Content-Type: multipart/mixed; boundary="-------------0301170245789" This is a multi-part message in MIME format. ---------------0301170245789 Content-Type: text/plain; name="03-19.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="03-19.keywords" weak coupling limit, perturbative expansion, quantum scattering cross section, stationary phase ---------------0301170245789 Content-Type: application/postscript; name="bcep-fin.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="bcep-fin.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %%Title: bcep-fin.dvi %%Pages: 24 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips bcep-fin.dvi -o %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2003.01.17:0924 %%BeginProcSet: texc.pro %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S 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Fm(\)\))p Fk(!)3168 1832 y Fh(j)688 2057 y Fk(u)745 2015 y Fh(cl)745 2081 y(`)778 2091 y Fe(j)821 2057 y Fm(\()p Fk(t)896 2072 y Fh(j)t Fr(+1)1038 2057 y Fm(\))k(=)i Fk(u)1267 2015 y Fh(cl)1267 2081 y(`)1300 2091 y Fe(j)1342 2057 y Fm(\()p Fk(t)1417 2072 y Fh(j)1459 2057 y Fm(\))22 b Fj(\000)1631 1989 y Fm(1)g(+)h Fk(\033)1860 2004 y Fh(j)p 1631 2034 V 1742 2125 a Fm(2)1914 2057 y(\()p Fk(!)2015 2072 y Fh(j)2079 2057 y Fj(\001)f Fm(\()p Fk(u)2225 2015 y Fh(cl)2225 2081 y(`)2258 2091 y Fe(j)2300 2057 y Fm(\()p Fk(t)2375 2072 y Fh(j)2417 2057 y Fm(\))f Fj(\000)i Fk(u)2634 2015 y Fh(cl)2634 2081 y(j)t Fr(+1)2777 2057 y Fm(\()p Fk(t)2852 2072 y Fh(j)2894 2057 y Fm(\)\))p Fk(!)3034 2072 y Fh(j)688 2254 y Fk(u)745 2213 y Fh(cl)745 2279 y(r)811 2254 y Fm(\()p Fk(t)886 2269 y Fh(j)t Fr(+1)1029 2254 y Fm(\))k(=)h Fk(u)1257 2213 y Fh(cl)1257 2279 y(r)1324 2254 y Fm(\()p Fk(t)1399 2269 y Fh(j)1440 2254 y Fm(\))160 b(if)61 b Fk(r)31 b Fm(=)-63 b Fk(=)28 b(`)1968 2269 y Fh(j)2038 2254 y Fk(:)3643 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Fh(s)2185 3240 y Fk(u)2242 3199 y Fh(cl)2242 3265 y(j)2308 3240 y Fm(\()p Fk(\034)11 b Fm(\))17 b Fk(d\034)6 b(:)1055 b Fm(\(3)p Fk(:)p Fm(15\))0 3524 y(Note)35 b(that,)h(b)s(ecause)h(of)f(the)g(factors)g(\(1)24 b(+)g Fk(\033)1749 3539 y Fh(r)1793 3524 y Fm(\))p Fk(=)p Fm(2,)36 b(when)g Fk(\033)2315 3539 y Fh(r)2391 3524 y Fm(=)d Fj(\000)p Fm(1)j(the)g(v)m(elo)s(cit)m(y)e(is)i(unc)m(hanged)i (at)0 3643 y(time)30 b Fk(t)261 3658 y Fh(r)306 3643 y Fm(,)h(so)h(pro)s(ducing)g(a)g(loss)g(term,)f(while)g(when)i Fk(\033)2061 3658 y Fh(r)2133 3643 y Fm(=)28 b(1,)j(the)h(v)m(elo)s (cit)m(y)f(c)m(hanges)i(b)m(y)f(a)f(term)g(suc)m(h)0 3763 y(that)i(the)g(conserv)-6 b(ation)34 b(of)g(energy)f(is)g (ensured.)46 b(Finally)-8 b(,)1361 3990 y Fk(y)1414 3949 y Fh(cl)1410 4015 y(j)1507 3990 y Fm(=)29 b Fk(y)1666 3949 y Fh(cl)1662 4015 y(j)1731 3990 y Fm(\(0\))p Fk(;)115 b(u)2059 3949 y Fh(cl)2059 4015 y(j)2153 3990 y Fm(=)28 b Fk(u)2315 3949 y Fh(cl)2315 4015 y(j)2382 3990 y Fm(\(0\))p Fk(:)1105 b 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Fr(2)223 5757 y Fk(f)272 5772 y Fh(n)p Fr(+1)427 5757 y Fm(\()7 b(\026)-57 b Fk(y)515 5772 y Fr(1)559 5757 y Fk(;)17 b(:)g(:)g(:)d(;)23 b Fm(\026)-56 b Fk(y)830 5772 y Fh(n)p Fr(+1)984 5757 y Fm(;)23 b(\026)-56 b Fk(u)1086 5772 y Fr(1)1130 5757 y Fk(;)33 b(:)17 b(:)g(:)e(;)39 b Fm(\026)-56 b Fk(u)1442 5772 y Fh(n)p Fr(+1)1597 5757 y Fm(\))1697 5633 y Fh(n)1658 5663 y Fg(Y)1653 5875 y Fh(j)t Fr(=1)1807 5622 y Fg(Z)1906 5646 y Fr(+)p Ff(1)1862 5848 y Fr(0)2069 5757 y Fk(ds)17 b Fm(exp)2353 5677 y Fg(\002)2416 5757 y Fj(\000)23 b Fk(isk)2649 5772 y Fh(j)2713 5757 y Fj(\001)f Fm([\()e(\026)-70 b Fk(w)2901 5772 y Fh(j)2965 5757 y Fm(+)22 b Fk(k)3116 5772 y Fh(j)3158 5757 y Fk(\033)3215 5772 y Fh(j)3257 5757 y Fm(\)])3324 5677 y Fg(\003)3393 5757 y Fk(;)3643 5492 y Fm(\(3)p Fk(:)p Fm(41\))p eop %%Page: 21 21 21 20 bop 1508 50 a Fp(BENEDETTO)36 b(ET)g(AL.)1424 b(21)0 289 y Fm(where)26 b(the)f(in)m(tegrals)g(on)g(the)h Fk(s)p 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