Isospin-breaking nuclear forces with delta degrees of freedom

I discuss the leading contributions to the isospin-violating (IV) two- and three-nucleon forces in effective field theory with explicit delta degrees of freedom.     

Relativistic theory of nuclear forces

A theory of nuclear forces is proposed which results in a nonlinear relativistic equation for their potential. This equation is used to explain nuclear saturation.     

Neutron star models and nuclear forces

Equations of state of cold neutron matter are calculated by the method of unitary transformations for a hard-core and a soft-core potential. Equilibrium configurations are constructed in the Newtonian and the general relativistic theory of gravitation. It is found that Newtonian treatment to a certain extent gives very good results. On the other hand neutron star models are strongly affected by the nuclear forces used in the equation of state.     

Abnormal nuclear matter and many-body forces

Qualitative aspects of quantum corrections to the Lee-Wick abnormal nuclear matter are studied in terms of many-body forces in the normal nuclear matter implied by the σ-model Lagrangian field theory. Using a simplified model for the scalar meson self-energy in the nuclear medium and restricting to a set of graphs which in non-relativistic normal nuclear matter reduces to the well-known random phase approximation (RPA), we have found that an abnormal nuclear state can be bound or unbound depending upon whether strongly attractive multi-body forces are present or absent in the normal matter. This is in support of our previous result obtained heuristically from some general considerations of quantum corrections. A strongly bound abnormal matter with an equilibrium density of a few times the normal nuclear matter density ρ₀ can be formed if large attractive manybody forces can be accommodated in the normal nuclear matter. However if one accepts the present status of theories of nuclear matter binding energy in which no attractive many-body forces are called for, then the abnormal state can occur only at large densities (perhaps 8 to 10 times ρ₀) and is expected to be unbound by several hundred MeV per particle.     

Quark structure and nuclear effective forces

We formulate the quark meson coupling model as a many-body effective Hamiltonian. This leads naturally to the appearance of many-body forces. We investigate the zero range limit of the model and compare its Hartree-Fock Hamiltonian to that corresponding to the Skyrme effective force. By fixing the three parameters of the model to reproduce the binding and symmetry energy of nuclear matter, we find that it allows a very satisfactory interpretation of the Skyrme force.     

Nucleon core size and nuclear forces

Knowledge of nuclear forces is used to obtain information on the size of the quark core of nucleons. A RMS radius of 0.3–0.5 fm appears to be favored by a quark model of the nucleon-nucleon spin-orbit forces, with both one-gluon and ϱ-, ω-meson exchange qq interactions, depending on the relative strength of these qq interactions. The limitations of this estimate are briefly discussed.     

Quark mass dependence of the nuclear forces

We investigate the behavior of the nuclear force as a function of the light-quark masses m _q in the framework of chiral effective field theory at next-to-leading order. The unknown m _q -dependent short-range contribution is estimated by means of dimensional analysis. We calculate various observables for different values of m _q . We found no new bound states and a larger deuteron binding energy, MeV, in the chiral limit.Received: 30 September 2002, Published online: 22 October 2003PACS: 11.30.Rd Chiral symmetries - 13.75.Cs Nucleon-nucleon interactions (including antinucleons, deuterons, etc.) - 21.30.Cb Nuclear forces in vacuum - 21.30.Fe Forces in hadronic systems and effective interactions     

Saturation of nuclear forces in Brueckner theory

The basic equations in the Brueckner theory of nuclear matter are solved for a two-nucleon potential taken as a rectangular well with a rectangular repulsive sphere and the properties of the solutions are investigated for various dimensions of the repulsive sphere. The two-nucleon interaction is considered to be non-vanishing only if the nucleons are in theS-state. Under such assumptions a two nucleon potential always gives saturation, i.e. a minimum of the mean binding energy per nucleon, at a finite nuclear density. It is shown that the nuclear density and the mean binding energy decreases if the height or the width of the repulsive sphere increases. If the repulsive sphere is infinitely high a nucleus can exist as a bound state only if the width of this sphere is sufficiently small. The limit value for the width of the sphere is given. It is shown in the conclusion how the solution of the basic equations will change if the two-nucleon potential does not contain an infinite repulsive sphere, but only a very high one.     

Evolution of zero-dispersion peaks in fluctuation spectra with temperature

Zero-dispersion peaks (ZDPs) can arise in fluctuation spectra of underdamped systems for which the dependence of the eigenfrequency on energy has an extremum. It is shown that ZDPs exist only for temperatures T higher than the critical one, T_c. The shape of the ZDP is described analytically as well as the process of the onset of this peak at T ≈ T_c. In the low-friction limit the shape of the ZDP turns out to be universal for T > T_c.     

