%!PS-Adobe-2.0 %%Creator: dvipsk 5.58f Copyright 1986, 1994 Radical Eye Software %%Title: brazil7.dvi %%Pages: 8 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentPaperSizes: a4 %%EndComments %DVIPSCommandLine: dvips brazil7 %DVIPSParameters: dpi=600, compressed, comments removed %DVIPSSource: TeX output 1998.05.05:0819 %%BeginProcSet: texc.pro /TeXDict 250 dict def TeXDict begin /N{def}def /B{bind def}N /S{exch}N /X{S N}B /TR{translate}N /isls false N /vsize 11 72 mul N /hsize 8.5 72 mul N /landplus90{false}def /@rigin{isls{[0 landplus90{1 -1}{-1 1} ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[matrix currentmatrix{dup dup round sub abs 0.00001 lt{round}if} forall round exch round exch]setmatrix}N /@landscape{/isls true N}B /@manualfeed{statusdict /manualfeed true put}B /@copies{/#copies X}B /FMat[1 0 0 -1 0 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Ft(j)p Fv(M)2290 4803 y Fu(\001)2349 4791 y Fs(\000)2401 4763 y Fu(2)2401 4812 y(tot)2523 4735 y Fv(:)618 b Fs(\(3\))1839 4980 y(2)p eop %%Page: 3 3 3 2 bop 450 863 a Fs(In)38 b(these)f(expressions,)i Fh(p)1305 883 y Fk(\031)1387 863 y Fs(is)f(the)g(pion)f(and)g Fh(k)j Fs(the)e(photon)f(3-momen)n(tum)g(in)h(the)450 963 y(reference)29 b(frame)h(in)h(whic)n(h)f(the)h(\001)g(is)f(at)g(rest,)h Fv(M)2083 975 y Fk(N)2176 963 y Fs(is)f(the)h(n)n(ucleon)f(mass,)g(and) h Fv(M)3189 975 y Fu(\001)3247 963 y Fs(,)450 1062 y(\000)502 1074 y Fu(tot)622 1062 y Fs(and)g(\000)839 1074 y Fk(\031)r(N)971 1062 y Ft(\031)d Fs(\000)1116 1074 y Fu(tot)1236 1062 y Fs(are)i(the)h(resonance)e(mass,)i(the)h(total)e(and)h(the)g(partial) f(deca)n(y)450 1162 y(widths,)39 b(resp)r(ectiv)n(ely)-7 b(.)61 b(The)36 b(electropro)r(duction)f(amplitudes)h(are)f(functions)i (of)f(the)450 1262 y(photon)27 b(virtualit)n(y)g Fv(K)1175 1231 y Fu(2)1235 1262 y Fs(=)c Fv(!)1378 1231 y Fu(2)1433 1262 y Ft(\000)18 b Fh(k)1568 1224 y Fu(2)1633 1262 y Fs(and)27 b(the)h(follo)n(wing)f(kinematical)g(relations)f(hold:)597 1488 y Fv(!)f Fs(=)772 1432 y Fv(M)862 1402 y Fu(2)853 1455 y(\001)930 1432 y Ft(\000)18 b Fv(M)1103 1402 y Fu(2)1094 1455 y Fk(N)1174 1432 y Fs(+)h Fv(K)1335 1402 y Fu(2)p 772 1469 600 4 v 981 1545 a Fs(2)p Fv(M)1104 1557 y Fu(\001)1395 1488 y Fs(;)180 b Fh(k)1650 1451 y Fu(2)1710 1488 y Ft(\021)23 b Fv(k)1844 1454 y Fu(2)1904 1488 y Fs(=)1991 1371 y Fi(\024)2045 1432 y Fv(M)2135 1402 y Fu(2)2126 1455 y(\001)2203 1432 y Fs(+)18 b Fv(M)2376 1402 y Fu(2)2367 1455 y Fk(N)2448 1432 y Ft(\000)g Fv(K)2608 1402 y Fu(2)p 2045 1469 V 2254 1545 a Fs(2)p Fv(M)2377 1557 y Fu(\001)2654 1371 y Fi(\025)2698 1388 y Fu(2)2754 1488 y Ft(\000)g Fv(M)2927 1454 y Fu(2)2918 1509 y Fk(N)2994 1488 y Fv(:)147 b Fs(\(4\))450 1703 y(The)29 b(parameter)f Fv(k)1064 1715 y Fk(W)1165 1703 y Ft(\021)d Fv(!)s Fs(\()p Fv(K)31 b Fs(=)25 b(0\))h(=)f(0)p Fv(:)p Fs(259)i(GeV)i(app)r(earing)f (in)i(\(3\))f(and)g(in)g(the)h(ex-)450 1802 y(pansion)22 b(of)i(the)f(photon)g(\014eld)h(in)f(\(5\))h(is)f(in)n(tro)r(duced)g (\(rather)f(than)h Fv(!)s Fs(\))h(for)e(con)n(v)n(enience)450 1902 y(since)27 b Fv(!)k Fs(go)r(es)26 b(through)h(0)g(at)h Fv(K)1480 1872 y Fu(2)1540 1902 y Fs(=)22 b Fv(M)1717 1872 y Fu(2)1708 1925 y Fk(N)1789 1902 y Ft(\000)c Fv(M)1962 1872 y Fu(2)1953 1925 y(\001)2012 1902 y Fs(.)600 2002 y(The)32 b Fv(M)9 b Fs(1)30 b(and)h Fv(E)5 b Fs(2)32 b(amplitudes)f(for)g(the)h(transition)f Fv(\015)2374 2014 y Fu(v)2413 2002 y Fv(N)38 b Ft(!)29 b Fs(\001)j(are)f(usually)g (ex-)450 2101 y(pressed)c(in)h(terms)f(of)g(helicit)n(y)h(amplitudes)g (de\014ned)g(as)888 2304 y Fv(A)950 2316 y Fk(\025)1017 2304 y Fs(=)22 b Ft(\000)1274 2247 y Fv(e)p 1179 2284 230 4 v 1179 2301 a Ft(p)p 1248 2301 161 4 v 65 x Fs(2)p Fv(k)1333 2378 y Fk(W)1432 2304 y Ft(h)p Fs(\001)1533 2269 y Fu(+)1589 2304 y Fv(;)14 b(\025)g Ft(j)1725 2191 y Fi(Z)1821 2304 y Fs(d)1868 2266 y Fu(3)1905 2304 y Fh(r)i(\017)j Ft(\001)2073 2282 y Fi(b)2065 2304 y Fh(J)9 b Fs(\()p Fh(r)s Fs(\))14 b(e)2288 2269 y(i)p Fh(k)r Fl(\001)p Fh(r)2447 2304 y Ft(j)g Fv(p;)g(\025)k Ft(\000)g Fs(1)p Ft(i)23 b Fv(;)332 b Fs(\(5\))450 2524 y(with)28 b Fv(\025)c Fs(=)e(1)p Fv(=)p Fs(2)p Fv(;)k Fs(3)p Fv(=)p Fs(2)h(and)g Fh(\017)c Fs(=)g Ft(\000)1540 2491 y Fu(1)p 1512 2505 88 4 v 1512 2514 a Fl(p)p 1567 2514 34 3 v 48 x Fu(2)1624 2524 y Fs(\()14 b(1)27 b(i)h(0)14 b(\))27 b(as)g(follo)n(ws:)557 2752 y Fv(M)9 b Fs(1)22 b(=)h Ft(\000)929 2696 y Fs(1)p 874 2733 153 4 v 874 2818 a(2)916 2750 y Ft(p)p 984 2750 42 4 v 984 2818 a Fs(3)1050 2660 y Fi(h)1089 2752 y Fs(3)14 b Fv(A)1207 2767 y Fu(3)p Fk(=)p Fu(2)1329 2752 y Fs(+)1412 2680 y Ft(p)p 1481 2680 V 72 x Fs(3)p Fv(A)1585 2767 y Fu(1)p Fk(=)p Fu(2)1690 2660 y Fi(i)1766 2752 y Fv(;)180 b(E)5 b Fs(2)22 b(=)2252 2696 y(1)p 2197 2733 153 4 v 2197 2818 a(2)2239 2750 y Ft(p)p 2308 2750 42 4 v 68 x Fs(3)2373 2660 y Fi(h)2412 2752 y Fv(A)2474 2767 y Fu(3)p Fk(=)p Fu(2)2597 2752 y Ft(\000)2680 2680 y(p)p 2749 2680 V 72 x Fs(3)p Fv(A)2853 2767 y Fu(1)p Fk(=)p Fu(2)2957 2660 y Fi(i)3034 2752 y Fv(:)107 b Fs(\(6\))450 2984 y(In)23 b(\(5\))h(and)e(\(8\))i(b)r(elo) n(w,)29 b Fi(b)-52 b Fv(\032)p Fs(\()p Fh(r)s Fs(\))24 b(and)1561 2963 y Fi(b)1554 2984 y Fh(J)8 b Fs(\()p Fh(r)s Fs(\))24 b(are)e(the)h(comp)r(onen)n(ts)g(of)g(the)g(electromagnetic) 450 3094 y(curren)n(t,)d(i.e.)913 3073 y Fi(b)895 3094 y Fv(J)941 3106 y Fk(e:m:)1098 3094 y Fs(=)j(\()5 b Fi(b)-51 b Fv(\032;)1319 3073 y Fi(b)1312 3094 y Fh(J)9 b Fs(\),)21 b(and)e Ft(j)p Fs(\001)1694 3064 y Fu(+)1750 3094 y Fv(;)27 b(s)p Ft(i)20 b Fs(\()p Ft(j)p Fv(p;)28 b(s)2078 3064 y Fl(0)2101 3094 y Ft(i)p Fs(\))20 b(is)f(the)h(mo)r(del)f(state)h (represen)n(ting)450 3194 y(the)28 b(\001)g(\(proton\))f(with)h(spin)g (third)g(comp)r(onen)n(t)f Fv(s)h Fs(\()p Fv(s)2157 3164 y Fl(0)2180 3194 y Fs(\).)600 3293 y(Angular)d(momen)n(tum)h(and)g (parit)n(y)f(conserv)-5 b(ation)24 b(imply)j(that)f(only)f Fv(M)9 b Fs(1,)26 b Fv(E)5 b Fs(2)25 b(and)450 3393 y Fv(C)6 b Fs(2)23 b(transitions)g(are)g(allo)n(w)n(ed.)34 b(It)24 b(is,)g(therefore,)g(v)n(ery)e(helpful)j(to)e(p)r(erform)g(a)h (m)n(ultip)r(ole)450 3493 y(decomp)r(osition)j(of)h(the)g(amplitudes,)f Fv(A)1744 3505 y Fk(\025)1811 3493 y Fs(=)c Fv(A)1961 3505 y Fk(\025)2005 3493 y Fs(\()p Fv(M)9 b Fs(1\))18 b(+)g Fv(A)2364 3505 y Fk(\025)2408 3493 y Fs(\()p Fv(E)5 b Fs(2\):)484 3700 y Fv(A)546 3712 y Fk(\025)590 3700 y Fs(\()p Fv(E)g Fs(2\))41 b(=)983 3644 y Ft(\000)p Fv(e)p 919 3681 230 4 v 919 3697 a Ft(p)p 989 3697 161 4 v 989 3762 a Fs(2)p Fv(k)1074 3774 y Fk(W)1173 3700 y Ft(h)p Fs(\001)1274 3665 y Fu(+)1315 3700 y Fv(;\025)p Ft(j)1409 3627 y(p)p 1479 3627 134 4 v 1479 3700 a Fs(10)p Fv(\031)1639 3644 y Fs(1)p 1636 3681 46 4 v 1636 3757 a Fv(k)1692 3587 y Fi(Z)1761 3700 y Fs(d)1807 3663 y Fu(3)1845 3700 y Fh(r)1891 3632 y Fi(\010)1940 3700 y Fg(r)t Ft(\002)2094 3632 y Fi(\002)2128 3700 y Fv(j)2162 3712 y Fu(2)2199 3700 y Fs(\()p Fv(k)s(r)r Fs(\))14 b Fh(Y)2440 3663 y Fu(1)2440 3720 y(2)e(2)2522 3700 y Fs(\()2557 3699 y(^)2554 3700 y Fh(r)s Fs(\))2633 3632 y Fi(\003\011)2721 3700 y Ft(\001)2756 3678 y Fi(b)2749 3700 y Fh(J)c Fs(\()p Fh(r)s Fs(\))14 b Ft(j)p Fv(p;)g(\025)19 b Ft(\000)f Fs(1)p Ft(i)3164 3872 y Fs(\(7\))460 4039 y Fv(A)522 4051 y Fk(\025)566 4039 y Fs(\()p Fv(M)9 b Fs(1\))41 b(=)1015 3983 y Fv(e)p 919 4020 230 4 v 919 4037 a Ft(p)p 989 4037 161 4 v 989 4101 a Fs(2)p Fv(k)1074 4113 y Fk(W)1173 4039 y Fs(i)14 b Ft(h)p Fs(\001)1311 4005 