Low Energy States of $^{81}_{31} Ga_{50}$ : Elements on the Doubly-Magic Nature of $^{78}$Ni

0.2 MB·English

by  David Verney

Low Energy States of 81Ga :
31 50
Elements on the Doubly-Magic Nature of 78Ni
D. Verney,1,2,∗ F. Ibrahim,1 C. Bourgeois,1 C. Donzaud,1 S. Essabaa,1 S. Gal`es,2,1 L.
Gaudefroy,2,1 D. Guillemaud-Mueller,1 F. Hammache,1 C. Lau,1 F. Le Blanc,1 A.C.
Mueller,1 O. Perru,1 F. Pougheon,1 B. Roussi`ere,1 J. Sauvage,1 and O. Sorlin2,1
(the PARRNe Collaboration)1
1Institut de Physique Nucl´eaire CNRS-IN2P3/Univ. Paris Sud-XI, F-91406 Orsay Cedex, France
2GANIL, BP 55027, F-14076 Caen Cedex 5, France
(Dated: February 8, 2008)
Excited levels were attributed to 8311Ga50 for the first time which were fed in the β-decay of its
mother nucleus 81Zn produced in the fission of natU using the ISOL technique. We show that the
7 structure of this nucleus is consistent with that of the less exotic proton-deficient N =50 isotones
0 within theassumption of strong proton Z =28 and neutron N =50 effective shell effects.
0
2 PACSnumbers: 21.60.Cs,23.20.Lv,23.40.-s27.50.+e59≤A≤89

n
a
The persistence of the magic character of the number NeverthelessthestudyofthetwomagicnumbersZ =28
J
of nucleons of one family, protons or neutrons, while the and N = 50 in its vicinity has already been undertaken
6
population of the other is varied has been clearly traced for a long time and is still the object of active experi-
2
back to the interplay between the monopole part of the mental and theoretical research. The Z = 28 (nickel)

1 effective nuclearinteractionandcorrelationsofotherna- isotopes are well known for being magic nuclei, however
v ture. The monopole partis responsible for the changein the experimentally observed[9] evolutionof the effective
6
theeffectivesingleparticleenergies(SPE)andithasbeen SPE of the proton 1f in Cu isotopes could be consid-
6 5/2
shownthatitstensortermistoplayasignificantrole[1]. ered as a preliminary indication of the reduction of the
0
1 The main origin of the competing correlations of other Z = 28 shell gap, depending on the simultaneous evolu-
0 naturearepairingcorrelationsandquadrupolecoherence tion of the effective SPE of the π1f orbital. How the
7/2
7 [2]. This interplay can enhance the magic character of a N = 50 shell gap evolves below Z = 38 was somewhat
0
number whichdoes notbelong to the historicalsequence debated [10, 11] but it has been shown recently that the
/
x 2, 8, 20, 28, 50, 82, 126 like N = 40 in the case of 68Ni associated shell effect should dominate the structure of
e [3]. Onthe opposite, it canlead to complete inversionof the low lying states in nuclei with Z as low as 32 (Ge)
-
l the 0p-0h and 2p-2h configurations leading to the van- [12]. New experimental data on proton-deficient N =50
c
ishing of its magic character like for N = 20 in the case isotonesisclearlyneededinordertoclarifythesituation.
u
n of 32Mg [5]. Those effects have been seen however to be Inthis Letter we reportonthe firstdiscoveryof the low-
: very localized within a small number of nucleons and it lying structure of 81Ga which, with Z =31 and N =50,
v
i is known that the robustness of spin-orbit (SO) closures has only three protons more than 78Ni.
