The distortion effects are investigated for the ($\alpha ,2\mathrm{}\alpha$) reaction in the framework of the distorted-wave impulse approximation at intermediate energies (> 100 MeV) for various nuclei. It has been found that the main effect of the distortion is to reduce the cross section. This reduction factor decreases with the energy and, at a particular energy, increases with the mass number. The distortion is also found to change the shape of the "distorted" momentum distribution around the secondary maxima. Comparison of the calculated results with the available data at 850 MeV on ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ gives the spectroscopic factor in excellent agreement with the theoretically estimated value.

[NUCLEAR REACTIONS Intermediate energies, ($\alpha ,2\mathrm{}\alpha$), DWIA.]

Shell model calculations were performed to obtain spectroscopic factors from microscopic wave functions of nuclei which were studied with the (d,${}_{}{}^6{}_{}{}^{}\mathrm{Li}$) reaction in the $A=90\mathrm{}$ mass region. Though experimental level schemes for Zr, Nb, and Mo isotopes are reproduced rather well by the calculations, relative strengths measured for the Mo(d,${}_{}{}^6{}_{}{}^{}\mathrm{Li}$)Zr reaction are less well explained.

The validity of the random phase approximation in a deformed Hartree-Fock basis is investigated in a soluble model. There is strong evidence that the random phase approximation reproduces well the vibrational excitations of the system. Within the framework of the Green's function technique, the significance of the deformed single particle basis is established.

The suppressed ratio of (${\pi }^{-},\mathrm{pn}$) to (${\pi }^{+},\mathrm{pp}$) pion absorption cross sections on ${}_{}{}^{3,4}{}_{}{}^{}\mathrm{He}$ has an important contribution from NN′ intermediate states, where N′ denotes a $P_{11} \pi \mathrm{N}$ interaction. The order-of-magnitude energy variation of this ratio, from stopped pions to pions above the (3,3) resonance, is reproduced in calculations using a unitary isobar model. We predict a strong asymmetry in the angular distribution of the ratio of higher pion energies.

The possibility is discussed that the enhanced clustering in the nuclear surface of some nuclei observed by Samanta et al. [Phys. Rev. C 26, 1379 (1982)] is due to the modification of the wave function of a discrete nuclear state at the nuclear surface by unbound states. The modification is formulated in a model with unified description of bound and unbound states. Experimental data from knockout reactions on odd nuclei are necessary in order to test the theoretical statements.

[NUCLEAR REACTIONS Cluster knockout, light nuclei, spectroscopic factors, continuum shell model, nuclear surface.]

The numerical results of a recent paper on nn and pp clustering are explained in terms of a simple schematic model which emphasizes the role of positive and negative parity single particles.

A recent claim that forbidden nuclear beta decay can, by the application of a high-intensity radio-frequency field, be enhanced by many orders of magnitude is contested. The effect is shown to be nonexistent, at least within the theoretical model which has been adopted thus far.

The negative conclusion in the Comment of Becker, Schlicher, and Scully about electromagnetic enhancement of beta decay is shown to be faulty. They have found an algebraic oversight in my paper, but correction of that oversight yields results strongly resembling the original. Becker, Schlicher, and Scully fail to find this. They then conduct an analysis which is highly implicit and incomplete. In attempting to analyze their very complicated expressions they claim not to find significant electromagnetic effects. Yet they also lose completely the electron retardation term of conventional forbidden beta decay. When they attempt to explain the difference between their results and mine, they misconstrue the momentumtranslation technique and end up in a logical contradiction. They attempt also to apply a "no-go" theorem applicable only to plane-wave particles to my theory, which is built around the use of bound-state nuclear wave functions. This makes the no-go theorem inapplicable.

The differences between the Saclay and Livermore photoneutron cross sections are discussed. It is shown that the differences between Saclay and Livermore ($\gamma ,\mathrm{n}$) and ($\gamma ,2\mathrm{n}$) cross sections arise from the neutron multiplicity sorting.

[NUCLEAR REACTIONS Photoneutron cross sections analyzed.]

It is shown that a conventional Kisslinger model analysis of the 64.8 MeV $\pi -{}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ elastic scattering data of Dam et al. indicates that the optical model potentials are the same for ${\pi }^{\pm }$. This is in disagreement with the earlier analysis of Dam et al. but in agreement with the requirements of charge symmetry.

One of the purposes of this paper is to make critical comments on some observations made by Tezuka who used the $\sigma$ model to study the possible phase transition in nuclear matter. Also an elegant method, based on the property of the cubic equation, is suggested for calculating the effective nucleon mass as a function of the Fermi momentum in nuclear matter.

Fission and evaporation residue excitation functions of ${}_{}{}^{153}{}_{}{}^{}\mathrm{Tb}$ and ${}_{}{}^{181}{}_{}{}^{}\mathrm{Re}$ compound systems are investigated in the context of angular-momentum-dependent fission barrier calculations in which effects of the finite range of the nuclear force and of the diffuseness of the nuclear surface are included. Carbon- and neon-induced reactions are studied in both the ${}_{}{}^{153}{}_{}{}^{}\mathrm{Tb}$ and ${}_{}{}^{181}{}_{}{}^{}\mathrm{Re}$ cases. Reasonable agreement is found between experimental and calculated excitation functions without adjustments of the theoretical fission barriers.

Using the $K$-matrix formalism, we give a simplified reformulation of the $S$-wave rank-one inverse scattering problem. The resulting Cauchy integral equation, obtained differently by Gourdin and Martin in their first paper, is tailored to rational representations of $F\left(k\right)=kcot\left({\delta }_0\right)$. Use of such $F\left(k\right)\mathrm{}$ permits a simple but general solution without integration, giving analytic form factors having a pole structure like the $S$ matrix that are reducible to rational expressions using Padé approximants. Finally, we show a bound state pole condition is necessary, and makes the form factor unique.

A convenient new method, the quasiadiabatic approximation, is developed for the standard three-body model of deuteron-induced stripping and breakup. The approximation gives the breakup wave function at "coincidence" (${\overrightarrow{\mathrm{r}}}_{\mathrm{n}}={\overrightarrow{\mathrm{r}}}_{\mathrm{p}}$) directly as the solution of a simple differential equation with a source term that depends on the elastic channel wave function. The derivation assumes only that the internal Hamiltonian of the broken up deuteron can be replaced by a constant, ${\overline{\epsilon }}_L$, whose value depends on the c.m. angular momentum $L$. No approximation restricting the relative n-p angular momentum is needed. The quasiadiabatic approximation reduces to the Johnson-Soper adiabatic approximation if ${\overline{\epsilon }}_L$ is replaced by $-{\epsilon }_{\mathrm{d}}$, the internal energy of the bound deuteron. The adiabatic approximation for the elastic channel wave function gives an estimate of the quasiadiabatic approximation source term. The behavior of the coincidence breakup wave function in the nuclear interior (previously calculated using a coupled channels method) is well explained by the quasiadiabatic approximation with the use of a simple prescription for ${\overline{\epsilon }}_L$. The separation of internal and external breakup, and the "$L=9\mathrm{}$" effect are easily explained by the use of the quasiadiabatic approximation. The decrease of the coincidence breakup wave function at large distances is not reproduced by this approximation. In applications to stripping calculations the quasiadiabatic approximation coincidence wave function gives a marked improvement over the Johnson-Soper adiabatic wave function, and it seems promising for practical calculations. This is tested by means of a previously described distorted-wave Born iteration applied to the adiabatic wave function. The rather lengthy distorted-wave Born iteration adiabatic calculations agree with the stripping derived by coupled channel calculations and give a good description of the long-range features of the coincidence breakup wave function. The stripping comparisons are complicated by the necessity of allowing for "closed" breakup channels, which are absent from the coupled-channel comparison, optional in the distorted-wave Born iteration adiabatic approximation, and fully included in the quasiadiabatic approximation. The empirical use of phenomenological local deuteron optical potentials is discussed.

Excitation curves for the ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$(${}_{}{}^3{}_{}{}^{}\mathrm{He}$,${\mathrm{n}}_0$)${}_{}{}^{34}{}_{}{}^{}\mathrm{Ar}$ reaction at selected angles, and ${\mathrm{n}}_0$ and ${\mathrm{n}}_1$ angular distributions at four energies below the Coulomb barrier were measured. The data were analyzed by considering the interference between direct-reaction and compound-nucleus formation amplitudes.

