ISSN: 0256-307X 中国物理快报 Chinese Physics Letters

Volume 29 Number 6 June 2012 A Series Journal of the Chinese Physical Society Distributed by IOP Publishing Online: http://iopscience.iop.org/cpl http://cpl.iphy.ac.cn

C HINESE P HYSICAL S OCIETY CHIN. PHYS. LETT. Vol. 29, No. 6 (2012) 062101 The Symmetry Energy from the Neutron-Rich Nucleus Produced in the Intermediate-Energy 40,48Ca and 58,64Ni Projectile Fragmentation *

MA Chun-Wang(马春旺)**, PU Jie(普洁), WANG Shan-Shan(王闪闪), WEI Hui-Ling(魏慧玲) Department of Physics, Henan Normal University, Xinxiang 453007

(Received 9 January 2012) In the framework of a modified Fisher model, using the isobaric yield ratio method, we investigate the fragments produced in the 140 퐴 MeV 40,48Ca+9Be and 58,64Ni+9Be projectile fragmentation reactions. Using different approximation methods, 푎sym/푇 (the ratio of symmetry-energy coefficient to temperature) of symmetric and neutron-rich fragments are extracted. It is found that 푎sym/푇 of fragments depend on the reference nucleus and the neutron excess of fragments. The 푎sym/푇 of the isobar decreases when the neutron-excess of the isobar increases, while for a fragment with the same neutron-excess, 푎sym/푇 increases as the mass of the fragment increases but saturate when the mass of the fragment becomes larger.

PACS: 21.65.Cd, 21.65.Ef, 21.65.Mn DOI: 10.1088/0256-307X/29/6/062101

The symmetry energy, which is an important pa- 140 퐴 MeV 40,48Ca and 58,64Ni projectile fragmenta- rameter in the equation of the state of nuclear matter, tion data well.[25] In this Letter, the IYR for fragments is very important in nuclear physics and astrophysics. in the 40,48Ca and 58,64Ni projectile fragmentation[26] The symmetry energy of nuclear matter both of sub- will be revisited, and 푎sym/푇 of neutron-rich frag- saturation and supra-saturation density, and at high ments will be extracted using the IYR methods. temperature are still unclear due to its complex de- Following the MFM theory,[23,24] the yield of a pendence on both density and temperature. Large fragment with mass number 퐴 and neutron excess difference of theoretical results of symmetry energy 퐼(퐼 ≡ 푁 − 푍), 푌 (퐴, 퐼) is given by for nuclear matter has been demonstrated from differ- −휏 ent models, and even for the same model but using 푌 (퐴, 퐼) = 퐶퐴 exp{[푊 (퐴, 퐼) + 휇푛푁 + 휇푝푍]/푇 different interactions.[1−4] Many experimental works + 푁 ln(푁/퐴) + 푍 ln(푍/퐴)}, (1) have concentrated on studying the nuclear equation of state and the liquid-gas phase transition in nu- where 퐶 is a constant. The 퐴−휏 term originates from clear matter[5−11] in heavy-ion collisions (HIC). The the entropy of the fragment, 휏’s for all fragments are [23] symmetry energy and temperature of hot emitting identical; 휇푛 and 휇푝 are the neutron and proton sources at different densities and temperatures were chemical potentials, respectively; and 푊 (퐴, 퐼) is the also investigated using the isotopic yields in different free energy of the cluster, which is supposed to equal models.[9,5,12−21] its binding energy at a given 푇 and density 휌. Using In the early 1980s, a study of the isotopic-yield dis- the semiclassical mass formula,[27,28] 푊 (퐴, 퐼) can be tributions of intermediate mass fragments produced in written as high-energy proton-induced multifragmentation reac- 2 1/3 tions showed that the distributions can be well de- 푊 (퐴, 퐼) = − 푎sym(휌, 푇 )퐼 /퐴−푎푐(휌, 푇 )푍(푍−1)/퐴 scribed by a modified Fisher model (MFM),[22,23] in 2/3 + 푎푣(휌, 푇 )퐴 − 푎푠(휌, 푇 )퐴 − 훿(푁, 푍). which the isotope production is governed by the avail- (2) able free energy. Instead of attempting to determine a unique set of the parameters globally, parameters are For simplification, the 푇 and 휌 dependences of 푎푖(휌, 푇 ) related to the isobaric yields in MFM. In the ratios in Eq. (2) are written as 푎푖 (푖 = 푣, 푠, 푐, sym), where between isobars, many terms contributing to the free the indexes 푣, 푠, 푐, and sym represent the coefficients energy cancel out and one can study the specific terms of volume-, surface-, Coulomb-, and symmetry-energy individually and discuss the meaning of the extracted terms, respectively; 훿(푁, 푍) is the pairing energy. It parameters more clearly. Huang et al.[24] addressed should be kept in mind that these coefficients still the advantage of extracting the coefficient of symme- depend on density and temperature and they actu- try energy to temperature (in the form of 푎sym/푇 , ally include both the binding energy and the entropy where 푇 is the temperature) of measured fragments contributions.[23] In the MFM model and other models by the isobaric yield ratio (IYR) methods. Correla- based on free energy, it is difficult to separate 푎푖 and tions between 푎sym/푇 and IYRs were found to fit the 푇 . Only 푎푖/푇 can be extracted according to Eq. (2).

