Comparison of calculated and measured yields of medical isotopes

!"#$
%&'"(")(%
*+
,.-/0-1%24365798;:<3>=@?0AB-CD-E162%FHG;FHIJ:<3>=@?"16-LK-1M795NI62%5NO68:HO6=QPSRT-AB-UVG;F<WYXZ:HG[6=QP
?]\_^a`cbedgfDbehdZ`cdZiHdZjk]^alnmiHoqprjstl"ujqhjsalvoqwtxy<zyt{a|a}~TiH€qbsaxu‚i_hh`cs
P%ƒgjqdZdZ„9h€…i_lv†ˆ‡‰^apcprj†qj…xƒgjqdZdZ„9h€qiHlІ‹Œy%Ž<aa‘axY’“eŒ
–” •˜—N™9ša›6œ™
UV5NGž74FHŸ O¢¡£5N[6Ÿ ¤NF_¥Ÿ 8;:…79:HIJ5N8S¤…FHO¢¦J5ˆI%G;:[6§6¤N5…[¨WYŸ©742¢26Ÿ ªH2«G;FH[6Ÿ :HOe§6¤…¥LŸ [65¬I6§%G;Ÿ©7D­®3>Ÿ F°¯²±˜=O6³
FHO6['¯´±=I%³YG5NFH¤µ74Ÿ :HO68¶§68;Ÿ O6ª·¦%G;5N¡£88¸74GFH26¥ §6O6ª¹I%26:…74:_O68¶Fq7º5…¥L5…¤79G;:HO«FH¤N¤…5N¥ 5NG;Fq74:HG8S8;§%¤»2¢FH8
¡£ŸL¤…G;:…79G;:HO¼¹½V¾H¿H=ÀXZ:HGg5Á>FH¡£I6¥ 5N=J:HG
¥LŸ O6FH¤":HXH79265"O65WÂCDÃÄAB/ÅXZFH¤NŸ ¥ ŸÆ7D­ÇFq7
74265Vȝ:HŸ O97ÄCDO68¸79ŸÆ79§M745
XZ:HG/0§6¤…¥L5…FHGÃÄ5…8;5NF_G;¤»26-˜ÉÊ5BI>5…G;XZ:HG¡#742%5¼¹UV/ÄËÌ¡£:[65…¥LŸ O6ªÄ:HXt79265B5NO65…G;ª…­8I>5…¤74GFH=%F_O6ªH§6¥ FHG
[6Ÿ 8¸74GŸL¦%§M74Ÿ :HOFHO6[ÌÍ6§tÁ‰5…8:HX
¦6G5N¡£8;8ž74G;F_26¥L§%O6ª¨I%26:…74:_O68ÎXZG;:_¡)FYÉ 79FHG;ª_57.F_O6[Ì8;§6¦%8;5NÏe§65…O97
¤NFH¥ ¤N§%¥LF…79ŸL:_O68¨:_X"­>Ÿ 5N¥ [68¨:_X¶Ÿ 8;:…79:HIJ5N8Ç:HXYŸLO9745…G;5…8¸74-ÐÉÊ5Ñ6O6[ÒFHOÅFHªHG;5…5N¡£5NO97Ó¦>5µ7DWÎ5…5NO#79265
¤NFH¥ ¤N§%¥LF…795N[&F_O6[&I6§6¦%¥LŸ 8;265…[Ä­>ŸL5…¥L[%8‚:HX_ÔDÔ4¼·:H=_PDÕDÖ4ËB§6=MPDÕq×;ØWYŸ©7426Ÿ O&FÄXZFH¤79:HG:HXÙÛÚNÜ´¿H-16I>5…¤NŸ Ñ6¤N8
XZ:HGÝ¡£5…[6ŸL¤…FH¥JŸL8:…74:HIJ5N8I6G;:[6§6¤µ74Ÿ :HO¬F…774265ÄCDÃÄAB/Ò5N¥ 5N¤µ74G;:_O–¥LŸ O6FH¤ÄŸL88;§6Gž35­65N[ŸLOˆ¤N:HO%¤N¥ §68;Ÿ :HO6Þß&àVáEâ®ãÌäÌå
àVæ;â¨ß
16Ÿ O6¤N5YFH¥ ¥¡Ftç:HG"26:H8;I%ŸÆ79FH¥L8n§685¶GFH[6Ÿ :HŸL8:…74:_I>5…8ÄXZ:HG"[6Ÿ FHªHO%:H8;Ÿ 8;=¦6Ÿ :¤»2%5N¡£ŸL¤…FH¥FHO6FH¥©­>8;Ÿ 80FHO6[G;F_[6ŸL:qè
742%5NG;F_I4­H=674265Y[65N¡£FHO%[·XZ:HGg79265N¡éŸ 8ÄGFHI6Ÿ [6¥©­ŸLO%¤NG;5…FH8;Ÿ O6ªH-ļ¹:H8ž7&:HX742%5N8;5¶ŸL8:…74:_I>5…8ÄFHG5êI6G;:[6§6¤…5N[
FH8êFH¤µ74Ÿ©3%Fq74Ÿ :HOI6G;:[6§6¤µ748YŸLOOe§6¤N¥ 5NF_G¶G5NFH¤µ74:HG8;=8;:H¡£5ëìŸLO®¤­>¤…¥L:…79G;:HO%8;-A¥ 5N¤µ74G:HO«F_¤N¤N5…¥L5…G;F…79:HG;8=
26:<W0535…G;=I6G:»3>Ÿ [65YFHO–FH¥©745NGO6F…79ŸÆ365YIJ:H88;Ÿ ¦6ŸL¥ Ÿ©7D­®XZ:HGVI6G;:[6§6¤…ŸLO%ªGFH[6Ÿ :HŸ 8;:…79:HI>5…8;=E5…8;IJ5N¤…ŸLFH¥ ¥©­®F…7;79G;FH¤µè
74Ÿ©35ŸLO"3>ŸL5µWí:_X%¤N5…G¸79FHŸLOSO§%¤N¥ 5NFHG˜¡5…[6Ÿ ¤NŸ O65TG;5…ªH§6¥ F…74Ÿ :HO68˜ªH:<35…G;O6Ÿ O6ªÎGFH[6Ÿ :HI626FHG¡£FH¤N5…§M74Ÿ ¤NFH¥Ïe§6FH¥ ŸÆ7D­HAB¥L5…¤79G;:HO«FH¤N¤…5N¥ 5NG;Fq74:HG8¶I6G:[%§6¤N5£26Ÿ ªH2Mè<5NO65…G;ª…­î¦6G5N¡£8;8ž74FH2%¥L§6O%ª¹I626:…79:HO68T742%F…7ˆ¤NFHO®ŸLO%[6§6¤N5I626:qè
