(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 7.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 72420, 1546] NotebookOptionsPosition[ 69695, 1448] NotebookOutlinePosition[ 70105, 1464] CellTagsIndexPosition[ 70062, 1461] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["Tutorial on Scattering Physics", "Title", CellChangeTimes->{{3.472202970426105*^9, 3.4722029826144543`*^9}}], Cell[TextData[{ "Scattering off a 3D spherically symmetric potential in the ", StyleBox["s", FontSlant->"Italic"], "-wave collision regime" }], "Subtitle", CellChangeTimes->{{3.472202986847107*^9, 3.472203006893474*^9}}], Cell[CellGroupData[{ Cell["General Setup", "Section", CellChangeTimes->{{3.4722038105892973`*^9, 3.472203821930862*^9}}], Cell[CellGroupData[{ Cell["Make font on plots a bit bigger", "Subsubsection", CellChangeTimes->{{3.4722038280832644`*^9, 3.4722038472819033`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"SetOptions", "[", RowBox[{"Plot", ",", " ", RowBox[{"BaseStyle", " ", "->", " ", RowBox[{"{", RowBox[{ RowBox[{"FontFamily", " ", "->", " ", "\"\\""}], ",", " ", RowBox[{"FontSize", " ", "->", " ", "14"}]}], "}"}]}]}], "]"}], ";"}]], "Input", CellChangeTimes->{{3.472203824819725*^9, 3.472203867641654*^9}, { 3.47222598094627*^9, 3.472225981147769*^9}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Setup of Parameters for Box Potential", "Section", CellChangeTimes->{{3.472203009502245*^9, 3.4722030463242903`*^9}}], Cell[CellGroupData[{ Cell["System Parameters", "Subsection", CellChangeTimes->{{3.472203366546508*^9, 3.472203370201877*^9}}], Cell[CellGroupData[{ Cell["\<\ Radius of potential (here set to 1 \[Micro]m)\ \>", "Subsubsection", CellChangeTimes->{{3.472203067885144*^9, 3.472203071131837*^9}, { 3.472203263789631*^9, 3.472203272948977*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"r0", ":=", SuperscriptBox["10", RowBox[{"-", "6"}]]}], ";"}]], "Input", CellChangeTimes->{{3.472183961787767*^9, 3.472183970566271*^9}}] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "Potential depth (attractive potential) ", Cell[BoxData[ FormBox[ RowBox[{ SubscriptBox["E", "0"], "=", RowBox[{"-", FractionBox[ RowBox[{ SuperscriptBox["hbar", "2"], SuperscriptBox["k0", "2"]}], RowBox[{"2", "m"}]]}]}], TraditionalForm]], "None", FormatType->"TraditionalForm"] }], "Subsubsection", CellChangeTimes->{{3.472203076804104*^9, 3.472203102514536*^9}, { 3.472203144701137*^9, 3.472203207141362*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"k0", ":=", FractionBox["\[Pi]", "r0"]}], ";"}]], "Input", CellChangeTimes->{{3.4721845389064007`*^9, 3.47218457223452*^9}, { 3.472185560953815*^9, 3.4721855611133738`*^9}, {3.472185840946266*^9, 3.4721858583191853`*^9}, {3.472186305130147*^9, 3.472186311063815*^9}, { 3.472188447634137*^9, 3.4721884510716953`*^9}, 3.472188867480177*^9, 3.472203251183502*^9, 3.472228153433476*^9}] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "Wavevector of incoming plane wave (determined by energy of particle) ", Cell[BoxData[ FormBox[ RowBox[{"E", "=", FractionBox[ RowBox[{ SuperscriptBox["hbar", "2"], SuperscriptBox["k", "2"]}], RowBox[{"2", "m"}]]}], TraditionalForm]], "None"] }], "Subsubsection", CellChangeTimes->{{3.4722032171367292`*^9, 3.4722032458459044`*^9}, { 3.472203301494193*^9, 3.472203309919332*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"k", ":=", RowBox[{"0.05", "*", "k0"}]}], ";"}]], "Input", CellChangeTimes->{{3.472184588596615*^9, 3.472184621378902*^9}, { 3.472184985846957*^9, 3.4721849868286133`*^9}, {3.47218552602669*^9, 3.472185526794777*^9}, 3.472185586080613*^9, 3.472186036730908*^9, { 3.472186449868618*^9, 3.472186470346231*^9}, {3.472186502155581*^9, 3.472186503425126*^9}, {3.472186543162137*^9, 3.472186543279724*^9}, { 3.472188418458747*^9, 3.4721884185355864`*^9}, {3.472188455107733*^9, 3.4721884552390614`*^9}, {3.472211279771822*^9, 3.4722112798819513`*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["Wavevector of wave inside potential well", "Subsubsection", CellChangeTimes->{{3.472203314772174*^9, 3.472203326187347*^9}}], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"kplus", "[", RowBox[{"k_", ",", "k0_"}], "]"}], ":=", SqrtBox[ RowBox[{ SuperscriptBox["k", "2"], "+", SuperscriptBox["k0", "2"]}]]}], ";"}]], "Input", CellChangeTimes->{{3.472183543620707*^9, 3.4721836078197107`*^9}, { 3.472183949048378*^9, 3.472183958839422*^9}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Wavefunction inside potential well (s-wave scattering)", "Subsection", CellChangeTimes->{{3.472203344602955*^9, 3.4722033557222424`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"ChiIn", "[", RowBox[{"k_", ",", "k0_", ",", "r_"}], "]"}], ":=", " ", RowBox[{"Sin", "[", RowBox[{ RowBox[{"kplus", "[", RowBox[{"k", ",", "k0"}], "]"}], " ", "r"}], "]"}]}], ";"}]], "Input", CellChangeTimes->{{3.472183639675737*^9, 3.472183708316799*^9}, { 3.472184441943719*^9, 3.472184445126837*^9}, {3.4721889534156322`*^9, 3.4721889665345907`*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["Wavefunction outside potential well (s-wave scattering)", "Subsection", CellChangeTimes->{{3.4722033590578537`*^9, 3.472203385993222*^9}}], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"ChiOut", "[", RowBox[{"k_", ",", "delta_", ",", "r_", ",", "r0_", ",", "k0_"}], "]"}], ":=", RowBox[{ FractionBox[ RowBox[{"Sin", "[", RowBox[{ RowBox[{"kplus", "[", RowBox[{"k", ",", "k0"}], "]"}], " ", "r0"}], "]"}], RowBox[{"Sin", "[", RowBox[{ RowBox[{"k", " ", "r0"}], " ", "+", " ", "delta"}], "]"}]], " ", RowBox[{"Sin", "[", RowBox[{ RowBox[{"k", " ", "r"}], " ", "+", " ", "delta"}], "]"}]}]}], ";"}]], "Input", CellChangeTimes->{{3.472183710169305*^9, 3.472183747870387*^9}, { 3.472184329109552*^9, 3.4721844578882847`*^9}, {3.4721852461331387`*^9, 3.472185253796788*^9}, {3.472185449049366*^9, 3.472185449688324*^9}, 3.472186167224028*^9, 3.472186388305113*^9, {3.472188922138322*^9, 3.472188922691265*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["Define Total Wavefunction", "Subsection", CellChangeTimes->{{3.47221111050206*^9, 3.4722111212374763`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"Chi", "[", RowBox[{"k_", ",", "k0_", ",", "r0_", ",", "r_"}], "]"}], ":=", RowBox[{"If", "[", RowBox[{ RowBox[{"r", "<", "r0"}], ",", RowBox[{"ChiIn", "[", RowBox[{"k", ",", "k0", ",", "r"}], "]"}], ",", RowBox[{"ChiOut", "[", RowBox[{"k", ",", RowBox[{"Delta", "[", RowBox[{"k", ",", RowBox[{"ascatt", "[", RowBox[{"k0", ",", "r0"}], "]"}]}], "]"}], ",", "r", ",", "r0", ",", "k0"}], "]"}]}], "]"}]}], ";"}]], "Input", CellChangeTimes->{{3.472210761904554*^9, 3.47221076582663*^9}, { 3.47221097949161*^9, 3.4722111080984*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Scattering Length (depending on potential depth and potential range)\ \>", "Subsection", CellChangeTimes->{{3.472203448688889*^9, 3.4722034862381477`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ RowBox[{"ascatt", "[", RowBox[{"k0_", ",", "r0_"}], "]"}], ":=", " ", RowBox[{"r0", " ", RowBox[{"(", RowBox[{"1", "-", " ", RowBox[{ RowBox[{"(", FractionBox["1", RowBox[{"k0", " ", "r0"}]], ")"}], RowBox[{"Tan", "[", RowBox[{"k0", " ", "r0"}], "]"}]}]}], ")"}]}]}], ";"}], " "}]], "Input", CellChangeTimes->{{3.47218379420339*^9, 3.4721838525897512`*^9}, { 3.4721882686899233`*^9, 3.472188308813587*^9}}], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"ascatt", "[", "k0r0_", "]"}], ":=", RowBox[{"(", RowBox[{"1", "-", " ", RowBox[{ RowBox[{"(", FractionBox["1", "k0r0"], ")"}], RowBox[{"Tan", "[", "k0r0", "]"}]}]}], ")"}]}], ";"}]], "Input", CellChangeTimes->{{3.47220390572104*^9, 3.472203926643084*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{"ascatt", "[", RowBox[{"r0k0", "*", "\[Pi]"}], "]"}], ",", RowBox[{"{", RowBox[{"r0k0", ",", "0", ",", "3"}], "}"}], ",", " ", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"FrameLabel", "\[Rule]", RowBox[{"{", RowBox[{ "\"\<\!\(\*SubscriptBox[\(k\), \(0\)]\)\!