High-resolution, accurate multiple-reflection time-of-flight mass spectrometry for short-lived, exotic nuclei of a few events in their ground and low-lying isomeric states
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High- esolu ion, accu a e mul iple- e lec ion ime-o - ligh mass spec ome y o sho -
li ed, exo ic nuclei o a ew e en s in hei g ound and low-lying isome ic s a es
© The Au ho s, 2019.
Published e sion
And és, Samuel Aye San; Ho nung, Ch is ine; Ebe , Jens; Plaß, Wol gang R.;
Dickel, Timo; Geissel, Hans; Scheidenbe ge , Ch is oph; Be gmann, Julian;
G eine , Flo ian; Hae ne , Emma; Jesch, Ch is ian; Lippe , Wayne; Ma do ,
Is ael; Miskun, I an; Pa yk, Zygmun ; Pie i, S ephane; Pihk ele , Alexande ;
Pu usho haman, Si aji; Rei e , Mo i z P.; Rink, Ann-Ka h in; Weick, Helmu ;
Ya o , Mikhail I.; Bagchi, Soumya; Cha iako a, Volha; Cons an in, Paul; Diwisch,
Ma cel; Finlay, And ew; Kau , Sa bi ; Knöbel, Ronja; Lang, Johannes; Mei, Bo;
Moo e, Iain; O o, Jan-Hend ik; Pohjalainen, Ilkka; P ochazka, And ej; Rappold,
Ch is ophe; Takechi, Maya; Tanaka, Yoshiki K.; Win ield, John S.; Xu, Xiaodong
And és, S. A. S., Ho nung, C., Ebe , J., Plaß, W. R., Dickel, T., Geissel, H., Scheidenbe ge , C.,
Be gmann, J., G eine , F., Hae ne , E., Jesch, C., Lippe , W., Ma do , I., Miskun, I., Pa yk, Z.,
Pie i, S., Pihk ele , A., Pu usho haman, S., Rei e , M. P., . . . Xu, X. (2019). High- esolu ion,
accu a e mul iple- e lec ion ime-o - ligh mass spec ome y o sho -li ed, exo ic nuclei o a
ew e en s in hei g ound and low-lying isome ic s a es. Physical Re iew C, 99(6), A icle
064313. h ps://doi.o g/10.1103/PhysRe C.99.064313
2019
PHYSICAL REVIEW C 99, 064313 (2019)
High- esolu ion, accu a e mul iple- e lec ion ime-o - ligh mass spec ome y o sho -li ed, exo ic
nuclei o a ew e en s in hei g ound and low-lying isome ic s a es
Samuel Aye San And és,1,2Ch is ine Ho nung,1Jens Ebe ,1Wol gang R. Plaß,1,2Timo Dickel,1,2,*Hans Geissel,1,2
Ch is oph Scheidenbe ge ,1,2Julian Be gmann,1Flo ian G eine ,1Emma Hae ne ,2Ch is ian Jesch,1Wayne Lippe ,1
Is ael Ma do ,3,4I an Miskun,1Zygmun Pa yk,5S ephane Pie i,2Alexande Pihk ele ,6Si aji Pu usho haman,2
Mo i z P. Rei e ,1,7Ann-Ka h in Rink,1Helmu Weick,2Mikhail I. Ya o ,8Soumya Bagchi,1,2,9Volha Cha iako a,5
Paul Cons an in,10 Ma cel Diwisch,1And ew Finlay,7Sa bi Kau ,9Ronja Knöbel,2Johannes Lang,1Bo Mei,10
Iain D. Moo e,11 Jan-Hend ik O o,1Ilkka Pohjalainen,11 And ej P ochazka,2Ch is ophe Rappold,1,2Maya Takechi,2
Yoshiki K. Tanaka,2John S. Win ield,2and Xiaodong Xu1
1II. Physikalisches Ins i u , Jus us-Liebig-Uni e si ä Gießen, 35392 Gießen, Ge many
2GSI Helmhol zzen um ü Schwe ionen o schung GmbH, 64291 Da ms ad , Ge many
3School o Physics and As onomy, Tel A i Uni e si y, 6997801 Tel A i , Is ael
4So eq Nuclea Resea ch Cen e , 81800 Ya ne, Is ael
5Na ional Cen e o Nuclea Resea ch, Ho˙za 69, 00-681 Wa szawa, Poland
6Ins i u e o Ene gy P oblems o Chemical Physics, RAS, 142432 Che nogolo ka, Moscow, Russia
7TRIUMF, Vancou e , Canada BC V6T 2A3
8Ins i u e o Analy ical Ins umen a ion, RAS, 190103 S . Pe e sbu g, Russia
9As onomy and Physics Depa men , Sain Ma y’s Uni e si y, Hali ax, Canada NS B3H 3C3
10IFIN-HH/ELI-NP, 077126 M˘agu ele, Bucha es , Romania
11Depa men o Physics, Uni e si y o Jy äskylä, 40014 Jy äskylä, Finland
(Recei ed 31 Janua y 2019; published 11 June 2019)
Mass measu emen s o ission and p ojec ile agmen s, p oduced ia 238Uand124Xe p ima y beams, ha e
been pe o med wi h he mul iple- e lec ion ime-o - ligh mass spec ome e (MR-TOF-MS) o he F agmen
Sepa a o (FRS) Ion Ca che wi h a mass esol ing powe (FWHM) o up o 410 000 and an unce ain y o
down o 6 ×10−8. The nuclides we e p oduced and sepa a ed in ligh wi h he agmen sepa a o FRS a 300 o
1000 MeV/u and he malized in a c yogenic s opping cell. The da a-analysis p ocedu e was de eloped o de e -
mine wi h highes accu acy he mass alues and he co esponding unce ain ies o he mos challenging condi-
ions: down o a ew e en s in a spec um and o e lapping dis ibu ions, which can be dis inguished om a single
peak only by a b oade peak shape. Wi h his p ocedu e, he esolu ion o low-lying isome s is inc eased by a ac-
o o up o 3 compa ed o s anda d da a analysis. The g ound-s a e masses o 31 sho -li ed nuclides o 15 di e -
en elemen s wi h hal -li es o down o 17.9 ms and coun a es as low as 11 e en s pe nuclide we e de e mined.
This is he i s di ec mass measu emen o se en nuclides. The exci a ion ene gies and he isome - o-g ound-
s a e a ios o six isome ic s a es wi h exci a ion ene gies o as li le as 280 keV we e measu ed. Fo nuclides
wi h known mass alues, he a e age ela i e de ia ion om he li e a u e alues is (4.5±5.3) ×10−8.The
measu ed wo-neu on sepa a ion ene gies and hei slopes nea and a he N=126 and Z=82 shell closu es
indica e a s ong elemen -dependen binding ene gy o he i s neu on abo e he closed p o on shell Z=82.
The expe imen al esul s de ia e s ongly om he heo e ical p edic ions, especially o N=126 and N=127.
DOI: 10.1103/PhysRe C.99.064313
I. INTRODUCTION
Masses a e a key p ope y o a omic nuclei. Accu a e mea-
su emen s a e needed o unde s and he e olu ion o nuclea
*Co esponding au ho : [email p o ec ed]
Published by he Ame ican Physical Socie y unde he e ms o he
C ea i e Commons A ibu ion 4.0 In e na ional license. Fu he
dis ibu ion o his wo k mus main ain a ibu ion o he au ho (s)
and he published a icle’s i le, jou nal ci a ion, and DOI.
s uc u e [1] and s ella nucleosyn hesis [2]. In pa icula , nu-
clea masses indica e he limi s o nuclea exis ence, changes
in nuclea de o ma ion, and he onse o nuclea collec i i y
[3]. Accu a e mass alues a e an impo an nuclea ing edien
o -p ocess calcula ions [4]. They signi ican ly a ec he
desc ip ion o he equa ion-o -s a e o nuclea ma e , which
can be ex ended o desc ibe neu on-s a ma e and c us al
composi ion [5].
The knowledge o isome exci a ion ene gies and isome -
o-g ound-s a e a ios a e o g ea impo ance o nuclea
s uc u e and eac ions. Di ec measu emen s o exci a-
ion ene gies can be complemen a y o γde-exci a ion
2469-9985/2019/99(6)/064313(21) 064313-1 Published by he Ame ican Physical Socie y
SAMUEL AYET SAN ANDRÉS e al. PHYSICAL REVIEW C 99, 064313 (2019)
measu emen s. Mass measu emen s a e o long-li ed isome s
he only applicable me hod [6,7].
