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b(large)d(susceptibilit)m(y)h(of)g(the)h(in)m(tracell)328 3077 y(O{O)39 b(c)m(harge)h(transfer)g(to)f(the)h(o)m(xygen)g(energy)h (splitting)c(has)j(b)s(een)g(asso)s(ciated)g(in)328 3234 y(previous)g(w)m(ork)h([12)o(,)f(13)o(,)g(14])f(with)g(the)i(F)-8 b(ermi)37 b(energy)k(b)s(eing)e(on)g(the)h(logarithmic)328 3390 y(v)-5 b(an)26 b(Ho)m(v)m(e)g(\(vH\))h(singularit)m(y)c(of)j(the)g (square)g(lattice.)40 b(Of)25 b(course,)k(this)c(can)h(also)e(a\013ect) 328 3547 y(the)33 b(sup)s(erconducting)g(transition)e(itself.)474 3703 y(In)49 b(order)g(to)f(test)h(the)g(v)-5 b(alidit)m(y)46 b(of)i(this)g(p)s(oin)m(t)g(of)f(view,)53 b(it)48 b(is)g(imp)s(ortan)m (t)e(to)328 3860 y(calculate)37 b(the)h(e\013ects)h(of)e(an)h(imp)s (ending)d(AF)j(transition)e(on)i(the)g(electrons)g(at)f(the)328 4016 y(vH)i(singularit)m(y)-8 b(,)37 b(what)i(has)f(not)g(b)s(een)h (singled)e(out)h(for)g(atten)m(tion)f(b)s(efore.)61 b(As)38 b(the)328 4173 y(AF)32 b(mo)s(de)f(softens,)j(a)e(pseudogap)h(app)s (ears)g(in)e(the)i(densit)m(y)g(of)f(states)h(at)f(the)h(F)-8 b(ermi)328 4329 y(energy)g(,)40 b(as)e(a)f(precursor)i(of)e(the)h(AF)g (gap.)58 b(The)39 b(question)f(is,)g(will)e(it)g(suppress)k(the)328 4486 y(vH)33 b(singularit)m(y?)474 4642 y(Note)f(that)g(the)h(usual)e (argumen)m(t)h(in)f(fa)m(v)m(or)h(of)g(a)g(pseudogap)h(do)s(es)f(not)g (apply)-8 b(.)43 b(It)328 4799 y(is)26 b(based)h(on)f(the)g(adiabatic)e (appro)m(ximation,)h(in)h(e\013ect)h(claiming)22 b(that)k(fast)g (electrons)328 4955 y(see)j(little)c(di\013erence)j(b)s(et)m(w)m(een)h (an)f(almost)d(static)i(AF)h(mo)s(de)e(and)i(a)f(truly)g(static)g(one.) 1922 5214 y(2)p eop %%Page: 3 3 3 2 bop 328 631 a Fm(Ho)m(w)m(ev)m(er,)34 b(electrons)d(at)g(the)h(vH)g (p)s(oin)m(t)e(are)h(not)g(fast;)h(their)f(v)m(elo)s(cit)m(y)g(is)f (zero,)i(and)g(it)328 787 y(is)k(kno)m(wn)h(from)e(a)h(previous)g (one-dimensional)d(electron-phonon)j(calculation)e(that)328 944 y(the)42 b(pseudogap)h(app)s(ears)f(only)g(for)f(electron)h(v)m (elo)s(cities)f(larger)f(than)i(the)g(phonon)328 1100 y(v)m(elo)s(cit)m(y)32 b(at)h(the)g(instabilit)m(y)d([15)o(].)474 1257 y(W)-8 b(e)35 b(shall)e(sho)m(w)j(in)e(this)g(w)m(ork)h(that)g(an) f(analogous)g(situation)f(exists)i(in)f(t)m(w)m(o)h(di-)328 1413 y(mensions.)43 b(F)-8 b(or)30 b(quasi-static)f(electrons)i(at)g (the)g(vH)g(singularit)m(y)-8 b(,)30 b(there)h(is)f(no)h(damp-)328 1570 y(ing)39 b(and)h(no)f(energy)i(shift,)h Fh(i.e.)64 b Fm(the)40 b(singularit)m(y)f(is)g(not)h(suppressed)i(b)m(y)f(the)f (soft-)328 1726 y(ening)c(of)f(the)h(AF)g(mo)s(de,)g(assuming)g(that)g (the)g(latter)f(is)g(c)m(haracterized)i(b)m(y)g(a)f(\014nite)328 1883 y(frequency)-8 b(.)66 b(The)41 b(strength)f(of)f(the)h(singularit) m(y)e(do)s(es,)k(of)d(course,)j(decrease)g(as)d(the)328 2039 y(transition)31 b(is)h(approac)m(hed.)328 2427 y Fl(2)161 b(Mo)t(del)54 b(and)g(Approac)l(h)328 2682 y Fm(The)32 b(essen)m(tial)e(ph)m(ysical)h(assumption)f(of)h(the)g (presen)m(t)h(w)m(ork)g(is)e(that)h(the)g(AF)f(\015uctu-)328 2839 y(ations)e(in)g(the)h(paramagnetic)e(phase)j(ha)m(v)m(e)g(a)f(gap) f(whic)m(h)h(go)s(es)g(to)f(zero)i(only)e(at)g(their)328 2995 y(condensation)37 b(temp)s(erature.)57 b(This)37 b(gap)g(has)g(b)s(een)h(observ)m(ed)h(in)d(neutron)i(scatter-)328 3152 y(ing)h([3,)g(4])h(and)g(is)f(mo)s(deled)g(b)m(y)i(the)f (parameter)47 b(~)-57 b Fj(!)43 b Fm(in)c(the)h(disp)s(ersion)g(in)m (tro)s(duced)328 3308 y(b)s(elo)m(w.)48 b(W)-8 b(e)34 b(do)g(not)g(exp)s(ect)i(our)d(result)i(to)e(dep)s(end)i(critically)d (on)i(other)g(asp)s(ects)h(of)328 3465 y(the)e(phenomenology)-8 b(.)474 3621 y(As)35 b(for)f(the)h(electrons,)h(the)f(only)f (assumptions)g(w)m(e)i(use)g(are)e(that)g(the)h(vH)h(p)s(oin)m(t)328 3778 y(is)27 b(a)g(saddle-p)s(oin)m(t)f(of)h(the)h(disp)s(ersion,)g (and)g(that)f(hopping)g(is)g(isotropic)f(in)g(the)i(plane,)328 3934 y(c)m(haracterized)33 b(b)m(y)h(some)e(scale)h Fj(t)p Fm(.)474 4091 y(The)44 b(ob)5 b(jection)44 b(can)f(b)s(e)h(made)e(that) h(the)h(pro)s(cedure)g(w)m(e)h(use)f(is)f(not)g(self-con-)328 4247 y(sisten)m(t:)55 b(it)37 b(is)h(assumed)h(that)f(there)h(is)e(a)h (gap)g(in)f(the)i(spin)f(excitations,)h(while)e(the)328 4404 y(electron)h(sp)s(ectrum)g(used)g(has)g(no)g(gap.)58 b(Ho)m(w)m(ev)m(er,)42 b(w)m(e)c(in)m(v)m(estigate)g(precisely)g(that) 328 4560 y(one-lo)s(op)23 b(diagram)f(whic)m(h)j(one)f(exp)s(ects)j(to) d(b)s(e)g(dominan)m(t)f(\(see,)k Fh(e.g.)p Fm(,)f(Ref.)40 b([5]\))25 b(in)e(the)328 4717 y(op)s(ening)k(of)h(a)g(gap)g(in)f(the)i (electron)f(sp)s(ectrum.)42 b(Indeed,)31 b(w)m(e)e(obtain)e(a)h(gap)g (at)g(nearly)328 4873 y(the)45 b(whole)f(F)-8 b(ermi)42 b(surface,)49 b(but)44 b(w)m(e)i(sho)m(w)f(that)f(it)g(is)g(absen)m(t)h (in)f(the)g(immediate)1922 5214 y(3)p eop %%Page: 4 4 4 3 bop 328 631 a Fm(vicinit)m(y)31 b(of)h(the)h(v.H.)g(p)s(oin)m(ts.) 43 b(The)34 b(absence)g(of)e(a)g(gap)g(in)g(this)g(region)f(is)h(due)h (to)f(the)328 787 y(electrons)h(b)s(eing)f(slo)m(w)g(there,)i(and)e(is) h(the)g(main)d(result)j(of)f(our)g(w)m(ork.)474 944 y(Another)j(t)m(yp) s(e)g(of)e(consistency)j(ob)5 b(jection)34 b(w)m(ould)g(b)s(e)g(to)f (ask)i(wh)m(y)h(w)m(e)f(ha)m(v)m(e)g(not)328 1100 y(included)h(b)s(oth) g(c)m(harge)g(and)h(spin)f(instabilities.)51 b(A)36 b(careful)f (treatmen)m(t)i(of)e(all)f(suc)m(h)328 1257 y(e\013ects)40 b(b)m(y)h(the)e(w)m(eak-coupling)g(parquet)h(approac)m(h)g(is)e(found)i (in)e(Ref.)64 b([7)o(].)g(These)328 1413 y(authors)39 b(\014nd)h(that)f(the)h(b)s(eha)m(vior)f(of)g(the)g(mo)s(del)f(in)h (most)f(of)h(parameter)g(space)h(is)328 1570 y(RP)-8 b(A-lik)m(e,)38 b Fh(i.e.)58 b Fm(there)38 b(exist)g(stable)f(regimes)g (of)g(the)h(parquet)h(equations)e(in)g(whic)m(h)328 1726 y(one)c(of)f(these)i(t)m(w)m(o)f(instabilities)c(is)j(dominan)m(t.)474 1883 y(F)-8 b(urthermore,)28 b(the)f(reader)g(should)g(note)g(that)f (our)h(`gap')f(in)g(the)i(spin)e(excitations)328 2039 y(is)f(at)g(the)h(nesting)g(w)m(a)m(v)m(e)h(v)m(ector)f Fg(q)i Fm(=)g Fg(Q)g Ff(\021)g Fm(\()p Fj(\031)t(;)17 b(\031)t Fm(\),)26 b(and)g(not)f(at)g Fg(q)j Fm(=)g(0,)e(whic)m(h)g(is) f(what)328 2196 y(\014rst)32 b(comes)g(to)f(mind)f(when)j(one)f(men)m (tions)f(a)g(gap.)43 b(It)31 b(migh)m(t)g(b)s(e)g(in)m(teresting)g(to)h (see)328 2352 y(what)j(is)f(the)h(e\013ect)h(of)e(v.H.)h(singularities) e(on)h(the)h(real)f(part)h(of)f(the)h(spin)f(structure)328 2509 y(factor)47 b(at)g Fg(q)53 b Fm(=)g(0,)e Fj(\037)1185 2473 y Fe(0)1209 2509 y Fm(\()p Fg(q)i Fm(=)g(0\),)e(esp)s(ecially)46 b(since)i(the)g(latter)e(is)h(exp)s(erimen)m(tally)328 2665 y(accessible)27 b(via)g(the)g(Knigh)m(t)f(shift,)i(whose)g(b)s (eha)m(vior,)g(to)f(the)g(b)s(est)g(of)g(our)g(kno)m(wledge,)328 2822 y(has)f(so)f(far)g(not)g(b)s(een)h(satisfactorily)e(explained.)40 b(Again,)26 b(the)g(w)m(ork)g(of)f(Ref.)41 b([7])25 b(treats)328 2978 y(v.H.)33 b(e\013ects)h(prop)s(erly)-8 b(,)32 b(but)h Fj(\037)1484 2942 y Fe(0)1508 2978 y Fm(\()p Fg(q)27 b Fm(=)h(0\))k(has)h(not)f(b)s(een)i(lo)s(ok)m(ed)e(at.)474 3135 y(W)-8 b(orking)32 b(at)h(\014nite)f(temp)s(erature)g(and)h(ab)s (o)m(v)m(e)h(the)f(instabilit)m(y)-8 b(,)30 b(w)m(e)k(assume)f(that)328 3291 y(the)g(AF)f(\015uctuations)h(ha)m(v)m(e)h(the)f(disp)s(ersion) 1376 3548 y Fj(!)1437 3563 y Fk(D)1501 3548 y Fm(\()p Fg(Q)22 b Fm(+)g Fg(q)p Fm(\))28 b(=)1971 3441 y Fd(q)p 2054 3441 404 4 v 2062 3548 a Fm(~)-57 b Fj(!)2119 3519 y Fi(2)2180 3548 y Fm(+)22 b Fj(c)2320 3519 y Fi(2)2360 3548 y Fg(q)2419 3519 y Fi(2)2491 3548 y Fm(,)923 b(\(1\))328 3804 y(where)49 b Fj(c)g Fm(is)e(their)h(v)m(elo)s(cit)m(y)g(a)m(w)m(a) m(y)h(from)e Fg(Q)55 b Fm(=)f(\()p Fj(\031)t(;)17 b(\031)t Fm(\).)90 b(Since)48 b(the)h(AF)f(mo)s(de)f(is)328 3960 y(anomalously)35 b(p)s(opulated)h(as)h(the)g(transition)e(\()8 b(~)-57 b Fj(!)38 b Ff(!)d Fm(0\))h(is)g(approac)m(hed,)j(the)f(F)-8 b(ermi)328 4117 y(o)s(ccupation)36 b(n)m(um)m(b)s(ers)h(can)f(b)s(e)h (neglected)g(with)f(resp)s(ect)h(to)f(the)h(Bose)g(ones,)h(whic)m(h)328 4273 y(are)f(appro)m(ximated)g(classically)-8 b(.)56 b(The)39 b(one-lo)s(op)d(expression)i(for)f(the)h(electron)g(self-)328 4430 y(energy)c(without)e(v)m(ertex)i(corrections)f([16)o(])g(then)g(b) s(ecomes)875 4686 y(\006\()p Fj(!)t Fm(\))83 b Ff(\021)g Fm(\006)1399 4645 y Fk(R)1457 4686 y Fm(\()p Fg(p)p Fj(;)17 b(!)t Fm(\))1169 4880 y Ff(/)1329 4763 y Fd(Z)1429 4880 y Fj(d)1480 4839 y Fi(2)1519 4880 y Fj(q)1582 4763 y Fd(Z)1682 4880 y Fj(d!)1798 4839 y Fe(0)2150 4813 y Fm(1)p 1830 4857 690 4 v 1830 4949 a Fj(!)26 b Ff(\000)c Fj(\017)2055 4964 y Fc(p)p Fe(\000)p Fc(Q)p Fi(+)p Fc(q)2341 4949 y Fm(+)g Fj(i\016)2548 4813 y(k)s(T)p 2539 4857 143 4 v 2539 4949 a Fm(\026)-50 b Fj(h!)2659 4920 y Fe(0)2692 4880 y Fj(\037)2753 4839 y Fe(00)2796 4880 y Fm(\()p Fj(!)2899 4839 y Fe(0)2921 4880 y Fm(\))33 b(.)422 b(\(2\))1922 5214 y(4)p eop %%Page: 5 5 5 4 bop 328 631 a Fm(where)34 b(w)m(e)f(use)h(the)f(follo)m(wing)d (phenomenological)g(expression)j(for)g Fj(\037)2968 595 y Fe(00)3010 631 y Fm(:)1330 905 y Fj(\037)1391 863 y Fe(00)1434 905 y Fm(\()p Fj(!)t Fm(\))27 b(=)1995 837 y(2\000)p Fj(!)2170 801 y Fi(2)2166 862 y(0)2209 837 y Fj(!)p 1715 881 839 4 v 1715 973 a Fm(\()p Fj(!)1818 944 y Fi(2)1879 973 y Ff(\000)22 b Fj(!)2043 939 y Fi(2)2039 997 y Fk(D)2103 973 y Fm(\))2141 944 y Fi(2)2203 973 y Fm(+)g(4\000)2411 944 y Fi(2)2450 973 y Fj(!)2515 944 y Fi(2)3441 905 y Fm(\(3\))328 1175 y(Putting)37 b(the)i(external)f (electron)g(momen)m(tum)f Fg(p)h Fm(precisely)g(at)g(the)g(vH)h(p)s (oin)m(t)e Fg(K)g Fm(=)328 1331 y(\(0)p Fj(;)17 b(\031)t Fm(\),)33 b(w)m(e)i(expand)g(the)g(electron)e(disp)s(ersion)h(to)f (quadratic)h(terms)f(\(the)i(v)m(elo)s(cit)m(y)e(is)328 1488 y(zero!\))44 b(and)32 b(obtain)867 1795 y(\006\()p Fj(!)t Fm(\))27 b(=)h Fj(F)1302 1678 y Fd(Z)1385 1704 y Fk(!)1429 1713 y Fb(0)p 1385 1727 83 4 v 1354 1867 a Fi(~)-41 b Fk(!)p 1348 1880 51 4 v 1576 1728 a Fj(du)p 1495 1772 270 4 v 1495 1863 a(u)21 b Fm(+)h Fj(i)p Fm(\000)p 1703 1876 61 4 v 1791 1624 a Fd(2)1791 1774 y(4)2054 1728 y Fm(1)p 1856 1772 445 4 v 1856 1789 a Fd(q)p 1939 1789 362 4 v 100 x Fj(P)2002 1904 y Fi(+)2061 1889 y Fm(\()p Fj(!)p 2099 1902 65 4 v 3 w Fm(;)17 b Fj(u)p Fm(\))2333 1795 y(+)2639 1728 y(1)p 2441 1772 445 4 v 2441 1789 a Fd(q)p 2524 1789 362 4 v 100 x Fj(P)2587 1904 y Fe(\000)2646 1889 y Fm(\()p Fj(!)p 2684 1902 65 4 v 3 w Fm(;)g Fj(u)p Fm(\))2895 1624 y Fd(3)2895 1774 y(5)2999 1795 y Fm(,)415 b(\(4\))328 2117 y(where)33 b Fj(P)672 2132 y Fi(+)762 2117 y Fm(and)f Fj(P)1014 2132 y Fe(\000)1105 2117 y Fm(are)f(fourth-order)h(p)s(olynomials)c (\(complex)j(for)h(\000)27 b Fj(>)h Fm(0\),)j(coming)328 2274 y(resp)s(ectiv)m(ely)44 b(from)e(the)i(absorption)e(and)i (emission)e(diagrams.)73 b(A)44 b(dimensionless)328 2430 y(reduction)32 b(has)h(app)s(eared,)h(to)e(b)s(e)h(denoted)g(b)m(y)h (an)e(underline,)1743 2686 y Fj(!)p 1743 2699 V 31 w Ff(\021)1966 2619 y Fj(!)t(t)p 1951 2663 131 4 v 1951 2755 a Fm(2)p Fj(c)2042 2726 y Fi(2)2123 2686 y Fm(.)1291 b(\(5\))328 2943 y(The)32 b(in)m(tegration)d(o)m(v)m(er)j(a)f(disk)g (around)g(the)g(vH)h(p)s(oin)m(t)e(is)h(restricted)g(b)m(y)h(a)f (frequency)328 3099 y(cuto\013)f(for)g(the)h(\015uctuations,)g Fj(!)1530 3114 y Fi(0)p 1469 3127 101 4 v 1569 3099 a Fm(.)43 b(The)31 b(factor)f Fj(F)44 b Fm(con)m(tains)30 b(the)h(ph)m(ysical)f(constan)m(ts:)1626 3385 y Fj(F)41 b Ff(/)28 b Fj(k)s(T)14 b(g)2011 3344 y Fi(2)2060 3317 y Fj(!)2125 3281 y Fi(2)2121 3342 y(0)2163 3317 y Fj(t)p 2060 3362 139 4 v 2088 3453 a(c)2130 3424 y Fi(4)2241 3385 y Fm(,)1173 b(\(6\))328 3641 y(where)44 b Fj(!)681 3656 y Fi(0)p 620 3669 101 4 v 762 3641 a Fm(is)e(a)g(c)m (haracteristic)g(frequency)j(of)c(the)i(bare)g(\015uctuations,)i(and)d Fj(g)3368 3605 y Fi(2)3449 3641 y Fm(\(of)328 3797 y(dimension)26 b(energy\))i(is)f(mo)s(del-dep)s(enden)m(t.)42 b(The)28 b(app)s(earance)g(of)f(a)g(`univ)m(ersal')h(scale)328 3954 y(\(5\))k(is,)g(of)g(course,)i(a)e(consequence)k(of)c(the)h (simplicit)m(y)d(of)i(our)h(assumptions.)328 4342 y Fl(3)161 b(Results)53 b(and)h(Discussion)328 4597 y Fm(The)46 b(basic)g(result)f(is)h(that)f(for)g(zero)h(damping,)h(Im\006\()p Fj(!)t Fm(\))i(=)h(0)45 b(for)h Ff(j)p Fj(!)t Ff(j)i Fj(<)58 b Fm(~)-57 b Fj(!)49 b Fm(and)328 4753 y(Re\006\(0\))31 b(=)f(0.)49 b(Th)m(us)36 b(the)f(quasiparticle)e(p)s(eak)i(is)e (preserv)m(ed)k(as)e(long)e(as)i(the)f(\015uctu-)328 4910 y(ation)i(`bandhead')46 b(~)-56 b Fj(!)39 b(>)d Fm(0.)58 b(In)37 b(the)h(underdamp)s(ed)g(regime)f(with)g(damping)f (\000,)i(the)1922 5214 y(5)p eop %%Page: 6 6 6 5 bop 328 631 a Fm(quasiparticle)23 b(p)s(eak)i(gets)g(smeared)g(out) g(\(see)g(Fig.)40 b(1\),)26 b(while)e(its)g(in)m(tegrated)g(strength) 328 787 y(remains)32 b(more)f(or)i(less)g(the)g(same)f(as)h(in)f(the)h (case)g(of)f(zero)h(damping)e(\(see)j(Fig.)42 b(2\).)474 944 y(Figure)32 b(1)g(sho)m(ws)i(the)f(dimensionless)f(sp)s(ectral)g (densit)m(y)-8 b(,)1018 1192 y(~)993 1218 y Fj(A)p Fm(\()p Fj(!)p 1104 1231 65 4 v 3 w Fm(\))28 b Ff(\021)1349 1150 y Fm(2)p Fj(c)1440 1114 y Fi(2)p 1349 1194 131 4 v 1396 1286 a Fj(t)1489 1218 y(A)p Fm(\()p Fj(!)t Fm(\))f(=)1848 1150 y(1)p 1843 1194 59 4 v 1843 1286 a Fj(\031)2245 1150 y Ff(\000)p Fm(Im\006)p 2439 1163 71 4 v 1922 1194 910 4 v 1922 1286 a(\()p Fj(!)p 1960 1299 65 4 v 26 w Ff(\000)22 b Fm(Re\006)p 2261 1299 71 4 v 1 w(\))2370 1257 y Fi(2)2431 1286 y Fm(+)g(\(Im\006)p 2684 1299 V(\))2792 1257 y Fi(2)2874 1218 y Fm(,)540 b(\(7\))328 1488 y(o)m(v)m(er)38 b(three)g(orders)g(of)f(magnitude)f(of)h Fj(F)p 1812 1501 77 4 v 14 w Fm(.)57 b(It)37 b(is)g(ob)m(vious)h(ho)m(w)g(the)f (strength)h(of)f(the)328 1644 y(side)c(lob)s(es)f(increases)h(with)f Fj(F)p 1400 1657 V 14 w Fm(,)h(while)e(the)i(gap)g(b)s(et)m(w)m(een)h (them)f(widens.)474 1801 y(The)f(strength)g(of)f(the)g(quasiparticle)f (p)s(eak)i(is)e(mostly)g(sensitiv)m(e)i(to)39 b(~)-57 b Fj(!)p 3056 1814 65 4 v 3 w Fm(.)43 b(W)-8 b(e)32 b(sho)m(w)328 1957 y(it)e(in)g(Fig.)42 b(2)31 b(b)s(oth)f(with)h(and)g(without)g (damping.)41 b(In)32 b(the)f(latter)f(case,)j(the)e(strength)328 2114 y(is)f(calculated)f(through)h(Eq.)44 b(\(9\))30 b(b)s(elo)m(w,)g(while)g(for)f(a)h(\014nite)g(\000)g(w)m(e)i(\014t)e (the)h(calculated)328 2270 y(curv)m(es)50 b(to)d(a)h(sum)g(of)f(Loren)m (tzians,)52 b(and)c(read)g(o\013)f(the)i(strength)f(of)g(the)g(cen)m (tral)328 2427 y(p)s(eak)31 b(\(whic)m(h)h Fh(is)f Fm(Loren)m(tzian\))g (from)f(the)h(b)s(est)h(\014t)f(b)m(y)h(a)f(Lev)m(en)m(b)s (erg{Marquardt)i([17])328 2583 y(pro)s(cedure.)43 b(As)28 b(ma)m(y)f(b)s(e)h(seen,)i(the)e(strength)g(dep)s(ends)h(v)m(ery)g (little)c(on)i(the)h(damping,)328 2740 y(at)k(least)g(in)g(the)h (underdamp)s(ed)g(regime.)474 2896 y(The)k(sensitivit)m(y)f(to)43 b(~)-57 b Fj(!)39 b Fm(is)c(mainly)f(con)m(tained)i(in)f(the)h(fact)f (that,)i(when)44 b(~)-56 b Fj(!)p 3224 2909 V 39 w Fm(is)35 b(not)328 3053 y(to)s(o)d(large,)1525 3163 y Fj(@)5 b Fm(Re)q(\006)p 1525 3207 243 4 v 1586 3298 a Fj(@)g(!)1778 3081 y Fd(\014)1778 3130 y(\014)1778 3180 y(\014)1778 3230 y(\014)1778 3280 y(\014)1805 3334 y Fk(!)r Fi(=0)1974 3230 y Ff(\031)28 b(\000)2204 3163 y Fj(F)p 2204 3176 77 4 v 2166 3207 153 4 v 2166 3299 a Fm(2)8 b(~)-57 b Fj(!)p 2215 3312 65 4 v 2279 3260 a Fi(2)2361 3230 y Fm(.)1053 b(\(8\))328 3465 y(This)39 b(giv)m(es)g(an)f(excellen)m(t)h (appro)m(ximation)d(for)i(the)h(sp)s(ectral)f(w)m(eigh)m(t)h(of)f(the)h (quasi-)328 3622 y(particle)31 b(p)s(eak,)1522 3799 y Fj(P)41 b Ff(\021)1910 3732 y Fm(1)p 1751 3776 366 4 v 1751 3871 a(1)22 b Ff(\000)1932 3832 y Fk(@)t Fi(Re\006)p 1932 3848 176 4 v 1976 3905 a Fk(@)t(!)2127 3649 y Fd(\014)2127 3699 y(\014)2127 3749 y(\014)2127 3799 y(\014)2127 3849 y(\014)2155 3909 y Fk(!)r Fi(=0)2344 3799 y Fm(,)1070 b(\(9\))328 4041 y(as)41 b(sho)m(wn)h(in)e(Fig.)67 b(2.)i(As)41 b(the)h(AF)e(mo)s(de)g(condenses,)46 b(the)41 b(strength)h Fj(P)54 b Fm(v)-5 b(anishes)328 4197 y(quadratically)31 b(with)40 b(~)-57 b Fj(!)p 1141 4210 65 4 v 3 w Fm(,)33 b(th)m(us)g(op)s(ening)f(a)g(true)h(gap)g(in)f(the)h(electron)f(sp)s (ectrum.)474 4354 y(This)i(b)s(eha)m(vior)e(is)h(di\013eren)m(t)g(from) f(the)i(usual)e(pseudogap)i(situation,)e(where)i(the)328 4510 y(densit)m(y)47 b(of)f(states)h(at)f Fj(!)p 1227 4523 V 54 w Fm(=)51 b(0)46 b(comes)g(from)f(the)i(tails)d(of)i(damp)s (ed)g(quasiparticle)328 4667 y(p)s(eaks)34 b(cen)m(tered)h(elsewhere,)f Fh(i.e.)44 b Fm(it)32 b(is)g(due)i(to)e(Im\006\(0\))c Ff(6)p Fm(=)g(0,)33 b(while)f(here)i(w)m(e)g(ha)m(v)m(e)g(a)328 4823 y(quasiparticle)27 b(at)i(the)g(F)-8 b(ermi)27 b(lev)m(el)h(all)f (the)i(w)m(a)m(y)h(do)m(wn)g(to)e(the)h(transition,)f(alb)s(eit)f(the) 1922 5214 y(6)p eop %%Page: 7 7 7 6 bop 328 631 a Fm(probabilit)m(y)35 b(of)h(\014nding)g(an)h (electron)f(there)i(\(Fig.)54 b(2\))37 b(gets)g(lo)m(w)m(er)g(as)f (condensation)328 787 y(is)c(approac)m(hed.)474 944 y(Finally)20 b(let)h(us)i(discuss)g(the)f(ph)m(ysical)g(v)-5 b(alues)22 b(of)g(the)g(parameters.)40 b(It)22 b(is)g(imp)s(ortan)m(t)328 1100 y(to)38 b(establish)g(that)h(w)m(e)g(ma)m(y)g(use)g(Eq.)62 b(\(3\))39 b(in)e(the)i(underdamp)s(ed)h(regime,)e Fh(i.e.)61 b Fm(for)328 1257 y(\000)48 b Fj(<)56 b Fm(~)-56 b Fj(!)s Fm(.)80 b(In)45 b(Fig.)78 b(3,)48 b(w)m(e)e(\014t)f(Eq.)81 b(\(3\))44 b(to)g(the)h(exp)s(erimen)m(tal)f(data)h(of)f([3].)80 b(The)328 1413 y(quan)m(titativ)m(e)40 b(asp)s(ects)i(of)f(the)g(\014t) g(are)g(not)f(v)m(ery)i(relev)-5 b(an)m(t)41 b(here;)46 b(qualitativ)m(ely)-8 b(,)41 b(w)m(e)328 1570 y(\014nd)f(that)f(the)h (damping)e(is)h(ab)s(out)g(50\045)g(of)g(the)h(`bandhead')48 b(~)-57 b Fj(!)t Fm(.)64 b(W)-8 b(e)39 b(iden)m(tify)g(the)328 1726 y(large)e(frequency)k Fj(!)1081 1741 y Fi(0)1158 1726 y Fm(with)d Fj(c=\030)5 b Fm(,)39 b(the)g(cuto\013)f(in)g(Eq.)61 b(\(4\).)g(The)39 b(exp)s(erimen)m(tal)e(data)328 1883 y(con)m(tain)26 b(an)g(arbitrary)f(v)m(ertical)h(scale)g(factor,)i(so)e (w)m(e)h(cannot)g(obtain)e Fj(!)2995 1898 y Fi(0)3061 1883 y Fm(from)g(the)i(\014t.)328 2039 y(T)-8 b(aking)30 b Fj(!)712 2054 y Fi(0)781 2039 y Fm(at)g(200{300)f(meV,)h(with)g Fj(\030)i Ff(\030)c Fm(2,)i(enables)h(us)g(to)f(estimate)f(the)i (reduction)328 2196 y(\(5\))h(at)g Ff(\030)c Fm(1)p Fj(eV)882 2160 y Fe(\000)p Fi(1)976 2196 y Fm(.)474 2352 y(As)38 b(to)g(the)g(ph)m(ysical)f(prefactor)h Fj(F)14 b Fm(,)38 b(w)m(e)h(need)f(to)g(estimate)e(the)i(coupling)f Fj(g)3383 2316 y Fi(2)3421 2352 y Fm(,)i(of)328 2509 y(dimension)d(energy)-8 b(.)58 b(In)37 b(the)h(w)m(orst)g(case,)h(it)d(is)h Ff(\030)f Fj(U)2349 2473 y Fi(2)2389 2509 y Fj(=!)2499 2524 y Fi(0)2575 2509 y Fm(\(static)h(external)g(p)s(ertur-)328 2665 y(bation\),)30 b(giving)g Fj(F)p 984 2678 77 4 v 41 w Ff(\030)e Fm(10)1291 2629 y Fe(\000)p Fi(3)1385 2665 y Fm(.)43 b(More)32 b(ph)m(ysically)-8 b(,)31 b(one)g(w)m(ould)g(put)h Ff(\030)c Fj(t)2955 2629 y Fi(2)2995 2665 y Fj(=U)41 b Fm(\(Hubbard)328 2822 y(mo)s(del)29 b(in)g(the)i Fj(t)17 b Ff(\000)h Fj(J)40 b Fm(limit\))26 b(or)k Ff(\030)e Fj(t)1659 2786 y Fi(2)1699 2822 y Fj(=)p Fm(\001)i(\(Emery)h(mo)s(del)d(in)i(the)h(large-)p Fj(U)39 b Fm(limit,)27 b(with)328 2978 y(\001)i(the)h(copp)s(er-o)m(xygen)h (splitting\),)d(whic)m(h)h(giv)m(es)h Fj(F)p 2204 2991 V 41 w Ff(\030)f Fm(10)2512 2942 y Fe(\000)p Fi(5)2635 2978 y Fm(or)g(10)2849 2942 y Fe(\000)p Fi(4)2943 2978 y Fm(.)42 b(This)29 b(analysis)328 3135 y(w)m(ould)42 b(imply)e(that)i(in)g(Fig.)71 b(2)41 b(it)h(is)f(the)i(regime)e(of)h (small)d Fj(F)p 2681 3148 V 56 w Fm(whic)m(h)k(is)f(ph)m(ysical.)328 3291 y(Although,)37 b(as)g(w)m(e)g(ha)m(v)m(e)h(already)e(noted,)i(the) f(app)s(earance)g(of)f(a)h(univ)m(ersal)f(scale)h(in)328 3448 y(our)d(calculation)d(should)j(not)g(b)s(e)g(tak)m(en)h(to)s(o)e (seriously)-8 b(,)34 b(it)f(is)g(encouraging)h(that)f(the)328 3604 y(e\013ectiv)m(e)h(coupling)d(constan)m(t)i(seems)h(to)e(b)s(e)h (reduced)h(for)e(vH)h(electrons.)474 3761 y(Inciden)m(tally)-8 b(,)35 b(due)g(to)f(the)i(fact)e(that)h(at)f Fj(T)45 b Fm(=)31 b(5)p Fj(K)42 b Fm(the)35 b(measured)g Fj(\037)3087 3725 y Fe(00)3164 3761 y Fm(is)f(strictly)328 3917 y(zero)c(b)s(elo)m (w)g(10)f(meV,)g(the)i(exp)s(erimen)m(tal)d(situation)h(at)g(that)g (temp)s(erature)h(is)f(b)s(etter)328 4074 y(describ)s(ed)i(b)m(y)h(the) f(zero-damping)e(situation)h(than)g(b)m(y)i(the)f(damp)s(ed)g(curv)m(e) h(\(3\))e(with)328 4230 y(whic)m(h)j(w)m(e)h(\014t)e(the)h(data)f(in)g (Fig.)42 b(3.)474 4387 y(If)g(one)g(mo)m(v)m(es)h(sligh)m(tly)d(o\013)h (the)i(vH)f(singularit)m(y)-8 b(,)42 b(writing)f Fg(p)28 b Fm(=)f Fg(K)22 b Fm(+)g Fg(k)42 b Fm(for)f(the)328 4543 y(electron)35 b(momen)m(tum,)g(w)m(orst-case)i(estimates)e(in)g (the)h(case)g(of)f(zero)h(damping)e(indi-)328 4700 y(cate)29 b(that)f(the)h(quasiparticle)e(regime)g(p)s(ersists,)j(but)e(in)g(a)g (narro)m(w)m(ed)h(region:)41 b(instead)328 4856 y(of)i Ff(j)p Fj(!)p 478 4869 65 4 v 3 w Ff(j)k Fj(<)54 b Fm(~)-56 b Fj(!)p 740 4869 V 3 w Fm(,)47 b(one)d(no)m(w)g(has)h Ff(j)p Fj(!)p 1496 4869 V 3 w Ff(j)h Fj(<)55 b Fm(~)-57 b Fj(!)p 1757 4869 V 33 w Ff(\000)30 b Fj(!)2019 4871 y Fk(k)p 1958 4885 104 4 v 2062 4820 a Fi(2)2101 4856 y Fj(=)p Fm(2,)47 b(where)e Fj(!)2627 4871 y Fk(k)p 2566 4885 V 2716 4856 a Ff(\021)i Fj(tk)s(=)p Fm(2)p Fj(c)p Fm(.)78 b(This)44 b(is)f(a)1922 5214 y(7)p eop %%Page: 8 8 8 7 bop 328 631 a Fm(quadratic)42 b(correction)f(in)h(the)g(reduced)h (frequencies)h(and)e(th)m(us)h(alw)m(a)m(ys)g(negligible)328 787 y(for)f(small)f(enough)i Fg(k)p Fm(.)75 b(Th)m(us)44 b(the)f(an)m(tiadiabatic)e(e\013ect)j(found)f(here)g(should)g(con-)328 944 y(tribute)c(with)g(\014nite)g(measure)g(in)g(the)g(momen)m(tum)f (in)m(tegral)g(when)i(one)f(calculates)328 1100 y(the)33 b(densit)m(y)g(of)g(states.)474 1257 y(Finally)-8 b(,)46 b(since)g(the)g(factor)f Fj(k)s(T)59 b Fm(in)45 b Fj(F)59 b Fm(\(whose)47 b(reduction)e(b)m(y)h(\(5\))f(is)g(basically)328 1413 y(what)i(mak)m(es)g Fj(F)p 893 1426 77 4 v 61 w Fm(small\))d(is)j(due)g(to)g(our)f(taking)g(the)h(high-temp)s(erature)f (limit)d(of)328 1570 y(the)33 b(structure)h(factor,)f(w)m(e)g(note)g (that)g(the)g(coupling)e(in)h(the)h(lo)m(w-temp)s(erature)f(limit)328 1726 y(b)s(ecomes)h(exp)s(onen)m(tially)f(small.)474 1883 y(W)-8 b(e)33 b(conclude)g(that)f(the)h(previous)g(in)m (terpretation)e(of)h(certain)g(anomalies)f(in)g(the)328 2039 y(b)s(eha)m(vior)c(of)h(optical)e(phonons)i(as)g(b)s(eing)f(due)h (to)g(the)g(logarithmically)22 b(singular)27 b(den-)328 2196 y(sit)m(y)33 b(of)f(states)h(is)f(not)h(imp)s(eriled)d(b)m(y)j(an) g(imp)s(ending)d(AF)j(transition.)328 2584 y Fl(4)161 b(Ac)l(kno)l(wledgemen)l(ts)328 2839 y Fm(W)-8 b(e)30 b(w)m(ould)g(lik)m(e)f(to)h(thank)g(E.)g(T)-8 b(uti)j(\024)-44 b(s,)31 b(A.)f(Bjeli)-5 b(\024)-44 b(s)28 b(and)i(J.)g(F)-8 b(riedel)29 b(for)g(v)-5 b(aluable)28 b(discus-)328 2995 y(sions.)46 b(One)34 b(of)f(the)g(authors)h(\(DKS\))f(b)s(ecame)g(in)m (terested)i(in)d(this)h(sub)5 b(ject)35 b(while)e(an)328 3152 y(Alexander)g(v)m(on)g(Hum)m(b)s(oldt)f(F)-8 b(ello)m(w.)1922 5214 y(8)p eop %%Page: 9 9 9 8 bop 328 631 a Fl(References)377 886 y Fm([1])48 b(R.J.)39 b(Birgenau,)g(Y.)g(Endoh,)h(K.)e(Kakura,)i(Y.)f(Hidak)-5 b(a,)39 b(T.)g(Murahami,)f(M.A.)528 1043 y(Kastner,)i(T.R.)e(Th)m (urston,)i(G.)d(Shirane)h(and)f(K.)h(Y)-8 b(amada,)37 b(Ph)m(ys.)j(Rev.)e Fg(B39)528 1199 y Fm(\(1989\))32 b(2868.)377 1439 y([2])48 b(M.)32 b(T)-8 b(akiga)m(w)m(a,)31 b(A.P)-8 b(.)31 b(Rey)m(es,)i(P)-8 b(.C.)32 b(Hammel,)d(J.D.)h (Thompson,)i(R.H.)f(He\013ner,)528 1595 y(Z.)i(Fisk)f(and)h(K.C.)g (Ott,)f(Ph)m(ys.)i(Rev.)g Fg(B43)e Fm(\(1991\))f(247,)528 1752 y(H.)i(Monien,)g(D.)f(Pines)h(and)g(M.)g(T)-8 b(akiga)m(w)m(a,)32 b Fh(ibid.)p Fm(,)g(p.)h(258,)528 1908 y(H.)g(Monien,)g(P)-8 b(.)33 b(Mon)m(thoux)g(and)g(D.)f(Pines,)h Fh(ibid.)p Fm(,)f(p.)h(275.)377 2148 y([3])48 b(J.)h(Rossat-Migno)s(d,)j(L.P)-8 b(.)48 b(Regnault,)k(C.)d(V)-8 b(ettier,)52 b(P)-8 b(.)49 b(Bourges,)k(P)-8 b(.)49 b(Burlet,)528 2304 y(J.)40 b(Bossy)-8 b(,)42 b(J.Y.)d(Henry)h(and)f(G.)g(Lap)s(ertot,)h Fh(Spin)g(Dynamics)g (in)h(the)g(High-T)3532 2319 y Fk(c)528 2461 y Fh(System)48 b Fm(YBa)1066 2476 y Fi(2)1105 2461 y Fm(Cu)1229 2476 y Fi(3)1269 2461 y Fm(O)1345 2476 y Fi(6)1386 2461 y Fm(+)q Fj(x)p Fm(,)24 b(In)m(ternational)d(Conference)j(on)f(Neutron)f (Scattering)528 2617 y(\(in)m(vited)33 b(talk\),)e(Oxford,)i(August)g (1991.,)f(and)h(Ph)m(ysica)g Fg(B169)g Fm(\(1991\))e(58.)377 2857 y([4])48 b(J.M.)f(T)-8 b(ranquada,)50 b(W.J.L.)d(Buy)m(ers,)k(H.)c (Chou,)j(T.E.)d(Masan,)j(M.)c(Sato,)k(S.)528 3013 y(Shamoto)32 b(and)h(G.)f(Shirane,)g(Ph)m(ys.)j(Rev.)e(Lett.)g Fg(64)f Fm(\(1990\))g(800.)377 3253 y([5])48 b(A.)33 b(Kampf)f(and)g(J.C.)i(Sc) m(hrie\013er,)f(Ph)m(ys.)h(Rev.)f Fg(B41)g Fm(\(1990\))e(6399.)377 3492 y([6])48 b(P)-8 b(.W.)34 b(Anderson,)g(Science)f Fg(235)g Fm(\(1987\))e(1196.)377 3732 y([7])48 b(I.E.)34 b(Dzy)m(aloshinskii)d(and)i(V.M.)g(Y)-8 b(ak)m(o)m(v)m(enk)m(o,)35 b(In)m(t.)e(J.)g(Mo)s(d.)g(Ph)m(ys.)i Fg(B5)d Fm(\(1988\))528 3888 y(667.)377 4128 y([8])48 b(E.)33 b(T)-8 b(uti)j(\024)-44 b(s,)33 b(to)f(b)s(e)h(published.)377 4367 y([9])48 b(G.)33 b(Kotliar,)d(In)m(t.)j(J.)g(Mo)s(d.)f(Ph)m(ys.)j Fg(B5)d Fm(\(1988\))f(711.)328 4607 y([10])48 b(J.D.)31 b(Axe,)h(A.H.)e (Moudden,)j(D.)d(Hohlw)m(ein,)g(D.E.)h(Co)m(x,)h(K.M.)f(Mohan)m(t)m(y) -8 b(,)32 b(A.R.)528 4763 y(Mo)s(o)s(den)m(baugh)h(and)g(Xu)g(Y)-8 b(ou)m(w)m(en,)34 b(Ph)m(ys.)h(Rev.)e(Lett.)g Fg(62)f Fm(\(1989\))g(2751.)1922 5214 y(9)p eop %%Page: 10 10 10 9 bop 328 631 a Fm([11])48 b(A.)28 b(Wittlin,)d(R.)i(Liu,)h(M.)f (Cordona,)h(L.)f(Genzl,)h(W.)f(K\177)-49 b(onig,)27 b(W.)g(Bahnhofer,)i (Hj.)528 787 y(Mattausc)m(h)34 b(and)f(A.)g(Simon,)e(Sol.)h(St.)g(Comm) m(un.)g Fg(64)p Fm(,)h(\(1987\))f(477.)328 1027 y([12])48 b(J.)33 b(F)-8 b(riedel,)31 b(J.)i(Ph)m(ys.:)45 b(Condensed)35 b(Matter)e Fg(1)g Fm(\(1989\))e(7757.)328 1267 y([13])48 b(S.)30 b(Bari)-5 b(\024)-44 b(si)m(\023)e(c,)29 b(I.)h(Kup)m(\024)-46 b(ci)m(\023)g(c)30 b(and)g(I.)f(Batisti)m(\023)-46 b(c,)29 b(In)m(t.)i(J.)f(Mo)s(d.)f(Ph)m(ys.)j Fg(B3)d Fm(\(1989\))g(2051.)328 1506 y([14])48 b(S.)33 b(Bari)-5 b(\024)-44 b(si)m(\023)e(c,)32 b(In)m(t.)h(J.)g(Mo)s(d.)f(Ph)m(ys.)j Fg(B5)p Fm(\(1991\)2439.)328 1746 y([15])48 b(A.)33 b(Bjeli)-5 b(\024)-44 b(s)32 b(and)g(S.)h(Bari) -5 b(\024)-44 b(si)m(\023)e(c,)32 b(J.)g(Ph)m(ysique)j({)d(Lettres,)i Fg(36)e Fm(\(1975\))g(L-169.)328 1985 y([16])48 b(A.A.)29 b(Abrik)m(oso)m(v,)g(L.P)-8 b(.)28 b(Gork)m(o)m(v)h(and)e(I.E.)i(Dzy)m (aloshinskii,)e Fh(Metho)-5 b(ds)30 b(of)g(Quan-)528 2142 y(tum)49 b(Field)d(The)-5 b(ory)48 b(in)f(Statistic)-5 b(al)48 b(Physics)p Fm(,)i(Do)m(v)m(er,)g(New)e(Y)-8 b(ork)47 b(1975,)i(Eq.)528 2298 y(\(21.26\).)328 2538 y([17])f(W.H.)31 b(Press,)h(B.P)-8 b(.)30 b(Flannery)-8 b(,)30 b(S.A.)h(T)-8 b(euk)m(olsky)g(,)32 b(W.T.)f(V)-8 b(etterling,)29 b Fh(Numeric)-5 b(al)528 2694 y(R)g(e)g(cip)g(es)35 b(in)f(C)p Fm(,)e(Cam)m(bridge)g(Univ)m(ersit)m(y)i(Press,)g(1988.)1898 5214 y(10)p eop %%Page: 11 11 11 10 bop 1484 631 a Fa(Figure)45 b(Captions)140 895 y Fm(Figure)31 b(1.)49 b(The)36 b(dimensionless)e(sp)s(ectral)h(densit) m(y)h(for)43 b(~)-57 b Fj(!)p 2246 908 65 4 v 36 w Fm(=)32 b(0)p Fj(:)p Fm(03,)j(\000)p 2687 908 61 4 v 32 w(=)d(0)p Fj(:)p Fm(015,)k Fj(!)3235 910 y Fi(0)p 3174 924 101 4 v 3306 895 a Fm(=)c(0)p Fj(:)p Fm(4,)572 1052 y(and)43 b(three)h(v)-5 b(alues)44 b(of)f(the)g(reduced)i(coupling)d(constan)m (t.)77 b(F)-8 b(ull)41 b(line)h(:)65 b Fj(F)p 3367 1065 77 4 v 60 w Fm(=)572 1208 y(0)p Fj(:)p Fm(0001.)42 b(Dotted)32 b(line)g(:)43 b Fj(F)p 1497 1221 V 42 w Fm(=)27 b(0)p Fj(:)p Fm(001.)43 b(Dashed)33 b(line)e(:)43 b Fj(F)p 2598 1221 V 42 w Fm(=)27 b(0)p Fj(:)p Fm(01.)140 1448 y(Figure)k(2.)49 b(Strength)42 b(of)f(the)i(quasiparticle)d(p)s(eak)i (in)f(Fig.)70 b(1.)h(Squares:)63 b Fj(F)p 3028 1461 V 57 w Fm(=)44 b(0)p Fj(:)p Fm(0001.)572 1604 y(T)-8 b(riangles:)68 b Fj(F)p 1056 1617 V 63 w Fm(=)49 b(0)p Fj(:)p Fm(001.)80 b(Diamonds:)67 b Fj(F)p 2160 1617 V 63 w Fm(=)50 b(0)p Fj(:)p Fm(01.)80 b(Empt)m(y)46 b(sym)m(b)s(ols:)69 b(no)572 1761 y(damping.)64 b(Filled)38 b(sym)m(b)s(ols:)58 b(damping)39 b(is)h(50\045)f(of)48 b(~)-57 b Fj(!)s Fm(.)66 b(F)-8 b(ull)38 b(lines:)58 b(Eq.)67 b(\(9\))572 1917 y(with)32 b(the)h(analytical)d(appro)m(ximation)g(\(8\).)140 2157 y(Figure)h(3.)49 b(Fits)40 b(of)g(Eq.)70 b(\(3\))40 b(at)h Fg(q)h Fm(=)f(0)g(to)g(the)g(exp)s(erimen)m(tal)f(data)g(of)h(Ref.)68 b([3].)h(The)572 2313 y(parameters)43 b(are,)i(with)e(increasing)f (temp)s(erature,)k(\000)f(=)g(5)p Fj(:)p Fm(8)p Fj(;)17 b Fm(7)p Fj(:)p Fm(6)p Fj(;)g Fm(14)p Fj(:)p Fm(4)p Fj(;)g Fm(14)p Fj(:)p Fm(5,)580 2470 y(~)-57 b Fj(!)51 b Fm(=)d(24)p Fj(;)17 b Fm(25)p Fj(;)g Fm(30)p Fj(;)g Fm(28,)30 b Fj(!)1450 2485 y Fi(0)1537 2470 y Fm(=)48 b(200)p Fj(;)17 b Fm(220)p Fj(;)g Fm(320)p Fj(;)g Fm(270,)44 b(all)f(in)g(meV.)i(Note)f(that)h Fj(!)3527 2485 y Fi(0)572 2626 y Fm(cannot)40 b(b)s(e)g(estimated)f (from)f(the)i(\014ts)g(b)s(ecause)i(the)e(exp)s(erimen)m(tal)e(data)i (are)572 2783 y(arbitrarily)30 b(scaled.)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF