Analysis of scattering and reactions of aligned7Li-nuclei in a double folding model

Previously measured angular distributions of the differential cross section and the tensor analyzing powerT ₂₀ for the scattering of⁷Li from⁵¹V in the energy range from 10 to 18 MeV were analyzed with the double folding model using the effective nucleon-nucleon interaction M3Y as well as a zero range effective nucleon-nucleon interaction. Due to the spectroscopic deformation of the⁷Li-nucleus the interaction potential contains a central and aT _R -tensor part. The latter one is the origin of the observed tensor analyzing powers. Within the same model the scattering of aligned⁷Li-nuclei from⁵⁸Ni at 14.2 and 20.3 MeV is well described. The strength of theT _R -tensor potential in relation to the spectroscopic mass deformation of⁷Li is discussed. Using the real interaction potential obtained by the double folding model the energy dependence of the total reaction cross sectionσ ^r and its tensor analyzing powerT ₂₀ ^r for the system⁷Li?⁵¹V is well described within a barrier penetration model.     

Effective pairing interaction for the Argonne nucleon-nucleon potential v<Subscript>18</Subscript>

The effective pairing interaction corresponding to the Argonne nucleon-nucleon potential v₁₈ is found within the local potential approximation for several values of the boundary energy E ₀ that specifies the model subspace S ₀. A detailed comparison with the analogous effective interaction calculated previously for the Paris nucleon-nucleon potential is performed. It is shown that the effective interactions obtained for the two different nucleon-nucleon potentials at the same value of E ₀ are very close to each other. In the case of the Paris potential, a very wide subspace S′ complementary to S ₀ was required in calculating the effective interaction (the corresponding cutoff momentum being k _max = 160?180 fm^?1), whereas a much narrower subspace S′ corresponding to k _max = 10?12 fm^?1 could be used in the case of the Argonne potential.     

Constructing effective nucleon-nucleon interaction on the basis of the Idaho potential

An effective nucleon-nucleon interaction at an energy of 200 MeV is constructed for the Idaho nucleon-nucleon potential obtained on the basis of the theory of spontaneous chiral-symmetry breaking. This interaction approximates the nonlocal t matrix obtained for free nucleon-nucleon scattering from a solution to the Lippmann-Schwinger equation for the Idaho potential. The exact and approximated t matrices for the Paris potential, Idaho potential, and the von Geramb Hamburg potential are compared. The effective potential obtained in the way outlined above is used to calculate the inelastic scattering of 200-MeV polarized protons that is accompanied by the excitation of the 2⁺ level at 4.44 MeV and the 1⁺ level at 15.11 MeV in the ¹²C nucleus and the 6^? level at 14.1 MeV in the ²⁸Si nucleus. The results are compared with the results of the calculations on the basis of the Paris potential.     

Analytic approach to the problem of constructing effective nucleon-nucleon potentials in the region of low and intermediate energies

A new relativistic approach to the problem of constructing effective local hadron-hadron potentials is proposed on the basis of analytic S-matrix theory and Gelfand-Levitan-Marchenko-Martin methods for solving the inverse quantum scattering problem. An effective potential is defined as a local operator in a partial-wave equation of the quasipotential type such that it generates an on-shell relativistic (Feynman) scattering amplitude that has required discontinuities at dynamical cuts. The method is used to construct nucleon-nucleon potentials in the ¹ S ₀-and ³ S ₁-wave states. The dynamical discontinuities of partial-wave amplitudes for nucleon-nucleon scattering are calculated on the basis of the one-bosonexchange model that takes into account the exchanges of π, σ, ρ, ω, η, and α ₀ mesons. It is shown that the nonlinear relation between the discontinuities of partial-wave scattering amplitudes at dynamical cuts and interaction operators generates additional short-range repulsion not associated with omega-meson exchange. The experimental energy dependences of phase shifts in the channels of nucleon-nucleon scattering that are considered here are faithfully reproduced by the results of the calculations up to the projectile-nucleon kinetic energies in the range T = 1.5–2.0 GeV.     

On the nuclear interaction potential in the reactions with heavy ions

The interaction potential of heavy ions⁴He,⁶Li,¹²C and¹⁶O is constructed in the folding model. The density distribution of nuclear matter for these nuclei is calculated in the framework of the hyperspherical function method. For the calculation of the folding potentials we have employed the Skyrme nucleon-nucleon forces. The influence of several effects on the results of calculations is studied: the role of the three-body forces of the nucleon-nucleon interaction, dependence of the folding potential on the mass numbers of the colliding nuclei and the possibility of observing the monopole resonance in the ion inelastic scattering. Using our folding potential as a real part of the optical potential we have calculated the differential cross section of elastic scattering of⁶Li from¹²C at laboratory energy of lithium ionsT _L =90.0 MeV. Reasonable agreement with experiment is obtained.     

Testing effective nucleon-nucleon forces to describe diagonal spin-transfer coefficients for the scattering of polarized protons with the excitation of the 1+ levels in 12C

The diagonal coefficients of spin-transfer D _ii in the small-angle inelastic scattering of polarized protons with the excitation of the two lowest 1⁺ levels in ¹²C are analyzed. The isoscalar (T = 0, E* = 12.71MeV) and isovector (T = 1, E* = 15.11 MeV) transitions are considered. The coefficients D _ii are calculated within DWBA using different effective nucleon-nucleon (NN) interactions between an incident proton and the nucleons of the nucleus. We consider the Franey-Love interaction and the Geramb effective interactions based on the Paris NN potential, and also the effective NN potential based on the chiral perturbation theory, etc. The impact of the wave function antisymmetrization is studied from the coefficients D _ii in a system that includes a projectile and nucleons of the nucleus, along with the impact of other effects.     

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.     

Simple microscopic model for the scalar-isoscalar component of the Landau-Migdal amplitude

A simple microscopic model is proposed that describes the coordinate dependence of the zeroth harmonic f ₀(r) of the scalar-isoscalar component of the Landau-Migdal amplitude. In the theory of finite Fermi systems due to Migdal, such a dependence was introduced phenomenologically. The model presented in this study is based on a previous analysis of the Brueckner G matrix for a planar slab of nuclear matter; it expresses the function f ₀(r) in terms of the off-mass-shell T matrix for free nucleon-nucleon scattering. The result involves the T matrix taken at the negative energy value equal to the doubled chemical potential μ of the nucleus being considered. The amplitude f ₀(r) found in this way is substituted into the condition that, in the theory of finite Fermi systems, ensures consistency of the self-energy operator, effective quasiparticle interaction, and the density distribution. The calculated isoscalar component of the mean nuclear field V(r) agrees fairly well with a phenomenological nuclear potential. Owing to a strong E dependence of the T matrix at low energies, the potential-well depth V(0) depends sharply on μ, increasing as |μ| is reduced. This effect must additionally stabilize nuclei near the nucleon drip line, where μ vanishes.     

Schiff moment of the mercury nucleus and the proton dipole moment

The Schiff moment of the ¹⁹⁹Hg nucleus is calculated using finite range P-and T-violating weak nucleon-nucleon interaction. Both the contributions of the P-and T-odd interaction and of internal nucleon electric dipole moments to the Schiff moment of ¹⁹⁹Hg are calculated. The contribution of the proton electric dipole moment is obtained via core-polarization effects treated in the framework of RPA with effective residual interactions. We derive a new upper bound |d _p |<5.4×10^?24e cm for the proton electric dipole moment.     

Simulation of the Pauli-principle effects in the description of light ion scattering and bound states

A simple model which takes care phenomenologically of the effects of the Pauli principle is proposed to calculate, in the framework of the resonating group method, bound and scattering states of nuclear systems comprised of two light nuclei (n, t and α-particles) without performing a complete antisymmetrization of the wave functions. Retaining only the antisymmetrization between the nucleons belonging to a given cluster, the contributions of the terms corresponding to the exchange of two nucleons belonging to two different clusters are simulated by the matrix elements of an effective central, local, l-dependent, energy-independent nucleon-nucleon potential. The lowenergy levels of ⁸Be and ⁷Li as well as the phase shifts for l = 0 to 4 for energies below 10 MeV (c.m.) have been calculated with this effective potential (added to the regular nucleon-nucleon potential). Good agreement between exact and model calculations is achieved.     

The role of iterative isobar processes in nuclear matter and the effective nucleon-nucleon interaction

A calculation is performed using lowest order Brueckner theory in momentum space, with explicit isobar configurations included through the coupled channel mathod. The effective interaction for the¹ S ₀-⁵ D ₀ channel is extracted from this calculation. Two different transition potentials are used — one due to Green and Niskanen (1976), the other, due to Green and co-workers (1978). The nucleon-nucleon (NN) interaction used is the Reid soft core potential, compensated for the inclusion of the explicit isobar channel. The effective interaction shows marked momentum dependence in the intermediate range. The loss of attraction depends on the transition potential one chooses. The correlation function involving the nucleon-isobar intermediate state is anti-correlated to the NN part.     

Surface and volume contributions to real and imaginary parts of the heavy-ion optical potential

Starting from the Feshbach expression for the optical potential, explicit formulae for the real and the imaginary parts of the optical potential between two heavy ions (HI's) are obtained. They are each composed of a volume and a surface term. The contributions to the volume term are calculated in two nuclear Fermi liquids which flow through each other starting from the realistic Reid soft core nucleon-nucleon (NN) interaction. Since the Fermi surface is formed by two spheres one obtains a complex Brueckner reaction matrix which is approximated by a complex, effective local interaction. It is used in a fully antisymmetrized double folding procedure to obtain the volume terms of the optical potential between the two HI's. The surface contributions are directly calculated in the collision of the two finite HI's. The collective surface vibrations (3^? octupole state and 2⁺, 4⁺ (T = 0) giant resonances for the ¹⁶O?¹⁶O collision) are included as intermediate states. This yields especially an imaginary contribution at the surface which reduces the transparency found with the volume terms alone. The method is applied to ¹⁶O?¹⁶O scattering at 83 and 332 MeV laboratory energy. The local approximations to the real and imaginary parts obtained in this way agree well with phenomenological fits. The surface terms improve the agreement of the differential cross section at 80 MeV where experimental data are available.     

Parity non-conservation in low energy scattering of nucleons by light nuclei: (I). Theoretical framework

The low energy scattering of nucleons by ²H, ³He and ⁴He are analyzed for parity non-conserving effects. The asymmetry in the total cross section of longitudinally polarized projectiles is formulated in terms of the optical theorem and a distorted wave Born approximation. For two nucleons at low energies it is only necessary to consider l = 0 to l = 1 matrix elements of the weak nucleon-nucleon potential. The asymmetries in the scattering from nuclear targets are related to the parameters of an effective weak nucleon-nucleon potential, so that they may be used to help differentiate between various proposed theoretical potentials.     

The properties of nuclear matter at zero and finite temperatures

The properties of nuclear matter are studied in the frame of the Brueckner theory. The Brueckner-Hartree-Fock approximation plus two-body density-dependent Skyrme potential which is equivalent to three-body interaction are used. Various modern nucleon-nucleon potentials are used in the framework of the Brueckner-Hartree-Fock approximation, e.g.: CD-Bonn potential, Nijm1 potential, and Reid 93 potential. These modern nucleon-nucleon potentials fit the deuteron properties and are phase shifts equivalent. The equation of state at T = 0, pressure at T = 0, 8, and 12 MeV, free energy at T = 8 and 12 MeV, nuclear matter incompressibility, and the symmetry energy calculation are presented. The hot properties of nuclear matter are calculated using T ²-approximation method at low temperatures. Good agreement is obtained in comparison with previous theoretical estimates and experimental data, especially at low densities.     

Potential pockets in the238U+238U system and their possible consequences

Within the double-folding model the separation, shape, and orientation dependence of the interaction potential is studied for two heavy ions. An effective nucleon-nucleon interaction (M3Y) derived fromG-matrix elements and based upon the Reid soft-core potential is used. Deformed Fermi-type matter densities with static quadrupole and hexadecapole deformations were utilized. The model is applied to the²³⁸U+²³⁸U system and shows dramatic dependence on the deformations and orientations.     

A density expansion of the pion-nucleus optical potential. II. Second order terms

The second order terms in a density expansion of the pion optical potential V_opt are evaluated quantitatively. The coefficients of these terms are proportional to various combinations of on- and off-shell nucleon-nucleon T-matrices, averaged over the distribution of two nucleon relative momenta in the Fermi sea. The on-shell contributions can be obtained directly from experimental phase shifts, but the calculation of the off-shell-parts requires a model for the nucleon-nucleon potential. We consider a number of realistic local and nonlocal, separable potentials which fit nucleon-nucleon phase shifts, in order to study the variations in V_opt which arise from differences in the off-shell behavior of T. We find absorptive (imaginary) and dispersive (real) contributions to V_opt which are of comparable magnitude. The dispersive part, which leads to a real energy shift associated with the two nucleon absorptive process, has not been previously estimated quantitatively. We compare our results to empirical potentials obtained by fitting energy level shifts and widths in pi-mesic atoms, as well as theoretical estimates based on threshold cross sections for the processes π + N + N ? N + N.     

<Emphasis Type="Italic">P</Emphasis>-and <Emphasis Type="Italic">T</Emphasis>-violating Schiff moment of the mercury nucleus

The Schiff moment of the ¹⁹⁹Hg nucleus was calculated using finite-range P-and T-violating weak nucleon-nucleon interaction. Effects of the core polarization were considered in the framework of RPA with effective residual forces.     

Meson exchange effects in thermal n-p radiative capture

It is shown that the meson exchange contributions to the n-p radiative capture matrix element are nearly independent from the nucleon-nucleon potential model. The resulting interaction effect, including the N₃₃¹ contribution calculated by Stranahan, is ～ 9%.     

The transverse electron scattering response function of 3He

Results on the transverse response function R _T (q,ω) of ³He obtained within the Lorentz integral transform [LIT] [1] method are presented. The response is calculated using the BonnRA nucleon-nucleon potential [2], the Tucson-Melbourne [3] three-body force, and the Coulomb potential for various momentum transfers. The results are compared with available data.