y Fu(+)1366 4039 y Fv(;)g(\025)g Ft(j)1488 3967 y(p)p 1558 3967 92 4 v 1558 4039 a Fs(6)p Fv(\031)1691 3926 y Fi(Z)1788 4039 y Fs(d)1834 4002 y Fu(3)1871 4039 y Fh(r)j Fv(j)1966 4051 y Fu(1)2003 4039 y Fs(\()p Fv(k)s(r)r Fs(\))d Fh(Y)2244 4003 y Fu(1)2244 4060 y(1)e(1)2326 4039 y Fs(\()2361 4038 y(^)2358 4039 y Fh(r)s Fs(\))18 b Ft(\001)2504 4018 y Fi(b)2497 4039 y Fh(J)9 b Fs(\()p Fh(r)s Fs(\))14 b Ft(j)g Fv(p;)g(\025)k Ft(\000)g Fs(1)p Ft(i)c Fv(:)450 4255 y Fs(In)34 b(these)f(expressions,)h Fh(Y)1319 4215 y Fk(\026)1319 4279 y(J)16 b(L)1422 4255 y Fs(\()1457 4254 y(^)1454 4255 y Fh(r)s Fs(\))34 b(are)e(the)i(v)n(ector)e (spherical)h(harmonics.)53 b(Using)34 b(the)450 4354 y(Wigner-Ec)n(k)-5 b(art)18 b(theorem)i(the)h(matrix)e(elemen)n(ts)i Fv(M)9 b Fs(1)19 b(and)h Fv(E)5 b Fs(2)20 b(are)g(expressed)f(in)h (terms)450 4454 y(of)28 b Fv(A)607 4469 y Fu(1)p Fk(=)p Fu(2)739 4454 y Fs(only:)36 b Fv(M)9 b Fs(1)22 b(=)h Ft(\000)p Fs(2)14 b Fv(A)1378 4469 y Fu(1)p Fk(=)p Fu(2)1482 4454 y Fs(\()p Fv(M)9 b Fs(1\))27 b(and)g Fv(E)5 b Fs(2)23 b(=)g Ft(\000)p Fs(2)14 b Fv(A)2268 4469 y Fu(1)p Fk(=)p Fu(2)2371 4454 y Fs(\()p Fv(E)5 b Fs(2\))23 b Fv(=)p Fs(3)14 b(.)600 4554 y(Similarly)-7 b(,)27 b(w)n(e)g(ha)n(v)n(e)g(for)g (the)h(scalar)e(amplitude:)498 4756 y Fv(S)549 4771 y Fu(1)p Fk(=)p Fu(2)653 4756 y Fs(\()p Fv(C)6 b Fs(2\))24 b(=)e Fv(C)6 b Fs(2)23 b(=)1226 4700 y Ft(\000)p Fv(e)p 1163 4737 230 4 v 1163 4754 a Ft(p)p 1232 4754 161 4 v 64 x Fs(2)p Fv(k)1317 4830 y Fk(W)1460 4700 y Fs(1)p 1426 4737 111 4 v 1426 4754 a Ft(p)p 1495 4754 42 4 v 68 x Fs(2)1560 4756 y Ft(h)p Fs(\001)1661 4722 y Fu(+)1703 4756 y Fv(;)1750 4723 y Fu(1)p 1750 4737 34 4 v 1750 4785 a(2)1793 4756 y Ft(j)1816 4683 y(p)p 1885 4683 134 4 v 73 x Fs(20)p Fv(\031)2019 4643 y Fi(Z)2102 4756 y Fs(d)2148 4719 y Fu(3)2185 4756 y Fh(r)16 b Fv(j)2279 4768 y Fu(2)2317 4756 y Fs(\()p Fv(k)s(r)r Fs(\))e Fv(Y)2528 4768 y Fu(20)2599 4756 y Fs(\()2634 4755 y(^)2631 4756 y Fh(r)s Fs(\))20 b Fi(b)-52 b Fv(\032)p Fs(\()p Fh(r)s Fs(\))p Ft(j)14 b Fv(p;)3004 4723 y Fu(1)p 3004 4737 34 4 v 3004 4785 a(2)3047 4756 y Ft(i)g Fv(:)48 b Fs(\(8\))1839 4980 y(3)p eop %%Page: 4 4 4 3 bop 450 863 a Fs(Note)25 b(that)g(\(8\))g(remains)e(\014nite)j(for) e Fv(K)1673 833 y Fu(2)1732 863 y Ft(!)g Fs(0)g(in)h(con)n(trast)e(to)i (the)g(Coulom)n(b)f(amplitude)450 963 y(de\014ned)k(as)f Fv(C)897 978 y Fu(1)p Fk(=)p Fu(2)1025 963 y Fs(=)1122 930 y Fk(K)p 1122 944 60 4 v 1134 991 a(k)1206 963 y Fv(S)1257 978 y Fu(1)p Fk(=)p Fu(2)1389 963 y Fs(whic)n(h)g(v)-5 b(anishes)27 b(at)h(the)g(photon)f(p)r(oin)n(t.)600 1062 y(One)g(usually)g(de\014nes)h(m)n(ultip)r(ole)g(momen)n(ts)561 1280 y Ft(M)661 1246 y Fk(M)6 b Fu(1)768 1280 y Fs(\()p Fv(k)s Fs(\))41 b(=)h Ft(\000)1101 1224 y Fs(3)p 1101 1261 42 4 v 1101 1337 a(2)1165 1167 y Fi(Z)1262 1280 y Fs(d)1308 1243 y Fu(3)1346 1280 y Fh(r)16 b Ft(h)p Fs(\001)1507 1246 y Fu(+)1563 1280 y Fv(;)1609 1247 y Fu(1)p 1609 1261 34 4 v 1609 1308 a(2)1653 1280 y Ft(j)e Fs(\()1725 1279 y(^)1722 1280 y Fh(r)21 b Ft(\002)1877 1259 y Fi(b)1870 1280 y Fh(J)9 b Fs(\))1963 1292 y Fu(1)2014 1280 y Ft(j)p Fv(p;)14 b Ft(\000)2191 1247 y Fu(1)p 2190 1261 V 2190 1308 a(2)2233 1280 y Ft(i)g Fv(j)2313 1292 y Fu(1)2351 1280 y Fs(\()p Fv(k)s(r)r Fs(\))g Fv(;)627 b Fs(\(9\))545 1516 y Ft(M)645 1482 y Fk(E)s Fu(2)741 1457 y Ff(0)768 1516 y Fs(\()p Fv(k)s Fs(\))41 b(=)h Ft(\000)1101 1391 y(p)p 1169 1391 134 4 v 1169 1460 a Fs(10)p Fv(\031)p 1101 1497 203 4 v 1178 1573 a(k)1326 1403 y Fi(Z)1423 1516 y Fs(d)1469 1479 y Fu(3)1507 1516 y Fh(r)16 b Ft(h)p Fs(\001)1668 1482 y Fu(+)1710 1516 y Fv(;)1743 1483 y Fu(1)p 1743 1497 34 4 v 1743 1545 a(2)1786 1516 y Ft(j)1809 1399 y Fi(\024)1853 1516 y Fg(r)i Ft(\002)g Fv(j)2068 1528 y Fu(2)2105 1516 y Fs(\()p Fv(k)s(r)r Fs(\))p Fh(Y)2333 1480 y Fu(1)2333 1537 y(22)2403 1516 y Fs(\()2438 1515 y(^)2435 1516 y Fh(r)s Fs(\))2514 1399 y Fi(\025)2562 1516 y Ft(\001)2597 1495 y Fi(b)2590 1516 y Fh(J)9 b Fs(\()p Fh(r)s Fs(\))14 b Ft(j)g Fv(p;)p Ft(\000)2953 1483 y Fu(1)p 2952 1497 V 2952 1545 a(2)2995 1516 y Ft(i)g Fv(;)58 b Fs(\(10\))579 1741 y Ft(M)679 1707 y Fk(C)t Fu(2)768 1741 y Fs(\()p Fv(k)s Fs(\))41 b(=)h Ft(\000)1091 1668 y(p)p 1159 1668 134 4 v 1159 1741 a Fs(20)p Fv(\031)1320 1628 y Fi(Z)1417 1741 y Fs(d)1463 1704 y Fu(3)1501 1741 y Fh(r)16 b Ft(h)p Fs(\001)1662 1707 y Fu(+)1718 1741 y Fv(;)1764 1708 y Fu(1)p 1764 1722 34 4 v 1764 1770 a(2)1807 1741 y Ft(j)k Fi(b)-52 b Fv(\032)p Fs(\()p Fh(r)s Fs(\))14 b Ft(j)p Fv(p;)2124 1708 y Fu(1)p 2124 1722 V 2124 1770 a(2)2167 1741 y Ft(i)g Fv(Y)2261 1753 y Fu(20)2332 1741 y Fs(\()2367 1740 y(^)2364 1741 y Fh(r)r Fs(\))g Fv(j)2490 1753 y Fu(2)2528 1741 y Fs(\()p Fv(k)s(r)r Fs(\))g Fv(;)408 b Fs(\(11\))450 1976 y(whic)n(h)26 b(are)f(just)i Fv(A)1048 1991 y Fu(1)p Fk(=)p Fu(2)1152 1976 y Fs(\()p Fv(M)9 b Fs(1\),)27 b Fv(A)1460 1991 y Fu(1)p Fk(=)p Fu(2)1564 1976 y Fs(\()p Fv(E)5 b Fs(2\))27 b(and)1923 1908 y Ft(p)p 1992 1908 42 4 v 68 x Fs(2)13 b Fv(S)2098 1991 y Fu(1)p Fk(=)p Fu(2)2202 1976 y Fs(\()p Fv(C)6 b Fs(2\),)27 b(resp)r(ectiv)n(ely)-7 b(,)26 b(divided)g(b)n(y)450 2085 y Fv(e=)531 2021 y Ft(p)p 599 2021 161 4 v 599 2085 a Fs(2)p Fv(k)684 2097 y Fk(W)760 2085 y Fs(.)37 b(The)27 b(Eq.)37 b(\(10\))27 b(can)g(b)r(e)h(re-written)f(as)503 2332 y Ft(M)603 2297 y Fk(E)s Fu(2)688 2272 y Ff(0)715 2332 y Fs(\()p Fv(k)s Fs(\))c(=)g Ft(\000)1022 2275 y Fs(i)p 1011 2312 46 4 v 1011 2388 a Fv(k)1080 2201 y Fi(r)p 1163 2201 112 4 v 1173 2275 a Fs(5)p Fv(\031)p 1173 2312 92 4 v 1198 2388 a Fs(3)1275 2219 y Fi(Z)1358 2332 y Fs(d)1404 2294 y Fu(3)1441 2332 y Fh(r)16 b Ft(h)p Fs(\001)1602 2297 y Fu(+)1644 2332 y Fv(;)1677 2299 y Fu(1)p 1677 2313 34 4 v 1677 2360 a(2)1720 2332 y Ft(j)j(\000)f Fg(r)t Ft(\001)1964 2310 y Fi(b)1957 2332 y Fh(J)8 b Fs(\()p Fh(r)s Fs(\))p Ft(j)p Fv(p;)p Ft(\000)2291 2299 y Fu(1)p 2291 2313 V 2291 2360 a(2)2334 2332 y Ft(i)14 b Fv(Y)2428 2344 y Fu(2)e(1)2510 2332 y Fs(\()2545 2331 y(^)2542 2332 y Fh(r)s Fs(\))2637 2275 y Fv(@)p 2631 2312 89 4 v 2631 2388 a(@)5 b(r)2743 2332 y Fs([)p Fv(r)17 b(j)2854 2344 y Fu(2)2891 2332 y Fs(\()p Fv(k)s(r)r Fs(\)])586 2573 y Ft(\000)p Fs(i)d Fv(k)747 2443 y Fi(r)p 830 2443 112 4 v 840 2517 a Fs(5)p Fv(\031)p 840 2554 92 4 v 866 2630 a Fs(3)970 2460 y Fi(Z)1067 2573 y Fs(d)1113 2536 y Fu(3)1150 2573 y Fh(r)i Ft(h)p Fs(\001)1311 2539 y Fu(+)1367 2573 y Fv(;)1414 2541 y Fu(1)p 1414 2555 34 4 v 1414 2602 a(2)1457 2573 y Ft(j)p Fh(r)21 b Ft(\001)1594 2552 y Fi(b)1586 2573 y Fh(J)9 b Fs(\()p Fh(r)s Fs(\))p Ft(j)p Fv(p;)14 b Ft(\000)1935 2541 y Fu(1)p 1935 2555 V 1935 2602 a(2)1978 2573 y Ft(i)g Fv(Y)2072 2585 y Fu(2)d(1)2154 2573 y Fs(\()2189 2572 y(^)2186 2573 y Fh(r)s Fs(\))j Fv(j)2313 2585 y Fu(2)2350 2573 y Fs(\()p Fv(k)s(r)r Fs(\))g Fv(:)586 b Fs(\(12\))450 2814 y(The)29 b(con)n(tin)n(uit)n(y)g (equation)f(for)g(the)i(electromagnetic)e(curren)n(t,)g Fv(@)2583 2826 y Fk(\026)2659 2793 y Fi(b)2642 2814 y Fv(J)2696 2784 y Fk(\026)2688 2835 y(e:m:)2847 2814 y Fs(=)d(0,)k(can)g(b)r(e)450 2927 y(used)h(to)g(write)g Fg(r)20 b Ft(\001)1111 2906 y Fi(b)1104 2927 y Fh(J)36 b Fs(=)27 b Ft(\000)1347 2908 y Fi(b)1365 2927 y Fs(_)-39 b Fv(\032)26 b Fs(=)h Ft(\000)p Fs(i)14 b([)1668 2906 y Fi(b)1649 2927 y Fv(H)6 b(;)20 b Fi(b)-52 b Fv(\032)14 b Fs(].)45 b(No)n(w,)30 b(if)h(the)f(\001)g(and)g(the)h(n)n(ucleon)f (states)450 3027 y(in)e(\(12\))f(w)n(ere)g(energy)f(eigenstates)h(the)h (follo)n(wing)e(substitution)643 3217 y Ft(h)p Fs(\001)744 3183 y Fu(+)799 3217 y Fv(;)846 3185 y Fu(1)p 846 3199 V 846 3246 a(2)889 3217 y Ft(j)p Fg(r)18 b Ft(\001)1059 3196 y Fi(b)1052 3217 y Fh(J)9 b Fs(\()p Fh(r)r Fs(\))p Ft(j)p Fv(p;)14 b Ft(\000)1400 3185 y Fu(1)p 1400 3199 V 1400 3246 a(2)1443 3217 y Ft(i)79 b(!)f(\000)14 b Fs(i)f(\()p Fv(E)1923 3229 y Fu(\001)2001 3217 y Ft(\000)18 b Fv(E)2145 3229 y Fk(N)2208 3217 y Fs(\))c Ft(h)p Fs(\001)2355 3183 y Fu(+)2411 3217 y Fv(;)2458 3185 y Fu(1)p 2458 3199 V 2458 3246 a(2)2501 3217 y Ft(j)5 b Fi(b)-51 b Fv(\032)p Fs(\()p Fh(r)s Fs(\))p Ft(j)p Fv(p;)14 b Ft(\000)2855 3185 y Fu(1)p 2854 3199 V 2854 3246 a(2)2897 3217 y Ft(i)193 b Fs(\(13\))450 3397 y(with)28 b(\()p Fv(E)732 3409 y Fu(\001)810 3397 y Ft(\000)18 b Fv(E)954 3409 y Fk(N)1017 3397 y Fs(\))23 b(=)g Fv(!)30 b Fs(could)e(b)r(e)g(carried)e(out)i(in)f (\(12\))h(yielding)660 3643 y Ft(M)760 3609 y Fk(E)s Fu(2)849 3643 y Fs(\()p Fv(k)s Fs(\))42 b(=)f Ft(\000)1172 3513 y Fi(r)p 1255 3513 112 4 v 1265 3587 a Fs(5)p Fv(\031)p 1265 3624 92 4 v 1290 3700 a Fs(2)1390 3587 y Fv(!)p 1390 3624 55 4 v 1394 3700 a(k)1483 3530 y Fi(Z)1579 3643 y Fs(d)1625 3606 y Fu(3)1663 3643 y Fh(r)16 b Ft(h)p Fs(\001)1824 3609 y Fu(+)1880 3643 y Fv(;)1927 3611 y Fu(1)p 1927 3625 34 4 v 1927 3672 a(2)1970 3643 y Ft(j)5 b Fi(b)-51 b Fv(\032)p Fs(\()p Fh(r)r Fs(\))p Ft(j)p Fv(p;)2258 3611 y Fu(1)p 2258 3625 V 2258 3672 a(2)2301 3643 y Ft(i)14 b Fv(Y)2395 3655 y Fu(2)e(0)2477 3643 y Fs(\()2512 3642 y(^)2509 3643 y Fh(r)s Fs(\))2618 3587 y Fv(@)p 2612 3624 89 4 v 2612 3700 a(@)5 b(r)2725 3643 y Fs([)p Fv(r)16 b(j)2835 3655 y Fu(2)2873 3643 y Fs(\()p Fv(k)s(r)r Fs(\)])1001 3885 y(+)41 b(i)1144 3755 y Fi(r)p 1227 3755 112 4 v 1237 3829 a Fs(5)p Fv(\031)p 1237 3866 92 4 v 1262 3942 a Fs(2)1353 3885 y Fv(k)1426 3772 y Fi(Z)1523 3885 y Fs(d)1569 3848 y Fu(3)1606 3885 y Fh(r)17 b Ft(h)p Fs(\001)1768 3851 y Fu(+)1823 3885 y Fv(;)1870 3852 y Fu(1)p 1870 3866 34 4 v 1870 3914 a(2)1913 3885 y Ft(j)p Fh(r)k Ft(\001)2050 3864 y Fi(b)2043 3885 y Fh(J)9 b Fs(\()p Fh(r)r Fs(\))p Ft(j)p Fv(p;)2326 3852 y Fu(1)p 2326 3866 V 2326 3914 a(2)2369 3885 y Ft(i)14 b Fv(Y)2463 3897 y Fu(2)e(0)2545 3885 y Fs(\()2580 3884 y(^)2577 3885 y Fh(r)s Fs(\))i Fv(j)2704 3897 y Fu(2)2742 3885 y Fs(\()p Fv(k)s(r)r Fs(\))g Fv(:)194 b Fs(\(14\))450 4103 y(Ho)n(w)n(ev)n(er,)28 b(in)h(practice,)g(the)h(n)n(ucleon)e(and)h (the)h(\001)f(mo)r(del)h(states)f(are)f(not)h(eigenstates)450 4202 y(of)g(the)h(Hamiltonian)f(and)g(hence)h(one)f(should)g(not)g(exp) r(ect)h(\(12\))f(and)g(\(14\))g(to)g(lead)g(to)450 4302 y(the)h(same)g(result.)44 b(W)-7 b(e)30 b(ha)n(v)n(e)f(computed)h(the)h (matrix)e(elemen)n(ts)h(\(12\))g(and)g(\(14\))f(using)450 4401 y(the)e(mo)r(del)h(states)e(describ)r(ed)h(in)g(the)h(next)f (Section.)37 b(W)-7 b(e)27 b(found)g(out)g(that)h(the)f(former)450 4501 y(is)i(to)r(o)f(sensitiv)n(e)g(to)g(the)h(asymptotic)g(b)r(eha)n (vior)e(of)h(the)h(pion)g(\014eld)g(in)g(the)g(\001)g(whic)n(h)f(is)450 4601 y(not)h(particularly)f(w)n(ell)h(describ)r(ed)g(in)h(our)e (approac)n(h;)h(w)n(e)f(therefore)h(preferred)f(to)h(use)450 4700 y(the)36 b(\\c)n(harge)d(densit)n(y")i(form)g(\(14\))g(rather)g (than)g(the)h(\\curren)n(t)e(densit)n(y")h(form)g(\(12\))450 4800 y(but)28 b(this)g(p)r(oin)n(t)g(deserv)n(es)e(a)h(more)g(detailed) h(analysis.)1839 4980 y(4)p eop %%Page: 5 5 5 4 bop 600 863 a Fs(W)-7 b(e)33 b(did)g(not)g(consider)f(an)n(y)g (further)g(simpli\014cations)h(of)f(expression)g(\(14\))g(whic)n(h)450 963 y(are)25 b(v)n(ery)h(common)g(in)g(the)h(literature.)36 b(In)26 b(fact,)h(b)n(y)g(assuming)e(that)i Fv(k)s(r)e Ft(\034)e Fs(1)k(and)f(that)450 1062 y Fv(k)g Ft(\030)d Fv(!)i Ft(!)e Fs(0,)k(the)f(second)g(term)h(of)f(\(14\))h(is)f(usually) g(neglected)g(and,)h(in)g(the)g(\014rst)f(term,)450 1162 y(the)c(limit,)815 1129 y Fk(@)p 813 1143 72 4 v 813 1191 a(@)t(r)895 1162 y Fs([)p Fv(r)16 b(j)1005 1174 y Fu(2)1043 1162 y Fs(\()p Fv(k)s(r)r Fs(\)])24 b Ft(\030)f Fs(3)14 b Fv(j)1417 1174 y Fu(2)1453 1162 y Fs(\()p Fv(k)s(r)r Fs(\),)24 b(whic)n(h)d(is)h(v)-5 b(alid)21 b(for)g(v)n(ery)f(small)h Fv(k)s(r)r Fs(,)i(is)e(considered.)450 1277 y(With)28 b(suc)n(h)g(simpli\014cations,)f(one)g(\014nds)h(that)f Ft(M)2050 1247 y Fk(E)s Fu(2)2162 1277 y Ft(!)d(M)2369 1247 y Fk(E)s Fu(2)2465 1222 y Ff(00)2533 1277 y Fs(=)e(3)p Ft(M)2762 1247 y Fk(C)t Fu(2)2850 1277 y Fv(=)p Fs(\(2)2966 1208 y Ft(p)p 3035 1208 42 4 v 69 x Fs(2)o(\))28 b(and)450 1377 y(the)g(follo)n(wing)f(ratios)1058 1555 y Fv(E)5 b Fs(2)p 1046 1592 132 4 v 1046 1668 a Fv(M)k Fs(1)1210 1611 y(=)1308 1555 y(1)p 1308 1592 42 4 v 1308 1668 a(3)1378 1555 y Ft(M)1478 1525 y Fk(E)s Fu(2)1567 1555 y Fs(\()p Fv(k)s Fs(\))p 1369 1592 317 4 v 1369 1668 a Ft(M)1469 1644 y Fk(M)d Fu(1)1576 1668 y Fs(\()p Fv(k)s Fs(\))1710 1611 y Fv(;)1935 1555 y(C)g Fs(2)p 1923 1592 132 4 v 1923 1668 a Fv(M)j Fs(1)2087 1611 y(=)2240 1555 y(1)p 2185 1592 153 4 v 2185 1678 a(2)2227 1609 y Ft(p)p 2295 1609 42 4 v 2295 1678 a Fs(2)2366 1555 y Ft(M)2466 1525 y Fk(C)t Fu(2)2554 1555 y Fs(\()p Fv(k)s Fs(\))p 2357 1592 317 4 v 2357 1668 a Ft(M)2457 1644 y Fk(M)d Fu(1)2563 1668 y Fs(\()p Fv(k)s Fs(\))3122 1611 y(\(15\))450 1839 y(b)r(ecome)26 b(equal.)36 b(The)26 b(pro)r(cedure)e(to)i(relate)f(the) i(electric)e(quadrup)r(ole)g(momen)n(t)h(to)g(the)450 1939 y(quadrup)r(ole)21 b(coulom)n(b)f(momen)n(t)i(is)f(kno)n(wn)g(as)g (the)h(Siegert's)e(theorem)2713 1909 y Fu(9)2750 1939 y Fs(.)35 b(According)20 b(to)450 2039 y(our)26 b(results,)g(in)h(b)r (oth)h(the)f(LSM)g(and)f(CDM,)h(the)h(t)n(w)n(o)e(ratios)f(\(15\))h (di\013er)h(b)n(y)g(t)n(ypically)450 2138 y(25\045)32 b(at)h(the)g(photon)g(p)r(oin)n(t.)53 b(F)-7 b(or)33 b Ft(\000)p Fv(K)1739 2108 y Fu(2)1807 2138 y Fv(>)e Fs(0,)j(the)g(use)e(of)h(the)h(Siegert's)e(theorem)g(is)450 2238 y(de\014nitely)c(not)g(justi\014ed.)450 2466 y Fw(3)95 b(The)32 b(mo)s(dels)450 2649 y Fs(The)c(Lagrangian)d(of)i(the)h(mo)r (dels)g(can)f(b)r(e)h(written)g(as)2217 2619 y Fu(1)492 2867 y Ft(L)23 b Fs(=)f(i)7 b(\026)-48 b Fv(q)s(\015)771 2833 y Fk(\026)815 2867 y Fv(@)859 2879 y Fk(\026)903 2867 y Fv(q)21 b Fs(+)1054 2811 y(1)p 1054 2848 42 4 v 1054 2924 a(2)1105 2867 y Fv(@)1149 2879 y Fk(\026)1198 2867 y Fs(^)-46 b Fv(\033)17 b(@)1307 2833 y Fk(\026)1356 2867 y Fs(^)-47 b Fv(\033)21 b Fs(+)1512 2811 y(1)p 1512 2848 V 1512 2924 a(2)1563 2867 y Fv(@)1607 2879 y Fk(\026)1656 2844 y Fs(^)1650 2867 y Fv(~)-40 b(\031)21 b Ft(\001)d Fv(@)1810 2833 y Fk(\026)1859 2844 y Fs(^)1852 2867 y Fv(~)-40 b(\031)21 b Ft(\000)d(U)8 b Fs(\()2101 2844 y(^)2095 2867 y Fv(~)-40 b(\031)2148 2807 y Fu(2)2203 2867 y Fs(+)22 b(^)-47 b Fv(\033)2335 2833 y Fu(2)2373 2867 y Fs(\))18 b(+)g Ft(L)2563 2879 y Fk(q)r Fl(\000)p Fu(meson)2849 2867 y Fs(+)g Ft(L)2989 2879 y Fk(\037)3058 2867 y Fv(;)41 b Fs(\(16\))450 3115 y(where)25 b Ft(U)8 b Fs(\()784 3092 y(^)778 3115 y Fv(~)-40 b(\031)831 3054 y Fu(2)882 3115 y Fs(+)19 b(^)-47 b Fv(\033)1011 3085 y Fu(2)1049 3115 y Fs(\))26 b(is)f(the)h(mexican-hat)f(p)r(oten)n (tial;)h(the)g(quark)f(meson)g(in)n(teraction)f(is)450 3215 y(giv)n(en)j(b)n(y)1265 3333 y Ft(L)1322 3345 y Fk(q)r Fl(\000)p Fu(meson)1614 3333 y Fs(=)1735 3277 y Fv(g)p 1711 3314 91 4 v 1711 3390 a(\037)1763 3366 y Fk(p)1832 3333 y Fs(\026)-48 b Fv(q)16 b Fs(\()t(^)-46 b Fv(\033)23 b Fs(+)18 b(i)n Fv(~)-40 b(\034)28 b Ft(\001)2197 3309 y Fs(^)2190 3333 y