\(\*SubscriptBox[\(r\), \ \(0\)]\)(\[Pi])\>\"", ",", "\"\\""}], "}"}]}], ",", RowBox[{"PlotRange", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"-", "5"}], " ", ",", " ", "10"}], " ", "}"}]}], ",", RowBox[{"PlotPoints", "\[Rule]", "50"}]}], "]"}]], "Input", CellChangeTimes->{{3.4721839798528223`*^9, 3.472184131362524*^9}, { 3.4722039492993402`*^9, 3.472203980880558*^9}, {3.472204044927442*^9, 3.4722040831495523`*^9}, {3.472204140595211*^9, 3.472204141323852*^9}, { 3.472204272776309*^9, 3.4722043004714823`*^9}}], Cell[BoxData[ GraphicsBox[{{}, {}, {Hue[0.67, 0.6, 0.6], LineBox[CompressedData[" 1:eJwd1nk41dkfB/CvXWm52WmTRGqyNlKN+6FEZMvSyBaFRJFqJGnckUq2hDAi qcbORLaQz9dOhGu597qXki2ZspOG+N35nec5z3lez/s55/xxnnPOZ8dZH0s3 XoIgSrj9v3HxhHeKhc9lKvFfo4m8ueuqtLtd0QwIItGqybGx6t3EsGekohPX gW99HT9V5UhwnvYmu3OtkShp9G/V1KujERcVvbkeORLoKISyyoyKVeYVIHRl N+/SE0Ud/zD15mQ/bv61N9xIFp0bqRkxLgFcm1bxDe/AYMnZLQ6KvwNBUm7Z OilhZ6FVc8w8jWudh52x+9CVvS/kGzMYiIEeJb0jGjjPIwwO5SFAWOj8+EVa C+8qD34nk+8CQWkYGD1xCKVOVhbtCgoFIvrOR6N+Kmb6x/uEuYQB4bzKe3BU D1sajUesFKOAsH1ss/OsIeZfF7Vw4I8G4vh94VB3Y7weHpQXNc91Il3jy5+m KPzqtMcsMwYIcZ74cQNL7GhoqN/VHAsE7ZiylpI1/snW3GlbHgfEoniH2PZT uId3w/vK5Hju+g0uSTZ2OCNx8/BkZAIQRQxvszgHrFAeS9wRlAhEqEx39rgT mpyssbrrkgRERDv90KQL+jz1azZXfAJEdoJkqO951C4aUgyWSgUiV3Tdx0kP JFx3H7HjfwpExw+PPQGe2Hz9UWrEPNe0UfaTwktol+pjN818xt1/MKPu9BWk KiveD7N4DkRNUcbk8aso/6qvdGcz1wRVaBf1Gv7TYCRxqvwFEJNiWq8P+WHg xM6O8uR0IHbM/twVGIDO/uwVK4kMINrMnyUn30R93of7vkZyTXnYeLcmENdL roRtD8oEYux1frNcED7RYR0LcckGWmWJT6FYMFZHRFSYKuYDLWRGn+flPawa 720VycoHouf4HuXgUKw8rvS+ee/fQKNF7Vhvex/teV2I59IvgfaHyVbxjeFo U7Ukv31bARCfEzZdyo5CYy11DynlV0Dun6v3M4nF4yPMy36er0D3/euuzd2x aBj3+42enFdAnAjNK3WMQ/2ZlrBYlSKgnY/+yvZ7hNR897yN+4tBV8renq86 ATUVk2eEoBR04/oWYkqSUaPnyJI7rRSIIZFj4U4pqBbyma+hmmupU0FJwk9Q ZVBLIkS/DIhMG47guVTc/YR+gDB+Dc63vEJypdNwi6TQrUXrChiw1HsgtPkF ytbn3fk1vgIIxhcDU9oLlLlmHVXCrADnrPTqwtEXKNmZlnrNrhJ0darKBkv+ QkrULzVTZ96As5Fv96prBgoIXhH67IngrC6qdv97No4ZBW2czUAYmBp7GHIh B99GRkj9GEagGTxuiGbnYGNYV2yoKglPc8HrI+ZiuOjE8+QsrodH5yMS8lFc fmddXUo1DBjn52pSC1CgTrnJqLIapmwm9cSCCnDBTa21jV0NFlalfffIAmRl 6XSzpGog+rLhc81jhZiibjv85WENUGw2xOTbvEJFvUh+ibu1QGFEmvPHFaPU UKxw0guuq0+pPH9fjMJ3ktZtr60FtXCq66hyCY43ZYgrE3Xc+7lG0qmmBP+2 qFHQCeA6nSqqvlSK2s7f9N2864Fyfeesa2Q5GgW53Ck+1QiZKwbqrttI1HhQ bZB2rRGaHs0m7DMjcUvqDuHImEYgfJRaT/9O4lTVxzDXtkZ4qrknvv8DifEr LtFiBk3gbFMvkJlRjcO3zj72/bkZ1Iqm9y8Z12JbZI2Do1UzdLi8qDP/oxbL UuS3Gfk2g67kjb3iZbUY/mbwqVweN+dLkZtSrEONH2fT2xXegn+JOblhbT3S As8V7BNvAYudJvPVow3oGVF7RUajBVid53zvKTSidfLO/QIWLdAkrUq2nm1E pcqhkr7wFrC9Zm3GGWjEtqVzleF8raC78tF891ATbrnp2vh5phWkaz0tonla sPSGW/9f9DbQllcN/pbfjulUL6bsTBuYzMg18fF1YDyfL/2BaDsUHTZTn1bp QL/IwPobVu0wQLdLJkI7UCstNs+0px34e6nzm4CO9sMDVQEXO6CMXy53Y00n djYMHS4O7IDLU5v33JrrROOs0bLJiA7gV1GhuCp14SHvL4Wuedy8QofxPKoL ZRe/pZtNdICckfe8+LluZItsfCB/mQ77xw+Pyu1ioOXEpnWONDoIr3CMP5xh 4NsO8fsJ0XTIvR3ws/pjBpY/kr29roAOmbGPVRPEmJi0XfH6wjQdQo8uZT0T YaGdps6Zt1c7oY/x/UKULBt77bxUr1zvgrjC8Wv5de8xbNDwYsLdLqBZ2/B2 Uj7gIU+FrMpHXRAaVzBT6fgBk2/0ywsVdQG/R5jB3PcP6JxoLpk81QUNmqs+ W58M4KcezR/1F7ohomug7rf5j5joSDn0j383iPv0Z9yUH+S+J1/8KKHdEBPo 57RqPojZc39N2aV3w5E3N4VDcwfRW0x6eHKwG+LYzpMMryGct1h+K+PQA870 z8M2AiOYzmIJgVcPTIiIaBw8PIKnnIv1XQN6QHpp4WWV7wiW+XhX5Sf2wFqP tdoVAyMYGDVQcLSnBxSvOmS9bRhFvta6xEtmDFgbYvhptXgMi6zSemIcGcDY q2Z89dsYunJuiZZdZACZ57BSefAzNoxrRfCGM6DTOMJyiPyMYWuyghIaGaCb sk59unccNxlGulfrMmGQx91/6+GvqJ9VCXtPMmF/FZtvOOYr+ot8kX7kwgTX mTskz5evONBu3OIRzIREduQbl2cT+NJWWI1Sx4QObe1/TChTOFx+YE1ANxME +fRhVW8KpbeeHxwaZsIvOarngq5NIe1jfVypAAsUSnPfL3Om0MLz9ncnQxZ4 P/TXoBVPY0hrYWfTrywI674cozkxjWUqgzkaHizoDFKqH1CaQblZXSfB+ywo vOZlcuTJDE7dXKnJe8uCYLlls8GEWYyOvBGxbNoLhOTca7/6eaybzHRzd+oF jay0lxabFnDxJIva4d0LEwGprGynBXSWPDD9/EEv+Kf7RqxfWUC11DmbE/Re sPvGbPtksYiuPAqqxR97YX9R7bvN2YuYeM5KePtMLwSXpFVqC3xHYndh+Ywo G35SN2y5WP0dO176bE+yZoP0Own/NKsl5BdLXeRzY8MeR6Ok5TdLqP1bG/3S b2w4/s3KpmvPMj49uC9EL54NlqnhdNN1P/ByzfjYGJMNi9UjtvumV/CFgmyN 5Rib+18eOy1xZRVZd40eVy6ygTzaXWeysIq6JzJNo2U4QDovuyeEcKukbrfC A/Yc2GRgcds1n4fU/ao3bu3FgTi7/oTkZR7ysuA2+Ss3OfCHIFEgYMpL0rUZ D3Mfc+DWXJZTyxwvyWtZ2NycwwHJk+dz7E34SA2vKJ5PFRzQurT1WUg6HxmT YuC7o48DVfw3qmXO8ZM1JfJZ1C8cOHGsQr2xnp+cbV8ZsF/mcM/XVDF6rwBp zVtqEb+lDy6UqUhs5BEkJc4rqYk49oGHXrRYNEuINKDxeey+1AcaVP9xtq0w 6ffnh9Rjt/pAu/WlbG2/MMloSdhIS+kDxoZRiasLa0jBkauGKXl9ELHmqUJL 2FrywIp5UPmbPlj7QFpkUEGETFQTnpzr7wOK2ZmxfK91ZJPRsKLoBHf+Dz6L 3TLrycWzpJPqSh9Yq6UsjL1bT55+5N92YVs/qPx9ym23+UYyLN9a8J5KPwwW PLS030AhyxvVqC+o/ZAqktTEuEEhZf8dy3vv1A/zM/rP9Z03kcZi9SNL3v3w fnpU8ztnExnwU9pWmaB+yC6ojhtzFCU5TqcjrVL7YWkH9ewVPzEygLfUfTKv H/5fTxPi5P8A7wDI4Q== "]], LineBox[CompressedData[" 1:eJwtV3s41GvUHdeGknuFUqSU6CRSVNav4rjUQRK6SYkoRVLJQXShlJTilBRJ SS6nVFJiBp2ShES5VMzVjEsxt18YfPN9z7f/eZ/1PHvvd/+x17PWNtob5hko T5GFHIXyv6+CW/esq497QPm/MCGmP3/nVC/DC2Kf7X04Mp/YcD13g1t5DyaD LeuLVswnoo7GooXWg25+3ie1BGOiyNN3tfe7HniqGOZP7zQiGJZWKzsbe/Cw 8g9DKxgRrkO8pczvPXjNtaonF80j4ppqzYI4PZg7oFaj7jOXeFpyZ2HfQA/8 /hmImh1qSMw+5GUoGOvB+Jv7ts702YTHpj/0jyswsE+raiMpNSDOLVGdMarK wMWG7Zr5DgbETz5NTV6fAS6/g3VmWI8wfp+pkmjEgOTuF+mirXqEz8NjSqqL Gbib1S8pp88i6EFLxjVXMXDO9GSte/FMQuyoPJIOBkybqUZeFjMJswUMkZ4T A2qOGRtXP51BXGNlDBh5M3DB9dZHkyZdoq7mCO/+LgaUjib1HNunS0jvbmIv DmSgbHPIQccJHSLIX/6bZSQDPQ57ZrvY6xCrvh/6sC6NAVsvkdJ+vhZRsjhC NziTAXPF6DW30rUIk+PHd1/OZSD6ZFaHtqMWoaF+SthZykDo2rMLZxRrEok7 zqyVq2Ag/Na9UNdATUKan5RkWsvA8rkqD2bO0yT4xBWDyM8MrO8MbxzO0iD8 U64HZnYx8JCEEc1Pg/jSceNfOouBlU0GdfeNNYiaiLsb1EQMeLGf9xX6qxOZ eaUHH+gwUadrYhZVrUZoDJc9b5jNxEa5KYoJe9SIxLUVkwITJiLSbJ/sU1Qj Ir7UXsMKJnqbQqj2ntOIjdS2ivatTCgP1TbMnzqVqPHqUJrcxYR+aQOzu0qV WHX3u/uCICa0P/o734tUJUzsuKwjx5kQyC0K+cVRIaQHyalT/2Hi/D3Kppzv VCKifGyrZTYT5fvuSa5mUwmeIiXHJ58JntIQTS6ASrTeplrnvWAir+rfgQU/ pxDFTXo717Yz8YN00jLTmUKYzDZ8ENDDhCihzPxJjzKRGWw8dIHHhNf+nSnb SpSJRLklZ7/8ZiK5qJ3P26RM+FmtKQrTY8GuI0aolaFEtJ4iJOlGLGgSOtNL DygRrg0OxOvFLFD6iv0sCSViZeBfrVQ7Frx99kwvG1QkNP7xk97dzkK88kba Ek9Fono0flPrLRbcPpBz5q5RIFr1IiRh91jInXNKb5WhAsFdFZAztZCFj3uu XfhIUSCmnXAUrX/Fgmh+dMeed/KEt1Al60k7C5d/2vUwtskTff1p/Zd12VCw aLXUTJMjpKpn083msNHGz7cqj5Yj1M2O4a0JG/KjLqufB8gR1sE+18at2Eh3 3qb6yEaOOMU2WB3qycbYh5dr3XoohM73vGSXVDbcnHclzV9HIRZK0605GWzo 70z/uX8phbA1SPoRf4eNfe922PUZUAi/bSHLy4vZmNganOj0axIFbRadCxvY iN5GWZYRMAn7xrLFiiocvDkUbqDqPwGPwfzP2RocNI+NrPZYN4GAaTdjV8/i INqD6yUwnsB5178/RZhy4PWXh6pD7zg+v8VJhiMHjpXUasHRcQTT6uqqTnMQ OeYrXp8lxYithrF1Mgd9er6zDc5IkfzM5++CqxzobCp9anNAisICrsX1HA5U 5ULHrGyl+HlN8VpIFQemrzbeNOscQ2QwsUtnlIMh9xuCFaZjUGIllV2Q4yJz SrbdJ80xZOxqUp+kchGzYdzrrnQULzz9avgzZTicOfytZRSja2JMaSu4WK71 3rI4YRTxmuXDIUe4GC2uM5rFG4HmpUnX7iguprf+phS1jSBX2SnPK54LvxUr x0NqR1A71uaNVC7W0q9N2Zs9AmWusEKnmAuTzvvTrLaN4NKrPxJpPC4CY+q7 OZ9/42ZAvr6ufy+qqYH0ACaJ0I2zasyDe6GzucBa/zMJe6sLIQ7hvXBXar4w XEuCKX+w/Gh8L8b8bBbIPSBhnrvUuyWnF8vsOwtuHCRR1fP8aiqjFy26Z8o8 pRKwdr2hqgbwYL1Vj7xsKUGZ44rHRgd5OO78aGfxAgnOWzzwsT3Kw6zPRQKG ngTm40kPgs/wUPTEsfCSvATHszY6vLvHw8O4m3sZrWJQu1pOnWXz0CAXcWJL rBgWvgzJRCAfQQS/pKdLhCwtTFw8xEdxNIU+0iKC6scsJb1jfGSFfN03r14E 3jpfHauzfPy86sZMLxchb0mT5f5cPtQtZqobZoigP/k6tOkHH+uUZ6ckbRFB +cENZrZPH16H0h6IvghxzF/CN9/dB7f+ubfONQnB1vcafhnUBy6JjHl1QlSn qlNaj/Whs/LKhsiXQsScTJxDvd6HafwgaWqWEIJNkb7hzX24JdWoObdPiB9C 90bCpR8lxGGT76MCXDb4Oj98cz/ujBs7TggFsN/gdzJ7Wz8yBwqIRYMCZKeF mkyE9ONK2YWjGd0C+FteiK5I7sd0/5yzHW8EYB2uWWjT0I9TRAmPd0UAHt/6 1BL3AZyLohcXLhVA0K23bMbWQXhqrzjqEDuMeQGk9dxdgwhy2/ZySdQw3Lmt tosCB/GukaiceXQYRQOpG+yODeLSUHPLePAwgkaUfPzSB5FipqUit3UYnVqC 2Adtg9A2qDzfaTGMasf6DzbeP9Gll62ezhzClcLo/T4+v9AqN8xe5T2EherU v6JuDSEgZsFzyuefKAuPL7ycPYzS6VnyjYIBtC64NmVzmgDs9PUxmxf2w8V0 1qpDGQI0WbvMmW/Yj6pFt4MvZAqQGFFJHdLtR8GS/PfVuQJMuhQc+lupH3GW FReXPxUgotvV3Jvdh0VrWeo6rQKY5ZhXUe/2IcbLatZXXSFc5krf0XX7MLy1 3FmoJ8R5A+mB5ml9CPJZe1LdUAiKSWxAu0IfNm936nRaKMSSgkp28zAfC/13 ZJXbCCGutFfc85GP5oNn5mX6CLE7/vcJ1mk+TM58XrTrphBRccdmXuTy4Fuq YBl0Wwjv/f7x/3zj4RLDyjbsrhCLB7rCbrTwIMZ1l4QCIaIXXHY4UcXDW6nX gfuyvckgJ7zy0nkIOf6lcLBDiPazdaUZ63goCelYGqcvQm5N97nUy71g3lBZ mWQognRRXXHr6V7MrLPFFWMR3iZnLKOe6EX8wkz3XDMZ/lO80XZ3Lzaztoe/ tRPBg/b0zeulvRDt/PZk+g4Rrp3+9+K0ei5sPbqts2+JsLb2q6ToFweveUqD e7NFcM6m1ZkyObBPML+/8J4IBUl9e5NbOXAoPalb8khWf3HiqtJLDtx0dCSv X4qQnBYqeB/Pwd525xedX2X5TtVKNlM5YIeHhd2R8dSbd1tMkbKxXyXDdG+3 COdKR44UD7ARasf6h88V4ceaVPuCj2wZ/2OjfotlvFZy+mV4mY2L/qW2M3TE WKrhMe0qlY3pI+3DHTPF8PJWdbclWbhydbLgtoEYBay2ilccFjJqNukvmC9G UZHbzT9rWMgx6R21Wi6Gf36rZ/hJFp7xDF5v9hCjIoV6NKybCZuE9ZG6XmLY VJwt8/3AxEu9EPMOHzFeVTqnqct8QJVrWZb/bjFy78dlMlNkPqbIIzbssBhm /tsvKNoy8T38nH3KJTGOJ25J3X6WAQqdPif3iqx/GH3jwwMMmKhLpWXXxWgM rtyS78HAgeKIip4sMc4bd3aVGjDwm797lXWxGG68xkPNxT3QCrBb3vVRjGe6 bybkE7phU3pMc+iTGOvZFqt11ndjm9yTIcUvYjR/tVZzke9GTrbpv0t/iBH9 duyISvwPWHzTMT/9U7Zli5RzPMK/w3nrrwWL1SWoX3p8T7VhFw7mmSnZa0vQ V75AbXtTJy4LA9meMyV4dkflxJO4TrRd/ZYbM1eC0/6VF//u6MDexvdzm/+Q YGClafG5uHYkzlGaZFtJ8O3rc8pck3YUhBI/RlZKYPjno+UWdV8xpPoiaz4h QUmAPS1m6lfEOuXpnfCQINTVdcfd2DbkZHT/vuglgX/B7d9Zum14w9Fvz/GV wPp8sHNhYStUz17NqPeX1dslX/nv02fcoMdpGx6RgC5Nc7BRbEGp7Ta1/65K sObRrML3rA8wESRnXU+XIHzsqlF1ez3SH71esu+mTGeO+GywqnuPKIN5rgp3 JXjcPUE2pr+D/Tg3cd1jCVblyPP3cmvw+PmsGZrPJAjOe539qqAaRodd7/e8 kOFjjS8YgXQodhfXnqJJ0LMjSmyRWoEP9EhKVaMEvkbRvcGbH2PNyQepKS0S aJw4Lq5+9Agllu2Gu75IEP8qa9jpUh7SclevlX6XgJIuStb2TYXvWflou0EJ chokT7iP7tHq11irqA7L8kk391HFQtpqceCNDpFs3j90hsdcntAMg96XRcl0 dVnxnG55i5c0ttMVYdlUElFL76wYsfqP5k2pOZ2oTsK/2DUyLvEd7V25UNNb mwS1zrppuP897dFin2VifRI9n2uHDwgbabOZ52lvDEk4m/C7qj4001IyX7ld NybhO+ry7K/FLbTwqYaHrMxkOv/oJT9CpY3GrHWXyi8l0Uys+HtPyhfalpiE iy2WJBbpt1DPz22n2QyyC47YkqDozSyvPdJFG28s5P7rLPvfTldheySDdjjp +7FTm0h4+mlLgmKYsstOXcndg0RQlNXOL6ks2pvHEfN/+pCwOTOYL+7i0GxC 8kord5Bo1JfO85/RS8s3+rIuZTeJ2RnMtAe7ebTkNFt/8/2y/vfpDbbz+2lS 14O/xg6QiP4Vm0bNGaAdUrgd9+EwCfn05KGqZT9pHpGU2weOk3j2VNeUqB+i 1ZgvN7eLJrE0ruJQwfNhmhUnoEIljkSkspNRW4mANsP7XcfDcyToLvsv32gS 0f5ck0cEXiDxtj3Ec55ITDthnJBvlEKiXtstK3cJSXtI9Zv+4wqJxy30MJWo 37T2n3bHMq/LzIH/1snTXSM0lbaZ37xvkFjzrlec4jtGs6sQrdfOItEwNSOB KpDSbiWVaFy6R2J8t++KqQ4UesOhiyec80kQ/iO2CX/K0aVbgn8oFpJ4Mja2 5+FuebqFnaNjdQmJz8buWrlpCnS/ecZFsaUkVhpYLDdjKdIvK09q2ZWRuN0b 4Vq1VZlOG+g6KXlJ4rDlAbNPv6bQh1rKe0orSRz/uEteo1yFPu9lulNYNYlv rzcS9LKpdI/siJIl/5HQClmxbJ1EjZ5wzl2XV0eiqVbegrFOg1560Dwmr4GE wxXt1yblmnTmZhWWfzMJ95N7f+iFaNOfv/euiv1E/v+9r0P/Hy8PEc4= "]], LineBox[CompressedData[" 1:eJwdVnk8VO/3n7lXZSlLKVKpVIhUiIScJxVSlCwVPhRREUWSUCGRtSiytlCR hGyhMpYsSUVSEmMfDBMztjuL8Zvv7/nnPud1zrnv836f+zz3bHS6dNwFI5FI MmQS6X/P5Wf7StPkCSD9/9qMejWVLdsFNm38gn9Q5yYkKbeoIk6BAMPm9bW0 0Y1oH6l/g7kiAUqyTj8UbTcgb1pluKgKAc1/O950K8ijjObUf/VqBMRhuUEl vDWordDP+rY6AdfHaU7RW+WQULL1B9AiwP/Txf30R7Jo1y2NTTwdAn5+8mob 05VBLi4SkWX6ArzjopQ/wqtQ4uHxSR9EQMyfAfu9HGlUr/75hPoBAg7bJr8z FJFGczIvKxnGBFzdp9d6WH0FUuaHbMk5TIAV3XXdc8/l6OSgY7TrUQIqZVsT DlVKoYgm/SkFSwIiPz9K/7ROClUUrLbtsSFA9ZGmgWiUJKInzlal2hJwYcvh ahchSbTmRpvSSQcCKNLde75LSqAjzgWx0k4EfKUyYgpUxVHgoZiZFhcCdGZa u+1OLENvdrjZx1wgYKNGfbNw/FJEXWlce8iDgKxlvWfVOsUQ9JPianwIONRY //NtjCiSvMWSb/EjQO5Y3eZQugjqXzOY2x1IQPqDzE0jFiKoqKxddyyIgHcO 9OfUGmEUat3QSIQS8Fr/fFK4vjCyYZXZLI4gIMjw1OV1lUuQ0r2cwRUxBHiH JRxnGi1BTY0xpB0JBDw/UfVt1n0xSnO5FaufTIDpV46qwpLFyAPzWmuaTsCT h8lc/6xFSFLfSsflBQE5TzR0dswKof6Og/XerwjwS1i5qidTCBVd3W0V9IaA hKSPcs7WQsgmX+5yagkBmzd6bOyrwZHykaX87HIC6r/067rexBF7ZD6q9KMA r/DJ5Z/6OEpT6MtqrSPAJTh7UUk1hjwoP7R6PhNQ09pJag/HkIH9p9rxrwQc GfydqHMMQ30JWT1LfhHwptl+wGiYjAo1kj1WdhIgXaXbW1JCRqHfI7kKVAIG 1+2Ln7xDRooinjIGNAJyOeIL51TJ6GLgrqM+swQI61jUSd4lIYPVit3BHAJk NmVbBDuRkESpjPs9PgHQmrB9owEJFU5wwnIWsyH3x8B5D+YCzDlVV/auYsMn WpfG+yk+NC4UHvknx4Ywt6L65jI+pKQ97+TKs6FT1e/S7Vt80P8VPrtKiQ1H h3Y9SZHiQ8gh8+1mu9nwI9Tj3EejebCiwQdbPTZkrNgovFdmHrbcVjc9D2yw Kl/cOD7Cg8YP0q63jdmgXzcZlH+PB+I7/6aXn2BDCy72MnOUC73NzaoNdoJ4 nSd5wTVceHuhsvyno8A+7hpomMYFq8xn7RPn2LDmm32D2XEuJK86v0zRjw3/ ihM1Gxo4ULb22OF/AYL4skdZG15xoENBJ6L0FhsOFaolSUVxQHaH8CLjcDYo xPg6Zh/jQKJxNu9cIhtyQoIpu/vZUGp2X3dnChvysX68s4ENvyz9/Ih0Nmh/ jM2dfsOGladNpu++YAP9Q452mADnod/I2KtiNnjECX2uW8OG4pstW73LBPml 7OF2ITa0hZad0/3ABpqUxSHjfwQsj7s70FTLhhCjGokDNYJ75JXy37EfbFAT Nal28SQgtvN8kxqTDftCo0pD2+cgr/eY8Ow0G1LcdDVyaufgK03HqJJgQ22/ brNU4RwsnRKuMSdxYBH9T9Cze3MQJfaq/JIEB+K3h5ilmc3BXf3R7LdqHBjf KjQ02jYL2YattOvqHKAeKZZPrJuFBpPyzYZaAh26Ei283s3CYuuIpz/0ObAg /4tekDoLdzy2Jk0d5oA/TWaPvusshDy+EK7lJoiXUGj5js2CoZ3ruLknB06J KMQvnZ0BXNbZ4rw3B64daOvyGp2B0Dj7Nan+HDCvPThS2DIDYaFH80n/60OV 6yz76QxEuGn9/vKaAxUHrtBwkxkwVdLQH8rnwBlV90KfvTMgOrj9Gb+IA7ce 7grGNWcg8j9ld/UPHPjmbSV2XX4Goo+tWUhs5kCgitD7ktlpuK9NVnJiCPSw 6xcTz52GY1PzUQFMDtznyJZuyZwGqQLO5MMZAZ6snJZVyjTEb52uaJjnwHaa 757pu9PwYO2wuZo4F95N+QRrn5uGROyrL7GdC41ylioBStOQ/i2pPvYyFyIO 7qOKl0zB2nKEJ/hwIaPrSnpE3hSkZY5Aqh8XXl63mpTKnhLsdcqzgrigfJny 0DR1CpIVOl5X3efCbvqXHpuQKUjwlYljFXDh230aKj0+BTHyiXY2TC70df5I i+CyYKmIQZL9DBfKL8/vujDLguipoZ9ObC6kIrMvFkwWRDVqmV8i82DrIf3Q vcMsiPBuR3eleKDkztULbGPBnXppxQp1HjQXFxYFvWHBDc8Hk+u8eWAvOfN+ yTkWmNaod1Ov8iD1tk/2BmcWyK5q+fzkOg+ibgAZHFlQ/HFp5sZgHiSuLqVE nWABfWmY9Zb7PEh/O8F0NmHBydd+FdvyePAvVaweV2XBrpH/QvXoPLAKNGa9 mWICps+7zGPwoL05yMR+kgkt91L++8jkwUjl1QRxBhPcd//WBrYAryaccZPG hIywY6OGwvOg3DYTF/OHCZJb9pubKs7D09mbVNsqJoydUZY95TQPPy/MEAH3 mWB78a+qu+s8JJfeAtsYJjT6xsINt3nI1L7K14tkwouoaddn3vPgwzOpFQll gmNJVcloyDyIKhy/8fUaE9qET1n6Z84D/W1nxj9HJrzPj4hNHZyHS5U3Ljpr MCFqni5EdeXDanqN3xvqJJh4PWzMceODAeVykn3XJAgN7Y2+5skHn6hS22Wd k3Cz+f4KKV8+tJd/f3elfRIup2orHLjDBzVNdXfL5kmw2RMCOZl8cOvlhdpV TILC1dX+vr18yFO13u/7aBIqxo0nxG0XYN4cC91iPQm/tuj0624moS/vX9BX l03A+a3OOx68ICH34ZSfBRX/oNrGLmCfPBmtaJUKTq9lQH38ysYjG8ioQ7cv TpvCgOZv36VPKpDRITvuxq8VDOgwOpDnqUhG2e2rUllvGTCprdaXup2MwClu dN1TBsjLLBjNGpARyUboKiOAAf6/M5a/diSj6iXLdJXUGRC04j/H0jNkdGZf VKL9NgaEHZXJrXYmI4kdp9bGKjEgriHqYMc5wX+Kk+I1tI4B2e98/BZdJqNL /jJ/nUUZ8OuREdUxiIyY7VenH/SPg+ZJ+ivpZ2S0Z+lnbbt749Db+MR8PoOM AllDf60jxyF6j/XU0HMyMuu+E3b4zjjQ5Kr032WT0U0N2bdKAeOQ0p3w/VQB GU2vXl/0zHUcMOd9M48pZOSQ9jIyVn8cWjyS0FYqGbHK32a0DozBDarZkFQv GblssYheSh0DlaN4JKdPUK+KuT7qGIPQnZ5tX4bISLWvLjGueQx2T+139WSQ UfBKs7I/xWPw2G8iqohHRgMNzoX022Nw8bbR771rMOSZkBxutWYMiMjW4bXr MCQkL3QiWXoM7sTbE1x5DJlujeptWybIf+a9ukIBQzUuRulbSWPQQnlsp62C oW/rehcsB+mgyZvt2b4HQ4zP3W9Cc+hQhYdMLtPDkNs1vSvSmXQ4IraMzNDH UI6U2pNHqXQ4K7dJ4TXC0JcwmaBr0XRI1Dl6VskEQ7LfxB4kedCB45M1sv4E ho6YavZrq9EhLFCDzT+JoVqJoVvDm+mwIvSjCNUWQ8GGa2/dXUuHbQ/aVNIc MDTYYFyTIkYHh7cLF2VdMbTi0E4hzsgoVDNOMCWvYkj+vs9Wj6ejcNdVmEN+ gKHeumWO6qRRcPm87rFIAoY4vq6vgqZHwHCbpqHUIwzlLsq4WjgyAlzmf5Eb UjGUZXfqzvuWEfC8USQHmRhymdP0tnoyAtYPHfQCiwT49nki8tojoDF3ped2 CYY0bnycO6Y8AuK2Ebej3mFI2m7JM3u5EWhcX/wl5T2Gzt47qMSdHwb91yL2 5bUC261l3qB2GBRqigNn2wRzV2fB3/UHh2Fhc9MGfjuGWNQfZdd3DUNXeM+n RR0Y6pRi/UjfNAyJZqLLVnZhyOG7rTYiD4PIH8d0zUEMrc2I12wupwFNTzCJ 0zB03GDpS5ssGtQ8jhwyHBH0JyHC5dlDGgSeLVE7Pi7Q22z7em9PGkxOiFZe nsbQ9IcTDr/kafD1+AYnv1lB//5aO+wRpUFOidbiIEJQX2iu0rGZIXAOOG1+ j4ehuj1/+uOahuDX4lLqGyFc0M9Qi51eQ/Bx3ZkFujSORA/p7J7OHQRU4sX9 vgpHPYVWKxwfDsKnIyFzxbI4cshqLDsXMAjNAZkTN9fiKMnj1B0Tk0Ho+jPU s3wzjk5vi77I7xqA016zf+e24KgLwx3FqwdgUHhJR5cSjixK0qRfPh+A8d3K LS9VcUQfyupxdBsAXoJbla4mjvy32vanTvRDkFrAh/VaOMrdu+VBxPd+EKqL KhPajaNsnjOjL68flk7nFnzTxRHVXde+2r0f1h6feOpkiKNzfSp5Zd19oCfu ExxpgaO7em3hX9J7ofJF6I1Llji6HGi1d9arFwz3Jly3ssbRf2kHJLYf7AXT i6Ve8qdwJO8p9tW4tQdsm4gzhacFc3l+RZPVQSpQz4g4PHLCkWfrifDQrm5w Yq+2DTyLo+f4EmyXVze4KesdNzqPI++oIZXC+C7wD7th2HkJR73iil4HijqB vy7WgOKFo83e7jbxmp0QUvJY9/kVgZ5NEyGBBX8gcpCi4XkNR6XJI4oJTzpA PLBlu+V1gb6Otft9pTogfkWfik4Ajmy4rtknb/2GFENsE3YLR3k/ByYumv8C +c7l64eDcHQ24Rtjb347ZHhtWtMcgqOWPXfI5mLtkPP0wIrEMAH/51VXjIvb oJwfhqvE4mibI8vyXk0LxDI3Pth9H0fFvufkJj5/B6fBDwoH4wX1VknYW/O/ gmgTa9/pRAHf8/x+cY0moH6IafVIEujL3+JgvKMRivKVzwSk4Cg6U1GxS6Ye 7BMcghIf4yj07JBo/4tq2HmXLfH8KY42LDlP7b5fCUIBD5+8zcDR+XHfkuXP yuHN6abK5pc4qtIa03BSzoMQSxfzzmwcSYp5H+jtzgAbIxJ1OEfgp9pdW1CI Br6q9jyWL/jejvIt77pnUH7It0ZLvsXRMY1lIoZSBZQsqYtr5YtwNNm3/KGw 6TvKsblnenveCfgvclINuV5L2UzX/2JUjqOd1GuHsyoaKETXb1ur9zgqcL1P zdZvpjyrWeZ/iSLIj5CgkMTbKL4l2SI3qgXvL9e60FvbTjHN3p8cWYujI9Ny o+XZHRT5VKpyUp3AH3PzUnD1Xwor5nrZiwYBPzNR7sCKHkp9kLRJ0WeBXi/o m7Qs+yipV/J/V30R8Asqn7dAA5QDp4Zm/37HUZCQSbRX0jBF9khQ2GiroF4V v9evxemUcYM1q+bacDTCkeu+RxmnVKmXvhD6hSOSG8mpvGiCkrDZQmt5B450 /9WZffJnUtxkxj+t78TRAdf88W8mUxQD0XArtS4c/RIN2Ek5PENZPr9xUJeK I/vdRW26MXMU2sSHKya9OAr89558bjWHUtF/ArfpF/C5uzKtboFHudfOince xFE6Y3Wqrgqp6mxjjIIXDUdjRyOeL1qNVem8Vy68OYIjU6qYj6aDUNXSvNp9 0XQckQ8f1olbvqSq96lDa/I4jmwlJL67nxKtKn7APp31T3A+wsKh3lW8KiLs 4WTxJI4USWVPTOqkqjpdfaclWQJ+/7+kq/4PIpuC5Q== "]], LineBox[CompressedData[" 1:eJwdlgs01dkXxy/O7/fziiSaIs8iN7pSKmH2JomIPEpJomRM00O5VKhoKCkT 6YFkklRKhkokJYXkWWn6kxQ1jPT6/e51XZL87/9/1jrrrL3OWd+z92fvs9cx 3LjDe7M8j8c7J5v/WzfcNn5jq0SQ9/8xA/f1/+ean8wOWCFWtak0Ru/OXbab VQiuCa8+cznJAE1aJjTumkDwD1GX38kcXfz24Ip/nDpBo94JSuFrp2LLzSUD KRoEK0WHYia1a+NB+1u9aZoEd2ns1lrWOxkXPJ7Rc0qLYN8HwaxsT00cWHnq deYUgtqW50usxzUw5xXVfm4qQdMp5soV7yeid0hUW64Owcx8QbrZe3Wkv/S1 5E+X6S8s8vgL1bBit19DgT7B+x+KWyPaVHGbXH3tdUOCL3/Rf/lvmgoaHF1U XWJMkBPufH9RqIwvJhdUls4k6DqqdrAjUgmTcqaW3zEl2Kn5OeFdqiLazUq+ ec+M4CSBqar8QwbZkm9F1bMJuls6lfJpBi/a/na11oLgjMT9Ve3+NK6p7cx/ IiDoESOkJPcoVPV0z22eK7P5UxSqLCh80F6Z/WyejFd4xve7VwgKN1pk/G1N sG7I9kuBTGfWp3PpHQsJEnuXlZF3FfB1pNrxLhuCKe+Sflh6KWDq+P7kHluC +xwDH6p/kUenI18Te+0JnhGK9DekyeO17Kexnx0IKmQMvRL1y2GgicMebgnB 9FrfQutsOZxUXBIhWUrwvBv1ottHDqMfndgy5kqQrt3jNd7CwzkrFELl3Al+ /H64+HkaD9+9jAimPAiKhgq4Rj8eLh/wXTPBm+C/h/n6ie3j8COi1kfDl+Dm 1I+Pi4TjcGPM2lNrNcHXZsKwA1rjME1jivN0f1k8GWWf/970A1qyDjsYBhC8 wNnFNk/8AQdnDNvNDJRxOPPm5YrqMfiwsGOexUaCcut6VZXNxyC72lUwN4Sg 5lrDwp7e77DSrYJvHUpQv6yxcs+F71AeeNbQfgvB4iCNiUuNv0NS4nr1FbsI 2jm3FqXDKNiptyh7CQkKXNONjqqMApvxM70qiqBV01Vjp45v4FeoPxYQTfD2 yfjB3L3fQHlB6nBQLMEsFSVuuvs3uF/FGwzZT9D5/fVMJYNvYNLWM7D1oKze SoYffmwcgVcB3n3hCQSHV26tfZg3An/0PewRHiKYkVzv2RA7AkMjee2xyQQX 8ltbrK1GoNYgtO7YCYLdC0+YzysYBoO3z6ZuP0nwdK5b8bqjwxB9zn6b52mC BfleQtw+DJbTtCZPyiI49mC1hfGCYcjWrAk+k0vQqft7WE6zFKTPBKV78ghG XVP0kd6SgnfqWUX/fIIV78z5XdlSUJwQ8ZdugUz/dHqb3XYpCGmjsdxighp+ /5S0aUuhtSZl5e83ZLyCT5Bp8lLg/z6SF3KL4Dbpk9Smz0PQPf50uWk5wS+R NpN/rRsC95EDGYVVBG9JypfwY4dgxqeueWUtBF2KP8Tsl0rgwFXXwxlPCe71 H5q/qF8Cr8JKX+19TlD15ftH1h0SSO09Fm/3UsZD/svPkrsS+P7GtrW6i+Cb mjg1vwQJ+J27bJT3lqCvJj+Yt1sCN9ZpRiX0yOrd5+yD7l8lENY+oLusl+Ci I262Disl8OJZ5pamTwTXk8056/UlIEil7l//IvOvoPDAWU0JJHvs1DjOyvIb zFylFSWAjS7lXoMES24cuBbEDUJhjZT6z6jsfVxO72TqBiGhbFVujzKFI35n 5QOjBsHymVvSR1UK5/rwL9lsHYTOAYcdEjUKKxsEvy/eOAhWenPslTQpvDvz 78wrHoPwNoHusNShcE7HsSADs0FY7F02MW42hZv64oN63ouh77fr0iOyPkCH vuss7xRDWmLem3SBbP9xxr2rbWLoLz9eeHmerG80WmV1PhLDKf0wl1ZbCmvV Ymo35YuB/fRTnJ47hWYKbNqVrWLIptV/meVBYWN3+6Qvm8WwzIDysFopu58a lDpvEEOOD6fj7Eth9KX5R+Z6i8Gt4knZtgAK974XR3YvEsOlw9FfK7dSGNUt bxKsJIYAo9eB61IofNF5xVa/VARF4c3nHI9TmCS4s+pMsQjkqu6/NkujUCum 1GdqoQgurcv1Hz5Jodj6+W+L80TAngxdfSqbwqe+c5w+p4kggeFWtF6j0C4+ 13ckXASFnyj7JQ0U/qutJP5nvgh+LJbG8Jtk/JbUtQbOFYHXkf4KjRYKdSOH dd5aiGBoZuOi7mcUXh7rLRaZiAA3pM7f10Hha2/PC5umimT5n2Ze1k/h4kOx ngHjHIzeFujMZmg08c3fNr+VgznZQ7WKSjSycf5rw5o4CIq/F96nTOPwbe24 8084qHFzq8tVo9HcMMhzeg0Hx7pDd/6kTeOASsTNZXc40FXOeUzNpNFoVSxZ fZEDu/Wqwm5HGsMm6V3Q3MfBdsc2vftONF5aNauxIpqD86ZZT84603gyZ95I yB4OiMhU3285jaap/ksfRnDQdGhJQ7MXjV06aQ1/buEgoDja4G4QjeLTjjbd aziIVfjQdGo/jUMt7UKXhRz8WLJYJTuOxqZKA7kp1hzEJxx1vXCQRhWlLJN+ Kw4OUXPqig7RuNeFMToxh4PjTETV4z9obIw+bkhMOLigMlYykkOjTbX8HX8t Dp5oapxZX0Vjyibz9AIJC9ozbIJn8hisSKr0Lr/LAmYmShXlGZRrq4/Sr2Dh V7XnKZ8UGPSw+rn5cDkLlcNbKm4yDLqm69ABpSxsbM7WdFRn8HEmu3bSXywU RfHqAvUYfOpgIrh1gQXnJ4/5GXYMNqTcbqxIZmH39tWDynsZTDIxcPNdz4Lu gpB6kxgGv16cqtO0joUHYzuzHfcx2FpZdsvJnwXllBSn6HgG49a2LF7kx0LO tZqTH44wKOWK3Wd5sVDXb2Vdn8Wgw77gzfylLEzepB6VWMng/SMuCpcsWLjD n7489z6DY58CQq3MWQgU8fXuPWDQbkeuSxWfhSvxznWDNQxGH9c9+MqUBdvz +7RDmmX+nZYe0zaSxdf18bbjGwbDta3N8rRZYPJHkgO7GfQ9fTlugRYLhVuZ DdHvGHy99aJ1gyYLQ6NGzI0+2b+gTLlYNJGF5Gn+foZfGcyq2HF9mQoLgne/ zLbnGLxqoFHepcTCi4LI8TVi2fkMqbpQkQU9m7TLqVIGN35I/DOXYuER78+Y whEGw+aatS0iLITVF3rWj8r4+ii6P5VnQTW1wvifMQa3WxorhsmxUOJXLx0f Z3BBeDTF47HwXyqIZWs= "]], LineBox[{{1.49953582656483, -5.}, {1.4995707543834969`, 10.}}], LineBox[{{0.5000367950683544, -5.}, {0.5000523370684159, 10.}}], LineBox[{{2.5000649410245686`, -5.}, {2.5001569624295437`, 10.}}]}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->True, AxesOrigin->{0, 0}, BaseStyle->{FontFamily -> "Times", FontSize -> 14}, Frame->True, FrameLabel->{ FormBox[ "\"\\!\\(\\*SubscriptBox[\\(k\\), \ \\(0\\)]\\)\\!\\(\\*SubscriptBox[\\(r\\), \\(0\\)]\\)(\[Pi])\"", TraditionalForm], FormBox[ "\"a/\\!\\(\\*SubscriptBox[\\(r\\), \\(0\\)]\\)\"", TraditionalForm]}, PlotRange->{{0, 3}, {-5, 10}}, PlotRangeClipping->True, PlotRangePadding->{ Scaled[0.02], Automatic}]], "Output", CellChangeTimes->{3.4722260223747597`*^9, 3.472347758211281*^9, 3.472359296086553*^9, 3.472364525292976*^9, 3.472364816310223*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Scattering Phase Shift", "Subsection", CellChangeTimes->{{3.4722043391943407`*^9, 3.472204342785879*^9}}], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"Delta", "[", RowBox[{"k_", ",", "ascatt_"}], "]"}], ":=", RowBox[{ RowBox[{"-", "k"}], " ", "ascatt"}]}], ";"}]], "Input", CellChangeTimes->{{3.4721841550005293`*^9, 3.472184177375527*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{ RowBox[{"Delta", "[", RowBox[{"k", ",", RowBox[{ RowBox[{"ascatt", "[", RowBox[{"k0r0", "*", "\[Pi]"}], "]"}], "r0"}]}], "]"}], "/", "\[Pi]"}], ",", RowBox[{"{", RowBox[{"k0r0", ",", "0", ",", "3"}], "}"}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"FrameLabel", "\[Rule]", RowBox[{"{", RowBox[{ "\"\<\!\(\*SubscriptBox[\(k\), \(0\)]\)\!\(\*SubscriptBox[\(r\), \ \(0\)]\)(\[Pi])\>\"", ",", "\"\<\!\(\*SubscriptBox[\(\[Delta]\), \(0\)]\) (\[Pi])\>\""}], "}"}]}], ",", RowBox[{"PlotRange", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"-", "0.5"}], ",", "0.5"}], "}"}]}], ",", RowBox[{"PlotPoints", "\[Rule]", "50"}]}], "]"}]], "Input", CellChangeTimes->{{3.472359253600622*^9, 3.472359290659091*^9}, { 3.472359342706201*^9, 3.4723593436075993`*^9}, {3.472359399735548*^9, 3.4723594643659897`*^9}, {3.472359517702189*^9, 3.472359562514382*^9}, { 3.472359608468506*^9, 3.472359639472003*^9}}], Cell[BoxData[ GraphicsBox[{{}, {}, {Hue[0.67, 0.6, 0.6], LineBox[CompressedData[" 1:eJwllwkwFWobxw+yXSpL1uumVIduKUvJLc6fS7ZURJsQxalkK2WLyJY9O0eE bKnIvu9rONl1LOecJEWytd24iu983/fMvPPMf/6/Z+aZZ9555322X3I6ZctO IBDaWee/efmYY6qRkzOJ8L9oVwuykZXrJZ4Alfp8s0ORH+nVwpRdBNES6+v7 h2WLHpOeiYynj6aQcYUcqXOUu4y0VKIVbk90ZPn+BxWKmkmSu1/XrNNuQlnZ Yg/PwVckdfdQxc4UVyRT6rZkcg+TrDpIuTHWnixe9xdnOp3kJ/pVypx4F2Ty RpuJoknSQLFJZ8x3X1b9msbtvGmSzZh8wA+aH4uXyelRmSd9Z+OBeXUACBo2 ib+efyYF7Z5caUwJgpLLI99A3u8kMePa0l0+wejmfzTNXbRMeuKe4BRqHQol ZaXrkZk/Sd0dBu9NiJFQFtYX/FjKjgI3ISPzDVGg2nMfHtzKCbcwn/zI71Es f9ODMwXc4Ck5f/UrLQbUuQM7tEkb0dfe3rarM5Y1H7v7ltICoIwp7zhXHQdy u4CGa7Eg/mTfxKxNSYCtjuoJPUERfBG5c2QxIhHkf5hhfAxR1OyeSdrukwTK X2/pNTXiMDRuNgmyTgZhQrz8R5EUnNJdO08SH2H9/vNnfzXJQLX0HdFPLA3r i5ucJb/uAMFG7m+zDelYx5pJ8L5d6HSLTwv/ns7qZ+sL8WZZmKU5mX2mPYYt 0W7UwVwepN3EkFCjTFCumfJLjO+DTAm9YkdnJmvea6oVigr41K4vcqY6C5Rd WnviXirCa2FHX3VKDgil3388UTgIK/exNRORXFCz+MveiapAmz1afj6Cpflv 2XOyH8JG0bVQaZ8nIGxbreeeVsUj9ZGjAdZPYftvXbHRnBqawsNrjhMLsH5N 7tCBr3+jfnaUypdXAApjcLvpQy3U6skyO/e8AEU5e9pZRxsX2K0JmeKFUGb7 rSgv+yhO16/KSG8twrqJjubZYD0YqCheFdtdAmp1EG/9xAnovac5u9qVYL3z gXR71Unoxt31GH5WAoJa+tkVAyNof+kOjd1XCuWqnLOTe4xBKiDnbz5QBvIb Pa9eggmUiSlfuFEBJQGDmNvLZ6A0/Pcq2bcCyidf9w3fPQuFgI8c7U0VIAu5 r7/lOod9kyoiAdqVIAdpe3FKnYfco/5DBIMqUFefpeebXYCUKLf3smkNPoy/ yk4TsYJkW37g2YQaENzrVLPIVpC4ZRpZTquBxPZTbA8qrSA6kJF2y6wW5MS1 9t8vWkMgUq156WIdJDPMBJQrLoGT6yb3R7sGfIjY1OgQZ4sZfZ/NX3Mb4BMx n8uxYIuuiHCxX1MNWO8XGXDRI6MjdDA2eH8jDOvWg6fXyQgTWshMyWtEsX9g tLrHVWyR2dHamtoEsqDBlqqE6+Bs3f1Sv7YJJbXHVALXruMfWwVqz1gTfCrD OnDFHiN56kMjYs04Ps03EHjEAamK56bmopvxwdS73HvREUTNiA0iQS3IFeTL UdG6AbF3sTzJWS0YJbz5PHP3BngCk/mlW1pg5pRUvrXmBmZf5m7ZTWhl3d8M QfGDN/HCqHmnumcrlD+t3TLb7wJVqx/ato5twEUp81n129D3sQ4sO9MBl8Qb M391eUDpQZNOxi2Wrg08/0LUE1Jp23kiYjpAEMdE82VPLNW/DbXp6UB3oNbS y3VPJKxZRwnrvMTagqOaC7ww5X3p4Y2DnfAxkaqxZN5FT0SzuYVJJ0p6Bx0M D/qgMlVmq/6NTlDPXBCaD/dBWN1k+rb8TuSkePsSpX2h9OtSTu/OLrRbjlJG hnzh63W5SH5LN/g/qrUeOOUHu/CWmxJK3fC4/TEizd8Ppik7DnAadYNLt4Hi XOYH2dp35fQwlt/iyqcv6Y+e1cu1YRxUkLtL+edn/CF1x6bj4xcqPNgXR0eT A1HhYcvI7u9BzIkGtvZzIcghXadJfumB0OwVF/tHIUjguNH/QKgXQRcLfy+b CoFrhFebh0kvKFKW8gdcQqGSEZt/fLgX6U2JNVJJYbgwNVHvad8HYgZFx5Aj EgPt746UefXhmGSs66pJJAzyPlQuhvchTb/wg312JA47zhXb5PfBMGZ/XZrB A0gu/8g5sdCHYoewH1onozDGt/mBjHM/zGt+BhyviMapBUF+C99+pCu+O2L4 IRpdfVtCEqP6IaMS/6NRJAbV8ZL+/EX9kHb1ChdyjUGyNNHtn88svjd+u59a LMyU1S92uQxAX2j1Pt9kHEbNru+/6TYIemSwxbnUJIRO6tonBg2i29XtoeZY Eg7b7cyrjR9EmlbThS4xClI8GDLcpYPoncu43hJHgVXSSdGUpUGoVa35xCck Y3pY+VfbtSG8qbySsViTgiQLgcOf3IcQdDeef4UjlfWezLkKBA+hXP5sV7dh Kp5+y14yyxkCx6W9uaMTqXAUFp9anBxClQWbz2ehNHw3+tklYT4MSc0Ff8H+ dOSMjHDj+jA+Oz1ukv+ZjjNWZdo2nsN4Ht/W2C2bgUonx/qCpGFkVDm2x/tm wCtyokhreBiBzaLbH6s+Bge1NcnhxGsc4eCqorZmotQkYzjG4jXcQ4g8u1cy YTPuLVRp/xrUs97dCvuy0D6rEs4e9hpPeNRvn0zOQihvnk9iB8v3djaTvZMN Qd0IcpMGDWUHPq14X8qFdl4t9hjTYN5951r5k1y4882Jx1vTUB7ZT2ZbysVE r0H3VT8ahCdpXdP3nqDwHI+CQCsNhk3EowUleZiqPsTrOUQDj+rgmiLHU4j/ cWXy3RQNy4ISnOsmT+H7ti2ugnMEafWeiXErT2Fk579iqTsCPT+zWcrp5wig Fg+8PDsC1+pp/1OFz1G5b/KZ0tURlK3zDSfz52PbVw1LrhCWrnbP5+jKx9Kd teb8rhGkvFoRszv/AlERHuE/j4+CIhhl3WZXhNbFJ7Zky1HImd5rdMktwrLx CKnPcRS79kt4nn5fBCvRQ58zH4yifWtkJs2mGApp304f6x9FfoxH9pxLCWzY du4vezuKf8yv3dCvKUHSZRMe6S+jYIspvSy/oRQEueLqL0JjOCNr71SXXIq+ QifpZNMxPFdn7r1HL8MG4bRlDtsxBBsMvU1QLIfq7Z5+h9tj4FrZLJgXXI70 v+QDNBPGoGnIu4lPvQLOzbMzM7QxxLJ9Ev7cWImsnZLNp2bGQOg6tEVQrgoj QfoPa5fHsM7O4KBFV0Hj2JPjURLjoFyR52twqIbAkG3xoQvjOJ5Zcv2wQS00 5jVnTa+PQ7p19YtVRy2cubbK3LzD4tWVf+fVq0O/6uvo5w/HsWrimuhuWg/2 U8Wdnc/GUXdv5FnMRD1YvyK26ZpxhNyJVxlybkBMqs6N7fRxKNn9+0r3ZCOa y2XySHPj4O2P/6b6qBFfe9cmLvwcx+zyb4E5i40wZa8wSpCi437sObebyU0Q uSKrwGdBxza2ja45wi3Q8eW4KudAxzeb2Bo9zxa4Ut6kHfWmY0XNTCRlqgWv uxM3+6bS4ZZtzJRrawXXexfd1Hw6eB0/lA8facOhtZM+1XV0ZGQLq/1e0YYk BZ7Fbww6wCcxH1bbjpf6U0ShBTqe2qi4mOh2YPlSo+X+NToY58Vi5mkdOB/v 3nNtKwN1u4SMt/F3IrTAlOv+Pgaufiz7I6awE9UdCqQsEgMUoaixUPMuSP47 k8+0ZGC+YujR4VfdMBBue7/qyEC8FJ+JXCwVnnsz/pDwYSDPr7d64+VXGLc8 H2GSxsCP3k6V2R294Hc/2Ob8goG+Fxm0M3x9UIsW/BXRwECI/eMP/mF9SGnp tH/5hoHfvE9/y3vcDyo9O+v9IgNa8oVC3EcG8PP7PTo7gYnb164V/6IPYO9m yy3bBJjYe2jKxjtkEBZyhw3VtzHx6pvKp3jNIURqigaYKbB4HZ4eL65h1Jt9 qXHTYII40/xn3OgwtkY83VNsxUShkULcYiENJ3KCLvc6M/G1MmFxT9UI7jZc ejjny8TpnIOSObRRFIyQBnmjmeA6ULDLcPM43nyW5JPNYKJj352l+Mt0CPD9 +Fu7iIlY6h/GOSMMaOwc9LRuYkIxa8HY1eUNGAcFu83bmfj/PjGB/wBymgHz "]], LineBox[CompressedData[" 1:eJw1WHk01QvUJREalEQopYQiEk9IjkqPpKhEKvLyTMlYil6oiJLMZHZxkWSe uzimKELmKcMdXCQ9w733Vy/l831rfeefs/ba66x99lr7/HOkb7hesF3DxcXF y83F9b+d59z49ojCCeD6v5rATWUt+q2rOE0p6MgwexxPRqefPFc5Ab+yp3P0 q8fQ67YPdOMqPuFifDpxFN9cuHzUrGUC/F99cBcL/4xUFdUjwx0TAMuTH87H jaDh/LQSbXQCmgUvbpYdGULfzsYDdpMTMFlN5r4tPIQl+SmyX75OQJFw8EEf s0Hc4WwqtfhzAj58qmjR5BpAEyNlibs8VHg88rfAD5t+fKIgKPqfIBX6+//J fvKpD7/N4MY1ElSYDaIaq9f34p4PCQKB0lSwPHeqdbdeL5q/8uQV3E8FCcNn 76zbe7DOTuHXFg0q3PxqnbRhoRvZp/h+xAAVvm5YV5oT3I0H9lFZ4vpUOHbE S3tZvhuj6LFfpc2o0OtSMODv0YXvG9ynMy2pkMzmlVDY2YXLaUaM/bZUsDpu Wn2z7RPaWa/5rHKHCuJHSkV7VT6hxqhz2/FIKoRenHPVOdGB+fs9tjkkUGGr MydKobodZe7evR6aToVG+Rb2haPtuFnIb2m4mAreMT1uew0+YuBV/2PcFCr4 veOlnuxrw+XsoCC5RipI2o5oh9i14YxuuOSdHip0ciTEyqNb0fpFtG3CCBVu 48cOFZVW7B+KK6ijU6HGV1FXoOsDNnikndzIooLQToU9eyU+YAK52ClLhAa3 tphQfrS34OaF8rKPO2jQ267Bo/aoBQOPUVYWZWhQv0mJVa7egh79jVHwBw0u