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Submitted on 1 Jan 1978
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Evidence for Gallagher-Moszkowski doublets in 180Ta
E. Warde, R. Seltz, G. Costa, D. Magnac, C. Gerardin
To cite this version:
EVIDENCE FOR GALLAGHER-MOSZKOWSKI
DOUBLETS
IN
180Ta
E. WARDE
(*),
R.SELTZ,
G.COSTA,
D. MAGNAC and C.GÉRARDIN
C.R.N. and
U.L.P.,
BassesEnergies,
67037Strasbourg,
France(Re(!u
le 3 avril1978,
accepte
le 12 avril1978)
Résumé. 2014 A partir d’une étude
expérimentale
du 180Ta par la réaction(p,
d), on déduit leséléments de matrice de l’interaction résiduelle neutron-proton pour certains doublets Gallagher-Moszkowski.
Abstract. 2014 Some residual
neutron-proton interaction matrix elements have been deduced for band-head doublets in the odd-odd nucleus 180Ta from a spectroscopic study using the
(p,
d) reaction.Classification Physics Abstracts 21 . 10H -- 21. 60
Spectroscopic
studies of odd-odd nuclei in the rareearth
region
have beenwidely
used in the frame of agiven
model to deduce an estimate of the effectiveresidual interaction
Vnp
between theunpaired
proton and the neutron.Following
Boisson et al.[1]
the Hamiltonian of anodd-odd
axially symmetric
nucleus isgiven
by
where
Hadiab
is the adiabatical part of the Hamiltonian andHRPc corresponds
to the Corioliscoupling.
The intrinsic part of the
eigenfunction
ofHadiab
is a directproduct
of the Nilsson states of theunpaired
proton and the neutron xk =XUp
~. Because of axialsymmetry
theprojections
of thespins
~2p
andQn
cancouple
eitherparallel
orantiparallel giving
the
projection
quantum numbers for theresulting
band-head doubletwith ~ = ~ + 2~ and E =
± 2,
corresponding
tospin up T
ordown ~ respectively.
Following
theGallagher-Moszkowski (G-M)
empi-ricalrule,
thelower-energy
member of the doubletcorresponds
toparallel
coupling
of the intrinsicspins [2].
It may be theK,
or the~
state. Theparity
IIis deduced from the
parities
of theodd-particle
states :II =
.
In the absence of Coriolis
coupling
andneglecting
the
off-diagonal
elements ofVnp,
the energy separa-tion of the doublet band-head members isgiven
by
where A is the G-M term, B the
Newby
term ofVnp
which appearsonly
for K = 0[3],
and a thedecoupl-ing
parameter.The aim of this paper is to estimate the two terms
A and B from an
experimental study
ofl~gTa107’
Spectroscopic
information on this nucleus was verypoor up to now.
Only
two states, bothisomeric,
wereknown : the
ground
state withspin
8+ or9 -,
and a 1 + state,
7B/2 ~
8h,
at 32 keV[4,
5].
An expe-rimentalstudy
of the181Ta(p, d) 18 °Ta
reaction wastherefore undertaken.
With the
assumption
of a direct reactionmecha-nism,
the odd proton is aspectator
such that its orbitis the same as in the
ground
state of thetargeti 8lTa
i.e.7/2+ [404 ~].
States observed in thelow-energy
part of the
resulting
18 °Ta spectrum
are thereforemembers of the rotational bands built on intrinsic
states obtained
by
thecoupling
of the7/2+
[404 ~]
proton
configuration
with the neutron intrinsic statesof the
neighbouring
isotones(179Hf, 181W...).
The reaction has been studied atEp
= 19 MeV onthe
Strasbourg
MP tandem. Theoutgoing
deuteronswere detected in the focal
plane
of a Buechner magnetspectrograph
and recorded in fourposition
sensitiveL-162 JOURNAL DE PHYSIQUE - LETTRES
FIG. 1. -
Experimental spectra for the 181Ta(p, d)18°Ta reaction observed in various detectors with overlapping magnetic fields.
detectors.
Targets
of 200Jlg/cm2
of naturaltanta-lum have been used
giving
an overall resolution ofabout 15 keV.
Figure
1 showsexperimental
spectra observed in various detectors withoverlapping
magne-tic fields. The absolute error for excitation
energies
was estimated to be better than 5 keV. Various
(p,
d)
reactions onlight
nuclei have been used for thespec-trograph
calibration. The excitationenergies reported
in
figure
1 refer to the centre ofgravity
of thepeaks
obtainedthrough
a curvefitting
program.Twenty-one
levels are observed up to 1 MeVexcitation and most of their
angular
distributionswere measured. A
preliminary
report of thisexperi-ment was
given
in a recent communication[6].
In the DWBA
analysis,
theoptical
modelpara-meters were taken from the survey of Elbek and
Tjom
[7].
Forcomparison
withexperiment
only
transfers with(d~/dS~)~,~R >
1ub/sr
have been consi-dered. Someangular
distributions show obvious Ivalues. This was a
great
help
in the firststep
of theidentification of the states. The identification of observed levels with levels
predicted by
the model wasobtained
through
thefollowing procedure.
1)
The band-headenergies
were estimated withthe aid of
equation (43)
in reference[8]
from knownNilsson neutron states in 17 9Hf
[9]
e.g.9/2+
[624
T],
7/2-
[514 ~
1/2- [510
j],
5/2- [512 ~ 1/2-
[521 ~j
and3 /2 - [512 ~ ] ;
the initial values of matrix elements ofVnp
and inertia parameters are taken from refe-rence[1]
and estimated fromneighbouring
nuclei[10],
respectively.
2)
The initial values of these parameters are variedin order to obtain the best
agreement
betweentheory
andexperiment
inreproducing
(i)
the energyspec-trum,
(ii)
theangular
distributionshapes
and(iii)
the absolute cross section[11].
The final values for the A and B terms of
equation
(2)
are then deduced.
Among
theodd-parity
levels,
thetwo states I’ = 3 - and 1" = 4 - due to the
coupling
p
7/2+ [404 ~],
n1/2-
[521 are
expected
to have thelargest
cross sections in the excitation energy rangeconsidered.
They
are identified as the maincompo-nents of the two
peaks
observed in the spectrum at785 and 723
keV,
whereangular
distributions show dominant I = 1 transfer asexpected (Fig.
2).
SolidFIG. 2. - Angular distribution of levels at 723 keV and 785 keV.
TABLE I
Comparison of
the theoreticalenergies
and cross-sections with theexperimental
values.Energies
are in keVcurves are theoretical
predictions
for levels witheigenstate
componentsreported
in table I. Anormali-.
Y/1B
zation factor
6(o)"P
= 1.3 was necessary in order to( )th
obtain the fits of
figure
2. Due to theexperimental
resolution,
it islikely
that observedpeaks
aremulti-plets including
members of other bandscontributing
to the measured cross section. In the case of the two states studied here such a contribution has been
estimated to be smaller than 10
%.
In tableII,
the G-M term deduced from thisexperiment
iscompared
to values from other nuclei.The G-M doublet based on the p
7/2+
[404 1],
n 7/2-
[514 ~] coupling
iscomposed
of(7-,
7)
and(0-, 0)
levels. The first one is found with agood
evi-dence at 173 keV.
Among
thepossible
C~, j
=11/2,
I =
5, Q
=7/2
is the mostimportant
one and I = 5is dominant in the
shape
of theangular
distribution.The total value of the observed absolute cross section
is
explained
by
the presence in thisregion
of the 8 +member of the
1 +,
8+ G-M doublet p7/2+
[404
JJ,
n9/2+ [624 j]
deduced from the values of A[1]
andTABLE II
Comparison
withprevious
resultsof ~
Vnp ~
values deducedfrom
thisstudy. Energies
are in keV(") Present experiment.
(b) Ref. [1].
0 Eigenvalues of JC (Eq. (1)).
the rotational term.
Furthermore,
the(4+,
1)
member of the(1
+, 1 +)
band is also present in the same energyrange and the sum of the contributions of these three
states
gives
a better fit of the details of theangular
distribution
(Fig.
3).
FIG. 3. -
Angular distribution of a multiplet of states at
Ex = 173 keV. The curves are DWBA fits. The
dotted, the dashed-dotted and the solid lines refer respectively to the 8 +, 8 ; 7 -, 7
and the sum of three states (8+, 8 ; 7-, 7 and 4+, 1).
The second member
(0 -, 0)
of the doublet has acalculated cross section smaller than 1
~b/sr
and therefore cannot be observed in the presentexperiment
According
to themagnitude
of the G-M term[1],
onepredicts
this level to be located at 400 ± 50 keV because theNewby
term here decreases the energyof the odd members of the K = 0 rotational band. A
relatively
large
experimental
cross section is found fora level at 414 keV which shows an I = 3
angular
dis-tribution. The l-value and the cross section are
L-164 JOURNAL DE PHYSIQUE - LETTRES
coupling,
the lowered(2-, 0)
state and the(3-, 0)
state. This
places
the unobserved(0-, 0)
level at370 keV. The
resulting Newby
term, B
= 50keV,
and the shifts due to Coriolis
coupling
explain
thepositions
of the observed members of this band. The values of the matrix elementsVnp
deduced from thisstudy
arecompared
in table II with thevalues
given
by
Boisson et al.[1]
for othernuclei,
where Coriolis
coupling
andoff-diagonal
effectsof
Vnp
were taken into account.Acknowledgments.
- We thank Dr. R.Piepenbring
forstimulating
discussions and a criticalreading
of themanuscript.
References
[1] BOISSON, J. P., PIEPENBRING, R. and OGLE, W., Phys. Rep.
26 (1976) 99.
[2] GALLAGHER, C. J. and MOSZKOWSKI, S. A., Phys. Rev. 111 (1958) 1282.
[3] NEWBY, N. D., Phys. Rev. 125 (1962) 2063.
[4] GALLAGHER Jr., C. J., JORGENSEN, M. and SKIBREID, O.,
Nucl. Phys. 33 (1962) 285.
[5] WAPSTRA, A. H. and GovE, N. B., private communication quoted in Nucl. Data Sheets 15 (1975) 577.
[6] WARDE, E., COSTA, G. J., GÉRARDIN, C., MAGNAC, D. and
SELTZ, R., Proc. XV Winter School, Zakopane (1977) p. 277.
[7] ELBEK, B. and TJOM, P. O., Adv. Nucl. Phys. 3 (1969) 259.
[8] JONES, D. H., Ph. D. dissertation, Florida State University, Tallahassee (1969) unpublished.
[9] BUNKER, M. E. and REICH, C. W., Rev. Mod. Phys. 43 (1971)
348.
[10] STRUBLE, G. L., KERN, J. and SHELINE, R. K., Phys. Rev. 137 (1965) B 772.
[11] ELMORE, D. E. and ALFORD, W. P., Can. J. Phys. 54 (1976)