The two-step matrix element for two-nucleon transfer is evaluated by use of closure for the continuum intermediate states of relative motion of the transferred particles. Special assumptions that the intermediate system is a deuteron, or is in a particular spin state, are avoided.

The longitudinal response function of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ in the range of momentum transfers 200 MeV/c≤q≤550 MeV/c is calculated in the Tamm-Dancoff approximation. The particle-hole Green’s function is evaluated by means of a doorway-state expansion. This method allows us to take into account finite-range residual interactions in the continuum, including exchange processes. At low momentum transfers, calculations agree qualitatively with the data. The data cannot be reproduced at momentum transfers around 450 MeV/c. This discrepancy can be accounted for neither by uncertainties in the residual interaction, nor by more complicated processes in the nuclear final states.

The S matrix for central NN interactions is represented in the s wave as a rational function of k. Single and double Yukawa potential models of ${}_{}{}^1{}_{}{}^{}\mathrm{S}_0^{}{}_{}{}^{}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{S}_1^{}{}_{}{}^{}$ interactions are the starting point. Twelve terms of the effective range expansion are found, Padé approximants are calculated, and poles and zeros of the associated rational S matrix are located. For all the potentials, rational S matrices are shown to give excellent agreement with data through medium energies while satisfying Levinson’s theorem. Inverse scattering theory is easily applied to recover phase shift equivalent potentials, either local or nonlocal. Bound state and antibound state poles are precisely determined, suggesting this approach is a viable alternative for finding bound state eigenvalues. We truncate our potentials beyond a range R which we vary from 8 to 21 fm. Rigorously, the S matrix of such truncated potentials has no cuts, and the Jost functions are entire. Our analysis introduces distribution of poles and zeros that, as characteristic of Padé approximants, is seen to bear a relation to the Yukawa cuts of the full potentials. Statistical determinations of rational S matrices from experimental phase shifts, already found to be useful, are further supported by the present results.

Differential cross section and analyzing power of the breakup reaction ${}_{}{}^2{}_{}{}^{}\mathrm{H}$(parrow,pp)n have been measured in a kinematically complete coincidence experiment for two selected kinematical configurations, the final state interaction and the collinear configuration with the neutron at rest in the c.m. system. Faddeev calculations done with a code by Stuivenberg and in particular with a recent code by Doleschall show good agreement with the data. Even in the collinear case which is assumed to be most sensitive to effects of the three-body force, no influence of three-body forces is observed. Their contribution therefore cannot exceed the experimental error of 2–3 %. The results indicate that contributions from P and D waves as well as the tensor force are more important than effects from a three-body force.

Nonrelativistic quantum scattering processes can be calculated from strong approximations of Moller wave operators, based on finite rank approximations of the full and asymptotic Hamiltonians. Firstly, similarly to Faddeev-type integral equations, we show that this approach also reduces a three-body system with separable two-body interactions to an effective two-body system. In the simplest case of an s-wave interaction without tensor forces, it reduces to a one-dimensional equation after partial wave decomposition. Secondly, we show that the intertwining relation is approximately valid in this approach and holds in the limit where the approximation parameters tend to infinity. We give a proof for the two-body system with short range interactions and for the long range Coulomb interaction. Implications for practical calculations are discussed.

The 90° cross section yield curve for the ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$(n,${\gamma }_0$${)\mathrm{}}^{14}$C reaction has been measured from $E_{\mathrm{n}\left(E_x\right)=5.6\mathrm{}}$(13.4) to 17.0(24.0) MeV. Angular distributions of cross section and analyzing power were measured at seven energies spanning this excitation region. In addition, the fore-aft asymmetry and 90° analyzing power were measured as a function of energy from $E_{\mathrm{n}=7.75\mathrm{}}$ to 17.0 MeV. The data were compared to direct-semidirect model calculations which included the isovector dipole and isoscalar electric quadrupole transitions. These comparisons indicate the presence of two narrow M1 resonances at $E_x$=16.5 and 17.5 MeV and that σ(E2) is less than 2% of the total capture cross section in the energy region of this experiment.

Differential cross sections were measured for the ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$(d,n)${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ reaction at 79 MeV. Three different adiabatic model calculations as well as conventional distorted-wave Born approximation calculations were performed for transitions to the 0.0, 4.44, 9.64, 12.71, and 15.11 MeV states in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$. One of the adiabatic optical model parameter sets gave consistently better agreement than the rest with the experimental data. The spectroscopic factors obtained for the above states were compared with theory and with previous measurements.