*Supported by the National Natural Science Foundation of China under Grant No 10905017, the Program for Innovative Research Team (in Science and Technology) under Grant No 2010IRTSTHN002 in the Universities of Henan Province, and the Young Teacher Project in Henan Normal University. **Corresponding author. Email: [email protected] © 2012 Chinese Physical Society and IOP Publishing Ltd 062101-1 CHIN. PHYS. LETT. Vol. 29, No. 6 (2012) 062101

1/3 It should also be noted that for a neutron-rich nu- If replacing the [∆휇 + 2푎푐(푍 − 1)/퐴 ]/푇 term in cleus, the symmetry energy should be separated to Eq. (6) by ln[푅(1, −1, 퐴)], i.e., taking the IYR of the the surface-symmetry energy 푎surf and the volume- mirror nuclei as references, we have [29,30] symmetry energy 푎vol. To compare the results 푎sym 퐴 with Huang’s, the separation of 푎sym is not included = {ln[푅(1, −1, 퐴)] − ln[푅(퐼 + 2, 퐼, 퐴)] in this work. 푇 4(퐼 + 1) 1/3 The yield ratio between isobars differing by 2 units − 푎푐(퐼 + 1)/(퐴 푇 ) + Δ퐼 }. (7) in 퐼 is defined as Taking the IYR of the 퐼 − 2 fragments as the ref- 푅(퐼 + 2, 퐼, 퐴) = 푌 (퐴, 퐼 + 2)/푌 (퐴, 퐼) erences, we have = exp{[푊 (퐼 + 2, 퐴) − 푊 (퐼, 퐴) 푎 퐴 + (휇 − 휇 )]/푇 sym = {ln[푅(퐼, 퐼 − 2, 퐴)] − ln[푅(퐼 + 2, 퐼, 퐴)] 푛 푝 푇 8 + 푆mix(퐼 + 2, 퐴) − 푆mix(퐼, 퐴)}, 1/3 − Δ퐼−2 + Δ퐼 − 2푎푐/(퐴 푇 )}. (8) (3) Taking the fragments produced in the 140 퐴 MeV where 푆mix(퐼, 퐴) = 푁 ln(푁/퐴) + 푍 ln(푍/퐴). Assum- 40,48Ca+9Be and 58,64Ni+9Be reactions[26] as exam- ing that 푎푠, 푎푐, 휇푛, and 휇푝 for the 퐼 and 퐼 + 2 isobars are the same, inserting Eq. (2) to Eq. (3), and taking ples, the 푎sym/푇 of neutron-rich fragments will be ex- the logarithm of the resultant equation, one gets IYR tracted using Eqs. (6)–(8). for isobars with odd 퐼, In Fig. 1, the IYRs for the fragments with 퐼 from −1 to 7 are plotted. The IYR for mirror nuclei of 64 9 ln[푅(퐼 + 2, 퐼, 퐴)] − Δ퐼 = [∆휇 − 4푎sym(퐼 + 1)/퐴 the Ni+ Be reactions is absent due to the lack of 1/3 measured data. The IYRs for these isobars increase + 2푎푐(푍 − 1)/퐴 ]/푇, (4) almost “linearly” as 퐴 of the fragments increases, but the “slope” decreases when 퐼 increases. Equation (5) where Δ퐼 = 푆mix(퐼 +2, 퐴)−푆mix(퐼, 퐴), ∆휇 = 휇푛 −휇푝, can well fit the IYRs for the mirror nuclei as shown 퐴 and 푍 are for the reference nuclei with 퐼. The pair- by the lines. The fitted 푎푐/푇 (∆휇/푇 ) for the mirror ing energy of the odd-퐼 fragments is zero in Eq. (2) nuclei are: 0.3728 ± 0.0776 (−0.6427 ± 0.6237) of 40Ca according to Ref. [31]. reaction, 0.5053 ± 0.0791 (−0.8655 ± 0.7089) of 58Ni reaction, and 0.7842 ± 0.0622 (−1.6805 ± 0.5573) of 6 40Ca+9Be 48Ca+9Be 48Ca reaction, respectively. The n/p values of 40Ca, 4 I=-1 58 64 48 2 I=1 Ni, Ni, and Ca are 1.0, 1.07, 1.21, and 1.4, re- I=3 0 spectively. The extracted 푎푐/푇 increases when n/p of I -2 =5 projectile increases, while ∆휇/푇 decreases when n/p -4 I=7