74:_O65N§M79G;:HOïG5NFH¤µ74Ÿ :HO68;=ÄFHO6[ï¥ ŸLO6F_¤N8£¥LŸ ð_5&7926F…7:HXnCDÃÄAB/Ä=˜WYŸÆ792#5…¥L5…¤79G;:HOî5NO65…G;ª…­Ó3%F_G;Ÿ FH¦6¥ 5–§6I79:
FH¦J:H§M7n¿Hñ¼·5,.=ÀI6G:H¡£ŸL85"FY2%ŸLªH2%5NG
G;F_[6ŸL:_ŸL8:…74:HIJ5"I6§6GŸÆ7D­&WY2%ŸL¤»2ˆŸLOÎ74§%G;O¥LŸ ¡£ŸÆ7982e§6¡£FHOG;F_[6ŸLFq74Ÿ :HO
5Á>IJ:H8;§%G;5N½V265Ý­>Ÿ 5N¥ [68V:HXG;F_[6ŸL:_ŸL8:…74:HIJ5N8ÝFHG;5Χ%8;§6FH¥ ¥©­Ì:H¦M79FHŸ O65N[–5…¡I%ŸLGŸL¤…FH¥L¥©­-"AE35…O£7926:H§6ª_2¬¤N:H¡£I6G5N265…O68;Ÿ©35
I626:q74:HOe§6¤…¥L5…FHG¬[6F…79F¢5Á>Ÿ 8¸798;=V­‰Ÿ 5N¥ [¤NF_¥L¤…§6¥LFq74Ÿ :HO68¬FHG5·GFHG;5…¥Æ­òIJ5NG;XZ:_G;¡£5N[¦J5N¤…FH§68;574265µ­ÂG5NÏe§6Ÿ G;5
FªH::[®ðO%:»WY¥ 5N[%ªH5¬:HX¦6G;5…¡88¸79G;FH26¥ §6O6ª­‰Ÿ 5N¥ [68&F_O6[Ó8I>5…¤74GFH-¹½V265ˆRT579265è<ó05…ŸÆ79¥L5…Gn742%5N:HGž­îFHO6[
16¤»26Ÿ ô‚õ 8VFHO6FH¥©­e74Ÿ ¤NFH¥‰FHI6I6G:»Á>Ÿ ¡£F…74Ÿ :HOÇ:HX%742%5ÎI626:…79:HO–8;IJ5N¤µ74G§6¡öW05NG;5ÝWYŸ [65…¥Æ­¹§68;5…[Ÿ O&7426Ÿ OS74F_G;ªH5µ7
¤NF_¥L¤…§6¥LFq74Ÿ :HO68
FH8‚G53>Ÿ 5W05N[º¦9­¬÷Y:¤»2.FHO6[.¼·:…74øêù څú -Ýû¦6G5N¡£8;8ž74GFH26¥ §6O6ªT74FHGªH57VŸL8‚[%5NÑ6O65…[ˆF_8>7426Ÿ O
Ÿ X_74265¡S§6¥©74Ÿ I6¥ 5V5N¥ 5N¤79G;:HO.8¤NF…7745…G;Ÿ O6ªFHO6[&5…O65NGª…­º¥L:H88;5…8‚26F<35VO65…ªH¥ ŸLªHŸ ¦6¥ 5T5NôJ5N¤µ748‚:_OÄ74265ÝI6G;:[6§6¤…5N[
I626:q74:HO¨8;IJ5N¤79G;§6¡£=˜¥L5…8;87926FHO·ñ_-LñÀÚq¡¡£-ûg7n74265¶:…742%5NGn5Áe74G5N¡£5N=˜26ŸLª_265N8ž7.¦6G5N¡£8;8ž74G;F_26¥L§%O6ª–I6G;:qè
[6§6¤µ74Ÿ :HOÌ26F<35.¦J5N5…OÌ:H¦M79FHŸLO%5N[¹XZ:HGB74FHGªH579808§6¤»2FH879§6O6ªH8ž745NO:HXg8;5365NGFH¥‚¡£¡£-.½V265Ä742%5N:HG574Ÿ ¤NF_¥
[65…8;¤NGŸLIt74Ÿ :HOº:HXÀ¤»26F_G;ªH5…[Mè»I6F_G¸74Ÿ ¤N¥ 5nI6G;:¤N5…8;8;5…8Ÿ OÎ7426Ÿ ¤»ð074F_G;ªH5µ748
26FH8BF¥ :HO6ªH=ÀF26F_¥LXrè<¤N5NO979§6G¸­26Ÿ 8¸79:HG¸­
WYŸ©742I>5…G;26FHI%8g74265ê¡£:H8¸7YG5N¤…5NO97&¦9­RݟL5…¥LFMç5µW)ù©¾Hú -V½V265ê[65365N¥ :HI>5…[79265N:HG579ŸL¤…FH¥FHI6I6G:HFH¤»265…8"FHO6[
¡£:[%5N¥ 8WÎ5…G;5.Ÿ ¡£I6¥L5…¡£5NO9745…[«Ÿ OÌ8;5µ35NGFH¥‚¼¹:_O4795.UVFHG;¥ :¬¤…:[65…8ÎXZ:HGÄ8;Ÿ ¡S§6¥ F…7;79ŸLO%ª5…¥L5…¤79G;:HOÌ8¤NF…7745NGžè
Ÿ O6ªFHO6[ï¦6G;5…¡£8;8¸79G;FH2%¥L§6O%ªÓŸ OÌ7926Ÿ ¤»ð¨74FHGªH5798;-'½V2%5–¤N:[65N8£ABü¶1%ýH="ü¶ABû0/ĽþFHO%[îËBAB/0ABKÿêËBA
26F<35¶¦>5…5NO¹§%8;5N[¨G;5…¤N5NO979¥Æ­Ó¦9­ÀFH[%[65NªH:_O¨5µ7&FH¥ -£ùHúXZ:HGn¤NFH¥ ¤N§%¥LF…79ŸLO%ªºI626:q74:HO¨8;IJ5N¤79G;FˆFHO6[­>Ÿ 5N¥ [68
FHO6[·¤N:H¡£I6FHGŸLO%ªS74265…¡ÛWYŸ©742Ì¡£5NF_8;§6G5N¡£5NO9748ê:HO7426Ÿ ¤»ð·RT5…=gûÄ¥gFHO6[·Ë¦º79FHG;ª_5748ğLOº79265&5…¥L5…¤74G:HO