X prevents them from apparent eradication while closures In our experiment, γ-rays de-exciting levels in 81Ga fed
r ofotheroriginsaremorefragile[4]. Itmeansforinstance in the β-decay of 81Zn were observed. The sources of
a
that no 2p-2h configuration has been observed as main 81Zn (T1 = 290± 50 ms) were obtained at the PAR-
2
component of the ground state (g.s.) in nuclei with nu- RNe mass-separatoroperating on-line atthe 15MVMP-
cleon numbers of the SO sequence 28, 50, 82, 126. For Tandem of the Institute of Nuclear Physics, Orsay. A
how long this will stand remains an open question : ex- natU target of approximative mass 75 g made of a series
◦
perimental evidence found in the mostexotic partof the ofUC pelletsheatedat≃2000 Cwasassociatedwitha
x
◦
nuclide chart tends indeed to accumulate showing that hot (≃ 1800 C) plasma ion-source of the ISOLDE MK5
such configurations come very close to the g.s. like in type [13] and exposed to the neutron flux generated by
someN =28isotones[6,7]orinsomeZ =82(lead)iso- the reaction of the 26 MeV deuteron beam delivered by
topes [8]. From all these considerations the problem of the Tandem hitting the target container. The ions, ex-
78Ni is easy to formulate : with two SO historical magic tracted at 30 kV from the source and magnetically mass
numbersZ =28andN =50itshouldbeadoublymagic separatedweredepositedonaAl-coatedMylartapeclose
nucleus but a special one since, being far remotely sit- to the detectionsystem. The rateofimplanted81Znwas
uated from stability, the way the monopole-quadrupole estimatedto a few tens per second. The γ-detectionsys-
interplay will drive its structure remains an open ques- tem consisted in two coaxial large volume HPGe detec-
tion (and a challenging one). The study of the structure tors of the EUROGAM phase I type (70% relative ef-
of 78Ni itself belongs to the medium-term development ficiency) issued from the French/U.K. (IN2P3/EPSRC)
◦
of the next generation of radioactive ion beam facilities. Loan Pool. They were placed in 180 geometry close to
2
5 30 * ◊ a)
4
6000 A=81 * N) per 25 ms23 nsity (hits)1200
* ln(1 3T511/2.1= 3k9eV1 +/- 65 ms Inte 0
g
Intensity (hits)345000000000 Pb X-rays 216 keV backscatterin * * 00 200 40T0im6e05 0(1m1s8)0010001200 Intensity (hits)-123100000 b)
2000 * * ◊ ° ° ° * * -200 200 400 600 800 1000 1200 1400 1600 1800 2000 2200
** ° * E (keV)
1000
FIG.2: Parta): γ-rayspectrumincoincidencewiththepeak
100 200 300 400 500 600 700
E (keV) at351.1keV.Anarrowlineisclearlyobservableat451.7keV
(♦-symbol) which was barely visible in the direct spectra.
FIG.1: Part of theβ-gated γ-spectrumrecorded at mass81. Thewiderlinearound179keV(∗-symbol)isduetothe180◦-
Theobservedγ-lineshavebeenidentifiedastransitionsfedin backscatter of the 530.22 keV γ-ray from the 81Ga decay.
the β-decays of 81Ga(•-symbol), 81Ge (∗-symbol), 81As ((cid:4)- Part b) : γ-ray spectrum in coincidence with the peak at
symbol) andtheβ-ndecay of81Ga((cid:3)-symbol,Pn =11.9%). 451.7 keV. The 351.1 keV peak is clearly visible (•-symbol),
The activity of 132I (◦-symbol) is also identified, it comes thenegative-positiveoscillation around200keVhasasimilar
from a previous setting on mass 132 which is oftenly used as origin as ∗ in part a).
areferenceinourexperiments. Thenewlineat351.1keV(♦-
symbol)isclearlyvisibleandwellisolated. Theprojectionon
0.29(5)s
the time scale of the background substracted events in this 81
Zn
peak is shown in the insert. 30 n
7.5%
thepointatwhichthebeamwasdepositedontothetape 1621.6 1621.6
(collection point). The energy resolution achieved with
thesedetectorswasoftheorderof2.3keVat1MeV.The
cscoilnletciltliaotnorpofoinrtβw-daestseuctriroonu.nEdendhabnycaemtuebnet-oshfatpheedapctlaivsittiyc (3/2−) 451.7 802.8
of interest as respect to the longer lived activities from
the other collected isobars and the consequent Compton (3/2−) 351.1 351.1
background was made by moving cyclically (every 2100
ms) the tape after a short build-up (900 ms) and decay (5/2−) 0
81
Ga
time (1200 ms). The Z-identification of the γ-rays was 31
provided by the analysis of the evolution of their activi-
FIG. 3: Tentative experimental level scheme for 81Zn. The
ties during the decay part of the cycle. More details on
order of the two transitions seen in coincidence is based on
the experimental set-up and procedure can be found in
intensityconsideration. Theproposedspinassignationscome
[12] and Refs. therein. Part of the γ-spectrum recorded
from the discussion in the present Letter. The 1621.6 keV
at mass 81 is displayed in Fig. 1 along with the iden- levelisproposedaftertheobservation ofaveryweakpeakin
tification of the γ-lines. It is seen that the activity is thespectra, not discussed in thetext.
