content_image/409633.jpg content_image/409634.jpg content_image/409635.jpg content_image/409636.jpg content_image/409637.jpg content_image/409638.jpg content_image/409639.jpg content_image/409643.jpg
condition is the same as the requirement that the scalar density ¯ ψψ of the quark vanishes at the bag surface r = R . This leads to 

<img src='content_image/409633.jpg'>

or 

From Eq.(10), solution of the above equation is given by 

This result means that in order to keep the bag from being broken, the kinetic energy of any quark can not larger than p 0 m determined by the radius of the bag. 

Take p 0 m as the upper limit, we can separate the energy of quarks from the total of a proton 

For simplicity, we have neglected the chemical poten- tial, and treat the quarks as massless. Then g$_{q}$ = g$_{¯}$ q = N$_{c}$N$_{s}$N$_{f}$ = 3 × 2 × 2 = 12. 

The energy from gluon contribution provides the pres- sure effect directed from the region outside the bag 

Here M is the mass of the hadron. 

From Eq.(14), we can easily learn that the the bag pressure will change with radius as shown in Fig.(2). We also give the numerical formula 

The average kinetic energy of each quark can be calcu- lated as 

[1] Marc Vanderhaeghen, Nucl. Phys.A 805:210-220,2008. 

[2] J. Sowinski, Nucl.Phys.A 790:485-488,2007, 

[3] A. Bhattacharya, S. N. Banerjee, B.Chakraborti, S. Banerjee, Nucl. Phys. Proc. Suppl. 142 (2005) 13-15 

[4] F. Wilczek, Ann. Rev. Nucl. and Part. Sci. 32, 177(1982) 

[5] X. Artru and G. Mennessier, Nucl. Phys. B70, 93(1974),B.Andersson, G. Gustafson and B. S¨ oderberg, Z. Phys. C20,317(1983) 

<img src='content_image/409634.jpg'>

<img src='content_image/409635.jpg'>

## IV. BAG PRESSURE 

<img src='content_image/409636.jpg'>

<img src='content_image/409637.jpg'>

<img src='content_image/409638.jpg'>

<img src='content_image/409639.jpg'>

The energy carried by the valence quarks in a proton is then 3 × ¯ E$_{q}$ . So that contributions from gluons and sea quarks to the energy is M − 3 ¯ E$_{q}$ . The bag pressure decreases with the radium. This may be used to explain why the resonance particle (which has large radius thus small bag pressure) is usually unstable because their bags are more fragile. 

<img src='content_image/409643.jpg'>

In this work we have discussed some feature of a pro- ton from the bag model. Especially, we got the relations between temperature and the radius of the proton when a proton is treated as a non-interacting thermal equilib- rium QGP system. The bag pressure comes from the contribution of gluons. 

We are grateful to the financial support from China ChangSha University under grant No.SF080101. We also thank Prof. A. Bonasera for stimulating discussions and comments. 

[6] C. D. Detar and J. F. Donoghue, Ann. Rev. Nucl. Part. Sci. 33,235(1983) 

[7] Torbj¨ orn Sj¨ ostrand, Leif L¨ onnblad, Stephen Mrenna, Pe- ter Skrands, JHEP 0605(2006) 026 

[8] R. C. Hwa and C. B. Yang, J. Phys. G30(2004) S1117- S1120 

[9] C. B. YANG, Int. J. Mod. Phys. E 16, No. 10, 3148(2007) 

[10] C. Y. Wong, Introduction to High-Energy Heavy ion Col- 

## V. CONCLUSION 

## Acknowledgments 