Electron scattering cross section measurements on ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$ have been made at incident electron energies between 34 and 74 MeV and at scattering angles of 162.4° and 180°. Form factors were deduced for transitions to states at 8.11, 9.68, 10.05, 10.78, 11.12, and 11.63 MeV. Additional peaks at 7.12, 12.02, and 13.36 MeV were observed in some spectra. Comparisons of cross sections at different angles show that the above six transitions are transverse. Comparison of the experimental form factors with those calculated using an oscillator shell model indicate that the 8.11, 9.68, 11.12, and 11.63 MeV transitions are $M1\mathrm{}$. Transition probabilities $B\left(M1\mathrm{}\right)\mathrm{}\uparrow =1.14\mathrm{}\pm 0.18$, $0.69\pm 0.20$, $2.40\pm 0.22$, and $1.26\pm 0.20 {\mu }_0^2$, respectively, were determined for these four transitions. The $M1\mathrm{}$ form factors and transition probabilities are also compared with other theoretical shell model calculations. The transition at 10.78 MeV is probably $M2\mathrm{}$, or a mixture of $M2\mathrm{}$ and transverse $E2\mathrm{}$ transitions to unresolved states at about that energy.

Gamow states in momentum representation are defined as solutions of a homogeneous Lippmann-Schwinger equation for purely outgoing particles. We study their properties when the potential, local or nonlocal, is such that the trace of the kernel of the Lippmann-Schwinger equation exists. It is found that, contrary to what happens in position representation, Gamow states in momentum representation are square integrable functions. A norm is defined and expressions for matrix elements of operators between arbitrary states and properly normalized resonant states are given, free of divergence difficulties. It is also shown that bound and resonant states form a biorthonormal set of functions with their adjoints and that a square integrable function may be expanded in terms of a set containing bound states, resonant states, and a continuum of scattering functions. Resonant states may be transformed from momentum to position representation modifying, in a suitable way, the usual rule.

We have calculated effective range parameters for the $S$ and $P$ states for proton-proton and neutron-proton scattering and compared them with results from other authors. The calculations were done in the framework of a phase shift analysis. Different effective range expansions (with and without inclusion of the one-pion-exchange cut) were investigated. Taking into account features of the deuteron and of one pion exchange we give a low energy parametrization for the mixing parameter ${\epsilon }_1$.

The scattering solution to the Lippmann-Schwinger equation is expanded into a set of spherical Bessel functions of complex wave numbers, $K_j$, with $j=1,2,\cdots ,M$. The value of each $K_j$ is determined from the condition that the spherical Bessel function smoothly matches onto an asymptotically outgoing spherical Hankel (or Coulomb) function of the correct physical wave number at a matching point $R$. The spherical Bessel functions thus determined are Sturmian functions, and they form a complete set in the interval 0 to $R$. The coefficients of the expansion of the scattering function are determined by matrix inversion of a linear set of algebraic equations, which are equivalent to the solution of the $T$-matrix equation in complex momentum space. In view of the presence of a matching radius, no singularities are encountered for the Green's functions, and the inclusion of Coulomb potentials offers no computational difficulties. Three numerical examples are performed in order to illustrate the convergence of the elastic scattering matrix $S$ with $M$. One of these consists of a set of coupled equations which describe the breakup of a deuteron as it scatters from the nucleus on ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$. A value of $M$ of 15 or less is found sufficient to reproduce the exact $S$ matrix element to an accuracy of four figures after the decimal point.

A search has been made for a resonance in the ${}_{}{}^2{}_{}{}^{}\mathrm{H}{(\alpha ,\gamma )}^6\mathrm{Li}$ capture-reaction cross section at the energy corresponding to the $0^{+}$, $T=1\mathrm{}$, 3.56-MeV state of ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$. None was found, and an upper limit of 6.5×${10}^{-7\mathrm{}}$ eV was set on the parity-forbidden $\alpha$ width at the 90% confidence level. This limit is three orders of magnitude smaller than the best previous measurement.