Fv(~)-40 b(\031)t(\015)2286 3345 y Fu(5)2323 3333 y Fs(\))14 b Fv(q)26 b(:)667 b Fs(\(17\))450 3528 y(In)30 b(the)g(LSM,)g Fv(p)c Fs(=)h(0,)j(i.e.)43 b(there)30 b(is)f(no)h Fv(\037)f Fs(\014eld;)j(in)e(the)g(CDM)g(w)n(e)f (tak)n(e)g Fv(p)e Fs(=)f(1)j(\(other)450 3628 y(c)n(hoices)g(for)h Fv(p)g Fs(are)g(also)f(p)r(ossible\).)45 b(The)31 b(last)f(term)g(in)h (\(16\))f({)g(absen)n(t)g(in)g(the)h(LSM)f({)450 3728 y(con)n(tains)d(the)h(kinetic)f(and)h(the)g(p)r(oten)n(tial)f(piece)h (for)f(the)h Fv(\037)p Fs(-\014eld:)2599 3698 y Fk(a)1358 3946 y Ft(L)1415 3958 y Fk(\037)1484 3946 y Fs(=)1581 3890 y(1)p 1581 3927 42 4 v 1581 4003 a(2)1633 3946 y Fv(@)1677 3958 y Fk(\026)1731 3946 y Fs(^)-51 b Fv(\037)13 b(@)1836 3912 y Fk(\026)1890 3946 y Fs(^)-52 b Fv(\037)19 b Ft(\000)2044 3890 y Fs(1)p 2044 3927 V 2044 4003 a(2)2095 3946 y Fv(M)2185 3912 y Fu(2)2176 3967 y Fk(\037)2246 3946 y Fs(^)-52 b Fv(\037)2288 3912 y Fu(2)2339 3946 y Fv(;)760 b Fs(\(18\))450 4153 y(where)26 b Fv(M)770 4165 y Fk(\037)841 4153 y Fs(is)g(the)h Fv(\037)f Fs(mass.)36 b(The)26 b(free)g(parameters)e(of)j(the)f(mo)r(dels)g(ha)n(v)n(e)f(b)r (een)i(c)n(hosen)450 4253 y(b)n(y)21 b(requiring)f(that)h(the)h (calculated)f(static)g(prop)r(erties)f(of)h(the)h(n)n(ucleon)e(agree)g (b)r(est)i(with)450 4353 y(the)28 b(exp)r(erimen)n(tal)e(v)-5 b(alues.)37 b(In)27 b(the)g(LSM)h(mo)r(del)f(w)n(e)g(use)g Fv(g)f Fs(=)c(5)p Fv(:)p Fs(0.)36 b(In)28 b(the)f(considered)450 4452 y(v)n(ersion)34 b(of)i(the)h(CDM)f(the)h(results)e(are)g (predominan)n(tly)g(sensitiv)n(e)g(to)h(the)h(quan)n(tit)n(y)450 4552 y Fv(G)f Fs(=)651 4485 y Fi(p)p 735 4485 169 4 v 735 4552 a Fv(g)s(M)859 4564 y Fk(\037)903 4552 y Fs(;)j(w)n(e)c(tak)n (e)g Fv(G)h Fs(=)f(0)p Fv(:)p Fs(2)g(GeV)g(\(and)h Fv(g)i Fs(=)e(0)p Fv(:)p Fs(03)e(GeV\).)i(W)-7 b(e)35 b(ha)n(v)n(e)f(c)n(hec)n (k)n(ed)450 4651 y(that)k(our)f(results)g(dep)r(end)h(v)n(ery)f(w)n (eakly)g(on)g(the)h(v)-5 b(ariations)36 b(of)i(these)g(parameters.)p 450 4723 1128 4 v 539 4777 a Fe(a)577 4800 y Fp(W)-6 b(e)24 b(consider)g(just)g(a)g(mass)e(term)h(for)g(the)h Fo(\037)f Fp(p)r(oten)n(tial.)1839 4980 y Fs(5)p eop %%Page: 6 6 6 5 bop 450 863 a Fs(The)29 b(mo)r(dels)g(con)n(tain)g(three)g(other)g (parameters,)f(the)h(c)n(hiral)g(meson)f(masses)h(and)g(the)450 963 y(pion)f(deca)n(y)f(constan)n(t,)g(whic)n(h)h(are)f(\014xed)h(to)f (the)i(follo)n(wing)d(v)-5 b(alues:)37 b Fv(m)2750 975 y Fk(\031)2819 963 y Fs(=)23 b(0)p Fv(:)p Fs(14)k(GeV,)450 1062 y Fv(m)523 1074 y Fk(\033)591 1062 y Fs(=)22 b(1)p Fv(:)p Fs(2)27 b(GeV,)h Fv(f)1068 1074 y Fk(\031)1136 1062 y Fs(=)23 b(0)p Fv(:)p Fs(093)i(GeV.)600 1162 y(W)-7 b(e)40 b(used)f(coheren)n(t)g(states)g(to)g(describ)r(e)g(the)h(pion)f (and)h(the)f Fv(\033)s Fs(-meson)g(clouds,)450 1262 y(assuming)h(the)g (hedgehog)g(ansatz)f(for)h(the)h(pion)f(\014eld)h(and)f(for)g(the)h (three)f(v)-5 b(alence)450 1361 y(quarks)29 b(\(all)i(in)g(the)g(lo)n (w)n(est)e(s-state\).)46 b(The)30 b(resulting)g(state,)i Ft(j)p Fv(H)7 b Ft(i)p Fs(,)31 b(is)g(not)f(an)h(angular)450 1461 y(momen)n(tum)25 b(and)f(isospin)g(eigenstate)g(and)h(the)g(P)n (eierls-Y)-7 b(o)r(ccoz)22 b(pro)5 b(jection)23 b(is)i(used)f(to)450 1560 y(obtain)j(states)g(whic)n(h)h(are)f(eigenstates)f(of)i(these)f (op)r(erators:)2425 1530 y Fu(10)1003 1737 y Ft(j)p Fv(J)k Fs(=)22 b Fv(T)12 b Fs(;)i Fv(M)1369 1749 y Fk(T)1420 1737 y Fv(;)g(M)1538 1749 y Fk(J)1584 1737 y Ft(i)23 b Fs(=)g Ft(N)j Fs(\()p Ft(\000)p Fs(1\))1992 1702 y Fk(J)5 b Fu(+)p Fk(M)2148 1710 y Fd(T)2198 1737 y Fv(P)2263 1702 y Fk(J)2251 1757 y(M)2314 1765 y Fd(J)2355 1757 y Fk(;)p Fl(\000)p Fk(M)2490 1765 y Fd(T)2540 1737 y Ft(j)p Fv(H)i Ft(i)23 b Fv(;)405 b Fs(\(19\))450 1913 y(where)27 b Ft(N)40 b Fs(is)28 b(a)f(normalization)f(factor)h(and)995 2111 y Fv(P)1060 2077 y Fk(J)1048 2132 y(M)1111 2140 y Fd(J)1152 2132 y Fk(;)p Fl(\000)p Fk(M)1287 2140 y Fd(T)1360 2111 y Fs(=)1457 2055 y(2)p Fv(J)f Fs(+)18 b(1)p 1457 2092 239 4 v 1512 2168 a(8)p Fv(\031)1604 2144 y Fu(2)1720 1998 y Fi(Z)1816 2111 y Fs(d)1863 2074 y Fu(3)1900 2111 y Fs(\012)c Ft(D)2040 2077 y Fk(J)2038 2132 y(M)2101 2140 y Fd(J)2141 2132 y Fk(;)p Fl(\000)p Fk(M)2276 2140 y Fd(T)2326 2111 y Fs(\(\012\))2450 2077 y Fl(\003)2510 2090 y Fi(b)2503 2111 y Fs(R\(\012\))g Fv(:)397 b Fs(\(20\))450 2325 y(In)25 b(the)h(CDM)g(the)f Fv(\037)g Fs(\014eld,)h(whic)n(h)f(due)h(to)f(its)g(scalar-isoscalar)c (nature)k(is)g(not)g(a\013ected)450 2425 y(b)n(y)i(pro)5 b(jection,)26 b(is)h(included)g(in)g(the)h(same)e(w)n(a)n(y)g(as)g(the) h Fv(\033)s Fs(,)h(i.e.)37 b(as)26 b(a)g(coheren)n(t)g(state)h(of)450 2525 y(neutral)j(s-w)n(a)n(v)n(e)f(quan)n(ta.)45 b(Finally)-7 b(,)31 b(the)g(meson)g(and)f(quark)g(pro\014les)f(are)h(determined)450 2624 y(selfconsisten)n(tly)36 b(b)n(y)h(minimizing)h(the)f(exp)r (ectation)g(v)-5 b(alue)37 b(of)g(the)h(Hamiltonians)e(of)450 2724 y(the)31 b(mo)r(dels)g(in)g(the)g(pro)5 b(jected)31 b(states)f(\(19\).)46 b(This)31 b(is)g(kno)n(wn)f(as)g(the)i(v)-5 b(ariation)29 b(after)450 2823 y(pro)5 b(jection)31 b(tec)n(hnique.)49 b(Altogether)31 b(there)g(are)g(4)g(radial)f(pro\014les)h(\(5,)i(in)e (the)h(case)f(of)450 2923 y(CDM\))26 b(to)g(b)r(e)g(determined)f (separately)f(for)h(the)h(n)n(ucleon)f(and)g(for)g(the)h(\001.)37 b(T)-7 b(ec)n(hnically)450 3023 y(these)36 b(radial)e(functions)j(are)d (solutions)h(of)h(a)g(system)f(of)h(4)f(\(or)g(5\))h(coupled)g(in)n (tegro-)450 3122 y(di\013eren)n(tial)31 b(equations.)46 b(W)-7 b(e)32 b(should)e(men)n(tion)h(that)h(the)f(ansatz)f(\(19\))h (do)r(esn't)g(allo)n(w)450 3222 y(the)39 b(\001)g(to)g(b)r(ecome)g (asymptotically)f(a)g Fv(N)9 b(\031)42 b Fs(system,)g(a)c(dra)n(wbac)n (k)f(whic)n(h)i(deserv)n(es)450 3322 y(future)28 b(in)n(v)n (estigation.)600 3421 y(It)e(is)g(kno)n(wn)f(that)i(in)f(these)g(mo)r (dels)g(the)g(\001-N)g(mass)g(splitting)g(is)g(to)r(o)f(small)h(\(t)n (yp-)450 3521 y(ically)35 b(160)f(MeV)i(in)g(the)g(LSM)g(and)g(only)f (60)g(MeV)h(in)g(the)g(CDM\).)g(W)-7 b(e)36 b(cured)g(this)450 3620 y(de\014ciency)f(b)n(y)f(considering)g(di\013eren)n(t)h(masses)e (for)i(the)g Fc(b)l(ar)l(e)g Fs(n)n(ucleon)f(and)h(\001)g(in)g(or-)450 3720 y(der)g(to)g(repro)r(duce)f(the)i(ph)n(ysical)f(\001-N)g (splitting.)61 b(The)35 b(relev)-5 b(an)n(t)35 b(parameter)e(is)j(the) 450 3820 y(di\013erence)28 b(b)r(et)n(w)n(een)f(the)h(t)n(w)n(o)f(bare) g(masses.)600 3919 y(F)-7 b(or)32 b(the)h(mo)r(dels)f(describ)r(ed)g(b) n(y)h(\(16-18\))e(the)h(electromagnetic)g(curren)n(t)f(densit)n(y)450 4019 y(con)n(tains)c(a)g(quark)f(and)i(a)f(pion)g(part)g(and)h(reads:) 1124 4174 y Fi(b)1106 4195 y Fv(J)1160 4161 y Fk(\026)1152 4216 y(e:m:)1286 4195 y Fs(\()p Fh(r)s Fs(\))23 b(=)29 b(\026)-48 b Fv(q)17 b(\015)1610 4161 y Fk(\026)1668 4128 y Fi(\000)1716 4163 y Fu(1)p 1716 4177 34 4 v 1716 4224 a(6)1777 4195 y Fs(+)1870 4163 y Fu(1)p 1870 4177 V 1870 4224 a(2)1913 4195 y Fv(\034)1949 4207 y Fu(3)1987 4128 y Fi(\001)2039 4195 y Fv(q)k Fs(+)d(\()2216 4172 y(^)2210 4195 y Fv(~)-40 b(\031)22 b Ft(\002)c Fv(@)2413 4161 y Fk(\026)2462 4172 y Fs(^)2455 4195 y Fv(~)-40 b(\031)t Fs(\))2540 4207 y Fu(3)2591 4195 y Fv(:)508 b Fs(\(21\))450 4419 y Fw(4)95 b(Results)30 b(and)j(discussion)450 4601 y Fs(Ha)n(ving)40 b(determined)h(the)g(states)f(\(19\))g(for)h (the)g(n)n(ucleon)f(\()p Fv(J)53 b Fs(=)45 b Fv(T)56 b Fs(=)2864 4568 y Fu(1)p 2864 4582 V 2864 4629 a(2)2907 4601 y Fs(\))41 b(and)g(the)450 4700 y(\001)e(\()p