D i en by his mo i a ion, mul iple- e lec ion ime-o -
ligh mass spec ome y [8] has been de eloped o de e mine
nuclea masses o e y exo ic nuclei a g ound and isome ic
s a es, which ha e hal -li es as sho as a ew milliseconds and
which can only be p oduced wi h a ew e en s pe hou o day
[9]. I has a unique combina ion o pe o mance pa ame e s:
as (cycle imes o a ew milliseconds), accu a e ( ela i e
mass measu emen unce ain y below 10−6), sensi i e (only
a ew de ec ed ions pe nuclide a e equi ed o he accu a e
mass de e mina ion), and nonscanning (simul aneous mea-
su emen o many di e en nuclides). Es ablished me hods
o mass measu emen s o exo ic nuclei, such as isoch onous
[10] o Scho ky mass spec ome y [6,11] in s o age ings,
o TOF-ICR [12]) o PI-ICR [13] in Penning aps, do no
o e hese ou cha ac e is ics simul aneously. Typically, hey
a e ei he e y accu a e o as , bu no bo h a he same
ime. The e o e, mul iple- e lec ion ime-o - ligh mass spec-
ome y is he echnique o choice o highly accu a e mass
measu emen s o he mos exo ic nuclides, especially when
dealing wi h sho hal -li es, low a es, a high amoun o
con aminan s, o low-lying isome s.
Mul iple- e lec ion ime-o - ligh mass spec ome e s
(MR-TOF-MS) ha e been de eloped o mass measu emen s
a di e en a e iso ope beam (RIB) acili ies wo ld-wide
[14–17]. Such MR-TOF-MS measu emen s ha e been
pe o med a he o e on in he ield [18–21]. In hese
measu emen s, ypical mass esol ing powe s (FWHM) o
100 000 o 200 000 and ela i e accu acies in he ange
om 3 ×10−7 o 10−6ha e been achie ed, co esponding
o absolu e accu acies o 30 o 200 keV/c2
0. Recen ly, i has
e en been shown ha he unce ain ies in MR-TOF-MS mass
measu emen s can be educed by an o de o magni ude,
o well below 10−7[14,16,22], and hus i has eached an
accu acy egion ha was p e iously accessible wi h Penning
aps only. Howe e , he p esen MR-TOF-MS wi h a mass
esol ing powe (FWHM) o 100 000 equi es mo e han 1000
de ec ed ions o each a mass accu acy o 10−7. Fo a e exo ic
nuclei, such a measu emen equi es many hou s o e en days
o accele a o beam ime. Mo eo e , o en low-lying isome ic
s a es ende such a measu emen impossible, because g ound
and isome ic s a es canno be esol ed [22].
The MR-TOF-MS [14] de eloped o he FRS Ion Ca che
(FRS-IC) [23] and he p ecision Measu emen s o e y sho -
li ed nuclei using an Ad anced T apping Sys em o highly-
cha ged ions (MATS) expe iemen [24] a Facili y o An-
ip o ons and Ions Resea ch (FAIR) has been designed o o e -
come hese p oblems [9] and o enable mass measu emen s on
he accu acy le el o 1 ×10−7wi h a ew ens o de ec ed
ions. This can be achie ed due o i s much highe mass
esol ing powe han ha o MR-TOF-MS ins alled a o he
RIB acili ies a ound he wo ld. Howe e , e en a e y high
esol ing powe s, low-lying isome s can esul in o e lapping
peaks. The e o e, a da a-analysis p ocedu e is equi ed, which
is sui able o spec a wi h o e lapping peaks and ew e en s
only. Special measu es wi hin he da a-analysis p ocedu e
ha e o be aken o de e mine accu a ely he g ound-s a e
mass, he exci a ion ene gy, he isome - o-g ound-s a e a ios,
and hei espec i e unce ain ies.
FIG. 1. Schema ic mass- o-cha ge spec a illus a ing he ou
classes o close-lying peaks as de ined in he ex . The dis ances
be ween he mass dis ibu ions a e 10, 2, 1, and 0.3 FWHM o
classes A o D, espec i ely. The peak shape and he abundance a io
o 1 o 10 is selec ed o be iden ical o all classes. The hin black
cu es show he sum o bo h dis ibu ions.
In his wo k, close-lying peaks a e classi ied as ollows; a
co esponding illus a ion is gi en in Fig. 1.
Class A. The sum o he dis ibu ions eaches almos ze o
be ween he peaks. In his case, he dis ibu ions is conside ed
as nono e lapping and can be analyzed independen ly.
Class B. The sum o he dis ibu ions has a minimum
be ween he peaks, which is signi ican ly la ge han ze o,
e en a he minimum. The dis ibu ions can be conside ed
as esol ed o e lapping peaks and an app op ia e analysis is
pe o med. In his case, he de e mina ion o he exac peak
shape is impo an o he ex ac ion o accu a e alues o he
masses and hei abundance a ios.
Class C. The sum o he dis ibu ions does no ha e a
minimum be ween he peaks. The exis ence o a double peak
can be de e mined only om a change in he peak shape,
e.g., a peak shoulde o a peak b oadening, as compa ed
o an indi idual peak. In his challenging case, he p ope
de e mina ion o he peak shape is a c ucial p e equisi e in
o de o i s de ec he exis ence o a second peak and second
o ex ac he mass alues and abundance a ios o he peaks.
Class D. Bo h peaks o e lap almos comple ely. No change
in he peak shape can be obse ed in he sum o he dis ibu-
ions. In his case, he peaks mus be conside ed as un esol ed,
and he (possible) exis ence o o e lapping peaks can only be
aken in o accoun by inc easing he unce ain y o he mass
alue(s).
The mass- o-cha ge- a io di e ence be ween he dis ibu-
ions, he peak shapes, and he abundance a io de e mine
o which class a measu emen belongs. While simple da a-
analysis me hods can ob ain accu a e mass and abundance
alues only o classes A and B, he da a-analysis me hod
de eloped in his wo k is capable o ex ac ing accu a e mass
and abundance alues e en o class C and o peaks o a ew
e en s. Fo he example shown in Fig. 1, his co esponds o an
inc ease in he e ec i e mass esol ing powe o o e lapping
peaks by a ac o o abou 3.
064313-2
HIGH-RESOLUTION, ACCURATE MULTIPLE-REFLECTION … PHYSICAL REVIEW C 99, 064313 (2019)
FIG. 2. Schema ic igu e o he expe imen al se up, including
he FRS and he FRS Ion Ca che , which consis s o he c yogenic
s opping cell (CSC), he RFQ beamline, and he MR-TOF-MS.
In his publica ion, mass measu emen s o 238U and 124Xe
p ojec ile agmen s and o 238U ission agmen s wi h he
MR-TOF-MS o he FRS Ion Ca che a GSI (Ge many),
he da a-analysis p ocedu e and he esul s a e p esen ed. The
wo k includes he measu emen o ions wi h mass- o-cha ge-
a io di e ences co esponding o 280 keV/(c2
0e) and wi h 11
e en s. Fu he de ails can be ound in Re s. [25–27].
II. EXPERIMENTS
The FRS Ion Ca che is an expe imen al se up ins alled a
he inal ocal plane o he agmen sepa a o FRS [28]a
GSI. The FRS in combina ion wi h he FRS-IC enables expe -
imen s wi h he malized exo ic nuclei. In Fig. 2, a schema ic
iew o he FRS-IC wi h i s h ee main pa s is shown: (i) he
gas- illed c yogenic s opping cell (CSC) [29–32] o he mal-
iza ion o he exo ic nuclei p oduced a ela i is ic ene gies,
(ii) a beamline, based on adio equency quad upoles (RFQ)
[32–35] o mass-selec i e anspo and di e en ial pumping,
equipped wi h de ec o s (channel ons and silicon de ec o s)
o ion coun ing and α-decay spec oscopy and wi h ion
sou ces o diagnos ic pu poses, and (iii) he MR-TOF-MS
[14,36,37] o se e al pu poses, such as diagnos ics o he
ups eam beamline, ion iden i ica ion and coun ing, and di ec
mass measu emen s.
The MR-TOF-MS includes a bu e -gas- illed RFQ-based
swi chya d [25,38,39], which is capable o me ging, guiding,
and spli ing low-ene gy ion beams. A combina ion o a he -
mal ion sou ce (Hea wa eLabs, Wa son ille, CA, USA; mixed
sou ce: Ca, S , and Ba) and an elec on-impac ion sou ce
is moun ed on he op o he swi chya d, which gene a es
calib an ions o e a b oad mass- o-cha ge ange [25], using
a ious gases such as SF6, Xe, and/o C3F8. Addi ional ions
o calib a ion we e p o ided by an 223Ra open α- ecoil ion
sou ce moun ed inside he CSC. A e he i s wo expe i-
men s, he 223Ra ion sou ce was eplaced by he longe li ed
αemi e 228Th [40].
