!#"%$&''()*,+-.0/213&45687:9;7*<&=>?45"
B@ ACDFEGDFH#IKJMLON
PRQMST6U#VW'U-PYX[ZMU#T'\^]KTU`_aQcb[Xd]MV5QcePQ2f]MT6Qcbd]KT#gKhjiRV
X[ZMU#T#kXlb[gm]onqp=Qce X nO]MT'VrXdQMh?PYXGZMU#T#\s]MTU#hsputwvOxry2y{z
|}A}C~AJMRJML#EGJK
*U
QKTb[\^U#V5bB]on-=8gMkXdWkh&_!QMb[Xd]MVQMe!pU#V5bU#T*nO]KT}
K
U#ToW]M\a5b[X[V{t2e XdWQcb[Xl]MVrkh
iVrX[ZMU#T'kXlb[g]onqe[e X[V5]MX[k}QcbmiTf'QKVQcpu
QM\QMXMVrhiTf'QKVQMhsP,cM8z2
|{HJMY
85L#) ¡¢ ££¤{¥
¦§O¨o©6ª«¬#©§®°¯5±²©³°«µ´8©§¶Mª'±M·{¸¹c´{©§º±²ª·µ¹¨6«µ»¼
·±K©«µ¹c´
¨½±Kª§=¼r¨6§O°©¹¬±M·¬¼r·±²©§©³r§=§®¾{¼r«µ·µ«µ¿
ª«µ¼r»À¯ª¹c¯§ª6©«µ§O¨
¹KÁB³{Â
ª¹M¶c§O´«µ´~©³r§j
§´r¨6«Ã©Â>±M´r©§O»^¯§ª'±²©¼
ª§ª'±K´r¶c§j¹KÁ&ÄÅ ÆcÇmÈ>É®ÊË5Ì>ÍÏÎÐÍÊ8ŵɲÑMÇ=¶2¬»qË5ÒÓ±M´r
ÑKÊcÊcÊÐÍÔÕÍ×ÖMÑMÊ=ÊcÊcÊØsÙÛÚܧj©§¨o©}©³
§j±c¬O¬¼ª'±c¬#Â~¹MÁ*©³r§Ó¯r±M«ÃªÓ§O´r¨6«Ã©Â»-±K©6ª«ÃÝ>±M´r0±M´5±K·ÃÂ
Þ§j©³
§
§O¯§O´5§O´5¬#§°¹c´©³
§°¨oÂ
¨o©§»ß¨6«µÞO§Mà¹c´©³
§!©«µ»^§°¨o©§O¯q¹MÁY©³
§°¯5±²©³q«µ´8©§¶Mª'±M·½±M´5}¹c´©³
§!©Â¯§°¹MÁ´
¹8r±M·
¨6¼ª6Ál±c¬#§cÙÚ§*¬±M·¬¼r·±²©§&©³
§°§®¾{¼5±K©«µ¹M´q¹MÁ¨o©'±²©§B±K´5q¬#¹c»^¯5±²ª§!á«Ã©³Ó¹M©³r§#ªa»^¹8§O·µ¨ÁG¹Mª³{Âr8ª¹c¶M§O´qâM±M·µ«
«µ´m©³
«µ¨aª§O¶c«µ»^§cÙãr¼ª6©³r§ª®à᧬'³r±Kª'±M¬#©§ª«µÞO§s©³r§B¨o©'±K©§s¹KÁ³{Â
ª¹M¶c§O´m±M´rm§O¨¬#ª«µ¿§©³r§¬'³r±M´
¶c§O¨!ÁFª¹c»
±j¯r·±M¨6»-±q©¹)±M´±²©¹c»^«¬}±K´5»^¹c·µ§®¬#¼r·±Kª^·µ«¾{¼r«¿{±M´r±M·ÃÂÞO«µ´r¶j©³r§-¯5±K«Ãª-¬¹Mª6ª§·F±²©«µ¹c´ÁG¼r´r¬#©«µ¹c´r¨±M´r
§O¨o©«µ»-±²©«´
¶©³r§a´¼
»¿§ª¹MÁ=±K©¹M»^¨±M´r}»^¹c·µ§®¬#¼r·µ§O¨¯
ª§O¨6§´8©®Ù
Kä åæäçqè&é-êsëìqíBèBäOêsç
î6qï#DFH#J!ð8ñuH#òJ*ï'DGóqEFJ°ôKðóqRðrï'DFH#DGð=¢8ò55L#ð
õJK}J²öòDG÷DFHï
ï#L#L#D[ï'DGõ
EF-ôKðóqEGJ²ö`òRï#JaD[8õ
Ló¢{ø°òDGôOòD[ïH#òJ°ï#÷ùJcô®H
ð8ñÓ5óqJKLðRïJ²öRJML#DGóqJKrHE`8RúH#òJMðLJ²H#D[ôKE`8L#ðrôOòJcïKA
î60HòDGï}øaðLûu¢øJÜïHH#òJmòDGõò0HJKóqRJML8H#LJjLJKõ
DFóqJÓð8ñ
ü £
££×ýÿþ ý ü £££
£ ø°òJML#J ò55L#ð
õJK JKLõð5Jcï
ï#óð5ðH#ò;HLï#DHDFð
ø°DFH#ò DGôKL#Jcï#DFõ H#JMóuJKLO{HLJñdLðó
óqðEGJMôKEGL DGHòLðõ
ò8 8H#ðóqD[ô-LJKõ
DFóqJ`
EFEGÜH#ð
Høð>ô²ðóquðJMrHE[ï#óÓ ðñ&JKEGJMô²H#Lðïq8R0Lð8H#ð
ï ï#JKJ
DFõRA¤{¥O
A !òJÜL#ð
RJML'HDFJcï-ðñ&ò55L#ð
õJK0DG0HòDGïLJKõ
DFóqJ)L#J
ô²LôKDGEñdð
L&HòJqJ ðEGH#DGðð8ñï'HLïs8RH#òJqôOòR8LOô®HJKLDGï'H#D[ôKï
ð8ñH#òJ`8ð 5D[8)EGJ²HOïKA
{L#DGJ²H^ðñuï#DFó}EG8H#DGð}H#JcôOòD JMï?8R}8EGrH#D[ôK8E5óqð JKE[ï?ò J!÷RJMJKÓJ JKEGðuJM`H#ð-Jcï#ôKL#DG÷uJ°òrLðõ
JK{HEGð{øÐJM ï#DH
A !òDGïaLJKõDGóqJ&ò
ï÷uJKJMÜï'H#RDFJcjø°DFH#òÜôOòJKóqD[ôK8E½óqðJKE[ï
¤ 5¡ BHò{HJMïô²LDF÷uJ ò5LðõJM;ïmÀóqDö5HL#Jð8ñ-DG
HJKLOô²H DGõ~óð
EFJcô²EGJMïM¢!{H#ð
óÓïK¢ñdL#JMJL#ðH#ð
ïÓ8 JKEGJMô²H#LðïM
A !òJ
ôOòJMóD[ôKE
ôKðóqRðrï'DFH#DGð`DGïJ²HJKLóqDFJc^÷5sóDGDGóqDFIMDFõ8` Lð2öDFóÓ{HJ-ñdLJKJ}JKJML#õ
mñdô®HDFð
>ôKðï'H#Lô®HJMñdLðóÕû5ð{ø°
H#òJKðLJ²HDGôM8E°EGDFóqDFHïMA3î6ÐH#òD[ïÓRJMLM¢aøJÜñdðô²RïqðÛEFð{ø8
DG
HJKLóqJMD[{HJJKï#DHDFJcï !
¡ Û¤c£ "$# &
ý % ýÕ£ G¤ ü ¡õ
ô²'ó ")(
ô²ð
L#LJMï#uðDGõmH#ð0+¤ *-,/.102, 3¢ø°òJKLJqðJÓJKö5uJMô²HïsHòJ
ôOòJMóD[ôKEsóðJMEGïÜHð øaðLû3øaJKEGEsEHòðõò;HòJ~LðuJKL#H#DGJMï
ð8ñò5Lðõ
JK8LJ-J²HJKLóqDFJc÷5ÜH#òJô²ðóqEGJ²öDG
HJKLE[2)ð8ñ
EGð4õ LO8õ
JðEGðó}÷Bñdð
LôKJMï=EFJcDGõ!H#ðïHL#ð
õ*ô²ð
EGDFõ&8
÷uðï'H8H#JMï°
ï!øJMEFE
ï°JKõ
JKJML
ô²ÓJ 5uJcô®HïMA
EGE=HòJMï#J-6J 5½JMô²HïôK 8E[ï'ðÓ÷uJ}Jcï#ôKL#DG÷uJMñdLð7
ó LOïH&L#DG ô²DGEGJMïï'DGó`EG8H#DGð8
A !òJKLJm8LJ 9;:=<?>@<BAC<EDjóqJ²Hòðïï'ôOò ï
FHGJILKHMONQPCRSTLMUWVVPCKXCXZY;[]\Z^+\H_`6aWb6c6^^Zd+^efgih
j GJILKHMONQPCRSTLMUWVVPCKXCXZY)kiailaWb^WaWm6cin\On1k;e?aWoWn
LJMï'H#LD[ô®H#Jc-8H#òqDG
HJKõ
LECðrH#J&a8LEGðï#DFó}E[{H#DGðRï Cp î'C°¥
*38RJMï#DHñdô®HDFð
8EHòJKð
L# óqð
EFJcô²E[8L^5óD[ôKï
q| rC|^¥ Ls t¢ A !òJÓñdðôKï^ð8ñ!HòJjøaðLû DGï^H#ðHJMï'H-H#òJ
J1r{HDFð
ðñï'H{HJ E urvxw ¥`JKLyD JM ñdL#ð
ó ôOòJKóqD[ôKEaóqðJMEGï
ÓHòJ^ô²H#EuJMï#DH; H#JKóquJKLO{HL#JEGDFóqDFHïað8ñH#òzJ {8EGDGDFH
ðñ*H#òJÜôOòJMóqDGôM8EaDGô²H#LJA DFH#DGðEFEG¢øJÜLð rD[JÜ{HO
Hð J²HJKLóqDFJqHòJÓLóJKH#JMLïð8ñaH#òJÓñdL#JMJqJKJML#õ
óqð5JKE[ïKA
òJKóqDGôM8EóqðJMEGï}8LJÓJ²öRJcô®HJM>H#ð÷RJcô²ðóqJjDG
ôKô²L8H#JÓDG
LJKõ
DFð
ï}ð8ñBòDFõ
ò JMï'DFHÀø°òJML#JmH#òJÜEGDFñdJ²H#DGóqJð8ñóð
EFJcô²EGJMï
LJMô²JcïaH#ðÓ}ñdJKøúóð
EFJcô²E[8{L 5DG÷LO{H#DGðRï oA
|>J LJMï#JKrH)LJMï#EHOïÓñdLðó JKø^¢°óqð
L#J
ôKôKL8H#J
¢ p î'C
ï#DGó`E[{HDFð
ïK'A DFLOïHc¢=øaJ)8R8EGrIMJH#òJ)
ôKôKL
ô² ðñHòJjDFL
JKï#DH`óq8H#LDö8}H#òJ°JKLL#ð
LðñRHòJ }HDFóq+J ~sD[ïô²LJ²H#DGIM8H#DGðA
!òJKøJ!8EF5IMJHòr
J DFH#J°ï'DGIKJ°JMRJMJMô²J!ð8ñRH#òJ°JML#D Jc
uvxw 8D[ï#ôKïï!H#ò
J öJMðJ^JML#LðLOï!÷5mô²ð
óq8LDFõL6J ï#EFHïñdLðó ï#DFó}EG8H#DGðïRï'DGõ^ñdLJKJ°L'HDGôKEFJ p ¥ðJcï8R
{L#D[{HDFð
8EYðJcïK{
A L'HòJKLóqðLJ¢RøJ-ôM8E[ô²E[{HJ-8DGL&ôKðLL#J E[{HDFð
qñdô²H#DGðïø°òD[ôOòjøJ&ï'JBDFmô²ð8ùô®HDFð
jø°DFH#ò)}ô²EGHï HJKL8EFï#DGï!Hð)ôOòL
ô®H#JML#DGIKJHòJ}ï'H8H#J-ðñò5Lðõ
JK{HBD?ñ ñdJML#JMrHBHJKóqRJML8H#LJMï8RJMï'DFH#DGJMïMA |>J}ï#Jq{H#ð
óqDGô}DFHï
EFJMõ8HòïDGj@aðòLL
DGD8qJMJKLõDGJMïDF B8L#H#LJKJMﮥ=H#òL#ð
õò ð
H!H#òD[ï°øaðLûÓJ²öô²JMH*ø°òJML#JsDGD[ôK{HJMÜð8HòJKLø°D[ï'J
A
ä®äKå
°è×ä#çqèq}é;êsçqè íq`é?ê
q
è jêsë
é 4WW+W4
;W~iä W6 !òJ^JMï'DFHÓóÓ{HL#DFö |sC¥ð8ñ-ñdJML#óqDGðÜï'ï'H#JKó×{HaH#JKó¡
uJKLO{HL£J ¢¤¦
þ ¥ ¤ §¨ÛôK8÷RJqø°LDH#H#JM~
ïs8DGrH#JMõLO8Eð JML
EFEYR{H#òRï ©ªO¢
¬
10
14
200000
10
°
100000
®4
6
rs
Plasma
¯ 2.6
3
± Pa
10
±
0G
GP
a
¶ 01
50000
0.
