High-precision mass measurements of nickel, copper, and gallium isotopes and the purported shell closure at N=40

0.55 MB·English

by  C. Guenaut

High-pre
ision mass measurements of ni
kel,
opper, and gallium isotopes and the
purported shell
losure at N=40
∗
1, 1 2 2,3 4 5 2
C. Guénaut, G. Audi, D. Be
k, K. Blaum, G. Bollen, P. Delahaye, F. Herfurth,
†
5 2,6 7 1 4 8 2
A. Kellerbauer , H.-J. Kluge, J. Libert, D. Lunney, S. S
hwarz, L. S
hweikhard, and C. Yazidjian
1
CSNSM-IN2P3-CNRS, 91405 Orsay-Campus, Fran
e
2
GSI, Plan
kstraÿe 1, 64291 Darmstadt, Germany
3
Johannes Gutenberg-Universität, Institut für Physik, 55099 Mainz, Germany
4
NSCL, Mi
higan State University, East Lansing, MI 48824, USA
5
CERN, Physi
s Department, 1211 Genève 23, Switzerland
6
Physikalis
hes Institut, Universität Heidelberg, 69120 Heidelberg, Germany
7
Institut de Physique Nu
léaire, IN2P3-CNRS, 91406 Orsay-Campus, Fran
e
8
Institut für Physik, Ernst-Moritz-Arndt-Universität, 17487 Greifswald, Germany
7 (Dated: February 8, 2008)
0
0 High-pre
ision mass measurements of more than thirty neutron-ri
h nu
lides around the
2 Z=28
losed proton shell were performed with the triple-trap mass spe
trometer ISOLTRAP at
n ISO5L7D,60E,6/4C−E69RN tZo a=dd2r8ess6t5h−e74q,7u6estionZo=f a2p9ossible6n3e−u6t5r,6o8n−7s8hell
lZosu=re3a1t N=40. The results,
for Ni ( 1),0−8 Cu ( ), and 72−74,G76a ( ), have a relative un-
a

ertainty of the order of . In parti
ular, the masses of Cu have been measured for the
J
(cid:28)rst time. We analyse the resulting mass surfa
e for signs of magi
ity,
omparing the behavior of
2
N=40tothatofknownmagi
numbersandtomid-shellbehavior. Contrarytonu
learspe
tros
opy
2
studies, noindi
ations of a shell or sub-shell
losure are foundfor N=40.

1
PACSnumbers: 21.10.Dr,21.60.Cs,27.50.+e,32.10.Bi
v
9
2 N = 40
I. INTRODUCTION found. One
ase of parti
ular interest is that of
0
1 be
ause of the unexpe
ted events that have transpired
0 sin
e the (cid:28)rst studies in 1982. At that time, B68ernas
7 Astrikingparallelbetweentheatomi
andnu
learsys- et al0.+[10℄ showed that the (cid:28)rst ex
2i+ted sta0t+e of 28Ni40
0 tems is the o

urren
e of
losed shells. The behavior was , establishing a new
ase o4f0 and inversion.
x/ of the atomi
system is largely governed by what
an Thiswas
omparedtothe
aseof20Ca20,adoubly-magi
e be
onsidered as an in(cid:28)nitely massive and point-like nu- nu
lide[11℄ where su
h an invers6i8on was known. Conse-
-
leus. Des
ribing nu
lear behavior, however, is a par- quently,Bernasetal.
on
luded Nitobedoubly-magi
.
l
c ti
ularly di(cid:30)
ult task given its
omposition of neutrons
In 1995, Brodaet al.[12℄ published a
omprehensive
u and protons,similarin massyet di(cid:27)erent in
harge. The
n nu
leon intera
tion is so
ompli
ated that ground-state summaryofspe
tros
opyw68orksin
e1982andelaborated
v: properties are not globally predi
ted with parti
ularly the ex
ited0s+pe
trum of Ni, (cid:28)nding2t+he (cid:28)rst ex
ited
i good pre
ision. A property
ru
ial to the understanding state to be (as Be5r−nas et al.[10℄), as the se
ond
X ex
ited state and a 80 isomeri
state. As this is the
ofthenu
learsystemisthebehaviorofitsshellstru
ture
r as a fun
tion of the varying
omposition of protons and same6s8ituationforthe Zrex
itedstates,they
on
luded
a that Ni was spheri
al, implying a signi(cid:28)
ant sub-shell
neutrons. Thefa
tthatshellstru
tureseemstobemod- N = 40
N
losure at . Shell-model predi
tions of isomeri
i(cid:28)edinsystemswherethenumberofneutrons andthe
Z states near magi
nu
lides motivated the experimental
number of protons are unbalan
ed (i.e. far from the
investigations of Grzywa
z et al.[13℄ in 1998. T68hey dis-
equilibrium region of stable nu
lides) is one of the key

overedmany isomeri
states in the vi
inity of Ni, fur-
questions of today's nu
lear physi
s resear
h.
ther strengthening the
ase for its doubly-magi

hara
-
β
Overthelast20years,magi
numbershavebeenfound ter. In 1999, -de
ay studies were
arried out by Han-
to vanish in
ertain region of the
hart of nu
lides, the nawaldetal.[14℄,whofoundlonghalf-livesfortheneigh-
N = 40
(cid:28)rst one being N =20 for sodium[1℄ and later, magne- boring isotones (
opper, manganese) at indi
at-
β
sium[2℄. More re
ently, N =8 [3, 4℄ and N =28[5, 6℄ ing an in
rease in
olle
tivity. However, -de
ay studies
havealsodisappeared. Conversely,(cid:16)new(cid:17) magi
numbers by Mueller et al.[15℄ the same yearshowed that the sta-
N =40
su
h as N =16 [3℄ and N =32 [7, 8, 9℄ have also been bilizin6g8 e(cid:27)e
t of disappeared when moving away
from Ni.
The powe6r8ful tool of Coulomb ex
itation was brought
† to bBea(rEo2n) Ni in 2002 when Sorlin et al.[16℄ measured
∗1P03r9es8e0n,t69a0d2d9reHsse:idMelbaxergP,laGne
rkmIannsytitut für Kernphysik, Postfa
h the value (whi
h is0+the probability of transi2ti+on
between the ground state and the ex
ited state ).
Corresponding author; Present address: NSCL, Mi
higan State B(E2)
University, East Lansing, MI 48824, USA; E-mail address: is expe
ted to be small for magi
nu
lides whi
h
guenautns
l.msu.edu are di(cid:30)
ult to ex
ite, and to be large for deformed nu-
2
B(E2) B