A schema ic iew o he MR-TOF-MS o he FRS-IC is
shown in Fig. 3. The ions en e he MR-TOF-MS wi h a
kine ic ene gy o a ew eV. In a ap sys em, hey a e bunched,
hei e e ence po en ial is aised om abou −100 o 1300 V,
and hey a e injec ed wi h a epe i ion a e o 50 Hz owa d he
analyze , which is o med by wo elec os a ic e lec o s. The
d i ube is a g ound po en ial. The ou e elec odes o bo h
e lec o s a e swi ched o injec ion and ejec ion o he ions
FIG. 3. Schema ic igu e o he mul iple- e lec ion ime-o - ligh
mass spec ome e . The ions en e om he CSC in gas- illed adio-
equency quad upoles. They a e mixed wi h ions om he calib a-
ion sou ces and a e cooled and bunched in a sys em o linea RF
aps. F om he e, hey a e injec ed in he TOF analyze .
owa d he ime-o - ligh (TOF) de ec o (ETP MagneTOF).
In he cen e o he analyze is a mass- ange selec o (MRS)
based on a pulsed quad upola de lec o , which con ols he
ansmi ed mass- o-cha ge window; i.e., i ensu es an unam-
biguous mass- o-cha ge a io spec um.
A e he ions a e ejec ed om he analyze , hey pass
h ough he ime- ocus shi (TFS) e lec o [36,41,42], which
was p e iously e e ed o as pos anaylze e lec o because
o i s posi ion in he de ice, and impinge on he TOF de ec o .
As an al e na i e o measu emen s wi h he TOF de ec o , he
ions can also be spa ially sepa a ed wi h a B adbu y-Nielsen
064313-3
SAMUEL AYET SAN ANDRÉS e al. PHYSICAL REVIEW C 99, 064313 (2019)
FIG. 4. Mass esol ing powe (FWHM) ob ained wi h he MR-
TOF-MS o 39K+ions as a unc ion o he ime o ligh and o he
numbe o u ns. The kine ic ene gy o he ions in he d i ubes
was 1300 eV and he epe i ion a e was 50 Hz. The measu ed da a
a e shown as ull squa es. The solid line ep esen s a i o Eq. (8)
o he da a. The dashed line indica es he asymp o e ob ained om
he i o long ligh imes. The maximum mass esol ing powe
(FWHM) achie ed is 620 000; he asymp o e is 870 000. No e ha
he ligh ime was limi ed o 20 ms due o he epe i ion equency
o he expe imen .
ga e, such ha he MR-TOF-MS can be used as an isoba
and isome sepa a o [36,43]. The da a acquisi ion sys em
is based on a comme cial ime- o-digi al con e e (TDC),
model O ec-9353. The iming con ol o he di e en elec-
ode po en ials along he ion pa h a e pe o med ia an Field-
P og ammable Ga e A ay (FPGA) - based igge sys em
[44].
Recen ly, majo imp o emen s ha e been made o he MR-
TOF-MS. (i) The kine ic ene gy o he ions in he d i ube
has been inc eased by a ac o 1.7 [39]. Toge he wi h an
imp o ed ion-op ical uning, his has lead o an inc ease in he
mass esol ing powe (FWHM) o abo e 600 000. Figu e 4
shows he mass esol ing powe de e mined in a measu emen
o 39K+ions as a unc ion o he numbe o u ns in he ana-
lyze and he ime o ligh . A e a ligh ime o 2 ms, a mass
esol ing powe (FWHM) o mo e han 100 000 is ob ained.
A e a ligh ime o 20 ms, i.e., he maximum ime possible
o he chosen cycle equency o 50 Hz, a mass- esol ing
powe o 620 000 has been achie ed. The asymp o e, which
is de e mined by he ion-op ical abe a ion limi , amoun s
o almos 900 000. (ii) The maximum epe i ion a e o he
MR-TOF-MS has been inc eased o mo e han 1 kHz. This
inc eases he a e capabili y o he de ice and gi es access
o sho e -li ed nuclei. (iii) The ope a ional eliabili y and
s abili y ha e been imp o ed. (i ) The empe a u e coe icien
o MR-TOF-MS has been educed o 8 ppm/K. I is now
domina ed by he he mal expansion o he analyze . The
changes a e e y slow ( imescale o hou s) and can be easily
compensa ed by he ime- esol ed calib a ion; see Sec. IVA.
(i ) The cleanliness o he bu e gas in he RFQ and ap
sys em has been imp o ed, educing possible ion losses in he
de ice due o cha ge exchange and molecule o ma ion.
In ou expe imen s wi h he FRS-IC, a ious exo ic nuclei
we e p oduced ia p ojec ile agmen a ion and ab asion-
ission. The p ima y beams we e 300- and 1000-MeV/u238U
ions and a 600-MeV/u124Xe ions. The p io i y o hese
expe imen s was he commissioning and cha ac e iza ion o
he CSC [45]. De ails o he expe imen al condi ions and he
se ups a e discussed in he ollowing.
A. Expe imen I: 1000-MeV/u u anium agmen a ion
A 1000-MeV/u238U p ojec ile beam was p o ided om
he hea y-ion synch o on SIS-18 [46] wi h an in ensi y o up
o 7 ×108ions pe spill, wi h a spill leng h o 2 s. A be yllium
p oduc ion a ge wi h an a eal densi y o 1.629g/cm2wi h
a niobium backing o 0.233 g/cm2was used a he en ance
o he FRS. The ions we e ene gy bunched ia a mono-
ene ge ic deg ade wi h an a eal densi y o 4.063g/cm2a he
cen al ocal plane o he FRS [47,48]. The ions we e injec ed
in o he CSC wi h a helium a eal densi y o 3.5mg/cm2,
co esponding o a p essu e o 64 mba a a empe a u e o
88 K. Fo he measu emen o 211Po ions, he a eal densi y
was inc eased o 5.6mg/cm2, co esponding o a p essu e o
95 mba a a empe a u e o 86 K.
B. Expe imen II: 1000-MeV/u u anium ission
The same condi ions as o expe imen I we e used, bu
he a eal densi y o he be yllium p oduc ion a ge was
6.333g/cm2.
C. Expe imen III: 300-MeV/u u anium agmen a ion
A 300-MeV/u238U p ojec ile beam was p o ided om
he hea y-ion synch o on SIS-18 wi h an in ensi y o up
o 2.5×108ions pe spill, wi h a ypical spill leng h o
1 s. A be yllium p oduc ion a ge wi h an a eal densi y o
0.270 g/cm2was used. Because o he low p ima y beam
ene gy, he ma e in he beamline was minimized. The mono-
ene ge ic deg ade a he cen al ocal plane had an a eal
densi y o 737.1mg/cm2. The CSC had an a eal densi y o
4.2mg/cm2helium, co esponding o a p essu e o 64 mba
a a empe a u e o 77 K.
D. Expe imen IV: 600-MeV/u xenon agmen a ion
A 600-MeV/u124Xe p ojec ile beam was p o ided om
he SIS-18 wi h an in ensi y o up o 1 ×109ions pe spill,
wi h a ypical spill leng h o 500 ms. A be yllium p oduc ion
a ge wi h an a eal densi y o 1.622 g/cm2was used. The
monoene ge ic deg ade a he cen al ocal plane had an a eal
densi y o 737.1mg/cm2. The CSC had an a eal densi y o
4.6mg/cm2helium, co esponding o a p essu e o 75 mba
a a empe a u e o 82 K.
The p io i y in expe imen s III and IV was high ansmis-
sion om he p oduc ion a ge o he CSC, whe eas expe i-
men s I and II we e op imized o spa ial iso ope sepa a ion
wi h he FRS. Because o his di e ence, he abundance a io
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o backg ound o ion o in e es (IOI) deli e ed om he
FRS was abou 1000 imes highe in expe imen s III and IV
wi h espec o expe imen s I and II. In addi ion, mos o
he measu emen s in expe imen s III and IV we e done wi h
a b oade mass- o-cha ge ange, i.e., se e al mass- o-cha ge
uni s simul aneously in he spec um. This inc eased he
backg ound. The amoun o backg ound om molecula ions
was educed in expe imen IV by consecu i e ion isola ion
in he RF mass il e o he RFQ beamline, collision-induced
dissocia ion in an RFQ [49,50], and again ion isola ion, also
e e ed o as he isola ion-dissocia ion-isola ion (IDI) me hod
[51].
III. BASICS OF MR-TOF-MS
The ime o ligh (TOF) o al in he MR-TOF-MS is he
sum o he TOF om he injec ion ap o he de ec o wi hou
e lec ions in he analyze s and he TOF o Ni e lec ions,
o al = s +Ni i ,(1)
whe e Ni is he numbe o u ns in he analyze and i is he
TOF o each u n. Simila ly, he o al ligh pa h l o al is gi en
by
l o al =l s +Ni li ,(2)
whe e l s is he pa h leng h om he injec ion ap o he
de ec o and li is he pa h leng h o one u n in he analyze .