Fv(J)50 b Fs(=)41 b Fv(T)52 b Fs(=)1010 4668 y Fu(3)p 1010 4682 V 1010 4729 a(2)1053 4700 y Fs(\))39 b(and)f(using)h(the)g(explicit)g (form)f(of)h(the)g(op)r(erator)e(for)h(\(21\))g(it)h(is)450 4800 y(straigh)n(tforw)n(ard)33 b(to)j(ev)-5 b(aluate)36 b(the)h(matrix)f(elemen)n(ts)g(\(9\),)i(\(11\))e(and)g(\(14\).)63 b(T)-7 b(aking)1839 4980 y(6)p eop %%Page: 7 7 7 6 bop 450 913 a Fp(T)-6 b(able)21 b(1:)30 b(Ratio)21 b(E2/M1)f(\(v)l(alues)i(giv)n(en)f(in)f(\045\))h(at)g(the)g(photon)h(p) r(oin)n(t)f(in)g(v)l(arious)f(relativistic)g(mo)r(dels.)450 992 y(The)j(sym)n(b)r(ol)f(*)h(preceding)g(the)h(mo)r(del)e (denomination)h(means)f(that)i(the)f(v)l(alue)h(w)n(as)e(computed)i (using)615 1071 y(the)h(expression)f(for)f(C2/M1,)g(i.e.)31 b(b)n(y)24 b(assuming)e(the)j(v)l(alidit)n(y)f(of)f(the)i(Siegert's)e (theorem.)p 463 1163 2794 4 v 513 1232 a Fs(SU\(6\))100 b(MIT)107 b(*CBM)e(*Skyrme)124 b(*NJL)144 b(LSM)125 b(CDM)222 b(Exp)p 463 1266 V 600 1359 a(0)248 b(0)161 b Ft(\000)p Fs(0)p Fv(:)p Fs(92)1307 1329 y Fu(2)1479 1359 y Ft(\000)p Fs(5)p Fv(:)p Fs(0)1651 1329 y Fu(11)1856 1359 y Ft(\000)p Fs(2)p Fv(:)p Fs(28)2070 1329 y Fu(5)2205 1359 y Ft(\000)p Fs(1)p Fv(:)p Fs(87)97 b Ft(\000)p Fs(1)p Fv(:)p Fs(83)h Ft(\000)p Fs(1.5)p Ft(\006)p Fs(0.4)3172 1329 y Fu(8)1114 1459 y Ft(\000)p Fs(1)p Fv(:)p Fs(8)1286 1428 y Fu(3)1495 1459 y Ft(\000)p Fs(2)p Fv(:)p Fs(6)1667 1428 y Fu(4)2828 1459 y Ft(\000)p Fs(2.5)p Ft(\006)p Fs(0.2)3172 1428 y Fu(7)p 463 1492 V 450 1765 a Fs(adv)-5 b(an)n(tage)25 b(of)i(the)g(hedgehog)f(symmetry)h(the)g(ev)-5 b(aluation)26 b(of)h(suc)n(h)f(transition)h(matrix)450 1865 y(elemen)n(ts)k(b)r(et)n (w)n(een)h(the)g(pro)5 b(jected)30 b(states)h(represen)n(ting)f(the)i (n)n(ucleon)f(and)h(the)f(\001)h(is)450 1964 y(considerably)c (simpli\014ed.)41 b(Ho)n(w)n(ev)n(er,)28 b(the)h(\014nal)g(expressions) f(are)g(long)g(and)h(therefore)450 2064 y(they)f(are)e(omitted)i(here.) 600 2167 y(F)-7 b(or)24 b(the)h(c)n(hoice)f(of)g(parameters)f(men)n (tioned)h(b)r(efore)h(w)n(e)f(obtained)2739 2137 y Fu(12)2809 2167 y Fs(,)h(for)f Fv(K)3058 2137 y Fu(2)3118 2167 y Fs(=)e(0,)450 2267 y Fv(E)5 b Fs(2)p Fv(=)-5 b(M)9 b Fs(1)31 b(=)h Ft(\000)p Fs(1)p Fv(:)p Fs(87\045)f(\(in)j(the)f(LSM\))h (and)f Fv(E)5 b Fs(2)p Fv(=)-5 b(M)9 b Fs(1)30 b(=)i Ft(\000)p Fs(1)p Fv(:)p Fs(83\045)g(\(in)h(the)h(CDM\).)g(F)-7 b(or)450 2366 y(the)24 b(second)e(ratio)g(in)i(\(15\))e(w)n(e)h (obtained:)35 b Fv(C)6 b Fs(2)p Fv(=)-5 b(M)9 b Fs(1)21 b(=)i Ft(\000)p Fs(2)p Fv(:)p Fs(33\045)f(\(LSM\))i(and)f Fv(C)6 b Fs(2)p Fv(=)-5 b(M)9 b Fs(1)21 b(=)450 2466 y Ft(\000)p Fs(2)p Fv(:)p Fs(39\045)g(\(CDM\).)i(W)-7 b(e)23 b(stress)f(that)g(there)h(is)f(a)g(non-negligible)f (di\013erence)h(b)r(et)n(w)n(een)h(the)450 2566 y(t)n(w)n(o)h(ratios)f (\(15\),)i(whose)f(origin)f(lies)i(in)g(the)g(fact)f(that)h(the)g (condition)g Fv(k)2759 2578 y Fk(W)2834 2566 y Fv(r)h Ft(\034)d Fs(1)i(is)f(not)450 2665 y(satis\014ed)j(\(but)i(the)f (second)f(term)g(in)h(\(14\))f(is)h(indeed)g(v)n(ery)e(small\).)600 2769 y(F)-7 b(or)32 b(the)g(sak)n(e)f(of)i(comparison)d(of)i(v)-5 b(arious)31 b(mo)r(dels,)j(in)e(T)-7 b(able)32 b(1)g(w)n(e)g(presen)n (t)g(the)450 2868 y(predictions)27 b(for)h Fv(E)5 b Fs(2)p Fv(=)-5 b(M)9 b Fs(1,)26 b(at)i(the)g(photon)g(p)r(oin)n(t.)38 b(In)28 b(mo)r(dels)g(without)g(a)f(pion)h(cloud,)450 2968 y(as)36 b(the)g(non-relativistic)f(\(or)h(ev)n(en)g(relativized\)) f(quark)h(mo)r(dels,)i(t)n(ypical)e(v)-5 b(alues)36 b(for)450 3068 y(this)i(ratio)f(are,)i(in)f(absolute)f(v)-5 b(alue,)40 b(b)r(elo)n(w)d(1\045,)j(unless)d(an)h(unrealistically)e(strong)450 3167 y(admixture)g(of)g(d-state)f(quarks)g(is)h(in)n(tro)r(duced)g (\(the)g(quadrup)r(ole)g(photon)f(do)r(es)h(not)450 3267 y(couple)24 b(to)g(the)h(spherical)e(quarks\).)34 b(W)-7 b(e)25 b(ha)n(v)n(e)e(computed)h(p)r(erturbativ)n(ely)g(admixtures)450 3367 y(of)f(the)g(lo)n(w)n(est)e(d-sate)h(to)g(the)h(n)n(ucleon)g(and)f (the)h(\001,)h(in)f(the)g(CDM,)g(and)f(concluded)h(that)450 3466 y(the)f(con)n(tribution)g(of)g(suc)n(h)g(excitations)f(to)h(the)h (total)f(amplitudes)g(remains)f(b)r(elo)n(w)h(10\045)450 3566 y(of)31 b(the)g(total)f(v)-5 b(alue)31 b(at)f(the)h(photon)g(p)r (oin)n(t.)46 b(W)-7 b(e)31 b(w)n(arn)f(that)g(for)h(the)g(mo)r(dels)f (mark)n(ed)450 3665 y(with)e(*)f(in)h(T)-7 b(able)27 b(1)h(the)g(form)n(ula)e(for)h Fv(C)6 b Fs(2)p Fv(=)-5 b(M)9 b Fs(1)27 b(w)n(as)f(used)i(to)f(compute)h Fv(E)5 b Fs(2)p Fv(=)-5 b(M)9 b Fs(1.)600 3769 y(In)28 b(Figure)f(1)g(w)n(e)g (sho)n(w)g(the)g(prediction)h(of)f(the)h(t)n(w)n(o)f(mo)r(dels)g(for)g (the)h(helicit)n(y)g(am-)450 3868 y(plitudes)f(as)e(a)h(function)h(of)f Ft(\000)p Fv(K)1490 3838 y Fu(2)1526 3868 y Fs(.)37 b(Although)26 b(the)h(ratios)e Fv(E)5 b Fs(2)p Fv(=)-5 b(M)9 b Fs(1)24 b(and)i Fv(C)6 b Fs(2)p Fv(=)-5 b(M)9 b Fs(1)26 b(come)450 3968 y(out)f(essen)n(tially)f(the)h(same)f(in)i(b)r(oth)f(mo)r(dels,)g (the)h(amplitudes)f(are)f(b)r(etter)h(repro)r(duced)450 4068 y(in)37 b(the)g(LSM)g(than)f(in)h(the)g(CDM.)g(Relativ)n(ely)f (large)f(v)-5 b(alues)37 b(of)f(the)h Fv(C)6 b Fs(2)37 b(amplitude)450 4167 y(ma)n(y)29 b(b)r(e)h(an)f(imp)r(ortan)n(t)g (indication)g(of)g(the)h(presence)f(of)g(a)g(strong)f(pion)i(cloud)f (in)h(the)450 4267 y(in)n(terior)c(of)i(the)g(n)n(ucleon)f(and)g(the)h (\001.)450 4512 y Fw(Ac)m(kno)m(wledgmen)m(ts)450 4700 y Fs(This)k(w)n(ork)f(w)n(as)g(supp)r(orted)h(in)h(part)f(b)n(y)f(the)i (Ministry)f(of)g(Science)g(of)h(Slo)n(v)n(enia,)f(the)450 4800 y(Calouste)21 b(Gulb)r(enkian)h(F)-7 b(oundation)22 b(\(Lisb)r(on\))g(and)g(the)g(Europ)r(ean)f(Commission)g(con-)1839 4980 y(7)p eop %%Page: 8 8 8 7 bop 685 1814 4 987 v 685 1814 40 4 v 475 1839 a Fs({300)p 1799 1814 V 685 1650 V 475 1675 a({250)p 1799 1650 V 685 1486 V 475 1511 a({200)p 1799 1486 V 685 1320 V 475 1345 a({150)p 1799 1320 V 685 1156 V 475 1181 a({100)p 1799 1156 V 685 992 V 517 1017 a({50)p 1799 992 V 685 828 V 600 853 a(0)p 1799 828 V 685 1814 4 40 v 665 1929 a(0)p 685 868 V 915 1814 V 155 w(0.2)p 915 868 V 1147 1814 V 125 w(0.4)p 1147 868 V 1377 1814 V 123 w(0.6)p 1377 868 V 1609 1814 V 125 w(0.8)p 1609 868 V 1839 1814 V 156 w(1)p 1839 868 V 685 1814 1154 4 v 1839 1814 4 987 v 685 828 1154 4 v 1041 2058 a Ft(\000)p Fv(K)1183 2028 y Fu(2)1234 2058 y Fs([GeV)1421 2022 y Fu(2)1458 2058 y Fs(])1319 1652 y Fv(A)1381 1667 y Fu(1)p Fk(=)p Fu(2)1486 1652 y Fv(;)32 b(A)1603 1667 y Fu(3)p Fk(=)p Fu(2)p 685 1814 4 987 v 685 1178 4 4 v 687 1180 1 5 v 688 1182 V 688 1183 V 689 1184 V 690 1185 V 691 1186 V 692 1187 V 693 1188 V 694 1189 V 695 1190 V 696 1191 V 697 1192 V 698 1193 V 699 1194 V 700 1196 V 701 1197 V 702 1198 V 703 1199 V 704 1200 V 705 1201 V 706 1202 V 684 1178 4 3 v 708 1202 V 709 1204 5 1 v 710 1205 V 712 1206 V 713 1207 V 714 1208 V 715 1209 V 716 1210 V 717 1211 V 718 1212 V 719 1213 V 720 1214 V 721 1215 V 722 1216 V 724 1217 V 725 1218 V 726 1219 V 727 1220 V 709 1204 3 4 v 729 1224 V 731 1224 7 1 v 733 1225 V 735 1226 V 737 1227 V 738 1228 V 740 1229 V 742 1230 V 744 1231 V 745 1232 V 747 1233 V 749 1234 V 731 1224 4 4 v 752 1238 V 755 1238 7 1 v 757 1239 V 759 1240 V 761 1241 V 763 1242 V 765 1243 V 767 1244 V 769 1245 V 770 1246 V 755 1238 4 4 v 774 1250 V 777 1250 9 1 v 780 1251 V 782 1252 V 785 1253 V 788 1254 V 790 1255 V 793 1256 V 777 1250 5 4 v 797 1260 V 801 1260 10 1 v 804 1261 V 807 1262 V 810 1263 V 813 1264 V 801 1260 5 4 v 818 1268 V 823 1270 21 4 v 823 