Relativistic effects in the 3N continuum and the A y puzzle

The three-nucleon (3N) Faddeev equation is solved in a Poincaré-invariant model of the three-nucleon system. Two-body interactions are generated so that when they are added to the two-nucleon invariant mass operator (rest energy) the two-nucleon S-matrix is identical to the non-relativistic S-matrix with a CD Bonn interaction. Cluster properties of the three-nucleon S-matrix determine how these two-nucleon interactions are embedded in the three-nucleon mass operator. Differences in the predictions of the relativistic and corresponding non-relativistic models for elastic and breakup processes are investigated. Of special interest are the lowering of the A _y maximum in elastic nucleon-deuteron (Nd) scattering below ≈25?MeV caused by the Wigner spin rotations and the significant changes of the breakup cross sections in certain regions of the phase space.     

Off-energy-shell variations of two-nucleon transition matrix and three-nucleon problem

For a schematic three-nucleon problem, we derive approximate analytic expressions for the functional derivatives of measurable three-particle quantities with respect to off-shell variations of the triplet-s, two-nucleon transition matrix. Those quantities include neutron-deuteron scattering lengths, trinucleon binding energies, and the ³He charge form-factor minimum; correlations between off-shell changes in the latter two are discussed. We indicate how results of this kind may be used to decide whether or not a given set of discrepancies between calculated and experimental three-nucleon observables can be reconciled in terms of off-shell variations of a nonretarded hermitean two-nucleon interaction. The treatment is not restricted to special classes of phase-shift equivalent potentials or phase-shift preserving transformations but instead makes use of a systematic parameterization of off-shell variations in terms of symmetric rational approximants of increasing order.     

Trinucleon properties with one-boson-exchange potentials

The Faddeev equations are solved for two OBE potentials, HMl and EHM′. The two potentials differ primarily by the fact that HMl fits the¹ S ₀ n-p scattering data, while EHM′ fits the¹ S ₀ low-energy parameters of the Reid soft-core (RSC) potential. They give essentially identical values for the³ S ₁?³ D ₁ physical observables. The triton binding energy (E _T) and the³He charge form factor (CFF) are calculated for each OBE potential and compared with those of the RSC potential. Listed in the order (RSC, EHM′, HMl), the results forE _T are (7.0, 7.2, 7.5) MeV, while the positions of the minimum of the CFF areQ _MIN ² =(13.9, 15.3, 15.5) fm^?2. The two OBE potentials give increased binding in the triton, while simultaneously increasingQ _MIN ² .     

A test of a model t-matrix for direct reaction inelastic scattering

Differential cross sections and analyzing powers from the inelastic scattering of 65 MeV protons leading to the 1⁺T=0 (12.71 MeV) and 1⁺T = 1 (15.11 MeV) states in ¹²C have been analysed as tests of a model two-nucleon t-matrix.     

Variational calculations of asymmetric nuclear matter

We report on variational calculations of the energy E(ρ, β) of asymmetric nuclear matter having ? = ?_n + ?_p = 0.05 to 0.35 fm^?3, and β = (?_n ? ?_p/g9 = 0 to 1. The nuclear h used in this work consists of a realistic two-nucleon interaction, called v₁₄, that fits the available nucleon-nucleon scattering data up to 425 MeV, and a phenomenological three nucleon interaction adjusted to reproduce the empirical properties of symmetric nuclear matter. The variational many-body theory of symmetric nuclear matter is extended to treat matter with neutron excess. Numerical and analytic studies of the β-dependence of various contributions to the nuclear matter energy show that at ? < 0.35 fm^?3 the β⁴ terms are very small, and that the interaction energy EI(ρ, β) defined as E(ρ, β) ? T_F(ρ, β), where T_F is the Fermi-gas energy, is well approximated by EI₀(?) + β²EI₂(ρ). The calculated symmetry energy at equilibrium density is 30 MeV and it increases from 15 to 38 MeV as ? increases from 0.05 to 0.35 fm^?3.     

The deuteron wave function at short range and the triton

It is shown that if one assumes something between zero and the prediction of the scaling model with dipole fit for the neutron electric form factor, then a variety of short-range behaviour for the deuteron wave function is consistent with existing experimental data on the deuteron electric form factor. This still relatively wide latitude for the inner deuteron wave function, consistent with existing experimental electromagnetic data, gives rise to an off-shell variation of approximately 1.2 MeV in the triton binding energy with a fixed ¹S₀ interaction and a P_D varying from 4.5 to 6.5 %. Interactions with greater densities of matter at short range bind the triton more strongly and closer to the experimental value. An off-shell variation of 0.7 MeV is obtained with a fixed p_d and singlet interaction. However, a single measurement of the deuteron tensor polarization at about q² = 20 fm^?2 would severely restrict this variation.     

Three-nucleon interaction in 3-, 4- and ∞-body systems

We report results of variational calculations of ³H, ³He, ⁴He and nuclear matter with the Urbana v₁₄ two-nucleon interaction and realistic models of the three-nucleon interaction (TNI). These include the Tucson and isobar intermediate-state models of the two-pion exchange TNI. The latter is also studied with an intermediate-range three-nucleon repulsion. In general, realistic TNI helps to bring the theory closer to experiment by giving extra binding energy to the A = 3 and 4 nuclei and providing extra saturation to the nuclear matter binding energy. The Coulomb energy of ³He and the rms radii of A = 3, 4 nuclei are also well described. However, some problems remain unresolved. There is a slight overbinding of ⁴He, an underbinding of nuclear matter, and the charge form factors of ³He and ⁴He, calculated with impulse approximation, deviate from the experimental at q²>5 fm^?2.     

Relativistic Effects in Neutron�CDeuteron Elastic Scattering and Breakup

We solved the Faddeev equation in a Poincaré invariant model of the three-nucleon system. Two-body interactions are generated so that when they are added to the two-nucleon invariant mass operator (rest energy) the two-nucleon S matrix is identical to the experimental S matrix modeled with a given nucleon?Cnucleon interaction. Cluster properties of the three-nucleon S-matrix determine how these two-nucleon interactions are embedded in the three-nucleon mass operator. Differences in the predictions of the relativistic and corresponding non-relativistic models for elastic and breakup processes are investigated. Of special interest are effects of relativity on the elastic scattering angular distribution and total cross sections, the lowering of the A _y maximum in elastic nucleon-deuteron (Nd) scattering below ??25?MeV caused by the Wigner spin rotations and the significant changes of the breakup cross sections in certain regions of the phase-space.     

A coordinate-space study of kowalski's three-term separable approximation for the fully off-shell two-nucleon T-matrix

Using elementary coordinate-space methods, we show that a three-term separable approximate fully off-shell T-matrix proposed by Kowalski can be reduced to a simpler expression. This T-matrix incorporates off-shell unitarity exactly, is exact half off the energy shell, and is free from the spurious poles that arise in the Noyes approximation. However, numerical tests employing the wave-function model of Picker, Redish, and Stephenson show that for realistic ¹S_o interactions, the Noyes approximation is more accurate than Kowalski's approximation except near the spurious pole at 250 MeV. We give a plausible explanation of this result.     

A constraint on the off-shell effective range parameter in p-p scattering

Sauer has recently proposed fixing the zero-energy ¹S₀ state wave function as a means of constraining the off-shell behaviour of the N-N interaction. We propose as an alternative that the value of the off-shell effective range parameter I₀ be constrained. A value of I₀ = 13 ± 1 fm³ seems to be indicated if charge symmetry is required.     

Momentum-space calculations for three-nucleon scattering including a three-nucleon force

The formalism to include a three-nucleon force into three-nucleon continuum calculations is presented. First numerical results, obtained in momentum space, are shown. The two- and three-nucleon forces have been restricted to act only in the¹ S ₀ and³ S ₁-³ D ₁ partial-wave states. As two-nucleon interaction the Bonn-B potential and as three-nucleon interaction the Tucson-Melbourne two-pion exchange model has been used.     

Two-nucleon production of hyperons and the search for strange dibaryons

The double charge exchange reaction³He(K^?,π ⁺)Xn was studied at 870 MeV/c. In the X missing mass range below the sigma-nucleon production threshold (2130 MeV/c²), events were detected which can be attributed to the two-nucleon process pp(K^?,π ⁺)λn. This reaction and mass range also offers good prospects for finding theI=1/2,l=1 (¹ P₁) spin-singlet dibaryon D_s suggested as the lowest massS=?1 dibaryon in the MIT Bag Model. Although the existence of the D_s is not ruled out by the present data, there is no need to invoke such an object to account for the observed events below σ production threshold. We show that the cross section level for these events is compatible with a dominant two-nucleon mechanism K^?p→π ⁰λ,π ⁰p →π ⁺n. We also offer an interpretation of the recent (K^?,K⁺) data on nuclear targets from Iijimaet al., which display a broad peak centered around a K⁺ momentum of 600 MeV/c. We find that the two-nucleon mechanism K^?N →πY,πN→K⁺Y produces cross sections which are at least an order of magnitude smaller than those observed, and we suggest that the one nucleon process K^?p →Φλ, followed by the decayΦ → K⁺K^?, accounts for the data.     

Parametrization of the 1S0 two nucleon transition matrix

The ¹S₀ two-nucleon transition matrix T is constructed from the symmetric part σ of its half-shell elements. The on-shell component of σ is given by the phase shift, while a wide class of parametrizations is suggested for the off-shell part. Restrictions on the off-shell part of σ arising from the short range and the proper one-pion-exchange tail of the nucleon-nucleon interaction are investigated. Using σ in the ¹S₀ and the Reid soft-core potential in the other partial waves, the binding energy per particle in nuclear matter and ¹⁶O and the ¹⁸O shell-model spectrum are computed. The sensitivity of these nuclear-structure results is tested with respect to (i) smooth off-shell changes in σ, (ii) various assumptions on the high-energy phase shift, (iii) the charge dependence of the phase shift, and (iv) experimental uncertainties in the phase shift.     

Variational calculations of realistic models of nuclear matter

We report variational calculations of nuclear matter with a semi-realistic Reid v₁₂ model, and a realistic v₁₄ model of the two-nucleon interaction operator. The v₁₄ model fits the available nucleon-nucleon scattering data up to 425 MeV lab energy, and has relatively weak L² and $\text{(}\text{L}\text{·}\text{S}\text{)}{}^2$ interactions in addition to the standard central, tensor and ($\text{L}\text{·}\text{S}$). The L² and $\text{(}\text{L}\text{·}\text{S}\text{)}{}^2$ interactions are treated semiperturbatively; their contribution reduces the overbinding of nuclear matter. However, the equilibrium k_F = 1.7 fm^?1 and E₀ = ?17.5 MeV obtained with the v₁₄ model are both higher than their empirical values k_F = 1.33 fm^? and E₀ = ?16 MeV. We assume that the difference between the calculated and empirical E(ρ) is entirely due to three-nucleon interactions (TNI). The TNI contributions are phenomenologically added to the nuclear matter energy, and their parameters are adjusted to obtain the correct equilibrium energy, density and compressibility. The required TNI contributions appear to be of reasonable magnitude.     

The boundary condition approach to nucleon-nucleon potentials and the calculation of the T- and K-matrices

It has been shown that the off-shell T- and K-matrices can be obtained by means of boundary conditions imposed upon the off-shell wave function only. When there is a potential outside the boundary condition radius the method proposed permits to deduce in a rather simple way a renormalized Lippmann-Schwinger equation. The S-components of the T- and K-matrices are considered in detail using a potential of the exponential type in the exterior region. For such types of potentials a rather effective method for factorizing the K-matrix is given. Parameter fits to the ¹S₀ and ³S₁ phases are presented.     

Study of electric monopole transitions between the ground state and the first excited 0+ state in 40, 42, 44, 48Ca with high resolution inelastic electron scattering

Monopole transitions from the 0₁⁺ ground states to 0₂⁺ excited states at 3.353 MeV (⁴⁰Ca), 1.837 MeV (⁴²Ca), 1.884 MeV (⁴⁴Ca) and 4.272 MeV (⁴⁸Ca) have been investigated with high resolution inelastic electron scattering (FWHM ≈ 30 keV) at low momentum transfer (0.29 ≦ q ≦ 0.53 fm^?1). The respective monopole matrix elements are 2.53 ± 0.41 fm², 5.24 ± 0.39 fm², 5.45 ± 0.41 fm² and 2.28 ± 0.49 fm². These results are used together with known ground state charge radii and the average number of holes in the sd shell in the ground state to estimate the number of particle-hole excitations in the wave functions of the excited 0⁺ states.     

Analyzing power measurements for p-3He elastic scattering from 1.75 to 4.50 MeV

Analyzing powers for p-³He elastic scattering have been measured at 12 energies between 1.75 and 4.50 MeV for θ_c.m. = 40° to 150°. A comparison of our results with earlier data of Drigo et al. shows substantial differences at all energies. The R-matrix fits to our data that were included in the global search calculations of Hale and Dodder are shown. These calculations established the ordering of the lowest-lying T = 1 levels of ⁴He as J^π = 2^?, 1^? (triplet), 0^?, and 1^? (singlet), which is the WMI (MHI) ordering.     

The 12+ state of 3H and 3He below the break-up threshold: (II). Gammel-Brueckner potential

Results for the $\text{J}{}^{\mathrm{\pi }}\text{=}\text{1}\text{2}{}^{\mathrm{+}}$ state of ³H and ³He using the Gammel-Brueckner (GB) nucleon-nucleon potential are presented. Comparison is made with the predictions of the Hamada-Johnston (HJ) potential for bound-state properties and N-d scattering. Whilst the GB potential gives an ³He binding energy at ?7.75 MeV which is close to experiment, the Coulomb energy still remains low. The minimum in the electron scattering charge form factor is in worse agreement with experiment than HJ whilst the secondary maximum shows insufficient enhancement over the HJ results. The N-d doublet scattering length is closer to experiment than the results for HJ but there still appears to be a discrepancy with experiment. These results partially support the suggestion that a two-nucleon potential of HJ type with a larger hard-core radius than HJ, but fitted to a smaller deuteron D-state probability, may give a reasonable representation of the three-nucleon data apart from the Coulomb energy. Evidence now appears strong from this latter parameter for a small charge asymmetry in the two-nucleon potential.     

Parametrization of the S0 two nucleon transition matrix

The ¹S₀ two-nucleon transition matrix T is constructed from the symmetric part σ of its half-shell elements. The on-shell component of σ is given by the phase shift, while a wide class of parametrizations is suggested for the off-shell part. Restrictions on the off-shell part of σ arising from the short range and the proper one-pion-exchange tail of the nucleon-nucleon interaction are investigated. Using σ in the ¹S₀ and the Reid soft-core potential in the other partial waves, the binding energy per particle in nuclear matter and ¹⁶O and the ¹⁸O shell-model spectrum are computed. The sensitivity of these nuclear-structure results is tested with respect to (i) smooth off-shell changes in σ, (ii) various assumptions on the high-energy phase shift, (iii) the charge dependence of the phase shift, and (iv) experimental uncertainties in the phase shift.