lides. The measured value w68as unexpe
tedly paragraph). The magneti
(cid:28)eld is determined from a
small, reinfor
ing the magi
nature of Ni. Sorlinet al. measurementofthe
y
lotronfrequen
yofareferen
eion
attributed the la
k of
orroborating eviden
e from the whosemassiswellknown. Thesetupalsoin
ludesano(cid:27)-
N = 40
mass surfa
e to an erosion of the sub-shell, ero- line ion sour
e to produ
e stable ions, used as referen
e
sion
on(cid:28)rmed by re
ent measurements[17, 18℄. How- masses.
ever, a
on
erted theoreti
al e(cid:27)ort published by Lan-
gan68ke et al.[19℄ argued against theBd(Eou2b)ly-magi
nature
of Ni, noting that the (cid:16)missing(cid:17) strength lies at B. Mass measurement pro
edure
mu
h higher energy (>4MeV).
A

ordingtoBohrandMottelson[20℄: (cid:16)Intermsofthe
Ion
on(cid:28)nement in a Penning trap is based on the ap-
expansionofthetotalbindingenergy,the shellstru
ture
pli
ation of an ele
trostati
(cid:28)eld and a magneti
(cid:28)eld to
appears as a small
orre
tion
ompared to the surfa
e
storeions in the axial and radialdire
tions, respe
tively.
energy... Despite the smallness of these e(cid:27)e
ts on the
The ion motion in a Penning trap is a superposition of
s
ale of the total nu
lear energy, they are of de
isive
three independent harmoni
os
illator modes, one in the
importan
e for the stru
ture of the low-energy nu
lear νz
axialdire
tionwithfrequen
y andtwointheradialdi-
spe
tra...(cid:17) In the light of these
on(cid:29)i
ting experimental i.e.
re
tion, the
y
lotronmotionwithredu
edfrequen
y
and theoreti
al signatures as well as the relatively large ν+ ν−
,andthemagnetronmotionwithfrequen
y [30,31℄.
un
ertaintyonthebindingenergiesinthisinterestingre-
Inapurelyquadrupolarele
tri
(cid:28)eld,thefrequen
iesare
gion,high-pre
isionmassmeasurementswere
arriedout
related as follows:
withthemassspe
trometerISOLTRAPinanattemptto
bring some
lari(cid:28)
ation to this situation. Time-of-(cid:29)ight νc =ν++ν−.
(1)
massmeasurementshad been performedin 1994[21℄ but
N =40
althoughtheygavenoindi
ationthat wasmagi
,
IonbeamsarealternativelydeliveredfromISOLDEor
the pre
isionwasinsu(cid:30)
ient to be
on
lusive. The most
from an o(cid:27)-line ion sour
e and inje
ted into the RFQ,
a

uratemassmeasurementstodayareperformedinPen-
mounted on a 60-keV pedestal, where they are
ooled
ning traps[22, 23℄ and ISOLTRAP at CERN has pio-
and bun
hed. The ion bun
h from the RFQ is sent to
neered the appli
ation to radioa
tive nu
lides[24, 25℄.
the preparation trap. Ion
ollisions with the bu(cid:27)er gas
The experimental setup of ISOLTRAP is presented in
N =40 inside this trap (cid:28)rst
oolthe axialmotion. A dipolarex-
se
tionII,andthemeasurementsintheregionof ν−

itation with a frequen
y is then applied to in
rease
and their evaluation are des
ribed in se
tionIII. A
om-
the magnetron radius of all ion spe
ies, making it larger
parison to mass models follows in se
tion IV and the
N = 40 than the exit hole of the trap. To sele
t the ions of in-
question of is dis
ussed in the light of the new
terest, an azimuthal quadrupole radio-frequen
y ele
tri
results in the last se
tion. νc
(cid:28)eld at frequen
y is applied whi
h
ouples the radial
modes. Sin
e one mode is
ooled by the gas, the radius
is redu
ed and the ion
loud is
entered. In this way the
II. THE ISOLTRAP SETUP
Rtra=pmwo/r∆ksmasan10i4soba1r0s5eparatorwith aresolvingpower
of to [28℄.
A. Experimental setup The puri(cid:28)ed ion beam is transferred to the pre
ision
trap,wheredi(cid:27)erentex
itationsareperformed. Aphase-
ν
−
ISOLTRAP is a high-pre
ision Penning-trap mass sensitive dipolar ex
itation at is applied to in
rease
spe
trometer, lo
ated at CERN's ISOLDE fa
ility[26℄ the magnetron radius of the ion motion[32℄. If there
whi
h delivers mass-separated beams of radionu
lides. are
ontaminants (isobars or isomers), a se
ond, mass-
ν+
ISOLTRAP is
omposedofthreemainparts(see Fig.1). dependent dipolar ex
itation is performed at to re-
First, a linear gas-(cid:28)lled radio-frequen
y quadrupole movethem[33℄. Finally, an azimuthal quadrupole radio-
(RFQ) trap, used as
ooler and bun
her, adapts the 60- frequen
y(cid:28)eldisappliedto
onverttheinitialmagnetron
ν = ν
RF c
keV ISOLDE ion beam to the ISOLTRAP requirements motion into
y
lotron motion. At , a full
on-
with respe
t to kineti
energy, time stru
ture, and beam version is obtained, leading to an in
rease of the orbital
µ
emittan
e[27℄. These
ondpartisagas-(cid:28)lled,
ylindri
al magneti
moment andtheasso
iatedradialkineti
en-
E = µB
Penningtrap[28℄inwhi
hamass-sele
tiveheliumbu(cid:27)er- ergy [34℄. After eje
tion at low axial energy,
g1a0s5
oolingte
hnique[29℄witharesolvingpowerofupto ions pass the inhomogeneous part of the magneti
(cid:28)eld
isusedforisobari

