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b(Linear)e(Deviation)i(\()p Ff(cl)r(d)p Fl(\))g(of)f(13)g(mass)g(mo)r (dels)877 469 y(calculated)g(for)g(2)h(di\013eren)n(t)f(sets)h(of)f (measured)g(n)n(uclear)f(masses.)762 631 y(MODEL)p 1560 661 4 101 v 566 w(t)n(yp)r(e)p 1876 661 V 127 w Ff(cl)r(d)2033 601 y Fe(a)2276 631 y Fl(n)n(b)p 2469 661 V 182 w Ff(cl)r(d)2654 601 y Fe(b)2883 631 y Fl(n)n(b)p 3076 661 V 216 w Fd(cpr)p 3434 661 V 1560 760 4 100 v 1876 760 V 1927 731 a Fl(k)n(eV)p 2469 760 V 508 w(k)n(eV)p 3076 760 V 3434 760 V 482 830 a(1)100 b(P)n(ap)r(e)26 b(and)i(An)n(ton)n(y)p 1560 860 V 397 w(lo)r(cal)p 1876 860 V 99 w(154)165 b(\(85\))p 2469 860 V 251 w(72)h(\(3\))p 3076 860 V 3434 860 V 482 930 a(2)100 b(Dussel,Caurier,Zuk)n(er)p 1560 960 V 271 w(lo)r(cal)p 1876 960 V 99 w(176)82 b(\(1325\))p 2469 960 V 209 w(135)123 b(\(87\))p 3076 960 V 3434 960 V 482 1029 a(3)100 b(M\177)-42 b(oller)26 b(and)i(Nix)p 1560 1059 V 436 w(global)p 1876 1059 V 98 w(595)82 b(\(1589\))p 2469 1059 V 209 w(632)g(\(168\))p 3076 1059 V 209 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Fp(0)p Fc(g)o Fn(;)34 b Fp(whic)m(h)g(in)g(a)f(w)m(a)m(y)i(represen)m(ts)i(the)d(v)m (olume)g(com-)118 3112 y(prised)f(b)s(et)m(w)m(een)i(the)e(theoretical) e(surface)i(and)g(the)g(exp)s(erimen)m(tal)f(one.)118 3350 y(T)-8 b(able)32 b(1)g(presen)m(ts)j(the)e(results)g(of)f (calculated)f(deviations)h(for)g(the)h(13)f(theories)h(and)f(2)g(sets)i (of)118 3471 y(exp)s(erimen)m(tal)h(masses:)50 b(the)36 b(1655)f(masses)h(of)f(the)h(1986)f(table)g([88W)-8 b(ap)o(])36 b(and)g(the)g(set)g(of)f(the)118 3591 y(175)f(new)h(masses)g(measured)g (since)g(1986.)48 b(There)35 b(is)f(a)g(clear)g(increase)h(of)f(the)g (deviations)g(for)118 3711 y(the)j(set)h(of)e(new)i(masses.)57 b(Last)37 b(column)e(giv)m(es)j(the)f(ratios)f(b)s(et)m(w)m(een)j(the)e (deviations)f(for)g(the)118 3832 y(t)m(w)m(o)g(samples,)g(whic)m(h)g (ma)m(y)g(b)s(e)f(called)g Fk("close)40 b(predictiv)m(e)f(ratios")34 b Fp(or)h Fk(cpr)p Fp(.)52 b(The)37 b Fk(cpr)e Fp(for)118 3952 y(the)e("global")d(mo)s(dels)h(are)i(systematically)e(b)s(etter)i (than)g(for)f(the)h("lo)s(cal")d(ones.)118 4191 y Fk(3)38 b(DIVER)m(GENCES)c(OF)k(THE)f(MODELS)118 4429 y Fp(No)m(w)c(that)e(the) i(predictiv)m(e)f(p)s(o)m(w)m(er)g(of)g(the)g(mo)s(dels)f(ha)m(v)m(e)i (b)s(een)g(ev)-5 b(aluated,)31 b(one)i(ma)m(y)e(consider)118 4549 y(to)24 b(mak)m(e)h(an)f(adequate)h(statistical)e(treatmen)m(t)h (of)g(the)h(predictions,)g(pro)m(vided)g(the)g(div)m(ergences)118 4670 y(b)s(et)m(w)m(een)38 b(mo)s(dels)c(are)i(within)e(reasonable)h (limits)e(\(see)k(next)f(paragraph\))f(and)h(that)f(at)g(least)118 4790 y([90Hau])f(six)g(mo)s(dels)f(giv)m(e)h(predictions)g(for)g(a)g (giv)m(en)g(n)m(uclear)g(mass.)49 b(A)34 b(w)m(eigh)m(ted)h(a)m(v)m (erage)g(is)118 4911 y(b)s(eing)i(considered.)60 b(The)39 b(uncertain)m(t)m(y)g(asso)s(ciated)f(with)f(eac)m(h)i(theory's)g (prediction)e(in)g(that)118 5031 y(a)m(v)m(erage)k(is)e(tak)m(en)i(as:) 58 b Fn(\033)1084 4995 y Fo(th)1080 5056 y(i)1194 5031 y Fp(=)40 b 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2599 y(v)m(ery)27 b(go)s(o)s(d)g(agreemen)m(t)h(of)f(b)s(oth)g (predictions)d(with)i(the)h(kno)m(wn)f(masses.)40 b(Div)m(ergences)28 b(exceeding)f(10)118 2712 y(MeV)k(start)g(at)g Fb(N)10 b(F)j(S)31 b Fg(=)25 b(+14)31 b(on)f(the)g(neutron-ric)m(h)g(side.)118 2985 y Fp(The)d(a)m(v)m(erages)h(of)d(theoretical)g(masses)i(o)m(v)m (er)g(the)g(whole)f(c)m(hart)g(yielded)g(results)g(for)g(5018)f(n)m (uclei)118 3105 y(of)d(whic)m(h)i(4227)d(had)i(a)g(disp)s(ersion)f(b)s (elo)m(w)g(1)h(MeV.)g(These)i(crude)f(results)f(will)d(require)j (naturally)118 3226 y(careful)32 b(individual)e(and)j(global)d (analysis.)118 3464 y(F)-8 b(ollo)m(wing)40 b(Haustein)j([84Hau)o(])g (w)m(e)h(de\014ne)g(a)e(distance)h(with)f(resp)s(ect)i(to)f(the)g (stabilit)m(y)e(line)118 3585 y(called)47 b("neutrons-from-stabilit)m (y":)70 b Fn(N)10 b(F)k(S)60 b Fp(=)53 b Fn(N)33 b Fc(\000)22 b Fn(Z)29 b Fc(\000)23 b Fp(\(0)p Fn(:)p Fp(4)p Fn(A)2643 3548 y Fj(2)2682 3585 y Fp(\))p Fn(=)p Fp(\(200)e(+)h Fn(A)p Fp(\).)89 b(A)48 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b(of)i(mo)s(dels)e(making)g(predictions)g (far)h(enough)g(from)g(stabilit)m(y)-8 b(.)118 3580 y Fc(j)p Fn(N)10 b(F)k(S)6 b Fc(j)31 b Fp(=)h(20)i(is)h(hazardous)g(for)g (the)g(time)f(b)s(eing.)50 b(This)35 b(n)m(um)m(b)s(er)g(could)g (de\014ne)h(the)f(fron)m(tier)118 3701 y(separating)d(the)h (medium-range)e(extrap)s(olations)g(from)g(the)i(far)f(extrap)s (olations.)118 3939 y(The)24 b(a)m(v)m(eraged)g(v)-5 b(alues)23 b(obtained)f(for)g(the)i(medium-range)d(predictions)h(can)h (b)s(e)g(compared)g(with)118 4060 y(the)k(exp)s(erimen)m(tal)e(masses.) 