Table Of ContentShell-model interpretation of high-spin states in 134I
L. Coraggio1, A. Covello1,2, A. Gargano1, and N. Itaco1,2
1Istituto Nazionale di Fisica Nucleare, Complesso Universitario di Monte S. Angelo, I-80126 Napoli, Italy
2Dipartimento di Scienze Fisiche, Universita` di Napoli Federico II,
Complesso Universitario di Monte S. Angelo, I-80126 Napoli, Italy
(Dated: January 20, 2010)
New experimental information has been recently obtained on the odd-odd nucleus 134I. We in-
terpret the five observed excited states up to the energy of ∼3 MeV on the basis of a realistic
shell-model calculation, and make spin-parity assignments accordingly. A very good agreement is
found between theexperimental and calculated energies.
PACSnumbers: 21.60.Cs,21.30.Fe,27.60.+j
0
1
0 In a recent paper [1], excited levels up to an energy and let the valence protons and neutron hole occupy the
2 of about 3 MeV were identified for the first time in 134I fivelevels0g7/2,1d5/2,1d3/2,2s1/2,and0h11/2 ofthe50-
through the measurements of prompt γ rays from the 82shell. Thesingle-particleandsingle-holeenergieshave
n
spontaneous fission of 252Cf. A five transition cascade been taken from the experimental spectra [10] of 133Sb
a
J wasobserved,butthemeasuredangularcorrelationswere and131Sn,respectively. Theonlyexceptionistheproton
0 notsufficienttoassignspinsandparities. Inthisconnec- ǫs1/2 whichhasbeentakenfromRef.[11],sincethecorre-
2 tion, it may be mentioned that preliminary results were sponding single-particle level is still missing in the spec-
alsoreportedinRef.[2]onsomenewγ transitionsin134I trumof133Sb. Ouradoptedvalues forthe protonsingle-
] populated in the reaction 136Xe + 208Pb. It is the aim particleenergiesare (in MeV): ǫ =0.0, ǫ =0.962,
h g7/2 d5/2
l-t ooff tthhee opbresseernvtedpalepveerlst.o give a shell-model interpretation ǫthd3e/2n=eut2r.o4n39s,iǫnhg1l1e/-2ho=le2.e7n9e3r,giaensd: ǫǫs−1/12 ==20.8.00,0,ǫ−an1d fo=r
uc The study of nuclei in the vicinity of doubly magic 0.065, ǫ−1 = 0.332, ǫ−1 = 1.655d,3a/2nd ǫ−1 =h121/.4234.
n 132Sn is indeed a subject of great current experimental Note thas1t/2for the h d5le/2vel we have takeng7t/h2e position
[ and theoretical interest. Experimental information on 11/2
these nuclei, which have been long inaccessible to spec- suggested in Ref. [12].
1 troscopic studies, is now becoming available offering the Asinourrecentstudies[13–16]inthe132Snregion,we
v opportunity to test shell-modelcalculations in regionsof start from the CD-Bonn NN potential [17] and derive
1
50 sheTllhecloosdudr-eosdodffnsutcalbeiulisty1.34I with three protons and one tfmhe−V1.lowT−hkiswloitwh-maovmaleunetuofmthpeotceunttoiffal,pwariathmethteeraΛdd=iti2o.n2
3 neutron hole away from 132Sn represents an important of the Coulomb force for protons, is then used to derive
. source of information on the matrix elements of the the effective interactionVeff within the frameworkof the
01 proton-neutron hole interaction. Actually, the most ap- Qˆ-box folded diagram expansion [9] including diagrams
0 propriate system to study this interaction is 132Sb with up to second order in Vlow−k. The computation of these
1 onlyoneprotonvalenceparticleandoneneutronvalence diagramsisperformedwithintheharmonic-oscillatorba-
: hole. Experimentalinformation on this nucleus was pro- sis, using intermediate states composed of all possible
v
i vided by the studies of Refs. [3–5] and there have also holestatesandparticlestatesrestrictedtothe fiveshells
X beenvariousshell-modelstudiesemployingrealisticeffec- above the Fermi surface. This guarantees stability of
r tive interactions [6–8]. Both the calculations of Refs. [7] the results when increasing the number of intermediate
a and [8] start from the CD-Bonn nucleon-nucleon (NN) states. The oscillator parameter is ~ω =7.88 MeV.
potentialandderivetheeffectiveproton-neutroninterac- As mentioned above, the effective proton-neutron in-
tionwithintheparticle-holeformalism. Intheformerpa- teraction is derived directly in the particle-hole repre-
per,however,theshort-rangerepulsionoftheNN poten- sentation,while for the proton-protoninteractionweuse
tial is renormalized by means of the Vlow−k approach [9] the particle-particle formalism. The shell-model calcula-
while in [8] use is made of the traditional Brueckner G- tionshavebeenperformedusingtheOXBASHcomputer
matrix method. code [18].