leaning. Thispreparationtrapis ontheirwaytoan MCPdete
tor(re
entlyrepla
edby a
B
installed in a =4.7Tsuper
ondu
tingmagnet. Finally,
hanneltron dete
tor[35℄) at the top of the setup. Sin
e
the
ooled ion bun
h is transferred to the pre
ision Pen- theaxiala

elerationinthisfringe(cid:28)eldisproportionalto
µ ∂B/∂z
ning trap for isomeri
separation (when required) and · , the shortest time of (cid:29)ight (TOF) is observed
ν =ν
RF c
mass measurement. The pre
ision Penning trap is in- for [36℄.
B
stalled in a se
ond super
ondu
ting magnet ( =5.9T). The mass resolution in the pre
ision trap depends
The massisdetermined by measuringthe true
y
lotron strongly on the
onversion time used for the ex
itation.
ν = qB/(2πm) ∆ν
c
frequen
y of the stored ion (see next Thelinewidth oftheresonan
eismainlydetermined
3
MCP 3/Channeltron

440
420
400
)
sµ 380
(
F
O 360
T
n 340
a
e
M 320
68 +
300 Ni
280
1338918 1338920 1338922 1338924
Excitation frequency (Hz)
RFQ trap
-
-
FIG. 1: Sket
h of the experimental setup of the ISOLTRAP mass spe
trometer, in
luding the main parts: a gas-(cid:28)lled linear
radio-frequen
y quadrupole (RFQ) trap for
apturing and preparing the ISOLDE beam, a gas-(cid:28)lled
ylindri
al Penning trap for
isobari
separation, and a hyperboli
Penning trap for the mass measurement. The mi
ro-
hannel plate (MCP) dete
tors are
used to monitor the ion transfer and to measure the extra
ted-ion time of (cid:29)igh6t8(T+OF) together with the
hanneltron dete
tor.
The inset presents a time-of-(cid:29)ight (TOF)
y
lotron resonan
e for radioa
tive Ni ions.
T
RF
by the duration of the applied RF-(cid:28)eld ( ) used to solving power. With su(cid:30)
iently long ex
ita1t0i7on times

ouple the two radial motions. The relation is[34℄: (few se
onds), a resolving power of up to
an be
0.9 rea
hed. As an example of a
y
lotron frequen
y mea-
∆ν(FWHM) .
≈ T (2) surement, the inset of Fig.1 presents the time-of-(cid:29)ight
RF
(TOF)-resonan6
8e
urve of one of the two measurements
The statisti
al pre
ision in the
y
lotron frequen
y de- of radioa
tive Ni. The mean TOF of the ions as a
termination is given by[37℄: fun
tion of the applied radio-frequen
y (RF) is shown.
δν 1 The solid line is a (cid:28)t of the well-knownline-shape[31℄ to
,
ν ∝ νT √N (3) the data points. This measurement was pTerfor=me9d00with
RF RF
about 1000 ions using an ex
itati1o.n1 tim10e6 ms,
N R =νTRF resulting in a resolving power of × and a relative
with being the number of ions and the re-
4
δν/ν =6 10−8
frequen
y un
ertainty of × . ground-state properties, su
h an evaluation is unique to
mass measurements.
The mass values from the present measurements are
III. MEASUREMENTS OF THE NI, CU, AND presented in TablesI (Ni), II (Cu), and III (Ga). These
GA ISOTOPES t8a5ble+s give the ratio of the
y
lotron frequen
y of the
57,60,64−69 65−74,76 Rb [40℄ referen
e mass to that of the ion of interest.
63−T6h5,e68−7n8u
lides Ni, Cu, and The
orresponding un
ertainty takes into a

ount a sta-
Ga have been investigated with ISOLTRAP. tisti
alun
ertaintydependingonthenumberofions,and
They were produ
ed at ISOLDE by bombarding a a systemati
error[39℄. The derived mass ex
ess value
1.4
uranium
arbide(UC) target with -GeVprotonsfrom is indi
ated for
omparison with the AME tables from
CERN's Proton Syn
hroton Booster. The ionization 1995and 2003. Sin
e thelatest Atomi
-MassEvaluation
was a
hieved for gallium with a tungsten (W) surfa
e (AME2003[42℄)in
ludesthedatafromthis work,thein-
ionization ion sour
e and for
opper and ni
kel with (cid:29)uen
eoftheISOLTRAPmeasurementsisalsoprovided.
the resonan
e ionization laser ion-sour
e (RILIS)[38℄. Among the 36 nu
lides measured here, the in(cid:29)uen
e is
ISOLDE's General Purpose Separator (GPS), with a 100% for 22 of them.
mass resolving powe6r3−o6f5 about 1000 was used. The The ni
kel results are presented in TableI and in
proton-ri
h isotopes Ga were measured in a di(cid:27)er- Fig.2. This (cid:28)gure presents the di(cid:27)eren
e between the
ent experiment using a ZrO target and ISOLDE's High massex
essmeasured by ISOLTRAP and the AME1995
Resolution Separator(HRS), whi
hhasamass-resolving values. Note that even for the stable ni
kel isotopes
power of about 3000. Both3tar1g0e1t3s were bombarded the pre
ision of t6h9e mass values is improved. With
using pulses
ontaining up to × protons. the ex
eption of Ni (see below) the results are in
The1y0i5elds of ni
kel and
opper were fairly intense at good agreement with th5e7,6109,6955 table but mu
h more
about ions/s. The e(cid:30)
ien
y of ISOLTRAP is better pre
ise. The masses of Ni agree with the 1995
than 1% so a beam gate was used in order to limit the table within the error bars, and were measured with
number of ions sent to the pre
ision trap and minimize the same order of un
ertainty. The
ombination of
ion-ionintera
tionsthat
ausefrequen
yshifts. Thetyp- the previous value and the ISOLTRAP measurement
i
alnumberofionssimultaneouslystoredinthepre
ision redu
es69the (cid:28)nal un
ertainty. The results
ontributing
trap was between 1 and 8. to the Ni mass value are presented in Fig.3. This is a
Despite the good yields of ni
kel and
opper nu
lides, spe
ial
asebe
auseitisinstrongdisagreementwiththe
uptothreeordersofmagnitudemoresurfa
6e8-ionizedgal- AME1995 table[43℄: a di(cid:27)eren
e of more than 400keV
liumwaspresent. For6t8he measurementof Nishownin wa7s0obs1e4rved15. T69he AME1995 value was derived from
Fig.1, a
leaning of Ga was applied in68the prep6a8ra- a Zn( C, O) Ni rea
tion[44℄ and a time-of-(cid:29)ight
tion trap. The ratio between the yield of Ga and Ni measurement[21℄. The ISOLTRAP value disagrees
was (cid:16)only(cid:17) a fa
tor of ten whi
h was low enough to al- with the value from the rea
tion but is in agreement
low an e(cid:27)e
tive
leaning. This ratio was higher farther with the time-of-(cid:29)ight measurement. Sin
e the value
from stability and prevented the measurement of more of ISOLTRAP is mu
h more pre
ise, the AME2003
neutron-ri
hni
keland
oppersin
ethepreparationtrap in
ludes only this value.
was saturated by the gallium isobars. Similarly, a sig-
ni(cid:28)
ant
ontamination of titanium oxide prevented the
measurement of more proton-ri
h gallium isotopes, and
the presen
eof rubidium isobarsmade the measurement
of more neutron-ri
h gallium isotopes impossible.
The results from the data analysis is the ratio The
opper results are listed in TableII, a
ompar-
ν /ν m
c,ref c[39℄, sin
e the atomi
mass of the ions is
al- ison with the AME1995 values is given in Fig.4. An

ulated from the ratio between the
y
lotron frequen
y improvement of the mass un
ertainty was a
hieved
ν
of the referen
eion c,ref and the
y
lotronfrequen
y of for all investigated
opper isotopes. The values7a0re inn
ν
t8h5e ion of interest c, the atomi
mmass of the referen
e good agreement with previous values, ex
ept for Cu .
Rb[40℄, and the ele
tron mass e: This important di(cid:27)eren
e is due to an in
orre
t state
νc,ref assignm10e6nt. ISOLTRAP's high resβolving power of more
m= (m85Rb me)+me. than , in
ombination with -de
ay studies and
ν − (4)
c
sele
tive laser ionization allowed us to perform a
lear
identi(cid:28)
ation of ea
h state[45℄. Moreover, this high
Alltheresultswereevaluatedinordertoin
ludethem
reso68lving power allowed us to resolve isomeri
states
in theAtomi
-MassEvalution (AME) table[41℄. The ta-
in Cu[467℄2−an74d,76to measure them independently. The
ble of atomi
masses results from an evaluation of all
masses of Cu were previously unknown. They
available experimental data on masses, in
luding dire
t
are
ompared to model predi
tions in Se
tionIV.
measurementsaswellasde
ayandrea
tionstudies. The
AMEformsalinkednetworkandusesaleast-squaresad-
justmenttoderivetheatomi
masses. Amongallnu
lear
5
ν /ν
c,ref c
TABLE85I: IS+OLTRAP results for ni
kel isotopes: nu
lide; half life; frequen
y ratio of ni
kel isotope to referen
e
nu
lide Rb [40℄,
orresponding mass ex
ess (ME); mass ex
ess from AME1995; new mass ex
ess from AME2003; in(cid:29)uen
e
of the present result on the AME2003 value.
ν /ν
c,ref c
Isotopes Half life ISOLTRAP AME1995 AME2003 In(cid:29)uen
eon
T
1/2
ME (keV) ME (keV) ME (keV) AME2003
57
Ni 35.6 h 0.6705736693 (316) -56084.2 (2.5) -56075.5 (2.9) -56082.0 (1.8) 52.0%
60
Ni Stable 0.7057986239 (183) -64472.7 (1.4) -64468.1 (1.4) -64472.1 (0.6) 16.6%
64
Ni Stable 0.7528734602 (163) -67096.9 (1.3) -67095.9 (1.4) -67099.3 (0.6) 21.9%
65
Ni 2.5 h 0.7646753441 (285) -65129.0 (2.3) -65122.6 (1.5) -65126.1 (0.6) 7.8%
66
Ni 55 h 0.7764412560 (181) -66006.3 (1.4) -66028.7 (16.0) -66006.3 (1.4) 100%
67
Ni 21 s 0.7882468785 (362) -63742.7 (2.9) -63742.5 (19.1) -63742.7 (2.9) 100%
68
Ni 29 s 0.8000274080 (377) -63463.8 (3.0) -63486.0 (16.5) -63463.8 (3.0) 100%
69
Ni 12 s 0.8118484759 (466) -59978.6 (3.7) -60380 (140) -59979 (4) 100%
ν /ν
c,ref c
TABLE8I5I: I+SOLTRAP results for
opper isotopes: nu
lide; half life; frequen
y ratio of
opper isotope to referen
e
nu
lide Rb [40℄,
orresponding mass ex
ess (ME); mass ex
ess from AME1995; new mass ex
ess from AME2003; in(cid:29)uen
e
of the present result on the AME2003 value. Previously unknown values derived from systemati
trends are marked with #.
ν /ν
a c,ref c
Isotopes Half life ISOLTRAP AME1995 AME2003 In(cid:29)uen
e
T
1/2
ME (keV) ME (keV) ME (keV) on AME2003
65
Cu Stable 0.7646483448 (139) -67264.5 (1.1) -67259.7 (1.7) -67263.7 (0.7) 36.8%
66
Cu 5.1 m 0.7764380632 (257) -66258.8 (2.0) -66254.3 (1.7) -66258.3 (0.7) 11.1%
67
Cu 62 h 0.7882016658 (155) -67318.8 (1.2) -67300.2 (8.1) -67318.8 (1.2) 100%
68 g
Cu 31.1 s 0.8000008176 (199) -65567.0 (1.6) -65541.9 (45.6) -65567.0 (1.6) 100%
68 m
Cu 3.7 m 0.8000098791 (188) -64850.3 (1.5) -64818 (50) -64845.4 (1.7) 50%
69
Cu 2.8 m 0.8117756816 (174) -65736.2 (1.4) -65739.9 (8.1) -65736.2 (1.4) 100%
70 g
Cu 45 s 0.8235875816 (199) -62976.1 (1.6) -62960.3 (14.5) -62976.1 (1.6) 100%
70 m
Cu 33 s 0.8235888547 (258) -62875.4 (2.0) -62859 (15) -62875.4 (2.0) 100%
70 n
Cu 6.6 s 0.8235906419 (272) -62734.1 (2.1) -62617 (15) -62734.1 (2.1) 100%
71
Cu 19 s 0.8353679363 (194) -62711.1 (1.5) -62764.2 (35.2) -62711.1 (1.5) 100%
72
Cu 6.6 s 0.8471819597 (182) -59783.0 (1.4) -60060# (200#) -59783.0 (1.4) 100%
73
Cu 4.2 s 0.8589690332 (491) -58986.6 (3.9) -59160# (300#) -58987 (4) 100%
74
Cu 1.6 s 0.8707837184 (779) -56006.2 (6.2) -55700# (400#) -56006 (6) 100%
76
Cu 640 ms 0.8944013229 (843) -50976.0 (6.7) -50310# (600#) -50976 (7) 100%
ag,m,ndenotetheground,(cid:28)rstex
ited,andse
ondex
itedstate,
respe
tively,ofthenu
lide.
The galliu6m8 results are presentedδimn/TmableI5I.I4an1d0−in7 en
e of a 9.5-se
ond isomeri
state having an ex
ita-
Fig.5. The Ga mass un
ertainty, ≈ · tion energy of only 60 keV (this a