The helion elastic scattering cross section and polarization data for a target mass range 16≤A≤48 are fitted using the optical model, where the spin-orbit potential is deduced microscopically. The quenching effects on the spin-orbit potential of the nucleons occupying the spin-unsaturated shells in the target have been included through the nucleon-nucleus interaction in two different ways, one being an ad hoc approach, while the other is based on more rigorous calculations recently presented in the literature. Both methods produce very similar results and the predictions are comparable to the completely phenomenological approach, despite the contrasting shapes of the microscopic and phenomenological spin-orbit potentials. The valence quenching effects on elastic polarization are found to be small. The deduced N-nucleus spin-orbit potential strengths are consistent with the values obtained using realistic nucleon-nucleon calculations for the targets near closed-shell nuclei. The effects of using different nuclear densities and the sensitivity to the helion wave function are described.

The ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$(p,n${)}^{48}$Sc reaction was studied at 134 and 160 MeV. Neutron energy spectra were measured by the time-of-flight technique with resolutions from 320 to 460 keV at 11 angles from 0° to 60° spaced approximately 6° apart. The neutron spectra reveal strong excitation of the (π$f_{7/2}$,ν$f_{7/2}^{\mathrm{-}1}$) band of states at low excitation energies; five of the known eight members of the band are excited strongly, generally consistent with distorted-wave-impulse-approximation calculations with 1f-2p shell-model wave functions. The normalization of the distorted-wave-impulse-approximation calculations to the extracted angular distributions at 135 MeV vary from 0.40 for the $5^{+}$ state to 0.93 for the $0^{+}$, isobaric analog state. The normalization factor of 0.60 required for the $7^{+}$, stretched-state transition is significantly larger than those required for similar distorted-wave-impulse-approximation calculations of various stretched-state excitations observed in inelastic proton scattering, which involve promoting a nucleon up into the next major shell (a ‘‘1 ħω’’ excitation). The larger normalization factor required for the (π$f_{7/2}$,ν$f_{7/2}^{\mathrm{-}1}$) $7^{+}$ excitation (a ‘‘0 ħω’’ excitation) indicates that this strength is more highly concentrated in a single state. The $4^{+}$ and $6^{+}$ states of this band are observed to be only weakly excited, consistent with predictions that transitions dominated by the tensor term of the nucleon-nucleon interaction will predominantly excite non-normal parity states. The excitation of the $2^{+}$ member of this band shows both Δl=0 and Δl=2 contributions to the angular distribution and may indicate significant two-step processes for this transition.

Gamow-Teller strength in the ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$(p,n${)}^{48}$Sc reaction was studied at 134 and 160 MeV. Neutron energy spectra were measured by the time-of-flight technique with resolutions of about 320 and 460 keV, respectively. The cross sections reported at 160 MeV are increased (by a factor of about 1.4) from results reported previously. The $1^{+}$ Gamow-Teller strength is observed to be split into a low-lying state at $E_x$=2.52 MeV, the Gamow-Teller giant resonance in a complex of states between 4.5 and 14.5 MeV, and a single T=4 state at 16.8 MeV. The general distribution of the $1^{+}$ strength in ${}_{}{}^{48}{}_{}{}^{}\mathrm{Sc}$ is in good agreement with a shell-model prediction. The total $1^{+}$ strength observed in discrete states amounts to 43% of the simple Gamow-Teller sum rule, relative to the observed $0^{+}$, Fermi strength assumed to be concentrated into the isobaric analog state at 6.67 MeV. Consideration of the Δl=0 contributions to the background under the Gamow-Teller giant resonance and of the non-quasifree scattering contributions to the continuum (up to about 30 MeV) increases this fraction to about 70%. Possible Gamow-Teller strength in the quasifree scattering contributions to the continuum is discussed.

Under certain conditions the solution of a nonlocal, nonrelativistic Schrödinger equation is the same as the upper component of a relativistic four-spinor which obeys a local Dirac equation. This result is obtained by combining the observation recently made by Fiedeldey and Sofianos, that a nonlocal Schrödinger equation can be transformed into a local one if a gradient term (or velocity term) is added, together with the well-known fact that the upper component of the solution of a Dirac equation also obeys a second-order equation which has a gradient term. For the case of a nonlocality of the Perey-Buck–type, the gradient term is nearly equal to the Darwin term, and hence the conditions for the validity of the relativistic-nonrelativistic equivalence are nearly valid. A numerical example is presented for the case of 21.7 MeV neutrons scattering elastically from ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, for which a local relativistic optical potential has been recently obtained. The gradient term is given in terms of derivatives of the Wronskian of two independent solutions of the nonlocal equation, and numerical values for the latter are compared with the corresponding relativistic quantity. The differences are not larger than 25%. Results for the nonlocality due to exchange are also shown, and are found to be very similar to the Perey-Buck nonlocality. An implication of these results is that the relativistic optical potential may be less nonlocal than the nonrelativistic one.