The ion mo ion om he injec ion ap o he de ec o is made
isoch onous by he shi o he ime ocus ( ime- ocus shi ,
TFS) by means o he TFS e lec o . Each u n in he analyze
p ese es he isoch onici y [42].
In a ime-o - ligh mass spec ome e , he classical ela ion-
ship be ween TOF and mass- o-cha ge a io is gi en by
m
q=2Ue 2
o al
l2
o al
,(3)
whe e mand qa e he mass and cha ge o he ion, espec i ely.
Ue is he e ec i e ol age, which akes in o accoun he
a ia ion o he elec ic po en ial along he ligh pa h. In an
expe imen , he measu ed ime exp includes an ime delay 0
be ween he s a signal and he eal s a o ions, caused by
he cables and elec onic modules, and hus
exp = o al + 0.(4)
Subs i u ion o Eqs. (1), (2), and (4) in o Eq. (3) yields
m
q=c( exp − 0)2
(1 +Ni b)2,(5)
whe e b=li /l s and c=2Ue /l2
s.
The mass esol ing powe o a ime-o - ligh mass spec-
ome e is gi en by
m/q
(m/q)= o al
2 o al
,(6)
whe e o al is he sp ead in ime o ligh . Fo he MR-TOF-
MS, Eq. (6) can be w i en as [14,52]
m/q
(m/q)= s +Ni i
2 2
a + 2
s +(Ni i )2
,(7)
whe e a is he u na ound ime [53]. s is he ime sp ead
due o ion-op ical abe a ions om he injec ion ap o he
de ec o wi hou e lec ions in he analyze . a and s
oge he ep esen he e o o s. i is he ime sp ead
pe u n in he analyze , which is ypically domina ed by
ion-op ical abe a ions. Di iding by i allows o use measu ed
ligh - ime a ios o a e e ence ions. To simpli y u he ,
i /(2 i ) is eplaced by R∞, he mass esol ing powe o
Ni =∞. The u na ound ime is calcula ed o he e e ence
ion and IOI. The mass esol ing powe o all mass- o-cha ge
a ios and numbe o u ns measu ed unde he iden ical ion-
op ical condi ions can be calcula ed by
m
m(q,Ni )=
s, e
i , e +Ni
2q e
q a, e
i , e 2+ s, e
i , e 2+2Ni
R∞2.
(8)
IV. THE DATA-ANALYSIS PROCEDURE
The analysis p ocedu e o he MR-TOF-MS da a has spe-
ci ic equi emen s and challenges. The peak- i ing ou ine
mus be able o cope wi h o e lapping peaks wi h e y low
numbe o e en s, whe e he masses o he nuclei, hei
abundance, and hei unce ain ies ha e o be de e mined
wi h he highes accu acy possible. The knowledge o he
indi idual unce ain y con ibu ions a e impo an o ob ain
highe accu acies in u u e expe imen s.
The TOF o he di e en ions is eco ded using he Mass
Acquisi ion (MAc) so wa e [54]. This so wa e is also used
o he i s s eps o he da a-analysis p ocedu e. The inal
analysis is pe o med in he p og amming language R[55]. In
Fig. 5, a low diag am o he da a-analysis p ocedu e is shown.
In he ollowing, he da a-analysis p ocedu e is desc ibed.
A. The ime- esol ed mass calib a ion (TRC)
The i s s ep in he da a-analysis p ocedu e is he con e -
sion o he TOF spec um in o a mass- o-cha ge spec um.
The TOF o a ce ain mass- o-cha ge a io can luc ua e du ing
he measu emen , mainly due o wo easons: changes in he
po en ials applied o he e lec o elec odes in he analyze
and he mal expansion o he analyze . High- equency luc-
ua ions in he kHz ange and highe a e no ele an du ing
he ligh o he ions, since he ions a e s o ed in he analyze
o se e al milliseconds. The luc ua ions a lowe equency
(down o 0.1 Hz) a e minimized by cus om-made RC low-pass
il e s. To cope wi h e en slowe changes (mHz and lowe ),
a d i co ec ion in he TOF spec um [15,56] o a ime-
esol ed mass calib a ion (TRC) can be pe o med, as done
in he p esen wo k. In TRC, he co ec ion is pe o med in
he mass- o-cha ge spec um a he han in he TOF spec um.
The TRC is he mo e powe ul me hod, since i does no
in oduce addi ional unce ain ies; see Re . [57]. Fu he mo e,
i equi es only a single calib an , e en o ions wi h di e en
numbe o u ns. No e ha a ela i ely coa se mass- o-cha ge
de e mina ion is su icien o pe o m he TRC.
Equa ion (5) ela es he TOF o an ion o i s mass- o-cha ge
a io. The pa ame e s c, 0, and bha e o be de e mined using
calib an ions. The pa ame e 0is calcula ed, be o e o a e
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SAMUEL AYET SAN ANDRÉS e al. PHYSICAL REVIEW C 99, 064313 (2019)
FIG. 5. The low diag am o he da a-analysis p ocedu e. Only
he main s eps a e shown. LS is a leas -squa es i o de e mine
he peak shape and wMLE is he weigh ed maximum likelihood
es ima ion o he peak posi ion and a ea.
he ac ual mass measu emen o he IOI, using he TOF o
a leas wo calib an ion species ha we e measu ed wi hou
isoch onous u ns, in he ime- ocus shi (TFS) mode [42].
Two op ions a e possible o de e mine band c: (i) The high-
esolu ion mass- o-cha ge spec um con aining he IOI and
wo calib an ion species unde going di e en u n numbe s
yield bo h cand b. (ii) The high- esolu ion spec um con ains
calib an s wi h he same numbe o u ns, and hen bis calcu-
la ed om his spec um and c om he TFS measu emen .
The pa ame e 0is cons an as long as he elec onics and
cables a e no changed. In a high- esolu ion measu emen wi h
many u ns, he TOF du ing he TFS is sho compa ed o he
TOF in he analyze . Thus, empo al d i s du ing he TFS can
be neglec ed compa ed o he empo al d i s du ing he ligh
in he analyze . Hence, ccan be assumed o be cons an du ing
a measu emen , i a ime dependence o bis allowed o , and c
changes only when he ion-op ical se ings o he TFS mode is
changed. The e o e, i is su icien o ob ain he ime- esol ed
TOF o a single calib an .
In o de o pe o m he TRC, a ce ain numbe o spec a
( ypically a ew seconds) a e summed in o a single spec um
(calib a ion block). A de e mina ion o he pa ame e bis
pe o med o hese calib a ion blocks. Fo a gi en numbe
o o al e en s, he op imum choice o he numbe o spec a
in a calib a ion block is a comp omise be ween he accu acy
o each alue o band he ime esolu ion o he TRC. A linea
in e pola ion is applied be ween he calib a ion blocks.
The TRC ully co ec s he d i s, i he calib an ions and
he IOI expe ience he same elec ic ields. The FWHM o
he IOI is sligh ly la ge , i hey do no expe ience he same
elec ic ields. Since he wid h o he peak o he IOI mus be
in e ed om he measu ed wid h o he peak o he calib an
(Sec. IVC), he inc ease in he peak wid h was measu ed in
expe imen s I–IV. The peak wid h inc ease mainly depends
on he ime be ween successi e calib a ion blocks and on
he a e age numbe o coun s in each calib a ion block. An
e ec i e ime be ween calib a ion blocks is used, since he
ime be ween calib a ion blocks is no necessa ily cons an :
c,e =2( 1− begin)2+2( end − n)2
end − begin
+n
i=2( i− i−1)2
end − begin
,(9)
whe e iis he cen e o each calib a ion block, begin and end
a e he beginning and end o he measu emen o he IOI,
espec i ely, and nis he numbe o calib a ion blocks. The
inc ease o he peak wid h was calcula ed as he oo mean
squa e o he ela i e mass- o-cha ge de ia ion be ween he
ue mass- o-cha ge a io and he alue de e mined by he
linea in e pola ion be ween TRC blocks. This inc ease was
abula ed o di e en imes be ween blocks ( c,e ) and di -
e en numbe o es ions in each block. Fo all measu emen s
pe o med in expe imen s I–IV, he inc ease o he peak wid h
is ob ained om hese alues.
An example o he e ec o TRC is shown in Fig. 6,
whe e he mass- o-cha ge spec um is shown wi h a single
calib a ion a he beginning o he acquisi ion and wi h TRC.
Wi h he TRC me hod, he mass- o-cha ge a io o each
e en o he measu emen is calcula ed and sa ed in lis mode
o u he analysis.