ounts for the large
is mu
h higher than for all the other nu
lides. This AME1995errorbar in Fig.5). Spe
tros
opystudies per-
is due to the use of a shorter ex
itation time (100 ms formed in parallel with the mass measurements revealed

omparedto 900msforthe othernu
lides) and to ala
k no indi
ation that the isomer was produ
ed. A two-
of statisti
s: only 530 ions were observed,
ompared to se
ond ex
itation time was used in order to resolve this
atleast3000formostoftheotherones. TheISOLTRAP state in the pre
ision trap but it was not seen. More-
value is still in agreement with the AME1995 value but over, the z-
lass analysis[39℄ was performed to examine
hasnoin(cid:29)uen
e. Forallothergalliumisotopesmeasured anydependen
eoftheresultasafun
tionofionnumber,
by ISOLTRAP the un
ertainty was de
reased. For (cid:28)ve but revealed no indi
ation of a
ontaminant. Therefore
of them,63it was de
reased by more than a fa
tor of 20, we are
on(cid:28)dent that the present result is that of the
and for Ga, almost 100 times. ground-state mass.
74
The
aseof Gawas
ompli
atedbythepossiblepres-
6
ν /ν
c,ref c
TABLE8I5II:+ISOLTRAP results for gallium isotopes: nu
lide; half life; frequen
y ratio of gallium isotope to referen
e
nu
lide Rb [40℄,
orresponding mass ex
ess (ME); mass ex
ess from AME1995; new mass ex
ess from AME2003; in(cid:29)uen
e
of the present result on the AME2003 value.
ν /ν
c,ref c
Isotopes Half life ISOLTRAP AME1995 AME2003 In(cid:29)uen
e
T
1/2
ME (keV) ME (keV) ME (keV) on AME2003
63
Ga 32 s 0.7412298391 (167) -56547.1 (1.3) -56689.3 (100.0) -56547.1 (1.3) 100%
64
Ga 2.6 m 0.7529779275 (294) -58834.1 (2.3) -58834.7 (3.9) -58834.3 (2.0) 75.2%
65
Ga 15 m 0.7647065938 (176) -62657.3 (1.4) -62652.9 (1.8) -62657.2 (0.8) 35.6%
68
Ga 68 m 0.799981231 (431) -67116.2 (34.1) -67082.9 (2.0) -67086.1 (1.5) 0%
69
Ga Stable 0.8117302720 (193) -69327.9 (1.5) -69320.9 (3.0) -69327.8 (1.2) 65.3%
70
Ga 21 m 0.8235125549 (272) -68910.3 (2.2) -68904.7 (3.1) -68910.1 (1.2) 31.8%
71
Ga Stable 0.8352740255 (357) -70138.9 (2.8) -70136.8 (1.8) -70140.2 (1.0) 13.3%
72
Ga 14.1 h 0.8470706093 (182) -68590.2 (1.4) -68586.5 (2.0) -68589.4 (1.0) 53.0%
73
Ga 4.8 h 0.8588335898 (208) -69699.4 (1.7) -69703.8 (6.3) -69699.3 (1.7) 100%
74
Ga 8.1 m 0.8706314521 (469) -68049.6 (3.7) -68054.0 (70.7) -68050 (4) 100%
75
Ga 130 s 0.8824032092 (305) -68464.6 (2.4) -68464.2 (6.8) -68464.6 (2.4) 100%
76
Ga 33 s 0.8942076217 (246) -66296.7 (2.0) -66202.9 (90.0) -66296.6 (2.0) 100%
77
Ga 13 s 0.9059884728 (303) -65992.4 (2.4) -65874.1 (60.0) -65992.3 (2.4) 100%
78
Ga 5.1 s 0.9177943761 (307) -63706.6 (2.4) -63662.1 (80.1) -63706.6 (2.4) 100%

40 -59500
AME1995 AME1995 TOFI (1994)
500 69
ISOLTRAP
) AME2003 Ni
V
e30 400 (
I
k S
) ( O ISOLTRAP
5 300 L )
9920 TR eV-60000
1 A k
ME 200 P s (
A10 - es
A c
- 100 M x
P E E
A 1 s
R 0 0 9 s
T 9 a-60500
L 5 M
O )

S -100(k 70 14 15 69
-(I10 e Zn( C, O) Ni (1984)
V
)
-200
-20
-300 -61000
1 2 3
57 60 64 65 66 67 68 69
Measurement #