1268 11 4 v 837 1272 V 847 1274 20 4 v 847 1272 10 4 v 860 1276 V 869 1277 25 4 v 869 1276 12 4 v 881 1278 V 893 1279 23 4 v 893 1278 12 4 v 904 1280 V 939 1279 23 4 v 939 1280 12 4 v 950 1278 V 961 1277 25 4 v 961 1278 12 4 v 973 1276 V 985 1275 25 4 v 985 1276 12 4 v 997 1274 V 1009 1272 20 4 v 1009 1274 10 4 v 1022 1270 V 1031 1269 25 4 v 1031 1270 12 4 v 1043 1268 V 1055 1265 14 1 v 1060 1264 V 1064 1263 V 1055 1268 7 4 v 1071 1262 V 1077 1260 21 4 v 1077 1262 11 4 v 1091 1258 V 1101 1256 20 4 v 1101 1258 10 4 v 1114 1254 V 1123 1251 15 1 v 1128 1250 V 1133 1249 V 1123 1254 8 4 v 1140 1248 V 1147 1245 14 1 v 1152 1244 V 1156 1243 V 1147 1248 7 4 v 1163 1242 V 1169 1239 15 1 v 1174 1238 V 1179 1237 V 1169 1242 8 4 v 1186 1236 V 1193 1233 14 1 v 1198 1232 V 1202 1231 V 1193 1236 7 4 v 1209 1230 V 1215 1227 15 1 v 1220 1226 V 1225 1225 V 1215 1230 8 4 v 1232 1224 V 1239 1221 15 1 v 1244 1220 V 1249 1219 V 1239 1224 8 4 v 1256 1218 V 1263 1215 14 1 v 1268 1214 V 1272 1213 V 1263 1218 7 4 v 1279 1212 V 1285 1209 15 1 v 1290 1208 V 1295 1207 V 1285 1212 8 4 v 1302 1206 V 1309 1203 10 1 v 1312 1202 V 1315 1201 V 1318 1200 V 1321 1199 V 1309 1206 5 4 v 1326 1198 V 1331 1195 15 1 v 1336 1194 V 1341 1193 V 1331 1198 8 4 v 1348 1192 V 1355 1189 14 1 v 1360 1188 V 1364 1187 V 1355 1192 7 4 v 1371 1186 V 1377 1183 11 1 v 1381 1182 V 1384 1181 V 1387 1180 V 1391 1179 V 1377 1186 6 4 v 1396 1178 V 1401 1175 14 1 v 1406 1174 V 1410 1173 V 1401 1178 7 4 v 1417 1172 V 1423 1169 11 1 v 1427 1168 V 1430 1167 V 1433 1166 V 1437 1165 V 1423 1172 6 4 v 1442 1164 V 1447 1161 14 1 v 1452 1160 V 1456 1159 V 1447 1164 7 4 v 1463 1158 V 1469 1155 15 1 v 1474 1154 V 1479 1153 V 1469 1158 8 4 v 1486 1152 V 1493 1149 10 1 v 1496 1148 V 1499 1147 V 1502 1146 V 1505 1145 V 1493 1152 5 4 v 1510 1144 V 1515 1141 15 1 v 1520 1140 V 1525 1139 V 1515 1144 8 4 v 1532 1138 V 1539 1135 11 1 v 1543 1134 V 1546 1133 V 1549 1132 V 1553 1131 V 1539 1138 6 4 v 1558 1130 V 1563 1127 14 1 v 1568 1126 V 1572 1125 V 1563 1130 7 4 v 1579 1124 V 1585 1121 15 1 v 1590 1120 V 1595 1119 V 1585 1124 8 4 v 1602 1118 V 1609 1115 10 1 v 1612 1114 V 1615 1113 V 1618 1112 V 1621 1111 V 1609 1118 5 4 v 1626 1110 V 1631 1107 15 1 v 1636 1106 V 1641 1105 V 1631 1110 8 4 v 1648 1104 V 1655 1101 14 1 v 1660 1100 V 1664 1099 V 1655 1104 7 4 v 1671 1098 V 1677 1095 15 1 v 1682 1094 V 1687 1093 V 1677 1098 8 4 v 1694 1092 V 1701 1089 14 1 v 1706 1088 V 1710 1087 V 1701 1092 7 4 v 1717 1086 V 1723 1083 15 1 v 1728 1082 V 1733 1081 V 1723 1086 8 4 v 1740 1080 V 1747 1077 14 1 v 1752 1076 V 1756 1075 V 1747 1080 7 4 v 1763 1074 V 1769 1071 15 1 v 1774 1070 V 1779 1069 V 1769 1074 8 4 v 1786 1068 V 1793 1065 14 1 v 1798 1064 V 1802 1063 V 1793 1068 7 4 v 1809 1062 V 1815 1059 15 1 v 1820 1058 V 1825 1057 V 1815 1062 8 4 v 1832 1056 V 915 1280 25 4 v 685 1060 4 4 v 685 1060 V 723 1077 V 764 1085 V 805 1087 V 846 1084 V 887 1077 V 927 1067 V 968 1056 V 1007 1044 V 1047 1031 V 1086 1019 V 1125 1005 V 1165 991 V 1204 978 V 1243 964 V 1283 952 V 1323 940 V 1362 928 V 1402 917 V 1443 907 V 1483 896 V 1523 886 V 1564 880 V 1604 871 V 1645 863 V 1686 858 V 1727 851 V 1768 846 V 1810 842 V 1839 840 V 685 1485 7 7 v 688 1495 2 14 v 689 1497 V 690 1499 V 691 1501 V 692 1502 V 693 1504 V 694 1506 V 695 1508 V 696 1510 V 697 1511 V 698 1513 V 699 1515 V 700 1517 V 701 1519 V 702 1520 V 704 1522 V 705 1524 V 682 1489 7 7 v 706 1524 V 712 1535 2 12 v 713 1537 V 714 1538 V 715 1540 V 716 1541 V 717 1543 V 718 1544 V 719 1546 V 720 1547 V 721 1549 V 722 1550 V 723 1552 V 724 1553 V 725 1555 V 726 1556 V 706 1530 7 6 v 728 1556 V 731 1560 9 2 v 732 1561 V 733 1562 V 734 1563 V 735 1564 V 736 1565 V 737 1566 V 738 1567 V 739 1568 V 740 1569 V 741 1570 V 742 1571 V 743 1572 V 744 1573 V 745 1574 V 746 1575 V 747 1576 V 731 1559 5 7 v 751 1583 V 755 1584 10 2 v 757 1585 V 758 1586 V 759 1587 V 760 1588 V 761 1589 V 763 1590 V 764 1591 V 765 1592 V 766 1593 V 768 1594 V 755 1583 5 7 v 772 1601 V 777 1602 15 2 v 780 1603 V 782 1604 V 784 1605 V 786 1606 V 777 1601 8 7 v 794 1613 V 801 1614 17 2 v 804 1615 V 807 1616 V 801 1613 9 7 v 815 1623 V 823 1626 25 7 v 823 1623 12 7 v 835 1629 V 847 1631 23 7 v 847 1629 12 7 v 858 1633 V 893 1632 23 7 v 893 1633 12 7 v 904 1631 V 915 1630 25 7 v 915 1631 12 7 v 927 1629 V 939 1627 23 7 v 939 1629 12 7 v 950 1625 V 961 1622 25 7 v 961 1625 12 7 v 973 1619 V 985 1616 25 7 v 985 1619 12 7 v 997 1613 V 1009 1609 20 7 v 1009 1613 10 7 v 1021 1605 V 1031 1601 22 7 v 1031 1605 11 7 v 1045 1597 V 1055 1591 17 2 v 1058 1590 V 1061 1589 V 1055 1597 9 7 v 1069 1587 V 1077 1583 22 7 v 1077 1587 11 7 v 1091 1579 V 1101 1573 14 2 v 1103 1572 V 1105 1571 V 1107 1570 V 1110 1569 V 1101 1579 7 7 v 1116 1567 V 1123 1561 18 2 v 1127 1560 V 1130 1559 V 1123 1567 9 7 v 1139 1557 V 1147 1551 17 2 v 1150 1550 V 1153 1549 V 1147 1557 9 7 v 1161 1547 V 1169 1541 15 2 v 1172 1540 V 1174 1539 V 1176 1538 V 1178 1537 V 1169 1547 8 7 v 1186 1535 V 1193 1529 14 2 v 1195 1528 V 1197 1527 V 1199 1526 V 1202 1525 V 1193 1535 7 7 v 1208 1523 V 1215 1517 18 2 v 1219 1516 V 1222 1515 V 1215 1523 9 7 v 1231 1513 V 1239 1507 15 2 v 1242 1506 V 1244 1505 V 1246 1504 V 1248 1503 V 1239 1513 8 7 v 1256 1501 V 1263 1495 14 2 v 1265 1494 V 1267 1493 V 1269 1492 V 1272 1491 V 1263 1501 7 7 v 1278 1489 V 1285 1483 15 2 v 1288 1482 V 1290 1481 V 1292 1480 V 1294 1479 V 1285 1489 8 7 v 1302 1477 V 1309 1471 14 2 v 1311 1470 V 1313 1469 V 1315 1468 V 1318 1467 V 1309 1477 7 7 v 1324 1465 V 1331 1459 15 2 v 1334 1458 V 1336 1457 V 1338 1456 V 1340 1455 V 1331 1465 8 7 v 1348 1453 V 1355 1447 14 2 v 1357 1446 V 1359 1445 V 1361 1444 V 1364 1443 V 1355 1453 7 7 v 1370 1441 V 1377 1435 15 2 v 1380 1434 V 1382 1433 V 1384 1432 V 1386 1431 V 1377 1441 8 7 v 1394 1429 V 1401 1423 14 2 v 1403 1422 V 1405 1421 V 1408 1420 V 1410 1419 V 1401 1429 7 7 v 1416 1417 V 1423 1411 15 2 v 1426 1410 V 1428 1409 V 1430 1408 V 1432 1407 V 1423 1417 8 7 v 1440 1405 V 1447 1399 14 2 v 1449 1398 V 1451 1397 V 1454 1396 V 1456 1395 V 1447 1405 7 7 v 1462 1393 V 1469 1387 15 2 v 1472 1386 V 1474 1385 V 1476 1384 V 1478 1383 V 1469 1393 8 7 v 1486 1381 V 1493 1375 14 2 v 1495 1374 V 1497 1373 V 1500 1372 V 1502 1371 V 1493 1381 7 7 v 1508 1369 V 1515 1363 15 2 v 1518 1362 V 1520 1361 V 1522 1360 V 1524 1359 V 1515 1369 8 7 v 1532 1357 V 1539 1351 18 2 v 1543 1350 V 1546 1349 V 1539 1357 9 7 v 1555 1347 V 1563 1341 14 2 v 1565 1340 V 1567 1339 V 1570 1338 V 1572 1337 V 1563 1347 7 7 v 1578 1335 V 1585 1329 15 2 v 1588 1328 V 1590 1327 V 1592 1326 V 1594 1325 V 1585 1335 8 7 v 1602 1323 V 1609 1317 17 2 v 1612 1316 V 1615 1315 V 1609 1323 9 7 v 1623 1313 V 1631 1307 15 2 v 1634 1306 V 1636 1305 V 1638 1304 V 1640 1303 V 1631 1313 8 7 v 1648 1301 V 1655 1295 17 2 v 1658 1294 V 1661 1293 V 1655 1301 9 7 v 1669 1291 V 1677 1285 18 2 v 1681 1284 V 1684 1283 V 1677 1291 9 7 v 1693 1281 V 1701 1275 17 2 v 1704 1274 V 1707 1273 V 1701 1281 9 7 v 1715 1271 V 1723 1265 15 2 v 1726 1264 V 1728 1263 V 1730 1262 V 1732 1261 V 1723 1271 8 7 v 1740 1259 V 1747 1253 17 2 v 1750 1252 V 1753 1251 V 1747 1259 9 7 v 1761 1249 V 1769 1243 18 2 v 1773 1242 V 1776 1241 V 1769 1249 9 7 v 1785 1239 V 1793 1233 17 2 v 1796 1232 V 1799 1231 V 1793 1239 9 7 v 1807 1229 V 1815 1225 22 7 v 1815 1229 11 7 v 1829 1221 V 869 1633 25 7 v 685 1262 9 9 v 685 1262 V 719 1286 