dominated by that of 81Ga. In spite of this, a γ-line at
351.1 keV previously not reported at A = 81 is clearly
visible. Thefitofthe evolutionintimeoftheγ-intensity In a first attempt to understand the nature of the ob-
during the decay part of the counting cycle (see the in- servedstateswecomparedourresultstoshell-modelcal-
sertinFig. 1)givesahalf-lifevalueof391(65)mswhichis culations. The calculations were performed using the
consistentwiththe knownvalue for81ZnT =290(50) ANTOINE code from the Strasbourg group [15]. The
1/2
ms [14] : it was then attributed to a transition in 81Ga. modelspacechosenforthe calculationsconsistsinanin-
The statistics was sufficient to allow coincidence obser- ert 78Ni core and the proton single particle states from
vation : as can be seen in Fig. 2 a 451.7 keV γ-line was Z = 28 to Z =50 i.e. 1f ,2p ,2p ,1g . From
5/2 3/2 1/2 9/2
observedincoincidencewiththe351.1keVlinewhiches- the introductory remar(cid:8)ks this should be the nat(cid:9)ural va-
tablishesthe existenceofa802.8keVlevelinthe scheme lence space where the low-lying structure of 81Ga devel-
of 81Zn (see Fig. 3). opsanditisactuallytheonewhichhasbeentraditionally
3
80Zn (Z=30) 82Ge (Z=32) 81Ga (Z=31) 83As (Z=33)
2000
E (keV)11222260488000000000000 422112+++ (((242211+++))) 20241221++++ E (keV)11055000000 (3) 793531 393511 751 9531 79935351173 97535131 77535311 97353511
E (keV)112222604840000000000000 (((40212120+++21++))) 42021221++++ 0422011112+++++ E (keV)110500000 (1,3((,35531))) 73553135179 9735351153 3517335351 97753511353 ((((((131133,,,,,,353355931)))))) 15353119 953351 3311 35351
1
800 500 5 5 5 5 5 5 5
400 5 5
5
0 01+ 01+ 0 3 3 3 3 3 3 3 3 3 3
Exp. JW JW’jj4pnajj4b Exp. JW JW’jj4pnajj4b Exp. JW JW’jj4pnajj4b Exp. JW JW’jj4pnajj4b
84Se (Z=34) 86Kr (Z=36) 85Br (Z=35) 87Rb (Z=37)
FIG.4: Experimentalandcalculated spectraforthelast sta- FIG. 5: Experimental and calculated spectra for the last
ble(86Kr)andproton-deficientevenN =50isotones. “Exp.” stable (87Rb) and proton-deficient odd N = 50 isotones,
standsforexperimentallevels,“JW”forresultsofshell-model spin values are multiplied by two, only the three first Jπ =
′ − − − −
calculations using the interaction from [16], “JW” the same 3/2 ,5/2 ,7/2 and 9/2 calculated levels are displayed.
with modified pairing (see text), “jj4pna” and “jj4b” those Notation for the interactions is the same as in Fig. 4.
from [17] and [21] respectively.
mentbetweentheoryandexperimentisalreadydoubtful
(andsuccessfully)usedinshell-modeldescriptionsofthe for Z = 33 it is even more difficult to raise a conclu-
N =50 isotones. We used two different sets of SPE and sion for Z = 31. This can be understood as due to the
two-bodymatrixelements(TBME)fortheeffectiveinter- fact that the TBME involving the 1f5/2 proton states
action,bothweredeterminedasfreeparametersinaleast which determine the details of the structure of the most
squarefitprocedurefromexperimentallevelsandbinding proton-deficient isotones are necessarily the less safely
energies : the one proposed by Ji and Wildenthal (JW) determined parameters. It is easy to see for instance
some time ago [16] and the one, which includes new ex- thattheterm 1f5/21f5/2 V12 1f5/21f5/2 J=0 T=1 ofthe
perimental levels accumulated since that time, proposed JW interactio(cid:10)n (Tab. 1 i(cid:12)n Re(cid:12)f. [16]) whi(cid:11)ch corresponds
(cid:12) (cid:12)
morerecentlybyLisetskiyetal. (jj4pna)[17]. Ascanbe to the pairing energy between 1f5/2 protons is not well
seen from Fig. 4 a good agreement is obtained between converged in the fitting process and has a strangely low
theory and experiment for the energy of the 2+ excited value : −0.7854 MeV against −1.5115MeV in [17]. It is
1
states with both interactions while for the rest of the thentemptingtomodifytheTBMEinvolvingtheπ1f5/2
levelschemetheresultstendtodifferstrongly. Inpartic- orbit following empirical prescriptions in the light of our
ular the agreement is excellent — especially for the JW new experimental data. For this we make the voluntar-
interaction — for the surprisingly low energy of the 2+ ily oversimplifying hypothesis (in order to keep a clear
1
stateofthelastknownevenproton-deficientisotone82Ge physical image) that the main configuration in the g.s.
