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The electric polarizability and logarithmic mean-excitation energy are calculated for the deuteron using techniques introduced in atomic physics. These results are then used to improve limits on the atomic-deuterium frequency shift due to nuclear polarization in the unretarded dipole limit, as well as confirming previous results., Comment: 7 pages, latex -- To appear in Phys. Rev. C

Relativistic Hamiltonians are defined as the sum of relativistic one-body kinetic energies, two- and many-body interactions and their boost corrections. We review the calculation of the boost correction of the two-body interaction from commutation relations of the Poincar\'e group and show that its important terms can be easily understood from classical relativistic mechanics. The boost corrections for scalar- and vector-meson-exchange interactions, obtained from relativistic field theory, are shown to be in agreement with the results of the classical calculation. These boost corrections are also shown to be necessary to reproduce the known results of relativistic mean-field theories. We conclude with comments on the relativistic boost operator for the wave function of a nucleus. Some of the results presented in this article are known. We hope that a better understanding of relativistic Hamiltonians and their relation to relativistic field theory is obtained by putting them together with the new relations.

The impulse-approximation and pion-exchange current contributions to the radiative capture of thermal neutrons by deuterium have been calculated using initial- and final-state wave functions generated by solving the configuration-space Faddeev equations for several nucleon-nucleon and nucleon-nucleon-plus-three-body-force hamiltonian models. Numerical results are compared with previously published total cross section data and with recent measurements of the M1 photon polarization and the spin-quartet capture fraction.

Recent experiments observed unexpectedly strong interference between the E1-E1 and M1-M1 2\ensuremath{\gamma} decay modes of the ${0}^{+}$ (6.05 MeV) state in $^{16}\mathrm{O}$. We present the results of a detailed calculation which evaluates the two-photon amplitude between realistic nonspurious many-body wave functions derived from a large basis SU(3) shell-model calculation, including up to 5\ensuremath{\Elzxh}\ensuremath{\omega} of excitation. It is found that, as a result of strong cancellation between contributions to the transition polarizability from the giant dipole states built on the closed shell and the deformed (6.05 MeV) ${0}^{+}$ state, the 2E1 matrix element is greatly suppressed. Since the standard one-body M1 operator cannot excite the closed shell, strong cancellations are not seen in this case. The resulting 2M1 decay mode becomes competitive with the 2E1 decay, although it is still underestimated by the calculations.

Benchmark solutions for three-nucleon breakup amplitudes in {ital n}-{ital d} scattering have been produced by two groups separately using momentum space and configuration space techniques. These results have been obtained at two energies for both spin doublet and quartet configurations for an {ital s}-wave potential model and are in excellent agreement.

We examine the contributions of the off-mass-shell,s-wave πN scattering amplitude terms in the Tucson-Melbourne two-pion-exchange three-body force to the trion binding energy. While thea andc terms are not as important as thep-wave terms, they comprise a nonnegligible part of the three-nucleon force which produces nonperturbative effects in the triton wave function.

Calculations of the trinucleon S- and D-wave asymptotic normalization constants, with and without Coulomb effects, are extended to include all two-body partial waves up to j\ensuremath{\le}4 (34 three-body channels). Wave functions were generated with configuration-space, Faddeev-type equations for Hamiltonians based upon the two-body forces of Reid and the Argonne group, plus the Tucson-Melbourne and Brazilian model three-body forces. Comparison with previously published results is made. Results for ${C}_{S}$, ${C}_{D}$, \ensuremath{\eta}, and ${D}_{2}$ are interpolated as a function of binding to extract best estimates for $^{3}\mathrm{H}$ and $^{3}\mathrm{He}$. In agreement with our earlier (jl=1) calculations, we find that Coulomb effects increase the S-wave asymptotic normalization of $^{3}\mathrm{He}$ by less than 1% over that of $^{3}\mathrm{H}$ and that Coulomb effects decrease the D-wave asymptotic normalization of $^{3}\mathrm{He}$ relative to that of $^{3}\mathrm{H}$ by about 6%. The distorted-wave Born approximation D-wave parameter ${D}_{2}^{C}$ for $^{3}\mathrm{He}$ is almost identical to ${D}_{2}$ for $^{3}\mathrm{H}$. Finally, we predict the ratio of the the D-wave to S-wave asymptotic normalization constants to be \ensuremath{\eta}${(}^{3}$H)\ensuremath{\simeq}0.046 and ${\ensuremath{\eta}}^{C}$${(}^{3}$He)\ensuremath{\simeq}0.043. .AE