The proximity potential for the collision of two deformed and oriented nuclei is rederived in a completely simple and alternative method. Our method is applicable to axially symmetric nuclei lying in the same plane and we get an analytical expression for the shortest distance between two colliding surfaces. The method is applied to the calculation of ${}_{}{}^{238}{}_{}{}^{}$U${+\mathrm{}}^{238}$U interaction potential.

The high-spin states of ${}_{}{}^{88}{}_{}{}^{}\mathrm{Zr}$ and ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$ were studied up to ∼12-MeV excitation via the ${}_{}{}^{74}{}_{}{}^{}$,76Ge${(}^{18}$O,4nγ)${}^8$ 8,90Zr fusion evaporation reactions. Decay schemes were constructed on the basis of gamma-ray excitation functions, angular distribution and linear polarization measurements, γ-γ coincidences, and level lifetimes determined from both Doppler shift attenuation and recoil distance measurements. An effort was made to make as definite spin-parity assignments as possible and to delineate the reliability of these assignments. Probable spins up to ∼20ħ were formed in both nuclei. The experimental results are compared to preliminary results of a large-scale shell model calculation. The yrast spectra of both nuclei can be interpreted as arising from intrinsic modes of excitation with no evidence for collective behavior.

The level scheme of ${}_{}{}^{86}{}_{}{}^{}\mathrm{Zr}$ was studied by in-beam measurements on γ transitions in the ${}_{}{}^{60}{}_{}{}^{}\mathrm{Ni}$${(}^{29}$Si,2pnγ${)}^{86}$Zr reaction and by helium-jet studies of delayed γ-ray activity from the ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$${(}^{32}$S,3pn${)}^{86}$Nb(β +/EC${)}^{86}$Zr reaction. In the latter study, measurements consisted of γ-γ and β-γ coincidences, excitation functions, and a lifetime determination. An ${}_{}{}^{86}{}_{}{}^{}\mathrm{Nb}$ decay scheme was obtained which suggests $J^{\pi }$${=5\mathrm{}}^{+}$ for the ${}_{}{}^{86}{}_{}{}^{}\mathrm{Nb}$ ground state. The in-beam study consisted of γ-γ coincidences, excitation functions, angular distributions, and lifetime measurements via both Doppler shift attenuation and recoil distance methods. The high-spin decay scheme and level lifetimes obtained from the in-beam studies suggest intrinsic modes of excitation rather than the collective behavior seen in ${}_{}{}^{84}{}_{}{}^{}\mathrm{Zr}$.

We generalize a simple version of the optical background representation for the transition amplitude to the case of well-nested doorways. Using this simple generalization of the optical background representation an alternate statistical theory of multistep compound reactions is suggested, which uses the idea of nested averaging in the case of well-nested doorways and is valid under very general conditions. Simple connections are established between the present approach of multistep compound reactions and that of Feshbach, Kerman, and Koonin, of Agassi, Weidenmüller, and Mantzouranis, and of Hussein and McVoy. The present formulation exhibits the chaining condition of Feshbach, Kerman, and Koonin in the extreme low energy limit, is time reversal symmetric, and yields the Bohr description of compound nuclei in the appropriate limit.

The interaction cross section of a neon beam at ∼300 MeV/nucleon along with the partial production cross sections of its fragments is studied in nuclear emulsion. Projected angular distributions of fragments are measured and are correlated with the longitudinal momentum distributions which enable us to estimate the Fermi momentum of the projectile. The space angle distributions of singly and doubly charged particles are discussed on the basis of the Boltzmann distributions.

