%!PS-Adobe-2.0 %%Creator: dvipsk 5.58e Copyright 1986, 1994 Radical Eye Software %%Title: bernex.dvi %%Pages: 19 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%EndComments %DVIPSCommandLine: dvips bernex %DVIPSParameters: dpi=300, comments removed %DVIPSSource: TeX output 1993.03.16:1535 %%BeginProcSet: tex.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 0]N /FBB[0 0 0 0]N /nn 0 N /IE 0 N /ctr 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b(108,)h(F-91405)h(Orsa)o(y)e(Campus,)h(F)l(rance)282 930 y Fs(Abstract.)24 b Fq(An)15 b("In)o(teractiv)o(e)f(Graphical")j (to)q(ol)g(has)f(b)q(een)f(built)h(for)f(observing)h(the)282 990 y Fp(Surfac)n(e)21 b(of)f(Masses)k Fq(and)c(making)h(close)f (extrap)q(olations.)34 b(The)20 b(predictions)h(of)e(13)282 1050 y(mo)q(dels)h(are)g(thoroughly)g(examined)f(with)h(that)g(to)q (ol,)h(their)e(predictiv)o(e)g(p)q(o)o(w)o(er)g(are)282 1110 y(ev)m(aluated,)i(and)f(the)e(coherences)h(of)g(these)g(13)h (predictions)h(are)e(studied,)h(allo)o(wing)282 1171 y(th)o(us)12 b(to)g(set-up)g(a)g(metho)q(d,)h(based)f(on)g(a)o(v)o (eraging)g(of)g(these)g(predictions,)h(for)f(medium-)282 1231 y(range)17 b(extrap)q(olations.)33 1532 y Fs(1.)28 b(In)n(tro)r(duction)33 1650 y Fq(One)17 b(ma)o(y)g(imagine)h(that)g (when)f(all)i(n)o(uclear)e(masses)h(are)f(displa)o(y)o(ed)h(as)f(a)h (function)g(of)f(N)g(and)h(Z,)33 1710 y(one)i(w)o(ould)h(obtain)g(a)f ("surface")h(in)f(a)h(3-dimensional)h(space.)32 b(A)o(t)19 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b(v)m(ariet)o(y)f(of)h(presen)o (tations)h(will)g(b)q(e)f(p)q(ossible)h(for)f(these)f(deriv)m(ativ)o (es,)h(allo)o(wing)i(to)e(tak)o(e)f(care)g(of)33 2613 y(all)k(existing)g(constrain)o(ts)g(imp)q(osed)f(b)o(y)g(the)f(top)q (ology)j(of)e(the)f(mass)h(sheets.)31 b(As)19 b(examples)h(one)33 2673 y(ma)o(y)c(quote:)21 b(neutron)c(and)f(proton)i(separation)g (energies,)e Fo(\013)p Fq(-)g(and)h Fo(\014)s Fq(-deca)o(y)e(energies.) 89 2747 y Fn(1)122 2762 y Fm(IN2P3-Visitor,)g(on)e(lea)o(v)o(e)i(from)e (the)h(Institute)i(for)e(A)o(tomic)g(Ph)o(ysics,)h(Buc)o(harest.)955 2964 y Fq(1)p eop %%Page: 2 2 2 1 bop 149 50 a Fq(The)14 b(pioneering)h(w)o(ork)e(of)h(W)l(apstra)g ([85Bos])f(in)h(estimating)h(the)e(masses)h(of)g(some)f(unkno)o(wn)33 110 y(n)o(uclei)18 b(relied)f(mostly)h(on)f(observing)i(the)d (regularities)k(of)d(suc)o(h)g(deriv)m(ativ)o(es.)24 b(These)17 b(few)g(predic-)33 170 y(tions,)24 b(lab)q(elled)g ("systematics",)g(w)o(ere)d(used)h(primarily)h(as)f(a)h(means)e(to)i 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y(of)j(facilities)j(capable)d(of)h(deliv)o(ering)g (secondary)f(radioactiv)o(e)h(b)q(eams.)33 b(The)20 b(addressed)g(zone) g(of)33 954 y(in)o(terest)j(will)j(b)q(e)d(situated)h(in)g(the)f (immediate)h(vicinit)o(y)g(of)f(the)g(presen)o(t)g(limits)i(of)e (measured)33 1014 y(masses)17 b(\(close)g(extrap)q(olations\).)149 1083 y(Ho)o(w)o(ev)o(er)e(it)i(is)h(not)f(easy)g(to)f(obtain)j (reliable)f(extrap)q(olations)h(of)e(the)34 b Fp(Surfac)n(e)18 b(of)g(Masses)t Fq(.)33 1143 y(A)f(w)o(a)o(y)f(to)i(impro)o(v)o(e)e (this)i(reliabilit)o(y)l(,)g(is)g(to)f(observ)o(e)g(the)f(con)o(tin)o (uit)o(y)h(prop)q(ert)o(y)g(in)h(sev)o(eral)f(repre-)33 1203 y(sen)o(tations)f(of)g(the)e(v)m(arious)j(existing)f(deriv)m(ativ) o(es.)21 b(Therefore)15 b(an)g(in)o(teractiv)o(e)g(graphic)h(computer) 33 1264 y(program)h(w)o(as)g(dev)o(elop)q(ed)f(to)h(displa)o(y)g(sim)o (ultaneously)h(an)o(y)e(four)h(deriv)m(ativ)o(es)g(\(separation)h (ener-)33 1324 y(gies)d(S)153 1331 y Fl(n)177 1324 y Fq(,)e(S)231 1331 y Fr(2)p Fl(n)273 1324 y Fq(,)h(S)328 1331 y Fl(p)347 1324 y Fq(,)g(S)402 1331 y Fr(2)p Fl(p)440 1324 y Fq(,)g(deca)o(y)f(energies)h(Q)821 1331 y Fl(\013)846 1324 y Fq(,)g(Q)912 1331 y Fl(\014)935 1324 y Fq(,)g(Q)1001 1331 y Fr(2)p Fl(\014)1042 1324 y Fq(,)g(pairing)i(energies)e(\001)1456 1331 y Fl(nn)1501 1324 y Fq(,)g(\001)1570 1331 y Fl(np)1610 1324 y Fq(,)g(\001)1679 1331 y Fl(pp)1717 1324 y Fq(\))f(plotted)33 1384 y(as)19 b(a)f(function)g(of)g(an)o(y)g(of)g(the)f(parameters:)24 b(Z,)17 b(N,)g(A,)g(N-Z)g(or)h(2Z-N.)f(Con)o(tinous)j(lines)f(connect) 33 1444 y(\(optionally\))h(in)e(eac)o(h)e(plot)i(n)o(uclei)g(ha)o(ving) g(an)o(y)e(of)i(the)f(iso-prop)q(erties:)25 b(Z,)16 b(N,)g(A,)h(N-Z)f (or)i(2Z-N.)33 1504 y(One)h(suc)o(h)f(example)h(is)h(presen)o(ted)e(in) h(\014g.)30 b(1.)f(F)l(urthermore,)18 b(the)h(result)g(of)h(an)o(y)e (mass)i(form)o(ula)33 1564 y(can)14 b(b)q(e)g(sup)q(erimp)q(osed)h(on)g (the)e(same)h(\014gures.)21 b(In)o(teractiv)o(ely)l(,)12 b(an)o(y)i(p)q(oin)o(t)h(in)f(an)o(y)g(diagram)h(can)f(b)q(e)33 1625 y(displaced)21 b(and)f(all)g(the)g(subsequen)o(t)e(c)o(hanges)i (in)g(the)f(c)o(hosen)g(diagram)i(\(paren)o(tages)e(included\))33 1685 y(as)g(w)o(ell)g(as)f(in)h(the)f(others)g(will)i(follo)o(w.)29 b(Also)18 b(new)g(p)q(oin)o(ts)i(ma)o(y)d(b)q(e)h(created)g(in)h(an)o (y)f(of)g(the)g(four)33 1745 y(c)o(hosen)e(represen)o(tations)h(and)g (will)h(sho)o(w)f(up)f(ev)o(erywhere.)149 1814 y(This)26 b Fs("In)n(teractiv)n(e)h(Graphical")f Fq(to)q(ol)f(enforces)f(and)g (extends)g(th)o(us)g(the)g(metho)q(d)g(of)33 1874 y(W)l(apstra)14 b(and)f(no)o(w)h(allo)o(ws)g(us)f(to)h(mak)o(e)d(reliable)k(close)e (extrap)q(olations)i(starting)g(from)d(the)h(kno)o(wn)33 1934 y(masses.)21 b(It)12 b(will)j(do)f(of)f(course)g(ev)o(en)f(b)q (etter)h(for)g(in)o(terp)q(olations.)23 b(Ho)o(w)o(ev)o(er,)12 b(one)h(should)i(note)e(that)33 1994 y(it)g(has)f(a)h(v)o(ery)d (limited)j(\(if)g(an)o(y\))e(predictiv)o(e)h(capabilit)o(y)h(for)g 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y(masses)c(ma)o(y)f(render)g(the)g(predictions)i(of)f(a)g(giv)o (en)f(mass)h(form)o(ula)g(questionable)h(from)f(the)f(p)q(oin)o(t)33 2335 y(of)j(view)g(of)g(extrap)q(olations\(\014g.3\),)j(ev)o(en)17 b(if,)j(lik)o(e)e(in)i(the)e(presen)o(t)g(case,)h(it)g(is)h(a)f ("global")i(mo)q(del)33 2395 y(and)e(it)g(do)q(es)g(repro)q(duce)f (quite)g(w)o(ell)h(the)f(masses)h(of)g(n)o(uclei)f(close)h(to)g(the)f (b)q(ottom)h(of)f(the)g(v)m(alley)33 2455 y(of)h(stabilit)o(y)l(.)32 b(Though)20 b(not)f(illustrated,)j(let)d(us)g(men)o(tion)g(a)g(few)g (more)g(observ)m(ations:)29 b(only)19 b(few)33 2515 y(form)o(ulae)h ([88Jan)q(])f(repro)q(duce)g(the)h(subshell)h(closure)f(at)f(N=56,)i (the)e(w)o(ell)h(kno)o(wn)g(onset)f(of)h(de-)33 2575 y(formation)g(at)g(N=90,)f(the)g(shap)q(e)h(transition)h(at)e(N=108)h (and)f(the)g(drop)h(in)f(energy)g(at)g(N=152;)33 2636 y(some)c(irregularities)i(can)e(b)q(e)g(observ)o(ed)g(in)g([88Dus)q(])f (in)i(the)e Fo(\013)p Fq(-c)o(hains)j(connected)d(to)1636 2618 y Fr(125)p Fl(;)p Fr(126)1754 2636 y Fq(Sn)h(and)33 2696 y(around)20 b(A=185;)h(there)d(is)i(an)f(exceedingly)g(strong)h(o) o(v)o(erbinding)g(just)f(b)q(efore)g(shell)h(closures)g(in)33 2756 y(Spanier)c(and)f(Johansson's)h(liquid-drop)h(form)o(ula)f([88Spa) q(];)e(the)g(predictions)i(of)f(T)l(ac)o(hibana)h(et)f(al.)33 2816 y([88T)l(ac)q(])g(are)h(the)f(ones)h(that)g(repro)q(duce)g(the)f (b)q(est)h(the)f(smo)q(othness)i(prop)q(ert)o(y)f(of)g(the)32 b Fp(Surfac)n(e)17 b(of)955 2964 y Fq(4)p eop %%Page: 5 5 5 4 bop 165 1415 a Fk(Figure)17 b(3.)23 b Fj(Same)15 b(as)h(in)g(\014g.)23 b(2)16 b(for)f(another)h(prediction)g([88Sat)o (].)22 b(A)o(t)16 b(the)g(b)q(ottom)e(of)i(the)165 1471 y(v)m(alley)j(of)g(stabilit)o(y)e(the)j(mo)q(del)e(is)h(quite)g(close)g (to)g(the)h(exp)q(erimen)o(tal)e(v)m(alues,)i(and)g(giv)o(es)165 1528 y(consequen)o(tly)13 b(a)g(go)q(o)q(d)g(\014t)g(\(see)h(T)l(ables) f(1)g(and)g(2\).)19 b(Only)14 b(when)f(departing)g(from)f(the)h(kno)o (wn)165 1584 y(masses)8 b(do)j(v)o(ery)f(strong)f(oscillations)f(o)q (ccur,)j(rendering)g(its)e(predictions)h(questionable)g(when)165 1641 y(medium-range)17 b(or)j(far)f(extrap)q(olations)f(are)h (considered,)i(ev)o(en)f(though)g(it)f(is)g(a)h("global")165 1697 y(mo)q(del.)33 1859 y Fp(Masses)t Fq(,)e(only)g(few)g (irregularities)i(deserv)o(e)c(atten)o(tion,)j(at)f(N=136)g(and)g (N=156)g(for)g(example)g(or)33 1919 y(at)h(N=109,)h(where)f(isotones)h (b)q(elo)o(w)g(Z=73)g(are)e(underb)q(ound)i(whereas)g(those)f(ab)q(o)o (v)o(e)g(Z=73)g(are)33 1980 y(o)o(v)o(erb)q(ound;)h(strong)g (underbinding)h(of)e(n)o(uclei)g(around)h(A=215)g(and)f(around)1542 1962 y Fr(195)1597 1980 y Fq(F)l(r)g(are)g(eviden)o(t)33 2040 y(in)c(b)q(oth)h(M\177)-24 b(oller)15 b(and)g(Nix)g([88Mol)q(])f (and)h(M\177)-24 b(oller)15 b(et)f(al.)22 b([88MMST];)14 b(Du\015o's)h(calculation)i([92Duf)q(])33 2100 y(manifests)j (irregularities)h(for)e(n-ric)o(h)g(n)o(uclei)g(b)q(elo)o(w)g(N=50,)g (for)g(the)g(ligh)o(t)g(rare-earth,)h(the)e(ligh)o(t)33 2160 y(actinides)k(and)f(for)g(the)f(N-Z=45)h(n)o(uclei;)h(Liran)g(and) f(Zeldes)g([76Lir)q(])f(displa)o(y)i(a)f(quite)f(smo)q(oth)33 2220 y Fp(Surfac)n(e)i(of)g(Masses)j Fq(and)c(go)q(o)q(d)i(con)o(tin)o (uit)o(y)e(through)h(shell)g(closures;)h(the)e(ETFSI)g(mo)q(del)h (\(ex-)33 2281 y(tended)16 b(Thomas-F)l(ermi)g(plus)h(Strutinsky)f(in)o (tegral\))h([92P)o(ea)q(])e(also)i(repro)q(duces)f(w)o(ell)h(the)e (general)33 2341 y(smo)q(oth)g(b)q(eha)o(vior)g(of)f(the)28 b Fp(Surfac)n(e)16 b(of)e(Masses)t Fq(,)g(but)g(not)g(so)g(m)o(uc)o(h)f (the)g("Wigner")j(e\013ect)d(at)h(N=Z)33 2401 y(\(\014gure)j(9\).)149 2469 y(Similarly)d(to)e(the)f(impro)o(v)o(emen)o(ts)f(induced)i(b)o(y)f (the)g(analysis)i(of)f(P)l(.)f(Haustein)h([84Hau)q(])f(on)g(the)33 2530 y(mass)16 b(mo)q(dels,)f(w)o(e)g(hop)q(e)h(that)f(the)g(t)o(yp)q (e)f(of)i(analysis)h(dev)o(elop)q(ed)e(here,)f(based)h(on)h(the)f (deriv)m(ativ)o(es)33 2590 y(of)20 b(the)40 b Fp(Surfac)n(e)20 b(of)h(Masses)t Fq(,)e(will)j(help)d(impro)o(ving)i(furthermore)e(the)g (existing)i(mo)q(dels.)32 b(Suc)o(h)33 2650 y(impro)o(v)o(emen)o(ts)20 b(ma)o(y)g(re\015ect)g(p)q(ositiv)o(ely)j(on)e(the)g(predictiv)o(e)g(p) q(o)o(w)o(er)g(of)g(future)g(v)o(ersions)g(of)g(the)33 2710 y(mo)q(dels.)955 2964 y(5)p eop %%Page: 6 6 6 5 bop 165 1352 a Fk(Figure)16 b(4.)k Fj(Same)14 b(as)h(in)g(\014g.)20 b(2)15 b(for)f(the)i(predictions)e(of)h(Coma)o(y)e(et)i(al.)k([88Com)n (].)165 2805 y Fk(Figure)d(5.)k Fj(Same)14 b(as)h(in)g(\014g.)20 b(2)15 b(for)f(the)i(predictions)e(of)h(T)l(ac)o(hibana)g(et)g(al.)k ([88T)l(ac)o(].)955 2964 y Fq(6)p eop %%Page: 7 7 7 6 bop 165 1352 a Fk(Figure)16 b(6.)k Fj(Same)14 b(as)h(in)g(\014g.)20 b(2)15 b(for)f(the)i(predictions)e(of)h(Masson)f(and)i(J\177)-23 b(anec)o(k)o(e)15 b([88Mas)o(].)165 2805 y Fk(Figure)h(7.)k Fj(Same)14 b(as)h(in)g(\014g.)20 b(2)15 b(for)f(the)i(predictions)e(of) h(Du\015o)g([92Duf)o(].)955 2964 y Fq(7)p eop %%Page: 8 8 8 7 bop 165 1352 a Fk(Figure)16 b(8.)k Fj(Same)14 b(as)h(in)g(\014g.)20 b(2)15 b(for)f(the)i(predictions)e(of)h(Liran)g(and)g(Zeldes)h([76Lir)n (].)165 2805 y Fk(Figure)g(9.)k Fj(Same)14 b(as)h(in)g(\014g.)20 b(2)15 b(for)f(the)i(predictions)e(of)h(P)o(earson)f(et)i(al.)j([92P)o (ea)n(].)955 2964 y Fq(8)p eop %%Page: 9 9 9 8 bop 33 50 a Fs(3.)28 b(Extrap)r(olating)19 b(F)-5 b(urther)18 b(Out)33 168 y Fq(A)23 b(di\013eren)o(t)h(situation)i(is)e (encoun)o(tered)e(when)i(predictions)h(are)e(necessary)h(for)f(astroph) o(ysical)33 228 y(calculations)f(of)e(r-pro)q(cess)g(n)o(ucleosyn)o (thesis,)g(i.e.)31 b(to)o(w)o(ards)20 b(the)f(neutron)h(drip)g(line.)31 b(With)20 b(the)33 288 y(exception)i(of)f(ligh)o(t)i(masses,)g(the)e (neutron)h(drip)g(line)g(lies)g(far)g(a)o(w)o(a)o(y)f(from)h(the)f (last)h(measured)33 348 y(masses;)16 b(therefore)g(the)g(extrap)q (olations)j(to)o(w)o(ard)e(these)f(regions)h(will)h(b)q(e)f(called)g Fs(far)i(extrap)r(ola-)33 408 y(tions)p Fq(.)i(One)14 b(should)i(note)e(that)h(the)f(w)o(ord)g(far)h(in)g(this)g(case)f(do)q (es)h(not)g(refer)e(to)h(the)g(distance)h(from)33 469 y(the)h(b)q(ottom)h(of)f(the)g(v)m(alley)h(of)f(stabilit)o(y)l(,)h(but) f(rather)g(from)g(the)g(limits)i(presen)o(tly)d(de\014ned)h(b)o(y)f (the)33 529 y(n)o(uclei)i(with)g(kno)o(wn)f(masses,)h(whic)o(h)f(are)g (already)h("far)g(from)g(stabilit)o(y".)149 597 y(Although)22 b(the)e(metho)q(d)g(outlined)i(in)f(the)f(previous)h(section)g(p)q (ermits)f(to)h(go)g(b)q(ey)o(ond)f(the)33 657 y(usual)k(in)o(terp)q (olations,)i(the)d(limits)g(of)g(the)f(p)q(ossibili)q(ties)k(will)e(b)q (e)e(reac)o(hed)g(quite)g(so)q(on,)j(as)e(the)33 718 y(reliabilit)o(y)14 b(will)g(decrease)d(at)h(eac)o(h)f(step.)19 b(In)12 