lnR( I⇁֒I֒A )- ∆ -6 of projectile increases. The extracted 푎푐/푇 will be 6 used in the extraction of 푎sym/푇 for other neutron- 4 58Ni+9Be 64Ni+9Be rich isobars using Eqs. (6)–(8). Due to the lack of data 2 64 0 in the Ni reaction, the average values of 푎푐/푇 and -2 ∆휇/푇 of the 48Ca and 58Ni reactions are used instead. -4 In Fig. 2, the extracted 푎sym/푇 ’s of fragments with -6 ,(lnR( I⇁֒I֒A )- ∆ different 퐼 are plotted. The methods using Eqs. (6 20 30 40 50 20 30 40 50 60 A A (7), and (8) to extract 푎sym/푇 of fragments are labeled as (a), (b), and (c), respectively. Fig. 1. (Color online) The isobaric yield ratios {in the Firstly, we discuss the difference between the re- form of ln[푅(퐼 + 2, 퐼, 퐴)] − Δ} for fragments produced in the 140 퐴 MeV 40,48Ca + 9Be and 58,64Ni + 9Be reac- sults of methods (a), (b), and (c). Method (a) as- tions. The lines are the fitting results of the mirror nuclei sumes that ∆휇/푇 and 푎푐/푇 of all fragments are equal, isobars by Eq. (5). while methods (b) and (c) use the IYRs of other iso- For the mirror nuclei, Δ = 0, one obtains bars as the reference. Actually, 푎푐/푇 of the frag-

1/3 ments in the four reactions of the mirror nuclei are ln[푅(1, −1, 퐴)] = [∆휇 + 2푎푐(푍 − 1)/퐴 ]/푇, (5) very small. Assuming that 푎푐/푇 can be omitted, ln 푅(퐼, 퐼 + 2, 퐴) equals to the (휇 − 휇 )/푇 term. The ∆휇/푇 and 푎푐/푇 of the mirror nuclei can be obtained 푛 푝 decreasing ln 푅(퐼, 퐼 +2, 퐴) as shown in Fig. 1 indicates using Eq. (5). Assuming that ∆휇/푇 and 푎푐/푇 of all that (휇 − 휇 )/푇 decreases when the fragments be- the fragments are equal, and using the ∆휇/푇 and 푎푐/푇 푛 푝 values of the mirror nuclei, from Eq. (4) one obtains come more neutron-rich. The directly using (휇푛 − 휇푝) of the mirror nuclei to substitute ∆휇 in Eq. (6) will 푎sym 퐴 1/3 overestimate 푎 /푇 , as shown in Fig. 2. The method = {[∆휇 + 2푎푐(푍 − 1)/퐴 ]/푇 sym 푇 4(퐼 + 1) of using (휇푛 − 휇푝)/푇 and 푎푐/푇 directly or the method − ln[푅(퐼 + 2, 퐼, 퐴)] + Δ퐼 }. (6) of taking the IYR of the mirror nuclei are actually 062101-2 CHIN. PHYS. LETT. Vol. 29, No. 6 (2012) 062101 equivalent; the results of (a) and (b) have very little with mass, but saturate in larger mass fragments. The difference. In comparison of methods (a) and (c),the increase of 푎sym/푇 with mass becomes slower when 퐼 limitation of method (b) is that there is no correspond- increases. Though the isotopic(isotonic)-yield distri- [26,32] ing mirror nucleus as reference for the very neutron- bution shows no staggering, 푎sym/푇 ’s in (a), (b), rich nucleus. The results of (a), (b), and (c) indicate and (c) show staggering, especially in (c). that, for fragments with the same 퐼, 푎sym/푇 increases

25 40Ca+9Be 20 (a) / T 15 (b) sym

a 10 (c) 5 I=1 I=3        

48Ca+9Be 20 / T 10 sym a 0 I=1 I=3 I=5 I=7                    

30 58Ni+9Be I=7 / T 20 sym a 10 I=1 I=3 I=5  30 40 50 30 40 50 40 45 50 55    40 64Ni+9Be 30 / T 20 sym

a 10 0 I=1 I=3 I=5 I=7  30 40 50  30 40 50 60 30 40 50 60 40 45 50 55 60

AA AA 40,48 9 58,64 9 Fig. 2. (Color online) 푎sym/푇 of fragments produced in the 140 퐴 MeV Ca + Be and Ni + Be reactions. (a), (b), and (c) represent the results of different methods used. See the text for explanation. (a) (b) (c) ments with the increasing 퐼 is also shown. In Eqs. (7) 30 and (8), the 푎푐/푇 term have the same value, thus 25 the differences are introduced by the reference nuclei. 20 / T Theoretically, 푎sym/푇 ’s in Eqs. (7) and (8) are equal

sym 15

a if ln 푅(퐼, 퐼 + 2, 퐴) decrease equidifferently. Due to 10 ln 푅(퐼, 퐼 + 2, 퐴) decrease gradually as shown in Fig. 1,

I/ this accounts for the increasing difference between the 5 58Ni+9Be I/ I/ 48Ca+9Be results of (b) and (c). 0 I/ 40Ca+9Be  20 30 40 5060 20 30 40 50 20 30 40 50 60 Lastly, we discuss the results of 푎sym/푇 of isobars AAA that have different neutron-excess 퐼. The results in Fig. 2 are re-plotted in Fig. 3, in which different meth- Fig. 3. (Color online) 푎sym/푇 of the neutron-rich isobars produced in the 140 퐴 MeV 40,48Ca + 9Be and 58Ni + ods are grouped and used but with a direct comparison 9Be reactions but grouped as the methods used. (a), (b), of 푎sym/푇 of fragments with different 퐼. It is clearly and (c) are the results according to Eqs. (6), (7) and (8), shown that 푎sym/푇 ’s of isobars decrease as they be- respectively. come more neutron-rich both in results of (a) and (c). Secondly, we discuss the difference between meth- However, the difference becomes smaller when 퐼 be- ods (b) and (c), which take different IYRs as reference. comes larger, especially in results of (c). As for the The results of (b) and (c) of the 퐼 = 1 fragments are dependence on the n/p of projectile, there is no obvi- similar to (but a little smaller than) the results ob- ous difference in the results of the 퐼 = 1 isobars while tained in Ref. [24]. For the 퐼 = 1 fragments of 58Ni, in the more neutron-rich isobars, there are not enough 푎sym/푇 ’s form a plateau when 퐴 > 30. For the 퐼 = 1 data to compare. fragments, the results of (b) and (c) totally overlap, The secondary decay process in HIC influences the while for the 퐼 > 1 fragments, the difference between yield of fragment greatly, and thus influences the re- the results of (b) and (c) is clearly shown, and the sultant information based on yield of fragment.[17] If results of (b) are generally larger than those of (c). all fragments are formed at a time from the primary At the same time, the decreasing of 푎sym/푇 of frag- emitting source for a given density and temperature,

062101-3 CHIN. PHYS. LETT. Vol. 29, No. 6 (2012) 062101

푎sym/푇 of fragments should be a constant. In HIC, Davalos A, Menchaca-Rocha A, Nebbia G, Prete G, Rizzi the times when the fragment is created and when it V, Ruangma A, Shetty D V, Souliotis G, Stasze P, Veselsky is finally detected are quite different. The sequen- M, Viesti G, Winchester E M and Yennello S J 2005 Phys. Rev. C 71 054606 tial decay significantly modifies the 푎sym/푇 fragments. [12] Xu H S, Tsang M B, Liu T X, Liu X D, Lynch W G, Tan Thus, the result of Ref. [24] and this work show that W P, Molen A, Verde G, Wagner A, Xi H F, Gelbke C K, 푎sym/푇 of the fragment depends on its mass. Beaulieu L, Davin B, Larochelle Y, Lefort T, Souza R T, In summary, based on different approximations in Yanez R, Viola V E, Charity R J and Sobotka L G 2000 Phys. Rev. Lett. 85 716 the framework of MFM, the IYR methods are used to [13] Tsang M B, Bougault R, Charity R, Durand D, Friedman extract 푎sym/푇 of neutron-rich fragments produced in W A, Gulminelli F, Fèvre A L, Raduta A H, Raduta A R, the 140 퐴 MeV 40,48Ca+9Be and 58,64Ni+9Be projec- Souza S, Trautmann W and Wada R 2006 Eur. Phys. J. A 30 tile fragmentation. Due to the influence of sequential 129 [14] Wada R, Tezkratt R, Hagel K, Haddad F, Kolomiets A, Lou decay, the extracted 푎sym/푇 of the fragment is found Y, Li J, Shimooka M, Shlomo S, Utley D, Xiao B, Mdei- to have dependence on its mass. For fragments that wayeh N, Natowitz J B, Majka Z, Cibor J, Kozik T and Sosin Z 1997 Phys. Rev. C 55 227 have same 퐼, 푎sym/푇 increases with its mass but satu- [15] Tsang M B, Gelbke C K, Liu X D, Lynch W G, Tan W P, rates when the mass becomes large enough; while for Verde G, Xu H S, Friedman W A, Donangelo R, Souza S isobars, 푎sym/푇 decreases as 퐼 increases. It is found R, Das C B, Gupta S D and Zhabinsky D 2001 Phys. Rev. that 푎sym/푇 of the fragment extracted is influenced C 64 054615 by the reference nucleus used. However, the reference [16] Botvina A S, Lozhkin O V and Trautmann W 2002 Phys. Rev. C 65 044610 nucleus only modifies the results in some degree and [17] Zhou P, Tian W D, Y G, Cai X Z, Fang D Q and Wang does not change the trends of the 푎sym/푇 of the frag- H W 2011 Phys. Rev. C 84 037605 ments. [18] Y, Fang D Q, Ma Y G, Cai X Z, Tian W D, Wang H W We thank Dr. HUANG Mei-Rong and Professor and Guo W 2009 Chin. Phys. Lett. 26 082503 [19] Fang D Q, Ma Y G, Zhong C, Ma C W, Cai X Z, Chen J G, Roy Wada, at the Institute of Modern Physics, Chi- Guo W, Su Q M, Tian W D, Wang K, Yan T Z and Shen nese Academy of Science, for the full discussion. W Q 2007 J. Phys. G: Nucl. Part. Phys. 34 2173 [20] Ono A, Danielewicz P, Friedman W A, Lynch W G and Tsang M B 2003 Phys. Rev. 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062101-4 Chinese Physics Letters Volume 29 Number 6 June 2012