5NO%5NG;ªq­ÓGFHO6ªH5¶XZG;:H¡!ÚqñY74:Hñ¼¹5,&-g½V265¶¤NFH¥ ¤N§6¥ F…79ŸL:HO%80:HX>79265S¦%G;5N¡£88¸74GFH26¥ §6O6ª–¤»26F_G;FH¤µ745NGŸL8ž74Ÿ ¤N8
W05NG;5YXZ:H§6O%[£79:¦J5êŸLOÇF څñ$FHªHG;5…5N¡£5NO97nWYŸÆ792¨¡£5…FH8;§6G5N¡£5NO9798;ÿê§6GǪH:HFH¥026FH8¦>5…5NO°74:î¡:[65…¥Ý74265¦6G5N¡£8;8ž74G;F_26¥L§%O6ª'5NO%5NG;ªq­ 8;IJ5N¤79G;FH=.F_O6ªH§6¥ FHG–[6Ÿ 8¸79G;Ÿ ¦6§M74Ÿ :HO
FHO6[ÅÍ6§tÁ‰5…8ÇXZG;:H¡ F·74§6O%ªH8¸795NO°74FHGªH57F_O6[Ó74:°8§6¦68;5…Ïe§65NO974¥©­ö¤NFH¥ ¤N§%¥LF…795¬74265º­>Ÿ 5N¥ [68Ç:HXê8;5365NGFH¥
G;F_[6ŸL:_ŸL8:…74:HIJ5N8nXZ:HG‚WY26Ÿ ¤»2ˆ742%5NG;5YFHG5¶5µÁ‰Ÿ 8¸79ŸLO%ª¬¡£5NFH8§6G;5…[¹[6F…79FˆŸ O·:HG[65NG‚79:ê3FH¥ ŸL[%F…745V74265Y¼¹UV/ÄË
¯¸¼·:HO9745êUVFHG;¥ :/è»Ë˜FHG¸79ŸL¤…¥L5…³‚74G;F_O68;IJ:HG¸7¶¤…:[65ˆù©¿HúEXZ:HGV8§6¤»2·F_I6I6¥ ŸL¤…F…74Ÿ :HO6-
ånä àVæ4ß å
àVæ®æ;à
ÉÊ5n¤…FH¥ ¤N§6¥ F…745
742%5ÄFH¤µ74Ÿ©3>ŸÆ7D­ö¯²79265"O§%¡S¦J5NG:HX‰[65…¤NF<­>8ÝIJ5NGB8;5…¤N:HO%[6³ÝŸ O6[6§6¤…5N[ˆ¦4­FY¦J5NFH¡Ð:_X‰I626:qè
74:_O68B:HX>Í%§MÁ[65NO%8;Ÿ©7D­Y¯9³BFHXr795NGE74265"Ÿ G;GFH[6Ÿ F…74Ÿ :HOÎ74Ÿ ¡£5!#"$"T¦4­§%8;Ÿ O6ªSFê8¸79FHO6[6F_G;[5Á>I6G;5…8;8ŸL:HO
XZG;:_¡þFH¤µ74Ÿ©3%Fq74Ÿ :HO¨F_O6FH¥©­‰8ŸL8&%
('*),+Ó¯-!#"."…³/'0+21B¯ÚBë#5Á>I0ë3)4!#"."…³ 576 ; ¯<¶³&Y¯<=4³>?SÜ
¯;Úq³
598-:
ó05…G;5@+A1Ÿ 8g742%5Ý74:…79FH¥>Oe§6¡¶¦>5…G":HXO§%¤N¥ 5NŸ:HXF.¤»26:_8;5NOŸ 8;:…79:HI>5Ÿ OS742%5Ý74FHGªH57ê§%O6[65NGVŸ G;GFH[6Ÿ F…74Ÿ :HO6=
)ŸL8B74265&[%5N¤NF<­Ó¤N:HO%8¸74F_O47.XZ:HGB79265S[%FH§6ªH29745…GÎOe§6¤N¥ 5NŸB+¢¯C!#"."N³= ; ¯¶³ÄŸL8B74265&¤…G;:H88Î8;5…¤79ŸL:HOÌXZ:_GB79265
I6FHGž74Ÿ ¤N§6¥ FHGTI%26:…74:_G;5NF_¤74Ÿ :HO®¯ WYŸÆ792S7426G5N8;2%:H¥L[DECFH³TF…774265I62%:…74:HOº5NO65…G;ª…­G¶=WY2%ŸL¥ 5HY¯<=4³>?
Ÿ 8742%5ÎI626:…79:HOºÍ%§MÁ¹[%5NO68ŸÆ7D­¹ŸLO¶7926505…O65NGª…­·ŸLO9745…G¸3FH¥>¦>5µ7DWÎ5…5NOD F_O6[IKJK>?Y=>I6G:[%§6¤N5…[¬¦9­ˆ79265
5N¥ 5N¤µ74G:HO¬¦J5NFH¡ÂWYŸ©742¶7926505…O6[Mè»IJ:HŸ O975NO%5NG;ªq­G9-Vû088;§6¡£Ÿ O6ª0742%F…77926505…¥L5…¤79G;:HO¬¦J5NF_¡Ÿ G;GFH[6Ÿ F…745…8
742%5
WY2%:H¥L5"FHG5NF=L«:HX742%5
79FHG;ª_574=Ÿ O974G:[6§%¤NŸ O6ª"79265"5N¥ 5N¤µ74G;:_OˆŸ O9745NO%8;Ÿ©7D­°¯ 74265"Oe§6¡¶¦>5…G:HXJ5N¥ 5N¤µ74G:HO68
IJ5NG"8;5…¤N:HO6[%³2M&NM¯4³VF_O6[¨¤…:HO935…G¸74Ÿ O6ªˆXZG;:H¡ì5…¥L5…¤79G;:HO68
74:£I62%:…74:HO%8
W05VWYG;٩745
Y¯4³O>?P' MNM¯<L 4³ QSR ¯9³O>?
¯¸¾_³
FHO6[¤N:_G;G;5…8;IJ:HO6[6¥©­
('P)7+¢¯C!#"."N³/'0+A1 MNM¯<L 4³ ¯Ú
ë'5Á>I0ë3)4!#"."…³ 596 ; ¯<¶³ QSR ¯4³O>?