² ³Pa
1G
20000
0.1
10000
±
µ
0.1
T ´(K)
Atomic Fluid
GP
a
5000
Molecular Fluid
10
−3
−2
10
ρ (gcm
« −3)
10
−1
î ·A¤
p òï#J*D[8õLO8óßð8ñYò55L#ð
õJKqïsñdô²H#DGðÓð8ñ½HJK¡
ó u JKLO{H#L#Jj0JKRï'DFHñdð
L-HòJ)Dy5uJML#JMrH`L#JMõDGóqJMïM`E[ï#óÓ¢
H#òJ&{HðóqDGô°}H#òJ&óð
EFJcô²E[8LL#JMõDGóJ
A¸!òJBï#ò6ð8H?EGDFJcï
DGD[ôK{HJqH#òJjLð2öDFóÓ{HJ}÷uð8LDGJMïMA£!òJjô²Lð
ïï'Jcï&DGDy
ôK8H#JHòJ LóqJ²H#JMLïñdð
Ljø°òD[ôOò p î'C×ï#DFó}E[{H#DGðRïÓò J
÷uJKJK RJML'ñdð
L#óqJM¢jH#òJ ï'ð
EFD[ EGDFJcï L#J3D[ï'ð
÷8LOïM¢)8wHòJ
ï'òJc>EFDGJMïsLJKL#Jcï'JM
H-ôKðrH#ð
L^EFDGJcï^ð8ñ°ô²ð
ïHO8rH^RJML#ó} H8H#DGð L#ð
÷8÷DFEGDH>ð8ñ&H#òJÜJKEGJMô²H#Lðï
ï`DGD[ôK8H#JM ð0HòJ
EGDFJ
AÃ¥
¤
%
© ¹]ºZ©»½¼¨¥t¥ ¾¿;ÀÁ HÂ
ÁÄÃ
É © ªËÊ "ÍÌ@Î ÅÐÏ?Ñ ¤2¥
ÅÆZÇ ÅtÈ
©ª&ï'HïñdðLHòJqJKrH#DGL#Jq8H#òïsðñr¾ 8L#H#D[ô²EGJMïsDG>¡ÜDy
óqJKï#DGðEï'Rô²J©ª¥ BÒ4Ó ªº+½º Ò4Ô 'ª ¥u÷uJKõDGDGõ{H¸© ¹ 8
JKRDFõ8H¸Á ÕÖ©»½A¸Õ E[8÷uJKE[ïHòJ!RJML#ó}H8H#DGð}ð8ñHòJR8L#H#D[ô²EGJMï
8R HÂ ¤{¥ H#ðqDHOï!ï'DGõ8H#LJA ð
L!ðo LJKE[{H#D5
DGï'H#D[ô*R8L#H#D[ô²EGJMï
DG
HJKLOô²H#DGõ^ø°DHòjsRðH#JM
HDGEJ× Ü© ¥®¢HòJ&
ô®H#DGðqðñuHòJ*8H#ò
Ø © ª D[ï°õD
JMm÷5¢
»
¤{¥
Á
É © Û¥
ßÞÞ á$à É]Û ÞÞ × © Û ¥'¥Qä ô²ð
ïH+ ¥
¹
Þ
Þ
î6)L
ô®H#D[ô²JðJD[ïô²LJ²H#Þ DGIKJcï ½Þ âÐHòã Js{Hò)DG
Hðã ÖDFH#Js5ó¡
÷uJKLsð8ñDGóÓ8õ
DFL#mH#DGóqJï#EGDGôKJMïå ô²ð
L#LJMï#Rð
DGõÓHðÜ-AE<?æç
å A
è AQçHéê2¥¨§w
ðLqñdJML#óqDGðD[ôï'ï'H#JMóqï}HòJDFrHJKõLO{HDFð
D[ïÓô²ð
óEFD[ôK8H#JM
J!HðsH#òJBôK8Rô²JKEGE[{H#DGðð8ñ½uð
ï#DHDy
J!JKõr{HDy
J!ôKðrH#LDG÷
H#DGðRï*HðjH#òJ}DGrH#JKõ
LE
¢ AEëçì6ç6íæ¡<ED> è <ïî4>é$íZD;:ðyç-æ ¥OAsîoHòRï
÷uJKJKï#òð{ø° ¤M£¢Y¤¤Y Hò{H°ðJsôM8ÜJ{
8EG8H#JBH#òJs8H#òDFrHJ6
õLO8E½÷5ÓLJMï'H#LDGô²H#DGõ`HòJ^8H#òmH#ðqðEGjï#RJcô²DyR ôsRðrï'DFH#D
Jsô²ð
H#LDG÷H#DGðRïKA v JqDG
HL#ðRô²JMïsÜLJ²ñdJKLJKRô²JqRð
DFrH©'}ñ ð
HòJ
8H#òÓHò{Hï#uJMô²Dy JcïHòJ&ðJcïðñuHòJB|sC~¢;% ©Ëºi© ñ º Û ¥t¥ £A
>JD1ò4çó9ôD<Eò<?>
î {Hò ñdð
LB£'õ Û ýöÀ
¨ JKDFH#òJMLBHðôOòJMï*ðL
ô²Lð
ïï#JMïq>ðJ!% © Û ¥Wºi© ñ º Û ¥¥ ÷ £A;@aÀL#JcïHL#D[ô®HDFõHòJ
Ø ©ªC)¥ÚÙ
É;ÛzÜ+Ý
DGrH#JMõLO8EuH#ðÓðJo
ðD[DGõ`8H#òïM¢
%ø ©»ÍºZ© ñ ¼Z¨¥ ¥
ÙÖÉ ©¹q%ø ©¹]ºZ© ñ ¼£r¥
Ã
É © ªËÊ ")Ì@Î Å Ï Ñ º
ÅÆiÇÅtÈ;ù4úûyÅüZý
¡r¥
ÿ þ © ñ ¥JKð8H#JcïH#òJÐL#JcïHL#D[ô®HDFð
u¥H#òJÛô²ð
HL#DG÷HDFð
ï>8LJ
u ð
ï#DFH#D
Jm~HòJKLJ²ñdð
L#J p î'CLJKLJMï#JKrHïM¢DF L#DGôKDFEGJ¢
ï#ðEGHDFð
ÛH#ðÀHòJï#DGõ3Lð÷EGJKóA !òJóqJ²Hòð3DGï)J²öô²HmDFñ
HòJJ²öô²HñdJML#óqDGðD[ôB|sC DGïaï#JMjñdðLaH#òJsLJMï'H#LDGô²H#DGðA*ð{ø
+J JMLM¢uH#òJ}JKö
ô®H^|C D[ïBð
EGÜû5ð{ø°DF>jñdJMøßôK
ï'JcïKA-CðrïH
EGDGôM{HDFð
ïò JÓ8L#ð2öDGóÓ{H#JcH#òJqñdJKLóDGðDGôq|sC ÷5>
J²H#JML#óqDG8rH°ð8ñ?ï#DFõ
EFJsL'HDGôKEFJ^|sCïM¢
% Ó E Ò Ó º ÒÓ ¼ ¨¥&+% Ó EÒ Ô º ÒÓ ¼¨¥
+
+
+
% 8
© ºZ© ¼ ¨¥Ð¥ Þ
ÞÞ % Ó BÒ Ó º Ò Ô Z¼ ¨¥+% Ó BÒ Ô º Ò Ô ¼Z¨¥ ÞÞÞ
ÞÞ
ÞÞ *5¥
Þ
Þ
!òD[ïBLð
ôOòòïB÷RJMJKJ²ö5H#JMï'D
JMEF8EFDGJMï#DFõ)H#òJ
ñdLJKJ`8L#H#D[ô²EGJ p ¥!ðJcï&JML#D
JcÜñdL#ð
ó HòJ}ï#DFõEGJ6o 8L#H#D[ô²EGJ
JKï#DH)óq8H#LDö ¤
¤
% Ó{EÒ º Ò º ¨¥t¥
*¨¥ "J( J²ö
Â-BÒqÂ-Ò ¥ §*¨ ü ¥
ø°DFH#ò¥ áà §8 Ý ¢DGôKEFDFõÜ8EFD[ôK8H#DGðï!Hð)JMï'J}ò55L#ð4
õ
JK *3AsîoH^ôK ÷RJqï#òð{ø°â H#òR{H&ñdð
L&HJKóquJKâLO{H#L#Jcï&E[8LõJML
Hò8ÜHòJJML#óqDJMJKLõ
¢5H#òJ-DGrH#JML
ô®H#DGõqðE=ï'L'ñ
ô²J^8 L#ðrôOòJcïaH#òâ JÖ p ð58Eï#L#ñôKJAaî6 DFH#DGð=¢RDGH#òJ`EFDGóqDH
ðñEGð{ø JKï#DH
¢JKöôOòR8õ
JBJ 5uJcô®HïB8LJsJKõ
EFDGõDG÷EGJH#òJ^ð8E
ôKðï'H#LO8DGrH-òï}ï#óÓ8EGE6J 5½JMô²H}ð
0H#òJm{Hò 8R>H#òJML#JKñdðLJ
DFHï}LJMôKDGï#Jmï#ò8uJ)D[ï}ð8HDFóquðL#H8rHcA !ò'J p ðJMï8E[ï#ð
÷uJMôKðóqJjJKö
ô®H`DG0HòJ)EGDFóqDFHðñ°òDFõ
ò JMï'DFH>ø°òJKÀû5DGJ²HDGô
J 5uJcô®HOïðóqDG{HJ°ð JMLHòJ°DG
HJKLOô²H#DGðRðH#JKrHDGE
A *ð{øaJ JKLc¢
ñdð
LsH#òJÓJMï#DHDFJcï-8H#JMóqRJML8H#LJMïJKL`ôKðï#DGJKLO{H#DGð=¢
DGrH#JML
ô®H#DGðRïôKðE[ò Jqï'DGõyD RôM8rHJ 5uJcô®H-ð
HòJqð8E
ï#L#ñôKJMïMA
ðÓõ
8DG ï#ðóq
J r8rH#DFH8H#D J^JcïHDFóÓ{HJ-ð8ñHòJ`uð
ïï'DG÷EGJ^J²?ñ ñdJcô®HðñYH#òJ&ð8ERL#JcïHL#D[ô®HDFð
ð
qH#òJ*H#òJML#óqð58óqD[ô°Lð JML'HDFJcïK¢=DH`D[ïsJcô²JMïï8LH#ðH#L>EHJKL{HyD JAqî60DHDFð
H¡ð p ðJcïK¢øaJBRï'Jc)ðEï'L'ñ
ô²Jð8ñ {8LDG8H#DGðEuJK ï#DFH-óÓ{H#LDFö |C¥ ¤21 RJML#D Jc^ñdLðóz {8LD[{H#DGðR8E5LDFôKïD EFJ`H#ò8H&DFRô²EGJMïBDG
HJKLOô²H#DGðï* 8H#ðóqD[ô-8Róð
EFJcô²E[8L
÷uð)ï'H8H#JMïMA |J^
ï#ï#óqJB`H#LDGEY|C ø°DHòmLóqJ²H#JMLï Hò{H&JKuJKÜðÜDGóqõDG8LqH#DGóqJ ¨08 © ¢
3r¥
% ©8ºZ© ¼¨Ð
¥ ¥% ©Ëº Ó º+½ºs¥ @ajóqDGDGóDGIKDGõqHòJ^DFrHJKõLO8E
Qs ¥
Ù É © % ©Ëºi© ¼¨¥
% ©Ëºi© ¼¨¥! ¥3£ º
¨
ð
J*JKH#JKLóqDFJMï?J1
R{H#DGðRïãñdð L?HòJ*58óqD[ôKâï?ðñRHòJ*Ló¡
JKH#JMLï!DGDFóÓ8õ
DFR8LqH#DGóJ
¤
&
#" ' $( ¥ £ ø°òJKLJ ") Ù % % É ©7 r¥
%$
ã
¡
' +*
¥
qó 8H#LDömDGïM
Ù
EGDGÇ ó *
/
,.-
, É ©/% 8
© º r¼¨¥% Ë
© º ¼ ¨¥10ö r¥
$
$
â D[ï w EG8H#JMLJKH#JKLóqDFR8rHð8ñ=ï#DGõEGJ*L
|>JBïï#óqJ!H#òJ|C:
H#D[ô²EGJÖ·s8Rï#ï#DG)ñdô®HDFð
ï
% Ó B Ò º Ò º¨t¥ ¥ 32s¥ "J( JKö5 Â-BÒzÂ4 ¥ §2 É3 ¤c£r¥
ø°òJML#JwH#òJ 2L#D[{HDFð
8E~LóqJ²H#JMLï,L#JwH#òJÏã óJc8 4 ¢
iï R8LJMø°DGH#5
ò 2;8RÓ8óqâ EGDHJ É tA !òJ&â yD 5uJML#JMrH#D[8E1J R H#DGðRï°ñdðL*H#òD[ïBï{H#I-L#J^õ
yD JKDG ¤21 oA !òJ`DGDHDGEôKðyD H#DGðRï&{qH ¨ Â76 £j8L8J 2 ¥, ¨¢ 4 ¥ Ò 8 É ¥ú£ÓDGðLOJKL
H#ð L#JMõ
DFÛHòJ>ôKðLL#Jcô®2H p EGDGóDFHMA îoHmñdðEGEFð{ø*ïjñdL#ð
ó u uA s
H#òR{H{HEGð{øÀHJKóquJKLO{H#L#J
¢8H#òJ |sCõð5JMïHðsH#òJ*EGð{øaJMï'HJM JKLõø! J`ñdô²H#DGð~ø°DHòDGHò£J {8LDG8H#DGðE÷Rï#DGïMA ðL-8
D[ï'ð
EG8H#JM{H#ð
ó:ðL&óqð
EFJcô²EGJ`HòD[ï&ø°DGEFE÷uJ)÷Rð
ïHO{H#J
¢½DF
ô²ð
rH#LOï'HHð&HòJ*JKEGðôKEFDGIKJc`ï'H{HJ!ð8ñHò{J p |sC~A ñdL#H#òJKL
D[ï#ôKïï'DGð ðñH#òJ |C LðuJKL#H#DGJMïBDGïõD JM DG ¤c1 o:A 9*ðH#J
H#òR{HH#òJcï'JÜðJMï8LJ)ð
EG>Rï'Jc0H#ð~JKH#JKLóqDFJ)HòJmð58E
LJMï'H#LDGô²H#DGðÓDG u uA î#î®A ¡5¥OtA !òJBôKðóqEGJ²HJ&uð8H#JMrH#D[8EuDGïHûJK
DG
Hð ôMô²ð
H^DG~H#òJÓR{H#ò~DGrH#JKõ
LEô²H#DGð0ï^D[ïô²ïï'Jc>DF
JKH8DGEDG oA
;
Ö<$;>=@?AWJ2 7?@
!òJróJML#D[ôKEDGóqEGJKóqJKrH8H#DGðÐð8ñ*HòJ p î'C óJKH#òð
LJ+rDGL#Jcï&ð
J`HðmóÓûJ}ï#J
JKLO8E8L#ð2öDGóq8H#DGðïMAî6ôMô²LO
ô²DGJMïôK8÷uJ&ôKï'Jc`÷5ïHO{H#D[ï'H#D[ôK8EJKLL#ð
Lï=ñdL#ð
ó%HòJ&C DFrH6J õLO{HDFð
¢DGôMô²LOôKDFJcï!DFHòJ-5óqJKLD[ôK8EGEG)J²HJKLóqDFJc8DGL
JMï'DFHóÓ8H#LDGôKJMïM¢JMRJMJKRô²Jjð
HòJÓHDFóqJjï'H#JK0ðñHòJ
8H#òÀDGrH#JKõ
LE÷uJMôKï#J)ð8ñ ¾!÷uð ¾ ,¡r¥-ô²ð
L#LJKE[{HDFð
ïK¢
DFH#Jï'DGIKJ}6J 5½JMô²HïM¢½ðE=JML#LðLOï!ñdLðóÕ8L#ð2öDGóq8H#DGðï
DGjH#òJ*H#LD[8E½JKï#DFHóÓ8H#LDöYtA !òJKDGLa6J 5½JMô®HOïð
ÓH#òJ
ôKô²L
ô²
ð8ñH#òJÓôKðóqHJMH#òJML#óqð58óqD[ôq JKLO8õ
JMï*L#£J r8rHDHO H#D JMEF)JMï'H#DGóq8H#JcmDGÜH#òD[ï*ï#JMô²H#DGðA
w H8H#D[ïHDGôM8EJML#LðLOïDF~HòJÓJMï'H#DGóÓ{H#ð
Lï^ñdðLsH#òJÓH#òJML#óqð; óD[¡ô R8rH#DFH#DGJMï8LJ}ôM8E[ô²E[{HJMñdLðó:HòJ}÷EFðôOû JMLõJcï
õJMJKLO{HJM÷r H#òJjCßï'DGó`EG8H#DGðïMA !òJÓôKðLL#JMEG8H#DGðïB÷RJ HøaJKJK ÷EFðôOûïL#J~HO8ûJM DFrHð ôMô²ð
H ÷5úRJML'ñdð
L#óqDGõ
÷EGðôOûrDGõ8EFï#DGï ¤c¡ A !òJaL#Jcï'EHDFõBJKLL#ð
L=÷Lï ð
Jaï'H L+J 5DG8H#DGðu¥!L#J`õD JKÜñdð
LB8EGE=ð
÷ï#JKiL 2÷EGJMï!HòL#ð
õòðH
H#òDGïÓR8uJKL)
ïÓ5ó}÷RJMLjDGÐR8LJKrH#òJcï'D[ïqLJ²ñdJKLLDFõH#ð~HòJ
EGJMï'H*ï'DGõïD RôM8rH*DGõDFHMA
î6 HòJñdðEGEGð{ø°DFõ0D[ïô²ïï'DGð=¢øaJ ô²ðóqL#JmH#òJDFrH#JML#R8E
JKJKLõj8RjHòJ^LJMïï'LJBôM8E[ô²E[{HJMmï#DFõHòJ 5DFLDGEuH#òJMð LJKó
¤
¤2¥
¡ BED¡¥ G F ×
C
ø°òJML#J DsD[ïHòÐJ ðEGóqJð8ñHòJï#DGó`ã E[{HDFð
`ô²JMEFE¢ FÏH#òJû5DFJ²H#D[ô
JKJKLõ)!