ZJmSVF414xn+PsrgJRqkWKgL+qe/wwbTId4VSxrk12dM+9m+Q420UeN9djTw FJzS3HHgHcpoMenud2nAsg98u1jRhMtOxPr1L2lAMm7XfshoRI/Kn5dUUmmg +KVMYaS4EafXcpHMs2lQtbbuo/3jRuxN5lcjV9CgvA33zso0Yl6n+LVjgzTw /ZG66endBpTZIZVlM0GD/YkKwVfONmCCw575Z9M0EKoSdRfZ14CB3AoB/d9p oFWzlbJ7oB6tVLXfuIrTIeb+L/aIXj32+ulyYqTpcMfu5Hr5PfVo+FFPt3o/ HbieLvjKcdXjEduzvfxadBg9VaqjUFuHm19aLaddWeW7+eOrj9dh/X8PjXoT 6UAbW1SOa67FXnEPjmsGHZJutMnXxdYiU8OGtD6XDvqOT04U2NfihnunWCfe 0uECn2VD5/paNFsSSCoapMM2BhGfdK0Gv8xGzoZuY0AKtcp4ekc1LgsGxBzY yQCK0O1dLwgKCh3whGYZBjhwhCIp3RRUczCP+qXKgN135F/nBFPQjyF59NYF BjS9CVP24aKgyCg5+HQYA7YNK3l0c79F2eUYtclYBoQ1U3yG6FWoKRk09jCF AaTByPCTzVVoZeF4uDKPAb/uXdTQDKnCnL6Dw7IfGfAzz07Wa0cV6nSU718r MAmd5nW0XqNKNJnL7kndPAlDyj+VddUq0WZDvM/R7ZPwl27lZrZkJT41/KfL Q24STpKzXNS/VmBPM3hTT00Cj4qWPTusAh3w/fvax5MQpqzf5EAvxx+am/eo BU+Cab433aCzHINLzf/JiZiEz9ryHCtKOebmMA9Gkyahl2s+Zn90OX6LWhvl WDsJX6O1RfYYlOMdB11Lkf8mwSLrTzZRWYa89KDyZ9xMEOEzihnOLsNYy06h FX4mtK5RuTcVW4YVF6waZsSYYFN3LtTHswz/034gh38wgX1HKzRYrQwfbqlc cHRnwo3anqk3VaW4JWTFcNyLCes3t3DNvy7FdD59sulDJohFRLaaJpVi488+ MwhjQqxdTuojv1LkYy5RRPKYsMNASvCafimGvFUOxGkmVMQeZVZ8LsF4m2yJ bdZT0N5jwuUvWYK3zmxvUHSYgpyN0gcMhEpQR/WZo57bFHgcuZ0mx1OCtDVO lbcfTsH77e92qs0Wo2K6klk3aQqW/v5H+n51MdZOlEWEUafglV6nladNMdIt m/gFbaZhv56IItQXYfmpPwqlnaZBwZlCr6kowqcHs8w1b0/DG8+aq+fyi1Dx V1CWg/80mNUfqc5ILMK7SWf0WjKmITBOv0ziXhHyj3T7BTCmQSCxPlJIpQgP XqZyftvOQICq6SKzoBCThOH3c+cZmFdq/9jyqhAF25N4xT1noCBo3L8krRCn j18WUQ2YgcubPCRzowqRrNCpYp8+Ax7Bwhu2exWixEr1rc6xGUhIOT3QfaIQ +bLiaKnmX8BaZOWYaW0BelpzZhSvfwEfr3gr1+ICZEiYLlTZfQH+pZVnCVkF WB8mxNXr+QUsP0jc2h1WgA+8A3fyR38B4Vdka6Z1AS4a3bns9ukLWLWUOmqv K8CxJeMO3dOz4GNfSFKyysdQyYG9budnIfZGisuhi/moc9LKO9ViFq7p37XX NcjH1MhbMr8dZ4E573kh+HA+Wqs8u08JXp23a3duWJePdJcGWfWPs6BiXzic XZqH0zNqfgrGX6G3jkvUWywPF8fFD4lemoOKWdNK0s9c3G1DqO2ynIN+eqi8 91IuGjN7NeVt54As1qFkMZuLb76GndTynAPh0tIK5ZFctPvBa24VMwcieiYj apRcHBZe9Mnqm4PzCu+Hwx/kYv2p1jZ1s29gtT+uWHptLobn3rc3N/8XdqlL Hg3d+xplhfjPeiXOQ1lshWX7q1dY7vYwNzR1AVg69A6yfDb27otadz5yEcr1 /jh0vDITT8tt13COXQQPy3VFZUWZWCuf7PAsYRGSr/7tLJubiTkK2R/q0xch Lu2t+XJyJvqqUJ4fLlkEOXHXvV7+mSh/jC4k0rsIl0r2xpHOZuIDU9XtA9uW YJ34oR7VMTIuXKo0WBJfAs3TNns2DpDRzvyYt5DUEqwYvzSe6CTj+Sv6w/qy SyBtqvLldj0ZZa2vJlWqL4HV799JZ8lk/OTkvzvBfAkY8VE/yhzIKOPfI28Z vwSRbQe802cz8HIxj4pd8hKMPSmxe0PPwBCqqqZr2hK8fXZaNm8kA9kQffpR zhL8FaCTHNmWgc3Lpjczq5ZgS3Pc6MzrDHS82587N7QE4zxaDbn2GZjvOKTk K8GCqQ6/Lo/BdKTFCRwJkmKBchDf882d6Sj2XhPC97DAqW9MlvQuHR/KJhin H2BBskaTdnRxOp6nX3Fr1mJB5mGOeuvzdGRd+1y06SoLPB1CtI8dTUdNk3G1 1EQWvFyz9XpwSBpWT/PO3UhlAZ+4nXPVozTUeaSYKZvBgrnub5J9d9NQr9h7 W/5rFuS4xh3vsk7DcyIinOoqFmh5ztf3qqbhjUGDiuEBFgTdsu9q6iMhw83V NWWEBcJzYlYJH0hoLxArd2N8db+rf4Wa15Dwlhb95QyTBQwbsA0ik1bv38fr O5sFoim8FsXuJHxuXawpKsKGxQ26bsN8JNz0Y3BhSIwNF2tOnmEvpGJ4xEpO siQbsrv/jST6UjG2wUhi31425N0XaziWnIokman/VA+zwS7zbUWJfCqWTktW nzdhQxNNd/bM4RRUf3TizjZTNph9dw6WE07BKnFHxSFzNrBjsv2LF5Kx1rA8 yfo6G9YIqBCfCpLx/RsTH1cXNtxVPXBinXwyjro90XkRwoa9A5VnCL4k5Kqr 25kezoYIv3bh4dFElBFaXi6PZoPh8RtfdUoT8WaeB2UiiQ1ZyZzIgOuJ+H3m uoZaHhtoWQxaSUECCttoHR5pX9V/7Wi7Ri0e1Ys9t8x3scHBf+F9Dnc8WnAX za/tZ4OHt+UAqSMOSalyBUpjq6ly+sBytovDg59FFB9/Y8Pmt11GG1+8RINL /+7bL8QB533fz6oVx6AT+QCvzlYOmP73xS3fIwZDl2wZF8Q4EL7dJVLucAz2 RXxOf7CLA4klra7LedF4o+PDrk/KHKhW/Dp/My4KA3fyrjBUOXD6T6v27SZR mHNLd+zHEQ74pnwLDeaLwnnBiqS9uhx4vsN2JdY1En30yeL3TDiwpy+NdlYl Akmx49+fm3KAOWd4UGwsHJsmJQZJlzlg2RPYc+lZOAoGRMS2WnNANOLkFH95 GMbV+W6VcueAXfT5dcE9IVisabHxXQQHDj2deNprHIgyi8FJ0TEcCFEekVC7 /wRjXlcr/B3PgZ4rb9bsJwWgl+RuQ540Dsgy2xRh7DHq/GIGHi/kwGL8zU1O x3yxsGy76JZSDtx2bjncdOIBSrsYZk5UcMDjkqFFkvZ9XDue1+iHHHh42rpJ ZsNdbKu7w1XbwQFM5KwfkbyJ2t5ZYS+6OTD0PYKwv2SL+SqDUpb9HIj/KRqq 6WaNkelHjy2PckDtXnjfia2n8XLAmvtac6v8fRn/gXvXoVVbTUBwgQO2irAh JtkWjrJt44ZYHPDzuygZleMEUnYfyr2WOVBXI2a0RuYOMPTDl8rXE9BcW0RY cx6CGVfD40AhAsQXXBp/dz2GlsqlLWZbCeAjhXvUVwfA6/3mh9gSBPjmJLEo DU9hB+0pNkkRkNlzvPnleDC8SHh7LnoPAYscobe0TS/Abb2Us+oBAmqklb5d 7Q0HWqPx8holArK4Im6UCkbCxQePnnerELDbYKTnllEUqM8xctw1CYjPOxWV xIqBXx25zAIDAtaHU7quzSWCS9Cop58RAca/pOYHopJhAoR4jU0I4JfbdTDY KBWaCj32fjMn4ECSeWDTgzRQdyQX11wlwH3boSkjr3TIlu4//uI6AQVbHntW +mVAcKSmtaL9qr8AroGWskxYNnT69+dNAg5a/D7uzMwCZ55k3zYXArj1+mRX ZF+ByR2u5Jt3Cai6UO2uOvoaGhQPK2rdJ6Aw9h1t5NIbUJ20oQj4rvJuOn88 ZeSBqFnL0KsnBBx22ZW5NasQ/tQm69o+IyBlImhEPLwI7u15lC39ggCXHHf6 uWfF8IrfatNYOAEWnu2oFVUCg9+0PBOiCfB6eG8lsaAUBPrEPpvFEbCsERjh PlEGWhTWia1JBAhmbOngk6+AxKD8zSEZBCirXrnkxfcWPjo/v2eQvarffpXD TabA8kWHsbW5BEj+uK4+bFsDB7VOnarPJ0AqxdeE5zyC1e49b3yKCfhuYH6V UlYHoXwrwlrlBBhWyfepjNUDfh3x5lQRUHuF8k1XthHmuysnimsIsCIzuHWj mmB3VYy+az0B215qc7UrNINJqke+wjsCRnZHyKp9b4FHT4y3Tb8nQJQvhcrN 0wrFTooPyB8J0Di7y7rX4iPQzgvQrT+t5kv+SGvYpk7YqsE8vbOXAA7/taWX O7pAT6qxcGiAgKmVkM/nfnXDnbUksdgRAoZq7jHTdPsg88sD3wvjBPCKFly0 4R+E/k8Wk5voBPxU4FkZCRqBnSU3H9cwif//H8D/AMFQkb4= "]], LineBox[CompressedData[" 1:eJwtWGk4ll209j5PA32lCYkiUqQkMhXZmySlqBBJ5ilEKBFKpkJkzjxPmec5 S0SSSkTmKFSGUNLzvoaOc66z/+zr/rH2Xvew/iw+Y7tLZgQTExMXjYnpf+9t piPlcTwUYvq/MwzDR4U0ulbxifyBRqaXn2EL19rqEH4KXR8Wl7F/NgAKTF/2 qO2nUM8VsuLTgT5wGK97uEGYQixftweMcvdASlvsz2YRCm0iZs1fmnRDZ7Gz lpcYhQ49r/zO8vMjrInWqkWSFDJq33u9JrcTJO6L712SoZBT/Pxtv4gOMDPb 7F8pRyGJLFvx/KQPEKk6NXsLU2hD/q4dYi3t0Cz2WltMiULM7COhluvb4e+O jLrp0xTSIEK5lcvegdCK575sVQpVnpQ37nR/CzqjBo/N1SlkMl86k2XSBn6t cr/5NSh0W/GK6EfjN1BduFP382UKZdf5mGxxboWJyIX6WF0KKaQMvUtJeg3c 7p2COvoUEs92N0J9LXDOpDCIzZhCn1Tr0n7zt4DbmcA/7WYUar7Gqsrh8gry RK30Aq9T6PxV6xPH+5thiP1045kbFOKVL7kgoNIM6AtTSMMtCt3otB4UlG+C Lfd/8bQ7U+i0o/REXM1L+MI9mjvoRqGvij88fRVeQkll1/FJj1X9in96cb5v BG+tVy2UN4X8juzJSzRphMu/Ki+v86NQTOzd3+4rDSD4JHt0eyCFgqyVbgsm NkBrSyCTaASFPHPN06mZFxBndj9ILppC6+0j/NQSX8ANwn7X2XgKcWafft1y 6QVskdOUMUun0M/iq2G/XtbDl55TzQ7PVvll3xni9KqHktvSmh55FFLKe6qi rlQPlwu4bsaWrb4nqUJIJgAIndu4klVFoeTPViGpRwDo35cDyp+v+nuh7Xz1 qzqI4x/J/NC06t97LFdD1MEN6JD8/JpCRPnfGL6M5yCv97Jx6i2FcjpBW/D8 cxiJyPy8vptCBXfDZeTTa6FYPPoGex+FJtuE385o1YL3e/9F/qFVPV/TJjxY amE/i+0O+XEKKb8cNc1wrgEbNwn1WwsUQr8fMKs5VoP8zv2DDxgU0rZ2VJeU robN5Tusn6xQyPQ7/yhtuQqKZxi+2evoiF+xfM9cYBX8NX5RN8xBR3GVhUJL DZXQ8q/43E8uOpLR0lv7KawSYuLS+hZ56EjlchgQ5pUg1/1wgUOQjv67KHyO nbUSPM+oHT4vTUcKVgJVrdYVoDmOanVl6eib4jeb1lMVsM9L7KwloqMBkQ6b 53sqoKWWzdzrNB0ttv8+eqW3HFiP9MdXadPRJlJu0lOzHIbb2g6+ukpHTmHF ARKS5VB0va7qowEd9StURsZylINmanLXjAUducmftbHvL4NoDstN+53p6Hmw s16iTRlU7rqg+tP1f+tzebk0y6CHX8av/D4ddb7Q3s4qVwacosxrTz+kowcb Qu9rbCqDyNNZSxaRdKQpSTOnl5ZC+fng40di6OjXu9K4kcRS6NZwdqbi6eig afpe4YBSYDdUmX+UTkc/TbSaPhiXQrjz98lnpXTkn0l+lOYohdJ77QccKumo 7uBhjSGyFDq9Ky2O19LRZOam5I65EtgW8uhrayMdWcpY9sa9K4GQZ0L9kx10 JMCcFOMdUAJBfZatInN0xBRvR0ltLYH84QvMC/N0xMYfEfSTKIG34zLKddRq fVkLS/98MWz8zdygxsRAHzTzmdR6iyHgv2dVdpsZKDPg3Qb3tGJ4JPcjq0iE gWo1SW++k8WQpfhh3EWMgYpuNqrmSBfDK5UqAUVJBsr5mpOpe6gY1mn5JXXI MVDUmBK/IEcx+Nw4EPVblYHCJz8bmkwWgWfC9YeSVgw05KDm2BtbBIpXzafU bBko7zh3VmpIEZCcJhctHRjoYLzi2aCHReAdoscde5eB0ghrjQbHIvD1Vi9g CmCg7Uy8TeHni8DPSvLTmxwGaiEP+FxfVwRnBcXlxgoYiMuP/8/CciFsGD2c vFLCQNEnr1nE/SkE/2tC1mK1DGT/51mKyFghPL7A/S+yjYFMHkmJ6jcVQrAU TdB4moGkC9S60/wK4cLv5QDXOQZCEXkh3p6FsLWQMRv+h4GM8kaCnVwLIfTA fPWrZQYSqKREgm8UQtiub2oirIsoVE+YFnqpECKJt07U4UW0tuB2TQRvIcS/ i2oOurmI+piJ1h2PCmBXFSYjbi0iqfCpxSz3AohL/Y5inReR7ZPpcXXHAoh1 lqnK9FhEaeNvqgf1CyCavyenPngRaW/Zbj4nVQARTjtCfhUuoq9caRLPJ/Ih kCfy6uW5RWQZ4h2uaJAPG1nko/T+LKIGLtEaVu18ePx77KMxfRHpW6ic+qGW DwEtkmp2tCWEs8I6W+Tzwc+hCz/auoTknZsOifDmg08z2/5qsSU0XD3hY/El D9xtw2Z3OyyhQ1yP6On2eXC2QWxw6PYS0k+cdrSwzgNOjvbXiS5LaKglKlbM LA9Kn29M5XuwhPj19kZ/1smDiY2+WvuCl1C45/0fiTgPdHKcqw/lL6EzzadS E7fmgcT3a96yE0vIx9DhAkdVLhBySzeXppcQX75FX3NJLrQ/ibn2fG4J9Tyd qXHPzwVr6U9SiL6ETkr3qqyk5kKK74UfiszLqPei3w+VJ7mwZd9JtbP7l9Hb 56atf81zYdJIiPOK8TLyHaiZN+DKBV2b/oPW5svoz6yZ+DX2XGhxCkLuVsvI SvvRssGWXEgPmDdPdlhGU2EKa53W5YJBWX3ZD89lpEDuNv7yKwc6ma9o3E1d Rlm7QtYUteVATYFfUOzoMuJ4Knq6wysHApYn1gyZr6BApw+6X5azQcU+vCXb agUdMSutF2Fkw5qxE4/v2K4gn1PaL10XsuFeW/D2rU4rqObJ/ce8M9lwM1aK X8lnBZ2uVHP2Gc6Gy8c8UXbqCjoZE57c1JgN/Ld33nUaXkHsLjXWswHZUD11 eoZV9x8KLyKTuviyoXufzJfjAkzY7nVFDZvhM7A8YCIals6EH/EWnNSNyIIX l6+6KvDQcD9mlSh6nwnNoewt5/bQsLLxt8yDbZnQ9u49mw4/DR9zE+VOa8mE HmWlfNv9NDyV7fwl6EUmzEqJjMQepmFzbgU+1ZJM4NnxT3lBnobblNqDtSMz 4e6nlG05BjQcY7OhxUc3Ezy2XzMoN6JhDws758LLmeCrviP3hQkNI8jj6LmU CSGvAk71WNDwxUXX+d2qmZBVcct57U0a/mWUy+4lmwndT5WHDDxouF5JP/gZ dyYc1Zl4xpZMw0apN5rYezNguCVRbTmFhkX/VLht7cqAx8e0fo+l0bD9DmsZ lg8ZMM5VL1eRRcNif3IDp1oyIGYw4v2VQhoOHuHUe1CZAYSJwp8EoGHVwknb nsgMaL8RhQ8M0fDVw0Hf+9QzwH3o/NjWYRr2qth04oRqBgirk/6MERqu5Ot5 Ha2cAd5HbDvfjNHwIy7rUwonMkD690lz22kaltia1nxaOAMSnGcCSpZomLtT XYifzAAbL+VPJ7gJrKM00uFUkA6U/4dvu3YTuH007hRbdjr4hOpRizwEltW0 83iWlg4JyQ47q/kJbHFRZrQ6Oh3aIeGqlDCB00bPmTt5pcPRpYXPh48ReK/s vTkprXSoJz1nN8kS+GeT8ZOT6ulw7r9NtGm5Vdw3y6l8Jh1Mufby52ACp8i4 mB86kQ6RMuqmgioE/pwmt/muQDowbmV+59UmMEvXn1JqNg183cTpKzoEfo8q 2i5NpMF27+csQ7oElpAsNEv6mgaHwjqF4/QJXG5zzJK9Ow30i/7ZcJoTOOvG 7zij6jR4Ma09t+U2gXfga5raHmnwyJyZQQsj8Li0/H1BpjQwe707gSWCwC3U