¯_³
5 8-:
WY265…G;5=MNM¯<4³nŸ 8
74265êOe§6¡S¦J5NGÄ:HXg5…¥L5…¤79G;:HO68ĤNG:H8;8ŸLO6ªê74265êFHG5NFLÊIJ5NGn8;5N¤…:HO6[¨FHO6[ QR ¯<T9³"Ÿ 8
742%50Oe§6¡S¦J5NG:HXEI62%:…74:HO%8ÝIJ5NG§6O6Ÿ©75NO%5NG;ªq­·Ÿ O9745…G¸3FH¥JF…77926505…O65NGª…­öI6G:[%§6¤N5…[¬¦9­·:_O6505…¥L5…¤74G:HO
WYŸ©742.74265ê5NO%5NG;ªq­UYŸLOF£I6FHGž74Ÿ ¤N§6¥ FHG"¦6G;5…¡£8;8¸79G;FH2%¥L§6O%ªY74F_G;ªH5µ7=VS½V265Y5Á>IJ5NG;Ÿ ¡£5NO974F_¥¤…G;:H88Ä85N¤µ74Ÿ :HO68 ; ¯<Y³V¤NFHO¦>5êXZ:H§%O6[¨Ÿ OÇ¡£FMç:HG"I626:…79:HOe§6¤N¥ 5NF_GÄ[6Fq74F£¦6FH85N8SùÆýHú
WY26Ÿ ¥L5g79265V[6Ÿ ô>5…G;5…O479ŸLF_¥6I626:…79:HO.8;IJ5N¤µ74G§6¡ QR ¯4³‚¤…FHO.¦>5ݤNFH¥ ¤N§6¥ F…795N[£[6Ÿ G;5N¤µ74¥©­Ç¦9­S79265T¼¹UV/ÄË
¤N:[65ˆù©¿HúEXZ:HGVF[65N8ŸLG5N[£74FHGªH57=VÂ7426Ÿ ¤»ðeO65N88;W X[Z‚ä à\Z
Y
ÉÊ5¶26F<365SIJ5NG;XZ:_G;¡£5N[£74265Y¼¹UV/0ˍ¡£:[65N¥ Ÿ O6ªº:HX˜¦6G;5…¡£8;8¸79G;FH2%¥L§6O%ª–XZ:HGVFº857S:HXJ79§6O6ªH8ž745NO£74FHGªH5798
8;§%¦ç5N¤µ7074:FI6FHG;F_¥L¥ 5N¥¦J5NFH¡é:_X˜¡£:HO6:¤»26G:H¡£F…74Ÿ ¤¶5…¥L5…¤79G;:HO68BWYŸÆ792·5…O65NGªHŸL5…82SGFHO6ªHŸ O6ªXZG;:H¡þ¾Hñ
W 2 mm
Photons (10-2/per MeV/per electron)
100
Ee = 30 MeV
10
1
0.1
0.01
0
5
10
15
20
Photon energy (MeV)
25
30
‚Ÿ ªH§6G5ÇÚ]%Y½V265.¦6G;5…¡£8;8¸79G;FH2%¥L§6O%ª¨I62%:…74:HOÌ5…O65NGª…­ï8I>5…¤74G§6¡£-ˆ½V2%ŸL8Ÿ 8Ý74265.Ïe§6F_O479ŸÆ7D­ QSR ¯<=4³
¤NF_¥L¤…§6¥LFq745N[¦9­·79265.¼¹UV/ÄËí¤N:[65.XZ:HGB74265^_ñ…軼¹5µ, 5N¥ 5N¤µ74G:HO68Ÿ O6¤NŸ [65NO97ˆ:HOº79265.¾…軡£¡Ð74§%O6ªH8¸795NO
74F_G;ªH5µ74Target U-238
400
350
Cross section (mb)
300
_
250
200
150
100
50
0
6
8
10
12
14
Photon energy (MeV)
16
18
20
gŸLªH§%G;5¾%"½V265ê¤NG:H8;8n8;5…¤79ŸL:HO:HXÀ74265ˆ¯´±` Q ³VG;5…FH¤79ŸL:HOXZ:HGg79265"PDÕba4Ø Ÿ 8;:q74:HIJ5Ý74FHGªH579-
74:cHñ̼¹5,&-ݽFHG;ª_57480W05NG5–:HXV¾…è<¤N¡[6Ÿ FH¡£5745…G.[6Ÿ 8;ðe8£ñH-L¾74:¹ýH- ñÌ¡£¡ 7926Ÿ ¤»ð-ï½V265–Oe§6¡¶¦>5…G.:HX
I626:q74:HO68IJ5NG£ŸLO%¤NŸ [65NO97Ì5…¥L5…¤79G;:HO«W0FH88;FH¡£I6¥ 5N[ʟLOíڵ軼·5,)WYŸL[M792ÊI62%:…74:HOî5NO%5NG;ªq­í¦%ŸLO68Ÿ O68;Ÿ [65
8;5µ35…G;FH¥À¤N:_89dêŸ O9745…G¸3FH¥ 8¤…:HG;G5N8;IJ:HO6[%ŸLO6ªV74:V742%5nI%26:…74:_O5µÁ>ŸÆ7ÄFHO6ª_¥L5ed¦>5µ7DWÎ5…5NOˆñ?fE79:@gHñ?f‰WYŸÆ792ê79265
G;5…8;IJ5N¤µ7Ä79:074265êŸ O6¤NŸ [65NO97S5N¥ 5N¤µ74G;:_O¨[6Ÿ G;5…¤79ŸL:HO%-
É Ÿ©742F£¾…軡£¡ 74FHGªH579=74265êFHO%ªH§6¥ FHGVFH¤N¤…§6¡S§%¥LF…795N[
­>ŸL5…¥L[–:_XI626:…79:HO68WYŸ©742hjikc&¼¹5,íWÎFH8ÝXZ:H§6O6[¶79:&¦J52cH¿Û§6IS79:Hñ4fFHO6[lg_¾Û§6IS74:¶ýH¿?f-gÉÊ5
742%5NG;5…XZ:HG;5£I6G5N85NO97¶79265.[6Ÿ ô>5…G;5…O479ŸLF_¥5…O65NGª…­ï8I>5…¤74G§6¡ 8;§%¡¡£5…[Ó:<35…GYF_O6ªH¥ 5N8êXZG;:H¡ ñ?fž79:ý_¿?fÎFH8
F¼¹UV/0ËE軤…FH¥ ¤N§6¥ F…745…[ÌÏe§6FHO974Ÿ©7D­ ¯<=4³"826:<WYOÌXZ:HG"5Á>FH¡£I6¥ 5SŸ O‚Ÿ ªH-£ÚXZ:HG‚74265¶¾…軡£¡ö7926Ÿ ¤»ð
74§%O6ªH8¸795NO¨79FHG;ª_57êWYŸÆ792K'm_ñ¨QR ¼¹5µ,.-Cc7¬Ÿ 8Y§68;5…XZ§6¥79:¨¤…:H¡£I6FHG5ºI626:q74:HO–­>ŸL5…¥L[68SXZG;:H¡$3FHGŸL:_§68