A remark on the saturation of nuclear forces in nuclear matter

The paper deals with the problem of saturation in nuclear matter, when the two-nucleon interaction is described by the soft core potentials acting in a limited number of orbital states. The potentials used belong to the class of the realistic potentials.     

Hadron spectra from nuclear collisions

We describe high energy nuclear collisions by a superposition of isotropically decaying thermal sources (“fireballs”) of freeze-out temperature T = 0.15 GeV. The longitudinal fireball superposition is taken as boost-invariant, in a rapidity range determined by the average energy loss of nucleons in p?p collisions. The transverse fireball motion is assumed to be due to random walk initial state collisions; it is determined by p?A data and then extrapolated to central A?B interactions. We thus obtain parameter-free predictions for the rapidity and transverse momentum spectra of hadrons produced in high energy nucleus-nucleus collisions. The results account fully for the observed broadening of transverse momentum distributions, so that single-particle spectra require neither collective flow nor temperature increase.     

On the moment of inertia of large nuclear systems with pairing forces

The moment of inertia of large nuclear systems with pairing forces was shown to be that of an irrotational flow byPrange. Following an argument due toThirring, we will give here a very simple derivation of this important result.     

Polarization forces in elastic nuclear coulomb scattering

The polarization potential is determined for the adiabatic sub-Coulomb scattering of two nuclei. No collective coordinates are used. The relevant nuclear polarizabilities are evaluated by means of sum rules. The departure from the pure Rutherford scattering law is calculated for various nuclei. For adiabatic heavy-ion collision the differential cross section is found to be reduced below the Coulomb scattering by one percent at backward angles.     

Absorption spectra of quantum aggregates interacting via long-range forces

We present a simple formula by which the shape of the absorption spectrum of an aggregate of quantum "monomers" (cold atoms, molecules, quantum dots, nanoparticles, etc.) interacting via dipole-dipole forces can be calculated from the averaged spectrum of the quantum monomer itself. Spectral broadening, due to a wide variety of causes, is included explicitly so that the formula is applicable not only to the idealization of a discrete spectrum but also to the practical situation of a continuously broadened spectrum. In simple cases, analytic results are obtained showing the strong dependence of the aggregate spectrum on the precise nature of the broadening of the quantum monomer spectrum. The formula is compared with results of exact diagonalization of model aggregate Hamiltonians and with experiment.     

Particle mixing and charge asymmetric nuclear forces

The charge asymmetric effect of ?ω and πη electromagnetic mixing on the ¹S₀ NN potential is reviewed. It is found that the ?ω contribution dominates and leads to an n-n potential which is more attractive than the p-p potential. The shift in the scattering lengths is then calculated to be |a_nn|?|a_pp| ≈ 0.9 fm and the shift in effective ranges is r_nn?r_pp ≈ ?0.02 fm.     

Chiral effective field theory and nuclear forces

We review how nuclear forces emerge from low-energy QCD via chiral effective field theory. The presentation is accessible to the non-specialist. At the same time, we also provide considerable detailed information (mostly in appendices) for the benefit of researchers who wish to start working in this field.     

Coulomb energies and charge asymmetry of nuclear forces

Charge-symmetry-breaking potentials suggested in the literature to resolve the discrepancy between calculated Coulomb energy differences of analog states and the experimental values, are considered in detail. We calculate the contributions of these potentials to the ground state energy differences of the mirror nuclei ³He³H, ¹⁵O¹⁵N, ¹⁷F¹⁷O, ³⁹Ca³⁹K and ⁴¹Sc⁴¹Ca. It turns out, due to the short range character of these symmetry-breaking potentials, that their inclusion may resolve the ³He³H difficulty but not the ⁴¹Sc⁴¹Ca discrepancy.     

Coulomb forces in the three-body problem with application to direct nuclear reactions

Faddeev equations are considered in the case of three charged particles interacting with both separable nuclear two-body interactions and also including Coulomb forces. Modified Faddeev equations with Coulomb Green's functions are introduced. The three-body amplitudes are given into pure Coulomb and distorted-Coulomb amplitudes. Introducing a decomposition in the angular momentum states, a set of three-body integral equations is obtained. The effect of pure coulomb amplitudes is studied in direct nuclear reactions and found to give a large contribution to the cross sections. The three-body integral equations obtained are applied for direct nuclear reactions. The angular distributions for¹²C(⁶Li,d)¹⁶O,¹⁶O(⁶Li,d)²⁰Ne, and¹²C(⁶Li,α)¹⁴N transfer reactions are calculated as well as for the⁶Li elastic scattering on¹²C. From the good agreement between the theoretically calculated and experimental data, better spectroscopic factors are extracted. The effect of including Coulomb forces in the three-body problem is found to improve the results by about 16.26%.