The Nucleon-Nucleon Interaction in a Chiral Effective Field Theory
The Nucleon-Nucleon Interaction in a Chiral Effective Field Theory
The Nucleon-Nucleon Interaction in a Chiral Effective Field Theory
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
4 1. Introduction<br />
the Thcson-Melbourne 3NF does not lead to a significant improvement. This problem still rema<strong>in</strong>s<br />
unsolved [196].<br />
In spite of a very successful description of most of the experimental data the modern realistic<br />
N N potentials are quite phenomenological approaches. For <strong>in</strong>stance, one of the basic <strong>in</strong>gredients<br />
of these models is a fictitious (J' (550 MeV) boson, which is needed to produce the rather strong<br />
attraction <strong>in</strong> the central part of the potential. This attraction is evident from the N N scatter<strong>in</strong>g<br />
data, see also discussion <strong>in</strong> ref. [48]. Such a (J'-meson, however, has never been observed experimentally.<br />
For a recent discussion about the experimental evidence of the (J'-meson see ref. [49].<br />
Another common feature of the boson-exchange models is the ad hoc <strong>in</strong>troduction of the strong<br />
form-factors4 at each meson-nucleon vertex <strong>in</strong> order to correct the large momentum behavior of<br />
the potential and to allow for practical calculations. Such form-factors are usually <strong>in</strong>terpreted<br />
<strong>in</strong> terms of higher-order (<strong>in</strong> a coupl<strong>in</strong>g constant) meson-nucleon and meson-meson <strong>in</strong>teractions,<br />
dress<strong>in</strong>g each vertex. Because of the non-perturbative nature of such <strong>in</strong>teractions one is not able to<br />
directly calculate these form-factors and approximates them typically by some smooth functions<br />
of momenta. Only <strong>in</strong> the case of the so-called Ruhr-potential (RuhrPot) [50] the form-factors<br />
are generated dynamically by solv<strong>in</strong>g the correspond<strong>in</strong>g <strong>in</strong>tegral equations. Another <strong>in</strong>terest<strong>in</strong>g<br />
feature of this potential is its manifest energy <strong>in</strong>dependence result<strong>in</strong>g from the method of unitary<br />
transformation [51], [53] which has been used to def<strong>in</strong>e the nuclear force. On the contrary, the<br />
standard approach based on the time-ordered perturbation theory leads necessarily to an effective<br />
Hamiltonian which depends on the <strong>in</strong>itial energy of the nucleons (i.e. to an operator which<br />
depends explicitly on its own eigenvalue). Such an energy dependence of the nuclear forces causes<br />
many complications <strong>in</strong> practical calculations for more than two nucleons. Another problem of the<br />
various meson-exchange potentials is how to systematicaHy improve these models and whether<br />
the one-boson exchange approximation is well justified. Indeed, if one takes the meson-exchange<br />
picture of the nuclear force seriously, one would expect that two- and more-meson exchanges are<br />
also important (because of the strong meson-nucleon coupl<strong>in</strong>g). Usually one argues at this po<strong>in</strong>t<br />
that the force based on the two- and more-meson exchanges are, <strong>in</strong> general, of shorter range than<br />
the one-meson exchange force and thus are less relevant for the energy region of nuclear physics<br />
(with exception of pion-exchange <strong>in</strong>teractions). Although quite plausible, such arguments should<br />
be considered more qualitative than quantitative.<br />
<strong>The</strong> ma<strong>in</strong> conceptual problem of the OBE models, however, can be illustrated <strong>in</strong> terms of the<br />
follow<strong>in</strong>g "classical" picture [54]: ass urne that hadrons are hard spheres. <strong>The</strong> charge radius of the<br />
proton is .J(rI) rv 0.6 fm, while the typical size of light mesons is about 0.5 fm. <strong>The</strong>n mesons<br />
can not mediate the nuclear force at distances below rv 2 x 0.6 fm + 2 x 0.5 fm = 2.2 fm. Even if<br />
this picture is very much simplified and does not take <strong>in</strong>to account quantum mechanical effects,<br />
it becomes clear that the traditional meson-exchange picture should not be adequate to describe<br />
the nuclear matter phenomena at distances below 2 fm.<br />
One hopes that quantum chromodynamics (QCD), the fundamental theory of the strong <strong>in</strong>teraction,<br />
can help to avoid these problems of the OBE models and provide us with a deeper understand<strong>in</strong>g<br />
of the nature of the nuclear forces. QCD is a SU(3)color gauge theory of the strong<br />
<strong>in</strong>teraction, formulated <strong>in</strong> terms of quarks and gluons. <strong>The</strong> structure of nucleons as weH as <strong>in</strong>teractions<br />
between them are, <strong>in</strong> pr<strong>in</strong>ciple, completely determ<strong>in</strong>ed by QCD. Direct calculations of the<br />
nuclear force from QCD are not possible up to now. This is because at low energies the <strong>in</strong>teraction<br />
is too strong to apply the usual perturbative methods. However, many attempts were made<br />
to <strong>in</strong>corporate more <strong>in</strong>formation from QCD <strong>in</strong> models of the N N <strong>in</strong>teractions. In the so-called<br />
4 Such form-factors are anyway not well-def<strong>in</strong>ed <strong>in</strong> quantum field theory.