The mass spectra of both light and heavy mesons are studied in the Dirac equation with an equally mixed 4-vector and scalar power-law potential model. This potential provides an excellent fit not only to the mass spectra ofp°, ϕ, Ψ and υ families but also to those ofD, F andB mesons. The light quark masses inp° and ϕ as well as in atom-like mesons are very close to the current quark masses.

We show that both charmonium and upsilon spectra can be simultaneously fitted by an effective non-coulombic power-law potential with lowest order relativistic corrections. The fine-hyperfine splittings of these spectra can be well understood without considering the short distance coulombic part of the potential as suggested byqcd, if the Lorentz structure of the central potential is taken as an almost equal admixture of vector and scalar gluon exchanges. With this model we make several specific predictions for the upsilon spectra which could hopefully be tested in the near future.

A simple independent-quark-model based on the Dirac equation with logarithmic potential is used to calculate several properties of octet baryons such as magnetic moment, the axial vector coupling constantg_A (n) for neutronβ-decay and the charge radius of the proton. In view of the simplicity of the model, the results obtained are quite good.

The heavy mesons of the charmonium and upsilon family are described in an alternative static potential model chosen in a combination of Hulthen and linear potential. We find that the quark-confining potential in the form of an equal admixture of vector and scalar parts successfully explains the fine-hyperfine structures of$$c\bar c$$ and$$b\bar b$$ systems in a flavour-independent manner. The leptonic decay widths of the vector mesons ofψ and γ families are calculated taking into account the Poggio-Schnitzer correction. We obtain some of the bound states of the yet-to-be observed$$t\bar t$$ system for thet-quark mass ranging from 50 to 200 GeV.

A relativistic quark model based on Dirac equation with the independent-quark confining potential of the form (1 +γ⁰)[a ln(r/b)] is used to compute the weak electric and magnetic form factors for semileptonic baryonic decays in the electronic decay modes. The values obtained for (g₂/g₁) agree with the non relativistic results and those for (f₂/f₁) agree with the MIT bag model values of Donoghue and Holstein. The SU(3) symmetry breaking does not generate appreciable departures in (f₂/f₁) values from corresponding Cabibbo values.

The static properties such as magnetic moments, charge radii and axial vector coupling constant ratios of the quark core of baryons in the nucleon octet have been calculated in an independent-quark model based on the Dirac equation with equally mixed scalar-vector potential in linear form in the current quark mass limit. The results obtained with appropriate corrections due to centre-of-mass motion are in reasonable agreement with experimental data. The magnetic moments of the quark core of baryons in the charmed andb-flavoured sectors have also been calculated with this model and the overall predictions so obtained compare very well with other model predictions.

Weak electric and magnetic form factors for semileptonic baryon decays are calculated in a relativistic quark model based on the Dirac equation with the independent-quark confining potential of the formV_q(r)=1/2(1+γ⁰)(a²r+V₀). The values obtained for (g₂/g₁) are not very much different from the nonrelativistic results of Donoghue and Holstein. The values of (g₁/f₁) extracted from our model calculations of (f₂/f₁) in the Cabibbo limit compare well with the experimental values. The values of (f₂/f₁) for various semileptonic transitions are also estimated incorporating phenomenologically the effect of nonzerog₂ in the ratio (g₁/f₁). It is found that the SU(3)-symmetry breaking does not generate significant departures in (f₂/f₁) values from the corresponding Cabibbo predictions.

A relativistic model of independent quarks based on Dirac equation with an equally mixed scalar-vector square root confining potential is used to compute the quark core contributions to the static properties like magnetic moments, charge radii and axial vector coupling constant ratios of the baryon octet. The results obtained with appropriate corrections due to centre-of-mass motion agree fairly well with experimental values. The model is also extended to the study of magnetic moments of the quark core of baryons in the charmed andb-flavoured sectors and the overall predictions so obtained compare well with other model predictions.

The nucleon electromagnetic form factorsG_E^P(q²),G_M^P(q²) and the axial-vector form factor G_A(q²) are studied in a relativistic model of independent quarks confined by an equally mixed scalar-vector square root potentialV_q(r)=1/2(1+γ⁰)(ar^1/2+ν₀) taking into account the appropriate centre-of-mass corrections. The respective root-mean-square radii associated withG_E^P(q²) and G_A(q²) come out as [〈r²〉_E^P]^1/2=0.86 fm and 〈r_A²〉^1/2=0.88 fm. Restoration of chiral symmetry in this model is discussed to derive the pion-nucleon form factorG_πNN(q²) and consequently the pion-nucleon coupling constant is obtained asg_πNN(q²)=12.81 as compared tog_πNN(q²)_exp⋍13.