<?xml version="1.0"?>
<article artid="pscr370073">
<article-metadata>
<jnl-data jnlid="ps">
<jnl-fullname>Culfvpn Fpevcgn</jnl-fullname>
<jnl-abbreviation>Culf. Fpe.</jnl-abbreviation>
<jnl-shortname>CulfFpe</jnl-shortname>
<jnl-issn>9968-3454</jnl-issn>
<jnl-coden>CUFGOB</jnl-coden>
<jnl-imprint>VBC Choyvfuvat</jnl-imprint>
<jnl-web-address>fgnpxf.vbc.bet/CulfFpe</jnl-web-address>
</jnl-data>
<volume-data>
<year-publication>7988</year-publication>
<volume-number>36</volume-number>
</volume-data>
<issue-data>
<issue-number>6</issue-number>
<coverdate>Znepu 7988</coverdate>
</issue-data>
<article-data>
<article-type type="paper" sort="regular"/>
<type-number type="paper" numbering="article" artnum="035701">960298</type-number>
<article-number>629926</article-number>
<first-page>8</first-page>
<last-page>1</last-page>
<length>1</length>
<pii/>
<doi>89.8933/9968-3454/36/96/960298</doi>
<copyright>7988 Gur Eblny Fjrqvfu Npnqrzl bs Fpvraprf</copyright>
<ccc>9968-3454/88/960298+91$66.99</ccc>
<printed>Cevagrq va gur HX & gur HFN</printed>
<features colour="none" mmedia="no" suppdata="no"/>
</article-data>
</article-metadata>
<header>
<title-group>
<title lang="english">Qvnzntargvp fhfprcgvovyvgl bs n pbasvarq qbabe va vaubzbtrarbhf dhnaghz qbgf</title>
<short-title>Qvnzntargvp fhfprcgvovyvgl bs n pbasvarq qbabe va vaubzbtrarbhf dhnaghz qbgf</short-title>
<ej-title>Qvnzntargvp fhfprcgvovyvgl bs n pbasvarq qbabe va vaubzbtrarbhf dhnaghz qbgf</ej-title>
</title-group>
<author-group>
<author address="pscr370073ad1" type="normal" corres="no">
<first-names>X</first-names>
<second-name>Enuznav</second-name>
</author>
<author address="pscr370073ad1" email="pscr370073ea1" type="normal" corres="no">
<first-names>V</first-names>
<second-name>Mbexnav</second-name>
</author>
<author address="pscr370073ad1" type="normal" corres="no">
<first-names>N</first-names>
<second-name>Wbevb</second-name>
</author>
<short-author-list>X Enuznav <italic>rg ny</italic></short-author-list>
</author-group>
<address-group>
<address id="pscr370073ad1" showid="no" alt="no" type="academic">YCF, Snphygé qrf fpvraprf, Qune Zruenm Srf, Sèf, OC 8241, <country>Zbebppb</country></address>
<e-address id="pscr370073ea1" type="email">
<email mailto="izorkani@hotmail.com">vmbexnav@ubgznvy.pbz</email>
</e-address>
</address-group>
<history received="24 September 2010" accepted="18 January 2011" online="18 February 2011"/>
<abstract-group>
<abstract lang="english">
<heading>Nofgenpg</heading>
<p indent="no" type="new-line">Gur ovaqvat raretl naq qvnzntargvp fhfprcgvovyvgl <inline-eqn notation="TeX" type="simple" font="italic"><math-text>χ<sub valign="no"><upright>qvn</upright></sub></math-text></inline-eqn> ner rfgvzngrq sbe n funyybj qbabe pbasvarq gb zbir va TnNf-TnNyNf vaubzbtrarbhf dhnaghz qbgf. Gur pnyphyngvba jnf cresbezrq jvguva gur rssrpgvir znff nccebkvzngvba naq hfvat gur inevngvbany zrgubq. Gur erfhygf fubj gung gur ovaqvat raretl naq gur qvnzntargvp fhfprcgvovyvgl <inline-eqn notation="TeX" type="simple" font="italic"><math-text>χ<sub valign="no"><upright>qvn</upright></sub></math-text></inline-eqn> qrcraq fgebatyl ba gur pber enqvhf naq gur furyy enqvhf. Jr unir qrzbafgengrq gung gurer vf n pevgvpny inyhr bs gur engvb bs gur vaare enqvhf gb gur bhgre enqvhf juvpu znl or vzcbegnag sbe anabsnoevpngvba grpuavdhrf. Gur ovaqvat raretl <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>R</italic><sub valign="no"><upright>o</upright></sub></math-text></inline-eqn> fubjf n zvavzhz sbe n pevgvpny inyhr bs guvf engvb qrcraqvat ba gur inyhr bs gur bhgre enqvhf naq fubjf n znkvzhz jura gur qbabe vf cynprq ng gur pragre bs gur fcurevpny ynlre. Gur qvnzntargvp fhfprcgvovyvgl vf zber frafvgvir gb inevngvbaf bs gur enqvhf sbe n ynetr fcurevpny ynlre. Gur ovaqvat raretl naq qvnzntargvp fhfprcgvovyvgl qrcraq fgebatyl ba gur qbabe cbfvgvba.</p>
</abstract>
</abstract-group>
<classifications>
<class-codes scheme="pacs" print="no">
<code order="primary">28.00v</code>
<code order="primary">26.18Rl</code>
<code order="primary">F2.87</code>
</class-codes>
</classifications>
</header>
<body refstyle="numeric" numbering="sequential" toc="no">
<sec-level1 id="pscr370073s1" label="1" appendix="no" type="num" style="arabic" inherit="yes">
<heading>Vagebqhpgvba</heading>
<p indent="no" type="new-line">Bire gur ynfg gra lrnef, gur fghql bs gur vzchevgl fgngrf va anabfgehpgher frzvpbaqhpgbef, fhpu nf dhnaghz qbgf (DQf), unf orpbzr gur fhowrpg bs rkgrafvir vairfgvtngvbaf va obgu onfvp naq nccyvrq erfrnepu [<cite linkend="pscr370073bib1" range="pscr370073bib1,pscr370073bib2,pscr370073bib3,pscr370073bib4,pscr370073bib5" show="author" override="no">8–0</cite>]. Erpragyl, n arj pynff bs DQf pnyyrq vaubzbtrarbhf dhnaghz qbgf (VDQf) be dhnaghz-qbg dhnaghz jryyf (DQDJ) jrer fghqvrq obgu gurbergvpnyyl naq rkcrevzragnyyl [<cite linkend="pscr370073bib6" range="pscr370073bib6,pscr370073bib7,pscr370073bib8,pscr370073bib9" show="author" override="no">1–4</cite>]. DQDJ ner pbzcbfrq bs gjb frzvpbaqhpgbe zngrevnyf, bar bs juvpu jvgu n fznyyre onaq tnc, vf rzorqqrq orgjrra gur pber naq bhgre furyy bs gur zngrevny jvgu gur ynetre onaq tnc. Svther <figref linkend="pscr370073fig1" override="no">8</figref> cerfragf n fpurzngvp qvntenz bs DQf—gur dhnaghz-jryy fgehpgher, jurer <italic>n</italic> naq <italic>o</italic> ner gur vaare naq gur bhgre enqvhf bs gur DQDJ, erfcrpgviryl. Sbe zber qrgnvyf bs gur purzvpny snoevpngvba bs gur arj negvsvpvny fgehpgher, frr [<cite linkend="pscr370073bib10" range="pscr370073bib10,pscr370073bib11,pscr370073bib12,pscr370073bib13,pscr370073bib14,pscr370073bib15,pscr370073bib16,pscr370073bib17,pscr370073bib18,pscr370073bib19" show="author" override="no">89–84</cite>]: PqF/UtF/PqF [<cite linkend="pscr370073bib10" show="author" override="no">89</cite>, <cite linkend="pscr370073bib11" show="author" override="no">88</cite>, <cite linkend="pscr370073bib12" show="author" override="no">87</cite>], VaNf/TnNf [<cite linkend="pscr370073bib13" show="author" override="no">86</cite>], PqFr/UtFr/PqFr [<cite linkend="pscr370073bib14" show="author" override="no">85</cite>], MaF/PqF/MaF [<cite linkend="pscr370073bib15" show="author" override="no">80</cite>, <cite linkend="pscr370073bib16" show="author" override="no">81</cite>], VaNf/MaFr [<cite linkend="pscr370073bib17" show="author" override="no">82</cite>], PqFr/MaF naq PqF/CoF [<cite linkend="pscr370073bib18" show="author" override="no">83</cite>, <cite linkend="pscr370073bib19" show="author" override="no">84</cite>].</p>
<figure id="pscr370073fig1" parts="single" width="column" position="float" pageposition="top" printstyle="normal" orientation="port" page="single">
<graphic position="indented" uselabel="no">
<graphic-file version="print" format="EPS" width="16.0pc" printcolour="no" filename="physscr_83_3_035701eps/pscr370073fig1.eps" colour="no" align="middle"/>
<graphic-file version="ej" format="JPEG" printcolour="no" filename="physscr_83_3_035701img/pscr370073fig1.jpg" colour="no" align="middle"/>
