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Introduction
Hadrons are bound states of quarks and gluons. These constituents have color
charge degree of freedom. Due to the color charge, quarks and gluons interact through
strong force that is mediated by the exchange particles, the gluons. The theory that
explains the behavior of strongly interacting particles is called Quantum Chromo
Dynamics (QCD) [1]. According to Wilczek and Politzer [2], the strong interaction can
be studied perturbatively in the asymptotic region characterized by very high values of
squared four-momentum transfer, q2. This technique fails in the region associated with
very low momentum transfer squared values; non-perturbative QCD, where the running
coupling constant,  S , becomes divergent [1]. At this stage, the quarks and gluons
appear bound inside spatial volume, thus forming hadrons. Well-known examples of
hadrons are nucleons, proton and neutron. A nucleus is formed from such type of
hadrons. These hadrons themselves are confined inside nucleus due to residual strong
interaction of their quark/gluon constituents.
The extent of confinement of quarks/gluons inside hadrons and that of nucleons
inside nuclei can be studied theoretically as well as experimentally. The result of such
studies is especially obtained in the form of radii of hadrons/nuclei. Theoretical studies
have paid more attention to mesons as compared to baryons which have complex
structure. The only baryons receiving proper attention are proton and neutron which have
been the focus of many experimental and theoretical studies.
Experimentally nuclear properties such as rms radii of nuclei can be studied by
using neutron scattering, Alpha emission, mirror nuclei, Mesic atoms, Isospin effect and
electron scattering [3, 4]. The prominent techniques [4] are ‗neutron scattering‘, ‗Alpha
emission‘ and ‗electron scattering‘. Radii of hadrons have been calculated directly from
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the experimental data of hadronic form factors. Experimental sources of hadronic from
factor include hadron-hadron and lepton-hadron scattering. As discussed in Ref. [5], a lot
of experimental work has been done on the measurement of electromagnetic form factors
(EMFF) of baryons and mesons.
On the theoretical side, the nuclear properties like rms radii of nuclei can be
probed by using different techniques such as Liquid Drop Model [6], Relativistic Mean
Field Theory [6-8], Hartee-Fock Bogoliubov (HFB) with the Skyrme Force [9], HarteeFock Bogoliubov (HFB) with Gogny Force [9], Extended Thomas Fermi Model with
Strutinski Integral (ETFSI) [9] and Macroscopic-Microscopic (MM) Model [9]. For
studying hadronic properties including rms radii, there exist many models such as MIT
Bag Model [10], Flux Tube Model [11], Lattice QCD Model [12] and Chiral Symmetry
Breaking of QCD [13].
Theoretical techniques of studying hadronic/nuclear properties including radii
comprise geometrical models [14]. A brief account of the geometrical models including
Generalized Chou Yang Model [14] is given. In the realm of this model, we computed
rms radii for several hadrons and light nuclei. Computations are based upon the
electromagnetic form factors of hadrons/lighter nuclei, as predicted by the Generalized
Chou Yang model. A comparison of the computed radii and those from scattering
experiments and other models, shows consistency.
The computed radii of hadrons plotted against their masses, depict an interesting
aspect. The radii decrease with increasing number of strange or antistrange quark content
in the hadrons. This aspect was highlighted and probed for both mesons and baryons
separately.
From the computed radii of lighter nuclei, it is observed that radii of Deuteron and
Alpha decrease with an increase in their mass. It was concluded that the reason for the
decreasing radii can be associated with the increasing number of nucleons inside the
nucleus. Two protons and two neutrons of Alpha particle (Helium nucleus) will be more
tightly packed by the residual strong force as compared to the pair of proton and neutron
inside a Deuteron nucleus. Thus, it was concluded that an analogy among the decreasing
radii of hadrons and those of lighter nuclei does exist; meaning that in both cases radii
decrease with increasing mass value.
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In order to provide a comprehensive account of this interesting problem, we give
a detailed literature review of the experimental (Chapter 2) and theoretical (Chapter 3)
attempts in this direction. Details of the Generalized Chou-model and its relevant success
have been given in Chapter 4. Results of our computations on radii of hadrons/lighter
nuclei based on Generalized Chou Yang model are discussed in Chapter 5. Conclusions
have also been drawn in this chapter.
References
[1]
D. Drechsel and W. Walcher, Rev. Mod. Phys. 80, 731(2008)
[2]
D. J. Gross and F. Wilczek, 1973a, Phys. Rev. D 8, 3633; Gross, D. J., and F.
Wilczek, 1973b, Phys. Rev. Lett. 30, 1343; Politzer, H. D., 1973, Phys. Rev.
Lett. 30, 1346.
[3]
D. Halliday, Introduction to Nuclear Physics, 2nd Edition, John Wiley & Sons
7(1996)
[4]
J. M. Blatt, Theoretical Nuclear Physics, Victor Dover Publishers (October 4,
1991)
[5]
Y. –L. Liu and Ming-Qiu Huang: Phys. Rev D 79, 114031 (2009), and
references therein.
[6]
J. S. Wang et al., Nucl. Phys. A 691 (2001) 618-630, and references therein.
[7]
Y.K. Gambhir, P. Ring, A. Thimet, Ann. Phys. 198 132(1990)
[8]
G.A. Lalazissis, S. Raman, P. Ring, At. Data Nucl. Data Tables 71, 1 (1999).
[9]
Z. Patyk et al., Phys Rev C 59, 2 (1999), and references therein.
[10]
K. Johnson: Acta Physica Polonica, B6, 865(1975), and references therein.
[11]
N. Isgur and J. Paton, Phys. Rev. D31, 2910 (1985).
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H.-W. Lin, S. D. Cohen, R. G. Edwards, and D. G. Richards 0803.3020.
(2008).
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V. Dmitrasinovic, R.H. Lemmer, R. Tegen, Comments Nucl. Part. Phys. 21,
71 (1993) and Phys. Lett. B284, 201(1992); V. Dmitrasinovic, H-J. Schulze
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R. Tegen, R.H. Lemmer, Phys. Rev. D52, 2855(1995).
[14]
(a) F. Aleem et al., Int. J. Mod Phys. A19, 4455, (2004). F. Aleem et al,:
CP888 (American Institute of Physics),—MTPR-06, edited by L. El Nadi
241 (2007); MTPR-08, Cairo, Egypt (April 2008).
(b) F. Aleem et al., J. Phys. G16, 269L, (1991); Phys. Rev. D44, 81 (1991); F.
Aleem and M. Saleem, Monograph on ―Chou-Yang model and Elastic
Reactions at high energies" Hadronic Press, FL, USA (1992) and references
therin, M. Saleem, Fazal-e-Aleem and I.A. Azhar., Europhys. Lett. 6, 201
(1988); Fazal-e-Aleem and S. Ali, Had. Jour.14, 173(1991), and references
therein.
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