BLED WORKSHOPS
IN PHYSICS
VOL. 1, NO. 1
Proceedins of the Mini-Workshop
Few-Quark Problems (p. 52)
Bled, Slovenia, July 8-15, 2000
The new driving mechanism for nuclear force: lessons
of the workshop?
Vladimir I. Kukulin??
Institute of Nuclear Physics, Moscow State University, 119899 Moscow, Russia
Abstract. Instead of the Yukawa mechanism for intermediate- and short-range interac-
tion, some new approach based on formation of the symmetric six-quark bag in the statej(0s)6[6℄X; L = 0i dressed due to strong coupling to ,  and  fields are suggested. This
new mechanism offers both a strong intermediate-range attraction which replaces the ef-
fective -exchange (or excitation of two isobars in the intermediate state) in traditional
force models and also short-range repulsion. Simple illustrative model is developedwhich
demonstrates clearly how well the suggested new mechanism can reproduce NN data.
Some important lessons of the workshop discussions have been included in the talk.
It was found in recent years that the traditional models for NN forces, based
on the Yukawa concept of one- or two-meson exchanges between free nucleons
even at the quark level lead to numerous disagreements with newest precise ex-
perimental data for few-nucleon observables (especially for spin-polarised par-
ticles) [1–3]. There are also various inner inconsistencies and disagreements be-
tween the traditional NN force models and predictions of fundamental theories
for meson-baryon interaction (e.g. for meson-nucleon cut-off factors). All these
disagreements stimulate strongly new attempts to develop alternative forcemod-
els based either on chiral perturbation theory or a new quark-meson models.
Our recent studies in the field [1–3] have led us to a principally new mecha-
nism for intermediate- and short-range NN forces – the so called ”dressed” bag
mechanism which is able to explain the failure of the traditional Yukawa ex-
change models and also to solve many long-standing puzzles in the field. This
mechanism has good resources in explanation of many fundamental difficulties
of modern hadronic physics, e.g. the puzzles in baryon spectroscopy (e.g. normal
ordering in -sector and inverse ordering in nucleon sector for excited negative
and positive parity states), the complicated interplay between NN short-range
repulsion and intermediate range attraction, the ABC-puzzle in 2-production inpp and pd collisions etc.
The new model is based on the important observation [4] that two possible
six-quark space symmetries in even NN partial waves (for illustration we con-
sider here the S-wave only), viz. js6[6℄L = 0i and js4p2[42℄L = 0i correspond
to the states of different nature. The first states have almost equal projections? The respective original work included in the talk was done jointly with Drs.
I.T.Obukhovsky, V.N.Pomerantsev and Prof. A. Faessler?? E-mail:kukulin@nucl-th.sinp.msu.ru
The new driving mechanism for nuclear force 53
into the NN, 

 and CC channels and thus correspond to bag-like intermediate
states while the states of second type are projected mainly onto NN channel and
thus can be considered as clusterised NN states with nodal NN relative motion
wavefunctions. In the present work we develop this picture much further on the
quark-meson microscopic basis and derive the microscopic NN transition ampli-
tudes through six-quark +2 intermediate states in s-channel (see Fig. 1).
The transition is accompanied by a virtual emission and subsequent absorp-
tion of two tightly correlated pions by diquark pairs or, alternatively, by two 1p-
shell quarks when they jump from the 1p- to the 0s-shell orbit or vice versa. These
two pions can form both the scalar  and vector  mesons which surround the
symmetric six-quark bag.
6 + σ )(s
p
ST=01(10)
L=0,2
J = 0 (1 )
+ +
ST=10(01)
L=1
p _ _
J = 0 (1 )
ST=10(01)
L=1
p _ _
J = 0 (1 )
N
N
N
p
s
s
s
s
s
s
s
p s
p
p
A
s
s
s
s
s
s
π
π π
π
d’(d’’) d’(d’’)
σ(ρ)
A
N
p
ST=01(10)
L=0,2
J = 0 (1 )
+ + p
ST=01(10)
L=0
J = 0 (1 )
++
Fig. 1. The graph illustrates two sequential -meson emissions and absorptions via an in-
termediate - (or -) meson cloud and the generation of a symmetric six-quark bag.
It follows from previous studies (see e.g. [5]) for chiral symmetry restoration
effects in multiquark systems or in high density nuclear matter that some phase
transition happens when the quark density or the temperature of the system is
increased, which leads to a (partial) restoration of the broken chiral symmetry.
The consequence of the above restoration is a strengthening of the sigma-meson
field in the NN overlap region and reduction of the constituent quark mass. This
could be modeled by ”dressing” of the most compact six-quark configurationsjs6[6℄XL = 0i and js5p[51℄XL = 1i inside the NN overlap region with an effective
sigma-meson field. The resulting scalar- and vector-meson clouds will stabilize
the multi-quark bag due to a (partial) chiral symmetry restoration effect in the
dense multi-quark system and thus enhance all the contributions of such a type.
