First-Order Symmetry Energy Induced by Neutron–Proton Mass Difference
Jian-Min Dong1** , Wei Zuo1 , Jian-Zhong Gu2
1 Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 7300002 China Institute of Atomic Energy, Beijing 102413
Abstract ：The 1st-order symmetry energy coefficient of nuclear matter induced merely by the neutron–proton (n–p) mass difference is derived analytically, which turns out to be completely model-independent. Based on this result, the 1st-order symmetry energy $E_{\rm sym,1}^{({\rm npDM})}(A)$ of heavy nuclei such as $^{208}$Pb induced by the n–p mass difference is investigated with the help of a local density approximation combined with the Skyrme energy density functionals. Although $E_{\rm sym,1}^{({\rm npDM})}(A)$ is small compared with the second-order symmetry energy, it cannot be dropped simply for an accurate estimation of nuclear masses as it is still larger than the rms deviation given by some accurate mass formulas. It is therefore suggested that one perhaps needs to distinguish the neutron mass from the proton one in the construction of nuclear density functionals.
收稿日期: 2016-06-08
出版日期: 2016-10-27
:
21.65.Ef
(Symmetry energy)
21.65.Cd
(Asymmetric matter, neutron matter)
21.60.Jz
(Nuclear Density Functional Theory and extensions (includes Hartree-Fock and random-phase approximations))
23.60.+e
(α-decay)
[1] Xu C and Ren Z Z 2012 Chin. Phys. Lett. 29 122102 [2] Baran V, Colonna M, Greco V and Toro M D 2005 Phys. Rep. 410 335 [3] Li B A, Chen L W and Ko C M 2008 Phys. Rep. 464 113 [4] Lattimer J M and Prakash M 2007 Phys. Rep. 442 109 [5] Kumar S, Ma Y G, Zhang G Q and Zhou C L 2011 Phys. Rev. C 84 044620 [6] Feng Z Q 2011 Phys. Rev. C 83 067604 [7] Yong G C 2011 Phys. Rev. C 84 014607 [8] Ma C W, Wang F, Ma Y G and Chan J 2011 Phys. Rev. C 83 064620 [9] Ma C W, Wei H L, Wang S S, Ma Y G, Wada R and Zhang Y L 2015 Phys. Lett. B 742 19 and reference therein [10] Ma C W, Pu J, Wang S S and Wei H L 2012 Chin. Phys. Lett. 29 062101 [11] Dong J, Zuo W and Scheid W 2011 Phys. Rev. Lett. 107 012501 [12] Rizzo C, Baran V, Colonna M, Corsi A and Toro M D 2011 Phys. Rev. C 83 014604 [13] Horowitz C J and Piekarewicz J 2001 Phys. Rev. Lett. 86 5647 [14] Lattimer J M and Prakash M 2000 Phys. Rep. 333 121 [15] Cavagnoli R, Menezes D P and Providencia C 2011 Phys. Rev. C 84 065810 [16] Cai B J and Chen L W 2012 Phys. Rev. C 85 024302 [17] Xu J, Chen L W, Li B A and Ma H R 2009 Phys. Rev. C 79 035802 [18] Seif W M and Basu D N 2014 Phys. Rev. C 89 028801 [19] Moustakidis C C 2012 Phys. Rev. C 86 015801 [20] Jiang H, Bao M, Chen L W, Zhao Y M and Arima A 2014 Phys. Rev. C 90 064303 [21] Jiang H, Wang N, Chen L W, Zhao Y M and Arima A 2015 Phys. Rev. C 91 054302 [22] Centelles M, Roca-Maza X, Vi?as X and Warda M 2009 Phys. Rev. Lett. 102 122502 [23] De J N and Samaddar S K 2012 Phys. Rev. C 85 024310 [24] De J N, Samaddar S K and Agrawal B K 2012 Phys. Lett. B 716 361 [25] Dong J, Zhang H, Wang L and Zuo W 2013 Phys. Rev. C 88 014302 [26] Fan X, Dong J and Zuo W 2014 Phys. Rev. C 89 017305 [27] Dong J, Zuo W and Gu J 2015 Phys. Rev. C 91 034315 [28] Dong J, Zuo W and Gu J 2013 Phys. Rev. C 87 014303 [29] Zhang Z W, Bao S S, Hu J N and Shen H 2014 Phys. Rev. C 90 054302 [30] Bennaceur K and Dobaczewski J 2005 Comput. Phys. Commun. 168 96 [31] Stoitsov M V, Dobaczewski J and Nazarewicz W R 2005 Comput. Phys. Commun. 167 43 [32] Stone J R and Reinhard G P 2007 Prog. Part. Nucl. Phys. 58 587 and references therein [33] Nakamura K et al (Particle Data Group) 2010 J. Phys. G 37 075021 [34] Chabanat E, Bonche P, Haensel P, Meyer J and Schaeffer R 1997 Nucl. Phys. A 627 710 [35] Chabanat E, Bonche P, Haensel P, Meyer J and Schaeffer R 1998 Nucl. Phys. A 635 231 [36] Gambacurta D, Li L, Colò G, Lombardo U, Giai N V and Zuo W 2011 Phys. Rev. C 84 024301 [37] Goriely S, Chamel N and Pearson J M 2009 Phys. Rev. Lett. 102 152503 Goriely S, Chamel N and Pearson J M 2010 Phys. Rev. C 82 035804 [38] Reinhard P G and Flocard H 1995 Nucl. Phys. A 584 467 [39] Dobaczewski J, Flocard H and Treiner J 1984 Nucl. Phys. A 422 103 [40] Bartel J, Quentin P, Brack M, Guet C and Hatkansson H B 1982 Nucl. Phys. A 386 79 [41] Nguyen V G and Sagawa H 1981 Phys. Lett. B 106 379 [42] Tondeur F, Brack M, Farine M and Pearson J M 1984 Nucl. Phys. A 420 297 [43] Samyn M, Goriely S, Bender M and Pearson J M 2004 Phys. Rev. C 70 044309 [44] Tondeur F, Goriely S, Pearson J M and Onsi M 2000 Phys. Rev. C 62 024308 [45] Pearson J M and Goriely S 2001 Phys. Rev. C 64 027301 [46] Sharma M M, Lalazissis G, K? nig J and Ring P 1995 Phys. Rev. Lett. 74 3744 [47] Agrawal B K, Shlomo S and Au V K 2003 Phys. Rev. C 68 031304 [48] Beiner M, Flocard H, Giai N V and Quentin P 1975 Nucl. Phys. A 238 29 [49] Bennour L, Heenen P H, Bonche P, Dobaczewski J and Flocard H 1989 Phys. Rev. C 40 2834 [50] Chen L W, Ko C M, Li B A and Xu J 2010 Phys. Rev. C 82 024321 [51] Kohler H S 1976 Nucl. Phys. A 258 301 [52] Pearson J M and Nayak R C 2000 Nucl. Phys. A 668 163 [53] M?ller P, Myers W D, Sagawa H and Yoshida S 2012 Phys. Rev. Lett. 108 052501 [54] Zhang H, Dong J, Ma N, Royer G, Li J and Zhang H 2014 Nucl. Phys. A 929 38 [55] Wang N, Liu M, Wu X and Meng J 2014 Phys. Lett. B 734 215 [56] Zhao P W, Li Z P, Yao J M and Meng J 2010 Phys. Rev. C 82 054319 [57] Long W H, Meng J, Giai N V and Zhou S G 2004 Phys. Rev. C 69 034319
[1]
.
[2]
.
[3]
.
[4]
.
[5]
.
[6]
.
[7]
.
[8]
MA Chun-Wang, PU Jie, WANG Shan-Shan, WEI Hui-Ling. The Symmetry Energy from the Neutron-Rich Nucleus Produced in the Intermediate-Energy 40,48 Ca and 58,64 Ni Projectile Fragmentation
[9]
ZHANG Fang,HU Bi-Tao,YONG Gao-Chan,ZUO Wei. Effects of Symmetry Energy in the Reaction 40 Ca+124 Sn at 140 MeV/Nucleon
[10]
ZHANG Fang**,LIU Yang,YONG Gao-Chan,ZUO Wei. Probing Nuclear Symmetry Energy with the Sub-threshold Pion Production
[11]
LI Zeng-Hua;**;ZHANG Da-Peng;SCHULZE Hans-Josef;ZUO Wei. Second-Order Contribution of the Incompressibility in Asymmetric Nuclear Matter
[12]
ZHOU Pei;TIAN Wen-Dong**;MA Yu-Gang**;CAI Xiang-Zhou;FANG De-Qing;WANG Hong-Wei
. The influence of Multi-Step Sequential Decay on Isoscaling and Fragment Isospin Distribution in GEMINI Simulation
[13]
BAI Chun-Lin;**;ZHANG HUAN-Qiao;ZHANG Xi-Zhen;XU Fu-Rong;H. Sagawa;G. Colò. Effect of the Tensor Force on Charge-Exchange Spin-Dependent Multipole Excitations
[14]
Sanjeev Kumar;Suneel Kumar. Systematic Study on System Size Dependence of Global Stopping: Role of Momentum-Dependent Interactions and Symmetry Energy
[15]
JIANG Wei-Zhou;CHEN Yun-Peng;LU Xing. De-excitation Energy of Superdeformed Secondary Minima of Odd-Odd Au Isotopes and Its Sensitivity to the Density Dependence of Symmetry Energy
2016, Vol. 33 
