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.     

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.     

Microscopic calculation of the repulsive core in the elastic nucleon-nucleon scattering

The resonating group method is used to study the effective potential between two nucleons, due to the confining potential between quarks taken together with the Pauli principle for quarks. The potential used has harmonic form, unitary spin factor λ(1)·λ(2), and both ordinary and spin-spin components. Its parameters are determined by appeal to experimental data, and phase shifts are calculated for the¹ S ₀ and³ S ₁ states of the nuncleon-nucleon (NN) system. The results indicate that the repulsive core in theNN potential may arise from quark antisymmetrization required if nucleons are composed of quarks.     

Approximation of the microscopic effective pairing interaction by the off-shell T matrix for free nucleon-nucleon scattering

The effective pairing interaction in the ¹ S ₀ channel as calculated microscopically within the Brueckner method for a planar slab of nuclear matter by using the separable version of the Paris nucleon-nucleon potential is investigated. The effective interaction is determined for the model space including all negative-energy single-particle states. An analysis is performed for two values of the chemical potential, μ=?8 and ?4 MeV. It is shown that, to a high precision, the effective interaction can be approximated by the off-shell T matrix for free nucleon-nucleon interaction, the T matrix in question being taken at a negative value of the total energy of two nucleons E=2μ.     

Analysis of α-7Li elastic and inelastic scattering at low energy with a simple model of the pauli principle effects

The elastic and inelastic scattering of α on ⁷Li are calculated at different low energies in the framework of the resonating group method in which the ⁷Li is supposed to be comprised of two clusters, α and t. To reduce the time of calculation, the effects of the Pauli principle due to the exchange of two nucleons belonging to two different clusters are approximated with an effective nucleon-nucleon potential which has been determined previously in order to reproduce correctly the scattering and bound states of the nuclear systems comprised of two particles, 2α or α + t. This calculation takes into account the exchange of the incoming a with the a belonging to ⁷Li as well as the coupling with the ⁸Be + t channel. Without any free parameter, the model calculation reproduces correctly the main features of the experimental data when the projectile energy is less than 5 MeV (lab). It appears that the coupling with the ⁸Be + t channel cannot be neglected.     

Role of antisymmetrization in describing the excitation of the 1+, T = 1 level in the 12C nucleus by polarized protons

Inelastic polarized-proton scattering involving the excitation of the 1⁺, T = 1 level at 15.11 MeV in the ¹²C nucleus is described within the distorted-wave method. The effect of completely or approximately taking into account the antisymmetrization of the wave function for the projectile proton-intranuclear nucleons system on various observables, including the differential reaction cross section, the analyzing power, the difference of the polarization and analyzing power, and the depolarization parameter, is analyzed. The difference of the polarization and the analyzing power in the case of the excitation of anomalous-parity levels is shown to be especially sensitive to taking into account the above antisymmetrization. The reason for a large value of this difference for the level being studied and the sensitivity of this value to the parameters of the effective nucleon-nucleon interaction used are analyzed.     

The energy dependent nucleus-nucleus optical potential in a nuclear matter approach

We calculated the energy dependent real and imaginary part of the nucleus-nucleus optical potential in a lab. energy domain between 50MeV and 225MeV per nucleon for the systems¹²C-¹²C and⁵⁸Ni-⁵⁸Ni. In our model we assume that the energetical behaviour of the colliding nucleons inside of the two overlapping nuclei is locally that of two colliding nuclear matter systems. Therefore the effective nucleon-nucleon interaction is calculated using a Bethe-Goldstone equation that includes the Pauli blocking caused by the two Fermi spheres and takes account of the presence of the other nucleons by their mean field. Neglecting finite range effects one can calculate the real and imaginary part by a folding procedure.     

