strong narrow structures. A qualitative statistical analysis performed on the data gave useful information about the locations of possible nonstatistical structure, based primarily on the very strong cross-channel correlation observed in the data set.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ (${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, $x$); $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=5.25-20.0\mathrm{}$ MeV; measured $\sigma \mathrm{}\left(E\right)\mathrm{}$ for production of $A=16-23\mathrm{}$ reaction products; statistical analysis presented; deduced evidence for nonstatistical structure.

Cross sections for states populated in the ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$(${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$, ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}$)${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ and ${}_{}{}^{26}{}_{}{}^{}\mathrm{Mg}$(${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$, ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}$)${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}$ reactions at 83 MeV were measured. Equal strengths for population of ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ and ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}$ ground states were observed, in contrast to (${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$) and (${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^8{}_{}{}^{}\mathrm{Be}$) reactions, but in agreement with (${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, $d$) results and with theoretical predictions.

NUCLEAR REACTIONS ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ (${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$, ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}$), ${}_{}{}^{26}{}_{}{}^{}\mathrm{Mg}$(${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$, ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}$), $E=83\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$.

In an attempt to explore a possible new technique for the measurement of quadrupole moments of short-lived states, we have searched for an internal quadrupole field induced by a possible transient electric field gradient acting on fast-moving ions in solids. In the measurement we attempted to detect perturbations of the angular correlation pattern of $\gamma$ rays deexciting the first $2^{+}$ states in ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$ and ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, which were both Coulomb excited in the interaction of 125-MeV ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$ with ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$. No electric field gradient effect was seen (≤${10}^{21}$ V/${\mathrm{cm}}^2$). As a by-product, some information was obtained on vacuum deorientation coefficients for ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$ and ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$.

NUCLEAR REACTIONS ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$(${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$,${}_{}{}^{56}{}_{}{}^{}\prime \mathrm{Fe}$), $E_{\mathrm{lab}}=125\mathrm{}$ MeV; measured particle-$\gamma$ coincidence $\sigma$; deduced transient electric field gradient. Coupled channels analysis.

To compare with the wealth of new data on alpha-accompanied fission of ${}_{}{}^{236}{}_{}{}^{}\mathrm{U}$* we have made new trajectory calculations. Initial conditions for several parameters were selected from Gaussian distributions by the Monte Carlo method and about 15 000 trajectories were run for an alpha source at the electrostatic saddle point. Momentum and energy are fully conserved in the three-body problem, though the usual point charge approximation without nuclear forces was used. The main calculations center the alpha source at the electrostatic saddle. General agreement with experiment is remarkable including even the appearance of low-energy secondary peaks at large angles. Effects of shifting the source from the saddle point toward either fragment are studied, running an additional 15 000 trajectories for each of two shifts. Both the satellite peak phenomena and the angular distribution indicate the need for a small shift of source toward the light fragment.

NUCLEAR REACTIONS Alpha accompanied thermal neutron ternary fission ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}(n, f)$. Monte Carlo theory; trajectory calculations; $\alpha$-particle angular and energy distributions.