The nucleus 134I, with an additional pair of protons Letusnowstarttopresentourresultsbycomparingin
with respect to 132Sb, may certainly contribute to im- Table I the calculated low-energy spectrum of 134I with
prove our knowledge of the two-body effective interac- theexperimentalone[19]. Thelevelsshowninthistable,
tion, since it offers the opportunity to investigate its ef- which have all been identified in the 134Te β decay, were
fectswhenmovingawayfromtheoneproton-oneneutron also observed in the experiment of Ref. [1]. We see that
hole system. This wasalsothe motivationforextending, the experimental energies are very well reproduced by
in Ref. [7], our shell model calculations to the nucleus theory, the largest discrepancy, 160 keV, occurring for
130Sb with three neutron holes. the 8− state. For the two positive-parity states at 0.181
In our calculations we consider 132Sn as a closed core and 0.210 MeV excitation energy our calculation speaks
2
4.0
lowest-lying populated level does not lead to any theo-
134
I
TABLE I: Experimental and calculated energies (in keV) of
14– the lowest lying states in 134I. Wave-function components
3.0 with a percentage ≥ 10% are reported.
0.785
∨ ∨ 0.703 13– J(4πE)x+p EE0xp J4πT+h E0Th π(Cgonfi)3gνu(rdatio)n−1 Prob7a8bility
7/2 3/2
2.0 ∨ 0.752 ∨ 0.534 12– ((35))++ 7494 53++ 15212 ππ((gg77//22))33νν((dd33//22))−−11 8717
∨ 0.244 ∨ 0.231 11– (2,3)+ 181 2+ 158 π(g7/2)3ν(d3/2)−1 78
(2,3)+ 210 3+ 312 π(g )3ν(s )−1 60
0.640 0.652 πg7/2)3ν(d1/2)−1 24
1.0 ∨ ∨ 10– (8)− 316 8− 475 π(g7/2)2ν(h3/2 )−1 75
7/2 11/2
πg7/2(d3/2)2ν(h11/2)−1 12
0.952 1.022
0.0 ∨ 8– (0.316) ∨ 8– (0.475)
TABLE II: Wave functions of negative-parity yrast states of
Expt Calc 134I (components≥ 10 % are reported).
Jπ Component Probability
FIG. 1: The five-transition cascade observed in 134I is com- 10− π(g )3νh−1 89
pared with the calculated level scheme for negative-parity 7/2 11/2
11− π(g )2d νh−1 92
yrast states. 7/2 5/2 11/2
12− π(g )2d νh−1 93
7/2 5/2 11/2
13− π(g )3νh−1 66
7/2 11/2
in favour of a J =2 and 3 assignment, respectively. π(g7/2)2d5/2νh−111/2 32
As regards the wave functions, it turns out that the 14− π(g )2d νh−1 97
7/2 5/2 11/2
six considered states are dominated by a single configu-
ration,asisshownbythepercentagesreportedinTableI.
It is interesting to note that these states may be viewed
as the evolution of the six lowest-lying states in 132Sb, reticalsequencethatmatcheswellwiththe experimental
− energies and is consistent with the observed transitions.
the 8 state being tentatively identified [19] with the
It should be mentioned that at about 0.250 MeV below
0.200 MeV level. As discussed in Ref. [7], the first four
− −
positive-paritystatesin132Sbareinterpretedasmembers the10 statewefindthe yrast9 state,whoseprobabil-
−
of the πg νd−1 multiplet , while the 3+ and 8− states itytobepopulatedfromthe10 stateis,however,about
7/2 3/2 30 times smaller than that relative to the 8− state.
asthenexttothehighestJ memberoftheπg νs−1and
7/2 1/2 InTableII,wereportthepercentagesofconfigurations
πg7/2νh−111/2 multiplets, respectively. Thecorresponding larger than 10% for the Jπ = 10−, 11−, 12−, 13−, and
states in 134I aredominated by the same proton-neutron 14− states. As in the case of the low-lying states (see
hole configurationwith the remaining two protons form- Table I), each of these high-spin states is dominated by
ing a zero-coupledpair. The main feature of the proton- a single configuration. We see that in all five states the
neutronholemultiplets,namelythelowestpositionofthe neutronholeoccupiestheh11/2 levelwhilethethreepro-
state with next to the highest J, seems to be preserved tonsareinthe(g )3 or(g )2d configurations,with
7/2 7/2 5/2
whenaddingtwovalenceprotons. Wefind,however,that two protons coupled to J 6= 0. In particular, the two
in 134I the members of a given multiplet lie in a smaller highest-lying levels arise from the maximum spin align-
energyintervalwithrespectto132Sb,asisexperimentally ment of the corresponding configurations.
confirmed in the case of the πg7/2νd−3/12 multiplet. Insummary,wehavegivenherea shell-modeldescrip-
We now come to discuss the level scheme identified in tion of 134I, focusing attention on the energy levels re-
Ref. [1], which is reported in Fig. 1 together with our centlyidentifiedfromthespontaneousfissionof252Cf[1].
shell-model interpretation. The observed γ cascade is We have assigned spins and parity to the new observed
composedoffivetransitionsandwassupposedtobebuilt levels and obtained a very good agreement between ex-
−
on the 0.316 MeV 8 isomeric state. With this assump- perimental and calculated energies. Our shell-model ef-
tion, we find that the excitation energies of the experi- fective interaction has been derived from the CD-Bonn
mentallevelsarewellreproducedbythe calculatedyrast NN potential without using any adjustable parameter,
sequence shown in the figure. More quantitatively, the in line with our previous studies of other nuclei in the
rms deviation between the calculated and experimental 132Sn region. The accurate description obtained for all
energies is about 100 keV. the investigated nuclei makes us confident in the results
We have verified that a different assumption for the of the present work.
3
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