Rc23C6mgeOio4tanBJ6xUgu5Op0Ki3PX/PfEEpiXYyRetC8VbN1LuFAqgb0M FuafFaeCVri+rFsJgXft2Gd7Tz8VxP86fvYqI7CQqSndUSMVWHX9vAIqCDyg YsN1ViUVWnhL38TUrPbrsKYqQiwV5HJY9KoaCfyDb9ObKCIV+BtK3RY6CbzC JshREp8C/wRa96x0EfhqcZahUXAKDDz8/HJtD4FHMl9kjXqmQOT5DZvYBwh8 D30JMbdIAZZeg/ijowTm+M66IHc4BcZlbyvIjhNYIarb25k3BRoS/McUvxO4 Jns9z4MtKeBmWiZyaYrAcml1Y/NzyTA7s6Hu5jyBG48oc54qToa3l/YYOy8Q mI8j596r5GTILpNc50ER2JT0n9oYkgwmroZqT5YIvGZxmLvfNhm615UP5a0h V/1s77simAzPdxv9m2AjMfNHOqXnnwS4zH7xPQeJx64O3i52SoKX5zz/lnKS eNQnybDKOAnaXFNn7u0isYvASHznsSQY6B37vE2AxNHDLneXXyWCof1C/999 JKZbJYidjU2EUeb1PQOCJObmN3rYfSMRpqSF2jMOknjQrtcseksiLEVY1R8/ SuIDm6/FHzqXAB4irrW8kiRWXkrmGeBMgDVNAZVrpEm80WhdQdxoPGyczy18 d5zExi7XDCVd4mHXpZkkY0USO0gOnZmPiANZ1lsP/C+S2DF00mFbZAzUpXu7 22mQeOerPcaz6jGgeCLCRVOLxOGG64vPMMfAWZtye54rJC6a67p57FY06LZS RsWGJJ7SiWC+Ix0FQ0Ys+k+NSTy3afux+K9PwZi+U9fNlMTq1zskGgOfgpWQ 7CVlSxLPd03UvOiPhLu+7op9dqv/ocl6Kb0IWNkdJA/2JN4t5JfDuhAOnmUJ x9McSczZBZZHAsPBfxTEbe+QOIStunKwOAxY3doPa7is8t95/fpBhTAI3T4i LONK4juivNPKbaEQo0jsJe6TWGdQfb92Twjw9G3j/eZBYs87PdorOiGQYr+X u81zlb+RNK2nKxiyk5S2R/qS+Nxxiaoe3ydQteJLCgeReLvZbo2xdn8ImuML kw4m8YL+1IiOrR8Yj9bynwolcXn0xsLslYewofWXgmEkics0osp65r1hqDbw w40oEq8Tnxxde8ULSgqEjFxjSJyi7sNTmPsA9CL0PSITSLz+o+xQnJwbHHlE 35yWRGKPjqmiUUdnWOManliUQmKfvQYv+z1uQZ5ha11bBonNQ/ifqO2xBE8N M7W+LBKXbL1w/K2oPlxWZhr6lk3iNlUOupmnMqwclFomCkj8RnWZt8/5Gurg +fB4S9GqnhMjt6TKrqPMrTa7eEpI/PjBbaekZAd04W+y7LEKEqumXD/VLnQf CUzIvVGuInF90SGWqkVPRA180tWsWcWTvfemI31RcsOmu3aw6t/J+ytv3YKQ U1kWi/sLEmcwhDU9roegs1kno/0bSSwXzK55uDoM8cQOCUU1kbj3hNljC4lI 9CvQpTL9FYkvpdkalw9EoWYPNpWS1yT+T05pnVZlLIp1LPhU/4bEXEx6S+pv E5DSlbGF/ver80MmdesOpyDOcx6+Pz6s9l9D1/LrSUNT8twcfztX87joejbj XwaqFytPX9NNYvEac7VwvWcoQuCi5Lae1fx8tXNL+puDrHZMveTtI7HNzbG8 0b58JL/hoabIAIm32RnXm7EUoW3LfKPHh0j8temPovGnYjQ+U+uoMkxiE51I Cd6RUlT9RZu8/IXE6euG3NYcrUBPun6FmoySuIW9MUR4sAqZtgTy24+TWGmc 9WPXfC2SqREqvvedxLaq3Xp6qvVoY36jwuMJEsd0ddHx7QY0nKT/IXqKxK4I octsTag0jG6Y+ZPE5zs6xGUutSA/3/DZ0lkSp5rvj+6zbUP6LqIeDb9I3Dx4 LG/6ezsSt2nd3D5PYnv10ArHpx/ROgOzxMGF1XyaGi9ET/eiytOlAjoUif9/ H4P+B/296i8= "]], LineBox[CompressedData[" 1:eJwdlHk01vkXx1Wf7/O1JGOpqUiESEpTQ02YuVFaqWRpyJKEKUmRSstIEooQ ZXkYy1ieDc9jFy7Zs0SLLClMZEtM8qTNPL/fPeeee97n3nP/eN33uarOpy2O zxcTE0sU5f+qY6HaKwMJAmL/jz68MvyCYyPSOgPKl8LvvkaLnrMGx6UIhPnr /f6bTzeubpVuOitNIN3u6kWTwQ78XJll6y9DIH+F1LPbO59ha57JaJgsgXta f+meM32CAUb5g5HyBKaldWQ9itpQv169P2YxgQ6ZvIy6wVYcPRDzMu5HAur+ m5RCmpoxqZvqTFwm6k9xfWeoJrRw8X2aokigb/TfrJsBjciYGGpNX0Hg2Kz6 WdzUgKXnbR6xVhK4b2nbdUemHk/Na6jlqRI4XyKQPbSoDlVubaniqxGw1a4K WKFdi88UWGUFGgRO6f6WsNOhBoOTlhWXaBLY5RuaqJhZjYZaoXnlawhkaowb Jsyrxkn+5+yqtQTSVrfZW518iH8bnGTXriMQcCJ2znSgCg/X9qQ36hI4o2tP alyqcOH+fSktPxH4NViOeXyqEis7y5jtm0Q6TP7R16BK9HFeF/tcj8DmqMap m+qVqDWeeLdrM4Hko2BmFYX48tyiO72/ENi5eZGL+XAFRsxdDe03INDQdq9N sLsCt4e8vzFoREDNcnTOpaAcOcy2y++2ifZ9mBSOZpahw+ptF6ZMCBw4bclb ta4M5XL53h93EIiTSy1xK3mAftVRJ77tJiAhHl7Q9KYU15stcJ23j8Cr+oX5 owGlONDhfZQyJ1CgbqIkv7oU94xaHpa2IKD8dGIp8SvB7961h2QtCQR6l3lo aJeg4Jve/sXWBHIsq4PmeotxueyPpitsCejL19m82l+MrfE3t6keIWBWtWHD GeliDFD/ZKjhQEDr4tLXL1qKcGRz16Z1zgTmXS7y8rQuQmbVbt2fXAi87DNT M1cuwgN7S7X1XAnsdZS47zRciMUOCapGJwj8buaTkRhQiME37GXMzor8lnRW w7e5AA1lWiUP+hCYSjYueJ5agJOxvzKsfAloelmNMP0K0Ia78tsRPwK1JvO0 FdcXoKR+xCenywQWdySH8SUKsALFpl2uingq3VLwHMrH1U/7Rz0CCOiGO81X S8vH7iMWQ16BBBy7QzbPv56P4UMP+32CRP70TF74/Fg+zsymdV4OJRA10Sm1 Visfa1Vc625HERhy7LG+U5qHKq/bl3lGE9hxzbAyJzUP/RKNTu2/RyAo0Kfa 9VYebli+WEEuXuTnFk5ogEMeMuVrjt5PITDf7JHKoGQeCtt1Cy6kERBanTLW EQrQIiJB3DadwPqActU3/whQXNo7R4lFYPsOlsz9CgH6MFZ9S8kl4CO3wo51 QYCPa8IOXBeIeC0/16bgLkDt67NpLvkErHUMujtsBNg317ZHs1jET7juB8st Atw3+2csFwlUC+8yJ77yUX28d1NRKwE6zPJeUxQf/2TvvhnbRuBzf6T93SA+ drsXdF98QiBV9vofkX58jBi8fc2wQ/RP3CtitY/x8esrg8dVvQR+3BwvxdXn o01i5qq01wTYxg/MxHT4KLCT9w3sJ+DycnG8vyof3TtHlXYOEqg/ZfhVTJqP z9rjTjSPE8jVL7r6ZjAXdSOoCt4EgZlSNdfLL3Mx1PyM7J1JAjVvqeAtT3MR mnYVH5wm8CG8edXyqlzk1gipF18I9FiwcjyScjGwyCqlX5KC6Is5CXyHXNzQ vjd4bCEF01kTgdHWudgzuu30x0UUOD9HvRjzXNyovN5IQp6ChqLene9+zcXX gYyuDYoUTPWl5Q2p5OJWi6If/NdSsFlywc/zn+bg0EmeMGQdBZ4dC+5O1+Zg 5I20V3d1KUjstNWVLcnB4eI73MxNFMhdCKyu/SsHY1a673psIJp/UyPOOJ2D k+NL/ZX3USBN+Y+AQg4yGTJuWuYU9MZPj16WyMGdKpT5xgMU7BFX+fDiezYm HZpSNLWk4KHXzZ7hkWzcW9pYdOoIBXZPVqq5VWVjxk2/92UeFKi5tRu6n8vG I6teOtiFUfAuyscxdoKH2V4ticZ3KFi4Tyvk8FsezsOKl2siKTi09v0NrT4e Ztil2H6KpmDs/YicsJ2Hk9Gu1jFMCpZNLDm1q5CHgfSU2WMOBWv1Hr8Lv8ZD 7jhlZPKIgr/Vsw56qvLw+1bhJe1mCj5RkkOPFHl4MGS4VLaVgllL27qflvBw RqNpS1+7aN654+0KKR6CY8TPV7oocDo4qO/xkSu6/3KdomEKZiSiB+uauPil UFdxLc2A1CDx3aVXubieOVMrLsEAwc/CcPDjotO1cq8hSQbcniqPaznHxZq9 e+tSFjFgh/smwRcPLt7ucz2zdAkDTEzHxtLtuKgkmVRPaTBAP9hpq9pWLhra L/TpM2YAjH5lWnzhoKfxU+WK7QzosJLeESnkYLJmfGOCKQPebRivevaBg+Rf zZU2exiQPhQhfmKcg81BJo9aDjLgS5T5+eZeDh7J9VN54MSAQnXy0LWKg5cX jDTHXGVA+Rtb1cxbHPxuslWK6c8Abn18q3owB68F3tqdGsAAuaw1f2cEcjCI Wl+XHcSAae9OZuEVDt6hvbE+nAHna5YyGV4cTJX6xp9NYoCmXvu0vRUHG+Vl 79sjAwa2+I1lreLgEvVfjmqI0TAjHV30oZaNEHdDKD6fBr2x7tDj1Wz8Y9GT sPEFNORcP7arq5KNZZ9OlObRNPQo63jVPWCjcwtT3liGhs6HZjOFfDZm+4rV OSjTsEzfaOm7RDaaNtZrxxrS0DswuSPyPBvPe1pPS16kIcNIbMe79WxU0ndp WH2JBv6zjzUXddhY+e0M0/gKDfuO3r5Ja7NRMixsu981GubsrtSs1mBjEqcm eiSEhlsjb3neimysG96o1xBPg1uD+3MTcTYqHJPxvVFGQ4yMz5a0ARaWaK/Y k1JBQ3R/fdqBPhY6/KutXF5Jw7rBhO7vvSzMumZaN11Dw5o/PzPtu1hokHxl iUsLDWCDCuptLHTuHSs0fkXDkFpwT3s5C+n02VCHPhqUQ8+6hT5gIdeDdvQb oCFKgQ4xKWHhzJdVtGCIhicasv5F+SwMXW5ro/qehmr7fQPpHBbqDritNZqi wddNsdKZxcJnrHNzhz/QcFLz9jKVTBYq/xKZGSGkoa3n9EZmKgurxf66xJ0V 8VU8N2abzEL3Bu7+hi8ivkEgvzyJhQsjStXefKPhn7ykjK4EFvJtGoRzczRY +9unxsWx8D8lu7xG "]], LineBox[{{1.4995241839586075`, 0.5}, {1.4995707543834969`, -0.5}}], LineBox[{{0.5000316144016672, 0.5}, {0.5000523370684159, -0.5}}], LineBox[{{2.5000342672229103`, 0.5}, {2.5001569624295437`, -0.5}}]}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->True, AxesOrigin->{0, 0}, BaseStyle->{FontFamily -> "Times", FontSize -> 14}, Frame->True, FrameLabel->{ FormBox[ "\"\\!\\(\\*SubscriptBox[\\(k\\), \ \\(0\\)]\\)\\!\\(\\*SubscriptBox[\\(r\\), \\(0\\)]\\)(\[Pi])\"", TraditionalForm], FormBox[ "\"\\!\\(\\*SubscriptBox[\\(\[Delta]\\), \\(0\\)]\\) (\[Pi])\"", TraditionalForm]}, PlotRange->{{0, 3}, {-0.5, 0.5}}, PlotRangeClipping->True, PlotRangePadding->{ Scaled[0.02], Automatic}]], "Output", CellChangeTimes->{ 3.472359296159816*^9, {3.472359435091209*^9, 3.472359465427908*^9}, { 3.47235952216228*^9, 3.472359562891131*^9}, {3.4723596205093803`*^9, 3.4723596397610493`*^9}, 3.472364816393238*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Wavefunction vs Lattice Depth", "Subsection", CellChangeTimes->{{3.472204359282895*^9, 3.4722043644968843`*^9}}], Cell[CellGroupData[{ Cell["\<\ Try to use different plot ranges and ranges of potential depths (this is what \ the slider changes)!\ \>", "Subsubsection", CellChangeTimes->{{3.472375582465108*^9, 3.4723756179346447`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Animate", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"Show", "[", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"Plot", "[", RowBox[{ RowBox[{"Chi", "[", RowBox[{"k", ",", RowBox[{"a", " ", "k0"}], ",", "r0", ",", RowBox[{"x", " ", "*", " ", "r0"}]}], "]"}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "5"}], "}"}], ",", RowBox[{"PlotRange", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"-", "5"}], ",", "5"}], "}"}]}], ",", RowBox[{"PlotPoints", "\[Rule]", "100"}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"FrameLabel", "\[Rule]", RowBox[{"{", RowBox[{ "\"\\"", ",", "\"\<\!\(\*SubscriptBox[\(R\), \(0\)]\)(r) \ (1/\!