Mass number A
69
FIG. 3:70 M1a4ss 15eOx
e6s9s of Ni determined by the re-
FIG. 2: Di(cid:27)eren
e between the ISOLTRAP mass ex
ess re- a
tion Zn( C, ) Ni[44℄, and a time-of-(cid:29)ight mea-
sultsforni
kelisotopesandtheAME1995values[43℄. Dashed surement[21℄, the resulting AME1995 value[43℄, and the
lines represent the ISOLTRAP error bars. ISOLTRAP value. The AME2003 value[42℄ di(cid:27)ers by 400
keV with an un
ertainty 30 times smaller than the AME1995
value.
7

250
80 AME1995 AME1995
ISOLTRAP ISOLTRAP
200
60
) )
V V
e e
k 40 k 150
( (

) )
5 20 5
9 9 100
9 9
1 0 1
E E
M M 50
A -20 A

- -
P -40 P 0
A A
R -60 R
T T -50
L L
O -80 O
S S-100
(I-100 (I

-150
-120
-140 -200
65 66 67 68g68m69 70g70m70n 71 6364656869707172737475767778
Mass Number A Mass number A
FIG.4: Di(cid:27)eren
ebetweenISOLTRAPmass-ex
essvaluesfor FIG.5: Di(cid:27)eren
ebetweenISOLTRAPmass-ex
essvaluesfor

opper isotopes and the 1995 AME values[43℄. Dashed lines gallium isotopes and the 1995 AME values[43℄. Dashed lines
represent the ISOLTRAP error bars. g denotes ground states represent the ISOLTRAP error bars.
and m,n isomeri
states.
For many years, a hybrid approa
h was adopted for
IV. MASS-MODEL PREDICTIONS COMPARED
predi
ting masses based on a
ombination of the ma
ro-
WITH NEW DATA
s
opi
liquid drop model and mi
ros
opi
(e.g. shell)

orre
tions. The most developed form of these so-
Variousmodelsandformulaehavebeendevelopedover
alledmi
-ma
modelsistheFiniteRangeDropletModel
the years to predi
t properties of nu
lides, parti
ularly (FRDM)[50℄.
their mass. A review
an be found in[47℄ where asubset
The Du(cid:29)o-Zuker (DZ) mass formula[51℄, is a global
ofmassmodels wassingledoutfor
omparison. Wehave
approa
h, derived from a Shell-Model Hamiltonian and

hosen to
ompare our experimental data to those, as
gives the best (cid:28)t to the known masses. Shell-Model
al-
des
ribed below.

ulations, while well-suited for ex
itation energies, are
ThevenerableBethe-Weizsä
kermassformula[48,49℄,
less so for mass predi
tions although some e(cid:27)orts were
was based on the liquid drop model and did not in
lude
m made in this dire
tion[52℄.
shell e(cid:27)e
ts. The nu
lear mass is given by
Inthelastfewyears,Hartree-Fo
kBogolioubov(HFB)

al
ulations have been applied to the
onstru
tion of
m(N,Z)c2 = Zm c2+Nm c2 a A+a A2/3
p n v s
omplete mass tables. Skyrme for
es have tradition-
−
(Z A/2)2 ally aimed at predi
ting a wide range of nu
lear prop-
+ a Z2A−1/3+a − ,
c sym A (5) erties[53, 54, 55,56℄. The(cid:28)rstmi
ros
opi
Skyrme-for
e
mass formula HFBCS-1[57, 58℄ was rapidly super
eded
m m
where p and n arethe protonand neutron masses, by HFB-1[59℄ whi
h, in turn, was
onsiderably revised,
A
and the mass number of the nu
leus. The parame- resultinginHFB-2[60℄. Asystemati
studyofthedi(cid:27)er-
a a a
ters are: v the volume term, s the surfa
e term, c ent adjustable parameters followed, resulting in a series
a
the Coulomb parameter, and sym the asymmetry pa- of formulas up to HFB-9[61, 62, 63, 64℄.
rameter. Note that the tabulated masses are those of In additionto DZ and FRDM, the ISOLTRAP results
the neutral atoms, not of the bare atomi
nu
lei. While are therefore
ompared to HFB-2 and the re
ent HFB-8
inappropriate for mass predi
tions, it
an play an inter- (HFB-9 did not
hange the mass predi
tions appre
ia-
esting diagnosti
role
on
erning
losed shell e(cid:27)e
ts (see bly).
se
tionVD). One
hara
terization of a model is the root-mean-
8
rms
square ( ) deviation from the mass values to whi
h
its parameters were (cid:28)tted, de(cid:28)ned by 1.0
FRDM
DZ95
σrms = N1 vuutXi=N1(miexp−mith)2, (6) ) (MeV)0.5 HHFFBB28
L
E
N m D
exp
where is the number of experimental and theo- O
m
th M
reti
al masses being
ompared. A more
omplete
rms - 0.0
des
riptionofthe deviatioσn,in
ludingerrors,
anbe P
found in[47℄. Table IV shows rms for the models
om- A
R
paredwiththeAME95table[43℄,whi
hdoesnotin
lude T
L
the present ISOLTRAP results, and with AME03[42℄, O
-0.5
S
whi
h does. Our results improved the overall agreement
(I
for the HFB models, worsened it for the Du(cid:29)o-Zuker
(DZ) mass formula and for FDRM there is no
hange.
Examining the isotopi

hains individually, we see that
-1.0
in all
ases the HFB models improved and the DZ
model worsened. For the FRDM, the better (cid:28)t for the 34 36 38 40 42 44 46 48 50
gallium isotopes
ounters the worse (cid:28)t for
opper and
Neutron number N
ni
kel. The di(cid:27)eren
es are admittedly small (between
1 and 10%). While it is tempting to
on
lude that the
σ
rms