Short-range correlations with pseudopotentials. IV

Using a unitary model operator, the short-range correlations between nucleons in nuclei have been considered. To achieve healing in the wave functions, short-range pseudopotentials are required to be added to the nucleon-nucleon potential. With the introduction of the pseudopotentials, the matrix element for the effective interaction in nuclei is developed with correlated basis wave functions. The tensor forces and the short-range pseudopotentials are renormalized in second-order perturbation theory. Hartree-Fock calculations are carried out for the two finite closed-shell spherical nuclei¹⁶O and⁴⁰Ca. The calculations of the resulting effective Hamiltonian are carried out with an effective interaction derived from the Tabakin potential. The present calculations of the binding energies per particle for the¹⁶O and⁴⁰Ca nuclei are in agreement with the experimental measurements.     

A microscopic description of the (γ,pn)-reaction

The quasideuteron process has been investigated for photon energies 40 MeV<E _γ< 160 MeV on the basis of a shell model picture modified by short range nucleon-nucleon correlations. It turns out that the cross section for the (γ,pn)-reaction depends sensitively on the details of the correlation function, i.e. on the exchange of high momenta between otherwise independently moving nucleons. The final state interaction has been consistently taken care of by using optical model wave functions for the outgoing nucleons. The results of the calculations for¹⁶O indicate that precise measurements of the (γ,pn) cross section do contain information on the properties of the nuclear wave functions for small internucleonic distances.     

Generator-coordinate study of 3He+3He elastic scattering with a semirealistic nucleon-nucleon potential

The elastic scattering of ³He by ³He is studied in the framework of the generator coordinate method, using a new semirealistic nucleon-nucleon potential. All components of this potential have a soft core in the sense that they can be used in calculations where short-range correlations between nucleons are not taken into account. With this potential, a good agreement between calculated and measured cross sections and polarizations is obtained. The tensor component of the potential is found to be essential to explain the J-dependence of the empirical phase shifts, although the calculated polarizations are insensitive to the strength of the tensor potential.     

A microscopic description of inelastic 12C scattering from 208Pb

Heavy-ion inelastic scattering is described microscopically by using an effective nucleon-nucleon interaction and RPA hole-particle wave functions. The relative cross sections for different multipoles can be sensitive to the range of the interaction. The strength is determined by fitting elastic scattering. The model is used to analyze 98 MeV ¹²C ions exciting ²⁰⁸Pb. The range required is shorter than that for the bare interaction between nucleons. Collective model fits are also presented for comparison.     

Mean field and beyond in nuclei far from stability lines

We calculate, for the first time, the state-dependent pairing gap of a finite nucleus (¹²⁰Sn) diagonalizing the bare nucleon-nucleon potential (Argonne v₁₄) in a Hartree-Fock basis. The resulting gap accounts for about half of the experimental gap. Going beyond the mean field in the particle-particle channel, the combined effect of the bare nucleon-nucleon potential and of the induced pairing interaction arising from the exchange of low-lying surface vibrations between nucleons moving in time reversal states close to the Fermi energy accounts for the experimental gap. Examples for light, halo nuclei are also reported. The more studied effects of the particle-vibration coupling in the particle-hole channel are discussed for the low-lying quadrupole vibration in ¹²⁰Sn and the giant dipole resonance in the unstable oxygen isotopes and ¹³²Sn.     

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.     

Density-dependent Brueckner-Hartree-Fock approach in deformed nuclei

Recently a method has been developed which includes into the Brueckner-Hartree-Fock (BHF) approach in a finite nucleus those terms which produce the density dependence of the effective interaction between nucleons. This method is extended to the deformed open shell nuclei ¹²C and ²⁰Ne. The results indicate that it is possible to describe these nuclei starting from a bare realistic nucleon-nucleon interaction (Reid soft-core potential). Binding energies, quadrupole moments, root mean square radii are improved compared to the usual BHF approach with the same force or the HF approach with a phenomenological effective force.     

Antisymmetrization of a mean field calculation of the T-matrix

The usual definition of the prior (post) interactionV(V′) between projectile and target (resp. ejectile and residual target) being contradictory with full antisymmetrization between nucleons, an explicit antisymmetrization projectorA must be included in the definition of the transition operator, T≡V′A + V′A GV. We derive the suitably antisymmetrized mean field equations leading to a non perturbative estimate ofT. The theory is illustrated by a calculation of forwardα-α scattering, making use of self consistent symmetries.     

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.