Inclusive distribution of protons in nucleus-nucleus collisions at high energy has been studied in both forward and backward regions according to the hard scattering model. It is observed that proton production may occur in two ways: (1) the emitted proton is one of the interacting protons in the nucleus and (2) the proton is emitted from a secondary virtual pion along with an antinucleon. Process (1) is dominant in the interaction BA→px in the region 0≤${\mathrm{BX}}_F$≤1 when the inclusive cross section shows a rise with $X_F$ and process (2) is dominant in the region ${\mathrm{BX}}_F$≥1 with $X_F$≤1 where the cross section shows a sharp fall with $X_F$. This feature is found to be in good agreement with experiments. Besides, it is predicted that though there will be approximate scaling (very small change with energy) in the forward region, in the backward region scale breaking will be dominant.

The Boltzmann master equation model has been applied to the question of precompound nucleon deexcitation of reactions induced by 10–100 MeV/nucleon (c.m.) heavy ions. Test systems of ${}_{}{}^{16}{}_{}{}^{}$O${+\mathrm{}}^{60}$Ni and ${}_{}{}^{27}{}_{}{}^{}$Al${+\mathrm{}}^{86}$Kr were selected. Experimental neutron spectra in coincidence with evaporation residue and fission fragments from the ${}_{}{}^{20}{}_{}{}^{}$Ne${+\mathrm{}}^{165}$Ho system (due to Holub et al.) were reproduced quite well by the master equation with exciton numbers between 20 and 23. Exciton values of projectile mass and projectile mass plus 3 were therefore used in the extrapolations of the master equation. Results show major fractions of the excitation and up to 35 nucleons removed during the coalescence-equilibration period. The linear momentum transfer predicted by the master equation is shown to be in good agreement with a broad range of data. Calculations are provided as to the range of angular momenta which may be carried off by the precompound cascade.

High resolution study of the ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$${+}^{16}$O system at 15.5 ≤$E_{\mathrm{c}.\mathrm{m}.\mathrm{}}$≤17.0 MeV is reported including excitation functions for elastic scattering, and angle integrated cross sections for ${\alpha }_0$ and ${\alpha }_1$ exit channels and several γ-ray channels. All show correlated resonant structure. Fifteen angular distributions for the ${\alpha }_0$ and ${\alpha }_1$ exit channels are measured in Δ$E_{\mathrm{c}.\mathrm{m}.\mathrm{}}$≃50 keV steps for 15.5≤$E_{\mathrm{c}.\mathrm{m}.\mathrm{}}$≤16.4 MeV in the angular range 17°≤${\theta }_{\mathrm{c}.\mathrm{m}.\mathrm{}}$≤93° in steps of Δ${\theta }_{\mathrm{c}.\mathrm{m}.\mathrm{}}$≃2.5°. Phase shift analysis of the ${\alpha }_0$ angular distribution was carried out. Ambiguities in the extraction of the S matrix elements are removed using the usual techniques with an additional new constraint—the measurement of cross section at selected angles (zeros of $P_l$) arising from a single partial wave. Reaction amplitudes corresponding to a narrow l window around the grazing partial wave are shown to dominate the cross section around ${\theta }_{\mathrm{c}.\mathrm{m}.\mathrm{}}$=90°. The grazing partial wave shows broad nonresonant structure; a specific parametrization of the energy dependence of the nonresonant (background) cross section corresponding to the l window is presented. The interplay of background amplitudes (l window) and resonant amplitudes is emphasized. Resonances in the ${\alpha }_0$ channel are located at $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}$=15.8, 15.9, and 16.1 MeV having $J^{\pi }$${=10\mathrm{}}^{+}$, $8^{+}$, and $8^{+}$, respectively, and intermediate widths (Γ∼70 keV). Spin assignments are obtained via a phase shift analysis and study of excitation functions measured at zeros of Legendre polynomials. Parametrization of the resonance plus background cross section yields the result √${\Gamma }_0$${\Gamma }_{\alpha }$ /Γ≃1.0%. The extracted partial widths are analyzed in terms of the Wigner limit and suggest resonances not of dinuclear structure, but of more complicated structure. Such states, having $J^{\pi }$${=8\mathrm{}}^{+}$, are found to appear systematically at the empirically determined energies: $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}$=4×2.8+N×2.4 MeV (N=0,1,2 , . . .) in many different heavy ion resonant systems; this may suggest that the underlying alpha particle structure of the participant nuclei may play an ex- plicit role in these resonances.

A nucleon exchange model calculation followed by an evaporation model calculation has been used to predict the various parameters of the N and Z distributions for the reactions 465 MeV ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$, ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$. Comparison with the recent results of Breuer et al. shows overall good agreement, with the correlation coefficients particularly well reproduced. However, the neutron and proton drift in the asymmetric system is poorly reproduced.