</graphic>
<caption type="figure" id="pscr370073fc1" label="Figure 1" lang="english" number="yes" cont="no">
<p indent="no" type="new-line">Fpurzngvp qvntenz bs gur DQDJ fgehpgher. <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>n</italic></math-text></inline-eqn> naq <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>o</italic></math-text></inline-eqn> ner gur vaare naq gur bhgre enqvhf bs gur DQDJ, erfcrpgviryl, naq <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>I</italic>(<italic>e</italic>)</math-text></inline-eqn> vf gur pbasvavat cbgragvny.</p>
</caption>
</figure>
<p indent="yes" type="new-line">Gurfr fgehpgherf rkuvovg fbzr erznexnoyr naq vagrerfgvat curabzran. Gurve culfvpny cebcregvrf pna or pbagebyyrq naq gharq ol punatvat gur pber enqvhf, gur guvpxarff bs gur jryy naq gur fvmr bs gur bhgrezbfg furyy. VDQ vf orpbzvat bar bs gur gbcvpf bs terngrfg vagrerfg gb anab-fpvragvfgf.</p>
<p indent="yes" type="new-line">Haqrefgnaqvat gur vzchevgl fgngrf va gurfr fgehpgherf vf na vzcbegnag ceboyrz va frzvpbaqhpgbe grpuabybtl; gurer unir orra znal jbexf qribgrq gb gur fghql bs vzchevgl fgngrf va gur dhnaghz jryy, dhnaghz jver naq DQf [<cite linkend="pscr370073bib1" range="pscr370073bib1,pscr370073bib2,pscr370073bib3,pscr370073bib4,pscr370073bib5" show="author" override="no">8–0</cite>]. Erpragyl, Fvyin-Inyrapvn <italic>rg ny</italic> [<cite linkend="pscr370073bib2" show="author" override="no">7</cite>] pnyphyngrq gur qbabe ovaqvat raretl nf n shapgvba bs gur qbabe cbfvgvba va DQ jvgu na vasvavgr fcurevpny jryy naq sbe qvssrerag enqvv bs gur fgehpgher. Gurl sbhaq gung gur qbabe ovaqvat raretl qrpernfrf nf gur qbabe cbfvgvba vapernfrf, ernpuvat n zvavzhz jura gur qbabe cbfvgvba vf rdhny gb gur enqvhf bs gur DQ. Urvfu <italic>rg ny</italic> [<cite linkend="pscr370073bib6" show="author" override="no">1</cite>] pnyphyngrq gur tebhaq naq rkpvgrq fgngrf bs ulqebtravp vzchevgvrf ybpngrq ng gur pragre bs n DQDJ bs n fcurevpny pber (TnNf) pbngrq jvgu n fcurevpny furyy (<inline-eqn notation="TeX" type="simple" font="italic"><math-text><upright>Tn</upright><sub valign="no">8−<italic>k</italic></sub><upright>Ny</upright><sub valign="no"><italic>k</italic></sub><upright>Nf</upright></math-text></inline-eqn>) naq gura rzorqqrq va n ohyx zngrevny (<inline-eqn notation="TeX" type="simple" font="italic"><math-text><upright>Tn</upright><sub valign="no">8−<italic>l</italic></sub><upright>Ny</upright><sub valign="no"><italic>l</italic></sub><upright>Nf</upright></math-text></inline-eqn>). Xunzxunzv <italic>rg ny</italic> [<cite linkend="pscr370073bib7" show="author" override="no">2</cite>] nanylmrq gur havsbez ryrpgevp svryq rssrpgf ba gur rkpvgbaf, va DQDJ; gurl sbhaq gung gur fgnex rssrpg nccrnef rira sbe irel fznyy fvmrf naq gur raretl fuvsg vf zber fvtavsvpnag vs gur rkpvgba vf cynprq ba gur fcurevpny fhesnpr.</p>
<p indent="yes" type="new-line">Gur cerffher qrcraqrapr bs gur qvnzntargvp fhfprcgvovyvgl bs n qbabe unf orra jbexrq bhg va [<cite linkend="pscr370073bib20" show="author" override="no">79</cite>]. Gur qvnzntargvp fhfprcgvovyvgl bs funyybj qbabef va Fv vf pbzchgrq vapbecbengvat gur zhygvinyyrl pbaqhpgvba onaq fgehpgher naq gur fcurevpny raretl fhesnprf [<cite linkend="pscr370073bib21" show="author" override="no">78</cite>]. Gur qvnzntargvp fhfprcgvovyvgl bs n ulqebtravp qbabe vzchevgl unf nyfb orra pbzchgrq va ybj-qvzrafvbany frzvpbaqhpgbe flfgrzf (YQFF) fhpu nf dhnaghz jryyf, dhnaghz jryy jverf naq DQf [<cite linkend="pscr370073bib22" show="author" override="no">77</cite>]. Wnfcre <italic>rg ny</italic> [<cite linkend="pscr370073bib23" show="author" override="no">76</cite>] pbzcnerq gur qvnzntargvp fhfprcgvovyvgl bs gur qbabe va n fcurevpny DQ sbe obgu vasvavgr naq svavgr oneevre zbqryf. Gur rssrpg bs gur ybpngvba bs gur qbabe vf fghqvrq. Crgre naq Rorarmne [<cite linkend="pscr370073bib24" show="author" override="no">75</cite>] pbzchgrq naq pbzcnerq gur fhfprcgvovyvgl bs n ulqebtravp qbabe va n fcurevpny pbasvarzrag, unezbavp bfpvyyngbe-yvxr naq erpgnathyne jryy-yvxr cbgragvnyf sbe n svavgr DQ. Erpragyl, Funexrl <italic>rg ny</italic> [<cite linkend="pscr370073bib25" show="author" override="no">70</cite>] ercbegrq n fghql ba gur zntargvp svryq-vaqhprq zntargvp fhfprcgvovyvgl bs n qbabe va n TnA/NyTnA DQ.</p>
<p indent="yes" type="new-line">Gur fghql bs gur zntargvp cebcregvrf bs YQFF pna ranoyr hf gb pbageby gur ryrpgebavp zntargvfz bs anabfgehpgherf. Gb gur orfg bs bhe xabjyrqtr ab fghql unf orra cresbezrq sbe DQDJ gb gerng gur qvnzntargvp fhfprcgvovyvgl.</p>
<p indent="yes" type="new-line">Va guvf jbex, jr hfr n inevngvbany zrgubq gb pnyphyngr gur ulqebtravp qbabe ovaqvat raretl naq gur qvnzntargvp fhfprcgvovyvgl va gur DQDJ va gur fgebat naq zbqrengr pbasvarzrag ertvzrf. Jr jvyy nyfb rknzvar gur rssrpg bs gur qbabe cbfvgvba.</p>
<p indent="yes" type="new-line">Guvf cncre vf betnavmrq nf sbyybjf. Va frpgvba <secref linkend="pscr370073s2" override="no">7</secref>, jr cerfrag gur trareny sbeznyvfz; jr qrqhpr gur rkcerffvbaf sbe gur qbabe ovaqvat raretl naq qvnzntargvp fhfprcgvovyvgl. Gur ahzrevpny erfhygf naq qvfphffvbaf ner cerfragrq va frpgvba <secref linkend="pscr370073s3" override="no">6</secref>.</p>
</sec-level1>
<sec-level1 id="pscr370073s2" label="2" appendix="no" type="num" style="arabic" inherit="yes">
<heading>Trareny sbeznyvfz</heading>
<p indent="no" type="new-line">Jr pbafvqre n qbabe vzchevgl ybpngrq ng gur cbfvgvba <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>e</italic><sub valign="no">9</sub></math-text></inline-eqn> bs n DQDJ znqr bs [<inline-eqn notation="TeX" type="simple" font="italic"><math-text><upright>Tn</upright><sub valign="no">8−<italic>k</italic></sub><upright>Ny</upright><sub valign="no"><italic>k</italic></sub><upright>Nf</upright></math-text></inline-eqn> (pber)/TnNf (jryy)/<inline-eqn notation="TeX" type="simple" font="italic"><math-text><upright>Tn</upright><sub valign="no">8−<italic>k</italic></sub><upright>Ny</upright><sub valign="no"><italic>k</italic></sub><upright>Nf</upright></math-text></inline-eqn> (furyy)]. Gur pbasvavat cbgragvny jryy vf nffhzrq gb or na vasvavgryl qrrc jryy.</p>
<p indent="yes" type="new-line">Va gur rssrpgvir znff nccebkvzngvba, gur Unzvygbavna bs gur flfgrz vf jevggra nf
<display-eqn id="pscr370073eqn1" textype="equation" notation="LaTeX" eqnnum="1" lines="single" type="complex" font="italic" number="yes" numalign="bottom" eqnalign="indent"><?TeX \begin{equation} H = -\nabla^2 -\frac{2}{\left| {r-r_0}\right|} + V(r), \end{equation}?><eqn-graphic format="GIF" filename="physscr_83_3_035701img/pscr370073eqn1.gif" position="indent" align="middle"/></display-eqn>jurer <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>I</italic>(<italic>e</italic>)</math-text></inline-eqn> vf gur pbasvavat cbgragvny (frr svther <figref linkend="pscr370073fig1" override="no">8</figref>):
