Study Of A Quark Model Of Nuclear Structure

In this dissertation we aim to study symmetric nuclear matter. At the mention of nuclear matter one always thinks of such properties as saturation density ρ_b⁰,bulk binding energy W,symmetry energy coefficient a₄,mcompressibility (K_ν)^-1,and the ratio of effective nucleon mass to free nucleon mass M_N/M_N-⁰ at the saturation density.From [l],we haveAn empirical determination by Green [2] yields a₄ = 23.5 Mev.From [3],the range of mcompressibility (K_ν)^-1= k_F²[d²{E/A)/dk_F²]_equil [4] is 210 ± 30(Mev).And according to the related calculations in previous papers the ratio M_N/M_N-⁰ should between 0.5 and 0.7.In [4],the authors (Chin etal) calculated these properties of nuclear matter using the σ — ω model in the framework of QHD.The numerical results are good except (K_ν)^-1 = 550Mev .In [5], the authors (Sugahara etal) reduce the incompressibility to 281 Mev by introducing the self-interaction of σ meson and ω meson into Lagrangian.In this thesis we study the nuclear matter using the quark-meson coupling model (QMC).In this model the quarks interact with each other by exchanging mesons. QMC was proposed originally by Guichon in [6].In that article the author assumed that the nucleons distribute uniformly in the nuclear matter and keep static. This model interpreted successfully the saturation of nuclear matter.The sourse term of u> is proportional to the density of nucleon ,and the source term of a is proportional to the product of nucleon density and s(a).Since s(a) decreases with the increasing expectation value of a, the repulsive force due to lo increases faster than the attractive force due to a meson when the nucleon density rises.As a result the net repulsive force will reduce the nucleon density again. This is just the saturation property of nuclear matter. In addition the author calculated the properties of nuclear matter and what is worth mentioning is that the value of incompressibility is below 2AQMev.After that a lot of works were carried out with the help of this model. In[7],Fleck et al interpreted the saturation properties of nuclear matter when taking into account of the motion of nucleon. Moreover, the boost of the composite system and some centre-of-mass correction are new sources of repulsion and therefore strongly reduce the need for an uj meson.In the works of Guichon et ai [8] the QMC model was generalized to the finitenuclei and the motion of nucleon was taken into account under the Born-Oppenheimer Approximation. The value of incompressibility is less than 300Mev,butMN/M^is about 0.8.We first present the Lagrangian of QMC model with the self-interaction of a and uj meson and derive quark field equations and meson mean-field equation in the mean-field approximation. In the second section of the first chapter we introduce the covariant MIT bag model. In the third section we derive the quark field operator using the covariant MIT bag model and obtaine the expectation value of the quark density and quark scalar density in the ground state, and consequently the a and u mean field.Hence we can calculate the properties of nuclear matter.In the second chapter we present our numerical results. First we consider the case without self-interaction (g2 = g% = C3 = 0),and we find that {Kv)'1 is less than 300Mew,but MN/MN0 is about 0.8.Then we introduce self-interaction ,the coupling constants of the self-interaction are chosen from [5], namely c3 = 71.3075, g2 = -7.2325 frrr\g3 = 0.6183.As a result MN/MN0 decreases, while (Kv)^l rises.We think that a possible reason of the fact is that these coupling constants are not applicable to QMC because they are coming from QHD and heavy nuclei . So we adjust these coupling constants .When R? = 0.6,03 = 215,(KV)¹ is about240,and §￡ is about0.7.When i2g = 0.8,c3 = 300,^)"Hs about 260,and ^â– jf is about 0.7.We have also calculated the change of nucleon effective mass , the nucleon radius, meson mean field and the binding energy with the nucleon density. We find that the change of nucleon effective mass is consistent with the change of the nucleon radius. We also find that ga decreases with the increase of the nucleon density.