P. GUPTA, I. MEHROTRA 1535

Table 7. r, 1r and 2

r for bb .

r (GeV−1) 1r (GeV) 2

r (fm)

Present work [21] Present work [21] Present work [22]

1s 1.574 1.823 0.8706 0.685 0.206 0.196

2s 2.523 3.100 0.6946 0.486 0.510 0.490

3s 3.207 0.6701 0.790 0.781

1p 2.306 2.446 0.4927 0.467 0.415 0.395

2p 3.017 0.44212 0.715 0.693

than the bb system i.e. heavy quarkonium have smaller

radii.

4. Summary and Conclusion

Heavy quarkonia system (and bb) have been studied in

the framework of non-relativistic Schrodinger equation

with energy dependent potential. Such potentials consti-

tute a way to include nonlinear effects in the Schrodinger

equation. The interquark potential used in the present

work is of harmonic oscillator plus inverse square form

with a small energy dependent term in harmonic oscilla-

tor part. This potential is more realistic compared to the

energy dependent harmonic oscillator potential used in

the work of Lombard which does not have the asymptotic

term. The energy dependence in the potential results in

the compression of the spectrum. As the quantum num-

bers increase the energy eigenvalues increase an upper

bound. Though the choice of potential parameters is not

unique, the above form represents a class of potentials

which can give a satisfactory explanation of the satura-

tion pattern in the spectra as well as the correct order of

magnitude of Leptonic decay widths both for cc and

bb systems. Our results for the Leptonic decay width of

1s state (1s) are much closer to the experimental values

compared to those obtained by Lombard (values given

within bracket in Table 5) for both cc and bb sys-

tems. This shows the importance of the asymptotic term

in the interquark potential in determining the wavefunc-

tion at the origin.

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