Exact theoretical expressions for calculating the trinucleon $S$- and $D$-wave asymptotic normalization constants, with and without Coulomb effects, are presented. Configuration-space Faddeev-type equations are used to generate the trinucleon wave functions, and integral relations for the asymptotic norms are derived within this framework. The definition of the asymptotic norms in the presence of the Coulomb interaction is emphasized. Numerical calculations are carried out for the $s$-wave $\mathrm{NN}$ interaction models of Malfliet and Tjon and the tensor force model of Reid. Comparison with previously published results is made. The first estimate of Coulomb effects for the $D$-wave asymptotic norm is given. All theoretical values are carefully compared with experiment and suggestions are made for improving the experimental situation. We find that Coulomb effects increase the $^{3}\mathrm{He}$ $S$-wave asymptotic norm by less than 1% relative to that of $^{3}\mathrm{H}$, that Coulomb effects decrease the $^{3}\mathrm{He}$ $D$-wave asymptotic norm by approximately 8% relative to that of $^{3}\mathrm{H}$, and that the distorted-wave Born approximation $D$-state parameter, ${D}_{2}$, is only 1% smaller in magnitude for $^{3}\mathrm{He}$ than for $^{3}\mathrm{H}$ due to compensating Coulomb effects.NUCLEAR STRUCTURE $^{3}\mathrm{H}$ and $^{3}\mathrm{He}$, asymptotic normalization constants, Coulomb effects, Faddeev calculations.

An alternative approach to the recent results of Krajcik and Foldy is presented which stresses a different point of view, but is completely equivalent to their results.NUCLEAR REACTIONS Relativistic corrections to wave functions.

Using a wide variety of newly obtained solutions to the Feddeev equations for the triton ground state with diverse two-body and three-body potentials, we have calculated Coulomb energies, RMS charge radii, binding energies, and probabilities of various wave function components. We show how the various radii scale with the corresponding binding energies, and advance simple arguments for the sizes of various wave function components. The Coulomb energies are compared to the hyperspherical approximation, which is found to be very accurate. In addition to our quantitative conclusions, we provide very simple qualitative arguments which account for these conclusions. Comparisons with experimental data are made where applicable.

Impulse approximation and isovector pion-exchange current contributions to the trinucleon magnetic moments are calculated using wave functions generated from solutions of the configuration-space form of the Faddeev equations for the Reid soft core, Argonne V/sub 14/, and super-soft-core C nucleon-nucleon force models and the Tucson-Melbourne or Brazilian three-nucleon force models. Numerical results for solutions with two-body partial waves having jless than or equal to4 (up to 34 channels) are reported. Agreement between theory and experiment appears reasonable for these nonrelativistic Hamiltonians which are restricted to one-pion exchange currents.

The role of the intrinsic nucleon size in a phenomenological treatment of photon absorption by a nucleus is discussed. It is suggested that the complete transition matrix element should be written as a product of the purely nuclear matrix element and the intrinsic nucleon form factor. The latter is written as a function, not of q/sup 2/ (the four-momentum transfer), but of q/sup 2/ + ..omega../sup 2/, where ..omega.. is the excitation energy of the nucleus. We note that for real photons where q/sup 2/ = 0 this is essentially equivalent to q/sup 2/, i.e., the three-momentum transfer.

Formulation of s-wave zero-energy Faddeev-type scattering equations including a Coulomb interaction is discussed. Numerical solutions of these equations for the s-wave NN potential models of Malfliet and Tjon are obtained using spline techniques. Kohn variational estimates are presented and comparison is made to previously published results. Our quartet pd scattering lengths are larger than others previously obtained, and our pd doublet results are smaller than the corresponding nd results, and thus in contrast to the experimental values. An explication of this feature is presented in terms of a model two-body problem. Perturbation theory for the Coulomb corrections to the scattering length is developed and confirms the Kohn estimates.

The triton ground-state wave function calculated using the Reid soft-core potential is displayed in configuration space. Both the S-state and D-state Schrodinger wave function components and the Faddeev amplitudes from which they are constructed are plotted. Specific features resulting from the tensor nature of the two-body force and from the strong short-range repulsion of the potential are discussed. Comparisons with corresponding functions generated by the Malfliet-Tjon s-wave potential model are made. Several intuitive features of the Schrodinger wave function are discussed.

Realistic wave functions are used to calculate threshold ..pi../sup +/ photoproduction from /sup 3/He in the impulse approximation. The effects of the D-state components, the Coulomb interaction in /sup 3/He, and the nuclear size on this cross section are investigated. In particular, it is argued that since realistic forces underbind and produce too large a radius, such model calculations should be expected to give (approximately 10 percent) too small a cross section. The resulting theoretical estimate is in reasonable agreement with experimental data.

An iterative technique was used to solve the Faddeev equations, which determine the bound state of the triton, for the Reid soft core, Argonne v/sub 14/, super soft core (C), and de Tourreil-Rouben-Sprung (B) potential models. Separate solutions for each model were generated for 5, 9, 18, 26, and 34 three-body channels, the latter corresponding to all two-nucleon partial waves with J 4 partial waves probably contribute less than 10 keV. Coulomb energies, radii, and probability percentages of various wave function components were also calculated.

Nonlocal contributions of order (1/m)/sup 2/ to the rho-..omega.. mixing charge-symmetry-breaking nucleon-nucleon force are derived, including several aspects not previously considered. Numerical results for scattering lengths and effective ranges are generated which indicate a slightly larger effect than that found recently by others. The relativistic aspects of this force and its relationship to the electromagnetic Breit interaction are developed. The total correction due to all the (1/m/sup 2/) terms is approximately 10%. We estimate that ..delta..E (Pu3He-/sup 3/H) = +40/sup +/45/sub -/15 keV is due to the rho-..omega.. force.

The effect of the proton-proton Coulomb interaction in the $^{3}\mathrm{He}$ ground state is investigated. The rms radii, first-order and second-order Coulomb energy shifts, the validity of the hyperspherical approximation, and the various trinucleon densities are examined.

The finite nuclear size corrections to the s-state energy levels of light muonic (or hydrogenic) atoms are calculated analytically through order (Zα)6. In addition to the usual expression of order (Zα)4, the (Zα)5, (Zα)6 and (Zα)6 log(Zα) contributions have been determined. These corrections have been separated into terms of nonrelativistic and relativistic orders. The results have been checked by solving perturbatively the exact eigenvalue equations of the Schroedinger and Dirac problems of a particle orbiting in the Coulomb field of a uniform charge distribution of fixed radius. Application is made to the case of the μ-4He atom. Finite-size contributions to the hydrogen Lamb shift and the relativistic recoil effect are briefly discussed.

The n-d and p-d s-wave scattering lengths are calculated for the spin-doublet configuration, including a three-nucleon potential in the Hamiltonian. Numerical results for the Reid-soft-core two-body potential plus the Tucson-Melbourne or Brazil three-body forces are presented. Comparison is made with Kohn variational estimates computed using the wave functions obtained by solving the Faddeev equations. Inclusion of the three-nucleon potentials does not alter our previous conclusions about the scattering lengths; all calculated Sa/sub nd/ and Sa/sub pd/ values lie on separate Phillips curves. The experimental value of Sa/sub nd/ lies on the n-d Phillips curve, while a considerable discrepancy remains for the p-d case.

It is shown that several two-body unitary transformations which arise in the theory of meson-exchange currents can change the percentage $D$ state of the deuteron, implying that this percentage is not a measurable quantity. The connection of these transformations to meson-exchange contributions to the quadrupole moment, rms radius, magnetic moment, and the asymptotic $\frac{D}{S}$ ratio of the deuteron is discussed.NUCLEAR STRUCTURE $^{2}\mathrm{H}$; $q$, $\ensuremath{\mu}$, $\ensuremath{\rho}$; meson-exchange currents; percent $D$ state.

The standard partial wave (channel) representation for the Faddeev solution to the Schroedinger equation for the ground state of 3 nucleons is written in terms of functions which couple the interacting pair and spectator angular momenta to give S, P, and D waves. For each such coupling there are three terms, one for each of the three cyclic permutations of the nucleon coordinates. A series of spherical harmonic identities is developed which allows writing the Faddeev solution in terms of a basis set of 5 bipolar harmonics: 1 for S waves; 1 for P waves; and 3 for D waves. The choice of a D-wave basis is largely arbitrary, and specific choices correspond to the decomposition schemes of Derrick and Blatt, Sachs, Gibson and Schiff, and Bolsterli and Jezak. The bipolar harmonic form greatly simplifies applications which utilize the wave function, and we specifically discuss the isoscalar charge (or mass) density and the /sup 3/He Coulomb energy.

The deuteron photodisintegration with forwardgoing proton is calculated using a new formalism for organizing matrix elements. Relativistic effects are thoroughly discussed. Different ways of calculating retarded electric multipoles are investigated. Meson exchange currents are included in various approximations. The spin-orbit dipole operator is found to dominate the relativistic corrections.

Eikonal expansions are developed for the equivalent cases of the Dirac equation with scalar and vector potentials and the Schroedinger equation with central and spin-orbit potentials. Second-order corrections to the Glauber approximation are developed. Numerical calculations relevant to proton-nucleus elastic scattering illustrate that the sequence of eikonal amplitudes converge to the Dirac amplitudes in the 300--800 MeV range considered and for forward scattering angles 0/sup 0/< or =theta/sub c.m./< or approx. =40/sup 0/.

Monte Carlo integrations for binding energy and other expectation values in 3H and 3He using configuration-space Faddeev wavefunctions are reported. Nine combinations of two- and three-nucleon potentials are tested, several givin a significant contribution of ∼ Mev to the binding energies from the three-nucleon potentials. The energy contribution of the three-nucleon potential is found to be very sensitive to form factor parameters and to small components of the Faddeev wavefunction. The influence of the three-nucleon potential on the wavefunction is investigated using a simple one-parameter variation of the Faddeev wavefunction.

Various methods of removing the c.m. coordinate from single-particle wave functions are discussed. A non-unitary generalization of the Gartenhaus-Schwartz transformation is shown to incorporate both of the common methods for constructing translation-invariant wave functions as limiting cases. Using a simple single-particle model density for 4 He a family of charge form factor curves is generated. It is shown that two-body correlations may be sensitive to the procedure used to remove the c.m. coordinate from the problem.

Two recent papers are shown to be related, and the unifying ingredient is an energy-dependent Hamiltonian. (AIP)

The Faddeev equations in N space dimensions for three identical spinless particles in their ground state interacting via harmonic oscillator, two-body potentials is solved analytically. Unlike the well-known Schroedinger solution, the individual Faddeev amplitudes may be negative and contain a long-range component of arbitrary strength. Upon symmetrizing to obtain the full wave function, this component vanishes and the Schroedinger solution results. Three-dimensional plots of the various wave functions are presented.

Because of their purely electromagnetic interaction, charged leptons provide the most precise probe of the nuclear many-body wave function presently available. Although, in principle, precise scattering data for e +, e -, μ, +, and μ -, and bound-state energy levels for e - and μ - could provide a wealth of complementary information, in practice the most useful information presently arises from muonic X-rays in medium and heavy nuclei and from electron scattering data. The challenge to which this present review is addressed is to utilize the available information from muonic X-rays and elastic electron scattering as a tool to critically test our present theoretical understanding of the nuclear wave function.

Trinucleon charge densities and charge form factors are calculated in impulse approximation for a large set of wave functions obtained from solving the Faddeev equations for diverse combinations of four two-body force models and three three-nucleon force models. The three-nucleon forces improve the form factor predictions in the region of the secondary maximum slightly, but the experimental data are still substantially higher than the theoretical predictions, while the positions of the theoretical first diffraction minimum and secondary maximum are too high.

Impulse approximation and pion-exchange current contributions to the trinucleon magnetic moments are calculated using wave functions generated by solving the configuration-space Faddeev equations for a variety of nucleon-nucleon force models. Careful attention is paid to the origin of important exchange current contributions. Numerical results are compared with previously published calculations and with the experimental data. An attempt is made to isolate and understand sources of discrepancy between our results and those previously published. Calculations which include both impulse and pion-exchange current contributions are in fairly good agreement with experiment, whereas calculations which include only the impulse approximation term are not.