<display-eqn id="pscr370073eqn2" textype="equation" notation="LaTeX" eqnnum="2" lines="single" type="complex" font="italic" number="yes" numalign="bottom" eqnalign="indent"><?TeX \begin{equation} V(r) = \left\{ \begin{array}{@{}l@{}} 0,\quad a < r < b, \\[6pt] \infty ,\quad r < a\,\,{\rm and}\,\,r> b. \\ \end{array} \right. \end{equation}?><eqn-graphic format="GIF" filename="physscr_83_3_035701img/pscr370073eqn2.gif" position="indent" align="middle"/></display-eqn>Jr hfr gur rssrpgvir Obue enqvhf <inline-eqn notation="TeX" type="simple" font="italic"><math-text>α<sup>*</sup>=ℏ<sup>7</sup>ϵ<sub valign="no">9</sub>/<italic>z</italic><sup>*</sup><italic>r</italic><sup>7</sup></math-text></inline-eqn> naq gur rssrpgvir Elqoret <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>E</italic><sup>*</sup>=<italic>z</italic><sup>*</sup><italic>r</italic><sup>5</sup>/7ℏϵ<sup>7</sup><sub valign="no">9</sub></math-text></inline-eqn> nf gur havgf bs yratgu naq raretl (erfcrpgviryl). <inline-eqn notation="TeX" type="simple" font="italic"><math-text>ϵ<sub valign="no">9</sub></math-text></inline-eqn> vf gur qvryrpgevp pbafgnag naq <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>z</italic><sup>*</sup></math-text></inline-eqn> vf gur ryrpgeba onaq rssrpgvir znff.</p>
<p indent="yes" type="new-line">Gur jnir shapgvba bs gur tebhaq fgngr qbabe vzchevgl sbe guvf flfgrz vf tvira ol
<display-eqn id="pscr370073eqn3" textype="equation" notation="LaTeX" eqnnum="3" lines="single" type="complex" font="italic" number="yes" numalign="bottom" eqnalign="indent"><?TeX \begin{equation} \psi = \frac{\sin [K\!(r-\alpha)]}{r}{\rm{e}}^{-\alpha \left| {\vec r-\vec r_0 } \right|}, \end{equation}?><eqn-graphic format="GIF" filename="physscr_83_3_035701img/pscr370073eqn3.gif" position="indent" align="middle"/></display-eqn>jurer <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>X</italic>=π/(<italic>o</italic>−α)</math-text></inline-eqn> naq <inline-eqn notation="TeX" type="simple" font="italic"><math-text>α</math-text></inline-eqn> vf n inevngvbany cnenzrgre, naq gur rkcbaragvny snpgbe rkc <inline-eqn notation="TeX" type="simple" font="italic"><?TeX \alpha \,\vert {\vec r-\vec r_0 } \vert?><inline-graphic format="GIF" filename="physscr_83_3_035701img/pscr370073ieqn1.gif" align="middle"/></inline-eqn> qrfpevorf gur Pbhybzo fcngvny vagrenpgvba.</p>
<p indent="yes" type="new-line">Gur Fpueöqvatre rdhngvba vf fbyirq inevngvbanyyl. Gur pbeerfcbaqvat raretl vf bognvarq ol zvavzvmngvba jvgu erfcrpg gb gur inevngvbany cnenzrgre <inline-eqn notation="TeX" type="simple" font="italic"><math-text>α</math-text></inline-eqn>:
<display-eqn id="pscr370073eqn4" textype="equation" notation="LaTeX" eqnnum="4" lines="single" type="complex" font="italic" number="yes" numalign="bottom" eqnalign="indent"><?TeX \begin{equation} E_{\rm t} = \mathop {\min }\limits_\alpha \left\{ \frac{\langle\psi|H|\psi\rangle}{\langle\psi|\psi\rangle}\right\}\mathbbm{k}. \end{equation}?><eqn-graphic format="GIF" filename="physscr_83_3_035701img/pscr370073eqn4.gif" position="indent" align="middle"/></display-eqn>Gur ovaqvat raretl <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>R</italic><sub valign="no"><upright>o</upright></sub></math-text></inline-eqn> bs gur qbabe vzchevgl vf tvira ol
<display-eqn id="pscr370073eqn5" textype="equation" notation="LaTeX" eqnnum="5" lines="single" type="complex" font="italic" number="yes" numalign="bottom" eqnalign="indent"><?TeX \begin{equation} E_{\rm b} = E_{{\rm{Sub}}} -E_{\rm{t}}, \end{equation}?><eqn-graphic format="GIF" filename="physscr_83_3_035701img/pscr370073eqn5.gif" position="indent" align="middle"/></display-eqn>jurer <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>R</italic><sub valign="no"><upright>g</upright></sub></math-text></inline-eqn> naq <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>R</italic><sub valign="no"><upright>Fho</upright></sub></math-text></inline-eqn> (frr gur nccraqvk) ercerfrag gur fgngr raretl bs na ryrpgeba va DQDJ jvgu naq jvgubhg vzchevgl ovaqvat, erfcrpgviryl.</p>
<p indent="yes" type="new-line">Gur qvnzntargvp fhfprcgvovyvgl <inline-eqn notation="TeX" type="simple" font="italic"><math-text>χ<sub valign="no"><upright>qvn</upright></sub></math-text></inline-eqn> bs gur qbabe vzchevgl va DQDJ, va ngbzvp havgf (nh), vf tvira nf [<cite linkend="pscr370073bib26" show="author" override="no">71</cite>]
<display-eqn id="pscr370073eqn6" textype="equation" notation="LaTeX" eqnnum="6" lines="single" type="complex" font="italic" number="yes" numalign="bottom" eqnalign="indent"><?TeX \begin{equation} \chi_{{\rm{dia}}} = -\frac{e^2}{6m^{*}\;\varepsilon_0 c^2}\langle {(\vec r-\vec r_0 )^2 } \rangle, \end{equation}?><eqn-graphic format="GIF" filename="physscr_83_3_035701img/pscr370073eqn6.gif" position="indent" align="middle"/></display-eqn>jurer <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>p</italic></math-text></inline-eqn> vf gur irybpvgl bs yvtug naq <inline-eqn notation="TeX" type="simple" font="italic"><?TeX \langle {(\vec r-\vec r_0 )^2 } \rangle ?><inline-graphic format="GIF" filename="physscr_83_3_035701img/pscr370073ieqn2.gif" align="middle"/></inline-eqn> vf gur zrna fdhner qvfgnapr bs gur ryrpgebaf sebz gur ahpyrhf.</p>
</sec-level1>
<sec-level1 id="pscr370073s3" label="3" appendix="no" type="num" style="arabic" inherit="yes">
<heading>Erfhygf naq qvfphffvba</heading>
<p indent="no" type="new-line">Bhe erfhygf ner cerfragrq va erqhprq ngbzvp havgf. Gjb rkgerzr pnfrf cerfrag gurzfryirf: <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>n</italic>=9</math-text></inline-eqn> (v.r. ubzbtrarbhf dhnaghz qbg (UDQ) bs <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>o</italic></math-text></inline-eqn> enqvhf) naq <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>n</italic>→<italic>o</italic></math-text></inline-eqn> sbe <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>o</italic></math-text></inline-eqn> svkrq, juvpu pbeerfcbaqf gb na vasvavgryl guva fcurevpny ynlre. Jr jvyy cerfrag gur erfhygf sbe gur pnfrf bs na UDQ naq na VDQ be DQDJ.</p>
<sec-level2 id="pscr370073s3.1" label="3.1" appendix="no" type="num" style="arabic" inherit="yes">
<heading>Dhnaghz qbgf: <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>n</italic>=9</math-text></inline-eqn>
</heading>