Thus, the picture ofNN interaction emerged from the model can be referred to as
the 6q ”dressed” bag (DB) model for baryon-baryon interaction [1–3].
54 Vladimir I. Kukulin
The light ”” or a similar ”scalar-isoscalar meson” with mass m  300 MeV
is assumed to exist only in a high density environment and not in the vacuum,
contrary to the  and  mesons. This mechanism, being combined with an addi-
tional orthogonality requirement[6], can describe both the short-range repulsion
and the medium range attraction and can replace the t-channel exchange by -
and!-mesons in the conventional Yukawa-type picture of the NN force.
The direct calculation of the multiloop diagram on Fig. 1 [1,2] using quark
pair-creation model results for S- and D-partial waves (in NN-channel) in a sep-
arable operator of form:VL0LE (r0; r) =  g20G00(E)j2s(r0)ih2s(r)j g0g2G02(E)j2s(r0)ih2d(r)jg2g0G20(E)j2d(r0)ih2s(r)j g22G22(E)j2d(r0)ih2d(r)j ! ; (1)
where the generalised propagators Gll 0(E) are related to the DB intermediate
state [1,2]. The interaction given by Eq.(1) can be interpreted as an effective NN
potential in our model.
In accordance with this, the contribution of mechanism displayed in the dia-
gram in FIG. 1 to theNN interaction in the S andD partial waves can be expressed
through the matrix element:AL0LNN!d0+!NN = Z d3r0d3r	L0NN(E; r0)VL0LE (r0; r)	LNN(E; r) ; (2)
where 	LNN and 	L 0NN are the “proper” nodal NN scattering wave functions in
initial and final state respectively.
The interaction operator (1) mixes S- and D-partial waves in the triplet NN
channel and thus it leads to a specific tensor mixing with the range  1 fm (about
that of the intermediate DB state). Thus the proposed new mechanism for NN
interaction induced by the intermediate dressed six-quark bag js6+ 2i results in
a specific matrix separable form of interaction with nodal (in S- in P-partial waves)
form factors and a specific tensor mixing of new type [7].
An important question is arising in this development, what is an interrela-
tion between the new above mechanism and the traditional picture of NN inter-
action emerged from RGM. Let us to remind that the consistent RGM description
(i.e. with no -meson exchange between quarks), as was additionally confirmed
by Fl. Stancu in this Workshop, leads to purely repulsive NN interaction. The
strength of the repulsion is likely of right magnitude because it reproduces well
the slope of NN S-wave phase shifts at E > 200 MeV. Hence the new mecha-
nism for NN interaction considered here, which leads to a strong intermediate-
range attraction, being combined to the above RGM picture, is able to provide
full quark-meson microscopic framework for quantitative description of funda-
mental nuclear force.
Moreover, the proposed model will lead to the appearance of strong 3N and4N forcesmediated by 2 and  exchanges [3]. In thisWorkshop Prof.Moszkowski
has suggested to use specific features of 3N force resulted from the new model to
explain the saturation properties of nuclear matter. It should emphasized in this
connection that the 3N force followed from the new model has a new feature of
The new driving mechanism for nuclear force 55
“substitution” when the nuclear matter density arises. In this case the enhance-
ment of the attractive 3N force contribution should be accompanied by the re-
spective weakening two-body attractive contributions and vice versa. So by this
specific mechanism at the sufficiently high density the nuclear matter dynam-
ics will be governed mainly by three- and four-body nuclear forces rather than
two-body contributions. And this specific “substitution” mechanism leads, as is
evident, to relativistic Walecka model, in contrast to conventional force models.
The new 3N force includes both central and spin-orbit components. Such a
spin-orbit 3N force is extremely desirable to explain the low energy puzzle of
the analyzing power Ay in N-d scattering and also the behavior of Ay in the3N system at higher energies EN ' 250  350 MeV at backward angles. The
central components of the 3N and 4N forces are expected to be strongly attractive
and thus they must contribute to 3N and (may be) 4N binding energies possibly
resolving hereby the very old puzzle with the binding energies of the lightest
nuclei.
Future studies must show to what degree such expectations can be justified.
The author thanks greatly Profs. Mitja Rosina and Bojan Golli for very nice
hospitality during the Workshop and warm informal atmosphere for discussions
which helped strongly to elucidate many key problems in the field. He also ap-
preciate the Russian Foundation for Basic Research (grant RFBR-DFG No.92-02-
04020) and the Deutsche Forschungsgemeinschaft (grant No. Fa-67/20-1) for par-
tial financial support.
References
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in press.
3. V. I. Kukulin, Proceeds. of the V Winter School on Theoretical Physics PIYaF, Gatchina, S.-
Petersburg, 8 – 14 Febr. 1999., p. 142;
4. A. M. Kusainov, V. G. Neudatchin, and I. T. Obukhovsky, Phys.Rev. C 44, 2343 (1991).
5. T. Hatsuda and T. Kunihiro, Phys. Rep. 247, 221 (1994); T. Hatsuda, T. Kunihiro and
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