×H#òJ-uð8HJKrH#D[8E=JKJML#õ
A ôMô²LO{HJ^JMï'H#DGóÓ{H#DGð
ð8ñBH#òJL#Jcï#ï#LJmL+J rDGL#Jcïq~òDFõ
òÐ
ôKôKL
ô²0DG HòJû5DFJ²H#D[ô
8R0H#òJmuð8HJKrH#D[8E!JKJKLõDGJMï}÷RJcôK8Rï'J)H#òJM0H#JM0Hð>ôM8ôKJKE
ðHMA?î6jHòJ^óqðEGJMôKEGLLJKõ
DFóqJs{H°EGð{ø JKRï'DFH¢5÷uð8H#òÜHJKLóqïM¢
ð
óDG8H#JM ÷rDGrH#LO oóð
EFJcô²E[8LBô²ðrHL#DG÷HDFð
ïK¢½ôKô²JME=Hðm
E[8LõJÓJ²ö5HJKrH`EGJM 5DFõ÷RJMòDFR>H#òJmóð
EFJcô²E[8L`õ
ï-L#Jcï#ï#LJ¢
ø°òDGôOòÀD[ï}ó`ôOòÀEGJMïï^Hò8ÀH#òJÜDFrHJKLZóqðEGJMôKE[8L^ñdð
LôKJMïMA ï
~LJMï#EFHM¢aH#òJ LJMïï'LJD[ïK¢!DG3õJKJKLO8E¢aï#DFõ
yD RôK
HEF óqðLJ
ï#JKRï'DFH#D JHð 8L#ð2öDGóq8H#DGðïHò83ðH#òJM2L r8rHDHDFJcï)ï#ôOò
ïaH#òJ^DGrH#JML#EYJKJML#õ
A
ÿQKX[T°*U#V
k'X[b[g8HjQcb[T'XJI
2.0
M
1.5
Energy error (eV)
!òJ^ð
L#ó
2K+V
E−Eexact
1.0
P
0.5
0.0
−0.5
−1.0
K
0
L
1
O nA
order
M
2
N
3
QSR.TVUXWZY[]\\_^Z`aC\bdc!e^[email protected]^gtsaGeqsiCugc%iCkvewZx8qsciGy
tzaexfdw{bhfh`iC|xudaGeir}^gc.qsuZ|~fhq7x`xue%iC`fhx`c3qujewZxEx{y
aGugcqiuVkiC`r^Ztza~>W]kiC`ewZxaC\eqiu5aGugf~xuZx`|CbUv%wZx]\aGtz\_^hy
tzaexfWC}x_ZaC\_eaGts^Zxx{^gaCtscx`imaGugfewgxfhx{qzaeqiu
k`iCrewgxx_Za\e
iGexu{eqzaGtxuZx`|biCk]Wh Wx aG`xcwZi¡¢uEkiC`
fZqJ#x`xu{e8iC`fhx`ck`irc.qsr^gtsaGeqsiCugc8aGeE£¥¤¦§§§C§¨©^gcqug|
ª#«¬ ¤>§C®¨~U
R1kEiCuZx¯iCugtb°^Xc.x>f°ewZx±gaG`x
iCexu{eqsaCtaCc~qsu³²7UW´ewZx
`
s
q
r~qJeqx]a
Z
`ihqsr~aGeqsiCuVkiC`ewgxaC\_eqsiCu7µCewZxE\_iCux`|CxuX\_x
¡iC^gtsfV±7x]Cx`bc.tsi¡¶·G¸7aGuXf~¡i^ZtsfV`xc^ZtequaCu5x_e`xr~xtb
qsuZx¹5\qxu{e@r5aGub{y
aC`.eqs\txcqr^ZtsaGeqsiCugcUºR»uXc!exaCfµ8¡x°u^hy
r~x`qz\aCttsbVciCtsCxewZxe!¡iCy
aG`eqz\_tsx
`i±Ztsxr¼¡¢qJewewZxr5aGe`qJ
c{^gaG`qsuZ|%ex>\wZuZqz^gx¶>½¸1Uv¾]^Zr~x`qs\aGt{`x
`xcxu{eaGeqsiCugc3iCkhewZx
xZaC\e
aGqs`8fhxuXc.qe!b¯r~aGe`qs\xc¿aG`xc.ei`x>fÀqsuÀeaC±Ztsxc¿^gcxf±b
ewZx]lR.n@o°cqsr^Ztzaeqiu
`i|C`aGrÁ±bx
aGugfZquZ|8qsu~ewgxcr~aCtt
aC`qzaG±Ztsxc¢ÂaGugfÄÃgY
Å ÆÇ.ÆÈÊÉ ª ¤
¡¢wgx`x
Ó8¤
W
¶ Å Ë ÌÉ ª v
7
Å Ë ÌÈÊÉ ª ʸ
W X
Ð
¼Ï ÍGÎ Ï
Å Ð Ò Ô ÓÉ ª Ã{Õ Ò Â>ÕÖ Ð « Ò× ÇØ.>W{
Ë
ÐÑ ¬ Ò Ñ
Ù ÆhÙ>pÙ Æ È Ù Ú¤ÛÙ ÆÆ È ÙÜäÛÙ ÆZÙÝÙ Æ È ÙÞÇ
.ß
aCugfàÆjaGuXfàÆ È fZxuZiCex~ewgxc.x
aG`aeqiu@iGkewZx~e!¡i
aG`eqz\_tsxc
aGe:aCfá.a\_xu{e8eqr~xctqz\_x>cU%wZx5a\\_^g`a\_biGkewgxcx~eaG±gtx>cEqsc
\`^X\_qzaGt#kiC`aGtst\_ir
^hex>fj`xc^ZtecUâc.qsuZ|~ewgx
`x>\_ir
^hex>f
*
DFLJKï#DHóÓ{HL#D[ô²Jcï8EGEFð{ø*ïðJ!Hð-JKóqEGð{}^ó}ôOòqEGL#õ
JKL
H#DGóqJ}ï'H#JM ÷RJcôKï'J`ðJ`ï'HL'HOï*ø°DFH#ò)ï'ð
EFHDFð
ð8ñ?HòJ-Høað
L'HDGôKEFJ°Lð÷EFJMóÜADFõRA
sï#òð{ø*ïòð{ø
ôKôKL8H#JaH#òDGïóJKH#òð
D[ïKA !òJ`DG
HJKL8EJKJML#õ
)ðñ8D[ï'ð
EG8H#JMò5Lðõ
JK{HðóÕ{H
ï#h ãjô²DGJKrH#EGBEGð{øH#JKóquJKLO{HL#J þ ¥ ¤c£££
£ `¥DG`!E[8LõJ?÷uð2ö
ä ¥
35¥DGïôKðóqL#Jc`ø°DFH#òqHòJ°J²öô²HõLðR}ï'H8H#J°JKJKLõ
ð8ñ Â ¤c¡ 3?J A !òJ*HJKóqRJML8H#LJ&ø!ïôOòð
ï#JKÓEGð{ø3JKðõ
òjï'ð
H#òR{H*J²öôKDHJMïHO{HJMï°ôKm÷uJ^JMõEGJMô®HJMÍ ¼H#òJ-ôKðrH#LDF÷H#DGðmH#ð
H#òJ^JKJML#õ
ÓñdL#ð
óHòJ-ðôKôK{HDFð
mðñHòJ LOï'H!JKöô²DFH#JMï'H8H#J
D[ï svå ¤M£ "7æYJ {HH#òDGïHJKóquJKLO{H#L#J
A EGï#ð^ï'òð{ø°D[ï?òð{ø øaJKEGE
H#òJ-û5DFJKH#D[ô-JMJKLõÄ F8ÜHòJ`uð8HJKrH#D[8EJKJML#õ
' ×Ïï{HDGï'ñd
H#òqJ 5DGL#D[8ERH#òJMðLJKóG F × ¥;£¢rH#ò5ï!JKH#JML#óqDGDFõ-H#òJ
ô ô²L
ô²Üø°DHòø°òD[ôOòÓ HòJ}L#Jcï#ï#LJ}ôK ÷uJJKH#JML#óqDGJMYA ðL
ÜH#DGóqJmï'H#JM0ð8ñ ê)" ¥ ã ¤M£ ç6q¢H#òJ)8EGï'D[ï-ï#òð{ø*ï-!
rD[ôOû
ô²ð
JKLõJMô²Jø°DHòH#òJ°ð
LJML?ð8ñRH#JKLóÓïô²ð
ï#DGJML#Jc-DGH#òJ*
ô H#DGðÜJ²öï#DFð
u uA ¤2 ¥OmA èBï'DGõ}H#JKLóÓï!d é3ê¥;¡}L#JcôKJMï
H#òJJKLLðLqH#ðУ £¡
¡ ¡5¥rJ DG;JKJKLõÛ8ÐHð £ £]¡ 5¥rJ ñdðLqG F ×ÓA !òDGïô²ð
L#LJMï#Rð
ïsHð8 DF
ôKôKL
ô²DF0HòJ
LJMïï'L#J°1J yD {8EGJKrHHð}^ð oDFrHJKLOô®HDFõ^óð
EFJcô²E[8Lõ
ï{H
þ ¥ 4 3£ ã ¡£r¥ qA
ëíì
X[\-U!k'bU
î{U
U#Vî{U#VW'U
0.5
ð
ð
0.3
[X VrXlbU!rXõôKU°*U
U#Vî{U#VW'U
!òJJMï'H#DGóÓ{HDFð
ð8ñBH#òJ'DHJï#DGIKJÜJKLL#ð
Lï}DGïóqðLJDJã£
ôKEFH*H#ðÜïï'Jcï#ï!÷uJMôM8ï#J^H#òJ`JMJMJc p î'C ï#DFó}EG8H#DGðï&8LJ
ôKðóqHO{HDFð
8EGEF ó`ôOòÛóqðLJJKóÓ8RDFõA !òJL+J rDGL#Jc
ôKðóqHJKLH#DGóJBDFRô²LJMï#JMïLDGEFø°DHòÓH#òJ&5ó`÷uJKLað8ñYL HDGôKEFJcï^óÓ8û5DGõDHôOò8EGEFJMõDGõÜH#ðð
÷HDFÀôKð JML#õ
JML#Jcï'EFHï
ñdð
L°{Hòï°ô²ð
L#LJMï#uðDGõ}H#ðqE[8LõJ^ï'ï'H#JMóqïMA
CðrïH&LJMï#EFHï*ñdL#ð
ó×óÓ85; o÷Rðï'DGó`EG8H#DGðï&L#JMRð
L'HJMDG
HòD[ïmøaðLûÐøJML#J>ôK8E[ô²EG8H#JM;ø°DHò ¾ ¥ ¡
08DGLïmð8ñ}JKEGJMô HL#ð
ï^8RLð8HðïsDG0ÜRJML#DGðDGôM8EGEFL#JMRJc{H#Jc~ï'DGó`E[{HDFð
ôKJKEGE
tA ð`ï'H#qHòJ&J 5uJcô®H!ð ¾0¢5øaJ*uJKL#ñdðLóJcjï#DFó}EG8H#DGðï
ñdð
L ¾ ¥:+¤ 38
34*ÜR8DGLïsðñaLð8Hðï^JKEGJMô®HL#ð
ïñdðL}
JKï#DH ð8ñ . 0 ¥ 30Ðþ , ¤c£££
£ q
A |JôOòð
ï#JH#òJ
òDFõ
òJMï'H*JKï#DFHjJML*ô²ð
ï'D[JML8H#DGð)÷uJMôM8ï#JsðJsJKö5uJMô²Hï
HòJ DHJ}ï#DFIMJ`JKuJKRJKôKJ-Hðj÷RJ`EGL#õ
JMï'H°H#òJML#J`J-HðÓH#òJ
ï'H#LðõJKL!DGrH#JKLOô²H#DGðm÷RJKHøJMJKÜH#òJ-8H#ð
óqïMA
òÚó
0.2
0.2
0.1
0.1
0.0
0.5
1.0
−1
6
τ (10 K)
2.0
î·Ac¡½!òJJML#LðLYDG^H#òJÐ
5DFLD[8E
ï!ñdô²H#DGð-ðñ5H#òJró`÷uJKL
ð8ñ^HDFóqJ>ï'EGDGôKJMïjñdðL83D[ï'ð
EG8H#JMÛò5Lðõ
JKÛóqðEGJMô²EFJ
A ! òJ
ô²E[ïï#DGôM8E½5ô²EGJKD=L#Jz öJcÜ8H°H#òJ^J1r DFEGDG÷L#DGó×÷Rð
ÜEFJMõ8Hò¢
H#ò5ï&H#òJ`J²ö
ô®H{
8EGJ`ñdðL CF Ï
× D[ï&IMJKLðj{Hsjï'ZãÓôKDFJMrH#EG
EGð{ø;H#JMóqRJML8H#LJA
ã
u óqEGð{rDGõqHòJ`DFL8L#ð2öDGóq8H#DGðÜð8ñ?HòJ}JMï#DHÜóÓ
H#LDFöqð5JcïðHDGô²EGJô²ðLLJKE[{H#DGðqJ 5uJcô®HïñdðLH#òLJKJ&ðLóqð
L#J
L'HDGôKEFJcï ñdð
LJ²öóEFJ*÷uJ²HøaJKJMÓðJ&JKEGJMô®HL#ð
Ó8Høað-Lð H#ð
ﮥO!
A |>Jjð{ø JMï'H#DGóÓ{H#J)òð{øÏï'óÓ8EGEHòJÓHDFóqJmï'H#JM0ó`ï'H
÷uJÓH#ð ð
÷HDF0õ
yD JK0ôMô²LOôKñdðL}80D[ï'ð
EG8H#JM>óqðEGJMôKEGJA
DFõRA°¡ ï#òð{ø*ïmL#Jcï'EFHï)ñdðLyD 5½JKLJKrHmHDFóqJ~ïHJKï3HJK¡
ó uJKLO{H#L#Jcï-ø°DFH#òÀHòJÜrRô²EGJKDaûJKH öJcÀ{HH#òJm+J rDGEFDG÷LDFó
0.0
∆P/P
ï
2K+V (eV)
0.4
T=3906 K
T=1953 K
uð
ï#DFH#DGð ðññ¦¥¤4 *
£
£4AxLðóHòJ
5DGL#D[8EH#òJKðLJKó¢½DFHñdð
Eï
EGð{ø*ïaH#òR{H CF × ¥ £Ó8HBÓï'ZãÓôKDFJMrH#EG)EGð{ø HJKóqRJML8H#LJA
!òJmJKö
ô®HJKJML#õ
uJKLÓ{Hðó D[ï Â ¤ ü s ¡?J ¤+3A!òJÜþ
JKuJKJMô²J}DGïã ï#óqEFEï'õõJcïHDFõqH#ò8H&H#òJ`JKEGJMô²H#LðïB8LJ-DG
HòJ°õLð}ï'H8H#J
A &ð{ø+J JKLc¢{ðJ Ó ï^ï#DGõyD RôKrH?JKuJK JKôKJ}ð
HòJ`HDFóqJjï'H#JMA è&ï#DGõ ê)" ¥w2 0¤M£ çÏLJMRô²JMï
HòJÓJKLLðLDF>H#òJÓJKJML#õ
RJML-{HðóÕHð £ £4¡ 3 ¡5¥?J 8DG
F ×Hð £ 4£ £ +¤ 35¥rJ =A !òJÓH#DGóqJ)ïHJK0JML#LðL^D[ï-E[8LõJML
C
Hò8ÛHòJ JML#LðLOïð8ñsH#òJDF
ôKôKL
ô²DGJMïqDGÛH#òJ8DGL)JMï'DFH
óÓ8H#ãLDGôKJMïDGïô²Rï#ï#JM 8÷uð J
A !òJÜJKLLðL`DGÐC F × ôKðLL#J ï#uðïHð}LJMïï'LJ&ðñ8mð DGrH#JKLOô²H#DGõ-óqðEGJMôKE[8Laõ
ï
8Hþ ¥ s £
£ ¤c££r¥ q¢ø°òD[ôOòLð 5DGJMïBïø°DHò8ã >8L#ð2öyD óÓ8H#J°EGDFóqDFHð8ñYôKôKLOô²^DGH#òJ°1J r{HDFð
}ðñ½Ó ï'H8H#J*ôKEGôKE[{H#Jc
ñdLðó óq5] oL'HDGôKEFJsï'DGó`EG8H#DGðï!ø°DFH#ò ê)" ¥;¡ >¤MC£ ç+qA
−0.1
(P16−P64)/P64
(P32−P64)/P64
−0.2
−0.3
10000
ö
100000
ö
T (K)
÷
î ·$A *Ð
DGDHJ`ï#DFIMJ-JKLL#ð
L!ð8ñH#òJ`L#Jcï#ï#LJ^ï*ñdRô®H#DGððñ
HJKóquJKLO{H#L#J*LJKE[{HDy
J!H#ðï'DGó`E[{HDFð
ï?ø°DFH#ò'¾ ¥ö3*-R8DGLï?ðñ
L#ðH#ðRïaÜJKEGJMô²H#Lðï!{H&qJMï#DHjðñ . 0 ¥ 3A
!ò=
J DFH#Jï'DGIKJJMRJMJKRô²JÜð8ñ*HòJmL#Jcï#ï#LJ¢ï#òð{ø°ÀDG
ü
0.4
10
Saumon & Chabrier
PIMC FP
PIMC VDM
10
ÿ
rS=2.6
1
E16−E64
E32−E64
0.2
∆E (eV)
2
rS=4.0
10
0.0
10
û
0
4
ý
10
þ
T (K)
ý
10
5
î·A3!òJBJ5uJcô®H°ð)H#òJsLJMïï'L#JBð8ñHøaðDï5½JKLJKrH!ð8E
−0.2
ï#L#ñôKJMïM}ðñ°H#òJ)ñdL#JMJ)L'HDGôKEFJ)JKï#DH~óÓ{HL#DFö080ðñ°H#òJ
{L#D[{HDFð
8EYJMï'DFHjóÓ{HL#DFöYA
10000
ö
100000
ö
T (K)
÷
î ·A ü DGDFH#Jï'DGIKJBJKLL#ð
Lð8ñYHòJBDGrH#JML#EJMJKLõqïasñdô6
H#DGððñHJKóquJKLO{H#L#J-LJKE[{HDy
JH#ð)ï#DFó}E[{H#DGðRï°ø°DHò˾ ¥ 3*
DFLOï!ð8ñ8L#H#D[ô²EGJMï°8H°ÓJKï#DH)ð8ñ . 0 ¥; 3A
DGõA ü ï'òð{ø*ïH#ò8
J DFH#Jï#DFIMJJKLL#ð
LÓð8ñsH#òJ DFrHJKL8E*JM JKLõ
2A !òJ)ï#óÓ8EGEFJML-ï'ï'H#JMóqï`8LJóqð
L#Jjï'H#Lðõ
EF÷Rð
~÷5
8L#ð2öDGóÓ{H#JMEFq£ Ã ^J RJML°{H#ð
ó¢rL#ð
÷8÷EG÷RJcôK8Rï'Jð8ñHòJ
DG
HJKLOô²H#DGðÐð8ñ^>ôOòR8LõJÜø°DHòÐDFHïjð{ø° DGóÓ8õJ
A ð
LÓEFð{øaJKL
JMï'DFH#DGJMïM¢øaJsJ²öRJcô®H°HòDGï 2EFJBHðÓ÷RJ-ï#óÓ8EGEFJMLMA
x _a]î2Qcetc5T6]IMXG\^Qcb[Xd]KV
î60H#òJ8÷uð
J
¢øaJ)òR
Jjï'H#DGJM ô²ð
HL#ð
EFEGJM0Lð2öDFóÓ
H#DGðRïKA!òJðEGÀRô²ðrHL#ð
EFEGJM 8Lð2öDFóÓ8H#DGðÀDGÐH#òJLJ6
ï'H#LDGô²H#JM p î'C óqJ²H#òð5 DGï*H#òJ}ï'J`ð8ñ?H#LD[8EJKï#DHÜóÓ{HL#DFö
H#ð~ô²ð
ï'H#LO8DG0H#òJ8H#òïMA !òJðE!ï#L#ñôKJMï8LJ)DGóuðZL HrH!ð