GENERAL 060201 Exact Solutions of Nonlinear Evolution Equations in Mathematical Physics Using the Modified Simple Equation Method E. M. E. Zayed, S. A. Hoda Ibrahim 060202 The Reduction of Chazy Classes and Other Third-Order Differential Equations Related to Boundary Layer Flow Models K. Fakhar, A. H. Kara 060203 Exact Solutions to a Toda-Like Lattice Equation in 2+1 Dimensions WU Yong-Qi 060204 Weak Signal Frequency Detection Based on a Fractional-Order Bistable System HE Gui-Tian, LUO Mao-Kang 060301 Quantum Cyclotron Orbits of a Neutral Atom Trapped in a Triple Well with a Synthetic Gauge Field WANG Qiang, YE Chong, FU Li-Bin 060302 Macroscopic Quantum States and Quantum Phase Transition in the Dicke Model LIAN Jin-Ling, ZHANG Yuan-Wei, LIANG Jiu-Qing 060303 Quantum Teleportation between Two Distant Bose–Einstein Condensates GUO Yu, LUO Xiao-Bing 060304 Experimental Generation of Multimode Squeezing in an Optical Parametric Amplifier LIU Kui, CUI Shu-Zhen, YANG Rong-Guo, ZHANG Jun-Xiang, GAO Jiang-Rui 060305 Quantum Discord and Entanglement in Heisenberg XXZ Spin Chain after Quenches REN Jie, WU Yin-Zhong, ZHU Shi-Qun 060306 Energy Spectra of the Coulomb Perturbed Potential in N-Dimensional Hilbert Space Ramesh Kumar, Fakir Chand 060307 Solutions to the Klein–Gordon Equation with Equal Scalar and Vector Modified Hylleraas Plus Exponential Rosen Morse Potentials Akpan N. Ikot 060401 Influence of the Earth’s Rotation on Measurement of Newton’s Constant by using the Angular Acceleration Method LUO Jie, SHAO Cheng-Gang, WANG Dian-Hong, TIAN Yuan 060501 Bifurcation and Stability Analysis of the Hamiltonian–Casimir Model of Liquid Sloshing Salman Ahmad, YUE Bao-Zeng 060502 Modified Homotopy Perturbation Method for Certain Strongly Nonlinear Oscillators NIU Yao-Bin, WANG Zhong-Wei, DONG Si-Wei 060503 Role of the Bath Spectrum in the Specific Heat Anomalies of a Damped Oscillator BAI Zhan-Wu 060504 Study on Congestion and Bursting in Small-World Networks with Time Delay from the Viewpoint of Nonlinear Dynamics LIU Yan, LIU Li-Guang, WANG Hang 060505 Variational Approach for Fractional Diffusion-Wave Equations on Cantor Sets WU Guo-Cheng, WU Kai-Teng 060506 Dynamics in the Parameter Space of a Neuron Model Paulo C. Rech 060507 Amplitude Oscillations of the Resonant Phenomena in a Frenkel–Kontorova Model with an Incommensurate Structure YAN Yan-Zong, WANG Cang-Long, SHAO Zhi-Gang, YANG Lei 060508 New Wronskian Form of the N-Soliton Solution to a (2+1)-Dimensional Breaking Soliton Equation CUI Kai 060509 Non-Rational Rogue Waves Induced by Inhomogeneity HE Jing-Song, WANG You-Ying, LI Lin-Jing 060701 Influence of Passivation Layers for Metal Grating-Based Quantum Well Infrared Photodetectors LIU Dong, FU Yong-Qi, YANG Le-Chen, ZHANG Bao-Shun, LI Hai-Jun, FU Kai, XIONG Min 060702 Fatigue-Induced Micro-damage Characterization of Austenitic Stainless Steel 316 Using Innovative Nonlinear Acoustics Chung-Seok KIM, Kyung-Young JHANG

THE PHYSICS OF ELEMENTARY PARTICLES AND FIELDS 061201 An Improved Quasi-particle Model Framework for Quark-Gluon Plasma from the Path Integral Formalism CAO Jing, A-Meng, SUN Wei-Min, ZONG Hong-Shi

NUCLEAR PHYSICS 062101 The Symmetry Energy from the Neutron-Rich Nucleus Produced in the Intermediate-Energy 40,48Ca and 58,64Ni Projectile Fragmentation MA Chun-Wang, PU Jie, WANG Shan-Shan, WEI Hui-Ling 062102 High Spin States of 113In MA Ke-Yan, LU Jing-Bin, YANG Dong, LI Jian, WANG Hui-Dong, LIU Yun-Zuo, WU Xiao-Guang, ZHU Li-Hua, ZHENG Yun, HE Chuang-Ye 062103 High-Spin Structure in Odd-Odd 160Lu Nucleus WANG Lie-Lin, LU Jing-Bin, YANG Dong, MA Ke-Yan, ZHOU Yin-Hang, -Chang, WU Xiao-Guang, WEN Shu-Xian, LI Guang-Sheng, YANG Chun-Xiang 062104 Symmetry Potential and Effective Mass with Consistent Three-Body Force LI Zeng-Hua, ZUO Wei 062901 Radio-Frequency Power Test of a Four-Rod RFQ Accelerator for PKUNIFTY ZENG Hong-Jin, LIU Ge, LU Yuan-Rong, CHEN Wei, ZHOU Quan-Feng, ZHU Kun, XIA Wen-Long, SHI Ben-Liang, GAO Shu-Li, YAN Xue-Qing, GUO Zhi-Yu, CHEN Jia-Er

ATOMIC AND MOLECULAR PHYSICS 063101 Relativistic Quadrupole Polarizability for the Ground State of Hydrogen-Like Ions ZHANG Yong-Hui, TANG Li-Yan, ZHANG Xian-Zhou, SHI Ting-Yun, Jim Mitroy 063201 Shake-up Processes in the 3d Photoionization of Sr I and the Subsequent Auger Decay DING Xiao-Bin, DONG Chen-Zhong, Gerard O’Sullivan 063301 Chaotic Dynamics of Triatomic Normal Mode Molecules ZHAI Liang-Jun, ZHENG Yu-Jun, DING Shi-Liang 2 3 − 4 063401 The Rate Constant Calculations for the Reaction H( S)+NH(X Σ ) to N( S)+H2 by using Quantum Mechanics Method ZHAI Hong-Sheng, ZHOU Pan-Wang

FUNDAMENTAL AREAS OF PHENOMENOLOGY(INCLUDING APPLICATIONS) 064101 Electrostatic Levitation of Plant Seeds and Flower Buds HU Liang, WANG Hai-Peng, LI Liu-Hui, WEI Bing-Bo 064201 All-Fiber Gain-Switched Thulium-Doped Fiber Laser Pumped by 1.558 µm Laser ZHOU Ren-Lai, ZHAO Jie, YUANG-Chi, CHEN Zhao-Yu, JU You-Lun, WANG Yue-Zhu 064202 High-Stability Superfluorescent Fiber Source Based on an Er3+-Doped Photonic Crystal Fiber LIU Cheng-Xiang, ZHANG Li, WU Xu, RUAN Shuang-Chen

064203 Generation of Ultraviolet Radiation at 266 nm with RbBe2BO3F2 Crystal WANG Li-Rong, WANG Gui-Ling, ZHANG Xin, LIU Li-Juan, WANG Xiao-Yang, ZHU Yong, CHEN Chuang-Tian 064204 Characteristic Optimization of 1.3 µm High-Speed MQW InGaAsP-AlGaInAs Lasers MAO Yi-Wei, WANG Yao, CHEN Yang-Hua, XUE Zheng-Qun, LIN Qi, DUAN Yan-Min, SU Hui 064205 Optical Torque Exerted on a Rotator under Illumination of a Vortex Beam LI Dong-Hua, PU Ji-Xiong, WANG Xi-Qing 064206 A Polarization-Adjustable Picosecond Deep-Ultraviolet Laser for Spin- and Angle-Resolved Photoemission Spectroscopy ZHANG Feng-Feng, YANG Feng, ZHANG Shen-Jin, WANG Zhi-Min, XU Feng-Liang, PENG Qin-Jun, ZHANG Jing-Yuan, WANG Xiao-Yang, CHEN Chuang-Tian, XU Zu-Yan 064207 A Tunable Ultrafast Source by Sum-Frequency Generation between Two Actively Synchronized Ultrafast Lasers XUAN Hong-Wen, WANG Nan, ZHANG Yong-Dong, WANG Zhao-Hua, WEI Zhi-Yi 064208 Beam Splitting in Induced Inhomogeneous Media WANG Chun-Fang, BAI Yan-Feng, GUO Hong-Ju, CHENG Jing 064209 Experimental Study of Tunneling modes in Photonic Crystal Heterostructure Consisting of Single-Negative Materials ZHANG Li-Wei, ZHANG Ye-Wen, HE Li, WANG You-Zhen 064210 Optical 90◦ Hybrid Based on an InP 4 × 4 Multimode Interference Coupler for Coherent Receiver Application LIU Wei-Hua, ZHAO Yan-Li, XU Cheng-Zhi, ZHAO Jian-Yi, LIU Wen, XU Yuan-Zhong 064211 Self-Trapping of Three-Dimensional Spatiotemporal Solitary Waves in Self-Focusing Kerr Media YANG Zheng-Ping, ZHONG Wei-Ping 064212 The Laser Action of a Yb:CLNGG Crystal with an Efficiency Approaching Its Quantum Defect Imposed Limit ZHOU Zhi-Chao, TIAN Xue-Ping, DAI Qi-Biao, HAN Wen-Juan, HUANG Jia-Yin, LIU Jun-Hai, ZHANG Huai-Jin 064213 Self-Detection of Leaking Pipes by One-Dimensional Photonic Crystals ZHOU Yan, YIN Li-Qun 064214 A Surface Plasmon Polariton Electro-Optic Switch Based on a Metal-Insulator-Metal Structure with a Strip Waveguide and Two Side-Coupled Cavities ZHU Yun-Jin, HUANG Xu-Guang, MEI Xian 064301 Flow-Noise Calculation Using the Mutual Coupling Between Vulcanized Rubber and the Flow Around in Water LI Xue-Gang, YANG Kun-De, MA Yuan-Liang 064302 Broadband Attenuation in Phononic Beams Induced by Periodic Arrays of Feedback Shunted Piezoelectric Patches WANG Jian-Wei, WANG Gang, CHEN Sheng-Bing, WEN Ji-Hong 064701 Energy Measurement of Bubble Bursting Based on Vibration Signals LIU Xiao-Bo, ZHANG Jian-Run, LI Pu, LE Van-Quynh 064702 A New Method of Simulating Fiber Suspensions and Applications to Channel Flows YANG Wei, ZHOU Kun 064703 A Computational Study of Cavitation Model Validity Using a New Quantitative Criterion Hagar Alm El-Din, ZHANG Yu-Sheng, Medhat Elkelawy 064704 Large-Eddy Simulation of Underexpanded Supersonic Swirling Jets WANG Guo-Lei, LU Xi-Yun 064705 Reducing Spurious Velocities at the Interfaces of Two-Phase Flows for Lattice Boltzmann Simulations WEI Yi-Kun, QIAN Yue-Hong 064706 Fractal Analysis of Robertson-Stiff Fluid Flow in Porous Media YUN Mei-Juan, ZHENG Wei PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES 065201 Electrostatic Dust Acoustic Solitons in Pair-Ion-Electron Plasmas Hafeez Ur Rehman 065202 The Effect of Spectral Index Parameter κ on Obliquely Propagating Solitary Wave Structures in Magneto-Rotating Plasmas S. Hussain CONDENSED MATTER: STRUCTURE, MECHANICAL AND THERMAL PROPERTIES 066101 Self Ordering of Nematic Liquid Crystal Molecules in HPDLC Bragg Gratings CHENG Wen-Kai, GAO Bin, PU Hai-Hui, LIU Jian-Hua 066102 Laser-Induced Distortions and Disturbance Propagation of Delocalized Electronic States in Monatomic Carbon Chains YANG Gong-Xian, GONG Xiu-Fang 066201 Cross-over of the Plasticity Mechanism in Nanocrystalline Cu YUE Yong-Hai, WANG Li-Hua, ZHANG Ze, HAN Xiao-Dong

066202 Theoretical Study of the Structural and Thermodynamic Properties of Amorphous SiO2 and Amorphous SiO2 with an Oxygen Defect Center SU Wei, LOU Shu-Qin, YIN Guo-Lu 066301 Nano-Metal Film Thermal Conductivity Measurement by using the Femtosecond Laser Pump and Probe Method ZHU Li-Dan, SUN Fang-Yuan, ZHU Jie, TANG Da-Wei, LI Yu-Hua, GUO Chao-Hong