b(order)f(to)h(go)h(further)e(out,)h(some)g(ph)o(ysical)h(bac)o (kground)33 778 y(is)k(needed,)e(whic)o(h)i(can)f(b)q(e)h(pro)o(vided)f (b)o(y)g(the)g(existing)h(theories.)149 846 y(Before)h(doing)j(so,)e (the)g(predictiv)o(e)f(p)q(o)o(w)o(er)h(of)g(the)g(mo)q(dels)g(should)h (b)q(e)f(ev)m(aluated)h(so)f(as)h(to)33 907 y(serv)o(e)d(ev)o(en)o (tually)h(to)h(assign)h(w)o(eigh)o(ts)f(in)g(a)f(w)o(eigh)o(ted)g(a)o (v)o(erage.)27 b(Ho)o(w)18 b(far)h(one)f(can)g(go)h(this)h(w)o(a)o(y)33 967 y(will)f(result)f(from)f(an)g(analysis)i(of)f(the)e(coherences)h (and)g(div)o(ergences)g(among)h(the)f(predictions)h(of)33 1027 y(di\013eren)o(t)f(mo)q(dels.)149 1095 y(One)25 b(should)h(distinguish)h(t)o(w)o(o)d(main)h(t)o(yp)q(es)g(among)g(the)f (existing)i(mo)q(dels)f(for)g(n)o(uclear)33 1156 y(masses:)c(the)14 b("lo)q(cal")j(mo)q(dels)e(that)f(use)g(lo)q(cal)j(relations)f(and)e (the)g("global")j(ones)e(that)g(start)f(from)33 1216 y(a)g(n)o(uclear)g(mo)q(del)h(calculation)h(done)e(with)h(di\013eren)o (t)f(ingredien)o(ts)h(of)f(phenomenology)l(.)22 b(F)l(rom)13 b(this)33 1276 y(second)k(t)o(yp)q(e,)e(the)h(mo)q(del)h(of)f(P)o (earson)h(et)f(al.)22 b([92P)o(ea])16 b(has)h(b)q(een)f(strongly)i(adv) o(o)q(cated)f(for)f(astro-)33 1336 y(ph)o(ysical)k(purp)q(oses)g ([92Gor)q(].)29 b(A)18 b(further)h(distinction)i(within)f(the)f ("global")j(mo)q(dels)e(will)h(b)q(e)e(of)33 1396 y(use)14 b(in)g(the)f(presen)o(t)g(w)o(ork)g(for)h(those)f(predictions)i(ha)o (ving)f(some)g(of)f(their)h(parameters)f(\014tted)h(sepa-)33 1457 y(rately)h(for)f(the)g(di\013eren)o(t)g(regions)i(of)e(the)g(c)o (hart)g(of)g(n)o(uclei;)h(they)e(will)j(b)q(e)f(called)g("global-regio) q(nal)q(")33 1517 y(mo)q(dels.)21 b(While)14 b(for)f(the)f("lo)q(cal")k (mo)q(dels,)e(one)f(ma)o(y)f(exp)q(ect)g(that)h(a)g(gradual)i (deterioration)f(migh)o(t)33 1577 y(app)q(ear)j(when)f(getting)g(to)g (far)g(outer)g(masses,)g(for)f(the)h("global")j(ones,)c(in)h (principle,)h(ev)o(ery)d(ph)o(ys-)33 1637 y(ical)i(premise)f(is)h(con)o (tained)f(so)h(that,)f(ev)o(en)f(if)h(\014tted)g(to)g(a)h(particular)g (sample,)g(one)f(should)h(exp)q(ect)33 1697 y(not)f(to)q(o)h(large)g (div)o(ergences.)k(This)c(should)g(b)q(e)f(esp)q(ecially)i(true)d(for)h (the)g(theories)g(that)g(use)g(a)g(rela-)33 1758 y(tiv)o(ely)g(small)h (n)o(um)o(b)q(er)e(of)h(parameters.)21 b(In)15 b(order)g(to)g(con)o (vince)f(ourselv)o(es)h(of)h(this)f(last)h(statemen)o(t,)33 1818 y(w)o(e)h(tried)g(an)g("o)o(v)o(eradjustmen)o(t")f(for)h(eac)o(h)f (of)i(the)e(mo)q(dels)i(in)f(a)g(small)i(region)e(of)g(the)g(c)o(hart)f (\(the)33 1878 y(f-p)21 b(shell)g(for)f(b)q(oth)h(N)f(and)g(Z\).)g(T)l (o)g(the)g(mass)h(v)m(alues)g Fo(m)1141 1885 y Fl(th)1176 1878 y Fq(\()p Fo(N)r(;)8 b(Z)t Fq(\),)20 b(predicted)g(b)o(y)g(a)g(mo) q(del,)i(w)o(e)33 1938 y(added)15 b(in)h(a)f(rather)g(arti\014cial)i(w) o(a)o(y)e(six)g(terms:)20 b Fo(m)974 1945 y Fl(th)1009 1938 y Fq(\()p Fo(N)r(;)8 b(Z)t Fq(\))g(+)g Fo(aN)1271 1920 y Fr(2)1299 1938 y Fq(+)g Fo(bZ)1403 1920 y Fr(2)1431 1938 y Fq(+)g Fo(cN)d(Z)13 b Fq(+)8 b Fo(dN)14 b Fq(+)8 b Fo(eZ)k Fq(+)c Fo(f)33 1998 y Fq(and)16 b(minimized)g(the)f(distance) h(b)q(et)o(w)o(een)f(the)g(new)g(theoretical)33 b Fp(Surfac)n(e)17 b(of)f(Masses)j Fq(and)d(the)g(ex-)33 2058 y(p)q(erimen)o(tal)e(one)g (with)g(resp)q(ect)f(to)h(the)f(parameters)g Fo(a)5 b Fh(\000)g Fo(f)g Fq(.)21 b(The)13 b(results)h(w)o(ere)f(sp)q(ectacular) h(in)g(t)o(w)o(o)33 2119 y(resp)q(ects:)27 b(the)19 b(surfaces)g(of)g (the)g(theoretical)h(masses)f(near)g(the)g(b)q(ottom)h(of)f(the)g (stabilit)o(y)h(v)m(alley)33 2179 y(w)o(ere)12 b(to)q(o)j(w)o(ell)e (adjusted)h(to)f(the)g(exp)q(erimen)o(tal)g(surface)g(\(an)h(adjustmen) o(t)f(with)h(a)f(to)q(o)h(lo)o(w)g Fo(\037)1779 2161 y Fr(2)1812 2179 y Fq(is)g(as)33 2239 y(unreliable)i(as)f(one)f(with)i (a)e(to)q(o)i(large)f Fo(\037)781 2221 y Fr(2)800 2239 y Fq(\),)f(whereas)h(outside)g(the)f(domain)h(of)g(kno)o(wn)f(masses,)h (but)33 2299 y(still)k(inside)g(the)e(f-p)g(region,)h(the)f(surfaces)g (pro)o(vided)h(b)o(y)f(the)g(v)m(arious)h("o)o(v)o(eradjusted")g(form)o (ulae)33 2359 