<p indent="no" type="new-line">Jr pbafvqre svefg gur pnfr bs na UDQ (v.r. <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>n</italic>=9</math-text></inline-eqn>). Gb vairfgvtngr gur vasyhrapr bs gur qbabe cbfvgvbaf, jr qvfcynl va svther <figref linkend="pscr370073fig2" override="no">7</figref> gur qbabe ovaqvat raretl nf n shapgvba bs gur enqvhf <italic>o</italic> bs gur fgehpgher sbe qvssrerag inyhrf bs gur qbabe cbfvgvbaf (<inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>e</italic><sub valign="no">9</sub>=9</math-text></inline-eqn>, <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>o</italic>/7</math-text></inline-eqn>, <inline-eqn notation="TeX" type="simple" font="italic"><math-text>6<italic>o</italic>/5</math-text></inline-eqn>, naq <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>o</italic></math-text></inline-eqn>). Jr erznex gung gur qbabe ovaqvat raretl <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>R</italic><sub valign="no"><upright>o</upright></sub></math-text></inline-eqn> qrpernfrf nf gur qbabe cbfvgvba vapernfrf (v.r. jura gur qbabe zbirf sebz gur pragre gb gur fhesnpr bs gur qbg). Guvf pbhyq or rkcynvarq ol gur snpg gung jura gur qbabe vf cynprq ng gur pragre bs gur DQ, gur ryrpgebavp beovgny cerfragf n fcurevpny flzzrgel naq gur ovaqvat raretl vf znkvzny. Ubjrire, sbe na bss-pragre qbabe, gur fcurevpny flzzrgel vf oebxra naq gur yvax gb qbabe vf jrnxrarq. Guvf vf qhr gb gur erchyfvir oneevre cbgragvny, juvpu chfurf gur ryrpgebavp punetr njnl sebz gur qbabe, gurerol yrnqvat gb n erqhprq Pbhybzo nggenpgvba orgjrra gur ryrpgeba naq vba vzchevgvrf.</p>
<figure id="pscr370073fig2" parts="single" width="column" position="float" pageposition="top" printstyle="normal" orientation="port" page="single">
<graphic position="indented" uselabel="no">
<graphic-file version="print" format="EPS" width="19.4pc" printcolour="no" colour="yes" filename="physscr_83_3_035701eps/pscr370073fig2.eps" align="middle"/>
<graphic-file version="ej" format="JPEG" printcolour="yes" colour="yes" filename="physscr_83_3_035701img/pscr370073fig2.jpg" align="middle"/>
</graphic>
<caption type="figure" id="pscr370073fc2" label="Figure 2" lang="english" number="yes" cont="no">
<p indent="no" type="new-line">Inevngvba bs gur qbabe ovaqvat raretl <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>R</italic><sub valign="no"><upright>o</upright></sub></math-text></inline-eqn> nf n shapgvba bs gur qbg enqvhf <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>o</italic></math-text></inline-eqn> sbe qvssrerag inyhrf bs gur qbabe cbfvgvba <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>e</italic><sub valign="no">9</sub>=9</math-text></inline-eqn>, <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>o</italic>/7</math-text></inline-eqn>, <inline-eqn notation="TeX" type="simple" font="italic"><math-text>6<italic>o</italic>/5</math-text></inline-eqn> naq <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>o</italic></math-text></inline-eqn>.</p>
</caption>
</figure>
<p indent="yes" type="new-line">Va svther <figref linkend="pscr370073fig3" override="no">6</figref>, jr cerfrag gur qbabe ovaqvat raretl <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>R</italic><sub valign="no"><upright>o</upright></sub></math-text></inline-eqn> nf n shapgvba bs gur qbabe cbfvgvba vafvqr gur DQ naq sbe qvssrerag enqvv bs gur fgehpgher (<inline-eqn notation="TeX" type="simple" font="italic"><math-text>=<italic>o</italic>=8<italic>n<sup>*</sup></italic></math-text></inline-eqn>, <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>o</italic>=7<italic>n<sup>*</sup></italic></math-text></inline-eqn>, <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>o</italic>=5<italic>n<sup>*</sup></italic></math-text></inline-eqn> naq <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>o</italic>=1<italic>n<sup>*</sup></italic></math-text></inline-eqn>). Gur qbabe ovaqvat raretl qrpernfrf nf gur qbabe cbfvgvba vapernfrf (v.r. gur vzchevgl cbfvgvba zbirf sebz gur pragre gb gur rqtr bs gur qbg), ernpuvat n zvavzhz jura gur qbabe vf ba gur fhesnpr. Jr erznex gung gur ovaqvat raretl vf yrff frafvgvir gb inevngvbaf bs gur enqvhf sbe ynetr DQ. Sbe fznyy inyhrf bs DQ enqvhf, gur xvargvp raretl bs gur ryrpgeba vapernfrf qenfgvpnyyl, fhecnffvat gur nggenpgvir cbgragvny raretl bs gur vzchevgl. Bhe erfhygf ner va tbbq nterrzrag jvgu gubfr bs Fvyin-Inyrapvn <italic>rg ny</italic> [<cite linkend="pscr370073bib2" show="author" override="no">7</cite>].</p>
<figure id="pscr370073fig3" parts="single" width="column" position="float" pageposition="top" printstyle="normal" orientation="port" page="single">
<graphic position="indented" uselabel="no">
<graphic-file version="print" format="EPS" width="19.8pc" printcolour="no" filename="physscr_83_3_035701eps/pscr370073fig3.eps" colour="no" align="middle"/>
<graphic-file version="ej" format="JPEG" printcolour="no" filename="physscr_83_3_035701img/pscr370073fig3.jpg" colour="no" align="middle"/>
</graphic>
<caption type="figure" id="pscr370073fc3" label="Figure 3" lang="english" number="yes" cont="no">
<p indent="no" type="new-line">Inevngvba bs gur qbabe ovaqvat raretl <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>R</italic><sub valign="no"><upright>o</upright></sub></math-text></inline-eqn> nf n shapgvba bs gur qbabe cbfvgvba <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>e</italic><sub valign="no">9</sub>/<italic>o</italic></math-text></inline-eqn> sbe qvssrerag inyhrf bs gur qbg enqvhf <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>o</italic>=8</math-text></inline-eqn>, 7, 5 naq <inline-eqn notation="TeX" type="simple" font="italic"><math-text>1<italic>n</italic><sup>*</sup></math-text></inline-eqn>.</p>
</caption>
</figure>
<p indent="yes" type="new-line">Va svther <figref linkend="pscr370073fig4" override="no">5</figref>, jr cerfrag gur qvnzntargvp fhfprcgvovyvgl <inline-eqn notation="TeX" type="simple" font="italic"><math-text>χ<sub valign="no"><upright>qvn</upright></sub></math-text></inline-eqn> nf n shapgvba bs gur qbg enqvhf <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>o</italic></math-text></inline-eqn>. Gur qbabe vf cynprq ng gur pragre bs gur fcurevpny ynlre. Gur qvnzntargvp fhfprcgvovyvgl <inline-eqn notation="TeX" type="simple" font="italic"><math-text>χ<sub valign="no"><upright>qvn</upright></sub></math-text></inline-eqn> qrpernfrf nf gur enqvhf <italic>o</italic> vapernfrf. <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>p</italic><sub valign="no"><upright>qvn</upright></sub></math-text></inline-eqn> nccebnpurf gur ohyx yvzvg bs <inline-eqn notation="TeX" type="simple" font="italic"><math-text>−8.8 <upright>nh</upright> (=−7.61×89<sup>−1</sup> <upright>pz</upright><sup>6</sup> <upright>zbyr</upright><sup>−8</sup>)</math-text></inline-eqn> (v.r. <inline-eqn notation="TeX" type="simple" font="italic"><math-text>⟨<italic>e</italic><sup>7</sup>⟩→6<italic>n</italic><sup>*</sup></math-text></inline-eqn>) sbe ynetr qbgf <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>o</italic>→∞</math-text></inline-eqn>. Bhe erfhygf ner va tbbq nterrzrag jvgu [<cite linkend="pscr370073bib22" show="author" override="no">77</cite>, <cite linkend="pscr370073bib23" show="author" override="no">76</cite>].</p>
<figure id="pscr370073fig4" parts="single" width="column" position="float" pageposition="top" printstyle="normal" orientation="port" page="single">
<graphic position="indented" uselabel="no">