32
(78Ni+4 protons). Howeverwhen considering the results of the nuclei with 29 ≤ Z ≤ 34 is π1f5n/2 (1 ≤ n ≤ 6).
for the odd-nuclei (Fig. 5) the agreement deteriorates The configuration energy for n identical particles with
rapidly when going away from stability. Difficulties al- j = 5/2 coupled to the total angular momentum J and
readyshowupin83As(78Ni+5protons)wheretheexper- seniority v is a closed formula valid for any two body
33
imentally wellestablished 711-keVlevelcould not be ac- residual interaction [19] :
countedfornorwiththeJWinteraction—this wascon-
n
sthideerfierdstatsimaem[a1j8o]r—issnuoerawtitthhetthime me 83o33rAesrewceanststjju4dpinedafionr- hjnJv| Vik|jnJvi=nεf5/2 + 21n(n−1)a
Xi<k
teractionwhich predicts a compactgroupof three states
35 1
around 700 keV and no intermediate state around 300 + J(J +1)− n b+ (n−v)(8−n−v)c
(cid:18) 4 (cid:19) 2
keV. Besides, the two interactions does not agree on the
nature of the 83As g.s. : it is found Jπ =5/2− with JW with four parameters a,b,c and ε , the last one being
− 33 f5/2
and 3/2 with jj4pna. Since the quality of the agree- the SPE of the proton1f in the coremean field. As a
5/2
4
first guess, we assumed that the g.s. of 79Cu, 81Ga and (unpublished [21]) including, in particular, data on 84Se
83As were the J = 5/2 members of the 1fn configu- in the fit alongwith about 400other binding energyand
v 1 5/2
rations, which, as we shall see later, is not totally exact. energy level data. The resulting spectra are displayed in
We determined three relations between the parameters Figs. 4 and 5 (jj4b) where it is seen that the agreement
by fitting the quadratic dependence in n of the binding with the experimental spectra of the even-nuclei is very
energies (BE) of these nuclei taken relative to 78Ni. The goodandthedescriptionoftheodd-nucleiisimprovedin
′
BE values were taken from [20], in the case they were a similar way as with the JW set. Then the conclusion
not measured the estimated values were used, which is from the present work is straightforward : the first ex-
far sufficientinthe frameworkofthe crude hypothesisof cited levels of the proton-deficient N = 50 odd-isotones
pure configuration states. The fourth relation was pro- down to Z = 31 can be described in a coherent way by
vided by the energy separation between the ground and assuming : (i) an inert 78Ni core (ii) rather clean pro-
the second excited state of 81Ga taken from the present ton1fn configurationstatesor2p q.p. statesforthe
5/2 3/2
work (802.8 keV) : the second excited state in 81Ga was lowest states (iii) a reasonable pairing strength between
assumedtobetheJπ =3/2− memberoftheπ1f3 con- the 1f protons and (iv) (from the success of the jj4b
v 3 5/2 5/2
figuration (the last member J =9/2 should be weakly interaction) that the diffusion of pairs of protons across
v 3
fed in the β-decay of 81Zn which has most probably a Z = 28, should it exists, remains limited. We implic-
5/2+ g.s. of neutron 2d nature). By simply resolving itly confirm that the π1f single particle state is lower
5/2 5/2
the system, the three diagonal1f TBME plus the BE in energy that π2p for very neutron-rich nuclei which
5/2 3/2
of the π1f single particle were determined uniquely. correspondstoaninversionasrespecttotheknownorder
5/2
The value obtained for 55 V 55 is −1.478 atstability. SofarbothZ =28andN =50appeartobe
MeV : it is about twice(cid:10)t2h2e(cid:12)JW12(cid:12)v2a2lu(cid:11)Je=a0nTd=r1ather close effective gaps in the region of 81Ga, only three protons
to the jj4pna value. In orde(cid:12)r to(cid:12)reconnect properly the away from 78Ni.
