Particle-Nucleon Interactions

A description of nuclear matter as an ideal mixture of protons and neutrons, possibly in (5 equilibrium with electrons and neutrinos, is not sufficient to give a realistic description of dense matter. The account of the interaction between the nucleons can be performed in different ways. For instance we have effective nucleon-nucleon interactions, which reproduce empirical two-nucleon data, e.g. the PARIS and the BONN potential. On the other hand we have effective interactions like the Skyrme interaction, which are able to reproduce nuclear data within the mean-field approximation. The most advanced description is given by the Walecka model, which is based on a relativistic Lagrangian and models the nucleon-nucleon interactions by coupling to effective meson fields. Within the relativistic mean-field approximation, quasi-particles are introduced, which can be parameterized by a self-energy shift and an effective mass. 

Expressions for the medium modifications of the cluster distribution functions can be derived in a quantum statistical approach to the few-body states, starting from a Hamiltonian describing the nucleon-nucleon interaction by the potential V"(12, l/2/) (1 denoting momentum, spin and isospin). We first discuss the two-particle correlations which have been considered extensively in the literature [5,7], Results for different quantities such as the spectral function, the deuteron binding energy and wave function as well as the two-nucleon scattering phase shifts in the isospin singlet and triplet channel have been evaluated for different temperatures and densities. The composition as well as the phase instability was calculated. 

In the single-particle estimates of y-ray decay, one presumes a single nucleon interacts with a photon. This means there is an isospin selection rule... 

In conclusion, just as the IBM, the FDSM contains, for each low energy collective mode, a dynamical symmetry. For no broken pairs, some of the FDSM symmetries correspond to those experimentally known and studied previouly by the IBM. Thus all the IBM dynamical symmetries are recovered. In addition, as a natural consequence of the Hamiltonian, the model describes also the coupling of unpaired particles to such modes. Furthermore, since the model is fully microscopic, its parameters are calculable from effective nucleon-nucleon interactions. The uncanny resemblance of these preliminary results to well-established phenomenology leads us to speculate that fermion dynamical symmetries in nuclear structure may be far more pervasive than has commonly been supposed. 

The pion-nucleon interaction has been subject both to experimental and theoretical studies since the very beginning of the development of particle physics. On the theoretical side the description of the pion-nucleon system with QCD is considered to be a fundamental issue in the development of this theory. The understanding of strong interaction in the confinement regime has advanced recently, as chiral perturbation theory was developed to perform calculations at low energies [1,2]. 

A completely different reason for the knee is the idea to transfer energy in nucleon-nucleon interactions into particles, like gravitons Kazanas Niko-laidis 2001 or extremely high-energy muons Petrukhin 2003, which are not observable (or not yet observed) in air shower experiments. The latter proposal seems to be excluded by recent measurements of the Baikal experiment setting upper limits for the flux of muons above 105 GeV Wischnewski et al. 2004. 

Here and Na are the mass and number density of a particles, respectively, is the resonance energy (in the center-of-mass frame), I, is the relative width, and all other symbols have their usual meaning. These authors also introduced small variations in the strengths of the nucleon-nucleon interaction and in the... 

For the r-process the models for calculating /3-decay rates can again be divided into microscopic and statistical categories. Among the microscopic ones shell model is of limited use as this involves very neutron-rich nuclei all over the periodic table. Beyond the /p-shell nuclei shell model has been applied to nuclei with either a few valence particles or with more particles but with not too many valence orbits. The microscopic theory that has been widely used is the Random Phase Approximation (RPA) and its different improved version. We refer here to the review by Arnould, Goriely and Takahashi [39] for a detailed description and references. The effective nucleon-nucleon interaction is often taken to be of the spin-isospin type ([Pg.205]

Physicists and chemists have developed various perturbation-theory methods to deal with systems of many interacting particles (nucleons in a nucleus, atoms in a solid, electrons in an atom or molecule), and these methods constitute many-body perturbation theory (MBPT). In 1934, Mpller and Plesset proposed a perturbation treatment of atoms and molecules in which the unperturbed wave function is the Hartree-Fock function, and this form of MBPT is called Moller-Plesset (MP) perturbation theory. Actual molecular applications of MP perturbation theory began only in 1975 with the work of Pople and co-workers and Bartlett and co-workers [R. J. Bartlett, Ann. Rev. Phys. Chem.,31,359 (1981) Hehre et al.]. 

Kuo and Brown [3], where energies of the low-lying sd-like states of and were calculated from the underlying nucleon-nucleon interaction. The effective interaction used in this type of calculation is the reaction or G-matrix which sums the ladder diagrams including only particle-particle intermediate states. 