V 759 1298 V 800 1296 V 841 1288 V 879 1272 V 917 1255 V 954 1236 V 990 1216 V 1025 1194 V 1061 1173 V 1096 1151 V 1132 1129 V 1167 1108 V 1203 1087 V 1239 1066 V 1276 1047 V 1313 1028 V 1350 1009 V 1387 991 V 1425 974 V 1463 958 V 1502 943 V 1541 930 V 1580 916 V 1620 904 V 1660 893 V 1700 882 V 1741 874 V 1781 866 V 1822 859 V 1839 856 V 685 1290 a Fb(s)1031 1278 y(s)1205 1234 y(s)1377 1204 y(s)1563 1132 y(s)1355 1182 y(s)1805 1094 y(s)1355 1218 y(s)1805 1110 y(s)p 685 1314 4 47 v 665 1314 40 4 v 665 1268 V 1031 1284 4 10 v 1011 1284 40 4 v 1011 1274 V 1205 1242 4 10 v 1185 1242 40 4 v 1185 1232 V 1377 1212 4 14 v 1357 1212 40 4 v 1357 1198 V 1563 1140 4 14 v 1543 1140 40 4 v 1543 1126 V 1355 1202 4 34 v 1335 1202 40 4 v 1335 1168 V 1805 1110 4 27 v 1785 1110 40 4 v 1785 1084 V 1355 1232 4 25 v 1335 1232 40 4 v 1335 1208 V 1805 1126 4 29 v 1785 1126 40 4 v 1785 1098 V 729 1328 a(s)821 1300 y(s)955 1302 y(s)1045 1322 y(s)-163 b(s)1031 1276 y(s)1147 1254 y(s)1227 1208 y(s)1239 1204 y(s)1263 1210 y(s)1377 1158 y(s)1413 1148 y(s)1573 1102 y(s)1585 1106 y(s)1597 1098 y(s)1805 1066 y(s)-23 b(s)1089 1266 y(s)1839 1060 y(s)789 1334 y(s)939 1308 y(s)1215 1216 y(s)1585 1110 y(s)739 1402 y(s)835 1352 y(s)969 1262 y(s)1147 1276 y(s)p 729 1358 4 56 v 709 1358 40 4 v 709 1302 V 821 1336 4 70 v 801 1336 40 4 v 801 1266 V 955 1334 4 61 v 935 1334 40 4 v 935 1274 V 1045 1374 4 100 v 1025 1374 40 4 v 1025 1274 V 915 1340 4 32 v 895 1340 40 4 v 895 1308 V 1031 1294 4 32 v 1011 1294 40 4 v 1011 1262 V 1147 1270 4 30 v 1127 1270 40 4 v 1127 1240 V 1227 1220 4 23 v 1207 1220 40 4 v 1207 1198 V 1239 1218 4 25 v 1219 1218 40 4 v 1219 1194 V 1263 1224 4 25 v 1243 1224 40 4 v 1243 1200 V 1377 1168 4 16 v 1357 1168 40 4 v 1357 1152 V 1413 1158 4 16 v 1393 1158 40 4 v 1393 1142 V 1573 1114 4 20 v 1553 1114 40 4 v 1553 1094 V 1585 1116 4 18 v 1565 1116 40 4 v 1565 1098 V 1597 1108 4 18 v 1577 1108 40 4 v 1577 1090 V 1805 1080 4 25 v 1785 1080 40 4 v 1785 1056 V 1815 1080 4 25 v 1795 1080 40 4 v 1795 1056 V 1089 1286 4 36 v 1069 1286 40 4 v 1069 1250 V 1839 1074 4 23 v 1819 1074 40 4 v 1819 1052 V 789 1342 4 12 v 769 1342 40 4 v 769 1330 V 939 1316 4 12 v 919 1316 40 4 v 919 1304 V 1215 1222 4 9 v 1195 1222 40 4 v 1195 1214 V 1585 1118 4 10 v 1565 1118 40 4 v 1565 1108 V 739 1440 4 74 v 719 1440 40 4 v 719 1366 V 835 1392 4 76 v 815 1392 40 4 v 815 1316 V 969 1278 4 30 v 949 1278 40 4 v 949 1248 V 1147 1296 4 36 v 1127 1296 40 4 v 1127 1260 V 685 1674 a(c)1031 1556 y(c)1205 1482 y(c)1377 1430 y(c)1563 1306 y(c)1355 1392 y(c)1805 1240 y(c)1355 1452 y(c)1805 1266 y(c)p 685 1712 4 72 v 665 1712 40 4 v 665 1640 V 1031 1568 4 18 v 1011 1568 40 4 v 1011 1550 V 1205 1494 4 18 v 1185 1494 40 4 v 1185 1476 V 1377 1444 4 25 v 1357 1444 40 4 v 1357 1420 V 1563 1318 4 23 v 1543 1318 40 4 v 1543 1296 V 1355 1420 4 50 v 1335 1420 40 4 v 1335 1370 V 1805 1260 4 38 v 1785 1260 40 4 v 1785 1222 V 1355 1474 4 38 v 1335 1474 40 4 v 1335 1436 V 1805 1290 4 45 v 1785 1290 40 4 v 1785 1246 V 729 1694 a(c)821 1646 y(c)955 1648 y(c)1045 1688 y(c)915 1686 y(c)1031 1602 y(c)1147 1566 y(c)1227 1486 y(c)1239 1480 y(c)1263 1494 y(c)1377 1398 y(c)1413 1384 y(c)1573 1302 y(c)1585 1308 y(c)1597 1292 y(c)1805 1242 y(c)g(c)1089 1588 y(c)1839 1232 y(c)789 1706 y(c)939 1660 y(c)1215 1500 y(c)1585 1318 y(c)969 1580 y(c)835 1736 y(c)1147 1606 y(c)p 729 1744 4 96 v 709 1744 40 4 v 709 1648 V 821 1708 4 120 v 801 1708 40 4 v 801 1588 V 955 1702 4 103 v 935 1702 40 4 v 935 1600 V 1045 1776 4 172 v 1025 1776 40 4 v 1025 1604 V 915 1716 4 58 v 895 1716 40 4 v 895 1658 V 1031 1634 4 58 v 1011 1634 40 4 v 1011 1576 V 1147 1594 4 52 v 1127 1594 40 4 v 1127 1542 V 1227 1508 4 40 v 1207 1508 40 4 v 1207 1468 V 1239 1502 4 40 v 1219 1502 40 4 v 1219 1462 V 1263 1516 4 43 v 1243 1516 40 4 v 1243 1474 V 1377 1414 4 29 v 1357 1414 40 4 v 1357 1386 V 1413 1402 4 32 v 1393 1402 40 4 v 1393 1370 V 1573 1322 4 34 v 1553 1322 40 4 v 1553 1288 V 1585 1326 4 34 v 1565 1326 40 4 v 1565 1292 V 1597 1312 4 34 v 1577 1312 40 4 v 1577 1278 V 1805 1262 4 36 v 1785 1262 40 4 v 1785 1226 V 1815 1262 4 36 v 1795 1262 40 4 v 1795 1226 V 1089 1620 4 61 v 1069 1620 40 4 v 1069 1560 V 1839 1254 4 38 v 1819 1254 40 4 v 1819 1216 V 789 1720 4 25 v 769 1720 40 4 v 769 1696 V 939 1672 4 20 v 919 1672 40 4 v 919 1652 V 1215 1508 4 12 v 1195 1508 40 4 v 1195 1496 V 1585 1328 4 16 v 1565 1328 40 4 v 1565 1312 V 739 1814 4 56 v 719 1814 40 4 v 719 1758 V 969 1608 4 52 v 949 1608 40 4 v 949 1556 V 835 1802 4 129 v 815 1802 40 4 v 815 1674 V 1147 1640 4 65 v 1127 1640 40 4 v 1127 1576 V 2095 1814 4 987 v 2095 1814 40 4 v 1926 1839 a Fs({20)p 3209 1814 V 2095 1568 V 1926 1593 a({15)p 3209 1568 V 2095 1320 V 1926 1345 a({10)p 3209 1320 V 2095 1074 V 1968 1099 a({5)p 3209 1074 V 2095 828 V 2009 853 a(0)p 3209 828 V 2095 1814 4 40 v 2074 1929 a(0)p 2095 868 V 2325 1814 V 156 w(0.2)p 2325 868 V 2557 1814 V 125 w(0.4)p 2557 868 V 2787 1814 V 123 w(0.6)p 2787 868 V 3019 1814 V 125 w(0.8)p 3019 868 V 3249 1814 V 155 w(1)p 3249 868 V 2095 1814 1154 4 v 3249 1814 4 987 v 2095 828 1154 4 v 2451 2058 a Ft(\000)p Fv(K)2593 2028 y Fu(2)2643 2058 y Fs([GeV)2831 2022 y Fu(2)2868 2058 y Fs(])2985 1652 y Fv(S)3036 1667 y Fu(1)p Fk(=)p Fu(2)p 2095 1814 4 987 v 2095 1088 4 4 v 2096 1093 1 7 v 2097 1095 V 2098 1097 V 2099 1098 V 2100 1100 V 2101 1102 V 2102 1104 V 2103 1106 V 2104 1108 V 2105 1110 V 2106 1111 V 2107 1113 V 2108 1115 V 2109 1117 V 2110 1119 V 2111 1121 V 2112 1123 V 2113 1124 V 2114 1126 V 2115 1128 V 2116 1130 V 2093 1089 4 4 v 2117 1130 V 2120 1137 1 8 v 2121 1139 V 2122 1141 V 2123 1143 V 2124 1145 V 2125 1147 V 2126 1149 V 2127 1151 V 2128 1153 V 2129 1155 V 2130 1157 V 2131 1158 V 2132 1160 V 2133 1162 V 2134 1164 V 2135 1166 V 2136 1168 V 2137 1170 V 2138 1172 V 2117 1134 4 4 v 2139 1172 V 2142 1178 1 6 v 2143 1179 V 2144 1181 V 2145 1182 V 2146 1184 V 2147 1185 V 2148 1187 V 2149 1188 V 2150 1190 V 2151 1191 V 2152 1193 V 2153 1194 V 2154 1196 V 2155 1197 V 2156 1199 V 2157 1200 V 2158 1202 V 2159 1204 V 2160 1205 V 2161 1207 V 2162 1208 V 2139 1175 4 3 v 2163 1208 V 2166 1214 1 6 v 2167 1215 V 2168 1217 V 2169 1218 V 2170 1220 V 2171 1221 V 2172 1222 V 2173 1224 V 2174 1225 V 2175 1227 V 2176 1228 V 2177 1230 V 2178 1231 V 2179 1233 V 2180 1234 V 2181 1236 V 2182 1237 V 2183 1239 V 2184 1240 V 2163 1211 4 3 v 2185 1240 V 2188 1245 1 5 v 2189 1246 V 2190 1247 V 2191 1249 V 2192 1250 V 2193 1251 V 2194 1252 V 2195 1254 V 2196 1255 V 2197 1256 V 2198 1257 V 2199 1259 V 2200 1260 V 2201 1261 V 2202 1262 V 2203 1264 V 2204 1265 V 2205 1266 V 2206 1267 V 2207 1269 V 2208 1270 V 2185 1243 4 3 v 2209 1270 V 2212 1275 1 5 v 2213 1276 V 2214 1277 V 2215 1278 V 2216 1279 V 2217 1281 V 2218 1282 V 2219 1283 V 2220 1284 V 2221 1285 V 2222 1287 V 2223 1288 V 2224 1289 V 2225 1290 V 2226 1291 V 2227 1292 V 2228 1294 V 2229 1295 V 2230 1296 V 2209 1272 4 3 v 2231 1296 V 2234 1300 1 5 v 2235 1302 V 2236 1303 V 2237 1304 V 2238 1305 V 2239 1306 V 2240 1307 V 2241 1308 V 2242 1309 V 2243 1310 V 2244 1311 V 2245 1312 V 2246 1313 V 2247 1314 V 2248 1316 V 2249 1317 V 2250 1318 V 2251 1319 V 2252 1320 V 2253 1321 V 2254 1322 V 2231 1298 4 3 v 2255 1322 V 2257 1324 5 1 v 2258 1325 V 2259 1326 V 2260 1327 V 2261 1328 V 2262 1329 V 2263 1330 V 2265 1331 V 2266 1332 V 2267 1333 V 2268 1334 V 2269 1335 V 2270 1336 V 2271 1337 V 2272 1338 V 2273 1339 