74F_G;ªH5µ748N$WYo ŸÆ792S[6Ÿ ô>5…G;5…O47Ý5N¥ 5N¤µ74G:HO&5NO%5NG;ª_ŸL5…8n9=%Ÿ O"WY2%ŸL¤»2&¤…FH8;5WÎ58;2%:H§6¥ [&§68;5742%55…ô>5…¤74Ÿ©35I626:…79:HO
­>ŸL5…¥L[M R ¯<9³"Ÿ O4795NªHGF…745…[¨:<365NGAÐXZG;:H¡pECF='qcˆ¼·53¬79:r`s!t@'¾Hñ£¼¹5,u%
M R N<o ¯<9³' P QR ¯9³>v¶Ü
¯¸ý_³
a
½V265[cëê¾Hñ…è<¼¹5,)I62%:…74:HOºWYŸ O6[6:<W Ÿ 8Ý742%5.5NO65…G;ª…­ïGFHO6ªH50WY2%5NG;5Î79265.ü¶Ÿ FHO97[wŸ I6¥ :H¥L5.Ãn5N8:HO6FHO%¤N5
¯¸ü3wÃn³‚XZ:HGBI626:…79:HOe§6¤N¥ 5NF_G¤…G;:H8885N¤µ74Ÿ :HO68 ; ¯<Y³Ÿ 8B¤N:HO%¤N5NO979G;F…795N[¬XZ:HG
¡£:H8ž7Ä:HX>¡£Ÿ [6[6¥ 5ÄF_O6[ˆ2%5NF<3e­
¡£FH8;8£Oe§6¤…¥L5…ŸL-°É'5ǟ ¥L¥ §68ž74G;Fq745&7426Ÿ 8£¦9­Å5Á>FH¡£I6¥ 5¨Ÿ Ox‚ŸLª_-'¾XZ:HG074265£PDÕba4ØéŸ 8;:…79:HIJ5.79FHG;ª_57.WYŸ©742
:HO6¥©­&79265"¤NG;:_8;88;5N¤µ74Ÿ :HOXZ:HG‰74265¶¯²±B Q ³
G;5…FH¤79ŸL:_O¹¯ 74265¶¯´±`N¾ Q ³
FHO6[I626:q74:HÑ688;Ÿ :HOº¤»2%FHO6O65…¥L8FHG;5"O6:q7
Ÿ O6¤N¥ §6[65…[6³;-&RÝ5N¤NF_§68;5Ä7926Ÿ 8Îü=wà 8ž74G5NO6ª…792̤N:HO%¤N5NO979G;F…79ŸL:HO%=J742%5SŸ O4795NªHGFH¥gI%26:…74:_N$Oo ­>ŸL5…¥L[̦J5N¥ :<WþÙ
c¼¹5,&=WY2%ŸL¤»2«ŸL8YFH¦J:H§M7:HO65:HG[65NGê:HX¡£FHªHO6Ÿ©74§6[%5ˆ26Ÿ ªH265…G"7926FHO–74265έ>Ÿ 5N¥ [KM R ¯4³=[%:5…8¶O6:q7
¤N:_O479G;Ÿ ¦6§M795"79:79265êŸL8:…74:_I>5êI6G:[6§%¤74Ÿ :HO6½V265&O%5Áe707DW0:¬Ñ6ªH§%G;5N8=B‚Ÿ ªH-3ºFHO%[y‚Ÿ ªH-êýH=˜826:<WF¬8;Fq74§6GF…74Ÿ :HO·:_X‰74265¶5NôJ5N¤79ŸÆ365Ä­>ŸL5…¥L[zM R N<N<oo ¯<4³
WYŸ©7426Ÿ O·8535…G;FH¥¡£ŸL¥ ¥ ŸL¡£5795NG80:HXÀ74265V74§6O%ªH8¸795NO79FHG;ª_57¶FHO6[26:<WÂ742%5¶8F…74§6GF…745…[3FH¥ §65ê:HXnM R ¯<4³
[65…I>5…O6[68n:HO£79265ê5N¥ 5N¤µ74G;:_O¨5…O65NGª…­UYXZ:HGVF£¡£:HO6:¤»26G;:_¡Fq74Ÿ ¤¶5…¥L5…¤74G:HO¦>5…FH¡£ËBG;:[6§6¤…ŸLO6ªÄG;FH[%ŸL:HŸ 8;:q74:HIJ5N8ÀWYŸÆ792S¥ ŸLXZ5µ74Ÿ ¡5…8g:HO"74265:HG[65NG:HX%85365NG;F_¥%[6F<­>8V¯ž§68;Ÿ O6ª0Ÿ G;GFH[6Ÿ F…74Ÿ :HOV74Ÿ ¡£5N8
:HX˜FHO·:HG[65NGn:HX˜26:H§6G8;³n¡5…FHO68B7426F…7)4!#"."A{3{ÛÚêFHO6[FH¥ ¥L:<WY80§%8B79:ºIJ5NG;XZ:_G;¡ìFˆ8;5NGŸL5…805µÁ‰I%FHO68;Ÿ :HO
:HX%79265Î5Á>IJ:HO65…O479ŸLF_¥EXZ§6O6¤µ74Ÿ :HOǟLO–ABÏe-Y¯H³-gÉ'50¤NFHOS79265NO–5µÁ‰I%G;5N88e+21º7426G:H§6ªH2S79265Ρ£FH88B|!FHO6[
742%50¡£:H¥ FHGÝ¡£FH88~} :HX792650Ÿ 8;:…79:HIJ574F_G;ªH5µ7FHO6[ºŸLO974G:[%§6¤N57926502%FH¥LXrè<¥LŸ XZ5€ Ÿ O68ž745NF_[–:HX%74265Ä[65N¤…F<­
¤N:_O68¸79FHO97u)ˆ79:£:H¦M74F_ŸLO
 }| +2‚„ƒ M&N_¯L 4³ ! #"." ¥ O"¾ 596 ; ¯<Y³ QSR ¯9³O>?¶Ü
¯¸¿_³
½˜:£ªH5µ7V74265@…$†ˆ‡Š‰‹ŒŽ‰4‰C‹’‘‹!C“”]4‡jSù•V–tú˜—À¯¸¡£ª4™›š
ûœ59™ 8-26: ³;=WY26ŸL¤»2¨ŸL8V§%8;5N[¨ŸLOÇI6GFH¤79ŸL¤…5N=%W05ê5Á>I6G;5…8;8
½˜FH¦%¥L5ºÚ]%VUV:H¡£I6FHGŸL8:HO:HX˜¤…FH¥ ¤N§6¥ F…745…[·FHO%[¨5µÁ‰IJ5NGŸL¡£5…O479FH¥8;IJ5N¤…ŸLÑ6¤¶FH¤79ŸÆ3>Ÿ©7D­®G;F…795N8
CD8;:…79:HIJ5 bÃn 5NFH¤µ74Ÿ :HO ½ ?ž P =E2 A—¯¸¡£ª4™•š‚ûœ™L2%³.Ÿ s& Ÿ;=EðeRTÏ A—¯¸¡£ª4™•š‚ûœ™L2%³ N$tŠ¡ =ðeRTÏ Ãn5NXZ8¼¹:…èOggH¡ ? ¼¹:À¯²±B Q ³ ¢¢
¾H- ¾
H- ¾
ù›¢_ú
Øè<¾£ PDÕba Ø&¯´±` Q ³