B. Ion iden i ica ion
Based on he mass- o-cha ge a io o he ions, an pa icle
iden i ica ion o he peaks in he mass- o-cha ge spec a is
pe o med. The iden i ica ion can be checked acco ding o
se e al c i e ia: (i) a compa ison o absolu e and ela i e
de ec ed a es wi h he esul s o heo e ical simula ions o
expe imen al me hods, e.g., αspec oscopy o pa icle iden-
i ica ion in ligh wi h he de ec o s o he FRS, (ii) a compa -
ison o he iden i ica ion pe o med o measu emen s wi h
wo di e en u n numbe s, (iii) he coincidence be ween he
e en s in he MR-TOF-MS and he p ima y beam, and (i )
he co ela ion o he de ec ed e en s in he MR-TOF-MS
wi h he expe imen al a omic ange o he ions in ma e in
on o he CSC.
C. De e mina ion o he peak-shape pa ame e s
I is well known ha he mass esol ing powe o TOF
mass spec ome e s is mass independen ; hus, peak shapes
a e he same o all ions wi h he same cha ge s a e. Howe e ,
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FIG. 6. Example o he ime- esol ed calib a ion (TRC) o a
mass measu emen o 39K+ions ha pe o med 980 isoch onous
u ns in he MR-TOF-MS, co esponding o a o al ime-o - ligh o
18.92 ms. The op diag ams show he peak posi ions as a unc ion
o he expe imen ime wi hou TRC (a) and wi h TRC (b). The
TRC was pe o med e e y 5 s. In he bo om pa o he igu e,
he co esponding mass- o-cha ge spec a a e shown. Because o
TRC, an inc ease in he mass esol ing powe is ob ained; he mass-
esol ing powe (FWHM) a e he TRC amoun s o 510 000. No e
ha all ho izon al axes ha e he same scale o easie compa ison.
hei wid h is p opo ional o he mass o he ion. This has
also been s udied in de ail o MR-TOF-MS in Re . [44].
Thus, he peak shape o a dis ibu ion wi h high s a is ics is
aken and used o all o he dis ibu ions measu ed unde he
same expe imen al condi ions. The peak shapes can be well
desc ibed empi ically [58]. They can be de e mined by i ing
a sui able analy ical o mula o a peak wi h a la ge num-
be o e en s, ob ained simul aneously wi h he IOI. The i
is done by a leas -squa es (LS) minimiza ion based on he
Le enbe g-Ma qua d algo i hm [59]. Fo he LS i ing, he
da a ha e o be binned. The F eedmann-Diaconis ule [60]is
used o de e mine he bin wid h wbin, which is de ined as
wbin =2IQR(x)
3
√Ncoun s
,(10)
wi h Ncoun s being he numbe o e en s and IQR being he
in e qua ile ange (±25% o he coun s a ound he cen al
e en ) o a single nono e lapping peak. The analy ical o -
mula desc ibing he peaks ob ained wi h he MR-TOF-MS
is he Hype -EMG(L,R) [58] unc ion, which consis s o a
weigh ed sum o a gi en numbe o le (L) and igh (R) expo-
nen ially modi ied Gaussian (EMG) unc ions. The pa ame e
o he unc ion ha de e mines he mass- o-cha ge alues is
μG, which is he mean o he Gaussian in he EMG.
In some cases, a ela i ely small Gaussian dis ibu ion
(5–10% o he a ea o he main dis ibu ion) has o be added
in o de o ge a be e de e mina ion o he peak shape; see
Fig. 7. This Gaussian dis ibu ion appea s due o ion-op ical
FIG. 7. Measu ed mass spec um o 211Pb+ions, which was used
as a calib an in he mass measu emen o 213Rn+ions. The peak
shape equi es one exponen ial ail on each side [Hype -EMG(1,1)]
and addi ionally a Gaussian dis ibu ion ( ed ull line) on he le
side. The Gaussian dis ibu ion esul s om ion-op ical e ec s. In
addi ion, a Gaussian unc ion (o ange long-dashed line) and a Hype -
EMG(1,0) wi hou a Gaussian dis ibu ion (pu ple do ed line), a
Hype -EMG(1,0) plus a Gaussian dis ibu ion (g een dash-do ed
line), and a Hype -EMG(1,1) (blue dashed line) a e shown. The mass
spec um is shown in linea scale in he inse . A mass esol ing powe
(FWHM) o 200 000 was achie ed o he ime o ligh o 5.8 ms,
co esponding o 128 isoch onous u ns.
abe a ions in he MR-TOF-MS and i s s eng h depends on
he uning o he analyze . A uni o mly dis ibu ed back-
g ound can be aken in o accoun .
The de e mina ion o he peak shape wi h his high le el
o accu acy is needed o analyzing da a wi h o e lapping
peaks. The numbe o exponen ials and he exis ence o a
Gaussian dis ibu ion is de e mined based on he educed χ2,
he unce ain y o he i pa ame e s, and he accu acy o
he peak-shape model as de e mined wi h a Kolmogo ow-
Smi now es (KS es ) [58]. The peak shape is de e mined
o e a mass- o-cha ge window up o he limi s o one e en
pe bin on a e age.
Resul s o he peak de e mina ion ob ained wi h he MR-
TOF-MS a he FRS-IC a e p esen ed in Figs. 7and 8.In
bo h igu es, he da a a e compa ed wi h di e en Hype -EMG
unc ions and a egula Gaussian.
The peak-shape pa ame e s calcula ed om he calib an
dis ibu ion ha e been scaled o he IOI. The scaling ac o
akes in o accoun he gene al inc ease o he peak wid h wi h
inc easing mass- o-cha ge a io, as well as he di e en con-
ibu ions o he mass esol ing powe discussed in Sec. III.
The scaling ac o is gi en by
S=m
qIOIm/q
(m/q)cal
m
qcalm/q
(m/q)IOI
,(11)
whe e (m/q)IOI,cal a e he co esponding mass- o-cha ge a-
ios o he IOI and he calib an . ( m/q
(m/q))IOI,cal a e he co e-
sponding mass esol ing powe s o he IOI and he calib an
ion, as gi en by Eq. (8). Fo he scaling o he pa ame e s
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SAMUEL AYET SAN ANDRÉS e al. PHYSICAL REVIEW C 99, 064313 (2019)
FIG. 8. Measu ed mass spec um o 211Pb+ions, which was used
as a calib an in he mass measu emen o 212A ions. The peak shape
equi es one exponen ial ail on each side [Hype -EMG(1,1)] ( ed
ull line). In addi ion, a Gaussian unc ion (o ange long-dashed line),
a Hype -EMG(1,0) (pu ple do ed line), and a Hype -EMG(0,1) (g ay
dash-do ed line) a e shown. The mass spec um is shown in linea
scale in he inse . A mass esol ing powe (FWHM) o 180 000
was achie ed o he ime o ligh o 5.8 ms, co esponding o 128
isoch onous u ns.
o he peak ails, he u na ound ime is se o ze o, because
he peak ails a e due o op ical abe a ions. These abe a ions
do no depend on he u na ound ime. The peak b oadening,
which a ises i he IOI and he calib an do no expe ience he
same elec ic ields, is also aken in o accoun ; see Sec. IVA.
D. Fi ing o he mass- o-cha ge alue
The posi ion o he mass- o-cha ge alue o a gi en nu-
cleus in he expe imen al spec um has been de e mined by
using he weigh ed maximum-likelihood es ima ion (wMLE)
[61]. Howe e , he unc ion (xi) desc ibing he measu ed
dis ibu ion was de e mined by he leas -squa es (LS) i o
he calib an ion. In he wMLE i , all pa ame e s o he
Hype -EMG, besides μGand he a ea, a e ixed. In he wMLE
analysis, unbinned da a we e ea ed. This has he ad an age
o a oiding addi ional e o s due o he wid h and posi ion
o he bins. In addi ion, his me hod is supe io o LS i ing
o da a wi h low coun a es. The weigh ing o he da a
is used o inc ease he obus ness o he i by minimizing
he in luence o ou lie s on he de e mina ion o μG.The
weigh ing unc ion w(xi), dependen on he mass- o-cha ge
alue, has been chosen as he unca ed na u al loga i hm o
he unc ion (xi). The weigh ed log-likelihood unc ion is
gi en by
L=
n
i=1
w(xi)ln[ (xi)]
wi h w(xi)=0,i ln [ (xi)] <0
ln [ (xi)],o he wise .(12)
A e in es iga ions o se e al ypes o di e en weigh ing
unc ions, by applying boo s apping, his weigh ing unc ion
FIG. 9. Measu ed shi o he ime o ligh o 133Cs ions due o
he MRS as a unc ion o he numbe o isola ion cycles. The shi
is no malized by (m/q)1/2( o de ails, see ex ). The lines show a
i o Eq. (13) o he da a poin s. The esul ing i cons an is Am s =
1.1×10−11 s/√u/e.
was ound o be he bes comp omise among accu acy, ou lie
supp ession, and uni e sali y o he a omic mass de e mina-
ion [25].
