Xu-Hong Zhang, Hao-Ning Wang, Fu-Hu Liu, Khusniddin K. Olimov
{"title":"相对论重离子碰撞中形成的相互作用体系的热力学和流体力学特征","authors":"Xu-Hong Zhang, Hao-Ning Wang, Fu-Hu Liu, Khusniddin K. Olimov","doi":"10.1142/s0218301323500659","DOIUrl":null,"url":null,"abstract":"<p>To study the energy-dependent characteristics of thermodynamic and hydrodynamic parameters, based on the framework of a multi-source thermal model, we analyze the soft transverse momentum (<span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>p</mi></mrow><mrow><mi>T</mi></mrow></msub></math></span><span></span>) spectra of the charged particles (<span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup></math></span><span></span>, <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup></math></span><span></span>, <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup></math></span><span></span>, <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup></math></span><span></span>, <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><mover accent=\"true\"><mrow><mi>p</mi></mrow><mo>̄</mo></mover></math></span><span></span>, and <i>p</i>) produced in gold–gold (Au–Au) collisions at the center-of-mass energies <span><math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"><msqrt><mrow><msub><mrow><mi>s</mi></mrow><mrow><mi>N</mi><mi>N</mi></mrow></msub></mrow></msqrt><mo>=</mo><mn>7</mn><mo>.</mo><mn>7</mn></math></span><span></span>, 11.5, 14.5, 19.6, 27, 39, 62.4, and 200<span><math altimg=\"eq-00008.gif\" display=\"inline\" overflow=\"scroll\"><mspace width=\".17em\"></mspace></math></span><span></span>GeV from the STAR Collaboration and in lead–lead (Pb–Pb) collisions at <span><math altimg=\"eq-00009.gif\" display=\"inline\" overflow=\"scroll\"><msqrt><mrow><msub><mrow><mi>s</mi></mrow><mrow><mi>N</mi><mi>N</mi></mrow></msub></mrow></msqrt><mo>=</mo><mn>2</mn><mo>.</mo><mn>7</mn><mn>6</mn></math></span><span></span> and 5.02<span><math altimg=\"eq-00010.gif\" display=\"inline\" overflow=\"scroll\"><mspace width=\".17em\"></mspace></math></span><span></span>TeV from the ALICE Collaboration. In the rest framework of emission source, the probability density function obeyed by meson momenta satisfies the Bose–Einstein distribution, and that obeyed by baryon momenta satisfies the Fermi–Dirac distribution. To simulate the <span><math altimg=\"eq-00011.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>p</mi></mrow><mrow><mi>T</mi></mrow></msub></math></span><span></span> of the charged particles, the kinetic freeze-out temperature <i>T</i> and transverse expansion velocity <span><math altimg=\"eq-00012.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>β</mi></mrow><mrow><mi>T</mi></mrow></msub></math></span><span></span> of emission source are introduced into the relativistic ideal gas model. Our results, based on the Monte Carlo method for numerical calculation, show a good agreement with the experimental data. The excitation functions of thermodynamic parameter <i>T</i> and hydrodynamic parameter <span><math altimg=\"eq-00013.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>β</mi></mrow><mrow><mi>T</mi></mrow></msub></math></span><span></span> are then obtained from the analyses, which shows an increasing tendency from 7.7<span><math altimg=\"eq-00014.gif\" display=\"inline\" overflow=\"scroll\"><mspace width=\".17em\"></mspace></math></span><span></span>GeV to 5.02<span><math altimg=\"eq-00015.gif\" display=\"inline\" overflow=\"scroll\"><mspace width=\".17em\"></mspace></math></span><span></span>TeV in collisions with different centralities.</p>","PeriodicalId":50306,"journal":{"name":"International Journal of Modern Physics E","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2023-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Thermodynamic and hydrodynamic characteristics of interacting system formed in relativistic heavy ion collisions\",\"authors\":\"Xu-Hong Zhang, Hao-Ning Wang, Fu-Hu Liu, Khusniddin K. Olimov\",\"doi\":\"10.1142/s0218301323500659\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>To study the energy-dependent characteristics of thermodynamic and hydrodynamic parameters, based on the framework of a multi-source thermal model, we analyze the soft transverse momentum (<span><math altimg=\\\"eq-00001.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><msub><mrow><mi>p</mi></mrow><mrow><mi>T</mi></mrow></msub></math></span><span></span>) spectra of the charged particles (<span><math altimg=\\\"eq-00002.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup></math></span><span></span>, <span><math altimg=\\\"eq-00003.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup></math></span><span></span>, <span><math altimg=\\\"eq-00004.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup></math></span><span></span>, <span><math altimg=\\\"eq-00005.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup></math></span><span></span>, <span><math altimg=\\\"eq-00006.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><mover accent=\\\"true\\\"><mrow><mi>p</mi></mrow><mo>̄</mo></mover></math></span><span></span>, and <i>p</i>) produced in gold–gold (Au–Au) collisions at the center-of-mass energies <span><math altimg=\\\"eq-00007.