Ú¤¢H¾
ñH-˜g£
څ- ñ
ù›£_ú
ËB§M軾¥¢ PDÕq× /0I¯²±` Q ³ ¾H-Lý_¿4™ څñT¦
H- ñ4™ څñ4§ Õ
ýH- ý4™vڅñ?§ Õ
ù›c_ú
742%505N¥ 5N¤µ74G:HO–¦>5…FH¡ÛŸLO9795NO68ŸÆ7D­¹ŸLOš/ ¯¨¢H-L¾qÁ
Úqñ ?cP I6FHGž74Ÿ ¤N¥ 5N8TIJ5NG8;5…¤N:HO6[–XZ:_GÎÚ!š/ij;=742%50Ÿ G;G;F_[6ŸLFq74Ÿ :HO
74Ÿ ¡£5êŸLO26:H§6G8"FHO6[.74265T74F_G;ªH5µ7Y¡F_8;8| Ÿ O¨¡£ª%
2©¯C|Iª^™Tš«™4¬³/' L¾Ü-™4ge}«™Àڅ­ ®bñ9¯?Ô"™T8/§ ­ FŠ? ¯ 5 6 ; ¯¶³ QR ¯<T9³>?SÜ
¯¢_³
5 8C:
0.7
Photons per electron
0.6
°
0.5
0.4
0.3
0.2
0.1
0
10
20
30
40
50
60
Electron energy (MeV)
70
80
90
‚Ÿ ªH§6G5H%V½V265ê5NôJ5N¤µ74Ÿ©35V­‰Ÿ 5N¥ [M R N<o ¯<4³V:HXI626:…79:HO68VŸ O[%5NIJ5NO6[65…O68;5¶:HX74265ÝɍèŠ74FHGªH57V7926ŸL¤»ðeO65…8;8
XZ:HGV5…¥L5…¤74G:HO68
WYŸÆ792£79265ê5NO6[tè»IJ:HŸLO97¶5NO%5NG;ªq­®:HX`_ñ¼·5,.Ee = 30 MeV
Photons per electron
0.25
±
0.2
0.15
0.1
0.05
0
0
0.5
1
1.5
2
2.5
W-target thickness (mm)
3
3.5
‚Ÿ ªH§6G5¶ý%0½V265S5…ô>5…¤74Ÿ©350­>Ÿ 5N¥ [GM R N$o ¯4³n:HX‚I62%:…74:HO%80Ÿ O·[65…I>5…O6[65NO%8;5.:HX>79265S5…¥L5…¤79G;:HO¹5…O6[Mè<I>:HŸ O97
5NO%5NG;ªq­U Ô XZ:HGg742%5VɍèŠ74FHGªH579-
W 2 mm
Photons (10-2/per MeV/per electron)
100
Ee = 15-30 MeV
10
1
0.1
0.01
0
5
10
15
20
25
30
Photon energy (MeV)
‚Ÿ ªH§6G5¢¿% ½V2%5°¦6G;5…¡88¸79G;FH26¥ §6O6ªÒI626:q74:HO 5…O65NGª…­ 8I>5…¤74G§6¡ QR ¯N]³¹¤NFH¥ ¤N§%¥LF…795N[ ¦9­í79265
¼¹UV/ÄˤN:[65£XZ:HG5N¥ 5N¤µ74G:HO68TWYŸÆ792Ç79265£5NO6[tè»IJ:HŸLO975…O65NGªHŸL5…8NS§6O%ŸLXZ:HG¡£¥Æ­ï[%ŸL8ž74G;Ÿ ¦6§M795N[«XZG;:H¡ څ¿
¼¹5µ3–74:[Hñ£¼¹5,&½V265VÏe§6FHO979ŸÆ79ŸL5…8€} ­ ®²¯ FHO6[œ ­ F³¯ ŸLO07926ŸL8
XZ:_G;¡S§%¥LFFHG5T[6Ÿ ¡£5NO68ŸL:HO%¥L5…8;8FH¥Æ7926:H§6ª_2&5Á>I6G5N8;85N[ˆŸLO.ªHGFH¡£8
FHO6[º26:H§6G8;=JFH8WYGŸÆ7745NOº5Á>I6¥ ŸL¤…ŸÆ79¥Æ­H-n½V2%5Î[6Ÿ ¡5…O68;Ÿ :HO68Ý:HX742%50¤NG:H8;88;5…¤74Ÿ :HO ; ¯¶³0¯¸265…G;5ğLO¬¦%FHG;O68³
FHO6[.742%5YF_G;5NF´Lí¯¸¤N¡êP4³"¡S§t74§6FH¥ ¥©­®¤NFHO6¤…5N¥ ½V265¬G5N8§6¥Æ798&XZ:HGY¤NFH¥ ¤N§%¥LF…795N[¢F_O6[¢5Á>IJ5NGŸL¡£5NO979FH¥TFH¤µ74Ÿ©3‰Ÿ©74Ÿ 5N8SG;F…795N8SF_G;58;26:<WYO°Ÿ O¢½˜F_¦6¥L5¹Ú…-®½V265
G;5…I>:_G¸745…[°Oe§6¡S¦J5NG8F_G;5ºXZ:_Gn742%5u|Iª#:_Xg74265zT”²µv‡Ž‹’…·¶4<¶!†ˆ‡…»-Óû0O°FHªHG5N5…¡5…O97.WYŸÆ7926ŸLOïF¹XZF_¤74:_G
:HXˆÚ…- ¿ï¤NFHOŦJ5º7426:H§%ªH297®8;F…79ŸL8XZFH¤79:HG¸­ÂŸLOÒF·3>ŸL5µW :HXY8;5µ35NGFH¥XZFH¤µ74:HG8SWY26ŸL¤»2Ò¡£F<­ ¦>5ÌI%G;5N85NO97
Ÿ O°5Á>I>5…G;Ÿ ¡£5NO9748£¦6§M7–O6:…7S79FHð_5…O°FH¤N¤…:H§6O97:HXVŸ O¢¤NF_¥L¤…§6¥LFq74Ÿ :HO68;-ïCDO¢I%FHG¸79ŸL¤…§6¥LF_G;=g742%5¶WÎ:_G;ðùgHú:HX
742%5S÷ê26FHGð_:<3°CDO68ž74Ÿ©74§M795&:HX‚ËB29­>8;Ÿ ¤N8êFHO6[·½˜5…¤»26O6:H¥ :Hª…­¢ŸLO6[%ŸL¤…F…745…8FºG;:_¥L5¶:HX‰74265SG;5NF_¤74Ÿ :HOﯸ¸O¹’ Q ³
WY265…O–79265&5…¥L5…¤74G:HO68FHG5SO6:q7£G;5…¡:<365N[XZG;:H¡ 742%5&¦>5…FH¡)FHO6[¹IJ5NO65µ74GF…745.Ÿ O974:¶79265Ä74F_G;ªH5µ7£§6O6[65…G