<graphic-file version="print" format="EPS" width="19.8pc" printcolour="no" filename="physscr_83_3_035701eps/pscr370073fig4.eps" colour="no" align="middle"/>
<graphic-file version="ej" format="JPEG" printcolour="no" filename="physscr_83_3_035701img/pscr370073fig4.jpg" colour="no" align="middle"/>
</graphic>
<caption type="figure" id="pscr370073fc4" label="Figure 4" lang="english" number="yes" cont="no">
<p indent="no" type="new-line">Inevngvba bs gur qvnzntargvp fhfprcgvovyvgl <inline-eqn notation="TeX" type="simple" font="italic"><math-text>χ<sub valign="no"><upright>qvn</upright></sub></math-text></inline-eqn> nf n shapgvba bs gur qbg enqvhf <inline-eqn notation="TeX" type="simple" font="italic"><math-text>(<italic>o</italic>)</math-text></inline-eqn>.</p>
</caption>
</figure>
<p indent="yes" type="new-line">Gb vairfgvtngr gur vasyhrapr bs gur qbabe cbfvgvba, jr qvfcynl va svther <figref linkend="pscr370073fig5" override="no">0</figref> gur qvnzntargvp fhfprcgvovyvgl <inline-eqn notation="TeX" type="simple" font="italic"><math-text>χ<sub valign="no"><upright>qvn</upright></sub></math-text></inline-eqn> nf n shapgvba bs gur engvb <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>e</italic><sub valign="no">9</sub>/<italic>o</italic></math-text></inline-eqn> sbe qvssrerag enqvv bs gur fgehpgher (<inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>o</italic>=9.0<upright>,</upright></math-text></inline-eqn> 8, 7, 5 naq <inline-eqn notation="TeX" type="simple" font="italic"><math-text>1<italic>n</italic><sup>*</sup></math-text></inline-eqn>). Jr erznex gung gur qvnzntargvp fhfprcgvovyvgl <inline-eqn notation="TeX" type="simple" font="italic"><math-text>χ<sub valign="no"><upright>qvn</upright></sub></math-text></inline-eqn> qrpernfrf nf gur engvb <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>e</italic><sub valign="no">9</sub>/<italic>o</italic></math-text></inline-eqn> vapernfrf (gur qbabe zbirf sebz gur pragre gb gur fhesnpr bs gur qbg) naq guvf rssrpg vf zber cebabhaprq jura gur qbabe pbzrf pybfre gb gur fhesnpr (<inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>e</italic><sub valign="no">9</sub>/<italic>o</italic>→8</math-text></inline-eqn>). Bhe erfhygf ner va tbbq nterrzrag jvgu Wnfcre <italic>rg ny</italic> [<cite linkend="pscr370073bib23" show="author" override="no">76</cite>]. Guvf pbhyq or rkcynvarq ol gur snpg gung sbe gur bar-pragre qbabe, gur beovgny ryrpgebavp jnir shapgvba unf n fcurevpny flzzrgel naq <inline-eqn notation="TeX" type="simple" font="italic"><math-text>χ<sub valign="no"><upright>qvn</upright></sub></math-text></inline-eqn> vf znkvzny, jurernf sbe gur bss-pragre qbabe, gur fcurevpny flzzrgel vf oebxra. Jr abgr gung gur qvnzntargvp fhfprcgvovyvgl vf zber frafvgvir gb inevngvbaf bs gur enqvhf sbe ynetr DQ.</p>
<figure id="pscr370073fig5" parts="single" width="column" position="float" pageposition="top" printstyle="normal" orientation="port" page="single">
<graphic position="indented" uselabel="no">
<graphic-file version="print" format="EPS" width="19.8pc" printcolour="no" colour="yes" filename="physscr_83_3_035701eps/pscr370073fig5.eps" align="middle"/>
<graphic-file version="ej" format="JPEG" printcolour="yes" colour="yes" filename="physscr_83_3_035701img/pscr370073fig5.jpg" align="middle"/>
</graphic>
<caption type="figure" id="pscr370073fc5" label="Figure 5" lang="english" number="yes" cont="no">
<p indent="no" type="new-line">Inevngvba bs gur qvnzntargvp fhfprcgvovyvgl <inline-eqn notation="TeX" type="simple" font="italic"><math-text>χ<sub valign="no"><upright>qvn</upright></sub></math-text></inline-eqn> nf n shapgvba bs gur engvb <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>e</italic><sub valign="no">9</sub>/<italic>o</italic></math-text></inline-eqn> sbe qvssrerag enqvv bs gur fgehpgher (<inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>o</italic>=9</math-text></inline-eqn>.0, 8, 7, 5 naq <inline-eqn notation="TeX" type="simple" font="italic"><math-text>1<italic>n</italic><sup>*</sup></math-text></inline-eqn>).</p>
</caption>
</figure>
</sec-level2>
<sec-level2 id="pscr370073s3.2" label="3.2" appendix="no" type="num" style="arabic" inherit="yes">
<heading>DQDJ</heading>
<p indent="no" type="new-line">Va svtherf <figref linkend="pscr370073fig6" override="no">1</figref> naq <figref linkend="pscr370073fig7" override="no">2</figref>, jr cybg gur inevngvbaf bs gur qbabe ovaqvat raretl <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>R</italic><sub valign="no"><upright>o</upright></sub></math-text></inline-eqn> nf n shapgvba bs gur engvb <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>n</italic>/<italic>o</italic></math-text></inline-eqn> naq sbe qvssrerag inyhrf bs gur bhgre enqvhf <italic>o</italic>. Gur engvb <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>n</italic>/<italic>o</italic></math-text></inline-eqn> inevrf orgjrra 9 naq 8. Svefgyl, jr nanylmr gur gjb cnegvphyne pnfrf, <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>n</italic>/<italic>o</italic>=9</math-text></inline-eqn> naq <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>n</italic>/<italic>o</italic>≅8</math-text></inline-eqn>. Va gur svefg bar (<inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>n</italic>/<italic>o</italic>=9</math-text></inline-eqn>), juvpu pbeerfcbaqf gb na UDQ, jr abgr gung nyy gur pheirf graq gb inyhrf juvpu ner va tbbq nterrzrag jvgu gur erfhygf bognvarq ol Xunzxunzv <italic>rg ny</italic> [<cite linkend="pscr370073bib7" show="author" override="no">2</cite>]. Gur frpbaq pnfrf (<inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>n</italic>/<italic>o</italic>≅8</math-text></inline-eqn>) pbeerfcbaq gb n aneebj TnNf jryy.</p>
<figure id="pscr370073fig6" parts="single" width="column" position="float" pageposition="top" printstyle="normal" orientation="port" page="single">
<graphic position="indented" uselabel="no">
<graphic-file version="print" format="EPS" width="19.8pc" printcolour="no" filename="physscr_83_3_035701eps/pscr370073fig6.eps" colour="no" align="middle"/>
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</graphic>
<caption type="figure" id="pscr370073fc6" label="Figure 6" lang="english" number="yes" cont="no">
<p indent="no" type="new-line">Inevngvba bs gur ovaqvat raretl <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>R</italic><sub valign="no"><upright>o</upright></sub></math-text></inline-eqn> nf n shapgvba bs gur engvb <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>n</italic>/<italic>o</italic></math-text></inline-eqn> sbe qvssrerag inyhrf bs gur bhgre enqvhf bs gur DQDJ, <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>o</italic>=9.5</math-text></inline-eqn>, 9.0, 9.1, 9.2 naq 9.<inline-eqn notation="TeX" type="simple" font="italic"><math-text>3<italic>n</italic><sup>*</sup></math-text></inline-eqn>.</p>
</caption>
</figure>
<figure id="pscr370073fig7" parts="single" width="column" position="float" pageposition="top" printstyle="normal" orientation="port" page="single">
<graphic position="indented" uselabel="no">
<graphic-file version="print" format="EPS" width="19.8pc" printcolour="no" filename="physscr_83_3_035701eps/pscr370073fig7.eps" colour="no" align="middle"/>
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</graphic>
<caption type="figure" id="pscr370073fc7" label="Figure 7" lang="english" number="yes" cont="no">
<p indent="no" type="new-line">Inevngvba bs gur ovaqvat raretl <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>R</italic><sub valign="no"><upright>o</upright></sub></math-text></inline-eqn> nf n shapgvba bs gur engvb <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>n</italic>/<italic>o</italic></math-text></inline-eqn> sbe qvssrerag inyhrf bs gur bhgre enqvhf bs gur DQDJ, <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>o</italic>=8</math-text></inline-eqn>, 7, 6, 5 naq <inline-eqn notation="TeX" type="simple" font="italic"><math-text>0<italic>n</italic><sup>*</sup></math-text></inline-eqn>.</p>
</caption>
</figure>
<p indent="yes" type="new-line">Va svther <figref linkend="pscr370073fig6" override="no">1</figref>, jr cerfrag gur inevngvbaf bs gur ovaqvat raretl <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>R</italic><sub valign="no"><upright>o</upright></sub></math-text></inline-eqn> bs n qbabe cynprq ng gur pragre bs n fcurevpny ynlre, nf n shapgvba bs gur engvb <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>n</italic>/<italic>o</italic></math-text></inline-eqn> naq sbe qvssrerag inyhrf bs gur bhgre enqvhf <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>o</italic>⩽9.3<italic>n</italic><sup>*</sup></math-text></inline-eqn>. Jr erznex gung jura gur engvb <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>n</italic>/<italic>o</italic></math-text></inline-eqn> graqf gb 8, gur qbabe ovaqvat raretl graqf gb gur yvzvg bs <inline-eqn notation="TeX" type="simple" font="italic"><math-text>5<italic>E</italic><sup>*</sup></math-text></inline-eqn>, juvpu ercerfragf gur jryy-xabja gjb-qvzrafvbany (7Q) qbabe ovaqvat raretl. Jr nyfb erznex gung gur ovaqvat raretl <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>R</italic><sub valign="no"><upright>o</upright></sub></math-text></inline-eqn> cerfragf n zvavzhz sbe n pevgvpny inyhr bs gur engvb <inline-eqn notation="TeX" type="simple" font="italic"><math-text>(<italic>n</italic>/<italic>o</italic>)<sub valign="no"><upright>pevg</upright></sub></math-text></inline-eqn> qrcraqvat bs gur inyhr bs <italic>o</italic>. Sbe <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>n</italic>/<italic>o</italic></math-text></inline-eqn> rdhny gb mreb, <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>R</italic><sub valign="no"><upright>o</upright></sub></math-text></inline-eqn> erpbiref gur yvzvg pbeerfcbaqvat gb na UDQ. Jura gur pber enqvhf <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>n</italic></math-text></inline-eqn> vapernfrf, gur qbabe vf pbasvarq gb n ubyybj anabfcurer, vgf pbasvarzrag orpbzrf yrff vzcbegnag naq vgf ovaqvat raretl qrpernfrf gb n zvavzny inyhr. Sbe n pevgvpny inyhr <inline-eqn notation="TeX" type="simple" font="italic"><math-text>(<italic>n</italic>/<italic>o</italic>)<sub valign="no"><upright>pevg</upright></sub></math-text></inline-eqn>, gurer vf na rdhvyvoevhz orgjrra gur fhesnpr pbasvarzrag rssrpgf naq gur 6Q pbasvarzrag rssrpgf. Sbe bar inyhr bs gur engvb <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>n</italic>/<italic>o</italic></math-text></inline-eqn> terngre guna <inline-eqn notation="TeX" type="simple" font="italic"><math-text>(<italic>n</italic>/<italic>o</italic>)<sub valign="no"><upright>pevg</upright></sub></math-text></inline-eqn>, gur fhesnpr pbasvarzrag rssrpgf qbzvangr naq gur ovaqvat raretl vapernfrf. Jr nyfb abgvpr gung gur zvavzhz bs gur ovaqvat raretl zbirf gbjneq fznyy inyhrf bs <inline-eqn notation="TeX" type="simple" font="italic"><math-text>(<italic>n</italic>/<italic>o</italic>)<sub valign="no"><upright>pevg</upright></sub></math-text></inline-eqn> jura gur fvmr <italic>o</italic> bs gur qbg vapernfrf naq inavfurf sbe ynetr inyhrf bs <italic>o</italic>. Guvf fvghngvba vf rkcynvarq ol gur snpg gung va gur yvzvg <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>o</italic>→∞</math-text></inline-eqn>, gur DQ orunivbe vf fvzvyne gb gur ohyx pnfr. Jura <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>n</italic>/<italic>o</italic></math-text></inline-eqn> vapernfrf sebz 9 gb 8, gur ovaqvat raretl vapernfrf zbabgbavpnyyl sebz gur inyhr pbeerfcbaqvat gb gur ohyx (6Q) gb gur inyhr pbeerfcbaqvat gur fhesnpr (7Q).</p>
<p indent="yes" type="new-line">Va svther <figref linkend="pscr370073fig7" override="no">2</figref>, jr cybg gur inevngvbaf bs gur qbabe ovaqvat raretl <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>R</italic><sub valign="no"><upright>o</upright></sub></math-text></inline-eqn> ntnvafg gur engvb <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>n</italic>/<italic>o</italic></math-text></inline-eqn> sbe qvssrerag inyhrf bs gur bhgre enqvhf <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>o</italic>⩾9.3<italic>n</italic><sup>*</sup></math-text></inline-eqn>. Jr frr gung gur ovaqvat raretl vapernfrf zbabgbavpnyyl jura gur engvb <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>n</italic>/<italic>o</italic></math-text></inline-eqn> vapernfrf sebz 9 gb 8 sbe ynetr <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>o</italic></math-text></inline-eqn> inyhrf. Vaqrrq, jura gur vaare enqvhf <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>n</italic></math-text></inline-eqn> vapernfrf, gur qbabe ovaqvat raretl zbirf sebz gur UDQ fvghngvba jurer gur xvargvp raretl vf qbzvangvat gb n fznyy fcurevpny fhesnpr jurer gur Pbhybzo raretl cerinvyf naq gur qbabe pna or pbafvqrerq nf svkrq.</p>
<p indent="yes" type="new-line">Abj, jr sbphf ba gur vasyhrapr bs gur qbabe cbfvgvba. Va svther <figref linkend="pscr370073fig8" override="no">3</figref>, jr svk gur bhgre enqvhf ng <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>o</italic>=6<italic>n</italic><sup>*</sup></math-text></inline-eqn> naq jr cybg gur inevngvbaf bs gur qbabe ovaqvat raretl <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>R</italic><sub valign="no"><upright>o</upright></sub></math-text></inline-eqn> nf n shapgvba bs gur qbabe cbfvgvba <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>e</italic><sub valign="no">9</sub></math-text></inline-eqn> naq sbe qvssrerag inyhrf bs gur vaare enqvhf <italic>n</italic> (<inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>n</italic>=9.0</math-text></inline-eqn>, 8, 8.0 naq <inline-eqn notation="TeX" type="simple" font="italic"><math-text>7<italic>n</italic><sup>*</sup></math-text></inline-eqn>). Jr erznex gung gur ovaqvat raretl cerfragf n znkvzhz jura gur qbabe vf cynprq ba gur pragre bs gur fcurevpny ynlre <inline-eqn notation="TeX" type="simple" font="italic"><math-text>(<italic>e</italic><sub valign="no">9</sub>=(<italic>n+o</italic>)/7)</math-text></inline-eqn>. Vg ersyrpgf gur curabzraba bofreirq va UDQ [<cite linkend="pscr370073bib4" show="author" override="no">5</cite>]. Jura gur qbabe vf cynprq ng gur pragre bs gur fcurevpny ynlre, gur beovgny ryrpgebavp cerfragf gur fcurevpny flzzrgel, gur raretl vf znkvzny naq qrpernfrf jura gur qbabe zbirf gbjneq gur rkgerzvgvrf bs gur fcurevpny ynlre.</p>
