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Warm dense matter (WDM), a kind of transition state of matter between cold condensed matter and high temperature plasma, is one of the main research objects of high energy density physics (HEDP). Compared with the structure of isolated atom, the electron structure of WDM will change significantly because of the influences of density and temperature effect. As WDM is always strongly coupled and partly degenerate, accurate theoretical description is very complicated and the accurate experimental research is also very challenging. In this paper, the density effect on the warm dense matter electron structure based on the X-ray fluorescence spectroscopy is studied. The warm dense titanium with density larger than solid density is produced experimentally based on a specially designed hohlraum. Then, the titanium is pumped to emit fluorescence by using the characteristic line spectrum emitted by the laser irradiating the pump material (Vanadium). The X-ray fluorescence spectra of titanium with different states are diagnosed by changing the delay time between the pump laser and drive laser. The experimental fluorescence spectrum indicates that the difference in energy between
${\mathrm{K}}_{\text{β}} $ and$ {\mathrm{K}}_{\text{α}} $ ($\Delta E_{{\mathrm{K}}_{\text{β}}\text{-}{\mathrm{K}}_{\text{α}}}$ ) of the compressed titanium (7.2–9.2 g/cm3, 1.6–2.4 eV) is about 2 eV smaller than that of cold titanium. Two theoretical methods, i.e. finite-temperature relativistic density functional theory (FTRDFT) and two-step Hartree-Fock-Slater (TSHFS), are used to calculate the fluorescence spectrum of warm dense titanium. The calculated results indicate that the energy difference ($\Delta E_{{\mathrm{K}}_{\text{β}}\text{-}{\mathrm{K}}_{\text{α}}} $ ) decreases with the increase of density but changes slowly with the increase of temperature during the calculated state (4.5–13.5 g/cm3, 0.03–5 eV). The FTRDFT overestimates the density effect on the line shift, while TSHFS underestimates the density effect. The future work will focus on optimizing the experimental method of X-ray fluorescence spectroscopy, obtaining X-ray fluorescence spectrum of titanium with more states, and then testing the theoretical method for warm dense matter.[1] Saumon D, Chabrier G 1991 Phys. Rev. A 44 5122
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[31] Ramis R, Schmalz R, Meyer-Ter-Vehn J 1988 Comput. Phys. Comm. 49 475
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图 1 温稠密Ti的荧光光谱实验示意图 (a)荧光光谱测量; (b)样品处辐射源测量
Figure 1. Schematic of the X-ray fluorescence spectrum experiment of warm dense Ti: (a) Measurement of the fluorescence spectrum; (b) measurement of the incident flux of the sample
图 2 (a)样品处再发射流及入流; (b) Ti样品的密度温度演化过程模拟结果
Figure 2. (a) Reemission flux and incident flux of gold at the hohlraum center; (b) the simulated density and temperature evolution of Ti sample
图 3 不同状态Ti样品的荧光光谱 (a)原始图像; (b)解谱结果
Figure 3. The X-ray fluorescence spectrum of Ti samples with different state: (a) Original images; (b) spectral results
图 4 不同状态Ti样品$\Delta E_{{\mathrm{K}}_{\text{β}}\text{-}{\mathrm{K}}_{\text{α}}}$相对于冷样品的变化
Figure 4. Changes of $\Delta E_{{\mathrm{K}}_{\text{β}}\text{-}{\mathrm{K}}_{\text{α}}}$ of Ti with different density and temperature relative to cold samples
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[1] Saumon D, Chabrier G 1991 Phys. Rev. A 44 5122
Google Scholar
[2] Lindl J D 1995 Phys. Plasmas 2 3933
Google Scholar
[3] Lindl J D, Amendt P, Berger R L, Glendinning S G, Glenzer S H, Haan S W, Kauffman R L, Landen O L, Suter L J 2004 Phys. Plasmas 11 340
Google Scholar
[4] Hu S X, Militzer B, Goncharov V N, Skupsky S 2010 Phys. Rev. Lett. 104 235003
Google Scholar
[5] Hu S X, Collins L A, Goncharov V N, Boehly T R, Epstein R, McCrory R L, Skupsky S 2014 Phys. Rev. E 90 033111
Google Scholar
[6] Hu S X, Collins L A, Goncharov V N, Kress J D, McCrory R L, Skupsky S 2015 Phys. Rev. E 92 043104
Google Scholar
[7] Hu S X, Collins L A, Goncharov V N, Kress J D, McCrory R L, Skupsky S 2016 Phys. Plasmas 23 042704
Google Scholar
[8] Surh M P, Barbee T W, Yang L H 2001 Phys. Rev. Lett. 86 5958
Google Scholar
[9] Mazevet S, Zérah G 2008 Phys. Rev. Lett. 101 155001