y(displa)o(y)o(ed)c(m)o(uc)o(h)e(stronger)i(div)o 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y(of)h(Liran)h(and)e(Zeldes)h([76Lir)q(])f(published)i(in)f(1976,)h (since)e(the)g(1986)i(compilation)h(did)e(not)f(include)33 841 y(an)o(y)21 b("semi-empirical)i(shell)f(mo)q(del)f(form)o(ula".)37 b(The)21 b(n)o(um)o(b)q(ers)f(that)h(will)i(b)q(e)e(giv)o(en)g(b)q(elo) o(w)h(for)33 901 y([76Lir)r(])17 b(will)i(su\013er)f(comparativ)o(ely)g (from)f(\014tting)i(to)f(m)o(uc)o(h)e(older)j(data,)f(and)g(the)f (results)i(of)e(the)33 961 y(presen)o(t)g(analysis)j(for)e(this)h(mo)q (del)f(should)h(b)q(e)f(considered)g(with)h(sp)q(ecial)g(care.)26 b(In)17 b(selecting)h(the)33 1021 y(mo)q(dels,)e(w)o(e)f(follo)o(w)o (ed)h(the)e(same)h(p)q(olicy)i(outlined)f(b)o(y)f(Haustein)g([90Hau)q (])f(and)i(did)f(not)h(therefore)33 1081 y(consider)f(the)g(mo)q(dels)g (of)g(P)o(ap)q(e)g(and)g(An)o(ton)o(y)f(or)h(of)g(Dussel,)g(Caurier)h (and)f(Zuk)o(er,)e(whic)o(h)i("do)h(not)33 1142 y(con)o(tain)h (predictions)h(that)f(co)o(v)o(er)e(large)i(regions)g(far)g(from)f (stabilit)o(y")i([90Hau)q(].)149 1210 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1289 y(35)1582 1277 y Fj(Br)1632 1284 y Fr(28)1688 1277 y Fj(is)18 b(the)165 1334 y(last)12 b(isotop)q(e)g(to)h(ful\014ll)f (the)i(conditions)e(for)h(a)o(v)o(eraging)e(\(i.e.)18 b(6)13 b(accepted)h(predictions\).)19 b Fb(M)5 b(P)165 1390 y Fj(is)18 b(the)h(w)o(eigh)o(ted)f(a)o(v)o(erage)g(of)g (predicted)h(masses)f(with)g(its)g(error)g Fb(\033)1383 1397 y Fl(p)1422 1390 y Fj(within)g(brac)o(k)o(ets,)g(in)165 1447 y(MeV,)c Fb(w)q(v)r(f)5 b Fj(2)14 b(is)g(the)h(normalized)e Fb(\037)793 1430 y Fr(2)813 1447 y Fj(,)h(denoted)i Fb(\037)1040 1430 y Fr(2)1040 1458 y Fl(\027)1076 1447 y Fj(in)f(the)g(text,)f Fb(er)q(r)h Fj(is)f(the)h(external)f(error,)165 1503 y(i.e.)19 b Fb(\033)269 1510 y Fl(p)299 1503 y Fa(\002)10 b Fb(\037)372 1510 y Fl(\027)394 1503 y Fj(,)15 b(in)g(MeV.)149 1678 y Fq(No)o(w)j(that)h(the)e(predictiv)o(e)h(p)q(o)o(w)o(ers)g(of)h (the)e(mo)q(dels)i(ha)o(v)o(e)f(b)q(een)g(ev)m(aluated,)g(the)g (results)h(of)33 1738 y(the)h(ab)q(o)o(v)o(e)g(analysis)i(could)f(b)q 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y Fq(,)17 b(i.e.)24 b(the)17 b(comp)q(ensated)h (linear)g(deviation)h(for)f(the)f(set)g(of)g(mea-)33 2160 y(sured)h(masses)g(\(table)h(1)f(column)g(2\))g(times)g(the)f (square)h(of)g(the)g(corresp)q(onding)h(close)g(predictiv)o(e)33 2220 y(ratio)i(\(column)e(6\))h(with)g(a)g(limitation)i(to)d(1.5)h(MeV) e(due)h(to)h(the)f(observ)m(ation)i(ab)q(o)o(v)o(e.)30 b(The)20 b Fo(\033)1867 2202 y Fl(th)33 2280 y Fq(are)d(giv)o(en)g(in)h (the)f(last)h(column)g(of)f(table)h(1.)24 b(The)17 b(parab)q(olic)i (increase)e(with)h Fo(cpr)1570 2287 y Fl(i)1602 2280 y Fq(has)g(somewhat)33 2340 y(b)q(een)e(suggested)h(b)o(y)f(the)g(ev)o (olution)i(in)e(the)g(columns)h(7)g(and)g(8)g(in)g(table)f(2)h(and)g(b) o(y)f(the)g(c)o(haracter)33 2401 y(of)j(the)g(extrap)q(olations)i(w)o (e)e(are)g(in)o(terested)f(in,)i(namely)f Fp(b)n(eyond)g Fq(the)f("close")i(ones.)30 b(Ideograms)33 2461 y([92Pdg)q(])20 b(w)o(ere)g(pro)q(duced)h(for)g(four)f(complete)h(isotopic)h(series)f (in)g(the)f(f-p)h(region)g(\(Ni,)h(Br,)e(Mo)33 2521 y(and)h(Sn\))f (going)i(then)d(from)h(the)g(v)m(alley)h(of)f(stabilit)o(y)i(to)e(the)g (drip)g(lines.)34 b(A)19 b(few)h(examples)g(are)33 2581 y(sho)o(wn)15 b(in)f(\014gure)g(12.)21 b(Their)14 b(examination)i(sho)o (w)o(ed)d(that)h(the)g(disp)q(ersion)i(among)e(the)g(predictions)33 2641 y(from)i(di\013eren)o(t)g(mo)q(dels)h(increase)f(drastically)i (when)e(one)g(approac)o(hes)g(the)g(drip)g(lines.)22 b(Ho)o(w)o(ev)o(er,)33 2702 y(for)d(a)g(relativ)o(ely)g(large)g (region,)h(this)f(disp)q(ersion)i(is)e(within)h(reasonable)g(limits)g (\(the)f(normalised)33 2762 y Fo(\037)64 2744 y Fr(2)83 2762 y Fq(,)e(denoted)f Fo(\037)329 2744 y Fr(2)329 2774 y Fl(\027)350 2762 y Fq(,)h(close)g(to)g(unit)o(y\).)22 b(Under)16 b(the)g(conditions)j(ab)q(o)o(v)o(e,)d(the)g(a)o(v)o(erages) g(of)h(theoretical)33 2822 y(masses)i(for)f(399)i(n)o(uclei)e(in)h(the) f(f-p)h(shell)g(region)h(w)o(ere)d(calculated.)28 