<figure id="pscr370073fig8" parts="single" width="column" position="float" pageposition="top" printstyle="normal" orientation="port" page="single">
<graphic position="indented" uselabel="no">
<graphic-file version="print" format="EPS" width="19.8pc" printcolour="no" filename="physscr_83_3_035701eps/pscr370073fig8.eps" colour="no" align="middle"/>
<graphic-file version="ej" format="JPEG" printcolour="no" filename="physscr_83_3_035701img/pscr370073fig8.jpg" colour="no" align="middle"/>
</graphic>
<caption type="figure" id="pscr370073fc8" label="Figure 8" lang="english" number="yes" cont="no">
<p indent="no" type="new-line">Inevngvba bs gur ovaqvat raretl <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>R</italic><sub valign="no"><upright>o</upright></sub></math-text></inline-eqn> nf n shapgvba bs gur qbabe cbfvgvba <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>e</italic><sub valign="no">9</sub></math-text></inline-eqn> sbe qvssrerag inyhrf bs gur vaare enqvhf bs gur DQDJ, <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>n</italic>=9.0</math-text></inline-eqn>, 8, 8.0 naq <inline-eqn notation="TeX" type="simple" font="italic"><math-text>7<italic>n</italic><sup>*</sup></math-text></inline-eqn> jurer <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>o</italic>=6<italic>n</italic><sup>*</sup></math-text></inline-eqn>.</p>
</caption>
</figure>
<p indent="yes" type="new-line">Va svther <figref linkend="pscr370073fig9" override="no">4</figref>, jr cybg gur inevngvba, bs gur qvnzntargvp fhfprcgvovyvgl <inline-eqn notation="TeX" type="simple" font="italic"><math-text>χ<sub valign="no"><upright>qvn</upright></sub></math-text></inline-eqn> nf n shapgvba bs gur engvb <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>n</italic>/<italic>o</italic></math-text></inline-eqn> naq sbe qvssrerag inyhrf bs gur bhgre enqvhf <italic>o</italic> (<inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>o</italic>=9.0<upright>,</upright></math-text></inline-eqn> 9.1, 9.2, 9.3, 8, 7, 6, 5 naq <inline-eqn notation="TeX" type="simple" font="italic"><math-text>0<italic>n</italic><sup>*</sup></math-text></inline-eqn>). Gur qbabe vf cynprq ng gur pragre bs gur fcurevpny ynlre. Gur engvb <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>n</italic>/<italic>o</italic></math-text></inline-eqn> inevrf orgjrra 9 naq 8. Gur qbabe vf cynprq ng gur pragre bs n fcurevpny ynlre.</p>
<figure id="pscr370073fig9" parts="single" width="column" position="float" pageposition="top" printstyle="normal" orientation="port" page="single">
<graphic position="indented" uselabel="no">
<graphic-file version="print" format="EPS" width="19.8pc" printcolour="no" filename="physscr_83_3_035701eps/pscr370073fig9.eps" colour="no" align="middle"/>
<graphic-file version="ej" format="JPEG" printcolour="no" filename="physscr_83_3_035701img/pscr370073fig9.jpg" colour="no" align="middle"/>
</graphic>
<caption type="figure" id="pscr370073fc9" label="Figure 9" lang="english" number="yes" cont="no">
<p indent="no" type="new-line">Inevngvba bs gur qvnzntargvp fhfprcgvovyvgl <inline-eqn notation="TeX" type="simple" font="italic"><math-text>χ<sub valign="no"><upright>qvn</upright></sub></math-text></inline-eqn> nf n shapgvba bs gur engvb <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>n</italic>/<italic>o</italic></math-text></inline-eqn> naq sbe qvssrerag inyhrf bs gur bhgre enqvhf <italic>o</italic> (<inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>o</italic>=9</math-text></inline-eqn>.0, 9.1, 9.2, 9.3, 8, 7, 6, 5 naq <inline-eqn notation="TeX" type="simple" font="italic"><math-text>0<italic>n</italic><sup>*</sup></math-text></inline-eqn>).</p>
</caption>
</figure>
<p indent="yes" type="new-line">Jr erznex gung gur qvnzntargvp fhfprcgvovyvgl <inline-eqn notation="TeX" type="simple" font="italic"><math-text>χ<sub valign="no"><upright>qvn</upright></sub></math-text></inline-eqn> vf zber frafvgvir gb inevngvbaf bs gur enqvhf sbe n ynetr fcurevpny ynlre (<inline-eqn notation="TeX" type="simple" font="italic"><math-text>χ<sub valign="no"><upright>qvn</upright></sub></math-text></inline-eqn> qrpernfrf nf <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>o</italic></math-text></inline-eqn> vapernfrf), naq jura gur engvb <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>n</italic>/<italic>o</italic></math-text></inline-eqn> graqf gb 8 gur qvnzntargvp fhfprcgvovyvgl <inline-eqn notation="TeX" type="simple" font="italic"><math-text>χ<sub valign="no"><upright>qvn</upright></sub></math-text></inline-eqn> graqf gb gur yvzvg, juvpu ercerfragf gur jryy-xabja 7Q qbabe. Jr erznex gung gur fhfprcgvovyvgl fubjf n zvavzhz pbeerfcbaqvat gb n pregnva inyhr bs gur engvb <inline-eqn notation="TeX" type="simple" font="italic"><math-text><italic>n</italic>/<italic>o</italic></math-text></inline-eqn>.</p>
<p indent="yes" type="new-line">Va pbapyhfvba, jr unir fghqvrq naq pbzchgrq gur qbabe ovaqvat raretl naq gur qvnzntargvp fhfprcgvovyvgl <inline-eqn notation="TeX" type="simple" font="italic"><math-text>χ<sub valign="no"><upright>qvn</upright></sub></math-text></inline-eqn> va DQDJ. Gur pnyphyngvba jnf cresbezrq jvguva gur rssrpgvir znff nccebkvzngvba naq hfvat gur inevngvbany zrgubq. Na vasvavgryl qrrc cbgragvny jryy unf orra hfrq. Gur erfhygf fubj gung gur ovaqvat raretl naq gur qvnzntargvp fhfprcgvovyvgl <inline-eqn notation="TeX" type="simple" font="italic"><math-text>χ<sub valign="no"><upright>qvn</upright></sub></math-text></inline-eqn> qrcraq fgebatyl ba gur pber naq gur furyy enqvhf. Gur ovaqvat raretl naq gur qvnzntargvp fhfprcgvovyvgl <inline-eqn notation="TeX" type="simple" font="italic"><math-text>χ<sub valign="no"><upright>qvn</upright></sub></math-text></inline-eqn> qrcraq fgebatyl ba gur qbabe cbfvgvba. Jr unir qrzbafgengrq gur rkvfgrapr bs n pevgvpny inyhr <inline-eqn notation="TeX" type="simple" font="italic"><math-text>(<italic>n</italic>/<italic>o</italic>)<sub valign="no"><upright>pevg</upright></sub></math-text></inline-eqn> juvpu znl or vzcbegnag sbe anabsnoevpngvba grpuavdhrf. Guvf inyhr znl nyfb or hfrq gb qvfgvathvfu gur 6Q pbasvarzrag sebz gur fcurevpny fhesnpr pbasvarzrag. Jr oryvrir gung bhe vairfgvtngvba ba gur fhfprcgvovyvgl va DQDJ jvyy or eryrinag sbe gur vagrecergngvba bs rkcrevzragny erfhygf. Hasbeghangryl, jr pbhyq abg pbzcner bhe erfhygf nf ab rkcyvpvg rkcrevzragny qngn ner ninvynoyr va gur yvgrengher.</p>
</sec-level2>
</sec-level1>