π1f orbit to the rest of the valence space it was also
5/2
necessary to slightly modify the TBME determining the
position of the π1f -centro¨ıde and those which govern
5/2
the diffusion of pairs from the π1f orbit to the close
5/2 ∗
[email protected]
lying π2p . This gives a total of 8 TBME, all related
3/2 [1] T.Otsuka,T.Suzuki,R.Fujimoto,H.Grawe,Y.Akaishi,
to pairing properties, which have been modified as re- Phys. Rev.Lett. 95, 232502 (2005).
spect to the originalvalues of JW. The resulting spectra [2] A. P. Zuker,Physica Scripta T88,157 (2000).
are shown in Figs. 4 and 5 (JW′). As can be seen in [3] O. Sorlin et al., Phys.Rev.Lett. 88, 092501 (2002).
Fig. 5, a clear improvement is obtained for the lower [4] A. P. Zuker,Phys.Rev. Lett. 91, 179201-1 (2003).
part of the spectra of 81Ga and 83As. The major result [5] D. Guillemaud-Mueller et al., Nucl. Phys. A 246, 37
is that, for 83As the goodnumber of levels below the 1.5 (1984).
[6] D. Sohler et al.,Phys. Rev.C 66, 054302 (2002).
MeV group is obtained for the first time. In particular
[7] S. Gr´evy et al., Eur. Phys.J A 25, s01, 111 (2005).
the intermediate level which is observed at 711 keV in
[8] R Julin et al., Eur. Phys. J. A 15, 189 (2002) and refs.
−
this nucleus would correspond to the 1/2 state calcu- therein.
lated at 884 keV. Besides, the 83As g.s. becomes 3/2− [9] S. Franchoo et al., Phys.Rev.Lett. 81, 3100 (1998).
with a 2p q.p. nature and the 5/2− state of the [10] Y. H.Zhang et al., Phys.Rev.C 70, 024301 (2004).
3/2 v=1
1f−1 configuration becomes the first excited state. In [11] A. Pr´evost et al.,Eur. Phys. J A 22, 391 (2004).
5/2 [12] O. Perru et al.,Eur. Phys. J. A 28, 307 (2006).
81Ga the 5/2− member of the 1f3 configuration be-
v=1 5/2 [13] S.Sundell,H.L.Ravn,theISOLDECollaboration,Nucl.
comes the g.s. while the 2p3/2 q.p. becomes the first Instrum. Methods B 70, 160 (1992).
excited state. This provides a natural and simple ex- [14] C.M Baglin, Nuclear DataSheets 79, 447 (1996).
planation for a possible change of the g.s. spin value [15] E. Caurier, shell model code ANTOINE, IReS, Stras-
between 83As and 81Ga as being due to the lowering bourg 1989-2002 ; E. Caurier, F. Nowacki, Acta Physica
Polonica 30, 705 (1999)
of the proton Fermi level from the 2p to the 1f
3/2 5/2 [16] X. Ji and B. H. Wildenthal, Phys. Rev. C 37, 1256
orbitals while the JW calculation predicted an unnatu-
(1988).
ral 3/2− g.s for 81Ga. Our trivial manipulation of the
v=2 [17] A. F. Lisetskiy, B. A. Brown, M. Horoi and H. Grawe,
TBME tends to rigidify the structure of the even-nuclei Phys. Rev.C 70, 044314 (2004).
(see fig. 4) while it improves the results on odd-nuclei. [18] J. A.Winger et al.,Phys.Rev. C 38, 285 (1988).
This could be understood as the evidence that part of [19] I. Talmi and I. Unna, Ann. Rev. Nuclear Sci. 10, 353
the correlations which contributes to lower the 2+ ener- (1960).
gies toward 78Ni cannot be reproduced in such a1limited [20] G. Audi,A.H.WapstraandC. Thibault,Nucl.Phys.A
729, 337 (2003).
valence space and may come typically from the diffusion
[21] A.F.LisetskiyandB.A.Brownprivatecommunication.
of pairs across the Z = 28 shell-gap. However a proper
modification of the whole set of the interaction parame-
tershasbeenperformedrecentlybyA.F.Lisetskiyet al.