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><msqrt><mrow><msub><mrow><mi>s</mi></mrow><mrow><mi>N</mi><mi>N</mi></mrow></msub></mrow></msqrt><mo>=</mo><mn>7</mn><mo>.</mo><mn>7</mn></math></span><span></span>, 11.5, 14.5, 19.6, 27, 39, 62.4, and 200<span><math altimg=\\\"eq-00008.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><mspace width=\\\".17em\\\"></mspace></math></span><span></span>GeV from the STAR Collaboration and in lead–lead (Pb–Pb) collisions at <span><math altimg=\\\"eq-00009.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><msqrt><mrow><msub><mrow><mi>s</mi></mrow><mrow><mi>N</mi><mi>N</mi></mrow></msub></mrow></msqrt><mo>=</mo><mn>2</mn><mo>.</mo><mn>7</mn><mn>6</mn></math></span><span></span> and 5.02<span><math altimg=\\\"eq-00010.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><mspace width=\\\".17em\\\"></mspace></math></span><span></span>TeV from the ALICE Collaboration. In the rest framework of emission source, the probability density function obeyed by meson momenta satisfies the Bose–Einstein distribution, and that obeyed by baryon momenta satisfies the Fermi–Dirac distribution. To simulate the <span><math altimg=\\\"eq-00011.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><msub><mrow><mi>p</mi></mrow><mrow><mi>T</mi></mrow></msub></math></span><span></span> of the charged particles, the kinetic freeze-out temperature <i>T</i> and transverse expansion velocity <span><math altimg=\\\"eq-00012.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><msub><mrow><mi>β</mi></mrow><mrow><mi>T</mi></mrow></msub></math></span><span></span> of emission source are introduced into the relativistic ideal gas model. Our results, based on the Monte Carlo method for numerical calculation, show a good agreement with the experimental data. The excitation functions of thermodynamic parameter <i>T</i> and hydrodynamic parameter <span><math altimg=\\\"eq-00013.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><msub><mrow><mi>β</mi></mrow><mrow><mi>T</mi></mrow></msub></math></span><span></span> are then obtained from the analyses, which shows an increasing tendency from 7.7<span><math altimg=\\\"eq-00014.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><mspace width=\\\".17em\\\"></mspace></math></span><span></span>GeV to 5.02<span><math altimg=\\\"eq-00015.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><mspace width=\\\".17em\\\"></mspace></math></span><span></span>TeV in collisions with different centralities.</p>\",\"PeriodicalId\":50306,\"journal\":{\"name\":\"International Journal of Modern Physics E\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2023-12-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Modern Physics E\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1142/s0218301323500659\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"PHYSICS, NUCLEAR\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Modern Physics E","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1142/s0218301323500659","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"PHYSICS, NUCLEAR","Score":null,"Total":0}
引用次数: 0
摘要
为了研究热力学和流体力学参数随能量变化的特性,我们在多源热模型的框架下,分析了在质量中心能量sNN=7的金-金(Au-Au)对撞中产生的带电粒子(π-、π+、K-、K+、p̄和p)的软横动量(pT)谱图,以及在质量中心能量sNN=7的铅-铅(Pb-Pb)对撞中产生的带电粒子(π-、π+、K-、K+、p̄和p)的软横动量(pT)谱图。7、11.5、14.5、19.6、27、39、62.4 和 200GeV 的金-金(Au-Au)对撞中产生的,以及在 sNN=2.76 和 5.02TeV 的铅-铅(Pb-Pb)对撞中产生的。在发射源的静态框架中,介子矩服从的概率密度函数满足玻色-爱因斯坦分布,重子矩服从的概率密度函数满足费米-狄拉克分布。为了模拟带电粒子的 pT,在相对论理想气体模型中引入了发射源的动力学冻结温度 T 和横向膨胀速度 βT。我们采用蒙特卡洛方法进行数值计算,结果与实验数据非常吻合。分析结果表明,在不同中心度的对撞中,热力学参数 T 和流体力学参数 βT 的激发函数呈从 7.7GeV 到 5.02TeV 的递增趋势。
Thermodynamic and hydrodynamic characteristics of interacting system formed in relativistic heavy ion collisions
To study the energy-dependent characteristics of thermodynamic and hydrodynamic parameters, based on the framework of a multi-source thermal model, we analyze the soft transverse momentum () spectra of the charged particles (, , , , , and p) produced in gold–gold (Au–Au) collisions at the center-of-mass energies , 11.5, 14.5, 19.6, 27, 39, 62.4, and 200GeV from the STAR Collaboration and in lead–lead (Pb–Pb) collisions at and 5.02TeV from the ALICE Collaboration. In the rest framework of emission source, the probability density function obeyed by meson momenta satisfies the Bose–Einstein distribution, and that obeyed by baryon momenta satisfies the Fermi–Dirac distribution. To simulate the of the charged particles, the kinetic freeze-out temperature T and transverse expansion velocity of emission source are introduced into the relativistic ideal gas model. Our results, based on the Monte Carlo method for numerical calculation, show a good agreement with the experimental data. The excitation functions of thermodynamic parameter T and hydrodynamic parameter are then obtained from the analyses, which shows an increasing tendency from 7.7GeV to 5.02TeV in collisions with different centralities.
期刊介绍:
This journal covers the topics on experimental and theoretical nuclear physics, and its applications and interface with astrophysics and particle physics. The journal publishes research articles as well as review articles on topics of current interest.