E. E ec o he mass- ange selec o (MRS)
When measu ing ion species, which unde go di e en
numbe s o u ns, he mass- o-cha ge spec um can be am-
biguous. By isola ion o ions o a ce ain mass- o-cha ge
ange, i.e., emo al o all ions ou side his mass- o-cha ge
ange, an unambiguous iden i ica ion o all ion species can
be ob ained [14]. Isola ion is pe o med by he mass- ange
selec o (MRS), which is a de lec o moun ed in he middle
o he analyze . By swi ching he MRS de lec o be ween
ansmission and de lec ion wi h p ope iming, only he ions
o in e es ed a e ansmi ed.
A u n in he analyze wi h he MRS in ope a ion is e e ed
o as an isola ion cycle (IC). In each IC, he MRS is swi ched
ou imes. Each swi ching causes a small change in he
ol ages applied o he MRS. As a consequence, he ligh
imes o he ansmi ed ions shi . Fo a gi en elec ical se up
o he MRS, he shi is he same o all ions o he same
mass- o-cha ge a io and o he same numbe o IC. The
shi inc eases linea ly wi h numbe o IC, Nic, and acco ding
o Eq. (3) he shi in he ime-o - ligh is p opo ional o
(m/q)1/2. The e o e, a measu emen o he MRS shi can be
made and be used as he basis o a co ec ion o he MRS
shi in all subsequen mass measu emen s.
The esul o a measu emen o he MRS shi is shown
in Fig. 9. The measu ed shi in he ime-o - ligh m s was
no malized wi h (m/q)1/2
e o he ion, he e 133Cs ions, and i ed
o he equa ion
m s
m
q e =Am sNic.(13)
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TABLE I. Resul s o di ec mass measu emen s pe o med in he FRS-IC in expe imen s I–IV. The shown unce ain ies a e he o al
expe imen al unce ain y. In he expe imen III, he unce ain ies a e o en domina ed by highe backg ound; see Sec. II. Li e a u e alues a e
om Re s. [62,65].
Nuclide Hal -li e Exp. Re e ence ion MEFRS−IC MEAME16 MEFRS−IC -MEAME16 Numbe
(keV) (keV) (keV) o e en s
213F (34.14 ±0.06) s I 211Pb −3561.9±12.3−3553 ±5−8.9±13.3 6022
212F (20.0±0.6) min I 211Pb −3530 ±28 −3516 ±9−14 ±29 445
211F (3.10 ±0.02) min I 211Pb −4108 ±40 −4140 ±12 32 ±41 126
134I(52.5±0.2) min II 134Xe −84062 ±54 −84043 ±5−19 ±54 172
134Sb (780 ±60) ms II 134Xe −73915 ±122 −74021 ±2 106 ±122 12
134Te (41.8±0.8) min II 134Xe −82543 ±41 −82534 ±3−10 ±41 61
133I(20.83 ±0.08) h II 133Cs −85852 ±15 −85858 ±65±15 566
133Te (12.5 ±3) min II 133Cs −82932 ±40 −82937 ±25±40 423
126Cs (1.64 ±0.02) min III 126Xe −84340 ±46 −84351 ±10 11 ±47 22
125Cs (46.7±0.1) min III 126Xe −84040 ±42 −84088 ±848±43 609
124Cs (30.9±0.4) s III 126Xe −81700 ±39 −81269 ±831±40 23
119I(19.1±0.4) min III 12C219F5(A=119) −83796 ±34 −83766 ±28 −30 ±44 90
119Xe (5.8±0.3) min III 12C219F5(A=119) −78816 ±57 −78794 ±10 −22 ±58 31
117I(2.22 ±0.04) min III 12C219F5(A=119) −80488 ±47 −80436 ±26 −51 ±54 1022
116Te (2.49 ±0.04) h III 12C219F5(A=119) −85268 ±51 −85269 ±28 1 ±58 1183
114Sb (3.49 ±0.03) min III 12C219F5(A=119) −84497 ±47 −84497 ±22 −1±52 347
114Te (15.2±0.7) min III 12C219F5(A=119) −81893 ±50 −81889 ±28 −4±58 269
107Cd (6.50 ±0.02) h IV 84K 14N2(A=112) −86963 ±90 −86990 ±227±90 47
100Ag (2.01 ±0.09) min IV 12C219F4(A=100) −78146 ±41 −78138 ±5−8±41 36a
97Pd (3.10 ±0.09) min IV 12C216O19F3(A=97) −77790 ±37 −77806 ±516±37 35
96Pd (122 ±2) s IV 12C219F4(A=100) −76246 ±38 −76183 ±4−63 ±39 224
94Rh (70.6±0.6) sbIV 12C216O19F3(A=97) −72848 ±24 −72908 ±360±24 338
94Ru (51.8±0.6) min IV 12C313C19F3(A=94) −82547 ±26 −82584 ±337±26 88
93Ru (59.7±0.6) s IV 12C216O19F3(A=97) −77177 ±44 −77217 ±240±44 20
aTo al numbe o e en s o he un esol ed g ound and isome ic s a es.
bAssignmen o g ound s a e and isome is unce ain.
been measu ed wi h less han 100 e en s and abou a qua e
o he peaks a e no baseline esol ed; i.e., hey belong o
classesB,C,o D.
The nuclide 100Ag is known o ha e a low-lying isome ic
s a e wi h an exci a ion ene gy o 15.5 keV, which was no
esol ed in he measu emen . I s hal -li e is simila o he
imescale o he measu emen . The e o e, i is assumed o be
measu ed as a mix u e o bo h s a es.
B. Isome - o-g ound s a e a ios
Isome - o-g ound-s a e a ios shed ligh on agmen a ion
in pe iphe al hea y-ion collisions a ela i is ic ene gies,
guiding he e icien use o in- ligh agmen a ion a u u e
adioac i e beam acili ies [67]. When nuclides a e p oduced
by ission, isome - o-g ound-s a e a ios p o ide insigh s e-
ga ding he o igin o he angula momen um o he ission
agmen s, which in u n may e eal p ope ies o he dynam-
ical e olu ion o he issioning nucleus om he saddle poin
un il i s descen o scission [68].
The a ios o isome o g ound s a e measu ed wi h he
MR-TOF-MS a e gi en in Table II. The isome - o-g ound-
s a e a io o 134Sb ions has been s udied in 235U he mal
neu on-induced ission [69], 232Th 25-MeV p o on induced
ission [70], 252C spon aneous ission [71], and now wi h
238U ab asion ission.
TABLE II. Exci a ion ene gies and isome - o-g ound-s a e a ios measu ed wi h he MR-TOF-MS. The isome - o-g ound-s a e a ios a e
no co ec ed o decay losses, because he measu emen ime is sho compa ed o he hal -li e o he s udied s a es. Li e a u e alues a e om
Re s. [65,72].
Isome JπHal -li e Exp. Eex,FRS−IC Eex,LIT Eex,FRS−IC -Eex,LIT Isome - o-g ound-
(keV) (keV) (keV) s a e a io
211mPo 25/2+(25.2±0.6) s I 1578 ±84 1462 ±5 116 ±84 3.30 ±1.42
134mI8
−(3.52 ±0.04) min II 357 ±76 316.49 ±0.22 41 ±76 1.26 ±0.26
134mSb 7−(10.07 ±0.05) s II 212 ±171 279 ±1−67 ±171 1.08 ±0.73
134mXe 7−(290 ±17) ms II 1911 ±34 1965.5±0.5−55 ±34 0.035 ±0.006
133mI19/2−(9 ±2) s II 1643 ±14 1634.148 ±0.010 9 ±14 0.35 ±0.02
133mTe 19/2−(55.4±0.4) min II 332 ±45 334.26 ±0.04 −2±45 4.12 ±0.26
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SAMUEL AYET SAN ANDRÉS e al. PHYSICAL REVIEW C 99, 064313 (2019)
FIG. 17. Rela i e de ia ion o measu ed g ound-s a e masses (mFRS−IC −mAME16)/mFRS−IC (Table I) and isome exci a ion ene gies
(Eex,FRS−IC −Eex,AME16)/mFRS−IC (Table II) om he li e a u e alues gi en in AME2016 [62]. All ela i e de ia ions a e calcula ed wi h
espec o he g ound-s a e masses. The g ay band a ound he ho izon al axis ep esen s he li e a u e unce ain y. In he igh -hand panel, a
his og am o he ela i e de ia ions wi h a bin size o 2.5×10−7is shown. The weigh ed mean o all ela i e de ia ions is (4.5±5.3) ×10−8
and he s anda d de ia ion is 3.5×10−7.
C. Masses o sho -li ed nuclides di ec ly measu ed
o he i s ime
Abo e he doubly magic nucleus 208Pb,a egiono e y
sho -li ed nuclei opens up in he nuclea cha wi h hal -li es
down o nanoseconds. The masses o hese nuclei we e mea-
su ed so a only ia hei Q alues. They ela e he mo he and
daugh e nuclei masses ia αdecay. This is only unambiguous
i he ini ial and inal s a es a e known. The e o e, di ec mass
measu emen s a e desi able o he α-emi e s, such as he
ecen mass measu emen s pe o med a RIKEN [73]. In he
ollowing, i s - ime di ec mass measu emen s o se en α
emi e s in his egion o in e es a e p esen ed. The measu ed
esul s a e lis ed in Table III.
1. 212,213,218Rn iso opes
The 212Rn nucleus has a closed shell wi h 126 neu ons
and a hal -li e o 23.9 min, he neighbo ing iso ope 213Rn has
a much sho e hal -li e o 19.5 ms, and he 218Rn nucleus has
a hal -li e o 33.75(15) ms.
The p esen mass measu emen was pe o med wi h 128
isoch onous u ns, co esponding o a TOF o abou 5.8 ms
and a mass esol ing powe (FWHM) o abou 200 000. The
masses o hese h ee nuclides we e de e mined in he pas by
αdecay (212Rn [74,75]; 213Rn [76,77]; 218Rn [78,79]).
2. 211Po iso ope
The g ound and isome ic s a es o 211Po nuclei ha e been
s udied by αspec oscopy (e.g., Re s. [78,80,81]) in he pas .
In he p esen ed mass measu emen , he 211Po ions a eled
192 isoch onous u ns in he analyze o he MR-TOF-MS,
esul ing in a mass esol ing powe (FWHM) o 300 000. This
is no enough o esol e he g ound s a e o 211Pb and he iso-
me ic s a e o 211Po, sepa a ed by 574 keV/c2
0. The adioac i e
ion sou ce ins alled in he CSC has p oduced he 211Pb ions.
TABLE III. Resul s o i s - ime di ec mass measu emen s pe o med a he FRS-IC. The unce ain ies shown co espond o he o al
expe imen al unce ain y. Li e a u e alues a e om [62,65].
Nuclide Hal -li e Exp. Re e ence ion MEFRS−IC MEAME16 MEFRS−IC -MEAME16 Numbe
(keV) (keV) (keV) o e en s
220Ra (17.9±1.4) ms I 34S19F4(A=110) 10609 ±320 10270 ±8 339 ±320 11
218Rn (33.75 ±0.15) ms I 219Rn −5089 ±54 −5217.3±2.3−128 ±55 162
217A (32.62 ±0.24) ms I 219Rn 4433 ±135 4395 ±538±135 19
213Rn (19.5±0.1) ms I 211Pb −5737 ±63a−5696 ±3−41 ±63a165 +29a
212A (314 ±2) ms I 211Pb −8601 ±86 −8628.2±2.4−27 ±86 1496b
212Rn (23.9±1.2) min I 211Pb −8609 ±30 −8660 ±351±30 514
211Po (516 ±3) ms I 211Pb −12593 ±137a−12432.6±1.3−160 ±137a78 +411a
aWeigh ed mean alue including he esul s o a p e ious expe imen a he FRS-IC [25,44].
bTo al numbe o e en s o he un esol ed g ound and isome ic s a es.
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They we e used o calib a ion a he beginning and end o
he measu emen , when no beam en e ed he CSC. Du ing
ope a ion wi h beam, he 211Pb ion sou ce was blocked by an
elec ic ield (220 V, DC), bu some 211Pb backg ound ions
emained. This was aken in o accoun in he da a analysis by
including a hi d peak o 211Pb. The pa ame e s o his peak
was ixed. The unce ain y o he pa ame e s o he hi d peak,
especially he a e o he 211Pb backg ound ions, has been
conside ed o he inal mass unce ain y. Fo he (25/2)+
isome o 211Po, an exci a ion ene gy o 1578(84) keV was
measu ed, which is in ag eemen wi h ou p e iously di ec
measu emen 1472 (120) keV [14]; he li e a u e alue is
1462(5) keV [72].
3. 220Ra iso ope
The measu emen and da a analysis o 220Ra ions we e
especially challenging, because (i) 220Ra nuclides has a hal -
li e o 17.9 ms, which is he sho es -li ed iso ope measu ed
wi h an MR-TOF-MS up o now, (ii) he ion was measu ed as
doubly cha ged, and (iii) only 11 coun s we e eco ded. The
MR-TOF-MS and he da a-analysis p ocedu es desc ibed in
his pape ha e been de eloped o cope wi h hese challenges.
4. 212,217A iso opes
The 212A nucleus has a hal -li e o 314 ms o he (1)−
g ound s a e and 119 ms o he (9)−isome ic s a e wi h
an exci a ion ene gy o 222.9(0.9) keV. This mass di e ence
was no esol ed in he measu emen . Bo h s a es decay ia
αdecay. In his measu emen , he FRS was se o he e y
sho -li ed agmen 216F , which was s opped in he CSC and
decayed in o 212A ia αdecay. Bo h nuclei, 216F and 212A ,
ha e a (9)−isome ic s a e. The (9)−isome o 216F decays in
simila manne o i s g ound s a e (1)− ia αdecay [82]. The
g ound s a e and he (9)−isome ha e simila hal -li es: 700
and 850 ns, espec i ely. The e o e, bo h s a es decay in he
CSC, he ecoil ene gy is abso bed by he helium gas, and he
g ound and isome ic s a es o 212A a e popula ed. Ku cewicz
e al. [82] epo ed an isome ic a io o he (9)−s a e o
0.28(1) o 212A and 0.31(2) o 216F . The la e nucleus
was popula ed ia αdecay o 220Ac. In a la e in es iga ion
[83], he isome ic a io o he (9)−s a e in 212A was again
de e mined. The ob ained alue was 0.09(2), which di e s
s ongly om he epo ed alue o e e ence [82].
217A has a hal -li e o 32.3 ms. I s p oduc ion c oss sec ion
is 18μb, he smalles o all iso opes p esen ed he e. The e o e,
he unce ain y in i s mass measu emen is domina ed by
s a is ics, as he spec um included only 19 ions. The mass
o 217A nuclides was measu ed p e iously only by αspec-
oscopy [78,84].
VI. EXPERIMENTAL RESULTS COMPARED
WITH THEORETICAL PREDICTIONS AT THE LEAD
SHELL CLOSURES
Accu a e mass alues and also hei di e ences can p o ide
basic in o ma ion o he s ong in e ac ion in nuclei and a e
essen ial o he unde s anding o he syn hesis o he elemen s
in he uni e se [2]. Nuclea shell s abiliza ion is he eason o
FIG. 18. Two-neu on sepa a ion ene gy S2n s neu on numbe
including mass excess da a om AME16 (open symbols) and he
ones measu ed in his wo k ( ed illed symbols). The closed neu on
shell a N=126 appea s as a s eepe slope.
he exis ence o he hea ies expe imen ally known elemen s
and pa icula ly o he supe hea y elemen s [85,86]. The
doubly magic nucleus 208Pb, o med by bound 82 p o ons
and 126 neu ons, ep esen s he hea ies expe imen ally and
heo e ically well-known p o on shell closu e. The masses in
his domain ha e been expe imen ally de e mined mainly ia
decay da a and a e now o he i s ime di ec ly measu ed
wi h he MR-TOF-MS. The e o e, his egion o nuclides
is an ideal es ing g ound o he new expe imen al me hod
discussed in his wo k. The new mass alues, measu ed wi h
he MR-TOF-MS, ha e been applied, oge he wi h he expe -
imen ally known da a, o in es iga e he accu acy o di e en
basic heo e ical p edic ions in he Pb egion.
The wo-neu on sepa a ion ene gy (S2n) is de ined by he
ela ion o he mass excess alues (ME):
S2n(N,Z)=ME(N−2,Z)+2ME(n)−ME(N,Z),(30)
whe e ME(n) is he mass excess o he neu on. The S2n
su ace in he Pb mass egion is shown in Fig. 18.
As al eady p esen ed in he p e ious chap e s, he new
MR-TOF-MS da a a e in excellen ag eemen wi h p e iously
known da a, which ha e been de e mined ia Qα alues and
o he qui e di e en expe imen al me hods. The expe imen al
S2n alues show he expec ed s eep d op a he N=126 shell
o all elemen s in he egion. A close look indica es ha he
slope becomes shallowe wi h an inc easing di e ence o he
p o on numbe om he closed shell Z=82.
This e olu ion o he shell gap nea he double magici y can
be illus a ed by he slope o he di e ence o he wo-neu on
sepa a ion ene gies o di e en elemen s, gi en by
1nS2n(N,Z)=S2n(N+1,Z)−S2n(N,Z).(31)
Figu e 19 p esen s his co ela ion using he expe imen al da a
o his wo k and he AME2016 da abase [62]. The symbols
deno ed by a blue colo indica e he mass excess da a o he
p esen expe imen s.