8¸79§6[M­H-'½V265Ç÷ê26FHG;ðM:<3ÅCDO68¸79ŸÆ79§M745Ç26F_[î[%535…¥L:_I>5…[#FHO%[îI%§M7ŸLO979:®:_I>5…G;F…79ŸL:HO¹79265–¾Hñ…è<ð4É ¦J5NFH¡
IJ:»W05NGYKŸLO%FH¤ˆXZ:_G¡5…[6Ÿ ¤NFH¥BŸ 8;:…79:HI>5…8¶I%G;:[6§6¤79ŸL:_O6-·½V2655N¥ 5N¤µ74G:HOÓ5…O65NGª…­î¤NFHO«¦>5Î3FHGŸL5…[ӟ OÇ79265
Ÿ O4795NGž3%F_¥:_Xڅñ…è<¾H¿Ç¼¹5, ð_5…5NI6Ÿ O6ªˆ79265£5NO65…G;ª…­#8I6G;5…FH[WYŸ©7426Ÿ O¥ ùLÚqñHúL-.É Ÿ©7427926Ÿ 8¶FH¤…¤N5…¥L5…G;F…79:HG
Ÿ©7SŸ 8nI>:H88;Ÿ ¦6¥ 5N=XZ:HG"5Á>FH¡£I6¥ 5N=74:£I6G:[6§%¤N5V74265Y¼¹:…èOggH¡ WYŸ©742¨FH¤79ŸÆ3>Ÿ©7D­®ýˆUV§%G;Ÿ 5¶IJ5NG"[6F<­®§68ŸLO6ªˆF
O6F…79§6G;F_¥E¼¹:74FHGªH579-
º æZ‚ånäGZnZ‚æ;â¨ß ßÌã â¨ßÌå äGZ‚æ;â¨ß
BË 29­‰8ŸL¤…FH¥g8ž74FHGž74§6I¨:HXJ79265YÑ6G;8ž7&8ž74FHªH5Y:HXÀ74265YCDÃÄAB/þ¯¸CDO9745…O68;5¶ÃÄAB8:HO6FHO6¤…5S/Ä5N§M79G;:HO68³Ä8:H§6G¤N5SXZ:_G
O65…§M74G:HOÇ79ŸL¡£5µè»:HXrè<Í6ŸLª_247ˆFHI%I6¥LŸ ¤NFq74Ÿ :HO68Y26FH[–74::Hð¹I6¥ FH¤N5£Ÿ O«ÈF_O§%FHG¸­î¾Hñ_ñg«ùLÚHÚqúL-ÇCc748YI6G5N8;5…O97¬¿Hñqè
¼¹5µ, ¥ ŸLO6F_¤Ä¤…FHOºFH¥ 8;:¶¦>5n§685N[¬FH8FY8;:H§6G¤N5Ä:HX742%5Ħ6G5N¡£8;8ž74GFH26¥ §6O6ª0±è»GF<­‰8I6G;:[6§6¤…5N[ˆ¦4­¨F¬Úµè»ð9É
5N¥ 5N¤µ74G:HOˆ¦J5NF_¡-Ý16I>5…¤NŸ Ñ6¤N8:HX7426Ÿ 8B¥LŸ O6FH¤"Ÿ 8
Fê¦6G;:HF_[5…¥L5…¤79G;:HOˆ5NO65…G;ª…­Ç8I6G;5…FH[[6§65‚74:êFê26Ÿ ªH2£I6§6¥ 8;5
¤N§%G;G;5…O97Ç¥L:_FH[6Ÿ O6ªH-ËBG;5N¥ Ÿ ¡Ÿ O6FHGž­'8ž74§6[t­ ù ÚHڅúŸ O6[6Ÿ ¤NF…795º8;5µ35…G;FH¥I>:H88;Ÿ ¦6¥ 5¬8;26F_I>5…8&:HX˜79265º5…¥L5…¤74G:HO
8;IJ5N¤µ74GF¬[65NIJ5NO%[6ŸLO%ª¬:HO.74265¶FH¤N¤…5N¥ 5NG;Fq74Ÿ :HO¹G;5…ªHŸ ¡5…-CDO·:HG[65NG
74:5N8ž74Ÿ ¡£F…745&2%:»Wí7426Ÿ 80XZ5…F…74§6G5"WYŸ ¥ ¥
Ÿ O6Í6§65…O6¤N5
74265"Ÿ 8;:…79:HIJ5nI%G;:[6§6¤79ŸL:_OW05nI>5…G;XZ:HG¡5…[ˆ¤…FH¥ ¤N§6¥ F…74Ÿ :HO68B:HXJ¦6G5N¡£8;8ž74G;F_26¥L§%O6ªS:HXJ5N¥ 5N¤µ74G:HO68
WYŸ©74279265ê5NO6[tè»IJ:HŸLO97S5NO65…G;ªHŸ 5N8ħ6O6Ÿ XZ:HG;¡£¥©­®[6Ÿ 8¸74GŸL¦%§M745…[·XZG;:_¡Ú…¿¼¹53–79:Hñ¼¹5µ,.-½V265YG;5N8§6¥©7&Ÿ 8
8;2%:»WYOïŸ O«‚Ÿ ªH-¢¿H-°UV:H¡£I6F_G;Ÿ O6ªºWYŸÆ792«‚Ÿ ªH-ÅÚYW05¬¤N:HO%¤N¥ §6[65S742%F…7&742%5¬5NôJ5N¤µ74Ÿ©35«¯¸Ÿ O¨742%5¬G;FHO%ªH5
:HXc…è<¾Hñ–¼¹5,&³êI626:…79:HO¬­‰Ÿ 5N¥ [®ŸL8G5N[6§6¤…5N[«¦4­°F–XZFH¤79:HG:HXBFH¦J:H§M7£¾H-ºû ¥L:H88:HXFH¦>:_§M7Î742%58FH¡£5
XZFH¤µ74:HG‚Ÿ O0742%5˜­>ŸL5…¥L[:HXG;F_[6ŸL:_ŸL8:…74:HIJ5N8
¤…FHO.FH¥©WÎF<­>8B¦>5ݤN:H¡£IJ5NO68F…745…[¦9­¬FHO.ŸLO%¤NG;5…FH8;5":HX_79265g74F_G;ªH5µ7
742%ŸL¤»ðeO65…8;80F_O6[»—H:HGݟLO6¤…G;5…FH8;5ê:HX74265¦J5NF_¡þ5NO%5NG;ªq­-‚É'5F_¥L8:¤…:HO6¤…¥L§6[%5"7926F…7ê:H§%GVG;5N8§6¥©748‚3FH¥LŸ [6F…795
742%5Y¼·UV/0ˍ¤N:[65êXZ:HGVFK¼µ¡£5N[%ŸL¤…FH¥¾½FHI6I%¥LŸ ¤NF…79ŸL:_O6WYX[¿]X.áSX.ßÌåX[Z
څ-¢óÄ-ÆÉ -÷ê:¤»26=Vȝ-©É -ݼ·:…74ø…=¼µRTG;5…¡£8;8¸79G;FH2%¥L§6O%ª®¤…G;:H88&8;5…¤79ŸL:HOïXZ:HG¡S§6¥ FH8&F_O6[°G;5…¥LF…795N[°[6Fq74F½H=
ÀA‡‘vÁ€Â¶Ã4ÁŽÄÅ4“·…·Ár=ˆÆ`Çe=gH¾Hñ¨¯;Ú¤gH¿gH³¾H-VûÄ¥L5µÁy‚-JRTŸ 5N¥ FMç5WY=e¼µËB¥L§6GFH¥‰F_O6[–¡S§6¥©74Ÿ I6¥ 58;¡£FH¥ ¥Æè<FHO6ªH¥ 508¤NF…7745…G;Ÿ O6ª£XZG;:H¡ÛF&8¤NG;5…5NO65…[¨Ãn§M79265NGžè