EGjDñH#òJ^JMEFJcô®HL#ð
ï!8LJJMõJMJKLO{HJ{H°EFð{ø;H#JKóquJKZL {HLJMïðL^{HsòDGõò~JKRï'DFH#DGJMïMA ü°JcôKEFEH#òR{H^DFH#òDGïsøaðLûøJ
ñdðô²ïð
Àò55L#ð
õJK0ð
EG~8H}EGð{øJKRï'DFH¢ø°òJKLJjH#òJmJMEFJcô H#LðRï*8LJ^÷Rð
DG{HðóÓï*óqðEGJMô²EFJcï*8òR J-qEGð{ø
ðL}óqð5JKLO{H#JmJKõ
JKJML
ô²A u JKÀ8H`EGð{ø JKï#DH
¢?ðJmïHDFEGE
JMJMïsjð58E?ï'L'ñ
ô²J`DGð
LJKL*HðmL#+J JKrHBH#òJ}ñdðLóÓ{H#DGð
ð8ñò5ï#DGôM8E°ô²EGï'H#JKLOïEFDGûJ " ( 8 " # ð
LqJ JMÀHòJô²ðyE E[8ï#Jqð8ñaH#òJÓJM
HDFLJjï#5ï'H#JMó¢=÷H^HòJÓLJMôKDGï#Jjï'òR8uJðñHòJ
ðJcïD[ïðHDFóquðL#H
Ha{HEGð{ø3JKï#DFH
ïï#òð{ø°qDF2 DGõ;A 3A
ðóqL#DGË
õ p |sCæðJcï^ñdðÖL .10¥ 3¢ðJ)ðEG
ï=yD 5uJML#JMô²JcïDGsH#òJLJMïï'LJñdðL=þ ýú¤ ü 3r ü q¢Kø°òDGôOò^D[ï
8L#ð2öDGóÓ{H#JMEFø°òJKLJ¢=8H^H#òD[ï^JKRï'DFH¢=H#òJjï#ïHJKó ï#òð{ø*ï
~ï'DGõïD RôM8rHqóð
EFJcô²E[8LÓï#DFõ
{HLJ ï'JMJï#JMô²H#DGðÐî'î#î@8
DGõAu¤+35¥OAî6jH#òDGïL#JMõDGóqJ¢ p
ðJMïï'ï'H#JMóq8H#D[ôKEFEGqEFJcH#ð
Ó H#ð5ð)òDGõòL#Jcï#ï#LJ¢ø°òDFEGJ}ï#DFó}E[{H#DGðRï*ø°DFH#ò |CðJMï
ï'H2ô²EGð
ï#JKL?Hð-HòJ*LJMD[ô®HDFð
Óð8ñ=^ï#JKóqDyJMóDFLDGôM8EuôOòJKóqD[ôK8E
óqðJME ¤A H} EFð{øaJKL-JMï#DH
¢¸.0¥ *R¢LJMï#EFHïsñdLðó p
|C ðJMïqõLJKJjø°DFH#òDGÀHòJJKLL#ð
L`÷LïM
A !òJÜD?ñ −5
Saumon & Chabrier
PIMC FP
PIMC VDM
E (eV)
−0.4
−0.6
3
P (GPa)
DFõRA *¢?D[ïï#óÓ8EGE°{HqòDFõ
ò0H#JMóqRJML8H#LJMï÷HqõLð{ø*ï^Hð> Lð2öDFóÓ{HJKEGË* ¥ZøÕJML-þ ¥¡££
££qAÓî6>HòDGï`L#JMõDGóqJ¢
H#òJBò5LðõJMÓJML#õ
ð5JMïï'H#Lô²H#LO8E½ôOò8õJMïDF
ðE
rDGõ^HòJ
ñdðLóÓ{HDFð
^ð8ñR8H#ðóÓïM¢2ø°òDGôOò}5½JMô®HH#òJaLJMïï'L#J
A !òD[ïï'H#
Lð 5DGJcï^ï}ðEG>ø°DHò 8ÀJcïHDFóÓ8H#Jjðñ°H#ò2J DFH#Jmï#DGIKJm6J uJKJMô²J
A JKö5H#LO8uðE[{H#DGð~Hð ¾ 6úù øaðE[0L+J rDGL#J
ï#DFõ
ïD uôK8rHEFÓE[8LõJMLï#5ï'H#JMóÓïK¢ðH*ô²LL#JMrH#EG}ñdJcï#DF÷EFJ^{H!EGð{ø
H#JMóqRJML8H#LJMïMA
−10
−15
0
10000
20000
T (K)
30000
40000
î·A s î6rHJKL8E½JKJKLõÓô²ð
óH#Jc)ø°DFH#ò p î'C3ï#DFõ}Høað
Dï½5 JKLJKrH&ðE=ï#L'ñ
ô²JcïKH#òJ^ñdLJKJ`8L#H#D[ô²EGJ-JKRï'DFHmóÓ8H#LDö
)H#òJ{
8LD[{H#DGðR8EYJKRï'DFH)óÓ{HL#DFöYA
ñdJML#JMô²Jcï!DFÜHòJ^DFrHJKL8EYJMJKLõ
¢5
ï°ï'òð{ø°mDG!DGõA s ¢ï#DFõ
p |sC ð5JMïjL#Jï#DFõ
ïD uôK8rHEFÐï'óÓ8EGEGJKLqH#òR8ÐH#òJ
L#Jcï#ï#LJqJ 5DG8H#DGðïMA v JjJMDHòJKÖL ï}8õLJKJMóqJKrH-ø°DHòDG
HòJÜJKLL#ð
L`÷Lï}ðL}H#ò8H |sC ðJcï`L#JcDGô²HEGð{øaJKLDFrH#JML R8EJKJML#õ
DFJcïK¢½ø°òD[ôOòø!ïBï#JMDF ¤ s H#ðï'òð{ø H#ò8H |C
ð5JMï?8LJH#òJ°óqðLJ°ôMô²LO{HJðEï'L'ñ
ô²JA !òJ°ð÷Rï'JMZL JM
JMJKLõjïD 5½JKLJKôKJMï°D[Üð8H*JKöô²JKJcm@£ F¤=J uJKL&8H#ðóA
3
ä®ä®ä²å éRìè
Molecular gas
Fermi gas
Ideal
Saumon & Chabrier
25
PIMC
20
15
E (eV)
gas
Molecular
Atomic gas
−11
FVT
Saumon & Chabrier
−12
PIMC
ActEx
−13
−14
−15
−16
0
10000
T (K)
20000
î·A)!î6rH#JML#E=JMJKLõmRJML8H#ðó&
ïKA*H#JKóquJKLO{HL#J-ñdðLs
JKï#DHÜð8ñ.0qw
¥ ¤c£jïBï'òð{ø°DF8 DGõAJÓ
÷HsòJKLJ^ñdð
L&EGð{øJML
HJKóquJKLO{H#L#JcïaEGï#ðDFôKEFRDFõLJMï#EFHïañdLðóÏHòJ^ô²H#Dr
DFHjJKö;
R8ï#DFð
¤+ A
.0{¥,¤M£@ £¢ï°ï#òð{ø°mDGDGõAAt!òJKLJH#òJ w 3JKJML#õ
DFJcï!8LJ
ø°DFH#òDF`H#òJaJKLL#ð
L÷Lïð8ñHòJ p î'CLJMï#EHOïKA HòDGõòJKLH#JKó¡
uJKLO{HLJï#òð{ø° DG DGõA½ ¢YøJ >ï'ï'H#JMóq8H#D[ô}J
5DG8H#DGðï
ðñÜHð ü J RJML*{H#ð
ó×8H!þ ¥ ü ££££Ðq A ! òJK)DFDGôM{H#J
Hò{HH#òJ w JKJML#õ
DFJcï`8LJjHð5ðEGð{ø{HòDFõ
òÀHJKóqRJML8H#LJMï
Hð5ðmòDGõò>{HsDFrHJKLóJcD[{H#J}H#JMóqRJML8H#LJMï ï#JKJ£ DFõRA)5 ¥OA
v JBuð
ïï'DG÷EGJ&JKö5EG{HDFð
jñdðLH#òJsJ5
DG8H#DGðïa{H!òDGõò)H#JKó¡
uJKLO{HLJ°DGïH#ò8HH#òJ w óqðJKEuJML#JcïHDFóÓ8H#JMïH#òJBJKõ
L#JMJ
ðñDGðDGIM8H#DGð ï#JKJ-D[ïô²ïï'DGðmDF 8£ ¥OA
| J-8E[ï'ðÓï'H#DGJMÜHòJMï#J-J+r
D[{HDFð
ï°ï°ñdô®HDFð
ÜðñJK
>
ï#DFHA!! òJmôKL#ðrï#ïo ð
JKLBH#JMóqRJML8H#LJ¢?8÷uð
JÓø°òDGôOò~HòJ w Ð
uvxw JML#JcïHDFóÓ{HJMïsHòJjJMJKLõ
¢DGô²LJM
ï'Jcïsø°DHòÀJKRï'DFHA
X<$;s??AW;W
35
30
−10
E (eV)
ðL&J JMEFð{øaJKL°JMï'DFH¢H#òJ^ð5JMï&L#JsEGJMïï°LJKEGJ {8rH°÷RJ Kô ï#JqH#òJM÷uJMô²ð
óqJjðEGDGóqRð
L'HO8rH-DGÀô²ðEGEGDGï#DFð
~ð8ñaHøð
óqðEGJMôKEFJcïK¢ø°òD[ôOò0ðôKô²L-EFJcï#ï^ñdL#J1
JKrH#EG>8H-EFð{øaJKL-JKï#DH
A
!òD[ï?HL#JMÓôKj8E[ï'ð^÷uJ*JKLOïHðrðqDGqH#JML#óÓïðñ½H#òJ&JKõJM
JKLOôKð8ñaH#òJqJMEFJcô®H#LðRïKA !òJÓJMõLJKJqð8ñ!JKõ
JKJML
ô²óÓ8yD ñdJMï'HïDFHï#JKEFñRDG}H#òJ!8H#ò`DGrH#JMõLO8ErñdðLóÓ8EGDGï#ó,÷r-H#òJ!Lð÷÷DGïE DFHÓñdðL!HòJsJKEGJMô®HL#ð
ïH#ðq÷uJ^DF ð
yE JM)DFRJML#ó}H8H#DGðA H
òDGõòH#JMóuJKLO{HLJ¢YHòJÓ{Hòï^8L¡J JKL ï#òðL#H-8RJML#ó} H8H#DGðï`8LJÓLL#J
A H`EGð{øßHJKóqRJML8H#LJj8RòDFõ
ò~JKï#DH
¢
H#òJÜR{H#òRïL#JÜEGðõ~8 ôK ñdð
L#óEGðõ>uJKLó`HO{H#DGðÐô²; ô²EGJMïMqA &ð{ø+J JML*DFòrLðõ
JK{HEFð{ø%JKï#DH
¢HòJ{Hòï&L#J
EGð5ôM8EGDFIMJMÀJ)HðHòJ{H'HL
ô®HDFð
0DFÐ{H#ð
óÓï}ÀóqðEGJMôKEGJMï
8R0RJML#ó}H8H#DGðï8LJjLO8LJA DGõAa¤mï#òð{ø*ï-H#ò8H}HòJmuJKZL ó`H{HDFð
Lð÷R8÷DGEFDFH0+J JKLqLJM
ôOòJMï)¤ ø ñdð
¡L .0!¥ * ï#JKJ
8÷ARî#¥Oq
A ðLBòDFõ
òJKLJKRï'DFH#DGJMïM¢HòJ`uJKLó`H{HDFð
Lð÷÷DGïE DFHD[ï^DGô²LJM
ï'Jc>
ï^DGD[ôK{HJM~÷5 HòJmôKðrH#ð
L^EGDFJcïKA !òD[ï
D[ï)ô²ð
ï#DGï'H#JM
Hjø°DFH#òÛHòJHJKóqRJML8H#LJ 8R3JKï#DFH JMRJM JMô²J-ðñ?H#òJ`ð8EJKLL#ð
L°DF L#Jcï#ï#LJ-8DGrH#JKLE=JKJKLõ
D[ï#ôKïï'Jcm÷Rð JA
10
5
0
−5
20
−10
15
−15
−20
150000
10
î·AJ!î6
HJKL8EJKJML#õ
)uJKLs{Hðó&
5ïMA°HJKóqRJML8H#LJ-ñdð
LB
JMï'DFH`ðñJ. 0 ,
¥ ¤M£sôKðóq8LDGõH#òJ w Ð urvxw= ¤ ø°DFH#ò p î'C
5
0
50000
100000
T (K)
E (eV)
ôKEGôKE[{H#DGðRïKA
÷A5îõD Jcï?H#òJôKðóqEGJ²H#Jsï#J²H!ð8ñ=JMJKLõDGJMï8)L#Jcï#ï#LJMï
{H 3*JKRï'DFH#DGJMï8 °H#JKóquJKLO{HL#JcïK¸A |Jð{ø0ô²ðóqL#JHòJMï#J
LJMï#EHOï&ø°DFH#ò>ï'+J JMLE=óqðJKE[ïBñdðLòrLðõ
JKqA |J÷uJKõDGð
L
D[ï#ôKïï'DGð~÷5>ï'H#R5DFõ H#òJjDGrH#JML#EJMJKLõRJML`{Hðó ï
)ñdô®HDFð
ðñH#JMóuJKLO{HLJï#òð{ø° DG DGõ
ïM)A 2^¤¤`ñdðLBHøð
ï#JKEGJMô®HJM3JMï#DHDFJcïmôKðLL#Jcï'uðDFõ>Hð .10¥ ¤M£ £08R; 3A
·JKJKLO8EGEF
¢=øa£
J ~Üñ8DGL#EGõ
ð5ð5ð JMLEFE?õLJKJKóqJM
H^ø°DFH#ò
H#òJ uvxw ÷5 w ¤ =ð JMLHòJsJKrH#DGLJBHJKóquJKLO{H#L#J^8RmJM ï#DHjLO8õJ^D[ï#ôKï#ï#JMmDGmHòD[ï°øð
L#û½A !òJ^õLJKJKóqJM
H°D[ï°L H#D[ô²EGL#EG õ
ðrðÛDGÛH#òJóð
EFJcô²E[8Lm8Û{HðóqD[ôL#JMõDGóqJñdðL
Molecular gas
0
Fermi gas
Ideal
Saumon & Chabrier
−5
PIMC
−10
−15
−20
0
50000
100000
150000
T (K)
î·Aa¤M£}î6rH#JML#R8EJMJKLõ>uJKL}8H#ð
ó ïMAH#JMóqRJML8H#LJ)ï
ï#òð{ø°ÜDF DFõRA@ ÷H*òJML#Jñdð
L&qJKï#DFHjð8ñ.10{¥; 3A
s
−11
−12
14
40
10
rs
3
4
6
2.6
30
125000 K
−13
E (eV)
Molecular gas
Saumon & Chabrier
ActEx
FVT
PIMC VDM
PIMC FP
20
E (eV)
−14
−15
−16
10
PIMC
31250 K
0
−10
0
10000
T (K)
5000 K
20000
î·A¤¤
sî6
HJKL8EJMJKLõ uJKL-8H#ð
ó ïKAH#JMóqRJML8H#LJñdðL
JKï#DH~ðñ.10':
¥
3 ïï#òð{ø°0DF DFõRA¤c£ ÷HqòJML#J)ñdðL
EGð{øJMLÓH#JMóuJKLO{HLJMï)EGï#ð0DGô²EGDGõ LJMï#EFHïjñdL#ð
ó HòJ
ô
H#D5
DH J²öï'DGð ô®H u öR¥ ¤+B H#òJR DG{
L#D[{HDFð
8E
H#òJKðL & ¥ ¤1o A
Ð
H .0 ¥
& Chabrier
Saumon
ActEx
¤M@£ £¢{H#òJBô²Lð
ïHï oð JMLD[ï?Jc8L s £££
£ 3ô²ð
óR8LJM}H#ð
M¤ ¡
£££
£ DFõRA¤M£r¥*{Hx.10¥w 3A HH#JMóqRJML8H#LJMï÷uJKEGð{ø
8££££Ð~ñdðL.10{¥; 3¢2ðJEGï#ðïï#ðóqJï#óÓ8EGE
J+
rD[{HDFð
ï
ÜH#ðÓ£@ ü J RJML&{Hðó DFõRA¤¤{¥OA
DGõA?¤2 )ï#òð{ø*ïsô²ð
óR8LDGï#ðð8ñJMJKLõ!
ïMAJKï#DH ñdðL
ï#J JMLEHJKóqRJML8H#LJMïMA~îoHqï#òð{ø*ï`H#ò8H}HòJ w Ð uvxw ð JML JMï'H#DGóÓ{HJMï`H#òJmJKJML#õ
ñdð
L`&
þ ¥ ü £
££ 8RÀ¡¤ ü £ ×8
JKLJMï'H#DGóq8H#Jcï°DH&ñdðL-¤2 ü £
££ ñdðLBJKï#DFH#DGJMï*òDFõ
òJKL!Hò8
H#òð
ï#JsôKðLL#Jcï'uðRDFõ`H¡ð . 0 ¥ 3A
9*ð{øÕEGJ²Hïô²ðóqL#J H#òJ>LJMïï'LJñdLðó H#òJ w Ð
urvxw
ø°DFH#òúH#ò8HñdL#ð
ó H#òJ p î'CÕï#DGó`E[{HDFð
ï#DFõ u uA^¤¤>DF
8÷A
î®A |>
J RqL#JMóÓ8Lû2÷EG`õð5ðÓ8õ
L#JMJKóqJKrHðñuHòJ&JMrH#DGL#J
LO8õ
JmðñBHJKóqRJML8H#LJ 8R JMï#DH JML)ô²ð
ï'D[JML8H#DGðA
ð
L)~EGð{øJMï#DHÛï'RôOòÛ
ï .10¥ ¤c£ £¢H#òD[ïjD[ïjï#òð{ø°ÛDF
DFõRA¤c¡A ï`JKö5uJMô²H#JcY¢ð2
J ï`H#ò8H`÷uð8H#ò óqJ²H#òð5ï-DG H#JML#uðE[{HJ&÷uJ²HøaJKJMjH#òJBEGDFóqDFHaðñ8)DGJc8ÍE JML#óqDuõ
ï8HaòDGõò
H#JMóqRJML8H#LJMï8 ð DGrH#JKLOô²H#DGõóqð
EFJcô²E[8L}õ
ï{HqEGð{ø
H#JMóqRJML8H#LJMïMA DFõRA¤ *Óô²ð
LóÓïaH#òJ^õ
ðrð8õ
L#JMJKóqJKrH°{H&
òDGõòJML?JKï#DFH-ð8Jñ . 0 ¥; 3A ï?LJMï#EFHðñH#òJ!ï'H#LðõBDGrH#JKZL ô²H#DGðï{HH#òD[ïJKï#DH
¢
ð
J RïH#ò8HH#òJ&LJMïï'L#J*8HEGð{ø
H#JMóqRJML8H#LJMï)DGïÜï'DGõïD RôM8rH#EGÛ8÷uð JHòJð
oDFrH#JML
ô®HDFõ
óqðEGJMôKEGL!õ
ï!EGDGóDFHMA
|q
J jH#ò8HHòJ w Ð uvxw JML#JcïHDFóÓ8H#JMïH#òJBLJMïï#L#J
÷5j8÷uðH°{¡ øßñdð
L!