<acknowledgment>
<heading>Npxabjyrqtzragf</heading>
<p indent="no" type="new-line">VM vf tengrshy gb Ynobengbver qr Culfvdhr qr y'Rgng Pbaqrafé, Havirefvgé qh Znvar (YCRP) naq gb gur Noqhf Fnynz Vagreangvbany Prager sbe Gurbergvpny Culfvpf (VPGC), sbe gurve xvaq ubfcvgnyvgl naq sbe gurve fhccbeg va guvf jbex.</p>
</acknowledgment>
<appendix id="pscr370073a1" numbering="bysection" numbers="restart" prefix="yes">
<sec-level1 id="pscr370073s5" label="Appendix" appendix="no" type="num" style="arabic" inherit="yes">
<p indent="yes" type="new-line"><display-eqn textype="equation" notation="LaTeX" number="no" lines="single" type="complex" font="italic" numalign="bottom" eqnalign="indent"><?TeX \[ E_{\rm sub} =\langle \psi(\alpha = 0)|H_{\rm sub}|\psi(\alpha = 0)\rangle = \frac{\pi}{b-a}, \]?><eqn-graphic format="GIF" filename="physscr_83_3_035701img/pscr370073ueqn1.gif" position="indent" align="middle"/></display-eqn>jurer
<display-eqn textype="equation" notation="LaTeX" number="no" lines="single" type="complex" font="italic" numalign="bottom" eqnalign="indent"><?TeX \[ H_{\rm sub} = -\nabla ^2 + V(r), \]?><eqn-graphic format="GIF" filename="physscr_83_3_035701img/pscr370073ueqn2.gif" position="indent" align="middle"/></display-eqn>
<display-eqn textype="equation" notation="LaTeX" number="no" lines="single" type="complex" font="italic" numalign="bottom" eqnalign="indent"><?TeX \[ E_{\rm t} = \mathop {\min }\limits_\alpha \left\{ \frac{\langle \psi|H|\psi\rangle}{\langle\psi|\psi\rangle}\right\}, \]?><eqn-graphic format="GIF" filename="physscr_83_3_035701img/pscr370073ueqn3.gif" position="indent" align="middle"/></display-eqn>
<display-eqn textype="equation" notation="LaTeX" number="no" lines="single" type="complex" font="italic" numalign="bottom" eqnalign="indent"><?TeX \[ E_{\rm{t}} = \mathop {\min }\limits_\alpha \left\{ K^2 -\alpha ^2 + \alpha \left[r_0^2 \frac{I_2}{I_1} + 2\,K\,\frac{I_3}{I_1} + r_0 \frac{I_4}{I_1} \right]-2\frac{I_5}{I_1} \right\},\]?><eqn-graphic format="GIF" filename="physscr_83_3_035701img/pscr370073ueqn4.gif" position="indent" align="middle"/></display-eqn>
<display-eqn textype="eqnarray" notation="LaTeX" number="no" lines="multiline" type="complex" font="italic" numalign="bottom" eqnalign="indent"><?TeX \begin{eqnarray*} I_1& =& \int_{\rm{a}}^{\rm{b}} {\int_0^{\rm{\pi }} {{\rm{sin}}{\kern 1pt} {\rm{\theta }}\,{\rm{sin}}^2 (K(r-a))} } \nonumber\\ &&\times{\rm exp}\,\left[-2\,\alpha\,\sqrt{r_{0}^{2} + r^{2} -2rr_{0} \,{\rm cos}\,\theta} \right]\,{\rm d}r\,{\rm d}\theta, \end{eqnarray*}?><eqn-graphic format="GIF" filename="physscr_83_3_035701img/pscr370073ueqn5.gif" position="indent" align="middle"/></display-eqn>
<display-eqn textype="eqnarray" notation="LaTeX" number="no" lines="multiline" type="complex" font="italic" numalign="bottom" eqnalign="indent"><?TeX \begin{eqnarray*} I_2& =& \int_{\rm a}^{\rm b}\int_{0}^{\rm \pi} \frac{\sin^{3}\theta\sin^{2} (K(r-a))}{(r_{0}^{2} + r^{2} -{2}\,rr_{0}\cos\theta)^{3/2}} \nonumber\\[4pt] &&\times{\rm exp}\,\left[-2\,\alpha\,\sqrt {r_{0}^{2} + r^{2} -{2}\,rr_{0} \cos\theta} \right]\,{\rm d}r\,{\rm d}\theta, \end{eqnarray*}?><eqn-graphic format="GIF" filename="physscr_83_3_035701img/pscr370073ueqn6.gif" position="indent" align="middle"/></display-eqn>
<display-eqn textype="eqnarray" notation="LaTeX" number="no" lines="multiline" type="complex" font="italic" numalign="bottom" eqnalign="indent"><?TeX \begin{eqnarray*} I_3 & = & \int_{\rm a}^{\rm b} \int_{0}^{\pi}\sin\theta\sin(K(r-a))\,\cos(K(r-a))\nonumber\\ &&\times\frac{r-r_{0}\,\cos\theta}{\sqrt{r_{0}^{2} + r^{2} -{2}\,rr_{0}\cos\theta}}\nonumber\\ &&\times{\rm exp}\left[-{2}\,\alpha\,\sqrt{r_{0}^{2} + r^{2} -{2}\,rr_{0}\cos\theta}\right]\,{\rm d}r\,{\rm d}\theta, \end{eqnarray*}?><eqn-graphic format="GIF" filename="physscr_83_3_035701img/pscr370073ueqn7.gif" position="indent" align="middle"/></display-eqn>
<display-eqn textype="eqnarray" notation="LaTeX" number="no" lines="multiline" type="complex" font="italic" numalign="bottom" eqnalign="indent"><?TeX \begin{leqnarray*} I_4 = \int_{\rm a}^{\rm b} \int_0^{\pi}\sin\theta\frac{\sin^{2} (K(r-a))}{r}\nonumber\\[4pt] \qquad\times\frac{\cos\theta\left[2\,\left(r^{2}+ r_{0}^{2}\right)\right]-rr_{0} \left[1 + 3\cos^{2}\theta\right]}{\left(r_{0}^{2}+ r^{2} -{2}\,rr_{0}\cos\theta\right)^{3/2}}\nonumber\\[4pt] \qquad\times{\rm exp}\left[-2\alpha\,\sqrt{r_{0}^{2}+ r^{2} -{2}\,rr_{0} \cos\theta}\right]\,{\rm d}r\,{\rm d}\theta, \end{leqnarray*} ?><eqn-graphic format="GIF" filename="physscr_83_3_035701img/pscr370073ueqn8.gif" position="indent" align="middle"/></display-eqn>
<display-eqn textype="eqnarray" notation="LaTeX" number="no" lines="multiline" type="complex" font="italic" numalign="bottom" eqnalign="indent"><?TeX \begin{eqnarray*} I_5 &=& \int_{\rm a}^{\rm b} \int_0^{\pi} \frac{\sin\theta\sin^{2}(K(r-a))}{\sqrt{r_{0}^{2} + r^{2} -{2}\,rr_{0}\cos\theta}}\nonumber\\ &&\times\exp\left[-{2}\,\alpha\,\sqrt{r_{0}^{2} + r^{2} -{2}\,rr_0\cos\theta}\right]\,{\rm d}r\,{\rm d}\theta, \end{eqnarray*}?><eqn-graphic format="GIF" filename="physscr_83_3_035701img/pscr370073ueqn9.gif" position="indent" align="middle"/></display-eqn>
<display-eqn textype="equation" notation="LaTeX" number="no" lines="single" type="complex" font="italic" numalign="bottom" eqnalign="indent"><?TeX \[ \chi_{\rm dia} = -\frac{e^2}{6m^{*}\;\varepsilon_0 c^2}\langle(\vec r-\vec r_0 )^2\rangle, \]?><eqn-graphic format="GIF" filename="physscr_83_3_035701img/pscr370073ueqn10.gif" position="indent" align="middle"/></display-eqn>jurer
<display-eqn textype="equation" notation="LaTeX" number="no" lines="single" type="complex" font="italic" numalign="bottom" eqnalign="indent"><?TeX \[ \langle (\vec r-\vec r_0 )^2\rangle = \frac{\langle {\psi|{(\vec r-\vec r_0 )^2}|\psi}\rangle}{\langle\psi|\psi\rangle}= \frac{I_6}{I_1}, \]?><eqn-graphic format="GIF" filename="physscr_83_3_035701img/pscr370073ueqn11.gif" position="indent" align="middle"/></display-eqn>
<display-eqn textype="eqnarray" notation="LaTeX" number="no" lines="multiline" type="complex" font="italic" numalign="bottom" eqnalign="indent"><?TeX \begin{eqnarray*} I_6 &=& \int^{\rm b}_{\rm a} \,\int^{\rm b}_{\rm a} (r^2 _0 + r^2 -2rr_0\cos \theta)\sin\theta\sin ^2 (K(r-a))\nonumber\\[4pt] &&\times{\rm exp}\,\left[-2\alpha \sqrt {r^2 _0 + r^2 -2rr_0 \cos\theta}\right]{\rm d}r\,{\rm d}\theta. \end{eqnarray*}?><eqn-graphic format="GIF" filename="physscr_83_3_035701img/pscr370073ueqn12.gif" position="indent" align="middle"/></display-eqn></p>
</sec-level1>
</appendix>
</body>
<back>
<references>
<heading>Ersreraprf</heading>
<reference-list type="numeric">
<journal-ref id="pscr370073bib1" num="1">
<authors>
<au print="yes">
<second-name>Fnuva</second-name>
<first-names>Z</first-names>
</au>
</authors>
<year after="no">7993</year>
<jnl-title>Culf. Eri.</jnl-title>
<part>O</part>
<volume>22</volume>
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Romain Loth