Fig. 5. Particle spectral function for three different momenta, k = 0.79 (dotted), 1.74 (full) and 5.04fin (dashed). The high-energy tail is identical for all momenta below 5 fm and is related to the short-range repulsion in the nucleon-nucleon interaction.

In this model, which is also known as the optical model following Fernbach et alA, (who used it to describe high energy reactions) the complex potential iV is supposed to represent compound system formation, in the sense of the N. Bohr or uniform, model. It represents any processes which are not described by the single particle interaction with the potential. This model reproduces many of the experimental features of medium energy reactions. An important advance towards an interpretation of the potentials of the optical model in terms of two-nucleon interaction has recently been made by Brueckner . 

Theoretical level densities. It is now well understood that an enormous number of levels take part in nuclear reactions however, as we have pointed out in Sects. 8 and 10, the level density must increase very rapidly with excitation energy. The first theoretical estimate of the level density and its rate of increase with excitation energy was made by Bethe and by Oppenheimer and Serber on the assumption that the constituents of the nucleus behave like free particles and that the nucleus therefore behaves like a gas. The opposite extreme, that the nucleons interact strongly with one another, and that the nucleus as a whole behaves like a liquid drop, was proposed by Bohr and Kalckar. Quite generally, the level density co (E) at energy E, is related to the temperature (0) and to the entropy (S) through the relation ... 

The single-particle shell model is used for inclusion of the residual nucleon interactions [60Br39, 71Scl7] (see papers by R. Casten, V. Zelevinsky, and others, references in I/19B1). Strengths of 7-ray transitions in A = 91 — 150 nuclei and decay of first excited states in even-even nuclei were considered in compilations by P. Endt [81En06] and S. Raman [01Ra27]. 

The nucleons interact through their constituents, and their strong interaction can also be depicted as boson exchange. (All interaction quanta are bosons, i.e., particles with integer spins.) The strongly interacting bosons (particles with integer spins), which take part in the nucleon-nucleon interaction, are called mesons. These are n°, K", K°, K , ri°, p, p°, p ,... 

Equation (4.15) would be extremely onerous to evaluate by explicit treatment of the nucleons as a many-particle system. However, in Mossbauer spectroscopy, we are dealing with eigenstates of the nucleus that are characterized by the total angular momentum with quantum number 7. Fortunately, the electric quadrupole interaction can be readily expressed in terms of this momentum 7, which is called the nuclear spin other properties of the nucleus need not to be considered. This is possible because the transformational properties of the quadrupole moment, which is an irreducible 2nd rank tensor, make it possible to use Clebsch-Gordon coefficients and the Wigner-Eckart theorem to replace the awkward operators 3x,xy—(5,yr (in spatial coordinates) by angular momentum operators of the total... 

In a simplistic and conservative picture the core of a neutron star is modeled as a uniform fluid of neutron rich nuclear matter in equilibrium with respect to the weak interaction (/3-stable nuclear matter). However, due to the large value of the stellar central density and to the rapid increase of the nucleon chemical potentials with density, hyperons (A, E, E°, E+, E and E° particles) are expected to appear in the inner core of the star. Other exotic phases of hadronic matter such as a Bose-Einstein condensate of negative pion (7r ) or negative kaon (K ) could be present in the inner part of the star. 

As the weak interaction is the slowest of all, it was the first to find itself unable to keep up with the rapid expansion of the Universe. The neutrinos it produces, which serve as an indicator of the weak interaction, were the first to experience decoupling, the particle equivalent of social exclusion. By the first second, expansion-cooled neutrinos ceased to interact with other matter in the form of protons and neutrons. This left the latter free to organise themselves into nuclei. Indeed, fertile reactions soon got under way between protons and neutrons. However, the instability of species with atomic masses between 5 and 8 quickly put paid to this first attempt at nuclear architecture. The two species of nucleon, protons and neutrons, were distributed over a narrow range of nuclei from hydrogen to lithium-7, but in a quite unequal way. 

We consider a system made up of N fermions (nucleons or electrons) interacting through two-body forces and with an external field, with respective potentials >(r,r ) and V(r). We assume there exists a possibility of decomposing the one-particle density matrix into an averaged part and an oscillating part, i.e. ... 

PHOTONUCLEAR REACTION. A nuclear reaction induced by a photon. In some cases the reaction probably takes place via a compound nucleus formed by absorption of the photon followed by distribution of its energy among the nuclear constituents. One or more nuclear particles then "evaporate from the nuclear surface, or occasionally the nucleus undergoes pliotofissioii. In other cases the photon apparently interacts directly with a single nucleon, which is ejected as a photoneutron or photoproton without appreciable excitation of the rest of the nucleus. 

---