þ 3
ü ££ q¸A !òDGï!yD 5½JKLJKôKJBD[ï!ðHOï'D[J
H#òJJML#LðL÷R8LñdL#ð
ó HòJLð2öDFóÓ{HDFð
ïYDG p î'C>D[ï#ôKï#ï#JM
DGï#JMô®HDFð
î#î5@ ôKðE[ ÷uJqDFrHJKLL#JKH#Jc ïsÓñdL'HòJKLsDG D[ôK8H#DGð¢DG0DHDFð
HðmHòJÓð÷Rï'JMZL JM JMJKLõ J 5DG8H#DGðïM¢
H#òR{HsH#òJ w óðJMEJML#JcïHDFóÓ{HJMïBH#òJqJKõLJKJ}ð8ñDGðDFIc H#DGð;8H)òDGõòÛHJKóqRJML8H#LJMïMA ðL)DFrH#JML#óqJcDG8H#JHJKóquJKLO H#L#Jcï 3r ü £
£ ,Ïþ ,Õ¤ ü 3r ü q¢ðJ ïLJMïï#L#JmïD 5½JKZL JKRô²JMïM¢5ø°òD[ôOòm8LJ&ðñYH#òJ^ï8óqJ&óÓõDFH#J
ïHòJ RDHJ^ï'DGIKJ
6J 5½JMô²HïqDG p î'CBA ð
L`HJKóqRJML8H#LJMï÷uJKEGð{ø ¤ ü 3
ü q¢HòJ
DGô²LJM
ï'Jcï'H8H#D[ïHDGôM8EJML#LðLOïDF~HòJ p î'C LJMïï#L#JÓL#Jqð8ñ
−20
10
−3
−2
10
−3)
ρ (gcm
10
−1
î ·Aa¤c î6rHJKL8EaJKJML#õ
uJKLq{Hðó ïKA>JKï#DFHñdð
LDñ?
ñdJML#JMrHjH#JMóuJKLO{HLJMïqñdLðó w Ð urvxw ¤¢!HòJ
ô®HDy
5DFH JKö;
R8ï#DFð
ô®H u öR¥ +¤ ð8H&ï#òð{ø°)ñdðL ü £
££ ï#DGô²JsJc8LEF
D[JM
HDGôM8E½Hð w °¥a8 p î'C3ôKEGôKE[{H#DGðRïsA
HòJ-ï8óqJ^ï'DGIKJ^ïaHòJ^ð÷Rï'JMLZ
JM)J
5DG8H#DGðïMA
î6!
DFõRAY¤ ü AøaJ^ï'òð{ø H#òJ^L#Jcï#ï#LJ
ï°ñdô®HDFð
ð8ñJK
ï#DFH¢rø°òDGôOòmô²ð L#óÓïH#òJBõð5ðj8õ
L#JMJKóqJKrHMA !òJRõLJ&8E[ï#ð
DGD[ôK8H#JcïH#ò8HM¢r{H ü £
££ 3¡ .10q, *¢{HòJ*LJMïï'L#JaDGïô²EGð
ï#J
HðH#òJ^LJMïï#L#Jð8ñ?ð DGrH#JKLOô²H#DGõóð
EFJcô²E[8L°õrïMA
î60ðL-ô²ðóqL#D[ï#ð¢øJjEGï#ðDFôKEFRJM0LJMï#EFHïsñdLðó H#òJ
ô®HyD 5DFH^J²ö8Rï'DGð-÷5: ü°ð
õJMLï 1¤ o¢8ø°òD[ôOò}ï#òð{ø*ï JKLsõð5ð
õLJKJMóJMrH-DFÀL#Jcï#ï#LJj8~DGrH#JKLEJKJKLõ ï'JM2J DFõrïKA ¢
¤
¤¢~¤c r¥OrA !òJ`yD 5uJML#JMô²Jcï&L#J^ï#óqEFE÷H&DGôKL#Jcï#J^ø°DHò
JKï#DH
AÀî6ÀHòJóqðEGJMô²EGL 8H#ð
óD[ômL#JMõDGóJ
¢?ðJ8E[ï#ð
RïÓõ
ðrðÛ8õ
L#JMJKóqJKrHqø°DHòÛH#òË
J D[
{L#D[{HDFð
8E!HòJKð
L#
&¥÷5mLJKûjd ü*JMóqJKL +¤ ï!ï#òð{ø°)DG!
DGõ
ïMA ¢
¤
¤¢R¤M¡¢r8Ü+¤ *A ðLòDGõòJML?H#JMóuJKLO{HLJMïM¢8H#òqJ ÐóqðJKE
D[ï-ð8HEGDGôM8÷EGJ)ï#DFRô²JjDFHð5Jcï-ðH}DGô²EGJmDFð
DFIc{HDFð
>ðñ
8H#ð
óqïMA
;
;í]?66] y;s?7<))1?)
!òJML#JßL#J%ñdðLúïD 5½JKLJKrHú8DGL ôKðLL#JMEG8H#DGðñdô²H#DGðï
°ø òDGôOòÛôK ÷uJDFLJMô²H#EGÀð÷H8DGJcÀñdLðó óÓr;o÷Rð ï'DGó`
E[{HDFð
ïjL#ð
5D[J&DGL#Jcô®HaDFñdð
L#óÓ8H#DGðj8÷uðHHòJBï'H8H#J&ðñ
HòJ!ï'ï'H#JKóA w òð{ø°`DG-HòJñdðEGEFð{ø°DGõRõLJMïDGï8}J²ö5H#JMï#Dy
J
ï#J²H^ðñaDFL-ôKðLL#JMEG8H#DGðïBø°òD[ôOò08EGEFð{ø%ð
JqH#ðJcïHDFóÓ{HJqH#òJ
óqD[ô²Lð
ïô²ð
DGômïHL#Rô®H#L#JÜð8ñBH#òJï#5ï'H#JMó 8Ð8EGEGð{øDGLJMô®H
ôKðóqL#D[ï'ð
~ø°DHòÀð8HòJKLï'DGó`E[{HDFð
ïM8
A !òJjLð8Hð oLð8Hð
R8DGLqôKðLL#JMEG8H#DGð~ñdRô®H#DGðRïñdL#ð
ó p î'C ï#DGó`E[{HDFð
ïø°DHò
ñdLJKJ8L#H#D[ô²EGJð5JMï8LJï'òð{ø°^DF¡ DGõAr+¤ 3¸A ðL=
þ 8££
££ jRJc8û{HBH#òJ÷Rð
EGJKõH#ò ðñ*4¤ *)JMóJML#õ
JMïM¢ø°òD[ôOòôKEFJc8LEF
JKóqðï'H#LO{HJMï`H#òJÜñdð
L#óÓ{HDFð
Àð8ñBóð
EFJcô²EGJMïMA |>J)ñdð
DH
Rï'JKñdEHð`ó}EHDFEFqHòJ&DFL!ô²ð
L#LJKE[{HDFð
ñdô®HDFð
j÷5Ó8jJK;ö 1
10
d
P (GPa)
@ u î® p LJMïï'L#Ja8}DFrHJKL8E5JKJKLõ^uJKL{Hðó%-HòJ
LJMï#EHDFõÖ*õ
ðDGð8HÓ ñdL#ð
ó p î'CÐï'DGó`EG8H#DGðïø°DHò)¡
DFLOï
ð8ñ8L#H#D[ô²EGJMï°= ê " ¥ å ¤M£ ç %ï#DGõñdL#JMJR8L#H#D[ô²EGJð5JMï
J²öôKJKH^ñdð
L ñ ø°òJML#J |Cæð5JMï^øaJKLJqJKóqEGð{JM>DGï'H#JM
YA
!òJ}L#ð
÷8÷DFEGDHDFJc"
ï !ñdðL RDGõmÓL#ðH#ðDG)õD JK ï'H8H#J
ñdðLH#òJ*H#òL#JMJBð
óDG
H!ï'uJMôKDFJcïL#JBJKLyD JMñdLðóÏ`ôKEFRïHJKL
8R8EG5ï#D[ïKA B$#&%('*) D[ïqH#òJRJML#ó}H8H#DGðÛLð÷÷DFEGDFH0ñdðLÓHòJ
JKEGJMô²H#LðïMA
Ô .l0Ø /213.54 6Y&± /
78.l:§ 9;/ <>=@? < = < =BA 1DC-EGFIH
+-, "
:É J
Ù ÊmÖcÑKÊÊMÊcÊ J
Ù ÊMÊcKÊ .&Ö / L2Ö{Ù ÄcKÇ .MJN/
ÊÙ ÊMÊcÊ
:É J
Ù ÊɲÖMÑ=ÊMÊcÊ ÉcÙ ÄcÑcOÑ .&Ö / ÖMÄ8Ù &Ä PO.MJN/ ÊÙ ÄcÄ)ÊÙ ÊÉqÊÙ ÊcÊ ÊÙ ÊMÊcÊ
:É J
Ù Q
Ê L2ÖÑKÊcÊ ÊÙ ÄMÊ$É .&Ö / ÉcÉMÙ Æ2OÑ .MJN/ ÊÙ Ä2ÑjÊÙ Ê2Ñ)ÊÙ ÊcÊ ÊÙ ÊMÊcÊ
:É J
Ù Ê ÇÉuÖMÑMÊ ÊÙ ÇMRÇ JS.&Ö / TÖ{Ù &Ä PO.dUÇ / ÊÙ LRJmÊÙ VÇ LmÊÙ ÊcÊ ÊÙ ÊMÊcÊ
:É J
Ù Ê É²WÑ LcÖcÑ ÊٵɮVÖ PO.&Ö /XT5ÉMÉcÙ ÇcSÊ .MJN/ ÊÙ YÖ JmÊÙ PRLmÊÙ ÊcÊ ÊÙ ÊMÊcÊ
:É J
Ù Ê É®ÊÊMÊcÊ ÊÙ ÊMÆ$É .MJN/XT5É®Ö8Ù J2SÇ .*LU/ ÊٵɲÖjÊÙ PcÖ)ÊٵɲÑ;ÊÙ ÊMÊcÊ
:É J
Ù Ê PYÆ8É²Ö ÊÙ YÊ JUPO.&Ñ /ZT5ÉOÇÙ RÇ J.oÉ®UÇ / ÊÙ ÊcÆ)ÊÙ ÑMÆmÊÙ ÇcÇ ÊÙ ÊMÊcÊ
:É J
Ù Ê ÑYÊMÊcÊ ÊÙ ÊcÖMKÆ .*LU/ZT5É®Ñ8Ù ÊcSÊ .oɲ&Ö / ÊÙ ÊÉÊÙµÉcÉqÊÙ ÆcÆ ÊÙ ÊMÊcÊ
É®ÊÙ ÊmÖcÑKÊÊMÊcÊ É®Ê8Ù ÄMÊ2KÖ .MJN/ L2Ö{Ù ÊcKÊ .dUÇ /
ÊÙ ÊMÊcÊ
É®ÊÙ ÊɲÖMÑ=ÊMÊcÊ Ñ8Ù ÖMÑMKÄ .*LU/ ÖMÆ8Ù RÑ LK.dUÇ / ÊÙ ÄcÆ)ÊÙ Ê2Ö)ÊÙ ÊcÊ ÊÙ ÊMÊcÊ
É®ÊÙ Q
Ê L2ÖÑKÊcÊ Ö8Ù ÇcÖMKÄ .&Ñ / Ä8Ù J
$É .dUÇ / ÊÙ ÄcÊ)ÊٵɮÊmÊÙ ÊcÊ ÊÙ ÊMÊcÊ
É®ÊÙ Ê ÇÉuÖMÑMÊ ÊÙ ÆMÇ$É .&Ñ / TUJÙ Ä$É .dUÇ / ÊÙ VÑ PjÊÙ J2ÇmÊÙ ÊcÊ ÊÙ ÊMÊcÊ
É®ÊÙ Ê É²WÑ LcÖcÑ ÊÙ YÇ JVJS.MJN/XT5ÉMÉcÙ J2SÄ .dUÇ / ÊÙ ÖMÇ)ÊÙ PYJÜÊÙ Ê2Ö;ÊÙ ÊMÊcÊ
É®ÊÙ Ê É®ÊÊMÊcÊ ÊÙµÉOÄcKÆ .dUÄ /XT5É®Ö8Ù PMSÄ .&Ñ / ÊÙµÉcÉÊÙ LcÊmÊÙ VÖ P;ÊÙ ÊMÊcÊ
É®ÊÙ Ê PYÆ8É²Ö ÊÙµ[É JVJS.5P&/XT5ÉOÇÙ YÑ J.dUÄ / ÊÙ ÊcÇ)ÊÙ RÇ JÜÊÙ L2Ö;ÊÙ ÊMÊcÊ
É®ÊÙ Ê ÑYÊMÊcÊ Ê8Ù RÊ LcSÆ .oɲ&Ñ /\T5É®Ñ8Ù Ê2KÑ .5P&/ ÊÙ ÊcÊ)ÊÙ &Ê P)ÊÙ Ä2Ö;ÊÙ ÊMÊcÊ
LÙ ÊmÖcÑKÊÊMÊcÊ J2Ä8Ù J&LK.dUÇ / ÑMÄ8Ù ÇcKÇ .MJN/
ÊÙ ÊMÊcÊ
LÙ ÊɲÖMÑ=ÊMÊcÊ ÖMÇ8Ù ÊcKÊ .dUÇ / YÖ JÙ PMKÊ .MJN/ ÊÙ RÄ JmÊÙ VÊ LmÊÙ ÊcÊ ÊÙ ÊMÊcÊ
LÙ Q
Ê L2ÖÑKÊcÊ Ä8Ù RÑ LK.&Ö / JÙ PMKÄ .dUÇ / ÊÙ ÆcÊ)ÊÙ ÖMÊmÊÙ ÊcÊ ÊÙ ÊMÊcÊ
LÙ Ê ÇÉuÖMÑMÊ
Ç8Ù ÑMKÆ .dUÇ / TNL8Ù Ä2OÖ .MJN/ ÊÙ ÑcÖjÊÙ J&LmÊÙ ÊÉÐÊÙ ÊMÊcÊ
LÙ Ê É²WÑ LcÖcÑ
ÉMÙ ÑcOÖ .&Ö /XT5ÉMÉcÙ ÆcSÇ .MJN/ ÊÙ Ö8ÉÊÙ LcÆmÊÙ ÊcÄ ÊÙ ÊMÊÉ
LÙ Ê É®ÊÊMÊcÊ
Ê8Ù PVPO.MJN/XT5ÉOÇÙ ÇcSÆ .*LU/ ÊÙ ÊcÆ)ÊÙ J2ÄmÊÙ J2Ê ÊÙ ÊMÊcÊ
LÙ Ê PYÆ8ɲÖ
Ê8Ù LcKÇ .&Ñ /XT5ÉOÇÙ Ä2KÑ .5P&/ ÊÙ RÊ JmÊÙ ÇcÆmÊÙ RÑ L ÊÙ ÊMÊcÊ
LÙ Ê ÑYÊMÊcÊ
Ê8Ù ÖMKÄ .dUÄ /ZT5É®Ñ8Ùµ-É PK.oɲ&Ö / ÊÙ ÊcÊ)ÊÙ ÊcÄmÊÙ ÄcÊ ÊÙ ÊMÊcÊ
J
Ù ÊmÖcÑKÊÊMÊcÊ:É L2Ö{Ù JVL.oÉOUÊ / ÑcÑ{Ù LcKÇ .MJN/
ÊÙ ÊMÊcÊ
J
Ù ÊɲÖMÑ=ÊMÊc]
Ê PKÇÙ ÊcSÊ .ÖM&Ç /(^ ÖMÊ8Ù -Ö J\.d&Ä /(^ ÊÙ ÆcÆ)ÊٵɲÖ)ÊÙ ÊcÊ ÊÙ ÊMÊcÊ
J
Ù Q
Ê L2ÖÑKÊcÊ ÖKÄÙ PcKÑ .o_É L&/ ^ ÉcÙ ÖKSÇ .*L&/ ^ ÊÙ PcÖjÊÙ RÖ LmÊÙ ÊcÊ ÊÙ ÊMÊÉ
J
Ù Ê ÇÉuÖMÑMÊ ÉMÉcÙ ÖcKÖ .ÖcVÖ / ^ T8Æ8Ù ÇcSÖ .d&Æ / ^ ÊÙ JUPjÊÙ J&LmÊÙ ÊcÇ ÊÙ ÊMRÊ J
J
Ù Ê É²WÑ LcÖcÑ Ñ8Ù Ê`É .o-É PV/(^aTrÉcÉMÙ VÆ PS.*L&/(^ ÊٵɮÄ)ÊÙ ÑMÆmÊÙµÉ®Æ ÊÙ ÊMÊcÆ
J
Ù Ê É®ÊÊMÊcÊ ÇÙ ÖMSÇ .dÇc&Ê / ^ T5É®Ç8Ù J2Ç .oÉMYÉ / ^ ÊÙ ÊcÇ)ÊÙ ÇcÊmÊÙ LcÇ ÊÙ ÊMÊ2Ñ
J
Ù Ê PYÆ8É²Ö Ö8Ù ÖKSÊ .o[É JN/XT5[É J
Ù ÖMSÄ .*LU/ ÊÙ ÊÉÊٵɮÆmÊÙ ÆcÊ ÊÙ ÊMRÊ J
J
Ù Ê ÑYÊMÊcÊ ÉcÙµÉOSÄ .ÖM&Ñ /XT5É®Ñ8Ù ÖMSÊ .dUÄ / ÊÙ ÊcÊ)ÊÙµÉcÉqÊÙ ÆcÆ ÊÙ ÊMÊ2Ö
ÇÙ ÊmÖcÑKÊÊMÊcÊÜVÇ PYJÙ J&PS.o[É JN/ Ñ8ÉMÙ PMKÄ .&Ö /
ÊÙ ÊMÊcÊ
ÇÙ ÊɲÖMÑ=ÊMÊcÊ:É L2Ñ{Ù Ö{bÉ .ÖM&Ö / _É L8Ù ÑMKÆ .MJN/ ÊÙ ÆcÇ)ÊٵɲÑ)ÊÙ ÊÉÐÊÙ ÊMÊÉ
ÇÙ Q
Ê L2ÖÑKÊcQ
Ê L&P{Ù PKÊ .ÖM&Ñ / T5ÉMÙ RÊ JS.MJN/ ÊÙ LVL)ÊÙ ÖMÄmÊÙ ÊÉÐÊÙ ÊMÊ2Ñ
ÇÙ Ê ÇÉuÖMÑMÊ RÖ L8Ù LVPS.-Ö JN/ T8Ä8Ù Ê2OÖ .MJN/ ÊÙ J{ÑjÊÙ J2ÇmÊÙ VÊ L ÊÙ ÊcÖMÆ
ÇÙ Ê É²WÑ LcÖcÑ É®Ç8Ù ÊMÆ .ÖKUÆ /XT5É®Ö8Ù ÖMSÄ .MJN/ ÊٵɲÑjÊÙ J{Ö)ÊÙ RÇ J ÊÙ ÊcÑMÄ
ÇÙ Ê É®ÊÊMÊcÊ ÄÙ YÖ LS.YÖ LU/XT5ÉOÇÙ PMSÄ .MJN/ ÊÙ ÊcÇ)ÊÙ Ç2Ñ)ÊÙ LcÊ ÊÙ ÊM&Ç P
Ö8Ù LmÖcÑKÊÊMÊcÊ RÑ LRLÙ JS.MJN/ J2Ä8Ù ÑMKÆ .MJN/
ÊÙ ÊMÊcÊ
Ö8Ù LɲÖMÑ=ÊMÊcÊ YÖ JVLÙ Ê .VÑ /(^ :É JÙ RÑ PS.VÑ /(^ ÊÙ ÆcÊ)ÊÙµ-É P)ÊÙ ÊÉÐÊÙ ÊMÊ2Ö
Ö8Ù LQL2ÖÑKÊcÊ É®Ê8ÉcÙ PS.MJU/ ^ TÖ{Ù ÖMSÑ .MJU/ ^ ÊÙ L2ÑjÊÙ ÖMÆmÊÙ Ê2Ö;ÊÙ Ê8:É J
Ö8Ù L ÇÉuÖMÑMÊ J2Ç8Ùµ`É .VÑ / ^ T8Ä8Ù ÇMÆ .VÑ / ^ ÊÙ J{ÖjÊÙ ÇcÆmÊÙ ÊcÄ ÊÙ VÊ PMÆ
Ö8Ù L ɲWÑ LcÖcÑ É®Ä8Ù SÊ .d&Æ /(^aTrɲÖ{Ù Ñ{bÉ .d&Ä /(^ ÊÙµ:É JmÊÙ J{Ö)ÊÙ ÇcÇ ÊÙµ:É LcÆ
Ö8Ù L É®ÊÊMÊcÊ ÉcÉMÙ PK.d&Ä /(^8T5É®Ç8Ù PMÇ .oÉOUÊ /(^jÊÙ Ê2ÖjÊÙ RÇ JÜÊÙ LcÊ ÊٵɮRÖ L
Ideal Fermi gas
Ideal molecular gas
FVT
Saumon & Chabrier
PIMC
0
10
−1
10
K 4
10
T (K)
c
K 5
10
QSR.TVU{ßgYl`xcc.^Z`xhcUexr
x`ae^Z`xaeSa]fhxugcqe!biCkÌ&e¢¤ >§
cwZi¡¢qsuZ|E`x>c.^gtJecSk`irÁewgx fg^Zqzf~aC`qzaeqiugaGt{ewZxi`bĶJVg¸ÊµCewZx
h oy1² i h ¶_¸1µgaGugfÄlR.nàoÝcqr^ZtsaGeqsiCugcU
e`a@fhxugcqe!b@ka\ei`¤kjml&nc.iewgaeewZxÄaG`xa¯^ZuXfhx`ewZx
a oqzc
`i
i`.eqiugaGtZei:ewZx]r~itx>\_^ZtzaG`mk`aC\_eqsiCuUm%wZx
x>N
a o
xp
wgxqs|Cw{e|x_eccr5aGtstx`¡¢qew¯fhx\`x>aCcqug|fhxuXc.qe!baCc%a:`xc^ZteiCk
xu{e`i
qz\fhqzccih\_qzaeqiu¿iCkhewZxr~iCtsx\_^gtx>cµfh`qxu8±b]ewZxu^ZrVy
±7x`iGk^Zu±Xi^ZugfÀc.eaGex>cae]tsi¡fhxugcqe!bCU%%wZx`r5aGtfhqzcc.ih\_qzay
eqiuaCtsci`xfh^g\xcvewgxu^Zr±Xx`viCkgr~iCtsx\_^gtx>c¡¢qewVquX\_`xaCcqsuZ|
exr
x`ae^g`xUvQZi`Ì e;q r WZµ¡xx_
x\eewgae
`xcc.^g`xfhqscci\qJy
aGeqsiCuVfhqr~qsuZqzc.wZx>cSewZx¢u^Zr±Xx`iGkXr~itx>\_^ZtsxcS¡¢qew~quX\_`xaCcqsuZ|
fZxugcqJe!b¯¶·¸7±Z^heewZqzcfhxugcqJe!bV`aCuZ|Cx¢qzc±7xbiCugfVewZx]c\_i
xiCk
ewZqzc
a
x`>U
%wZx
`iGeiCuhy1xtsx\_e`iCu
aGqs`À\_i``xtzaeqiu k^Zug\_eqsiCur^gtJeqJy
t
s
q
a o
xf ±bewgx´fhxugc.qe!bqsccwZi¡¢u qu¥Qvqs|gUVhU %wZx
x>N
ugxaG`ewZxi`qs|Cqsu~c.wZi¡cmewZxqsug\`x>aCcxf
`iC±gaC±Zqtsqe!b:iGt
k sgugfZquZ|
aCu´xtx>\e`iu ugxaG`a
`iGeiCu³fh^Zx¯eiewZxàoi^Ztir±³aee`aC\y
eqiuUÀ%wZx
x>N
a owZxqs|Cw{efhx>\_`xac.x>c8¡¢qJewexr
x`aGe^Z`xdaGuXf
qsug\`x>aCcxc¡¢qJewÄfhxugcqJe!b5±7x\aG^gcxiCkewZx`r5aGt#qiuZqsaeqiudaGuXf
xu{e`i
b5qiuZqsaeqiud`xc
x>\eqxtsbCUm[e¢ti¡pexr
x`ae^Z`xµewZx
a o:\aCu±7x%qu{ex`
`xexfVaCcSih\\^
aGeqsiCuiCkX±7iC^ZuXfc.eaGexcmaCtJy
xp
ewZiC^g|Cw ^Zu±Xi^ZugfX]c\aeex`qsuZ|jc.eaGexc¿\aCu@aGtzcij\_iu{e`q±Z^ZexCU
Qg`ir
`iCeiuhyÊxtx>\e`iu
aGqs`¿\iC``xtsaGeqsiCuÀaCtiuZxCµ7iCuZx~\aCuZuZiCe
fZqsc.eqsuZ|C^gqscwj±7x_e!¡xxuaGu¯aeir~qs\EaGuXfÄaVr~iCtsx\^ZtzaG`¢c!eaexCU
QSq|{cU]R uaGuXfV gc.wgi¡ ewZxÀxtsx\_e`iCuhy1xtsx\_e`iCu
aGqs`d\iC`y
`xtzaeqiuÀk^ZuX\eqsiCuXcEkiC`
aCq`cE¡¢qewaGu{eqy
aG`aGtstxtmc
qsuU%wZx
a oaGeVcr5aGtstcx
aC`aGeqsiCugc\_iCr~x>c8k`iCr ewZxdkiC`r5aeqsiCuiCk
xp
ewZxVrVitx>\_^ZtzaG`±Xiugf3UEQZi`
aCq`ciGkxtsx\_e`iCugc]¡¢qJew
aC`aCttsxt
c
qsuµCiuZxaGts¡%ab`
c sXugfZca8c.e`iCuZ|E`x
^gtscqiu5fh^Zx%eiEewZx]lmaC^Ztq
xZ\_ts^gc.qsiCu
`qsug\_q
tsxaGugfVeiaEtx>ccx`x_exuemei8ewgx¿oiC^ZtsiCr±
`x
^ZtscqsiCuUm%wZqzc%qsc]c.wZi¡¢uÄqsu¯QSqs|gU3V gZU
v
wyx[z{x:|~}BD
-}BB|p
R»u ewZqzccx\_eqsiCuµ¡xfhqzc\_^gcc~ewg
x yBUYN5YpU iGkEwby
fZ`i|CxuaCc8cwZi¡¢u@qsuQSq|XUmCU5%wZxfhqzaG|`aCrc.wZi¡cewZxa
y
`ihqsr~aGex¿tih\aeqsiCu¯iCkvewZx8r~iCtsx\_^gtsaC`µewZx:aeiCr~qs\8aCugfjewZx
3
10
2
Ideal Fermi gas
Ideal molecular gas
FVT
Saumon & Chabrier
ActEx
PIMC VDM
62500
rs=10
rs=6
rs=4
rs=3
¿
rs=2.6
0.05
0.00
31250
10
0.05
0.00
P (GPa)
15625
rs=14
T (K)
n gpp(r)
10000
0.05
0.00
0.05
0.00
1
10
7812
10
4
T (K)
10
0.00
5
5000
î·A¤* p L#Jcï#ï#LJ
ïKAHJKóqRJML8H#LJ}8HsmJKRï'DFHð8ñÐ. 0 ¥
q3 ï°ï#òð{ø°ÜDFDFõRA¤M¡A
E[ï#óÓmLJKõ
DFóqJcïKA£!òJ p î'C ï#DFó}EG8H#DGðïM¢=ï#DFRô²JqH#òJKL#J
÷
ï'JcðH#òJ`÷
ï'D[ô-Jcï#ôKL#DGH#DGðDGH#JML#óÓïBð8ñ?JKEGJMô²H#LðïB8
Lð8HðïM¢uðmðHDGLJMô®HEFEGJKRH#òJKóÓï'JMEy
JMï&H#ðJ²HJKLóqDFDGõ
H#òJ*5ó`÷uJKLð8ñYô²ðóquðRq8L#H#D[ô²EGJMïï#ôOòÓïóð
EFJcô²EGJMï8
{HðóÓïMA CJ²HòðïsñdðL^JKH#JML#óqDGDFõmHòD[ïsñdL#ð
ó p î'C ï#DF¡ó E[{HDFð
ïÓø°DGEFEB÷RJDGïô²ïï#JMÐDF;>ñdH#LJ ÷EFD[ôK8H#DGðAµ¥:î6
ðLOJML^H#ðð÷HO8DG 80JcïHDFóÓ{HJ)ðñ°H#òJÜ{H#ð
óqDGôj0óqðEGJMôK
E[8LañdL
ô®HDFð
¢5øJBJKóqEGð{JMm}ôKEFRïHJKL°8EFï#DGïð8ñ=H#òJ p î'C
8H#ò3ô²ð
õL8H#DGðïMA ïjJcï#ôKL#DG÷uJMÐDF ¤ o¢!øJôKðï#DGJKL
HøaðL#ðH#ð
ï^ï^÷uJKEGðõDGõÜH#ð ð
Jjô²EGï'H#JKL`Dñ!H#òJKL#JÓEGJMïï
H#òR8>4¤ K{8R8L#HMA JKEGJMô²H#Lð)÷uJKEGðõ
ïH#ðqðJR8L#H#D[ô²E[8L
ô²EGï'H#JMLDFñ!DH^D[ïBEGJMïïBH#ò ]¤ * 2øa2ÜñdLðó 85Lð8HðDF
H#òJqôKEFRïHJKLc¡A !òJHøaðÜôKH oð 5ÀLODFDøaJKLJôOòðrï'JM ñdLðóÕHòJ
3
10
gas, T=5000K
Molecular
Saumon & Chabrier
2
PIMC
10
000
P (GPa)
1
125
10
K
50 K
312
0
10
00 K
100
−1
10
0K
500
−2
10
−3
10
−2
10
−3)
ρ (gcm
0.05
−1
10
¡`¢¤£¥t¦V§@¨`©Kª[«R¬[¬¤yª«®@¬R¥b¯>«Y°y¬±³²µ´¶*·ª\¯@±¹¸t«Yª[«Y°{²S²[«Yº¼»«Rª[½N²>ª[«R¬R¥
0.05
¾0 ¿2 À4 ¾0 ¿2 À4 ¾ 0 ¿2 À 4 ¾0 ¿ 2 À4 ¾ 0 ¿ 2 À 4 ¾0 ¿ 2 À4 Á 6
0.00
r
Â`äÄÅbÆRÇyÈ;ÉKÊ[ËNÌ[ËpÍ@ÎÐÏ>Ê[ËNÌ[ËpÍÏyÑNÒIÊÔÓ-ËpÊ[Ê[ÕYÖ×ÑUÌÒIËpÍØ*ÙyÍyÓ_Ì[Ò¹ËÍ3ÚÛÙyÖ³Ì[Ò³Î
ÏyÖ¹ÒIÕRÜaÝBÞ¼Ìß>ÕàÜ@ÕRÍyá¤Ò¹ÌµÞmâOÅKã ß>ÕÔÓ-ËÖ¹ÙyÚÍáÓ-ËpÊ[Ê[ÕRáÏËÍyܼÌËÌ[Ëåä&æ
ç ÑpÖ¹Ù>ÕVáÑNÍyÜèÌßyÕàÊËUé"á\Ì[˼Ü>Ò³êtÕYÊ[ÕYÍ{ÌÌÕRÚ¼ÏÕRÊ[ÑNÌÙ>Ê[ÕRá ëìÅ
Ú¼ËÖ¹ÕVÓ-Ù>Ö×ÑNÊíÑNÍyÜîÑNÌËpÚ¼Ò×Ó8ïÊËÙ>ÍyÜîá¤Ì[ÑUÌ[Õ3Ü@Ò×áµÌ[ÊÒIÝ>Ù@Ì[Ò¹ËÍðÅñã ßyÒIá
ÑpÍyÑNÖIÞ@á¤Ò×ábïpÒ ç ÕVáOÊ[ÕRÑpáËpÍÑNÝ>ÖIÕÕVáµÌ[Ò¹Ú~ÑNÌÕRáKØ*ËpÊOÌ[ß>Õ"Ú¼ËpÖIÕRÓYÙ>Ö×ÑNÊKÑNÍÜ
ÑNÌËÚÒ×ÓØ*Ê:ÑpÓ_Ì[Ò¹ËÍyá"ÑNÌ;Ö¹ËUéÌÕRÚ¼ÏÕRÊ[ÑNÌÙ>Ê[ÕRáRÅ\ò\Ì0ß>Ò¹ïßÌÕRÚÏDÕYÊ:ÑUÎ
Ì[Ù>Ê[Õpó&Ò³Ì$Ë ç ÕYÊ[ÕRá¤ÌÒIÚ~ÑUÌ[ÕRáDÌßyÕSÍBÙ>ÚÛÝDÕYÊôËNØ@ÝËÙ>ÍyÜìá¤Ì[ÑNÌÕVáðÝDÕRÓYÑpÙyáÕ
Õ ç ÕRÍ~Ò¹ÍèÑpÍ8õ*Ù>ÍBÝDËpÙ>ÍÜöKÓYËpÖIÖ¹Ò×áÒ¹ËÍðóN̵é\ËìÏyÑpʤÌ[ÒIÓYÖ¹ÕVáSÑNÊ[Õ"Ó-ËÙ>Í{ÌÕVÜ
Ø5ÑpÖIáÕYÖIÞ~ÑpáÝÕRÒ¹ÍyïÛÏyÑpʤÌ\ËNØWÌßyÕÓYÖ¹Ùyá¤ÌÕRÊRÅb÷ÕÓYËpÊ[ÊÕVÓ_Ì[ÕRÜØ*ËpÊÌßyÒIá
ÝBÞ3ÑpÏ>Ï>ÖIÞBÒ¹Í>ïÑNÍøÑpÜyÜ@Ò³Ì[Ò¹ËÍyÑNÖOÓYÊÒ¹ÌÕRÊÒIËpÍðÈÔÑíÏyÑNÊÌÒ×Ó-ÖIÕ¼ÓYÑNÍËpÍyÖ¹Þ
ÝDÕ¼Ó-ËpÍá¤Ò×Ü@ÕYÊ[ÕRÜùÑá;ÝDËpÙyÍyÜ8Ò¹ØKÌßyÕÜ@Ò¹êtÕYÊ[ÕYÍyÓYÕåÒIÍúÑÓ_ÌÒIËpÍ8ÌËèÊ[Õ-Î
Ú¼Ë ç ÕÛÒ¹ÌØ*Ê[ËpÚûÌ[ß>Õ~Ó-ÖIÙyá¤ÌÕYÊÔÒ×áÏË{á¤Ò¹ÌÒ ç ÕÅÛã ß>Ò×áÔÚÕYÌß>Ë@ÜúÖ¹ÕVÑpÜ>á
Ì[ËùÌßyÕaÕYüBÏDÕRÓ-ÌÕVÜýÓ-ËÊÊ[ÕRÓ-ÌÒIËpÍyáìÑNÌÛß>ÒIïpßþÌ[ÕYÚ¼ÏDÕYÊ:ÑUÌÙyÊÕÅõ5ã ß>Õ
Ê[ÕYïÒ¹Ú¼Õ~ÝDËpÙ>ÍÜ>ÑNÊ[Ò¹ÕVáÔÒ¹ÍýÂ`ÒIïyÅÆmÜ@ÒIá[Ó-ÙááÕRÜÝDÕYÖIËUéÿÑpÊÕ~ßyÑpÊ[Ü>Ö¹Þ
ÑNêDÕVÓ_Ì[ÕRÜíÝBÞ~Ìß>ÕìÑÜ>Ü@Ò¹ÌÒIËpÍyÑpÖðÓ-ËÊÊ[ÕRÓ-ÌÒIËpÍðÅ ö
ã ß>ÕÖIËUéÕRÊOÜ>Ñpáß>ÕRÜåÖIÒ¹Í>ÕÊ[ÕYÏyÊÕVá¤ÕRÍÌ:á`Ìß>ÕÊ[ÕYïÒ¹ËÍåéßyÕYÊ[Õ Ç ËpØ>ÌßyÕ\ÏyÊËpÌËpÍá$ÑpÊÕÝËÙ>ÍyÜìÒIÍÚËÖ¹ÕVÓ-Ù>ÖIÕRáRÅô÷îßyÕYÍåÌß>Õ\ÍBÙ>ÚÛÝDÕYÊ
ËpØOÏ>ÊËpÌËÍyáÝDËpÙ>ÍyÜ8Ò¹Í3ÑNÌËÚ¼áÛ
õ ;éÒ¹ÌßúÑNÍùÕYÖIÕRÓ-ÌÊ[ËpÍDöÜ@ÊËÏ
ÝDÕYÖIËU
é é\ÕKÖIÑpÝÕRÖ¹ÕVÜÌß>Ò×áôá¤Ì[ÑNÌÕSÑáWÏ>Ö×ÑpáÚ~Ñ"Ñpáðáß>ËUéÍÔÒIÍàÌß>Õ
ÙyÏ>ÏÕRÊ0Ü>Ñá¤ßyÕRÜBÎ(Ü@ËNÌÌÕVÜÖ¹ÒIÍ>ÕpÅ ÃÐÌÔá¤ß>ËÙ>Ö×ÜÝÕìÕRÚ¼Ï>ßyÑpáÒ YÕRÜíÌ[ßyÑUÌ
Ì[ß>ÕÖ¹Ë@ÓYÑNÌÒIËpÍmËpØðÌßyÕRáÕ;ÖIÒ¹Í>ÕVá Ü@ÕYÏDÕYÍyÜyáËÍmÌ[ß>ÕÓ:ßyËpÒ×Ó-Õ;ËpØWÌß>ÕVá¤Õ
ÖIÒIÚÒ¹Ì[áÑpáåé\ÕYÖIÖ\ÑáìËpÍýÌß>ÕíÓ-Ù@ÌÎ Ëpê Ê:ÑpÜ>Ò¹ÒÙyá¤ÕVÜøÌËÜ@Õ-Ì[ÕYÊ[Ú¼Ò¹Í>Õ
Ì[ß>ÕÛÓYÖ¹Ùyá¤ÌÕRÊ[á;Ò¹Í8Ìß>Ò×á"Ï>Ö×ÑpÓYÕpÅ"Â`ÒIïyÅôÆåÑNÖ×á¤Ëmáß>ËUé"á Ì[ß>ÕÛÖIË@ÓYÑUÌ[Ò¹ËÍ
ËpØSÒ×á¤ËÝyÑNÊ:áYótéß>Ò×Ó:ßøÑNÏ>ÏDÕRÑpÊÑáÑpÖ¹Ú¼Ë{áµÌàáµÌ[Ê[ÑpÒ¹ïß{ÌÖIÒ¹ÍyÕRáÒ¹ÍúÌßyÒIá
Ü>ËpÙ>Ý>ÖIÕÖIËpïÑpÊÒ¹ÌßyÚÒ×ÓïpÊ:ÑNÏ>ßðÅ`ã ß>Õ"áÖ¹ËÏÕÒ×áOÜ@Ò¹êDÕRÊÕRÍÌOØ*Ê[ËpÚ Ìß>Õ
Ò×Ü@ÕVÑNÖyï{ÑpáOÝDÕRÓRÑNÙyáÕÌ[ß>Õ"Ï>Ê[ÕRá[á¤ÙyÊÕ"Ü@ÕRÏÕRÍyÜ>áËpÍ~ÒIËpÍ>Ò RÑNÌÒIËpÍ~ÑNÍÜ
Ü>ÒIá[á¤Ë@ÓYÒIÑNÌÒIËpÍðÅ
ã`ÑNÝðÅ>à áß>ËUé"á\Ìß>ÕÔØ*Ê:ÑpÓ-ÌÒIËpÍíËNØ`Ìß>ÕìÌß>Ê[ÕYÕàÚ¼Ëá¤ÌØ*Ê[Õ {Ù>ÕYÍ{Ì[Ö¹Þ
Ø*ËÙ>ÍyÜúá¤ÏDÕRÓYÒ¹ÕVáYÈ"Ú¼ËÖ¹ÕVÓ-Ù>ÖIÕRáRóWÑUÌËÚ~á0ÑpÍyÜùØ*Ê[ÕYÕåÏ>ÊËpÌËÍyá;éßyÕYÊ[Õ
Ø ÍyÜ@ÒIÍ>ïÑ8Ï>ÊËpÌËÍþÒ¹Í Ñ
ÒIáÜ@Õ yÍ>ÕRÜ ÑpáìÌß>ÕaÏ>ÊËÝyÑNÝyÒ¹ÖIҳ̵ÞËN
ÓYÕYÊÌ[ÑpÒ¹Í3ÓYËpÚ¼ÏDËpÙ>ÍyÜúÏyÑpʤÌ[ÒIÓYÖ¹ÕÅàÃÐÌàáß>ËÙ>ÖIÜ3ÝÕ¼Í>ËpÌÕVÜùÌßÑUÌÔÌß>Õ
áÙ>ÚÈ Ò×ámÖIÕRá[á~Ì[ßyÑNÍ Æ8áÒIÍyÓ-Õ8ËpÌß>ÕRÊaÓYÖ¹Ùyá¤ÌÕRÊ[á
ßÑ ç ÕÑúÍyËpÍ@Î YÕRÊËÏ>Ê[ËpÝyÑpÝ>Ò¹ÖIҹ̵ÞpÅ ã ß>ÕÖIÑpÊïÕRá¤Ì¼ÓYËpÍ{ÌÊ[Ò¹ÝyÙ@ÌÒIËpÍyá
ÝDÕRáÒ×Ü@ÕRá"Ìß>Ë{á¤ÕåÖ¹Ò×áµÌ[ÕRÜùÑpÊÕ !" éÒ³Ì[ß3Ñ~Ú~ÑUü@ÒIÚÛÙ>ÚûËpØ Å Ç¼Ø*ËpÊ
æ #%$'& ǼÑpÍyÜíë # Æ (KÇ $ (*)Ø*ËpÖIÖ¹ËUé\ÕRÜaÝB+
ä
Þ -,ÔéÒ¹Ìß /. & 10
¦
2
rs=14
T (K)
rs=10
rs=6
rs=4
rs=3
4
rs=2.6
0.02
0.1
0.01
0.0
0.00
0.02
0.1
0.01
0.0
0.00
0.04
15625
0.3
0.01
n gee(r)
0.0
0.4
10000
0.3
0.00
0.04
0.03
0.2
0.02
0.1
0.01
0.0
0.00
0.04
7812
0.3
0.03
0.2
0.02
0.1
0.01
0.0
0.00
0.04
0.4
5000
0.03
0.02
0.4
7812
rs=2.6
0.03
0.2
0.1
10000
rs=3
0.04
31250
0.3
0.2
n gpe(r)
rs=4
0.03
0.2
0.4
15625
rs=6
0.04
62500
0.3
0.4
31250
rs=10
0.05
0.4
62500
rs=14
T (K)
0.5
5000
0.3
0.03
0.2
0.02
0.1
0.01
30 42 54 30 42 54 30 42 54 30 42 54 30 42 54 30 42 54 66
0.0
r
0 2 4 0 2 4 0 2 4 0 2 4 0 2 4 0 2 4 6
0.00
r
¡`¢¤£¥K8¦ 7@¨©Sª·p²·:° 9 « ;¹
« <_²[ª·°ù»y½N±I=
ª <-·ªª[« ;×½U²[±¹·°ù¶*>° <-²±I·p°øºÛ' ;>9
²±I»';I±¹«V¯@?B´¼²BA>«à¯@«Y°y¬±¹²µ´DCO¥FEGAy«H<Y·I;I>º¼°y¬G<-·pª[ª[«R¬»·°y¯¼²·¼¯@±¹¶9
¶*«Yª[«Y°{Ö
² .8J¼®UK½ ;I>«R¬å½N°y¯B² A>«èª[M· L"¬Ô²[·3¯@±¹¸D«Rª«R°²å²«Rº»D«Yª:½U²[>ª[«R¬
Nì¥
¡`¢¤£¥¦ >=
¨ Z;¹
« <_²[ª·:° 9 « ;¹
« <_²[ª·°ú»y½p±¹=
ª <Y·pª[ª« ;I½N²±I·p°ú¶*>° <-²±I·p°ø¶*·pª
«;¹«
<_²[ª·°y¬L±¹²SAù·p»y»·{¬¤±¹²«Û¬»>±I°ùºÛ';¹²±I»';I±¹«V¯?B´è²BA>«Û¯@«R°y¬±³²µ´C
±×¬"S¬ A>M· L°ð¥ EGA>=
« <-1· ;¹>º¼°y¬ <-·pª[ª[«R¬»·°y¯m²[·è¯@±¹¸D«Rª«R°{
²
J®UK½ ;I>«R¬
½p°y¯èS² A>«àª[M· L"¬²·m¯@±¹¸D«Rª«R°{²\²[«Yº¼»D«Yª:½U²yª«VG¬ Nì¥
½N°P
¯ O=QRL±¹S² ATVUW2X 2Y@¥ ZS®p«YP
° ;I½pSª [«Y\
ª <];Iy¬¤²«Yª:¬:· <<-yªà®p«Yª[´
I± °@¶*ª«
^{>«Y°{²S;I´p¥EGAy« <];Iy¬¤²«Yª½N°y½I;¹´@¬±I¬½I;I¬·_[±¹®«R¬"½p°í«V¬µ²[±¹º~½N²«
¶*·pª0²SAy«ì¶*ª:½I<_²[±¹·°8·N¶O¶*ª[«Y«å«;I«<-²ª[·p°y¬`aLAy±<bA3½I[pª[«Y«V¬L\«;;cL±¹²SA
²SAy«à°{yº ?D«Yª·N¶b±I·p°>± dY«V¯è»>ª[·N²[·p°y¬RF¨ Tefb¥
¡$± [yI¥ YI2;S¬ A>M· L"¬b
½ <Y·pº¼»y½pª±×¬¤·°ì·N¶S² A>«\¶*ª:I½ <-²±I·p°Û·p¶º¼I· ;I« <Y' ;I«R¬
½N°¯¼±¹·°>>± dR«R¯¼½U²[·pº~¬b¶*·Ðª .
Jg ¦ 2>*¥ h0°>« i°y¯>¬OB² Ay½U²SS² A>«"º¼1· ;¹
« <j9
;×½Nª;¶*ª[1½ <_²±I·p°¬0¯@
« <Y½&´@¬ª:½N»>±×:¯ ;Ik
'
´ L±³B² Aù²«Rº»D«Yª:½U²[>ª[«p
¥ EGAy«Ûª[]« 9
¬' ;³²[±¹° [½U²[·pº~¬~½Nª[«S² A>«R°î±¹·°>± dY«R¯ ½N²è«Y®«Yl
° A>± [IA>«Rª¼²«Yº¼»D«YSª 9
½U²[>ª[«RD
¬ ;I«R½¯@±¹° [þ²·øB² A>«31· ?y¬¤«Rª®«R¯ ±¹a° <-ª[«R½p¬«ù±I° S² A>«ú°{yº ?D«Yª
·N¶\¶*ª[«Y«m»>ª[·N²[·p°y¬R@
¥ EGA>«m©Sn¢ m/o »>ª«V¯@p± <_²±I·p°¬Ô¶*·pªàB² A>«mº¼I· ;I« <Y: 9
;×½Nª¶*ª[1½ <_²[±¹·°K½ [ª«R«è®p«Rªq
´ L\« ;;GL±³B² AB² A>s
« roÿº¼·@¯@« ;"½t
¬ L\« ;;
½p¬ L±³B² AùS² Ay«v¡ uEÔ¥ h0°ùB² A>«Û·pS² A>«Rª Ay½p°y¯ `S² A>«¼©Kn¢ m/o ª[«R¬' ;¹²[¬
S¬ A>M· L"¬b½à¬¤± [p°>>± ia<R½N°{S² ;Iw
´ A>± [IA>«RªK¯@« [ª«R«\·p¶D±I·p°y>± dV½U²±I·p°ÛS² Ay½p_
° ro0¥
EGA>«ì¬[½Nº¼=
« <-·º¼»y½Nª[±I¬·p°è¶*·pª;x
½ Ay>± [1A>«Yª"¯@«R°y¬±³²µ´a·N¶ .
JgyY:X z±¹°
¡`>± [c¥ Y@¦mS¬ A>M· L"¬B² Ay½U²ìB² A>_
« <];Iy¬¤²«RªÛ½N°yI½ ;¹´@¬±I\
¬ ;I«R½¯>¬Ô²[·8¬¤º~K½ ;;I«Yª
°B>º ?D«Yª·p¶`º¼1· ;¹
« <-' ;I«R¬\B² Ay½N°»>ª[«R¯@p± <_²[«R+
¯ ?B´mS² Ay« ro º¼·@¯@« ; ¥
rB>º¼º~½Nª[>± dR±¹'
° [Ô·°>« <Y½N°¬½&´ìS² Ay½N²`B² A>
« <];Iy¬¤²«RªK½N°yI½ ;¹´@¬±I¬`»>ª[K· 9
®B±I¯>«R¬ùys
¬ L±³B² A ª«V½p¬·p°yI½ ?';¹««R¬¤²±Iº~½U²[«R¬¶*·ªùS² A>«þ°B>t
º ?«Rª8·N¶
½U²[·pº~¬b½N°y¯Ûº¼I· ;I« <- ;¹«V¬$±I°åS² A>« <-·°y¬±I¯@«Rª«V¯ì¯@«R°y¬¤±¹²µ´ìª:½N'° [«p¥ {«
<Y½p@²±I·p° S² Ay«ùª«V½p¯@«RªåB² Ay½U²~·pS² A>«Rªm¯@]« iy°y±³²[±¹·°y¬~·N¶Ô½U²[·pº~¬~½N°y¯
º¼I· ;I« <Y' ;¹«V¬ `@»D·¬[¬>± ?';I«±¹°½º¼½p°B1´ 9?D·B¯>D
´ A{´@¯@ª[I· [«Y° `LA>± ;¹\
« [±¹® 9
±I'° [-^{yK½ ;I±¹²[½U²[±¹®« ;I´;¬±¹º¼± ;I½pªðª«V¬¤ ;³²:¬ `Vº~½&´0¯@±¹¸D«Rcª ^{y½p°²[±³²:½U²[±¹®« ;I´p¥
h0>ª <Y·pº¼»>@²[«R¯°B>º¼«Yª[p± <YK½ ;$®UK½ ;I>«R¬ºåy¬¤² ?«åy¬«Rk
¯ L±¹S² As<Y½p: 9
²±I·p°ô}¥ | ª[>± [·pª[·py¬ `Bº~½N°B´ 9~?D·@¯@´è¯@« iy°>±¹²±I·p°ù·N¶Ox
½ ?D·p>°y¯ù¬¤²[½N²«
ª[«Yº~½N±I°y¬$²\
· ?D« ½p»>'» ;I±¹«V¯W¥ rB«Y®«Yª:K½ ;{±I¯@«V½p¬O½pª« ¯@±×S¬ <Yy¬¬«R¯Û±¹k
° YIY
Ð¥
½p°y¯wi°y¯¼½;ª[«Yº~½NªBU½K?';I´\[p·B·@¯Û½I[pª[«Y«Yº¼«R°²FL±¹²SAå²SA>«ro9Zh\rt¥
£«R°>«Yª:K½ ;;II´ `N·°>« iy°y¯y¬bS² Ay½N²KS² Ay«;¯@«Y®B±×½U²[±¹·°y¬O±I°¼S² A>«"«R°>«YBª [p´å½Nª[«
º¼·ª«8»yª·°>·p>a° <-«R¯ B² Ay½N° S² A>«¯@±³¸t«Yª[«Ya° <-«R¬a±I°îS² A>«ú»>ª[«R¬[¬¤>ª[«p¥
{*
« i°y¯ì¬>± [°>± i<Y½N°{²$¯>«Y®B±I½N²±I·p°y¬ô±¹°ÔB² A>}« ZGh\r·N¶@²[«Yº¼»«Rª[½N²>ª[«R¬
² ;I>± « ;IP
´ <R½Ny¬«RP
¯ ?B´ú½N°ø>°¯@«Yª[«R¬¤²±Iº~½U²«~·p¶
¦ 212I2I212I`Dº¼·{¬µ=
²BA>«0¯>« [pª[«Y«0·N¶ð±I·p°>± dR½N²±I·p°è½N²SB² A>·¬«"²[«Yº¼»«Rª[½N²>ª[«R¬R¥`¢(°m¶*@²[>ª«
L\·pBª `IL\
« L± ;>;D]« B²«R°y¯¼B² A>±I¬ <-·º¼»y½Nª[±I¬·p°²[· A>± [IA>«Rª¯@«R°y¬±³²[±¹«V¬Y¥
EGAy«Yª[«\·°>«]« @»D« <-²[¬`²\
· i°y¯~¬¤ ?y¬µ²:½N°{²±×K½ ;>¯>±³¸t«Yª[«Y° <Y«RF¬ ?D«-² L\«Y«R°
²BA>D
« roº¼·@¯@« ;O½N°¯3©Kn¢ mPo`LAy± <bA8º~½p°>±³¶*«V¬µ²ÔB² A>«Yº~¬« ;I®p«R¬0±I°
½¼¯@±¹¸t«Yª[«Y°{²;n¬ Ay · <b_O;' [p·°>±I·N² ¹8¦ 7Ð¥
n@
\\_
vxaj\_
¢(°ÔS² A>±×¬ L\·pBª `L\«S¬¤²y¯@±I«R¯²BA>«Ay±>[1A:9G²[«Yº¼»D«Yª:½U²yª«O«
^½U²±I·p°
·N¶à¬¤²[½U²[«ù·N¶\AB´B¯>ª·1[p«Y° ½U²_;I·MLû½N°y¯ ±I°²[«Yª[º¼«R¯@±×½U²[«¯>«Y°y¬±³²[±¹«V¬
¡
¢x_-£¤c¥¦D§ ¨l¥x©H
EGA>« ½N@B² A>·pª:c
¬ L·' ;I¯ ;¹±p«²·0²SA½N°' Z;¥ ªS¥U©b·I;;¹·:<b0¶*·pªby¬«-¶*';
>¯ ±I¬B<-y¬[¬±¹·°y¬ ½p¬GL\«;;ô½p¬«å¥ar@½p>º¼·p°`>¡\¥¬·1[p«Rª[¬`@½N°y¯kOì¥N:9
ª:½N°y«8¶*·ªì»>ª[·U®B±I¯@±I°'[y¬ L±³²BAþ²SA>«R±¹ª®Zh\r3²[½I?';I«R¬R¥EGA>±×¬ìª[«]9
¬«R½pBª <bAlL ½p¬è¶*>°y¯@«V¯
¯ ?B´ ²SA>«°ì¥±rt¥«;«R»y½Nª²º¼«R°²·N¶ ZS°>«YªB[p´
²BA>ª[·p' [1A3B² A>_
« °"°>±I®p«Rª[¬±¹²µ´8·N¶ o\K½ ;I±³¶*·ª°y±I½í>°y¯>«Yt
ª rB ?<Y·p°{²ª:I½ <-²
°B>t
º ?«Rw
ª ²³I´y¦ ´1µK´a½N°y¯ú±¹°»y½pª¤\
² ?B´ùS² A>D
« °;°>±¹®«Yª:¬¤±¹²µ´ù·N
¶ o\K½ ;I± 9
¶*·ª°y±I ½ ¶Mªô8½ Lª[«Ya° <-*« ªð±I®p«Rªº¼·ª*« ·0½U²±I·p°K½ ; ªôK½ ?D·pª:½U²[·pª[®
´ ¸¹ªªc·-ªvº
y°y¯@«Y*ª <Y·p°{²ª:I½ <-²`°y·yv¥ {l97M´12M§ 9ZS'° [K9´1ya¥ {«y¬«R¯ÛS² A>
« <Y·pº¼»>: 9
²:½U²[±¹·°yK½ ;p¶5I½ <-± ;I±³²[±¹«V¬$½N²ôS² Ay}« ªªc·-ªa½N°y¯à½N²ôS² Ay}« ·;½N²±I·p°yI½ ;:o«R°{²«Yª
¶*·ª rB>»D«Ybª <-·º»y@²±I'° [D|"»>» ;¹p± <Y½N²±I·p°y¬R¥
¦¦
rs=14
T (K)
62500
rs=10
rs=6
rs=4
rs=3
½
rs=2.6
1.0
0.0
31250
1.0
0.0
15625
gee(r)
10000
1.0
0.0
1.0
0.0
7812
1.0
0.0
5000
1.0
»0 ¼ 5 10» » 0 ¼5 10» »0 ¼5 10» » 0 ¼ 5 10» »0 ¼5 10» »0 ¼5 10» 15¼
0.0
r
¡`¢¤£¥B¦µ>¨Z;¹«
<_²[ª·°:9 «;¹«
<_²[ª·°»½N±Iªv<Y·pª[ª«;I½N²±I·p°¶*>°<-²±I·p°ð¥FEGA>«
¬I· ;I±IR
¯ ;I±¹°>«V@
¬ <Y·pª[ª«V¬¤»D·p°y¯²·þ»½N±Iª[¬~·p¶« ;¹
« <_²[ª·°yD
¬ L±¹S² Aî»y½pª[I½ ;9
;I« ; ¬¤»>±I°ð¥8¡y·pªìB² A>«a¬[K½ «m·N
¶ <Y·pº¼»y½Nª[±×¬¤·° `cL\«èI½ ;I¬·8n¬ AyM· LñB² A>«
»y½p±¹w
ª <-·ªª[« ;×½U²[±¹·°¶*>° <-²±I·p°y¬Ô·p¶S»y½N±Iª:
¬ L±¹S² Aú·p»>»D·¬±¹²«~¬¤»y±¹°½p¬
¯>½n¬ A>«V/
¯ ;I±I°>«R¬R®
¥ EGAy±I¬¶*>a° <_²±I·p°ø±×¬à¬µ²[ª·'° [I;I´»«VK½ «R¯ú°>«R½pª0B² A>«
·pª[± [p±I°8±¹°úS² Ay«»yª«V¬¤«R° <-«·N¶Sº¼1· ;¹
« <-' ;I«R¬Ô½p¬ÔS¬ A>M· L°3±I°ø¡$± [y¥b
¦ >¥
EGA>
« <-1· ;¹yº°®
¬ <Y·pª[ª«V¬¤»D·p°¯ø²·ø¯@±¹¸D«Rª«R°D
² 8J~®UK½ ;I>«R¬~½p°y¯þB² A>«
ª[M· L"¬S²[·m¯@±¹¸D«Rª«R°² ²[«Yº¼»«Rª[½N²>ª[«RG¬ NÛ¥
¾=¥¿*¥¾=¥D
¥
¹¦]«å¥r>½N>º¼·p°½N°¯í£¥o}A½K?>ª[±¹«Rª`>©AB´B¬R¥:¬«Y®t¥|WÀÁ`YK2II´¸¤¦µ1µ1Y1º_¥
Y8*{ ¥aZ*D
? «I; ±¹°'m
[ ½p°y¯+{ ¥
¬ ±p<b>
A «Yª²y
` ©B
A ´B¬R¥:ð
ª «Y²¤²R¥a|àÄÅ`'{ §µ¸ ¦µ1 §:º ¥
³MÛ
O ¥Ô
Æ ±¹²[½Nºå>ª:½å½p°y¯t
r ¥>¢<b>
A ±Iº~½Nª[`>
¥>©B
A ´B¬R¥B
r ·:N< ¥ ½N»½N°ÁÇRÈnÉÊ`aµ §K2¸µ¦
µIµ1º:¥
´K0
o ¥©K±I«YªB¹; «R·p°>±~`:Û
« ¥
o «Y»D«YªB¹; «R´I`'
² ¥'\
² «Yª[°{>
` ½N°y¯{ ¥aù
m ½Ip[ ª[·@
` ©*B
A ´@¬R¥ "
¬ «Y®t¥ð
ª «Y²¤²V¥ÇÉ`Y@¦´{§+¸µ¦
µIµK´:º:¥
§8*{ ¥aà
¬ ¥aù
m ½Ip[ ª[·`:Û
« ¥ø
m ¥
o «Y»D«YªBI; «Y´I`a0
o ¥©K±I«YªB¹; «R·p°>±~>
` ½N°y¯
² ¥'\
² «Yª[°{>
` ©*B
A ´@¬Y¥'
¬ «R®t¥ð
ª «Y²¤²R¥ÇÁW
` ¦
YK´12¸µ¦µ1µIz º:¥
zM
² ¥aù
m ±>I; ±³²BYd «Rª`'{ ¥ù
m ½K[ ª·a{` ½p°y¯kÛ
« ¥
o «R»«RªSI; «Y´1`a
o ·p°{²ªV¥>©*×; ½p¬º~½å©B
A ´B¬±pY< ¬ÉËÂ1ÌjÍW
` ¦V§1Y@¤¸ ¦µ1µIµ_º ¥
±7
Ô
E ¥>
¥'ô
ª «Y°>·{¬nB
´I`W
r ¥à
¬ ¥\
² ±p<b
A ½Nºk`>
¥'å
« ¥Ô
Æ ª[«R¬[¬@
` ½p°y¯kK
ª ¥'ì
| ¥
o ·I;¹; ±I°y¬y
` ©*B
A ´@¬Y¥:
¬ «R®t¥²%ÁÂað
` ¦D¸~YK2I212_º ¥
M
£¥D£Ô½K;¹; ±~`à
¬ ¥;
O ·B·B¯`'ì
| ¥0
O ½KYd ±~y
` ½p°y¯a¡\¥£´ [ ±¹y
` ©B
A ´B¬R¥:
¬ «Y®t¥
² ¥ÁÂa`'µ12Iµk¸¹YI2I212:º ¥
µMå
« ¥þ
m ¥a
o «Y»D«YªB¹; «R´I`
¬ «R®t¥
m ·@¯W¥y©*B
A ´@¬R¥ÁÇ`Y17Kµ+¤¸ ¦µI{µ §1_º ¥
¹¦2Må
« ¥þ
m ¥a
o «Y»D«YªB¹; «R´I`ay
¥{r ²[½N²R¥y©B
A ´B¬R¥ÁÉW
` ¦8YK³7@µ¸ ¦
µIy
µ ¦8:º ¥
¹¦p¦]å
« ¥þ
m ¥a
o «Y»D«YªB¹; «R´P¸
Z ¯@±¹²ª[±Y< «=
o ·º¼»·{¬¤±¹²·ª±~`:
² ·1¹; ·1p[ °y½B
` ¢Ð²[½KI; ´Iô
` ¦µIµ1z_º ¥
¹¦
Y8
² ¥aù
m ±>I; ±³²BYd «Rª"½N°y¯k"
Z ¥'S
ª ¥y©b·I;I; · <b@
` ©*B
A ´@¬R¥ "
¬ «Y®t¥ZÎÁÂ`'³K´:7M2¸¹YI2I2I2 :º ¥
¹¦³M}þ
m ¥|;¹; «R°ù½N°y¯kå
« ¥E ±>×; ¯@«V¬nI; «Y´1`ÏÐKÑ-ÒÓ'Ô~ÕÖwרÑtÓ:Ù>ÚIÔØÐKÛÐnÜ-ÝFØÞÓ:Øß8à@¸~h-B
¶*·ª[¯"
° °>±I®p«Rª[¬±¹²µ´m©Kª[«R¬[¬`:"
· «L%K
á ·ªS`W¦
µI71º:¥
¹¦´K
² ¥aù
m ±>I; ±³²BYd «Rªy
` ©ð
A ¥Û
« ¥B²B>
A «R¬±I¬`;
° °>±¹®«Yª:¬¤±¹²µ´m·p¶$¢;¹; ±I°>·p±×¬½U²-;
° ªS
? ½N°y½K9o}y
A ½pº¼»y½N±p[ °/¸~YK212I2_º ¥
¹¦V§8ì
¬ ¥£¥a{
r ²[·pª[«Yª
`>
¥ù
m ½N²Sð
A ¥©*B
A ´@¬Y¥'Ë`µIzI´¤¸ ¦µIz1_º ¥
¹¦zM*{ ¥aÔ
Æ ·II; ·¬ ½N°y¯kS
ª ¥'ú
{ ·1¹; °y±¹«
L ±<dI`y
¥o}>
A «Yº¥>©{
A ´@¬R¥'ÀÂ`'³Iz 78´kµ¸ ¦
µIzK´::º ¥
¹¦87
² ¥aù
m ±>I; ±³²BYd «Rª"½N°y¯kå
« ¥aø
m ¥
o «R»«RªSI; «Y´1>
` ©*B
A ´@¬Y¥'
¬ «R®t¥'ð
ª «-²²R¥aÅâð
` ¦1µI2@¸~YK212I2_º ¥
¹¦MS
¡\¥"
¬ ·Ip[ «Rª[¬`:;
| ¬¤²ª[·p»'B
A ´@¬R¥>
¥ÉâaÍ`'zI1µ+¤¸ ¦µ1µI2_º ¥
¹¦µMÛ
O ¥ap >ª[½p°>«a
½N°y¯à
¬ ¥
¬ «V¯@º¼«Yª
`>
¥o}>
A «Yº¥y©{A ´@¬R¥¸¹YK212I2 :º ¥
YK2Må
« ¥>
r ½N>º¼·p°y
` £¥o}y
A ½Ky
? ª±I«Yª
@
` ½N°y¯kì
O ¥ø
m ¥:Û
u ¥;
O ·pª[°`0
| ¬µ²[ª·»'B
A ´B¬R¥'>
¥ËaË`aB
7 ¦
³+¤¸ ¦µI{µ §1_º ¥
@
Y ¦]
² ¥aù
m ±>I; ±³²BYd «Rª`'{ ¥ù
m ½K[ ª·a{` ½p°y¯kÛ
« ¥
o «R»«RªSI; «Y´P5¸ ©*I; «Y°B>º ©Kª[«R¬[¬`:;
· «LãK
á ·pªB@·á®ð
` ¦µ1µI_º ¥
YIY8}þ
m ¥Û
« ¥D£±¹ª:½Nª:¯@«R½p@
` ©*B
A ´@¬Y¥'"
¬ «Y®t¥|WÀcÂa`'z1µI³ §+µ¸ ¦
µIµ12:º ¥
¦8Y
1.0
0.8
0.6
x
æ
çFVT xH2
SC xH2
PIMC xH2
çPIMC xH+
SC xH+
0.4
0.2
0.0
4
10
ä
T (K)
å
10
ä
5
¡`¢¤£¥ YK2y¨¡>ª:I½ <-²±I·p° ·p¶Ûº¼I· ;I« <Y' ;¹«V¬½N°y¯ ¶*ª«R«ú»>ª[·N²[·p°y¬í½p¬½
¶*>°<-²±I·p°à·p¶{²[«Yº¼»D«Yª:½U²yª«O¶*·ª
Jg ¦2<-·º¼»y½Nª[±¹°[ ²SA>«<;¹¬µ²[«Yª
½N°K½ ;I´B¬±×¬·N¶bS² Ay«å©Kn¢ mPo ª[«R¬' ;¹²[¬ L±¹²SA8²SA>«xro º·@¯@«;¹¦jO½N°y¯
²SAy\
« èy>±×¯a®U½pª±×½U²[±¹·°yK½ ;DS² Ay«Y·pª[/
´ ¸Gc¡ uHE-º\¹¦ µ8Ð¥
1.0
FVT xH2
SC xH2
PIMC xH2
PIMC xH+
SC xH+
0.8
0.6
x
æ
0.4
0.2
0.0
4
ä
10
å
T (K)
ä
10
5
¡`¢¤£1¥ Y@¦¨ô¡>ª:I½ <-²±I·p°·N¶Dº1· ;¹
« <-' ;I«R¬b½p°y¯ì¶*ª[«Y« »>ª[·N²[·p°y¬O½¬b¬nA>·ML°
±I°¡`±[y¥YI2t?y@²A>«Yª[«¶*·pª"½~¯@«R°y¬±³²µ´m·p¶v8Jg¯Y:X z>¥
© Copyright 2026 Paperzz