42 b(An)26 b(example)f(is)h(sho)m(wn)h(in)e(\014g.)42 b(3.)f(The)27 b(smo)s(oth)e(c)m(haracter)i(of)e(the)118 4180 y(curv)m(es)36 b(is)e(preserv)m(ed)j(ev)m(en)f(for)e(the)h(region) e(of)h(the)h(outer)f(masses.)50 b(Of)34 b(course,)i(the)f(medium-)118 4300 y(range)23 b(extrap)s(olated)f(v)-5 b(alues)22 b(obtained)g(in)g (this)g(w)m(a)m(y)i(are)e(far)g(from)f(b)s(eing)h(p)s(erfect,)j(but)e (they)g(can)118 4421 y(b)s(e)35 b(considered)h(as)f(the)h(b)s(est)f (estimate)f(presen)m(tly)j(p)s(ossible)d(for)g(these)j(masses.)51 b(Eac)m(h)36 b(theory)118 4541 y(con)m(tains)44 b(some)h(truth)f(and)g (certainly)g(some)g(appro)m(ximations.)77 b(Being)44 b(constructed)i(quite)118 4662 y(di\013eren)m(tly)33 b(from)e(eac)m(h)j(other,)f(one)h(ma)m(y)e(exp)s(ect)j(that)d(the)i (e\013ects)g(of)e(these)i(appro)m(ximations)118 4782 y(do)25 b(not)f(coincide)g(and)h(w)m(ould)f(b)s(e)h(random.)40 b(If)25 b(this)f(is)g(the)h(case,)i(then)e(a)m(v)m(eraging)g(w)m(ould)f (b)s(e)h(licit)118 4902 y(and)36 b(could)g(b)s(e)g(considered)g(as)g (the)h(b)s(est)f(w)m(a)m(y)h(out)f(un)m(til)f(drastic)g(impro)m(v)m (emen)m(ts)h(in)g(theories)118 5023 y(is)c(ac)m(hiev)m(ed.)118 5261 y(T)-8 b(o)m(w)m(ards)37 b(the)e(neutron)h(drip)e(line,)h(w)m(e)h (ha)m(v)m(e)g(seen)h(that)e(the)g(ab)s(o)m(v)m(e)h(pro)s(cedure)g (fails)d(b)s(ecause)118 5382 y(of)43 b(the)g(imp)s(ortan)m(t)f(div)m (ergences)i(among)e(theories.)76 b(This)43 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b(result)e(of)h(these)h(analyses)f(sho)m(w)m(ed)i (that,)f(based)f(on)g(existing)f(mo)s(dels,)h(the)h(medium)d(range)118 1606 y(extrap)s(olations)k(are)i(reliable)e(while)h(extrap)s(olations)f (to)m(w)m(ard)i(drip)f(lines)g(\(far)g(extrap)s(olations\))118 1726 y(are)d(to)g(b)s(e)g(tak)m(en)i(with)d(m)m(uc)m(h)i(care)g(un)m (till)d(further)i(impro)m(v)m(emen)m(ts)g(in)g(the)g(theories)h(mak)m (e)f(them)118 1847 y(congruen)m(t)34 b(in)d(these)j(regions.)118 2085 y(Presen)m(tly)-8 b(,)43 b(the)d(metho)s(ds)g(for)f(close)g(and)h (medium-range)e(extrap)s(olations)g(are)h(de\014ned)i(and)118 2206 y(tested.)60 b(Serial)36 b(pro)s(duction)h(of)h(suc)m(h)h (predictions)e(is)g(the)i(next)f(step,)i(but)e(that)g(will)d(require) 118 2326 y(m)m(uc)m(h)d(care)f(and)h(time.)41 b(Close)31 b(extrap)s(olations)f(will)f(b)s(e)i(pro)s(duced)h(v)m(ery)h(so)s(on)e (to)g(b)s(e)g(included)118 2446 y(in)48 b(the)h(next)h(table)e(of)g (exp)s(erimen)m(tal)g(masses.)92 b(Medium-range)48 b(extrap)s(olations) f(ma)m(y)h(b)s(e)118 2567 y(ev)-5 b(aluated)39 b(and)g(en)m(ter)i(a)e (sp)s(ecial)f(table,)i(if)e(strong)i(in)m(terest)g(for)e(astroph)m (ysics)j(is)e(expressed.)118 2687 y(Sp)s(ecial)21 b(care)i(will)d(b)s (e)i(tak)m(en)i(to)d(ensure)j(the)f(con)m(tin)m(uit)m(y)f(prop)s(ert)m (y)h(of)f(the)h(Surface)g(of)f(Masses)46 b(at)118 2808 y(the)32 b(b)s(order)f(b)s(et)m(w)m(een)i(the)e(three)h(regions:)43 b(exp)s(erimen)m(tal)30 b(masses,)i(close)f(extrap)s(olations)e(and)118 2928 y(medium-range)i(extrap)s(olations.)118 3260 y Fa(References)118 3479 y Fp([76Lir])92 b(S.)33 b(Liran)f(and)g(N.)h(Zeldes,)g(1975)e (Mass)j(Predictions,)e(ADNDT)h Fk(17)f Fp(\(1976\))g(431.)118 3623 y([81Aud])49 b(G.)32 b(Audi,)h(PhD)f(thesis,)h(Univ)m(ersit)m (\023)-46 b(e)33 b(de)g(P)m(aris-Sud,)g(Orsa)m(y)g(\(1981\),)f (unpublished.)118 3766 y([84Hau])49 b(P)-8 b(.)28 b(E.)g(Haustein,)g (Pro)s(c.)g(7-th)f(In)m(t.)h(Conf.)g(on)f(A)m(tomic)g(Masses)i(and)f(F) -8 b(undam.)27 b(Const.)489 3886 y(AMCO-7,)33 b(Darmstadt)e(1984,)h(O.) h(Klepp)s(er)f(ed.,)h(p.413.)118 4030 y([85Bos])63 b(K.)33 b(Bos,)g(G.)f(Audi)g(and)h(A.)f(H.)h(W)-8 b(apstra,)33 b(Nucl.)f(Ph)m(ys.)j Fk(A432)d Fp(\(1985\))g(140.)118 4173 y([88Com])48 b(E.)33 b(Coma)m(y)-8 b(,)33 b(I.)f(Kelson)h(and)f (A.)h(Zidon,)f(in)f([88Hau])i(p.235.)118 4317 y([88Hau])49 b(P)-8 b(.)25 b(E.)h(Haustein,)h(1986-1987)c(A)m(tomic)h(Mass)j (Predictions,)g(ADNDT)e Fk(39)g Fp(\(1988\))f(185.)118 4462 y([88Jan])66 b(J.)33 b(J\177)-49 b(anec)m(k)m(e)35 b(and)d(P)-8 b(.)33 b(J.)g(Masson,)h(in)e([88Hau)o(])h(p.265.)118 4606 y([88Mol])53 b(P)-8 b(.)33 b(M\177)-49 b(oller)31 b(and)i(J.)g(R.)f(Nix,)g(in)g([88Hau])h(p.213.)118 4749 y([88Sat])78 b(L.)33 b(Satpath)m(y)g(and)g(R.)f(C.)h(Na)m(y)m(ak,)h(in) e([88Hau])g(p.241.)118 4892 y([88W)-8 b(ap])49 b(A.)32 b(H.)h(W)-8 b(apstra,)33 b(G.)f(Audi)g(and)h(R.)f(Ho)s(ekstra,)i(in)d ([88Hau])i(p.281.)118 5036 y([90Hau])49 b(P)-8 b(.)23 b(E.)g(Haustein,)i(Exotic)d(Nuclear)h(Sp)s(ectroscop)m(y)-8 b(,)26 b(W.)d(C.)g(McHarris)g(editor,)h(Plen)m(um)489 5156 y(Press,)35 b(New)e(Y)-8 b(ork,)33 b(1990.)118 5299 y([92Duf)7 b(])53 b(J.)33 b(Du\015o,)f(submitted)h(to)f(Nucl.)g(Ph)m (ys.,)j(Marc)m(h)e(1992.)118 5443 y([92Gor])55 b(S.)25 b(Goriely)e(and)i(M.)h(Arnould,)g(submitted)e(to)h(Astron.)g(Astroph)m (ys.,)j(F)-8 b(ebruary)25 b(1992.)p eop %%Page: 8 8 8 7 bop 118 407 a Fp([92P)m(ea])64 b(M.)32 b(P)m(earson)g(and)f(F.)g(T) -8 b(ondeur,)32 b(priv)-5 b(ate)31 b(comm)m(unication)d(and)j(Y.)h(Ab)s (oussir,)f(J.)g(M.)489 527 y(P)m(earson,)j(A.)f(K.)f(Dutta,)g(F.)h(T)-8 b(ondeur,)33 b(preprin)m(t.)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF

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