A paper dealing with the unitary off-shell ambiguity of effective interactions is criticized. A so-called optimal transformation of the resonating group equation is based on error and not valid.

The contact term in the ${\pi }^{\mathrm{-}}$p→${\pi }^{+}$${\pi }^{\mathrm{-}}$n reaction is known to partly cancel the dominant pion pole term. In this Comment we show that when such terms are used in connection with the double charge exchange reaction in pion nucleus collisions, the contact term vanishes for the reaction amplitude in the forward direction.

It is shown that in forward-angle pion-nucleus double charge exchange reactions leading to double analog states the contribution from the contact diagram of the virtual pion production does not vanish identically. Numerical effects of this diagram in various other double charge exchange reactions should, therefore, be examined case by case.

Transverse quasielastic electron scattering cross sections have been measured for the deuteron at 180° for incident electron energies of 220, 270, and 320 MeV. At the quasielastic peak the four-momentum transfers squared varied from 3.4 to 6.3 ${\mathrm{fm}}^{-2\mathrm{}}$. The measured spectra include the region from the elastic peak through the entire quasielastic peak. Results are compared with recent calculations incorporating meson-exchange currents and isobar configurations. At large neutron-proton separation energies, the data support the need for the inclusion of large isobar configuration components in the cross section.

Intermediate width resonance-like structures in the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$+${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ system have been studied via inelastic scattering to the ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$($0_2^{+}$) state. The dominant partial waves contributing to several structures have been determined by analysis of excitation functions at zeros of Legendre polynomials. The results disagree with spins extracted from angular correlation measurements in non-spin-zero channels.

Experimental evidence is presented for stable octupole deformation at high spin in ${}_{}{}^{150}{}_{}{}^{}\mathrm{Sm}$ and possibly other rare earth nuclei based on the evolution with increasing spin of the $K^{\pi }=0^{+} \mathrm{and} 0^{-}$ bands into a single band. Comparisons and contrasts in the corresponding band evolutions are presented between the 88 and 90 isotones in the rare earths, and 88 and 90 protons (Ra and Th isotopes) in the actinides where stable octupole deformation is established.

Spin-flip charge-exchange (d, ${}_{}{}^2{}_{}{}^{}\mathrm{He}$) reactions on ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$, and ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ were measured at $E_d=70\mathrm{}$ MeV. At forward angles, negative vector analyzing powers of -0.2 to -0.6 were observed for $\Delta L=0\mathrm{}$ transitions for all targets studied, whereas a positive value was obtained for the transition to the 4.4 MeV excited state of ${}_{}{}^{12}{}_{}{}^{}\mathrm{B}$ in the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(d,${}_{}{}^2{}_{}{}^{}\mathrm{He}$) reaction for which $\Delta L=1\mathrm{}$ is the main component. Distorted-wave Born-approximation calculations reproduce this $\Delta L$ dependence of the analyzing power. The fits to the data for $\Delta L=0\mathrm{}$ transitions are improved if the two-step processes via d-p-${}_{}{}^2{}_{}{}^{}\mathrm{He}$ and d-${}_{}{}^3{}_{}{}^{}\mathrm{He}$-${}_{}{}^2{}_{}{}^{}\mathrm{He}$ channels are taken into account.

Vector analyzing powers in the (↔d,${}_{}{}^6{}_{}{}^{}\mathrm{Li}$) reaction on ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ have been measured at $E_{\mathrm{d}}=51.7\mathrm{}$ MeV. A distinctive dependence of the analyzing powers on the transferred angular momentum $l_{\alpha }$ was observed at small angles. The distorted-wave Born approximation analysis shows that the deuteron spin-orbit force has a significant effect on the analyzing powers and the weak effect of ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ spin-orbit force is caused by the deep real central potential rather than a strong absorption.

The qualitative ideas put forward by Geyer and Lee are given quantitative content by constructing a similarity transformation which reexpresses the Dyson boson images of the single-$j$ shell fermion operators in terms of seniority bosons. It is shown that the results of Otsuka, Arima, and Iachello, or generalizations thereof which include $g$ bosons or even bosons with $J>\mathrm{}4\mathrm{}$, can be obtained in an economic and transparent way without resorting to any comparison of matrix elements.

We calculate total cross sections for coherent pion production using localized plane-wave approximations for the shell-structure of valence nucleons that are excited to $\Delta$ particles in the intermediate state in the (${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{B}$) and (${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{N}$) charge-exchange, heavy-ion reactions. We find comparable agreement to projectile downshift data for ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{B}$)${}_{}{}^{12}{}_{}{}^{}\mathrm{N}$. Then we improve the formalism by replacing the localized plane wave bound states with harmonic oscillator states which are imbedded in a multipole expansion approach and calculate pion differential cross sections to test for the sensitivity of the spectra to the single-particle mass parameter.

This paper is concerned with the reduction of the general deuteron-nucleus collision problem to a three-body model describing deuteron elastic scattering and elastic breakup. A formally exact reduction is carried out using an antisymmetrized, multiparticle scattering theory, viz., the Bencze-Redish-Sloan theory in precursor form. All effects of the Pauli principle due to the target nucleons are thus included in the Hamiltonian $H_3$ describing the three-body model. Since deuteron elastic scattering and breakup have been treated for quite some time via an empirical, three-body model Hamiltonian $H_M$, the main purpose of this work has been to establish the relation between $H_3$ and $H_M$. It is shown that, even with inclusion of the Pauli principle, $H_3$ has exactly the form conjectured some years ago by Austern and Richards using a distinguishable particle ansatz. That is, $H_3$ is a sum of the following terms: the two kinetic energy operators, the neutron-proton interaction $V_{\mathrm{np}}$ binding the deuteron, the sum of the exact (antisymmetrized) neutron-nucleus and proton-nucleus optical potentials, each evaluated at an ‘‘energy’’ shifted by the kinetic energy operator of the other (spectator) nucleon, and a three-body interaction. Contrary to other conjectures, the Pauli principle does not give rise to a term $V_{\mathrm{np}\mathrm{Q}}$ (or ${\mathrm{QV}}_{\mathrm{np}}$), where Q is a Pauli blocking factor, projecting off states occupied in the (exact) target ground state. The deuteron in a deuteron-nucleus collision is thus not like a nucleon pair in the structure problem described by the Bethe-Goldstone theory. The three-body interaction $W_{\mathrm{np}}$ is sufficiently complicated to necessitate approximate evaluation. Some relatively simple approximations to $W_{\mathrm{np}}$ are described within a multiple scattering type of framework.

We present a new momentum space approach to the two-body problem in partial waves. In contrast to the usual momentum space approaches, we treat the bound state case with the help of an inhomogeneous integral equation which possesses solutions for all (negative) energies. The bound state energies and corresponding wave functions are identified by an additional condition. This procedure straightforwardly leads to a nonsingular formulation of the scattering problem in terms of essentially the same equation and thus unifies the descriptions of both energy regimes. We show that the properties of our momentum-space approach can be understood in terms of the so-called regular solution of the Schrödinger equation in position space. The unified description of the bound state and scattering energy regimes in terms of one single, real, and manifestly nonsingular equation allows us to construct an exact representation of the two-body off-shell T matrix in which all the bound state pole and scattering cut information is contained in one single separable term, the remainder being real, nonsingular, and vanishing half on-shell. Such a representation may be of considerable advantage as input in three-body Faddeev-type integral equations. We demonstrate the applicability of our method by calculating bound state and scattering data for the two-nucleon system with the s-wave Malfliet–Tjon III potential.

The ${}_{}{}^{25}{}_{}{}^{}\mathrm{Mg}$(α, ${}_{}{}^3{}_{}{}^{}\mathrm{He}$${)}^{26}$Mg reaction was used at 80.9 MeV to investigate the stretched $6^{\mathrm{-}}$ states from the ($d_{5/2}^{\mathrm{-}1}$,$f_{7/2}$) particle-hole configuration, which had been identified by inelastic electron scattering. The summed spectroscopic factors for the T=1 $6^{\mathrm{-}}$ states are only about 27% of the expected strength and are to be compared to 85% of the extreme single model strength found in inelastic electron scattering. The T=1 $6^{\mathrm{-}}$ spectroscopic strength is considerably more fragmented in the mass 26 system than it is in mass 28.

The nucleon-nucleon (NN) interaction model includes a π-exchange and takes into account the first excited state Δ(1232) of the nucleon. It is supplemented by a short-range repulsion which has been derived from the nucleon form factor (rms radius $b_f$) combined with the three-quark wave function (rms radius $b_q$). The optimization of the model on empirical scattering phase shifts below 300 MeV gives, for a minimum ${\chi }^2$, the root-mean-square radii $b_f$=$b_q$=0.51 fm and a coupling constant $G_{\pi }^2$/4π=13.

Parity nonconservation in the hadronic interaction was studied by elastic scattering of 46 MeV longitudinally polarized protons on ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. The scattering chamber consisted of a 110 bar helium gas target, surrounded by a cylindrical ionization chamber in an axially symmetric arrangement, and a Faraday cup. The relative cross sections, ${\sigma }^{+}$ and ${\sigma }^{\mathrm{-}}$, for positive and negative helicity of the incident beam were measured by integrating the currents from the Faraday cup and from the ionization chamber during 20 ms intervals, and digitizing the charges. The angular acceptance function of the ionization chamber extends from ${\mathrm{theta}}_{\mathrm{lab}=31\mathrm{}}$° to approximately 80°, with maximum weight at 41°. The parity nonconserving longitudinal analyzing power $A_z$=(${\sigma }^{+}$-${\sigma }^{\mathrm{-}}$)/(${\sigma }^{+}$+σ ${}_{}{}^{\mathrm{-}}{}_{}{}^{}$) was deduced from 2.3×${10}^6$ individual measurements of $p_z$$A_z$. The magnitude of the beam polarization was ‖$p_z$‖≃0.83. The emphasis is on quantitative treatments of instrumental effects, the most important of which is caused by the nonuniform distribution of residual transverse polarization components of the beam. The final result for the longitudinal analyzing power at a mean laboratory energy of 46 MeV is $A_z$=-(3.3±0.9)×${10}^{\mathrm{-}7}$. The uncertainty includes the statistical error as well as the systematic uncertainties from transverse polarization, modulation of intensity, position, emittance, and energy of the beam associated with helicity reversal, double scattering, asymmetry from β decay, and electronic cross talk. The result is compared to theoretical predictions and to related experiments.

The static properties of the skyrmion and the skyrmion-skyrmion (SS) interaction are investigated within a modified Skyrme model in which the symmetric quartic and the ω-coupling terms are both included. We approximate the latter term by the infinitely large limit for the ω-meson mass. The model is considered to be an effective Lagrangian of pions at low energies. A good agreement of the static properties of the nucleon is obtained using the coupling constants to fit the ππ scattering data. The SS interaction potential is expressed by means of the generalized spin and isospin operators. As a result, the potential is easily projected onto the potentials for NN, NΔ, and ΔΔ states with definite spin and isospin. It is shown that the SS potential has a good correspondence with the one-boson-exchange potential of the π and ρ mesons at large distances. The symmetric quartic term, which is necessary to achieve agreement with the S- and D-wave ππ scattering data, has been expected to give rise to an ‘‘σ-meson’’-like attractive contribution at the intermediate range of the central potential. There exists, however, no such contribution, even if the strength of the symmetric quartic term is increased. This is because we must also increase the ω-coupling term to stabilize the skyrmion. We need further study of this problem.

A general method is developed for constructing on-shell equivalent transformations which eliminate the energy dependence of coupled channel equations with nonlocal linearly energy-dependent potentials. Our derivation shows that such transformations are not unique because of ambiguities of the half-off-shell t matrix compatible with the original Hermitian on-shell equivalent Hamiltonian. A class of such transformations for single and coupled channel cases is explicitly constructed. Our method is applied to a constituent quark-cluster model for nucleon-nucleon scattering.

Double-differential cross sections for the neutron-induced production of p, d, t, ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, and alpha particles from oxygen and nitrogen have been measured using an unpolarized neutron facility. Neutron beam energies of 27.4, 39.7, and 60.7 MeV were used. The charged particle energy spectra, at six forward laboratory angles, 15, 20, 35, 40, 45, and 65, and, where feasible, at three backward angles, 90, 130, and 150 deg, range up to the kinematic maximum, from a typical low-energy cutoff of 4 MeV for p, d, t, and alpha particles, and 8 MeV for ${}_{}{}^3{}_{}{}^{}\mathrm{He}$. Intranuclear cascade plus deexcitation calculations were carried out. The data are compared with these calculations and with available proton-induced (charge-symmetric) reaction spectra for oxygen.

Previously the inverse mean field method has been shown to lead to an analytical expression for the volume integral $J_V$(A) per nucleon over the self-energies of nuclei with mass numbers A and to specific energy dependences for real f($E_p$) and imaginary volume contributions to the optical model potential. These relations are now utilized to obtain $J_V$(A,$E_p$)=$J_V$(A,0)f($E_p$) and its imaginary counterpart, &(A,$E_p$)=$J_V$(A,0)[1 -f($E_p$)]/3. The results compare favorably with heuristic data and the findings of other approaches.