064313-17
SAMUEL AYET SAN ANDRÉS e al. PHYSICAL REVIEW C 99, 064313 (2019)
FIG. 19. Slope o he wo neu on sepa a ion ene gy 1nS2n s
p o on numbe . The black symbols show o he da a co esponding o
he AME16 and he blue symbols he measu emen s om his wo k.
The obse a ion is ha , excep o he chain o N=126
and N=127, he co ela ion is e y weak, mani es ed in
he ho izon al slopes wi h small s agge ing. The beha io o
N=127 and N=126 is signi ican ly di e en . The cu es
exhibi a posi i e slope beyond he Z=82 shell closu e
and unde go a minimum nea he p o on shell closu e. The
peculia expe imen al obse a ion has been mani es ed by he
di ec mass measu emen s p esen ed he e.
In he nex s ep o his s udy, i is in e es ing o in es iga e
he p edic ions o di e en heo e ical models in he same
mass ange. A compa ison o se e al success ul mass models
based on qui e di e en heo e ical app oaches was done.
The p edic i e powe o di e en models ha e been ecen ly
compa ed wi h expe imen al da a in Re . [87].
In Fig. 20, he heo e ical slopes o wo-neu on sepa a-
ion ene gies wi h neu on numbe s 124–128 a e shown as a
unc ion o he a omic numbe . In gene al, he heo e ical da a
s ongly de ia e om he expe imen al obse a ion, especially
o he N=126 and N=127 chains. In he op panel o
Fig. 20, he p edic ions o Mye s and Swia ecki [88], based on
he Thomas-Fe mi (TF) model, a e p esen ed. This model has
one o he bes p edic i e powe o e he ull ange o iso opes
[87]. The TF model indica es o all neu on chains ho izon al
slopes wi h small s agge ing ea u es. Excep o he N=126
and N=127 chains, his e lec s he expe imen al obse a-
ion. Howe e , o N=126 and N=127 he TF model de i-
a es s ongly and has de ia ions o se e al hund ed keV. The
wo o he heo e ical compa isons show wo pu e mic oscopic
app oaches. In he middle panel, a Ha ee-Fock-Bogolubo
model, deno ed as “HFB-21” [89], and in he bo om panel,
an ene gy densi y unc ional “UNEDF0” [90] we e employed.
The s ong de ia ion o expe imen al and heo e ical da a es-
pecially o N=126 and N=127 is mani es ed in all panels
o Fig. 20.
In he HFB-21 app oach, one can see a s agge ing wi h an
ampli ude nea 1 MeV, which is clea ly no obse ed in he
FIG. 20. Slope o he wo neu on sepa a ion ene gy 1nS2n s
p o on numbe in di e en mass models, Thomas-Fe mi [88], HBF21
[89], and UNDEF0 [90].
expe imen al da a. This sugges s ha he pai ing o ce is no
p ope ly adjus ed in his model. In he UNEDF0 app oach,
he co esponding cu es a e smoo h and ho izon al. Howe e ,
bo h heo ies canno ep oduce he expe imen al obse a ion.
The UNEDF0 model has e en a e e sed o de o he N=
126 and N=127 shells. The obse ed expe imen al peculia -
i y is ce ainly a s ingen es o he accu acy and limi a-
ion o he p esen heo ies. The e o e, i ep esen s a s ong
mo i a ion o heo e ical imp o emen s e en in he so-called
well-known domain o he doubly magic nucleus 208Pb and
o he domain o shell e ec s o supe hea y elemen s.
VII. SUMMARY AND OUTLOOK
Di ec mass measu emen s o ission and p ojec ile ag-
men s p oduced wi h 238U and 124Xe p ima y beams ha e
been pe o med wi h he MR-TOF-MS o he FRS Ion Ca che
in ou expe imen s. The nuclides we e p oduced, sepa a ed in
ligh , ene gy bunched wi h he FRS and inally he malized
in a gas- illed c yogenic s opping cell (CSC). An MR-TOF-
MS specialized o he accu a e mass measu emen s o a e
iso opes, wi h a ew coun s only, has been used in he p esen
expe imen s. A da a-analysis p ocedu e was de eloped o
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HIGH-RESOLUTION, ACCURATE MULTIPLE-REFLECTION … PHYSICAL REVIEW C 99, 064313 (2019)
de e mine he mass alues and hei unce ain ies. The anal-
ysis is well sui ed o o e lapping peaks, which solely can
be dis inguished om a single peak by a change in he peak
shape. Wi h his da a-analysis p ocedu e, he e ec i e mass-
esol ing powe o o e lapping peaks is inc eased by a ac o
o up o 3 compa ed o s anda d da a analysis. This p ocedu e
has a di ec impac o he esolu ion o low-lying isome s.
The masses o 31 uns able nuclides wi h hal -li es down
o 18 ms we e measu ed. Mass esol ing powe s (FWHM)
beyond 400 000 we e achie ed. This is he highes mass-
esol ing powe eached in mass measu emen s o sho -li ed
nuclides wi h an MR-TOF-MS up o now. The masses o six
isome ic s a es wi h exci a ion ene gies down o 280 keV we e
de e mined. Nuclides o 15 di e en elemen s we e measu ed
wi h coun a es as low as 11 e en s pe nuclide. I was u he
possible o ex ac mass alues o iso opes wi h ion de ec ion
a es o as low as 12 e en s pe hou . The weigh ed mean o he
ela i e de ia ions om li e a u e o all he measu ed masses
is (4.5±5.3) ×10−8. The minimum ela i e unce ain y ob-
ained wi h he MR-TOF-MS is 6 ×10−8.
The i s di ec mass measu emen s o se en iso opes close
o he double magic nucleus 208Pb allowed us o s udy he
e olu ion o he wo-neu on sepa a ion ene gies. A s ong
elemen dependency is seen o he i s neu on abo e he
closed p o on shell Z=82. The expe imen al esul s de ia e
s ongly om di e en heo e ical p edic ions, especially o
N=126 and N=127. The e o e, i is a new challenge o he
heo e ical models e en in he so-called well-known domain
o he doubly magic nucleus 208Pb.
These esul s demons a e he compe i i eness o a high-
esolu ion MR-TOF-MS o measu ing masses o sho -li ed
nuclides wi h an accu acy high enough o yield signi ican
in o ma ion o nuclea physics and as ophysics. I opens he
doo o measu emen s o unknown masses wi h an accu acy
ha was up o now only possible wi h Penning aps.
Fu u e e o s will ocus on he ollowing imp o emen s:
Isoba ic con inuous calib a ion will be p o ided by a newly
designed lase abla ion ca bon clus e ion sou ce included in
he upg aded RFQ beamline be ween he CSC and he MR-
TOF-MS [91], he imp o ed ope a ion mode and elec onics
o he MRS will make his unce ain y negligible [92], and
he esol ing powe will be u he inc eased by means o an
imp o ed ion-op ical uning, longe cycle imes, and u he
imp o ed s abili y o he ol ages supplied o he analyze .
Wi h hese imp o emen s, a ela i e unce ain y in he ange
o 2 ×10−8is wi hin each.
While in p e ious expe imen s wi h he FRS Ion Ca che
he ocus was placed on he commissioning and cha ac e -
iza ion o he CSC, expe imen s in he coming yea s will
be dedica ed physics expe imen s. Se e al expe imen al uns
will be pe o med du ing FAIR phase 0 a GSI/FAIR. These
expe imen s include mass measu emen s a N=126 below
208Pb [93] and o N=Znuclides below 100Sn [94]. Mo e-
o e he sys em will be used o iden i y eac ions and decay
p oduc s and he eby measu e β-delayed neu on emission
p obabili ies [95] and mul inucleon ans e eac ion p oduc
c oss sec ions [96].
ACKNOWLEDGMENTS
We g a e ully acknowledge he long-s anding, ui ul col-
labo a ion wi h ou colleague and iend A. Sobiczewski, who
passed away in la e 2017. We would like o hank K.-H. Beh ,
T. Bla z, A. B ünle, C. Ka agiannis, A. K a z, C. Lo ze, C.
Schlö , B. Szczepanczky, J. Sieb ing, T. Wasem, and R. Weiß
o excellen echnical suppo . We would like o hank L.
Schlü e , V. Munoz, G. K ipko-Koncz and M. Macko o help-
ing debug he da a-analysis code. This wo k was suppo ed
by he Ge man Fede al Minis y o Educa ion and Resea ch
(BMBF) unde unde Con ac s No. 05P12RGFN8 and No.
05P15RGFN1, by Jus us-Liebig-Uni e si ä Gießen and GSI
unde he JLU-GSI s a egic Helmhol z pa ne ship ag ee-
men , by HGS-HIRe, and by he Hessian Minis y o Science
and A (HMWK) h ough he LOEWE Cen e HIC o FAIR.
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