066801 The Structural Modification of LiTaO3 Crystal Induced by 100-keV H-ion Implantation PANG Li-Long, WANG Zhi-Guang, YAO Cun-Feng, ZANG Hang, LI Yuan-Fei, SUN Jian-Rong, SHEN Tie-Long, WEI Kong-Fang, ZHU Ya-Bin, SHENG Yan-Bin, CUI Ming-Huan, JIN Yun-Fan 066802 Modulation of Step Heights of Thin Pb Films by the Quantum Size Effect Observed by Non-Contact Atomic Force Microscopy MAO Han-Qing, LI Na, CHEN Xi, XUE Qi-Kun

CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES 067101 Coupled Optical Tamm States in a Planar Dielectric Mirror Structure Containing a Thin Metal Film ZHOU Hai-Chun, YANG Guang, WANG Kai, LONG Hua, LU Pei-Xiang 067301 Numerical Analysis of Efficiency Enhancement in Plasmonic Thin-Film Solar Cells by Using the SILVACO TCAD Simulator KIM Un-Chol, JIANG Xiao-Qing 067302 Impact of Interfacial Trap Density of States on the Stability of Amorphous InGaZnO-Based Thin-Film Transistors HUANG Xiao-Ming, WU Chen-Fei, LU Hai, XU Qing-Yu, ZHANG Rong, ZHENG You-Dou

067401 Effect of Cleaving Temperature on the Surface and Bulk Fermi Surface of Sr2RuO4 Investigated by High Resolution Angle-Resolved Photoemission -Yu, ZHANG Wen-Tao, WENG Hong-Ming, ZHAO Lin, LIU Hai-Yun, JIA Xiao-Wen, LIU Guo-Dong, DONG Xiao-Li, ZHANG Jun, MAO Zhi-Qiang, CHEN Chuang-Tian, XU Zu-Yan, DAI Xi, FANG Zhong, ZHOU Xing-Jiang 067402 NMR Study of Superconductivity and Spin Fluctuations in Hole-Doped Superconductor Ca1−xNaxFe2As2 (Tc = 32 K) MA Long, ZHANG Jin-Shan, WANG Du-Ming, HE Jun-Bao, XIA Tian-Long, CHEN Gen-Fu, YU Wei-Qiang 067501 Effect of Carrier Differences on Magnetoresistance in Organic and Inorganic Spin Valves YUAN Xiao-Bo, REN Jun-Feng, HU Gui-Chao 067502 Terahertz Emission of Ferromagnetic Ni-Fe Thin Films Excited by Ultrafast Laser Pulses SHEN Jian, ZHANG Huai-Wu, LI Yuan-Xun 067701 Electric and Magnetic Properties of the (1 − x)Ba0.6Sr0.4TiO3-xCoFe2O4 Multiferroic Composite Ceramics -An, WANG Yun-Bo, RAO Wei, GAO Jun-Xiong, ZHOU Wen-Li, YU Jun 067801 The Influences of Temperature, Concentration and Pressure Uncertainties on the Measurement Results of Wavelength Modulation Spectroscopy CHE Lu, DING Yan-Jun, PENG Zhi-Min

CROSS-DISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY 068101 Green Emission from a Strain-Modulated InGaN Active Layer WANG Guo-Biao, XIONG Huan, LIN You-Xi, FANG Zhi-Lai, KANG Jun-Yong, DUAN Yu, SHEN Wen-Zhong 068501 All-Optical Cesium Atomic Magnetometer with High Sensitivity ZHANG Jun-Hai, LIU Qiang, ZENG Xian-Jin, LI Jiu-Xing, SUN Wei-Min 068502 Noise Suppression Effect of Composites Containing Glass-Covered Amorphous CoFeSiBCr Wires ZHANG Jun-Feng, LI De-Ren, CHEN Zheng, LU Zhi-Chao, ZHOU Shao-Xiong 068701 Interaction between a Functionalized Single-Walled Carbon Nanotube and the YAP65WW Protein Domain: a Molecular Dynamics Simulation Study DOU Quan-Tao, ZUO Guang-Hong, FANG Hai-Ping 068702 Calculation of Collective Variable-based PMF by Combining WHAM with Umbrella Sampling XU Wei-Xin, LI Yang, ZHANG John Z. H. 068801 High Concentration InGaN/GaN Multi-Quantum Well Solar Cells with a Peak Open-Circuit Voltage of 2.45 V ZHANG Dong-Yan, ZHENG Xin-He, LI Xue-Fei, WU Yuan-Yuan, WANG Jian-Feng, YANG Hui 068901 Empirical Evidence for the Look-Ahead Behavior of Pedestrians in Bi-directional Flows GUO Ren-Yong, WONG S. C., XIA Yin-Hua, HUANG Hai-Jun, LAM William H. K., CHOI Keechoo

GEOPHYSICS, ASTRONOMY, AND ASTROPHYSICS 069701 Effects of the Recombination of Nucleons into α-Particles on the R-process in Proto-magnetar Wind CHEN Yan-Jun, YUAN Ye-Fei