Microscopic approach to the nucleon-nucleon effective interaction and nucleon-nucleon scattering in symmetric and isospin-asymmetric nuclear matter

After reviewing our microscopic approach to nuclear and neutron-rich matter, we focus on how nucleon-nucleon scattering is impacted by the presence of a dense hadronic medium, with special emphasis on the case where neutron and proton densities are different. We discuss in detail medium and isospin asymmetry effects on the total elastic cross section and the mean free path of a neutron or a proton in isospin-asymmetric nuclear matter. We point out that in-medium cross sections play an important role in heavy-ion simulations aimed at extracting constraints on the symmetry potential. We argue that medium and isospin dependence of microscopic cross sections are the result of a complex balance among various effects, and cannot be simulated with a simple phenomenological model.     

Approximation of off-shell scattering operators for non-lorentzian line shape calculations

A previously derived approximation for the matrix elements of the Fano relaxation operator m(ω), which gives rise to non-Lorentzian line wings, is examined. This approximation is expressed in terms of an off-the-energy shell scattering operator. Calculation of this operator by a second-order Born expansion is unsuitable because this procedure limits the radiation frequency dependence to the same order. The main part of this paper is devoted to expressing the off-shell scattering operator in the time-ordered formalism. In this form, a scattering operator approximation suggested by Dillonet al.⁽⁶⁾ can be applied which is not restrictive to the frequency dependence.     

Phenomenological renormalization of free nucleon-nucleon interaction

Low-lying spectra of⁶Li,¹⁸F,¹⁸O,⁴²Sc,⁴²Ca,⁵⁸Ni and⁹²Zr are studied with Sussex matrix elements (SME) and their central, spin-orbit and tensor components. It is observed that major contribution to level energies comes from the central part, while the tensor part provides the finer details of spectra, particularly forT=0 levels. The spin-orbit part does not make any appreciable contribution to level energies. A phenomenological renormalization of the SME is carried out to improve the agreement with the experimental results. It turns out that some of the low-lyingT=0 levels can be satisfactorily described if the SME in the³S₁ relative state are made (1+α) times their bare interaction value, whereα is a constant to be determined from a comparison with experimental level energies. Similarly, forT=1 levels, better agreement with the experimental results is obtained if aδ-function-plus-quadrupole interaction is added to the SME.     

A three-body approach to the effective nucleon-nucleon interaction

The problem of the effective nucleon-nucleon interaction is formulated in a three-body model. The interaction of two nucleons and a heavy core having internal excitations is described by means of Faddeev-type coupled equations. The elimination of the excited states of the core leads to a set of coupled equations with an effective kernel which incorporates the effect of the eliminated degrees of freedom. An exactly soluble model is constructed and solved. The exact and an approximate solution are compared. The comparison demonstrates the applicability of the model for the investigation of problems connected with the effective nucleon-nucleon interaction.     

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.     

Effective densities in local-density approximations of the nucleon-nucleon effective interaction

The choice of an effective local density for a finite-range density-dependent effective interaction is considered. The effect appears in the second-order perturbation energy for a density-independent bare force. Analysis of this energy shows that other finite-nucleus effects are more important than the uncertainties arising from the use of a c.m. density, or arithmetic or geometric mean density. The latter uncertainties are found to be $\text{1}\text{4}\text{?1}\text{MeV}\text{/A}$ for most nuclei. Since the actual uncertainties in fitted phenomenological interactions are only a fraction of these, we feel that any of these local densities can be used without introducing large errors.     

On the sensitivity of n-d scattering states to the nucleon-nucleon interaction

A new set of separable P-wave interactions and rank-2 tensor forces have been constructed and applied in three-body calculations for n-d elastic scattering at E_{n = 22.7 MeV}. A significant sensitivity of the polarizations to the different tensor forces and to the ³D₂ interaction has been found.     

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.     

Semi-microscopic model for the effective pairing interaction in atomic nuclei

A model has been proposed in which the ab initio effective pairing interaction in atomic nuclei is supplemented by a small phenomenological term containing one parameter universal for all intermediate-mass and heavy nuclei. The neutron and proton pairing gaps have been calculated for several chains of semimagic nuclei; these calculations demonstrate the applicability of this model.     

Combinatorial nuclear level densities based on the Gogny nucleon-nucleon effective interaction

A combinatorial method to calculate total level densities from an arbitrary single-particle level scheme is presented. Parity, angular momentum, pairing correlations as well as collective enhancements are explicitly treated. This method is employed using single-particle level schemes obtained from Hartree-Fock-Bogoliubov calculations based on the Gogny effective interaction. Sixty five even-even nuclei with masses 26 ?A? 250 are considered. Rather good agreements are obtained when comparing our predictions with experimental data for energies of the order of the neutron binding energies and for low excitation energies where discrete levels are experimentally observed. Received: 13 February 2001 / Accepted: 24 September 2001     

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.     