omparisonof the might be ademonstration of the FIG. 6: Mass di(cid:27)eren
e between ISOLTRAP results and
positiveevolutionofHFB-2to HFB-8, itis importantto m72,o7d3e,7l4,7p6redi
tions for the
opper isotopes. Note that
re
all that unlike FRDM and DZ, HFB-8 was adjusted Cuaremeasured forthe (cid:28)rsttimeandthat the more
to the masses of the AME03. re
ent parameter (cid:28)t for HFB-8 in
luded these results.
σ
rms
TABLE IV: The root-mean-square deviation (in MeV)
(cid:28)veneutronsmorethanthemostneutron-ri
hpreviously
for di(cid:27)erent models: the Du(cid:29)o-Zuker (DZ) mass formula,
knownmass. Thedi(cid:27)eren
esofthenewISOLTRAP
op-
the Finite Range Droplet Model (FRDM), and the Hartree-
per masses with respe
t to the above-mentioned models
Fo
k Bogolioubov (HFB)
al
ulations, performed with the
are shown in Fig.6.
AME tables of 1995 and 2003 (the latter in
ludes the present
ISOLTRAP data). Cal
ulations were made for the ni
kel, Despite going signi(cid:28)
antly farther from stability, it is

opper, and gallium isotopes measured by ISOLTRAP. The di(cid:30)
ult to asseswhi
hmode7l6doesabetterjob. The one
(cid:28)rst two rows present the
al
ulation for all nu
lides and the
losest to the new mass of Cu is HFB-8, however the
rms
followingrowsdes
ribetheresults forea
hisotopi

hainsep- other models are not far away. The errors on just
arately. thefourpreviouslyunknownmassesarealsosimilarwith
DZ (0.309 MeV) seeming to follow with a better trend

ompared to all the others (HFB-8: 0.400 MeV; HFB-
Nu
lide AMETable DZ FRDM HFB-2 HFB-8
2: 0.566 MeV; FRDM: 0.603 MeV). It is surprising that
Ni,Cu,Ga AME95 0.434 0.555 0.843 0.550 despite all models having their parameters adjusted to
N <43
Ni,Cu,Ga AME03 0.451 0.555 0.801 0.530 themasstablesthatin
ludedthosenu
lideswith ,
those masses are not very well reprodu
ed lo
ally.
Ni AME95 0.623 0.445 1.211 0.732
Some nu
leon-nu
leon e(cid:27)e
tive intera
tions (cid:21) like for
Ni AME03 0.640 0.476 1.174 0.678 instan
e Skyrme SKM*, SLy4, or Gogny D1 (cid:21) are de-
signedtogiverisetoarealisti
mean(cid:28)eld(in
ludingpair-
Cu AME95 0.426 0.471 0.644 0.601
ing). They arethereforeparameterized on the groundof
Cu AME03 0.451 0.530 0.626 0.563
afewavailablenu
leardataforwhi
hmean(cid:28)eld(in
lud-
Ga AME95 0.280 0.644 0.654 0.375 ing pairing) e(cid:27)e
ts
an be reasonably disentangle from
long range
orrelations ones (for instan
e, binding en-
Ga AME03 0.291 0.614 0.648 0.384
ergies of doubly magi
nu
lei only). Su
h approa
hes
of nu
lei in whi
h long range
orrelations are not intro-
du
ed in the mean (cid:28)eld in an e(cid:27)e
tive and somewhat
Of parti
ular interest for mass models is to
ompare un
ontrolled manner do not have as obje
tive to give a
predi
tionsasfaraspossiblefromwhatisalreadyknown. pre
isemassformulaatthemean(HFB)(in
ludingpair-
In the
ase of the
opper isotopes presented h76ere, four ing) level, but to
onstitutethe mean (cid:28)eld input ofmore
newmassesweredeterminedandoneofthem( Cu)has elaborated des
riptions of nu
lei
onsidering (cid:21) at least
9
plied with some noti
eable su

esses to di(cid:27)erent nu
lear
problems, for instan
e to shape
oexisten
e and tran-
sitions in light mer
ury isotopes[69℄, or Normal-Super-
AME2003 deformedphenomena[70,71℄hasbeen
onsidered. Using
2 HFB-D1S 2 a Generator Coordinateapproa
hunder Gaussian Over-
GCM-GOA lap Approximation (GCM-GOA) in a spa
e
onstituted
)
V byHFB(D1S)statesunderaxialandtriaxialquadrupole
e A
M 1 1 M
onstraintsallowsinthismodeltotreatonthesamefoot-
s ( E ing rotation and quadrupole vibrations. This approa
h
s S whi
h takes expli
itly into a

ount these important
or-
a
m 2n relations, has been applied to the
al
ulation of ni
kel
el 0 0 - m masses, and the results are shown in Fig.7 for
ompari-
od o sromn.sAlreadythe mass values (left) aregreatly improved
m d ( di(cid:27)eren
e of 0.701 MeV), as are the mass deriva-
e rms
- -1 -1 Sl tives (right, di(cid:27)eren
e of 0.335 MeV). It would ap-
s
s 2n pearthatgoingbeyondthemean(cid:28)eldistobeen
ouraged
ma (M for future mass predi
tions. Works in this spiriet.agr.e also
E -2 -2 e underway on the ground of Skyrme for
es (see [72℄).
V
M
)
A
V. ANALYSIS OF THE MASS SURFACE
-3 -3 AROUND Z=29 AND N=40
28 32 36 40 4428 32 36 40 44 As re
alled in the introdu
tion, Bohr and Mottel-
son[20℄ explain that the e(cid:27)e
ts of binding energy on nu-
N N
lear stru
ture are subtle but de
isive. As su
h, a

u-
rate massmeasurements areimportant in orderto (cid:28)nely
analyse the mass surfa
e, notably its derivatives. In this
FIG. 7: Di(cid:27)eren
e of the ni
kel results from the Atomi
se
tion we examine several mass-surfa
e derivatives and
MassEvaluation2003(AME2003)whi
halready in
ludesthe
variations.
present ISOLTRAP data and those predi
ted by HFB-D1S
N
(Gogny) and GCM-GOA as a fun
tion of neutron number
for (left) the mass and (right) the two-neutron separation en-
A. Study of the two-neutron separation energy
ergy.
S2n
The two-neutron separation energy ( ) given by
S2n(N,Z)=B(N,Z) B(N 2,Z),
− − (7)
some (cid:21) long range
orrelations up to the best and there-
B
fore able to des
ribe (cid:16)beyond(cid:17) mean (cid:28)eld a large
lass with for the binding energy, is remarkable for its reg-
of nu
lear observable (mass formula but also low energy ularity between shell
losures. Generally, S2n de
reases
N
spe
tros
opy, shape
oexisten
e, and transitions, et
...). smoothly with and shell e(cid:27)e
ts appear as dis
ontinu-
In this frame, we have performed triaxial HFB
al
ula- ities. In the past, dis
ontinuities of S2n versus N were
Q
tions, using numeri
al methods and
odes des
ribed in often tra
ed to ina

urate β endpoint measurements
[65℄, with the Gogny D1S for
e[66, 67, 68℄. Fig.7(left) and measurements with more reliable, dire
t te
hniques
presentsthedi(cid:27)eren
esbetweenthemeasuredNi massNes restored2t0h8eregularity(see,forexample,[73℄forthearea
and those predi
ted byrmHFsB-D1S, as a fun
tion of . around Pb). Hen
e, part of the motivationNw=as 4to0
There is a large o(cid:27)set ( di(cid:27)eren
e of 2.473 MeV) for
on(cid:28)rm any mass surfa
e irregularities in the
theHFB-D1Smasses,expe
ted,asexplainedabove,spe- region. Fig.8 presents the S2n values, from N = 36 to

ially for mid-shell nu
lei where long range
orrelations 50, prior and after the ISOLTRAP mass measurements.
N = 41
play an important role. Under these assumptions, we Most of the irregularities e.g. at for gallium

ould expe
t at least that the derivative of these quanti- are
on(cid:28)rmed. Moreover, the plot reveals a deviation
N = 39 N = 41
tiesmightbe
losertoreality. Therefore,inFig.7(righSt2)n, from the linear trend between and for
we have plotted the two-neutron separation energy ni
kel,
opper, and gallium. Also irregularities for gal-
N =46 49 N =43 46
[see eq.(7)℄ derived frormmsthe same results. The result is lium( − )and
opper( − )arevisible.
en
ouraging, with an deviation of only 0.508MeV. To study the stru
ture more
losely we subtra
t a lin-
S2n
In general, due to the existen
e of long range
orrela- earfun
tionofN determinedby the slopepre
eding
S2n
tions beyond mean (cid:28)eld, a unique HFB wave fun
tion is the purported shell
losure. The resulting redu
ed
N = 82
not well suited to des
ribe the nu
lear system. Thus, a values are presented in Fig.9 in the region of
N =40 N =82

on(cid:28)gurationmixingapproa
halreadydes
ribedandap- (for
omparison) and . The shell
losure
10

20
)
V 15
e
M

(
n
2
S
82
Ge
81
78 Ga
72 76 Zn
Ni Cu
10
71
68 Co
Fe
36 38 40 42 44 46 48 50 52
Neutron Number N
S2n Z =26 Z =32
FIG. 8: Two-neutron separation energies ( ) for iron ( ) to germanium ( ) around N=40. Dashed lines
orre-
spond to the data before the ISOLTRAPmeasurements. Points with large error bars were not dire
tly measured by ISOLTRAP
but their value was
hanged by the link to the measured masses.
N =40
is
learly visible on this plot: there is a
hange of slope and alsoinvestigatehowmid-shell gaps
ompare
N = 82 N = 84
between and . From these observations in strength and
omportment. Fig.10,
al
ulated from
N =40
we
an analysethe behaviorin the region: there AME2003 data[42℄, shows the shell gap as a fun
tion of
N = 39 N = 41 Z N
is a similar e(cid:27)e
t between and where the proton number for for various . This highlights
N = 39 N = 40
the break
an be seen at and not at , thelargeshellgapvaluesformagi
neutronnumberwith
N =50
surprisingforanoddnumber. Themagnitudeofthis de- peaks at magi
Z. It also shows that for there is
Z =39 Z =40

rease is far smaller (between 500keV and 1MeV) than apeak at , and not , whi
h isknownto be
N = 82
the one for the major shell
losure at (around semi-magi
. This behavior is probably due to the odd-
N =39 S2p
4MeV). A similar stru
ture is seen between and even e(cid:27)e
t in the two-protonseparationenergy . Not
N = 41 N =39
for ni
kel,
opper, and gallium, but this is not surprisingly, the mid-shell-gap ( , 66) energies are
N =40
an indi
ation ofshell
losure. It isstrangethatthe same quite small. From this point of view, the
ase of
Z
stru
ture is visible for both ni
kel (even ) and gallium resembles a mid-shell rather than a magi
number.
Z ∆
(odd ) whereas germanium is smooth and little is seen Fig.11 shows the details of adja
ent shell gaps N as
Z
in the
ase of zin
. Further measurements to redu
e the a fun
tion of the proton number for di(cid:27)erent regions:
un
ertainty on the neighboring
obalt isotopes will be (a) around a shell
losure, (b) in the region of interest,
needed. and (
) in a mid-shell region. In Fig.11(a), the behavior
N = 82
of a strong shell
losure is shown for whi
h is a
N =82
magi
number: thereisalargedi(cid:27)eren
ebetween
N = 81
B. The shell gap and , 83 and the
orresponding enhan
ed shell
Z = 50
gap for the
ase of magi
. Fig.11(
) shows the
N =66
The neutron shell gap, de(cid:28)ned as behaviorof the mid-shell region around (exa
tly
∆N(N,Z) = S2n(N,Z) S2n(N +2,Z) in between twNo=sh6el6l
losures: 50 and 82): Nthe=n6e5utron
− (8) shell gap for is between the one for and
= 2B(N,Z) B(N 2,Z) B(N +2,Z), N =67 N =40
− − − N =. F4i0g.11(b)presentstheshellgapaNrou=nd82 .
For a strong di(cid:27)eren
e (like for ) is not
N = 39
is a good indi
ator of shell strength. The shell gap def- visible and N =40 is distin
t from neither nor
N = 39
inition is usually only valid for spheri
al nu
lides, i.e. 41. Note that the mid-shell gap is larger than
N =38
around magi
numbers. Here, we examine the
ase of thoseof and 40forseveralvaluesofZ, espe
ially