\(\*SubscriptBox[\(r\), \(0\)]\))\>\""}], "}"}]}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Graphics", "[", RowBox[{"{", RowBox[{"Thick", ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", RowBox[{"-", "20"}]}], "}"}]}], "}"}], "]"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Graphics", "[", RowBox[{"Text", "[", RowBox[{ RowBox[{"\"\\"", "+", RowBox[{ RowBox[{"ascatt", "[", RowBox[{ RowBox[{"a", " ", "k0"}], ",", " ", "r0"}], "]"}], "/", "r0"}]}], ",", RowBox[{"{", RowBox[{"3", ",", "2"}], "}"}]}], "]"}], "]"}]}], "\[IndentingNewLine]", "}"}], "]"}], ",", RowBox[{"{", RowBox[{"a", ",", "0", ",", "5", ",", "0.001"}], "}"}]}], "]"}]], "Input",\ CellChangeTimes->{{3.472185355355687*^9, 3.4721853814397306`*^9}, { 3.472185631457844*^9, 3.4721856316074343`*^9}, {3.4721856800941677`*^9, 3.4721856973415956`*^9}, {3.472185760838234*^9, 3.472185787282242*^9}, { 3.4721858712497663`*^9, 3.472185872271412*^9}, {3.4721859567092876`*^9, 3.472185990571917*^9}, {3.472186046786305*^9, 3.472186051704232*^9}, { 3.4721862241959553`*^9, 3.472186286394659*^9}, {3.4721863360098867`*^9, 3.472186442662257*^9}, {3.472186511060011*^9, 3.4721865210148163`*^9}, { 3.4721865879039087`*^9, 3.472186850407578*^9}, {3.472186925398604*^9, 3.47218693761593*^9}, 3.47218699276484*^9, {3.4721873148959227`*^9, 3.4721873276151648`*^9}, {3.4721880194084587`*^9, 3.47218802356784*^9}, { 3.4721881017994823`*^9, 3.472188101893186*^9}, {3.47218918883503*^9, 3.4721891892328463`*^9}, {3.472189226296319*^9, 3.4721892477191763`*^9}, { 3.472202839039567*^9, 3.472202839294932*^9}, {3.472202873224287*^9, 3.472202873317906*^9}, {3.472202908749489*^9, 3.4722029119326677`*^9}, { 3.472204373685525*^9, 3.472204399852808*^9}, {3.472211184656348*^9, 3.472211184815749*^9}, {3.4722112276865683`*^9, 3.472211296099852*^9}, { 3.472211459609146*^9, 3.472211470214273*^9}, {3.472211563684773*^9, 3.472211571810956*^9}, {3.472211612243799*^9, 3.472211683808469*^9}, { 3.472211808023097*^9, 3.472211808716934*^9}, {3.472211844294277*^9, 3.4722118658419333`*^9}, {3.472212037997669*^9, 3.472212039908082*^9}, { 3.472212072980627*^9, 3.472212094651217*^9}, {3.472212231230185*^9, 3.4722122328007317`*^9}, {3.4722123735019197`*^9, 3.472212385641117*^9}, { 3.472224064051647*^9, 3.472224117218655*^9}, {3.472226010169546*^9, 3.472226195741992*^9}, {3.472226260395488*^9, 3.472226474249926*^9}, { 3.472226505849841*^9, 3.4722265620558043`*^9}, {3.4722266194082203`*^9, 3.4722266565684147`*^9}, {3.4722267393095617`*^9, 3.472226756245199*^9}, { 3.472226804091982*^9, 3.472226844803442*^9}, {3.472226874977627*^9, 3.472226875695374*^9}, {3.4722271572223454`*^9, 3.4722271586220407`*^9}, { 3.472227218061767*^9, 3.472227228077154*^9}, {3.4722273851298523`*^9, 3.472227428583352*^9}, {3.472227779215736*^9, 3.4722277797316637`*^9}, { 3.4722280486349497`*^9, 3.4722280488087053`*^9}, {3.472228181417314*^9, 3.472228181622279*^9}, {3.4722283157640867`*^9, 3.472228317778118*^9}, { 3.472228359624961*^9, 3.472228372039262*^9}, {3.4722284672521687`*^9, 3.472228467404258*^9}, {3.472228548933198*^9, 3.472228571881439*^9}, { 3.472348261788953*^9, 3.472348342593741*^9}, 3.472349210928842*^9, { 3.472349256874016*^9, 3.4723492795632668`*^9}, {3.4723493124487123`*^9, 3.472349312542355*^9}, {3.472349408911035*^9, 3.472349409093313*^9}, { 3.4723494424911947`*^9, 3.472349457409115*^9}, {3.472359711857437*^9, 3.472359711969195*^9}, {3.472364747257806*^9, 3.472364762784665*^9}, { 3.472364793864265*^9, 3.4723647958868923`*^9}, {3.472364934597707*^9, 3.472364934689152*^9}, {3.472366102015622*^9, 3.472366102109165*^9}, { 3.47236613288627*^9, 3.472366132994355*^9}, {3.47236621385284*^9, 3.472366213975725*^9}, {3.472367271370075*^9, 3.472367279146963*^9}, { 3.472367375966011*^9, 3.47236737626823*^9}, {3.472375544594553*^9, 3.47237557635275*^9}}], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`a$$ = 2.0220000000000002`, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{ Hold[$CellContext`a$$], 0, 5, 0.001}}, Typeset`size$$ = { 360., {115., 121.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = True, $CellContext`a$23528$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`a$$ = 0}, "ControllerVariables" :> { Hold[$CellContext`a$$, $CellContext`a$23528$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Show[{ Plot[ $CellContext`Chi[$CellContext`k, $CellContext`a$$ $CellContext`k0, \ $CellContext`r0, $CellContext`x $CellContext`r0], {$CellContext`x, 0, 5}, PlotRange -> {-5, 5}, PlotPoints -> 100, Frame -> True, FrameLabel -> { "r (\!\(\*SubscriptBox[\(r\), \(0\)]\))", "\!\(\*SubscriptBox[\(R\), \(0\)]\)(r) \ (1/\!\(\*SubscriptBox[\(r\), \(0\)]\))"}], Graphics[{Thick, Line[{{1, 0}, {1, -20}}]}], Graphics[ Text[ "a=" + $CellContext`ascatt[$CellContext`a$$ $CellContext`k0, \ $CellContext`r0]/$CellContext`r0, {3, 2}]]}], "Specifications" :> {{$CellContext`a$$, 0, 5, 0.001, AppearanceElements -> { "ProgressSlider", "PlayPauseButton", "FasterSlowerButtons", "DirectionButton"}}}, "Options" :> { ControlType -> Animator, AppearanceElements -> None, SynchronousUpdating -> True, ShrinkingDelay -> 10.}, "DefaultOptions" :> {}], ImageSizeCache->{403., {153.34375, 158.65625}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->CompressedData[" 1:eJwdxU8oQ3EAB/BnDvRKoq3MirB2kKRdbc2SIRGbAwdbrSSl3ijJn8MOe5Y/ M3vYAcXB0opa2zvYgW0t7bSt/CulbeLyDkSJms38vu/w6dNkZYyTEoqi5ASO 1vU4IxlB36bybmNV7xGPec96DF/J0te4wGgSeO7nNIn1DUXxTAdzi1Pd/BOu 3JoVcOu47gvHSjVlUTLtmG/Eu7q/wTzZ7LkYwZQpsIKtiz67+BLNYvvUwhr+ TrIuvBmqD+KZDV0J38sGWn7JJ3bDR4mscb+Jc3FpM5UV9O9xQYlHPx17EnKf jfbhQrrWj5elXBCfHSvCWB1+iOBhg62rnLxare3HXp4ZwncHJiNWuukEplwG 8TG/OYXVWssjVk0onnF7gH3F+9M7nRXkm1xePMc6Q7hKfh7Gl4dcFhc5ywv+ B9qi49s= "]] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Halo Bound State Solutions (negative energy solutions)", "Subsection", CellChangeTimes->{{3.4723597542222633`*^9, 3.47235977120758*^9}, { 3.472359961668297*^9, 3.472359962370727*^9}}], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"ChiInHalo", "[", RowBox[{"k0_", ",", "r0_", ",", "r_"}], "]"}], ":=", RowBox[{"Sin", "[", RowBox[{"k0", RowBox[{"(", RowBox[{"1", "-", FractionBox["1", RowBox[{"(", RowBox[{"k0", " ", "r0", " ", RowBox[{"ascatt", "[", RowBox[{"k0", " ", "r0"}], "]"}]}], ")"}]]}], ")"}], "r"}], "]"}]}], ";"}]], "Input", CellChangeTimes->{{3.472359967682876*^9, 3.472359996450993*^9}, { 3.472360613606929*^9, 3.47236061421457*^9}, {3.472360654261147*^9, 3.472360698092676*^9}, {3.4723610707934217`*^9, 3.472361095256596*^9}, { 3.472361275368651*^9, 3.472361308313748*^9}}], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"ChiOutHalo", "[", RowBox[{"k0_", ",", "r0_", ",", "r_"}], "]"}], ":=", RowBox[{ FractionBox[ RowBox[{"Sin", "[", RowBox[{"k0", " ", "r0"}], "]"}], RowBox[{"Exp", "[", RowBox[{ RowBox[{"-", "r0"}], "/", RowBox[{"ascatt", "[", RowBox[{"k0", ",", "r0"}], "]"}]}], "]"}]], RowBox[{"Exp", "[", RowBox[{ RowBox[{"-", "r"}], "/", RowBox[{"(", RowBox[{"r0", " ", RowBox[{"ascatt", "[", RowBox[{"k0", " ", "r0"}], "]"}]}], ")"}]}], "]"}]}]}], ";"}]], "Input", CellChangeTimes->{{3.472359997721394*^9, 3.472360153598629*^9}, { 3.47236034041527*^9, 3.472360347858961*^9}, {3.472360459727203*^9, 3.472360489474934*^9}, {3.472361106384907*^9, 3.472361122319594*^9}}], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"ChiHalo", "[", RowBox[{"k0_", ",", "r0_", ",", "r_"}], "]"}], ":=", RowBox[{"If", "[", RowBox[{ RowBox[{"r", "<", "r0"}], ",", RowBox[{"ChiInHalo", "[", RowBox[{"k0", ",", "r0", ",", "r"}], "]"}], ",", RowBox[{"ChiOutHalo", "[", RowBox[{"k0", ",", "r0", ",", "r"}], "]"}]}], "]"}]}], ";"}]], "Input", CellChangeTimes->{{3.4723601614974546`*^9, 3.472360211548354*^9}, 3.472360447911523*^9, {3.472360501371684*^9, 3.472360514842561*^9}, { 3.472360704405128*^9, 3.472360704676248*^9}}], Cell[CellGroupData[{ Cell[TextData[{ "Halo states (watch out, you have to tune to values, where ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ RowBox[{ SubscriptBox["k", "0"], SubscriptBox["r", "0"], " ", "is", " ", "slightly", " ", "larger", " ", "than", " ", RowBox[{"(", RowBox[{"n", "+", RowBox[{"1", "/", "2"}]}], ")"}], RowBox[{"\[Pi]", " ", "!"}]}], ")"}], " "}], TraditionalForm]], FormatType->"TraditionalForm"] }], "Subsubsection", CellChangeTimes->{{3.4723729498872766`*^9, 3.47237295333171*^9}, { 3.4723754311817913`*^9, 3.47237550833939*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Show", "[", RowBox[{"{", RowBox[{ RowBox[{"Plot", "[", RowBox[{ RowBox[{"ChiHalo", "[", RowBox[{ RowBox[{"1.51", "k0"}], ",", "r0", ",", RowBox[{"r", "*", "r0"}]}], "]"}], ",", RowBox[{"{", RowBox[{"r", ",", "0", ",", "5"}], "}"}], ",", RowBox[{"PlotRange", "\[Rule]", "All"}]}], "]"}], ",", RowBox[{"Graphics", "[", RowBox[{"{", RowBox[{"Thick", ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", RowBox[{"-", "3"}]}], "}"}]}], "}"}], "]"}]}], "}"}], "]"}]}], "}"}], "]"}]], "Input", CellChangeTimes->{{3.472360212822638*^9, 3.472360243450879*^9}, { 3.472360429766617*^9, 3.472360429923767*^9}, {3.472360545881617*^9, 3.472360601735442*^9}, {3.4723608085293283`*^9, 3.47236081018471*^9}, { 3.472360888948011*^9, 3.47236089293407*^9}, {3.472361337734301*^9, 3.472361572153537*^9}, {3.472361613097951*^9, 3.4723616252877913`*^9}, { 3.472365978903812*^9, 3.472366011884935*^9}, {3.472366259887475*^9, 3.4723662605319138`*^9}, {3.4723674424166183`*^9, 3.472367442663375*^9}}], Cell[BoxData[ GraphicsBox[{{{}, {}, {Hue[0.67, 0.6, 0.6], LineBox[CompressedData[" 1:eJwVVnk41VsbNZcM4dBFCBlChqKi8P5QRJIGUiJDGSJFEVEqyiy6pggXKbpk SBmSrUjmzI4pw3EOzvQjyXjzne+v/axn7+cd1ruetV85lxtnrnKwsbEJsrOx /f/MvO/Cs+9KsOE/M7HE4rRsw8ZeWcvzsheAb+kZW/16CGw21YXJynpCn5G0 yen1WMisj9vFLRsEdvx3791aewHeBv7Xl3dFwZFDrdJey0XQu+6RNL/rOZh7 hzU+otXClpEpZcauQqhWajomWdsOxPpP/vTZQnhZkAjDmR3w5lVaA63sDeS5 nBTQC+0EKz+ry1STIiBHC7S7ynZBCm9Nyox7CUydbmd6jXeDyItmjoXBcuAf /1Qtf6YfclqzfWm7qqHxcvTB82yj8Cvtvep4bDWUiWgW7/YdBVP3NlLPajU4 Sz8MeDQ5CnTOZZua3hrg25JkMF8/BroGVoejImoh5VdOnsPdcegq2eBQxhHc TXFm8HhNQmjrXot9lxuAzFP4u/3ZNBSUVSr9m9wAwXfZk5q+TENPmjGnYnsD xHG/kb/5cxoU3O1qxfUaQbBo6UCXNRlaOcM12Ahf4WB3sHspLwV2GIyIfG9q gp0znWW2XjPwtiRqxFujFcT8I03ezs0BVYQaa+HcCqNyomScjwrKARaGe5Ja oXx05NeQOhX+0efLIa22wpLW/rT8m1R41hLrdvFrGxQVR9cJ/qRCAOnpgtml DhCSvsBoJdGg3HQ+V/FpB1h41SY6sdEBL7Q+x/mlAy5OjAmnSdHB46ZwZZ1y Jzx5I69GO0uHi/89Czmw2AmXDzJL/qqjQzZfW5jwsS7YNeSfavCAAYYGwZce OHbB+Y8e8C2FAaM+agfwO12gq/vVm1HEAPGeGEr7my4ItlPXFCQyIDHN0jxS qBtWxm48eK7CBK3WDblllW44oWsauKnPhM71orWrJt1gnFTatHmKCdsuCxSZ BHRD93Ehz87bTAhT7BTcHOkGOamvOzOrmSB//v7M9aVueJxStuN7CxPqIzXq RwV74PXOlvjnQ0zYoMX71hj1QGrA3d3Ly0xIlwYLFfseYLP5byiKBwfdU7h8 2u0eyHp136hCFAf/8lN9/q97ILTS3u27Jg6i05tF0/U98HM6uRnp41AuVvr4 7HAP2CfFKpqZ48AMFDq0T6AXPqon7ZF0xsEdup/T/XohR79JsCMGB7bc3zUj Mb2gxb4r2SgZhzQuqdHWl73gk5fJb52FQ3OLm0zhQC98mzO1P1yCg9PeWEjD e0E+vHldrBKHlfgyp4itfXD6uYxsTB0Oe85t5F493AcBNRrJRu041H+Qazx3 tg8kuZ5XP+rBwU7CjGzi3Qe7enV5HYg4zAd782g/7oOPwQq+XWM4RP5IVJbP 6oOyobrx0SkcZI0qjwtX9oFBVOXRRzM4VOWNerJ19UHLTr7EehoO1jwcMfhs H/gd56xMxXGY9VAu+sHeDxfFD73ZsojDgzbLjg7JfvgkGHNZ6DcO4hp+zFrt fhi03NdRtoJDaULq9iLLfkgpK6TS1nA4vlirlXG1HwSXPpfWbeAwYTN1Ovp+ P9SiZAnVPzgEVm25FZTaDwmf4mU1NnEQ2qme5FHKil905UsrCxfeO/P+fAsr v4f0f5ssbDxxZ8B0qh8+M/m7Olh42Dhz+cB6P9S49h/RYWG//C/iiqIDcFvQ 3VibFX/b1lk9UfUB0D/LNtPKyp97TcCe03QAeArVNdZZ9R3u2B/y03EAKqNb pBtZ9fdo2mVO3mG9v7JRq8jq79qze3VdCQPgGawvKsvqn2MpdxwVDkBO30n1 dyx+0s83s5V8GYBjBGPCOIu//TUMuayRAVi0CezJY/HbKkUwifs1ANGCmYHs JBxcQnWvhAgMwkp/oegKaz5rkw6PvZQGYewI+UMEa35qrwu+mdsNgtS7hzZ+ rHk38nbO6voOQn0TM7DjKw6XvBd590QPwpHNnPnPLH3E7jO05KkdBP8jB/Xu sPSkkOR6falvEDDbh0d0X+NQ+zsyfpoxCKcUKL+esfRH/9jb9WUXEZqltvwR i8UhXGZ1oUyXCNaBD6MMH+Eg9VCGkHOaCOZ7Ek3YA3GwNPW0CQ0jQv+QSIuN Cw7TBfEBPi+IQBOLGZ6xxSGEryLV4T0RVPRevhI9gUNx15+hIzNEsM0iboX9 OJhqK6yrsg0Bc1Mb11fE4UeyuZSkxBCUhZdoDfyFg6B9kuOKxRDU2oTfGlln gg9ZhVTxdgisk1e4DiImTDgObf3cMgTGemlKZcVMOEuM1OiYHoIxolVOZQYT dNtmgsiSw7D4U+a9ewATOMvyhXZEDMO6VYn+JSUmBKjaHJTPHQb5AGP2w8JM mM3juqTxaRi0/X745q8zoDPF9bXp4jDwD0vlKH1nQFqInOGdyyNg8rUiY+Qm A7b97nINuzsCB6zyxLXsGHDvxoOop8kjcElnP7sYMMDFZbzvddsI7IspS0rk Y8De45lexEOjMNE9k+mUTYfPBInnekJjQOHKsSkvp4FOXHPdMbUxaPRx/2Hw Nw1e8QROnzYdg5qtf8U53aJB7OqA5rWQMbC8dMX4+n4a2I4nNaXPjkF0dPjb sn+pQH0j9Gu9/gf0P2tItYuZg21y4crjuhPwV+IPow2OGWjWT9S8f2wCStco BY7DFHhil3VI+swEFO2+7+RfRgGOhCoze68J6M8+PvHZkQJrf+jug5kTECvH 0KK8JwNt1KbgO8ckVDTfzBu0nYb2NGWV+vZJiGqIOu/pPgnxQm2qOU4kqKFK MmLa+8Fl5BzibKeAec0B7yfxX9C2jMnrvkMUKNixNzwjrAGVX/SRGqdQ4I9Z 5C33wEbEORwRVMM+A+w8KY/EnJvQS2KNtu+hGWCITVq4abQiSr9swY/cGfhL tlFifLgLXeuiJ1QHzYJw4ms5R00iEkkIAuWIWXCYJL2g5RBRzSkeZlLSLBR5 KSAp0SHE933XiZsls1D866W56/IQKuo4w61MnoXjuWj9TPUIYrZWBSVZz4GT sdXgSZVx5Ps13OWGMhVSQrN9zAankMy0Kc9vbSoINTL7x7lJqI2D900IRoUT N/7RPKxDQopY3ELUBSr4X1By3J9AQkM1yQ9exlDB906NteyxaWRU+iprCKcC r1ZCrF8uGTE7PYydNqhwMXSDm9xORhkMVQplKw3cKT4uQstktKRaov5LjqUL UbHspxYUVJhfWSt4jgaqV8pt5JgUJJzRPGxSRYOUbEkjGeVZVFcdfb+1kQYt 5SHBE5azyItoKX+6mwZHq419z/rNoq9i3Z6OVBpEXbd/bV47i4IShlYCWf+8 wM1cuWuWc2jyMXXH2wd0OOgtSBRzoKL4l0U1OnF0eFJ1rqXoHhUdafBx/Pic DumlhdaMTCpKZlvMby6nQ5jEt3ueY1RkHryuQ5qmw3s/jh0mdjRUdpP/rLg5 A95oYgRFAzpqTycEFdsyoKrT44nnRTqiNEpmG19hQOaSqZ7RHTqSlFCheYcy oPi4SX5BCR2Ffz4W9vk9A4SSBKdP7GSgLJploW0DA8wr7FJlDjBQldi577Qu BsyZBpk8tGIghqfLzh10Bkwv3uJYCmUgW5HQd9fkWXvF0LXxmDEGuqn/ZGhT kwluRzuE+xYZKNotbjPJgAkRq9HOhbxMhGoyTiA7JuxZIPKtaTPRHtcqEuEp E9w7f35XDWMi4zjEW/iCCa1Ojoq9yUx0qbJJ0/ANE5p12lR5Cpgoka8/2OMr E1ZNtLX42pho7d0C4RPLt9KMZhei+HAk+mNF7wwvDvtefI54IIkjja1sTjM7 cPBc+NC1uQdHrpcEi4RZvvhR4lx26lEc3X8i1vMKcDDZrvSx5DSO0kqlVo6c ZO0pw54fTjniqJ1L7aibBw5yOi4xSgE4omjsv7buj8Ozjle8Dg9xxHZBLyEh DIedpfdLJWNxdKDYbLSG5fNB5sw+1X9wZD1oxWFdhMP4WCL3vUIcXWO33UOu xuFt5mSjTTmOsmyu3N7ej0O/Y6Zn+hccVYV6pb9k7QniYXlCPK046i30q9eb x2F1S0zLcheOmL1BlM7/WPGty4JuDOKIKxTjKeeehxeDCqLBazgSFj36PIR/ HrYnhp+qWsGRTKHZXjPCPGCnP+Qt/caRbq/VmVHZeQj0iU65uYijYx5nyK+U 52F9u+qBtws4OvOfTaCvxjwcNEqh03AceSs7ZPHoz0P+aGe+Ox1HOcFeVK3z rPv6dCMnMo606nlXIhxY+H3C41oSjuq5CrjHXefhvJLkuPgUjibipmXjbs7D BQFST/cPVj3/OJyfi5qHPpL6p6NEHKU3nmrMqZ0HenxJhkYbjp4J6GSJyC/A 9MeXgSJlOHqUvXH6F30B/ggm35a8x+K7dwKrvbsIe4fvvdsrjiOl226B51SX 4OT4v87iRUw0vZRqy/fpN+i0a7s9O85EFuRr9575rgAPe2uz9A8GsppOUJOR WYPDhEtPt9xhIGqDy4Pm4nVAh5ZjFMQZSEN4QNrk8n8wHuD/4e9yOtoGS86j i3/g6Z6D6lts6MiMcXFZ3oYNMzgsdYp9gYaIX66wX9zLjk02Bx9STKCh95GN jrJL7Fj3u0NFywdpyI3bf6KzkwPzpYomxw1Skatf8Hv+dE7s64W7U/mhVKTp rtZp6cyFcSOb5KeqVPRdZC+fvx43ppSvMO7/fQ59fPsoYy8nD2ZkO3Y2IXgO BbOrWreP8WCSPpH3B+Tm0LbRu8d9KrZgA2p9FxZbZxH5lVxSdshWTNDU58ny 3VmUtEeCq9qGF0vk+bDpoDiLEtLdvjnLbsO8t0rrhQ/MoItJDp38M9swlef6 C/uiZ9DK0fzV7Do+TGhO19RfdwaRyMaBXyL4sRo+BcP9DArKNdi3s8NZANMx Mttd8oKCih/7C7urC2J6IWIuD85QUISN6wnOJUFMVZ2uXr6Ngg6M5hRGdGzH jr3RFOv7REZpKhnFHSeEsOtayRZb75BRaH1c2olqIawq6IrdOTUyOrnTJr9V QRgrMBW8zD3F8nOfb/bCUcIY8e/LvRFZ0yhbykWhfUkYe2WYomRtO40UGl6n WNmLYMVzWaHNhGmUoP5FtadOBNNo+PDLpZeE3Ba5ultUCViB8nqMTzwJuZT9 lI16SsD44u1XmVYk5P3o7IZFIgGzrzA26z9JQv5nKwb5/yZgKhmH8j9aklDk kn98QgoBu81ulhhpQUJv9VbXUzMJmFjKlMpuUxJa/bw58OpfAjZwALtkb0BC CT38cY3fCNh87X40qEZC6XnXPZ60ELBUNQGBelUSyrvdaXK8jYBVqhOvFaiQ 0IcdCWttnQTsqIW+bZAyCY1eJHj09hMwl8Dd9J27SUiZJGEyRSJgq365hCuS JKRVcVfmJZmAYToSTiclSOjw45HVqzME7CqPX+1BcRKyVM4snaMSsEeGTS95 d5CQn5eszMICAWMUjGuXCpNQiP7D1fJFAkbKOLn5XIiEHgtM9d1eImDOrinD YdtJKK0kL2ZlhYC19VTUnxcgodwHXO41awTMsCiyzYifhP49fdU4ZIOAWX7S pqjxkVCFfJO04R8CNiTzXmjHNhKqW1Ra3dwkYMQ5vhNsvCT0Px+7zm8= "]]}}, {Thickness[Large], LineBox[{{1, 0}, {1, -3}}]}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->True, AxesOrigin->{0, 0}, BaseStyle->{FontFamily -> "Times", FontSize -> 14}, PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]], "Output", CellChangeTimes->{{3.472361503143976*^9, 3.472361572646884*^9}, { 3.472361613457735*^9, 3.472361626093522*^9}, 3.472364816871069*^9, 3.4723659218577747`*^9, {3.472365980374215*^9, 3.472366012767681*^9}, 3.472366260818355*^9, 3.472367443113647*^9}] }, Open ]] }, Open ]] }, Open ]] }, Open ]] }, Open ]] }, WindowSize->{960, 1151}, WindowMargins->{{0, Automatic}, {Automatic, 0}}, FrontEndVersion->"7.0 for Mac OS X x86 (32-bit) (February 18, 2009)", StyleDefinitions->FrontEnd`FileName[{"Report"}, "StandardReport.nb", CharacterEncoding -> "UTF-8"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[567, 22, 115, 1, 74, "Title"], Cell[685, 25, 226, 6, 26, "Subtitle"], Cell[CellGroupData[{ Cell[936, 35, 100, 1, 69, "Section"], Cell[CellGroupData[{ Cell[1061, 40, 126, 1, 20, "Subsubsection"], Cell[1190, 43, 439, 11, 36, "Input"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[1678, 60, 124, 1, 69, "Section"], Cell[CellGroupData[{ Cell[1827, 65, 105, 1, 22, "Subsection"], Cell[CellGroupData[{ Cell[1957, 70, 193, 4, 20, "Subsubsection"], Cell[2153, 76, 181, 5, 39, "Input"] }, Open ]], Cell[CellGroupData[{ Cell[2371, 86, 483, 15, 37, "Subsubsection"], Cell[2857, 103, 435, 8, 54, "Input"] }, Open ]], Cell[CellGroupData[{ Cell[3329, 116, 434, 12, 37, "Subsubsection"], Cell[3766, 130, 605, 10, 36, "Input"] }, Open ]], Cell[CellGroupData[{ Cell[4408, 145, 131, 1, 20, "Subsubsection"], Cell[4542, 148, 339, 10, 48, "Input"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[4930, 164, 144, 1, 22, "Subsection"], Cell[5077, 167, 432, 11, 36, "Input"] }, Open ]], Cell[CellGroupData[{ Cell[5546, 183, 145, 1, 22, "Subsection"], Cell[5694, 186, 862, 22, 59, "Input"] }, Open ]], Cell[CellGroupData[{ Cell[6593, 213, 114, 1, 22, "Subsection"], Cell[6710, 216, 668, 18, 36, "Input"] }, Open ]], Cell[CellGroupData[{ Cell[7415, 239, 166, 3, 22, "Subsection"], Cell[7584, 244, 543, 17, 56, "Input"], Cell[8130, 263, 339, 10, 56, "Input"], Cell[CellGroupData[{ Cell[8494, 277, 953, 22, 54, "Input"], Cell[9450, 301, 19482, 331, 265, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[28981, 638, 112, 1, 22, "Subsection"], Cell[29096, 641, 250, 7, 36, "Input"], Cell[CellGroupData[{ Cell[29371, 652, 1074, 28, 54, "Input"], Cell[30448, 682, 20076, 343, 251, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[50573, 1031, 119, 1, 22, "Subsection"], Cell[CellGroupData[{ Cell[50717, 1036, 201, 4, 20, "Subsubsection"], Cell[CellGroupData[{ Cell[50943, 1044, 5220, 98, 130, "Input"], Cell[56166, 1144, 2840, 60, 338, "Output"] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[59067, 1211, 192, 2, 22, "Subsection"], Cell[59262, 1215, 692, 18, 58, "Input"], Cell[59957, 1235, 822, 24, 59, "Input"], Cell[60782, 1261, 582, 14, 36, "Input"], Cell[CellGroupData[{ Cell[61389, 1279, 603, 17, 26, "Subsubsection"], Cell[CellGroupData[{ Cell[62017, 1300, 1267, 31, 36, "Input"], Cell[63287, 1333, 6344, 108, 239, "Output"] }, Open ]] }, Open ]] }, Open ]] }, Open ]] }, Open ]] } ] *) (* End of internal cache information *)