b(Only)19 b(three)f(n)o(uclei)g(sho)o(w)o(ed)943 2964 y(15)p eop %%Page: 16 16 16 15 bop 165 1188 a Fk(Figure)18 b(13.)26 b Fj(Di\013erences)17 b(b)q(et)o(w)o(een)g(the)g(predictions)g(of)g(t)o(w)o(o)e("lo)q(cal")h (relations:)22 b(Coma)o(y)l(,)165 1245 y(Kelson)16 b(and)g(Zidon)g ([88Com)m(])g(and)g(J\177)-23 b(anec)o(k)o(e)17 b(and)f(Masson)f ([88Jan])g(plotted)h(as)f(a)h(function)165 1301 y(of)d("neutrons)h (from)e(stabilit)o(y")g(for)h(5707)g(n)o(uclei.)19 b(The)14 b(strong)f(coherence)i(around)f(stabilit)o(y)165 1357 y(\()p Fb(N)5 b(F)h(S)14 b Fj(=)f(0\))i(is)f(due)i(to)e(the)h(v)o(ery)g (go)q(o)q(d)g(agreemen)o(t)e(of)h(b)q(oth)i(predictions)e(with)g(the)h (kno)o(wn)165 1414 y(masses.)j(Div)o(ergences)d(exceeding)h(10)e(MeV)h (start)f(at)h Fb(N)5 b(F)h(S)15 b Fj(=)e(+14)i(on)g(the)g(n-ric)o(h)g (side.)33 1585 y Fq(more)20 b(than)g(t)o(w)o(o)g(standard)h (deviations.)34 b(Though)21 b(the)f(presen)o(t)f(study)i(w)o(as)f (limited)h(to)f(the)g(f-p)33 1645 y(region,)e(this)f(do)q(es)h(not)f (a\013ect)g(the)f(generalit)o(y)i(of)f(our)g(conclusions.)24 b(Av)o(eraging)18 b(p)q(erformed)e(o)o(v)o(er)33 1705 y(the)i(whole)h(c)o(hart)f(with)h(the)f(same)g(conditions)j(yielded)d (results)h(for)f(5018)i(n)o(uclei)f(of)f(whic)o(h)h(4227)33 1765 y(had)e(a)g(disp)q(ersion)h(b)q(elo)o(w)f(1)g(MeV;)e(they)g(span)i (v)m(alues)g(of)g Fo(N)5 b(F)i(S)19 b Fq(from)d(-20)h(to)g(+20.)22 b(These)16 b(crude)33 1825 y(results)h(will)h(require)e(careful)h (individual)i(and)e(global)h(analysis.)149 1894 y(T)l(o)e(get)f(an)h(o) o(v)o(erall)f(idea)h(ab)q(out)g(the)f(zone)g(where)g(di\013eren)o(t)g (predictions)h(are)g(still)g(coheren)o(t,)33 1954 y(one)g(ma)o(y)e (apply)i(the)f Fo(N)5 b(F)i(S)18 b Fq(diagrams)f(to)e(compare)g(an)o(y) h(t)o(w)o(o)f(theoretical)h(predictions,)g(similarly)33 2014 y(to)k(the)e(analysis)k(of)d([92Gor)q(].)29 b(With)20 b(these)f(diagrams)h(one)g(could)g(also)g(observ)o(e)f(the)g (deviations)33 2074 y(of)i(a)f(giv)o(en)h(mo)q(del)g(from)f(the)g 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b(but)h(m)o(uc)o(h)e(atten)o(uated)i(for)g(those)g ("global")j(mo)q(dels)d(that)g(mak)o(e)f(predictions)i(in)f(a)g(large) 33 2556 y(enough)i(domain)g(\(\014g.)24 b(14\).)g(The)17 b Fo(N)5 b(F)i(S)19 b Fq(analysis)h(con\014rmed)c(the)h(conclusion)i (of)e(the)g(statistical)33 2616 y(treatmen)o(t)10 b(that)i(going)h(b)q (ey)o(ond)e Fh(j)p Fo(N)5 b(F)i(S)s Fh(j)13 b Fq(=)h(20)e(is)f (hazardous)i(for)e(the)g(time)g(b)q(eing.)21 b(These)11 b(n)o(um)o(b)q(ers)33 2676 y(could)h(de\014ne)e(the)h(fron)o(tier)g (separating)i(the)d(")p Fs(medium-range)j(extrap)r(olations)p Fq(")e(from)g(the)g(")p Fs(far)33 2737 y(extrap)r(olations)p Fq(".)149 2805 y(Restricting)16 b(ourselv)o(es)f(to)g(these)g(orien)o (tational)i(limits,)f(the)f(a)o(v)o(eraged)f(v)m(alues)i(obtained)g (for)943 2964 y(16)p eop %%Page: 17 17 17 16 bop 165 1188 a Fk(Figure)23 b(14.)37 b Fj(Same)20 b(as)h(in)g(\014g.)37 b(13)21 b(for)f(t)o(w)o(o)g("global")f (predictions:)31 b(T)l(ac)o(hibana)20 b(et)h(al.)165 1245 y([88T)l(ac)o(])f(and)g(P)o(earson)g(et)g(al.)35 b([92P)o(ea)o(])20 b(for)g(6194)f(n)o(uclei.)36 b(Coherence)21 b(around)f(stabilit)o(y)165 1301 y(\()p Fb(N)5 b(F)h(S)14 b Fj(=)f(0\))g(is)g(naturally)f(w)o(eak)o(er)g(than)h(with)g(lo)q(cal)f (relations.)18 b(Div)o(ergences)13 b(exceeding)h(10)165 1357 y(MeV)g(start)e(at)i Fb(N)5 b(F)h(S)15 b Fj(=)e(+25)h(on)f(the)i (n-ric)o(h)f(side.)19 b(Only)14 b(few)g(di\013erences)g(exceed)h(20)f (MeV.)165 1414 y(Note)f(that)g(the)h("width")f(of)g(the)h(scattering)f (plot)g(is)g(almost)e(constan)o(t)i(for)g(the)h(whole)f(range)165 1470 y(of)h Fb(N)5 b(F)h(S)s Fj(.)33 1632 y Fq(the)16 b(medium-range)g(predictions)h(can)f(b)q(e)g(compared)f(with)i(the)e (exp)q(erimen)o(tal)h(masses)g(using)h(the)33 1692 y("In)o(teractiv)o (e)j(Graphical")j(to)q(ol)f(describ)q(ed)f(at)g(the)f(b)q(eginning.)36 b(An)20 b(example)h(is)g(sho)o(wn)g(in)g(\014g.)33 1753 y(15.)36 b(The)21 b(smo)q(oth)g(c)o(haracter)g(of)g(the)f(curv)o(es)g 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b(This)20 b(e\013ect)f(can)g(b)q (e)h(limited)g(if)g(the)f("lo)q(cal")33 2672 y(mo)q(dels)14 b(are)f(not)h(used)f(in)h(the)f(far)g(extrap)q(olations,)j(for)d(man)o (y)g(of)g(the)g(reasons)h(outlined)h(ab)q(o)o(v)o(e.)20 b(T)l(o)33 2732 y(comp)q(ensate)14 b(the)f(resulting)i(imp)q(o)o(v)o (erishmen)o(t)e(in)h(mo)q(dels,)g(it)g(w)o(ould)g(b)q(e)g(highly)h (desirable)f(to)g(ha)o(v)o(e)33 2793 y(all)h("global")h(mo)q(dels)e (extend)f(their)g(predictions)h(up)g(to)f(the)g(neutron)g(drip)h(line.) 21 b(Esp)q(ecially)15 b(since,)33 2853 y(among)j(the)e("global")k(mo)q (dels,)d(the)f("global-regi)q(ona)q(l")k(form)o(ulae,)d(whic)o(h)f (require)h(the)f(existence)943 2964 y(17)p eop %%Page: 18 18 18 17 bop 165 1413 a Fk(Figure)24 b(15.)39 b Fj(Av)o(erage)21 b(v)m(alues)h(of)f(theories,)h(obtained)g(as)f(describ)q(ed)i(in)e(the) h(text,)g(are)165 1469 y(compared)17 b(to)g(the)h(exp)q(erimen)o(tal)e (masses)h(\(p)q(oin)o(ts,)g(error)g(bars)h(and)g(dashed)g(lines\))f(in) h(an)165 1525 y(S)190 1532 y Fr(2)p Fl(n)248 1525 y Fj(represen)o (tation)e(for)g(N=28-50.)25 b(The)18 b(smo)q(oth)d(c)o(haracter)h(of)h (the)g(curv)o(es)g(is)g(preserv)o(ed)165 1582 y(ev)o(en)g(for)f(outer)g (masses.)23 b(F)l(urther)16 b(smo)q(othing)f(of)h(these)h(a)o(v)o (erages)e(ma)o(y)g(b)q(e)i(considered)g(in)165 1638 y(the)c(pro)q (duction)g(phase)h(of)f(our)g(w)o(ork.)19 b(Extension)12 b(of)h(these)h(predictions)f(on)g(the)h(n-ric)o(h)f(side)165 1695 y(is)i(limited,)d(due)k(to)f(the)h(small)d(n)o(um)o(b)q(er)i(of)g (mo)q(dels)f(making)f(predictions)i(far)g(enough)h(from)165 1751 y(stabilit)o(y)l(.)33 1917 y Fq(of)f(measured)f(masses)h(in)g(ev)o (ery)e(shell)j(region)f(\(e.g.)20 b(Liran)c(and)f(Zeldes)g(or)g(T)l(ac) o(hibana)g(et)g(al.\),)f(will)33 1977 y(not)g(b)q(e)f(able,)h(in)g(man) o(y)f(places,)h(to)g(reac)o(h)e(the)h(neutron)h(drip)g(line,)g (reducing)g(th)o(us)f(their)g(usefulness)33 2037 y(for)k(far)f(extrap)q (olations.)33 2205 y Fs(4.)28 b(Conclusions)33 2323 y Fq(An)22 b("In)o(teractiv)o(e)e(Graphical")25 b(to)q(ol)e(has)g(b)q (een)e(dev)o(elop)q(ed)h(in)h(order)e(to)i(b)q(etter)e(scrutinize)h (the)33 2383 y Fp(Surfac)n(e)f(of)f(Masses)j Fq(and)c(exploit)i(its)e (con)o(tin)o(uit)o(y)h(prop)q(ert)o(y)f(for)g(making)h(close)g(extrap)q (olations.)33 2443 y(By)i(p)q(oin)o(ting)i(at)f(the)f(qualities)i(and)f (the)f(w)o(eaknesses)h(of)f(eac)o(h)g(mass)h(prediction,)i(the)d (\014gures)33 2503 y(could)h(directly)f(suggest)h(impro)o(v)o(emen)o (ts)e(to)h(the)g(form)o(ulae)g(and)h(could)g(help)f(their)g(authors)i (in)33 2563 y(questioning)g(some)e(parameters.)39 b(An)21 b(analysis)j(of)f(the)f(predictiv)o(e)f(p)q(o)o(w)o(er)h(of)h(v)m (arious)g(mo)q(dels)33 2623 y(has)d(b)q(een)f(p)q(erformed)g(as)h(w)o (ell)f(as)h(of)f(the)g(coherence)f(of)i(the)e(mo)q(dels)j(in)e (predicting)h(masses)g(far)33 2684 y(from)g(stabilit)o(y)l(.)35 b(The)20 b(result)h(of)f(this)h(analysis)i(sho)o(w)o(ed)d(that,)h (based)g(on)f(existing)i(mo)q(dels,)f(the)33 2744 y(medium)j(range)g (extrap)q(olations)i(are)e(reliable)h(while)g(extrap)q(olations)i(to)o (w)o(ard)d(drip)g(lines)h(\(far)33 2804 y(extrap)q(olations\))14 b(are)d(to)h(b)q(e)f(tak)o(en)g(with)h(m)o(uc)o(h)e(care)h(un)o(till)h (further)f(impro)o(v)o(emen)o(ts)f(in)i(the)f(theories)33 2864 y(mak)o(e)16 b(them)f(congruen)o(t)h(in)h(these)f(regions.)943 2964 y(18)p eop %%Page: 19 19 19 18 bop 149 50 a Fq(The)11 b(metho)q(ds)h(for)f(close)h(and)f (medium-range)h(extrap)q(olations)h(are)e(no)o(w)h(de\014ned)e(and)i (tested.)33 110 y(Serial)i(pro)q(duction)g(of)f(suc)o(h)g(predictions)h (is)f(the)g(next)f(step,)h(but)g(that)g(will)h(require)f(m)o(uc)o(h)e (care)i(and)33 170 y(time.)27 b(It)17 b(w)o(ould)i(b)q(e)g(in)o (teresting)f(to)h(ha)o(v)o(e)e(close)i(extrap)q(olations)i(pro)q(duced) d(v)o(ery)f(so)q(on)i(in)g(order)33 230 y(to)d(include)g(them)e(in)i (the)f(next)g(table)h(of)f(exp)q(erimen)o(tal)g(masses.)22 b(Medium-range)15 b(extrap)q(olations)33 291 y(will)i(b)q(e)e(ev)m (aluated)g(and)g(ma)o(y)g(en)o(ter)e(a)i(sp)q(ecial)i(table,)e(if)g (real)g(in)o(terest)g(is)g(expressed.)20 b(Sp)q(ecial)c(care)33 351 y(will)j(b)q(e)e(tak)o(en)f(to)h(ensure)g(the)g(con)o(tin)o(uit)o (y)g(prop)q(ert)o(y)f(of)h(the)35 b Fp(Surfac)n(e)18 b(of)g(Masses)j Fq(at)c(the)g(b)q(order)33 411 y(b)q(et)o(w)o(een)d (the)g(three)g(regions:)22 b(exp)q(erimen)o(tal)14 b(masses,)h(close)g (extrap)q(olations)j(and)d(medium-range)33 471 y(extrap)q(olations.)149 540 y(W)l(e)j(wish)h(to)g(express)e(our)i(gratitude)g(to)f(A.)g(H.)f(W) l(apstra,)i(M.)e(P)o(earson)i(and)f(A.)g(P)o(ap)q(e)g(for)33 600 y(critical)g(reading)f(of)g(this)g(pap)q(er.)33 771 y Fs(References)33 885 y Fj([63Bar])45 b(R.)12 b(C.)f(Barb)q(er,)i(W.)e (McLatc)o(hie,)g(R.)h(L.)g(Bishop,)g(P)l(.)f(V)l(an)h(Ro)q(okh)o(uyzen) h(and)f(H.)f(E.)h(Duc)o(kw)o(orth,)282 942 y Fi(Can.)j(J.)h(Phys.)f Fk(41)g Fj(\(1963\))f(1482.)33 1018 y([76Lir])59 b(S.)15 b(Liran)f(and)h(N.)f(Zeldes,)g(1975)f(Mass)h(Predict.,)f(S.)i(Maripuu)f (ed.,)g Fi(ADNDT)20 b Fk(17)15 b Fj(\(1976\))d(431.)33 1094 y([76My)o(e])33 b(W.)15 b(D.)f(My)o(ers,)h(in)g(1975)f(Mass)g (Predictions,)g(S.)h(Maripuu)g(ed.,)g Fi(ADNDT)21 b Fk(17)15 b Fj(\(1976\))e(411.)33 1171 y([81Aud])34 b(G.)15 b(Audi,)g(PhD)g (thesis,)f(Univ)o(ersit)o(\023)-21 b(e)14 b(de)h(P)o(aris-Sud,)g(Orsa)o (y)f(\(1981\),)f(unpublished.)33 1247 y([84Hau])36 b(P)l(.)13 b(E.)f(Haustein,)h Fi(Pr)n(o)n(c.)g(7-th)i(Int.)e(Conf.)g(on)h(A)o (tomic)g(Masses)e(and)i(F)m(undam.)g(Const.)f(AMCO-)282 1303 y(7)p Fj(,)i(Darmstadt)d(1984,)i(O.)h(Klepp)q(er)h(ed.,)f(p.413.) 33 1380 y([85Bos])45 b(K.)16 b(Bos,)e(G.)h(Audi)g(and)g(A.)g(H.)g(W)l (apstra,)f Fi(Nucl.)i(Phys.)f Fk(A432)g Fj(\(1985\))e(140.)33 1456 y([85W)l(ap])28 b(A.)15 b(H.)g(W)l(apstra,)e(G.)i(Audi)g(and)h(R.) f(Ho)q(ekstra,)f Fi(Nucl.)i(Phys.)f Fk(A432)g Fj(\(1985\))e(185.)33 1532 y([88Com])26 b(E.)15 b(Coma)o(y)l(,)e(I.)i(Kelson)g(and)h(A.)f (Zidon,)f(in)h([88Hau)o(])g(p.235.)33 1609 y([88Dus])40 b(G.)15 b(Dussel,)f(E.)h(Caurier)f(and)i(A.)f(P)l(.)g(Zuk)o(er,)f(in)h ([88Hau)o(])g(p.205.)33 1685 y([88Hau])36 b(P)l(.)15 b(E.)g(Haustein,)g(1986-1987)e(A)o(tomic)g(Mass)h(Predictions,)g Fi(ADNDT)21 b Fk(39)16 b Fj(\(1988\))d(185.)33 1761 y([88Jan])47 b(J.)16 b(J\177)-23 b(anec)o(k)o(e)15 b(and)h(P)l(.)e(J.)i(Masson,)e (in)h([88Hau)o(])g(p.265.)33 1837 y([88Mas])35 b(P)l(.)15 b(J.)h(Masson)e(and)h(J.)g(J\177)-23 b(anec)o(k)o(e,)16 b(in)f([88Hau)o(])g(p.273.)33 1914 y([88Mol])40 b(P)l(.)15 b(M\177)-23 b(oller)14 b(and)i(J.)f(R.)g(Nix,)f(in)h([88Hau])f(p.213.) 33 1990 y([88MMST])27 b(P)l(.)15 b(M\177)-23 b(oller,)14 b(W.)g(D.)h(My)o(ers,)f(W.)g(J.)h(Swiatec)o(ki)f(and)i(J.)f(T)l (reiner,)g(in)g([88Hau)o(])g(p.225.)33 2066 y([88P)o(ap])40 b(A.)15 b(P)o(ap)q(e)h(and)f(M.)f(S.)h(An)o(ton)o(y)l(,)g(in)g([88Hau)o (])g(p.201.)33 2142 y([88Sat])52 b(L.)16 b(Satpath)o(y)e(and)h(R.)h(C.) e(Na)o(y)o(ak,)g(in)h([88Hau)o(])g(p.241.)33 2219 y([88Spa])45 b(L.)16 b(Spanier)f(and)g(S.)g(A.)g(E.)g(Johansson,)g(in)g([88Hau)o(])g (p.259.)33 2295 y([88T)l(ac])46 b(T.)15 b(T)l(ac)o(hibana,)f(M.)h(Uno,) g(M.)f(Y)l(amada)g(and)h(S.)g(Y)l(amada,)f(in)h([88Hau)o(])g(p.251.)33 2371 y([88W)l(ap])28 b(A.)15 b(H.)g(W)l(apstra,)e(G.)i(Audi)g(and)h(R.) f(Ho)q(ekstra,)f(in)h([88Hau)o(])g(p.281.)33 2447 y([90Hau])36 b(P)l(.)15 b(E.)f(Haustein,)g Fi(Exotic)h(Nucle)n(ar)h(Sp)n(e)n(ctr)n (osc)n(opy)p Fj(,)d(W.C.)g(McHarris)g(ed.,)h(Plen)o(um,)f(NY,)i(1990.) 33 2524 y([92Duf)t(])40 b(J.)16 b(Du\015o,)e(submitted)g(to)h Fi(Nucl.)h(Phys.)f Fj(,)f(Marc)o(h)h(1992.)33 2600 y([92Gor])41 b(S.)12 b(Goriely)e(and)h(M.)g(Arnould,)h(preprin)o(t)f(submitted)f(to) h Fi(Astr)n(on.)h(Astr)n(ophys.)f Fj(,)g(F)l(ebruary)h(1992.)33 2676 y([92Pdg])39 b(P)o(article)14 b(Data)g(Group,)h("Review)g(of)g(P)o (article)e(Prop)q(erties",)h Fi(Phys.)i(R)n(ev.)f Fk(D45)g Fj(\(1992\).)33 2753 y([92P)o(ea])45 b(M.)14 b(P)o(earson)f(and)i(F.)e (T)l(ondeur,)h Fi(private)i(c)n(ommunic)n(ation)e Fj(and)g(Y.)g(Ab)q (oussir,)g(J.)g(M.)f(P)o(earson,)282 2809 y(A.)h(K.)i(Dutta,)d(F.)i(T)l (ondeur,)g(preprin)o(t.)943 2964 y Fq(19)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF

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