Level spectra of A = 6 nuclei from the free nucleon-nucleon interaction

The calculational procedure recently discussed by Dawson, Talmi, and Walecka for calculating level spectra of double-magic-plus-two-nucleon nuclei from the free nucleon-nucleon interaction is applied to the A = 6 system. A Bethe-Goldstone equation is written for the two external nucleons and by working within an harmonic oscillator framework, the equation can be transformed to relative coordinates and solved. The free nonsingular nucleon-nucleon interaction (independent of the form used) is found to give a good fit to all the known levels, and the more sophisticated Brueckner-Gammel-Thaler and Hamada potentials are found to give essentially the same results, after careful examination of the effect of the strong tensor coupling in the T = 0 states. This, in a sense, justifies previous calculations of spectra of light nuclei with nonsingular interactions. Somewhat too much absolute binding energy is found, presumably because of our use of harmonic oscillator single-particle potentials. Quite good agreement is found for the magnetic moment of Li⁶ and the f_τ value for the ground state β decay He⁶ → Li⁶ (both within < 6%) and also for the quadrupole moment of Li⁶, using the more complicated potentials.     

Energy dependence of effective nucleon-nucleon interaction and position of the nucleon drip line

A semimicroscopic version of the self-consistent theory of finite Fermi systems is proposed. In this approach, the standard theory of finite Fermi systems is supplemented with relations that involve the external values of the invariant components of the Landau-Migdal amplitude and which follow from microscopic theory. The Landau-Migdal amplitude at the nuclear surface is expressed in terms of the off-shell T matrix for free nucleon-nucleon scattering at the energy E equal to the doubled chemical potential of the nucleus being considered. The strong energy dependence of the free T matrix at low E changes the properties of nuclei in the vicinity of the nucleon drip line. It is shown that, upon taking into account the energy dependence of the effective interaction, the neutron drip line is shifted considerably toward greater neutron-excess values. This effect is illustrated by considering the example of the tin-isotope chain.     

Spin, iso-spin dependence of nucleon-nucleon effective interaction in nuclear matter calculations

A set of density dependent nucleon-nucleon (N-N) interactions has been examined in nuclear matter calculations by varying spin-isospin contributions. Two sets of potentials have been considered. One having a density dependentσ-function type short range part followed by one term long range Gaussian part while the other having a density dependentσ-function part followed by two Gaussian terms. The strength parameters of the potential have been fitted to the saturation properties of nuclear matter, i.e. binding energy per particle of 15.5 MeV atk _F=1.35 fm⁻¹. Several sets of these two potentials have been generated by varying the strength parameterM of Majorana exchange operatorP _M. It is seen thatM indirectly controls the spin, iso-spin contribution to the interaction potential and thus affects the nuclear matter properties such as compressibility and symmetry energy considerably, while variation of these quantities with the range parameterμ for givenM is moderate at lowM values while at higherM values it is quite large.     

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.     

On the new definition of off-shell effective action

We analyze the recently proposed definition of the off-shell, gauge-invariant, gauge-independent, effective action $\text{Γ}$, utilizing an invariant metric on the field space. It is shown how to establish correspondence between $\text{Γ}$ and the standard effective action, calculated in some particular (Landau-type) gauge. Several examples are explicitly discussed, including Yang-Mills theory, the effective potential in scalar QED, and one-loop quantum gravity. Generalization to the case of super-invariant theories (e.g. super-Yang-Mills and supergravity) is also presented.     

Some studies of the effective interaction for the inelastic scattering of nucleons

The microscopic interpretation of the inelastic scattering of nucleons by nuclei is reviewed. Data for (p, p′), (nn′) and (p, n) reactions at medium energies on nuclei with simple shell-model configurations are analysed in terms of a simple effective nucleon-nucleon interaction. In many cases, a local Yukawa interaction with a range of about 1 fm, strength about 200 MeV and weak spin dependence is found to give fair agreement with the data. Discrepancies are also found, particularly for the heavy nucleus ²⁰⁸Pb and for the inelastic polarization of protons. Possible deficiencies of the model are discussed in some detail. Exchange effects of the knock-on type are neglected.     

On the investigation of nucleon-nucleon correlations by means of high-energy scattering

The possible effects of short-range dynamical nucleon-nucleon correlations on high-energy hadron scattering on ⁴He are examined. The Glauber theory of multiple scattering is used as the basis for the computations. The conclusion is that very small effects are to be expected for elastic and sum total inelastic scattering of commonly available projectiles.     

Study of nucleon-nucleon and alphanucleon elastic scattering by the Manning-Rosen potential

Although often used in molecular dynamics, in this work the Manning–Rosen potential is parameterized to compute the scattering phase shifts for the nucleon–nucleon and the alpha-nucleon systems by exploiting the standard phase function method. We obtain excellent agreement in phase shifts with the more sophisticated calculations up to partial waves ${\ell }=2.$