# (a) Finite size correction for interaction energy in Hartree ('y'), as a function of inverse particle number ('x').

# rs = 0.1, Fitted line smaller N
# x,y
0.000316227766016838,0.0398665178071652
0.000357323208096854,0.043733394972795
0.000403759216506716,0.047975342243278
0.000456229825603517,0.052628739771779
0.000515519263116941,0.0577334964265672
0.000582513671246893,0.0633333920608866
0.000658214350978696,0.0694764529814996
0.000743752727565905,0.0762153638360318
0.000840407260855404,0.0836079194515801
0.000949622553197156,0.0917175204996811
0.00107303094052616,0.100613717238606
0.00121247688931773,0.110372805996269
0.00137004456405399,0.121078483509361
0.00154808897722586,0.132822564730503
0.00174927118743984,0.145705770259541
0.00197659807170163,0.159838590152224
0.00223346726631486,0.175342231514525
0.00252371794808316,0.192349658009453
0.00285168821479347,0.211006730191457
0.00322227992259142,0.231473456448268
0.00364103194931068,0.253925365278598
0.00411420297875284,0.278555010674753
0.00464886504321483,0.305573623520753
0.00525300922235397,0.335212923168809
0.00593566507817007,0.367727104730774
0.00670703561118431,0.403395019128129
0.00757864975487513,0.442522564597248
0.00856353468755879,0.485445310160179
0.00967641053709454,0.532531373560556
0.0109339103884784,0.58418457834667
0.0123548288825675,0.640847917177727
0.0139604031215008,0.70300735105561
0.0157746300792397,0.771195977065434
0.0178246252612584,0.845998600368638
0.0201410279739255,0.928056749659325
0.0227584592607479,1.01807417909785
0.0257160393498115,1.1168229039078
0.0290579723462054,1.22514982139938
0.0328342069082666,1.34398397420299
0.0371011827821374,1.47434451800458
0.0419226743523692,1.61734946211632
0.0473707438163119,1.77422525784426
0.0535268182284711,1.94631731688556
0.0604829065123776,2.13510154996402
0.0683429746294767,2.34219702466265
0.0772244994583626,2.56937985101039
0.0872602246086974,2.81859841390969
0.0986001444122764,3.09199008304284
0.111413745744046,3.39189954356571
0.125892541179417,3.72089890479827

# rs = 0.1, Fitted line larger N
# x,y
7.94328234724282e-05,0.0113473625936767
8.97555318081962e-05,0.0125384101602271
0.000101419729754016,0.0138544730591136
0.000114599750858346,0.0153086732123802
0.000129492584220526,0.016915509851837
0.00014632081869739,0.018691004084939
0.000165335969724827,0.0206528586346611
0.000186822238477104,0.0228206343460702
0.000211100759548482,0.0252159452194683
0.000238534400643142,0.027862673914703
0.000269533186009762,0.0307872098753489
0.000304560424679615,0.034018712446999
0.000344139635101067,0.0375894016131102
0.000388862369666319,0.041534879247211
0.000439397056076079,0.0458944840845434
0.000496498987685534,0.0507116839524179
0.00056102161214771,0.056034509170047
0.00063392928707473,0.0619160314391092
0.000716311693363551,0.0684148929998657
0.000809400121608313,0.0755958913288261
0.000914585875016636,0.0835306252077439
0.00103344106388056,0.0922982086056307
0.00116774210239705,0.101986059491612
0.00131949625902256,0.112690771443554
0.00149097165718406,0.124519076742914
0.00168473117473854,0.13758891055843
0.00190367074884342,0.152030586829202
0.00215106265874406,0.167988097571395
0.00243060443338441,0.185620548563429
0.00274647411481605,0.205103745724277
0.00310339270337439,0.226631948001995
0.00350669471793017,0.250419804249824
0.00396240792581251,0.276704493401645
0.0044773434340498,0.305748089285613
0.00505919748843582,0.33784017365454
0.00571666650191362,0.373300723486485
0.0064595770314958,0.41248330134364
0.00729903264636138,0.455778580599262
0.00824757988222529,0.503618240681252
0.00931939576234077,0.556479271170229
0.0105304996878311,0.614888727666526
0.011898992864271,0.679428986844868
0.0134453288429976,0.750743553092744
0.0151926192206704,0.829543474628064
0.0171669790660786,0.916614433068586
0.019397917236958,1.01282457714028
0.0219187774205065,1.11913317863131
0.0247672364894082,1.23660019689664
0.0279858676218127,1.3663968472769
0.0316227766016838,1.50981727880504