V 2274 1340 V 2257 1324 3 4 v 2277 1344 V 2279 1344 5 1 v 2280 1345 V 2281 1346 V 2283 1347 V 2284 1348 V 2285 1349 V 2286 1350 V 2287 1351 V 2289 1352 V 2290 1353 V 2291 1354 V 2292 1355 V 2293 1356 V 2295 1357 V 2296 1358 V 2297 1359 V 2298 1360 V 2279 1344 3 4 v 2301 1364 V 2303 1364 5 1 v 2304 1365 V 2305 1366 V 2307 1367 V 2308 1368 V 2309 1369 V 2310 1370 V 2311 1371 V 2313 1372 V 2314 1373 V 2315 1374 V 2316 1375 V 2318 1376 V 2319 1377 V 2320 1378 V 2303 1364 3 4 v 2322 1382 V 2325 1382 7 1 v 2327 1383 V 2328 1384 V 2330 1385 V 2332 1386 V 2334 1387 V 2335 1388 V 2337 1389 V 2339 1390 V 2341 1391 V 2342 1392 V 2325 1382 4 4 v 2346 1396 V 2349 1396 7 1 v 2351 1397 V 2352 1398 V 2354 1399 V 2355 1400 V 2357 1401 V 2359 1402 V 2360 1403 V 2362 1404 V 2363 1405 V 2365 1406 V 2349 1396 4 4 v 2368 1410 V 2371 1410 8 1 v 2373 1411 V 2375 1412 V 2377 1413 V 2379 1414 V 2381 1415 V 2383 1416 V 2385 1417 V 2387 1418 V 2371 1410 4 4 v 2391 1422 V 2395 1422 9 1 v 2397 1423 V 2400 1424 V 2403 1425 V 2405 1426 V 2408 1427 V 2410 1428 V 2395 1422 5 4 v 2415 1432 V 2419 1432 10 1 v 2422 1433 V 2425 1434 V 2428 1435 V 2431 1436 V 2419 1432 5 4 v 2436 1440 V 2441 1440 11 1 v 2444 1441 V 2448 1442 V 2451 1443 V 2454 1444 V 2441 1440 6 4 v 2460 1448 V 2465 1448 14 1 v 2469 1449 V 2474 1450 V 2465 1448 7 4 v 2480 1454 V 2487 1454 15 1 v 2492 1455 V 2497 1456 V 2487 1454 8 4 v 2504 1460 V 2511 1462 20 4 v 2511 1460 10 4 v 2523 1464 V 2533 1466 21 4 v 2533 1464 11 4 v 2547 1468 V 2557 1469 23 4 v 2557 1468 12 4 v 2568 1470 V 2603 1471 23 4 v 2603 1470 12 4 v 2614 1472 V 2579 1470 25 4 v 2649 1471 V 2649 1472 12 4 v 2661 1470 V 2673 1469 23 4 v 2673 1470 12 4 v 2684 1468 V 2695 1467 25 4 v 2695 1468 12 4 v 2707 1466 V 2719 1465 23 4 v 2719 1466 12 4 v 2730 1464 V 2741 1462 21 4 v 2741 1464 11 4 v 2755 1460 V 2765 1458 20 4 v 2765 1460 10 4 v 2777 1456 V 2787 1454 21 4 v 2787 1456 11 4 v 2801 1452 V 2811 1450 20 4 v 2811 1452 10 4 v 2823 1448 V 2833 1445 15 1 v 2838 1444 V 2843 1443 V 2833 1448 8 4 v 2850 1442 V 2857 1440 20 4 v 2857 1442 10 4 v 2869 1438 V 2879 1435 15 1 v 2884 1434 V 2889 1433 V 2879 1438 8 4 v 2896 1432 V 2903 1429 14 1 v 2907 1428 V 2912 1427 V 2903 1432 7 4 v 2918 1426 V 2925 1423 15 1 v 2930 1422 V 2935 1421 V 2925 1426 8 4 v 2942 1420 V 2949 1417 15 1 v 2954 1416 V 2959 1415 V 2949 1420 8 4 v 2966 1414 V 2973 1411 10 1 v 2976 1410 V 2979 1409 V 2982 1408 V 2985 1407 V 2973 1414 5 4 v 2990 1406 V 2995 1403 15 1 v 3000 1402 V 3005 1401 V 2995 1406 8 4 v 3012 1400 V 3019 1397 10 1 v 3022 1396 V 3025 1395 V 3028 1394 V 3031 1393 V 3019 1400 5 4 v 3036 1392 V 3041 1389 15 1 v 3046 1388 V 3051 1387 V 3041 1392 8 4 v 3058 1386 V 3065 1383 10 1 v 3068 1382 V 3071 1381 V 3074 1380 V 3077 1379 V 3065 1386 5 4 v 3082 1378 V 3087 1375 11 1 v 3090 1374 V 3094 1373 V 3097 1372 V 3100 1371 V 3087 1378 6 4 v 3106 1370 V 3111 1367 14 1 v 3115 1366 V 3120 1365 V 3111 1370 7 4 v 3126 1364 V 3133 1361 11 1 v 3136 1360 V 3140 1359 V 3143 1358 V 3146 1357 V 3133 1364 6 4 v 3152 1356 V 3157 1353 10 1 v 3160 1352 V 3163 1351 V 3166 1350 V 3169 1349 V 3157 1356 5 4 v 3174 1348 V 3179 1345 11 1 v 3182 1344 V 3186 1343 V 3189 1342 V 3192 1341 V 3179 1348 6 4 v 3198 1340 V 3203 1337 10 1 v 3206 1336 V 3209 1335 V 3212 1334 V 3215 1333 V 3203 1340 5 4 v 3220 1332 V 3225 1329 11 1 v 3228 1328 V 3232 1327 V 3235 1326 V 3238 1325 V 3225 1332 6 4 v 3244 1324 V 2625 1472 25 4 v 2095 1008 4 4 v 2095 1008 V 2122 1039 V 2154 1066 V 2187 1090 V 2225 1108 V 2265 1120 V 2305 1126 V 2347 1128 V 2388 1126 V 2429 1120 V 2470 1112 V 2510 1102 V 2550 1091 V 2590 1079 V 2629 1066 V 2669 1053 V 2708 1039 V 2747 1026 V 2786 1012 V 2826 998 V 2865 985 V 2905 973 V 2944 961 V 2984 949 V 3024 938 V 3064 926 V 3104 917 V 3145 908 V 3185 899 V 3226 891 V 3249 886 V 2767 1408 a Fb(s)3217 1384 y(s)2441 1338 y(s)2441 1644 y(s)2615 1694 y(s)2787 1516 y(s)2973 1082 y(s)p 2767 1538 4 256 v 2747 1538 40 4 v 2747 1282 V 3217 1504 4 238 v 3197 1504 40 4 v 3197 1266 V 2441 1602 4 523 v 2421 1602 40 4 v 2421 1080 V 2441 1814 4 434 v 2421 1814 40 4 v 2421 1380 V 2615 1814 4 290 v 2595 1814 40 4 v 2595 1524 V 2787 1760 4 485 v 2767 1760 40 4 v 2767 1276 V 2973 1256 4 345 v 2953 1256 40 4 v 2953 912 V 450 2175 a Fp(Figure)20 b(1:)29 b(Helicit)n(y)20 b(amplitudes)f Fo(A)1420 2189 y Fn(1)p Fe(=)p Fn(2)1517 2175 y Fp(,)h Fo(A)1610 2189 y Fn(3)p Fe(=)p Fn(2)1726 2175 y Fp(and)h Fo(S)1903 2189 y Fn(1)p Fe(=)p Fn(2)2019 2175 y Fp(for)e(electro)r (excitation)k(of)d(the)g(\001)g(in)f(the)i(LSM)450 2273 y(\(solid)f(lines\))g(and)g(CDM)g(\(dotted)i(lines\))e(in)f(units)i(of) e(10)1977 2249 y Fa(\000)p Fn(3)2060 2273 y Fp(GeV)2200 2248 y Fa(\000)p Fn(1)p Fe(=)p Fn(2)2345 2273 y Fp(.)30 b(The)20 b(upp)r(er)g(curv)n(e)h(within)f(eac)n(h)450 2352 y(mo)r(del)26 b(and)i(full)e(\(exp)r(erimen)n(tal\))i(circles)e (corresp)r(ond)i(to)g Fo(A)2132 2366 y Fn(1)p Fe(=)p Fn(2)2228 2352 y Fp(,)g(the)g(lo)n(w)n(er)f(one)h(and)f(empt)n(y)g (circles)1732 2431 y(to)d Fo(A)1871 2445 y Fn(3)p Fe(=)p Fn(2)1968 2431 y Fp(.)450 2683 y Fs(tract)h(ERB-CIP)-7 b(A-CT-92-2287.)31 b(MF)25 b(is)g(grateful)g(to)g(GT)-7 b(AE)25 b(\(Lisb)r(on\))h(for)e(pro)n(viding)450 2783 y(a)32 b(tra)n(v)n(el)f(gran)n(t.)51 b(He)32 b(w)n(ould)g(also)g(lik)n (e)g(to)g(thank)h(the)g(w)n(arm)e(hospitalit)n(y)h(he)h(enjo)n(y)n(ed) 450 2882 y(during)27 b(the)h(w)n(orkshop.)450 3107 y Fw(References)551 3289 y Fs(1.)42 b(M.)27 b(C.)h(Birse,)f Fc(Pr)l(o)l(g.)39 b(Part.)g(Nucl.)f(Phys.)h Fw(25)p Fs(,)27 b(1)g(\(1990\).)551 3389 y(2.)42 b(G.)27 b(K\177)-42 b(alb)r(ermann)27 b(and)g(J.)h(M.)g(Eisen)n(b)r(erg,)e Fc(Phys.)39 b(R)l(ev.)f Fs(D)28 b Fw(28)p Fs(,)f(71)g(\(1983\).)551 3488 y(3.)42 b(K.)27 b(Berm)n(uth)g(et)h(al.,)f Fc(Phys.)40 b(R)l(ev.)d Fs(D)28 b Fw(37)p Fs(,)f(89)g(\(1988\).)551 3588 y(4.)42 b(A.)28 b(Wirzba)f(and)g(W.)h(W)-7 b(eise,)28 b Fc(Phys.)40 b(L)l(ett.)c Fs(B)28 b Fw(188)p Fs(,)f(6)g(\(1987\).)551 3687 y(5.)42 b(T.)27 b(W)-7 b(atab)r(e,)28 b(Chr.)37 b(Christo)n(v,)26 b(K.)h(Go)r(ek)n(e,)g Fc(Phys.)40 b(L)l(ett.)d Fs(B)27 b Fw(349)p Fs(,)g(197)f(\(1995\).)551 3787 y(6.)42 b(S.)24 b(Capstic)n(k)g(and)h(G.)g(Karl,)f Fc(Phys.)38 b(R)l(ev.)e Fs(D)26 b Fw(41)p Fs(,)e(2767)f(\(1990\);)i(S.)f(Capstic)n (k)g(and)658 3887 y(B.)j(D.)h(Keister,)f Fc(Phys.)40 b(R)l(ev.)d Fs(D)28 b Fw(51)p Fs(,)f(3598)f(\(1995\).)551 3986 y(7.)42 b(R.)27 b(Bec)n(k,)g(T)-7 b(alk)27 b(presen)n(ted)g(at)h (the)g(Bary)n(ons'95)c(Conference,)j(San)n(ta)g(F)-7 b(e,)28 b(1995.)551 4086 y(8.)42 b(P)n(article)26 b(Data)h(Group,)g Fc(Phys.)40 b(R)l(ev.)d Fs(D)28 b Fw(50)p Fs(,)f(1712)f(\(1994\).)551 4186 y(9.)42 b(U.)20 b(M.)g(Eisen)n(b)r(erg)e(and)h(W.)h(Greiner,)h Fc(Nucle)l(ar)h(The)l(ory)p Fs(,)h(V)-7 b(ol.)34 b(2)20 b(\(North-Holland,)658 4285 y(Amsterdam,)27 b(1976\).)510 4385 y(10.)41 b(B.)34 b(Golli)g(and)g(M.)g(Rosina,)h Fc(Phys.)57 b(L)l(ett.)f Fs(B)34 b Fw(165)p Fs(,)i(347)c(\(1985\);)k (M.)f(C.)f(Birse,)658 4484 y Fc(Phys.)39 b(R)l(ev.)e Fs(D)28 b Fw(33)p Fs(,)g(1934)d(\(1986\).)510 4584 y(11.)41 b(G.)27 b(S.)h(Adkins,)g(C.)g(R.)g(Nappi,)g(E.)f(Witten,)i Fc(Nucl.)38 b(Phys.)g Fs(B)28 b Fw(228)p Fs(,)f(552)f(\(1983\).)510 4684 y(12.)41 b(M.)27 b(Fiolhais,)g(B.)h(Golli)f(and)h(S.)1694 4663 y(\024)1692 4684 y(Sirca,)f Fc(Phys.)39 b(L)l(ett.)e Fs(B)27 b Fw(373)p Fs(,)g(229)f(\(1996\).)1839 4980 y(8)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF