3 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 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 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. 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. 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. FIG. 2: The bag pressure change with the radium of proton. The open circle is calculated with Eq.(14), and the line is its numerical simulation results, while the star is with the scenario that three quarks are surrounded by gluons. ¯ ψψ ∣ r = R = [ j$_{0}$ ( p $^{0}$R )] 2 − σ · ˆ r σ · ˆ r [ j$_{1}$ ( p $^{0}$R )] 2 = 0 [ j$_{0}$ ( p $^{0}$R )] 2 − [ j$_{1}$ ( p $^{0}$R )] 2 = 0 (11) p 0 $_{m}$R = 2 . 04 , or p 0 m = 2 . 04 R . (12) E$_{q}$ = ( g$_{q}$ + g$_{¯}$ $_{q}$) V 2 π $^{2}$¯ h 3 ∫ p 0 m 0 p $^{3}$dp 1 + e p/T ( R $_{)}$. (13) B = M − E$_{q}$ V . (14) B 1 / 4 = 0 . 17 R − 0 . $^{65}$. (15) ¯ E$_{q}$ = E$_{q}$ N$_{q}$ = ∫ p 0 m 0 p $^{3}$dp 1+ e p/T ( R ) p 0 m 0 p $^{2}$dp 1+ e p/T ( R ) . (16) Acknowledgments V. CONCLUSION IV. BAG PRESSURE 0.8 1 1.2 1.4 1.6 1.8 2 100 110 120 130 140 150 160 170 180 190 200 B$^{1/4}$ = 0.17 R −0.65 R (fm) B 1/4  (MeV) [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) [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-