# rs = 0.1
# x,y
0.1,2.10845578
0.05,1.47257658
0.02,0.872244382
0.01,0.55975025
0.005,0.342996022
0.002,0.164875708
0.001,0.0906666082
0.0005,0.0503890173
0.0002,0.0240823125
0.0001,0.0137638795

# rs = 0.3, Fitted line smaller N
# x,y
0.000316227766016838, 0.00370737597989703
0.000357323208096854, 0.00415106100354898
0.000403759216506716, 0.00464784460724258
0.000456229825603517, 0.00520408143233856
0.000515519263116941, 0.00582688662013554
0.000582513671246893, 0.00652422682568542
0.000658214350978696, 0.00730502212380496
0.000743752727565905, 0.00817926011082144
0.000840407260855404, 0.00915812366159249
0.000949622553197156, 0.0102541339760128
0.00107303094052616, 0.0114813107447968
0.00121247688931773, 0.0128553514833091
0.00137004456405399, 0.0143938323274032
0.00154808897722586, 0.0161164328597623
0.00174927118743984, 0.0180451878426242
0.00197659807170163, 0.0202047690769454
0.00223346726631486, 0.0226228009934265
0.00252371794808316, 0.0253302140123027
0.00285168821479347, 0.0283616401919235
0.00322227992259142, 0.0317558562270912
0.00364103194931068, 0.0355562794637968
0.00411420297875284, 0.0398115232751644
0.00464886504321483, 0.0445760189027301
0.00525300922235397, 0.0499107117173815
0.00593566507817007, 0.0558838408062276
0.00670703561118431, 0.0625718118575375
0.00757864975487513, 0.0700601745093147
0.00856353468755879, 0.0784447166633286
0.00967641053709454, 0.087832689762595
0.0109339103884784, 0.098344180705527
0.0123548288825675, 0.11011364794569
0.0139604031215008, 0.123291641426281
0.0157746300792397, 0.138046728350006
0.0178246252612584, 0.154567649417943
0.0201410279739255, 0.173065733119109
0.0227584592607479, 0.193777598953236
0.0257160393498115, 0.216968184165253
0.0290579723462054, 0.242934132708124
0.0328342069082666, 0.272007589784215
0.0371011827821374, 0.304560450503314
0.0419226743523692, 0.341009117004294
0.0473707438163119, 0.381819824891489
0.0535268182284711, 0.427514607119233
0.0604829065123776, 0.478677971612014
0.0683429746294767, 0.535964378037467
0.0772244994583626, 0.600106609371869
0.0872602246086974, 0.671925145343569
0.0986001444122764, 0.752338657655417
0.111413745744046, 0.842375761236531
0.125892541179417, 0.943188171840335

# rs = 0.3, Fitted line larger N
# x,y
7.94328234724282e-05,0.000811897014578178
8.97555318081962e-05,0.000918352254613915
0.000101419729754016,0.00103876581439659
0.000114599750858346,0.00117496789683676
0.000129492584220526,0.00132902867948051
0.00014632081869739,0.00150328977977779
0.000165335969724827,0.00170039984604976
0.000186822238477104,0.00192335481511317
0.000211100759548482,0.00217554344845005
0.000238534400643142,0.00246079883904075
0.000269533186009762,0.00278345667172886
0.000304560424679615,0.00314842112263513
0.000344139635101067,0.00356123939924603
0.000388862369666319,0.0040281860541348
0.000439397056076079,0.0045563583538252
0.000496498987685534,0.00515378415233893
0.00056102161214771,0.00582954390903007
0.00063392928707473,0.00659390870529316
0.000716311693363551,0.00745849635790376
0.000809400121608313,0.00843644800180633
0.000914585875016636,0.00954262782628554
0.00103344106388056,0.0107938490003734
0.00116774210239705,0.0122091292214015
0.00131949625902256,0.0138099797708605
0.00149097165718406,0.0156207324710159
0.00168473117473854,0.0176689095117949
0.00190367074884342,0.0199856417690567
0.00215106265874406,0.0226061419723966
0.00243060443338441,0.0255702399143058
0.00274647411481605,0.0289229878354975
0.00310339270337439,0.0327153451878376
0.00350669471793017,0.0370049531828031
0.00396240792581251,0.0418570108980703
0.0044773434340498,0.047345266258447
0.00505919748843582,0.0535531369533742
0.00571666650191362,0.0605749783281699
0.0064595770314958,0.0685175175200834
0.00729903264636138,0.0775014756370409
0.00824757988222529,0.0876634026350746
0.00931939576234077,0.099157752783307
0.0105304996878311,0.112159232262124
0.011898992864271,0.126865454576406
0.0134453288429976,0.143499944144262
0.0151926192206704,0.162315533713745
0.0171669790660786,0.183598207245933
0.019397917236958,0.207671446673536
0.0219187774205065,0.234901148602771
0.0247672364894082,0.265701185688965
0.0279858676218127,0.300539697214954
0.0316227766016838,0.339946204484732

# rs = 0.3
# x,y
0.1,0.508657252
0.05,0.323363074
0.02,0.164528328
0.01,0.0927283791
0.005,0.0497452363
0.002,0.0206958373
0.001,0.0103844714
0.0005,0.00521347846
0.0002,0.00207667478
0.0001,0.00101706155

# rs = 0.5, Fitted line smaller N
# x,y
0.000316227766016838,0.00126099120632255
0.000357323208096854,0.00141984618231702
0.000403759216506716,0.00159871311658024
0.000456229825603517,0.00180011304108648
0.000515519263116941,0.00202688457802927
0.000582513671246893,0.00228222394865454
0.000658214350978696,0.00256973002225738
0.000743752727565905,0.00289345504028381
0.000840407260855404,0.0032579617304659
0.000949622553197156,0.00366838761598286
0.00107303094052616,0.00413051742605093
0.00121247688931773,0.00465086462852952
0.00137004456405399,0.00523676323370153
0.00154808897722586,0.00589647116315203
0.00174927118743984,0.00663928664067327
0.00197659807170163,0.00747567924566242
0.00223346726631486,0.00841743747613833
0.00252371794808316,0.00947783490119763
0.00285168821479347,0.0106718172447383
0.00322227992259142,0.0120162130372944
0.00364103194931068,0.0135299708050036
0.00411420297875284,0.0152344261387586
0.00464886504321483,0.0171536024077348
0.00525300922235397,0.0193145493556886
0.00593566507817007,0.0217477243523563
0.00670703561118431,0.0244874216734842
0.00757864975487513,0.0275722558599588
0.00856353468755879,0.0310457059687192
0.00967641053709454,0.0349567283863732
0.0109339103884784,0.0393604468427903
0.0123548288825675,0.0443189293500375
0.0139604031215008,0.0499020630171883
0.0157746300792397,0.0561885390710442
0.0178246252612584,0.0632669619660977
0.0201410279739255,0.0712370982160379
0.0227584592607479,0.0802112825483982
0.0257160393498115,0.0903160012013304
0.0290579723462054,0.101693674678209
0.0328342069082666,0.114504665087022
0.0371011827821374,0.128929536356902
0.0419226743523692,0.145171599188317
0.0473707438163119,0.163459776606613
0.0535268182284711,0.184051830507314
0.0604829065123776,0.207237994669586
0.0683429746294767,0.233345065443208
0.0772244994583626,0.26274100776505
0.0872602246086974,0.295840141424355
0.0986001444122764,0.333108980674407
0.111413745744046,0.375072809496729
0.125892541179417,0.422323085192576

# rs = 0.5, Fitted line larger N
# x,y
7.94328234724282e-05,0.000272458983928092
8.97555318081962e-05,0.000309469570837055
0.000101419729754016,0.000351507643070955
0.000114599750858346,0.000399256129780705
0.000129492584220526,0.000453490728607825
0.00014632081869739,0.000515092507273997
0.000165335969724827,0.000585062216959368
0.000186822238477104,0.000664536549997474
0.000211100759548482,0.000754806606001041
0.000238534400643142,0.000857338866409944
0.000269533186009762,0.000973799018203182
0.000304560424679615,0.00110607901380275
0.000344139635101067,0.00125632780677091
0.000388862369666319,0.00142698626261729
0.000439397056076079,0.00162082681185912
0.000496498987685534,0.00184099848951803
0.00056102161214771,0.00209107809274211
0.00063392928707473,0.00237512828763415
0.000716311693363551,0.00269776360925973
0.000809400121608313,0.00306422542703813
0.000914585875016636,0.00348046709336534
0.00103344106388056,0.00395325065875064
0.00116774210239705,0.00449025672465164
0.00131949625902256,0.00510020921862091
0.00149097165718406,0.0057930171187982
0.00168473117473854,0.00657993543013189
0.00190367074884342,0.00747374802746776
0.00215106265874406,0.00848897533588086
0.00243060443338441,0.00964211022211966
0.00274647411481605,0.0109518859293349
0.00310339270337439,0.0124395804078244
0.00350669471793017,0.014129361985797
0.00396240792581251,0.0160486819957459
0.0044773434340498,0.0182287207348414
0.00505919748843582,0.020704894004188
0.00571666650191362,0.0235174284559244
0.0064595770314958,0.0267120150949652
0.00729903264636138,0.0303405515518384
0.00824757988222529,0.0344619851852089
0.00931939576234077,0.0391432707106998
0.0105304996878311,0.0444604579131661
0.011898992864271,0.0504999271128376
0.0134453288429976,0.0573597924560895
0.0151926192206704,0.0651514958279865
0.0171669790660786,0.0740016172804948
0.019397917236958,0.0840539313876575
0.0219187774205065,0.0954717429342347
0.0247672364894082,0.108440539882219
0.0279858676218127,0.123171006713972
0.0316227766016838,0.139902447105216

# rs = 0.5
# x,y
0.1 0.246015507
0.05 0.147362481
0.02 0.068929748
0.01 0.0366707914
0.005 0.0188407577
0.002 0.00760916407
0.001 0.0037839081
0.0005 0.00187197761
0.0002 0.000720488327
0.0001 0.000343050987

# rs = 1.0, Fitted line smaller N
# x,y
0.000316227766016838,0.000312414149362358
0.000357323208096854,0.000352915990842275
0.000403759216506716,0.000398668552133098
0.000456229825603517,0.000450352544469804
0.000515519263116941,0.000508736927518463
0.000582513671246893,0.000574690350035937
0.000658214350978696,0.000649194073713946
0.000743752727565905,0.000733356572489783
0.000840407260855404,0.000828430024533678
0.000949622553197156,0.000935828942282277
0.00107303094052616,0.00105715121769776
0.00121247688931773,0.0011942018958661
0.00137004456405399,0.00134902003064042
0.00154808897722586,0.00152390902189049
0.00174927118743984,0.00172147088571899
0.00197659807170163,0.0019446449675203
0.00223346726631486,0.0021967516738586
0.00252371794808316,0.0024815418738126
0.00285168821479347,0.0028032527047851
0.00322227992259142,0.00316667061306193
0.00364103194931068,0.00357720256704391
0.00411420297875284,0.00404095650266966
0.00464886504321483,0.00456483219790436
0.00525300922235397,0.00515662392833429
0.00593566507817007,0.00582513643118736
0.00670703561118431,0.00658031590310428
0.00757864975487513,0.00743339798065827
0.00856353468755879,0.00839707490529255
0.00967641053709454,0.00948568435977242
0.0109339103884784,0.0107154227856797
0.0123548288825675,0.012104586355709
0.0139604031215008,0.0136738431859759
0.0157746300792397,0.0154465408383389
0.0178246252612584,0.0174490536877868
0.0201410279739255,0.0197111753230576
0.0227584592607479,0.0222665618186652
0.0257160393498115,0.0251532324733811
0.0290579723462054,0.0284141354652067
0.0328342069082666,0.0320977868387106
0.0371011827821374,0.0362589923316467
0.0419226743523692,0.0409596627802651
0.0473707438163119,0.0462697352349957
0.0535268182284711,0.0522682134909594
0.0604829065123776,0.0590443435144235
0.0683429746294767,0.0666989412533154
0.0772244994583626,0.0753458925870937
0.0872602246086974,0.0851138477323834
0.0986001444122764,0.0961481353139115
0.111413745744046,0.108612924578488
0.125892541179417,0.122693667921664

# rs = 1.0
# x,y
0.1,0.0843764208
0.05,0.0461381946
0.02,0.0194606014
0.01,0.00984176847
0.005,0.00492998647
0.002,0.00197077186
0.001,0.00098127119

# rs = 3.23, Fitted line smaller N
# x,y
0.000316227766016838,3.42266658027302e-05
0.000357323208096854,3.86756454167855e-05
0.000403759216506716,4.37029290853565e-05
0.000456229825603517,4.93836881080405e-05
0.000515519263116941,5.58028649839255e-05
0.000582513671246893,6.30564435285103e-05
0.000658214350978696,7.12528840877537e-05
0.000743752727565905,8.05147453095313e-05
0.000840407260855404,9.09805167223102e-05
0.000949622553197156,0.000102806689522977
0.00107303094052616,0.000116170096537625
0.00121247688931773,0.000131270556343952
0.00137004456405399,0.000148333861091952
0.00154808897722586,0.000167615152698789
0.00174927118743984,0.000189402737900973
0.00197659807170163,0.000214022399209041
0.00223346726631486,0.000241842266225017
0.00252371794808316,0.000273278320161833
0.00285168821479347,0.000308800613871968
0.00322227992259142,0.000348940300391318
0.00364103194931068,0.000394297575093764
0.00411420297875284,0.000445550650212861
0.00464886504321483,0.000503465895923645
0.00525300922235397,0.000568909299620819
0.00593566507817007,0.000642859414740053
0.00670703561118431,0.000726421992741847
0.00757864975487513,0.000820846517045117
0.00856353468755879,0.000927544886136932
0.00967641053709454,0.0010481125252207
0.0109339103884784,0.00118435224207828
0.0123548288825675,0.00133830118385473
0.0139604031215008,0.00151226129784166
0.0157746300792397,0.00170883375172894
0.0178246252612584,0.00193095782799946
0.0201410279739255,0.00218195487404198
0.0227584592607479,0.0024655779651532
0.0257160393498115,0.00278606802302368
0.0290579723462054,0.00314821722882843
0.0328342069082666,0.00355744067911722
0.0371011827821374,0.00401985735595113
0.0419226743523692,0.00454238162200482
0.0473707438163119,0.00513282660873052
0.0535268182284711,0.00580002104351243
0.0604829065123776,0.00655394126268902
0.0683429746294767,0.0074058603843901
0.0772244994583626,0.00836851687172058
0.0872602246086974,0.00945630500675978
0.0986001444122764,0.0106854901234709
0.111413745744046,0.0120744518178267
0.125892541179417,0.0136439587717912

# rs = 3.23
# x,y
0.1 0.010988188
0.05 0.00542180511
0.02 0.00216623821
0.01 0.00108332439
0.005 0.000541586615
0.002 0.00021656414
0.001 0.000108247651

# rs = 10.0, Fitted line smaller N
# x,y
0.000316227766016838,4.80022970013281e-06
0.000357323208096854,5.42378241007316e-06
0.000403759216506716,6.1283349900954e-06
0.000456229825603517,6.92440937178395e-06
0.000515519263116941,7.82389429193116e-06
0.000582513671246893,8.84022284135153e-06
0.000658214350978696,9.98857307739311e-06
0.000743752727565905,1.12860946961342e-05
0.000840407260855404,1.27521651494343e-05
0.000949622553197156,1.44086790317421e-05
0.00107303094052616,1.6280375058425e-05
0.00121247688931773,1.83952055187767e-05
0.00137004456405399,2.07847537211941e-05
0.00154808897722586,2.34847056647303e-05
0.00174927118743984,2.65353829810655e-05
0.00197659807170163,2.99823451059594e-05
0.00223346726631486,3.38770696731339e-05
0.00252371794808316,3.82777212917296e-05
0.00285168821479347,4.32500201884134e-05
0.00322227992259142,4.88682236866155e-05
0.00364103194931068,5.52162351805066e-05
0.00411420297875284,6.23888571653578e-05
0.00464886504321483,7.04932070372949e-05
0.00525300922235397,7.96503168062869e-05
0.00593566507817007,8.99969406128088e-05
0.00670703561118431,0.000101687597042001
0.00757864975487513,0.00011489687673566
0.00856353468755879,0.000129822049764405
0.00967641053709454,0.000146686011699053
0.0109339103884784,0.000165740612378424
0.0123548288825675,0.000187270417086077
0.0139604031215008,0.00021159695630616
0.0157746300792397,0.000239083527525071
0.0178246252612584,0.000270140620790052
0.0201410279739255,0.000305232049051067
0.0227584592607479,0.000344881874837773
0.0257160393498115,0.000389682236715966
0.0290579723462054,0.000440302192405406
0.0328342069082666,0.000497497710623935
0.0371011827821374,0.000562122960878125
0.0419226743523692,0.000635143069804485
0.0473707438163119,0.000717648534567028
0.0535268182284711,0.000810871508563795
0.0604829065123776,0.00091620420265641
0.0683429746294767,0.00103521967673035
0.0772244994583626,0.00116969533209137
0.0872602246086974,0.00132163945553821
0.0986001444122764,0.00149332121152629
0.111413745744046,0.0016873045303314
0.125892541179417,0.00190648639830611

# rs = 10.0, Fitted line smaller N
# x,y
0.1,0.00146432758
0.05,0.000771221101
0.02,0.000302890149
0.01,0.000151693642
0.005,7.5846844e-05
0.002,3.03276703e-05
0.001,1.51710862e-05

# (b) Integral used for finite size corrections in Hartree ('y'), as a function of rs ('x').

# N = 10
# x,y
0.1,0.0247079018
0.3,0.06018483303
0.5,0.087499411
1.0,0.138073726
2.0,0.2037689096
3.23,0.2563390133895
5.0,0.3082480375
6.0,0.33104857788
7.0,0.3509716532
8.0,0.36882049024
9.0,0.38512745919
10.0,0.400261986

# N = 100
# x,y
0.1,0.00818158362
0.3,0.01592084709
0.5,0.0204092672
1.0,0.0270155533
2.0,0.03405548256
3.23,0.039273134376037
5.0,0.044431364
6.0,0.04673965536
7.0,0.048780656498
8.0,0.050624301696
9.0,0.052315697124
10.0,0.0538856115

# N = 1000
# x,y
0.1,0.00208594252
0.3,0.003102850278
0.5,0.00358274535
1.0,0.00424916084
2.0,0.00495065648
3.23,0.005471754017545
5.0,0.005987753675
6.0,0.006218661672
7.0,0.00642280044
8.0,0.006607206656
9.0,0.0067763968929
10.0,0.00693344243