Google Scholar
[10] 金阳, 张平, 李永军, 侯永, 曾交龙, 袁建民 2021 物理学报 70 073102
Google Scholar
Jin Y, Zhang P, Li Y J, Hou Y, Zeng J L, Yuan J M 2021 Acta Phys. Sin. 70 073102
Google Scholar
[11] Zhang S, Zhao S J, Kang W, Zhang P, He X T 2016 Phys. Rev. B 93 115114
Google Scholar
[12] Dai J Y, Hou Y, Yuan J M 2010 Phys. Rev. Lett. 104 245001
Google Scholar
[13] Wang C, He X T, Zhang P 2011 Phys. Rev. Lett. 106 145002
Google Scholar
[14] Ciricosta O, Vinko S M, Chung H K, Cho B I, Brown C R, Burian T, Chalupsky J, Engelhorn K, Falcone R W, Graves C, Hajkova V, Higginbotham A, Juha L, Krzywinski J, Lee H J, Messerschmidt M, Murphy C D, Ping Y, Rackstraw D S, Scherz A, Schlotter W, Toleikis S, Turner J J, Vysin L, Wang T, Wu B, Zastrau U, Zhu D, Lee R W, Heimann P, Nagler B, Wark J S 2012 Phys. Rev. Lett. 109 065002
Google Scholar
[15] Hoarty D J, Allan P, James S F, Brown C R D, Hobbs L M R, Hill M P, Harris J W O, Morton J, Brookes M G, Shepherd R, Dunn J, Chen H, Marley E V, Beiersdorfer P, Chung H K, Lee R W, Brown G, Emig J 2013 Phys. Rev. Lett. 110 265003
Google Scholar
[16] Mančić A, Lévy A, Harmand M, Nakatsutsumi M, Antici P, Audebert P, Combis P, Fourmaux S, Mazevet S, Peyrusse O, Recoules V, Renaudin P, Robiche J, Dorchies F, Fuchs J 2010 Phys. Rev. Lett. 104 035002
Google Scholar
[17] Park H, Remington B A, Braun D, Celliers P, Collins G W, Eggert J, Giraldez E, Pape S L, Lorenz T, Maddox B, Hamza A, Ho D, Hicks D, Patel P, Pollaine S, Prisbrey S, Smith R, Swift D, Wallace R 2008 J. Phys.: Conf. Ser. 112 042024
Google Scholar
[18] Lee H J, Neumayer P, Castor J, Döppner T, Falcone R W, Fortmann C, Hammel B A, Kritcher A L, Landen O L, Lee R W, Meyerhofer D D, Munro D H, Redmer R, Regan S P, Weber S, Glenzer S H 2009 Phys. Rev. Lett. 102 115001
Google Scholar
[19] Benuzzi-Mounaix A, Mazevet S, Ravasio A, Vinci T, Denoeud A, Koenig M, Amadou N, Brambrink E, Festa F, Levy A, Harmand M, Brygoo S, Huser G, Recoules V, Bouchet J, Morard G, Guyot F, Resseguier T, Myanishi K, Ozaki N, Dorchies F, Gaudin J, Leguay P M, Peyrusse O, Henry O, Raffestin D, Pape S, Smith R, Musella R 2014 Phys. Scr. T161 014060
Google Scholar
[20] Zhang Z Y, Zhao Y, Zhang J Y, Hu Z M, Jing L F, Qing B, Xiong G, Lv M, Du H B, Yang Y M, Zhan X Y, Yu R Z, Mei Y, Yang J M 2019 Phys. Plasmas 26 072704
Google Scholar
[21] Bradley D K, Kilkenny J, Rose S J, Hares J D 1987 Phys. Rev. Lett. 59 2995
Google Scholar
[22] DaSilva L, Ng A, Godwal B K, Chiu G, Cottet F, Richardson M C, Jaanimagi P A, Lee Y T 1989 Phys. Rev. Lett. 62 1623
Google Scholar
[23] Yaakobi B, Boehly T R, Sangster T C, Meyerhofer D D, Remington B A, Allen P G, Pollaine S M, Lorenzana H E, Lorenz K T, Hawreliak J A 2008 Phys. Plasmas 15 062703
Google Scholar
[24] Benuzzi-Mounaix A, Dorchies F, Recoules V, Festa F, Peyrusse O, Levy A, Ravasio A, Hall T, Koenig M, Amadou N, Brambrink E, Mazevet S 2011 Phys. Rev. Lett. 107 165006
Google Scholar
[25] Zhao Y, Yang J M, Zhang J Y, Yang G H, Wei M X, Xiong G, Song T M, Zhang Z Y, Bao L H, Deng B, Li Y K, He X A, Li C G, Mei Y, Yu R Z, Jiang S E, Liu S Y, Ding Y K, Zhang B H 2013 Phys. Rev. Lett. 111 155003
Google Scholar
[26] Zhao Y, Zhang Z Y, Qing B, Yang J M, Zhang J Y, Wei M X, Yang G H, Song T M, Xiong G, Lv M, Hu Z M, Deng B, Hu X, Zhang W H, Shang W L, Hou L F, Du H B, Zhan X Y, Yu R Z 2017 EPL 117 65001
Google Scholar
[27] Eidmann K, Andiel U, Pisani F, Hakel P, Mancini R C, Junkel-Vives G C, Abdallah J, Witte K 2003 J. Quant. Spectrosc. Radial. Transfer 81 133
Google Scholar
[28] Hansen S B, Harding E C, Knapp P F, Gomez M R, Nagayama T, Bailey J E 2017 High Energy Density Physics 24 39
Google Scholar
[29] Hansen S B, Harding E C, Knapp P F, Gomez M R, Nagayama T, Bailey J E 2018 Phys. Plasmas 25 056301
Google Scholar
[30] Jiang S, Lazicki A E, Hansen S B, Sterne P A, Grabowski P, Shepherd R, Scott H A 2020 Phys. Rev. E 101 023204
Google Scholar
[31] Ramis R, Schmalz R, Meyer-Ter-Vehn J 1988 Comput. Phys. Comm. 49 475
Google Scholar
[32] Liu W J, Wang F, Li L M 2003 J. Theor. Comput. Chem. 2 257
Google Scholar
[33] Son S K, Thiele R, Jurek Z, Ziaja B, Santra R 2014 Phys. Rev. X 4 031004
Google Scholar
[34] Lin C L 2019 Phys. Plasmas 26 122707
Google Scholar
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