XZ:HG[¤…G;:H88Ä85N¤µ74Ÿ :HO»½H=SÈeɉÊCÁ\Ë&Ìͅ·-”³ÉvÎDÁ€ÂK‡CÅ7¶ÃT…HÏÅ=,Ð9Ñ>=¾H¿£¨¯;Ú]g¥gHýH³;H-RTG;§%¤N5
û0-¥JF_[6[65Nª_:HOê57FH¥ -L=B¼DRT5NO6¤»2%¡F_G;ðeŸLO%ª0:HXe¼¹:HO9795UVF_G;¥ :n8ŸL¡¶§6¥ F…74Ÿ :HO68:HXe¦6G5N¡£8;8ž74G;F_26¥L§%O6ª
XZG;:_¡ 742%ŸL¤»ðS79FHG;ªH5µ748"F…7YGFH[6Ÿ :…74265…G;FHI9­®5…O65NGªHŸL5…8½H=Ò‡ŠÃ4Á€ÄÅ4“Ó…·Ár=ˆÆ9Ô`ÕÇÖ9×a=Eý_ñc¯¸¾Hñ_ñcH³;ýH-V¼¹:_8;¤N:<WÛ1t74F…795YØÄO6Ÿ©35NG8;Ÿ©7D­=H¼µUV5NO979G;§6¡éXZ:HGVI%26:…74:_O§%¤N¥ 5NFHGn5Á>IJ5NG;Ÿ ¡£5NO9748Ä[6F…79F½H=
297;79I»%¾—¥—H¤N[6XZ5…-L8ŸLO%I6-L¡£8§6-LG§»—H85NG¸3>Ÿ ¤N5…8—H1?ªHØ [%G;8;5…FHG;¤»2- 2974¡£¥
¿H-I‚-gRTG;Ÿ 5N8¡5…ŸL8ž745…G;=Ý5…[6- =[¼µ¼·UV/0Ë ëìFǪH5…O65NGFH¥
¼¹:HO9745£UVFHG¥L:OMè<I6FHG¸79ŸL¤…¥L5Î79G;FHO68I>:_G¸7¤N:[65…=
,n5NG8;Ÿ :HOýH¤T½H=KûBètÚ]£_ñg…軼·=‰K:H8"û0¥ FH¡£:H8"/0F…79ŸL:_O6FH¥EKFH¦J:HG;Fq74:HGž­=EK:H8VûÄ¥LFH¡£:H8¶¯ž¾HñHñHñH³¢H-û0-©,.-ê16F_¦>5…¥Lõ O6Ÿ ð_:<3>=ºÿê-¾w-êr ¼¹F_8;¥ :»3>=K-LüY-ê¼¹:H¥ :HðaFHO6:<3FHb=. ¼¹-©,.-Yü¶§68ž74:<3FH=£16- /0-3w¡Ÿ©74GŸL5µ3>=
¼µËBG;5…I6FHGF…74Ÿ :HOÌ:HXÔDÔ4¼¹:ÇFHO6[–ÔDÔ ½V¤.¦9­¹742%5&I626:…79:HOe§6¤N¥ 5NF_GS? ¼·:À¯´±= O6³ÎG;5…FH¤79ŸL:_O»½H=/ÀA4ÃT‹!¶‰Å7‡Î^Ù
‹’…·C”¤“t=ˆÚ9Ð`Õ&Û9×a=BÚ]gÀÚ£¯ž¾HñHñ¢H³£H-"û0-©,.-1%FH¦>5…¥Lõ O6Ÿ ð_:<3>=˜ÿê-˜w-E¼¹FH8¥L:<3>=¼¹-©,.-ü¶§%8¸74:<3FH=ûÄ-LüY-ERT5…¥L:<WY=16- /0-Sw¡£ŸÆ79G;Ÿ 53>=œ¼µËBG;5…I6FHG;Fqè
74Ÿ :HO¨:HX‰PDÕq×;Ø ¦9­–74265YI626:…79:HOe§6¤N¥ 5NF_GÝPDÕba4Ø.¯²±=LO6³nG;5…FH¤79ŸL:_O·:HO¨FHO¨5…¥L5…¤79G;:HO¹F_¤N¤N5…¥L5…G;F…79:HGn¡Ÿ ¤NG:…74G:HO
¼¹½gè<¾H¿½H=ÀA4ÃT‹!¶‰Å7‡Î^‹’…·C”³“M=,Ú9Ð`Õ&Û9×a=BÚ¤c¢¨¯¸¾HñHñ¥¢H³;cH-Y16- /0-Üw¡Ÿ©74GŸL5µ3>=gÿê-¾w-¼¹FH8¥L:<3>=gûÄ-Æ,&-˜1%FH¦>5…¥Lõ O6Ÿ ð_:<3>=
û0- ü¶-RT5…¥L:<3>=3¼µËBG5NI6FHGF…74Ÿ :HO¹:_XEPDÕDÖ4ËB§Ì¦4­
742%5 PDÕq× /ÄI¯´±= O6³"G;5…FH¤79ŸL:HO%=SÀ24ÃT‹!¶TÝÅ4‹’Î^‹’“„N=7Ú9Ö`Õ&Ñ9×a=E¿¥¨¯;Ú]gg¥cH³;gH-VûÄ-L/Ä-w:<3‰¦%O4­6FH=/0- ˉ-wŸ ðeŸÆ­H=¼¹- CD-˟ ¥ ŸLIJ5NO6ðM:H=»Þn§6-˜w-E½˜§%G;=,&-LK-Ø3FHG:<3‰=e¼µ/05µW ½5N¤»26O6:_¥L:Hªq­
:HX74265ê½V¤µèŠggH¡þËG:[%§6¤79ŸL:HO„½H=2ßݔ]T‹’Ì͋!TÌáà?¶TÉv”³Ì܏4ÊS¶!âãÀA4ÃT‹!¶4ÊC¶µ“M=E/Ä:H-¶Ú…=E¾¨¯Ú]gggH³Ú…ñH-IÞn§6-˜w-B½˜§6G=¼µKŸ O65NFHG¶5N¥ 5N¤µ74G;:_O°FH¤N¤…5N¥ 5NG;Fq74:HG¶XZ:HGn79265º¡£5N[%ŸL¤…FH¥ÝŸ 8;:…79:HIJ5N8SI%G;:[6§6¤79ŸL:_O»½H=TËBG;:qè
¤N5…5N[6Ÿ O6ª:HX£…742AB§6G:HI>5…FHOËgFHGž74Ÿ ¤N¥ 5£û0¤N¤…5N¥ 5NGF…74:HGUV:_O6XZ5NG5NO6¤…5äÄå3æBÙbç7è4è4èTé҆BÁ^ç7ê4ë4èN=J,.Ÿ 5NO6O6F_=
û0§%8¸74GŸLF_=¾HñHñHñHÚHڅ-ï,.- /0-"162935µ748:»3Â57·FH¥ -L=h¼µËB24­>8ŸL¤…FH¥Ä8ž74FHGž74§6I#:HX79265¨Ñ%G;8¸7·8¸79FHªH5:HX0CDÃnAB/ XZF_¤NŸ ¥LŸ©7D­,½H=œì,&C;C
CDO9745…G;O6F…79ŸL:_O6FH¥
165…¡Ÿ O6FHGê:HO®CDO9745…G;FH¤µ74Ÿ :HO«:_X/Ä5N§M79G;:HO68TWYŸ©742®/0§6¤…¥L5…ŸL=ËíÍË&ÈAÈeÙ¤î4ï´å3ð…·C”]4‰-…ŠéãäAñTÙ
ç7è4è4òTÙ¤ê4èN=‰I%-n¿¥cH=Eȝ:HŸ O97SCDO%8¸74Ÿ©74§t745YXZ:HGV/0§6¤…¥L5…FHG"ÃÄ5…8;5…FHG;¤»26=Òw§6¦%O6FH=¾HñHñ¥gH-