The Negative Parity Bands in 156 Gd
Michael Jentschel, Loic Sengele, Dominique Curien, Jerzy Dudek, Florent Haas
TThe Negative Parity Bands in Gd M Jentschel ∗ Institut Laue-Langevin, BP 156, 6 Rue Jules Horowitz, 38042 Grenoble Cedex 9, France
L Sengele, D Curien, J Dudek and F Haas
Institut Pluridisciplinaire Hubert Curien, 3 Rue du Loess, BP28, 67037 Strasbourg Cedex 2, France
Pacs Ref : 21.10.Dr, 21.10.Ma, 21.60.Cs, 21.60.Jz, 25.85.Ca
Abstract
The high flux reactor of the Institut Laue-Langevin is the worldmost intense neutron source for research. Using the ultra high-resolution crystal spectrometers GAMS installed at the in-pile targetposition H6/H7 it is possible to measure nuclear state lifetimes usingthe Gamma Ray Induced Recoil (GRID) technique. In bent crys-tal mode, the spectrometers allow to perform spectroscopy with adynamic range of up to six orders magnitude. At a very well colli-mated external neutron beam it is possible to install a highly efficientgermanium detector array to obtain coincidences and angular cor-relations. The mentioned techniques were used to study the firsttwo negative parity bands in
Gd. These bands have been in thefocus of interest since they seem to show signatures of a tetrahe-dral symmetry. A surprisingly high B(E2) value of about 1000 W.u.for the 4 − → − transition was discovered. It indicates that thetwo first negative parity bands cannot be considered to be signaturepartners.
1. Introduction
Theoretical prediction of the presence of the tetrahedralpoint group symmetry in nuclei have motivated a series ofexperimental investigations. The symmetry is expected toopen new gaps between the nucleonic orbitals helping tostabilise its shape at a non-zero value of the α tetrahe-dral deformation and leading to new so-called tetrahedralmagic gaps: 16, 20, 32, 40, 56, 64, 70, 90, 112 and 136,Refs. [1, 2]. The tetrahedral energy gaps at these nucleonnumbers, with the sizes sometimes comparable to thoseat the spherical magic numbers, correspond to pure tetra-hedral deformation ( α in terms of the nuclear surfacerepresentation with the help of the spherical harmonic ba-sis). Pure tetrahedral-symmetry shapes generate neitherquadrupole nor dipole moments, whereas the fact of be-ing non-spherical generates the rotational bands with theenergy-spin dependence as E I ∼ I ( I + 1). Therefore both,the population and detection, of such rotational states bytransitions other than the octupole ones should be consid-ered as very rare events. In other words, the transitionsother than E3, can be envisaged for instance as the resultof various types of polarisation in terms of shapes either ∗ e-mail: [email protected] by the valence particles, or by zero-point motion and/orCoriolis effects, but are not expected to be strong.According to theoretical predictions, in several nucleithe tetrahedral symmetry minima lie low in the energyscale and compete with the axial quadrupole-deformationground-state minima. Using the two-dimensional projec-tions of the calculated potential energy onto the ( α , α )deformation plane one obtains overall relatively flat land-scapes. Under these conditions calculations predict largeamplitude fluctuations in the α (tetrahedral) directionaround the quadrupole equilibrium as well as the accom-panying low vibration energies in the corresponding mode.Calculations by various theory groups suggest that whenthe two octupole modes, i.e. Y (tetrahedral) and Y (axial-octupole) come into competition - the tetrahedralmode wins energetically in majority of the studied cases,cf. [3] and references therein.The actual crucial question is whether this non axialdeformation α is experimentally distinguishable fromthe axial octupole α deformation? A particular focushas been on the first negative parity bands of the iso-tope Gd. First theoretical works [4, 5] suggested thatmissing E2 transitions between the low spin members ofthese bands could be considered as an indicator of miss-ing quadrupole deformation and favouring therefore a puretetrahedral – in contrast to the tetrahedral-oscillation – in-terpretation. A recent measurement employing the Braggspectroscopy [6] demonstrated however the presence ofweak E2 transitions (see Fig. 1) still carrying a relativelylarge quadrupole moment.At first this could have been seen as disfavouring thetetrahedral symmetry interpretation generally. However,later theoretical work [7] showed that the presence of thetetrahedral symmetry is compatible with the presence ofsome non-zero quadrupole moment if the so-called zero-point motion is taken into consideration. Moreover – thetetrahedral component in the nuclear mean field can verywell give rise to the ‘tetrahedral oscillations’ of the nuclearground-states leading to the K π = 2 − bands in full anal-ogy to the K π = 2 + bands (the well known γ -bands) withthe strong quadrupole moments present in both cases.The progress just mentioned has made the simplefingerprint of vanishing E2 strength in negative paritybands obsolete. Therefore the experimental activity has1 a r X i v : . [ nu c l - e x ] A p r oved to a more systematic investigation of the E1/E2branching ratios with a particular focus on the so-calledsignature(simplex)-partner bands. In fact, in Gd thefirst negative parity band with odd spins has a signaturepartner with even spins, which – if the negative-parityband can be associated with the octupole deformation –should show similar to the odd spin band E1/E2 branchingratios. In this context a series of lifetime, and branchingratio measurements was carried out to investigate the na-ture of the lowest lying negative parity bands in
Gd.
2. Experimental Setup
A first experimental investigation of the negative paritybands in
Gd with respect to an experimental searchof tetrahedral symmetry was carried out by Doan et al.[8] using a fusion-evaporation reaction
Sm( α ,2n). Thereaction allowed to populate the high spin states of thenegative parity bands (up to spin 17 ¯ h ) and the use of theJUROGAM γ -ray detector array and evaluation of γγγ coincidences allowed a clear assignment of all transitions.In the experiment all inter-band E1 transitions from thefirst two negative parity bands were assigned. VanishingE2 transitions at the bottom of the odd-spin band werenot detected below spin 9 − and also the experiment wasnot able to establish the 4 → Gd(n, γ ) Gd was carried out. This reaction hasa very strong cross section (64000 barn) and populatesmostly the lower spin states (below spin 7¯ h ) of the nega-tive parity bands. Experiments were carried out with thecrystal spectrometer GAMS5 in double flat crystal mode(see figure 2 and [6]) for the measurement of nuclear statelife times, in single bent crystal mode for the measurementof intensities of weak transitions. The reaction was alsostudied within the EXILL campaign [10], where a highlyefficient HPGe-detector array was placed around a neutronbeam. A simplified level scheme - showing the transitionsinvestigated within this work is shown in Figure 1. The instrument and its options as double flat and as sin-gle bent crystal spectrometer was already described in thecontext of former publications [6] and therefore only ashort summary shall be given here. In the double crystalmode the spectrometer is capable of achieving a relativeenergy resolution of ∆
E/E (cid:39) − . This extraordinaryresolution is achieved for the price of a very small effec-tive solid angle of 10 − . This allows to carry out ex-periments with massive samples of several grams of massonly. These samples are introduced into the in-pile beamtube H6/H7 of the research reactor of the Institut Laue-Langevin, where they are exposed to a neutron flux of5 × neutrons per second and cm . In double flat crys-tal mode the instrument can be operated in two diffraction + + + + + + + + + - - - - - - - - - - - - - - - - - - Ground state band odd spin negative parity band Even spin negative parity band
Fig.
1: The first two negative parity bands in
Gd. Thelevels excited by the
Gd(n, γ ) Gd are shown in blue to-gether with E2 transitions in green and E1 transitions in red.Energies, spins and parities are taken from [11]. geometries: i) The so called non-dispersive geometry, hav-ing the two crystals in a parallel alignment with respectto each other, allows measuring the instrument responsefunction. The measured response function is comparedto a theoretical calculation and the deviation is deducedas an universal parameter (essentially determined by thealignment and the vibration amplitude of the crystals). ii)The dispersive geometry, having between the two crystalsa well defined Bragg angle, allows measuring additional –with respect to the instrument response function – broad-ening of the γ -ray line. The primary source of broadeningof a γ -ray line is Doppler broadening due to the motionof the emitting nuclei. The resolution of the spectrometeris sufficiently good to detect Doppler broadening associ-ated with the thermal motion of atoms and this so calledthermal Doppler broadening corresponds to the minimumbroadening, which can be obtained in a measurement. An-other source of Doppler broadening can be observed in thecase of a γ -ray cascade: Every γ -ray emission is inducinga recoil to the emitting nucleus, which induces a recoilmotion of the nucleus being slowed down by inter-atomiccollisions. The energy of subsequently, within a sufficientlysmall time window after the recoil, emitted γ -rays areDoppler shifted if measured in a laboratory frame. Sincethe recoil process is isotropic one observes in a measure-ment a Doppler broadening. The measurement of Dopplerbroadening of these secondary γ -rays allows to determinethe time between γ -ray emissions - the nuclear lifetime ofthe intermediate level. This approach to measure nuclearstate lifetimes is called the GRID (Gamma Ray Induced2oppler broadening) lifetime technique and is in detail de-scribed in a number of publications, [12, 13]. Since it es-sentially requires the best possible energy resolution it canbe only realised in double flat crystal mode. Due to thelow luminosity of the spectrometer in this mode, massivesamples of about 10 grams Gd O powder with naturalisotopic abundance were used.The spectrometer can also be equipped with curvedcrystals, which help to increase the solid angle by fourorders of magnitude. This allowed to use samples of a fewtens of milligrams mass of isotopically 95% enriched sam-ples of Gd O . In this configuration the spectrometerhas an energy resolution of ∆ E/E (cid:39) − × E [keV]. Thismeans that up to an energy of about 1.5 MeV the resolu-tion is better compared to normal HPGe-detectors. Themain advantage of this geometry is, however, the possi-bility to obtain a very good measurement of relative in-tensities. This comes essentially from the fact that thedetector, used to count the diffracted γ -rays, is loaded pertime only with selected (by the diffraction process) ener-gies. This yields a dynamic range of up to 10 , allowingto search for very weak transitions. A former generationof this spectrometer was used to carry out a rather com-plete spectroscopy of Gd [9]. Due to the high neutroncapture cross section and the high flux at the sample posi-tion small sample masses are ‘burning out’ in the reactorwithin a few days. Since the focus in [9] was on a com-plete scan, the measurement was repeated to assure thatthe intensities of all branching depopulating the negativeparity bands were correctly assigned.Since the solid angle in both diffraction modes is verysmall it is impossible to consider a crystal spectrometer forcoincidence measurements. Therefore a direct assignmentof γ -rays to a particular band has to result from additionalmeasurements with HPGe-detector arrays. Complementary to GAMS5 in bent crystal mode, the useof a HPGe-array offers the higher resolution power for highenergies and, most importantly, the possibility to carry outcoincidence measurements. The latter option is also quiteimportant for the correct extraction of nuclear state life-times via the GRID technique. Since the Doppler broaden-ing is used to extract lifetimes, an important parameter isthe knowledge of the recoil velocity distribution. It resultsdirectly from the knowledge of the feeding of a particularlevel of interest (LOI). In the majority of cases the pub-lished information about the feeding is rather incomplete.By gating on γ -rays from below the LOI it is possible tore-construct a large part of the feeding.The concept of the EXILL campaign was to install ahighly efficient HPGe-detector array around a neutronbeam. The ILL research reactor is offering a large numberof neutron guide systems allowing to transport neutronsover hundreds of meters to experimental areas. The mostintense of these guides is the ballistic super mirror guide Reactor Gams 5Targetchanger source flatcrystal
Double flat crystal geometry n o n - d i s p e r s i v e d i s p e r s i v e Single bent crystal geometry source cry pcol det pcol m c o l Fig.
2: The upper part shows a schematic layout of the crys-tal spectrometer GAMS5, which is placed 17 meters from thein-pile source position. The beam from the source is firstpre-collimated (pcol) by a fixed collimation system, than amonochromatized beam is produced by the crystals (cry), sep-arated by a movable collimation system (mcol) from the di-rect beam and than counted by a detector (det). The indi-cated diffraction angles are strongly exaggerated for visualisa-tion purposes. In the lower part of the figure, the two crystaldiffraction modes and their different acceptance with respectto beam divergence are schematically visualised.
H113 with its end position Pf1b. A detailed description ofthe beam characteristics can be found in [14]. The beamguide delivers a thermal neutron capture equivalent fluxdensity of 2 × n s − cm − and an angular divergence ofabout 7 mrad on an exit window of 20 × . The beamprofile and its divergence is too large to be directly used incontext with a HPGe-array. Therefore a dedicated colli-mation system was developed allowing to shape the beamfive meters downstream from the end of the H113 guideto a circular cross section of 1 cm diameter and a neutronflux of about 1 × n s − cm . Connected to this collima-tion system was a target chamber of about 1 meter lengthcrossing the centre of a detector array and followed by aneutron beam dump. Both, collimation and target cham-ber were made out of Aluminium and all neutron opticalcomponents were made out of B C or isotopically enriched LiF. The target chamber was surrounded by HPGe de-tector array consisting of 10 EXOGAM clovers, 6 GASPcoaxial and 2 clover detectors from ILL. The entire systemwas connected to a trigger free digital acquisition systemallowing to record all detected events on a common timebase and to set coincidence conditions later. The samplematerial in this experiment was the same as used in thebent crystal mode. However, due to the very high neu-tron capture cross section and the high efficiency of thedetector array the sample mass was reduced to a few pow-der grains of an immeasurable small mass (below 1 mg).In this configuration the signals from the neutron cap-ture reaction on
Gd were still dominating and driving3 n t e n s i t y Energy - 944181 (eV) diffr. theorinstr. resp.dispersivenon-dispersivetherm. broadening
Fig.
3: Plot of the combined measurements of instrument re-sponse function and thermal broadening. The resolution wasabout 4 eV FWHM at 944.181 keV, essentially dominated bythe theoretical diffraction profile. The thermal Doppler broad-ening is rather low, the average thermal velocity was deter-mined to be 400 m/s. the detectors close to the measurable saturation threshold(about 18 kHz count rate on each channel).A more detailed description of the EXILL setup can befound in [10].
3. Experimental Results
In the earlier work [6], the odd-spin negative-parityband was already investigated. The lifetime of the5 − state was measured with the GRID technique tobe τ = 0 . (cid:0) . . (cid:1) ps yielding a B(E2,5 − → − ) =293 (cid:0) (cid:1) W.u. and a quadrupole moment for this bandhead to be Q = 7 . (cid:0) . . (cid:1) b. The main focus of this workwas on the even-spin negative parity band interpreted bysome authors [15, 16, 17] as the signature partner bandof the one with the odd spins. The nuclear state lifetimeof the 4 − state was measured via the Doppler broaden-ing of the 1180 keV transition and the lifetime of the 2 − state via the 1231 keV transition respectively. A measure-ment of 6 − state was not possible since this state is tooweekly populated in the neutron capture reaction and thelow solid angle of the double flat crystal mode was notallowing to obtain sufficient statistics.The instrument response function and the thermalbroadening were determined by non-dispersive and disper-sive third order measurements of the 944.181 keV transi-tion of Gd. The transition is very intense, depopulat-ing a rather long lived state ( τ > v T = 393(37)m/s,which is rather high compared to earlier experiments. Thiscan be explained by the rather large sample mass of 9grams causing a higher self-heating of the samples in thereactor.The measurement of the nuclear state lifetimes was per-formed by means of the measurement of supplementaryDoppler broadening in dispersive third orders scans. Eachgamma cascade, populating the LOI, contributes to a re-coil velocity distribution, which needs to be known for fit-ting the Doppler broadened lineshapes. The recoil veloc-ity distribution is calculated using a Monte Carlo routine,following all possible feeding paths. It adds for each sim-ulated gamma transition a recoil vector while also takinginto account possible slowing down between consecutiverecoil events. Only a small fraction (about 25%) of thefeeding of the 4 − is known from the literature [11]. Toour knowledge the published (n, γ ) level scheme has so farnever been verified via coincidence measurements. There-fore it was verified with the results of the EXILL setup,which allowed at the present status of data evaluation asubstantial correction/adding to the feeding scenario upto about 56%. The remaining unknown part of the feed-ing was substituted by a virtual two step cascade. For thispurpose one assumes that the level of interest E LOI is con-nected with the capture state E CAP via a two step cascadeover an intermediate level of energy E s with lifetime τ s .The values of these parameters are left free to minimisea global χ . The range of variation for the energy waschosen to be E LOI + 200keV < E s < E CAP − τ LOI from theDoppler broadening data. For each parameter set ( E s , τ s ),a χ ( τ LOI ) curve is generated. All simulated ( E s , τ s ) com-binations yield a manifold of χ ( τ LOI ) curves, which isused to extract the most probable lifetime and also to as-sign an error. The result for the 1180 keV transition isshown in the upper part of Figure 4. The extracted life-time is τ = 1 . (cid:0) . . (cid:1) ps. The same evaluation procedurewas applied for the evaluation of the 1231 keV transitionto extract the lifetime for the 2 − state to be 2 . (cid:0) . . (cid:1) ps.
4. Discussion
A conversion of the obtained lifetime values into reducedbranching ratios, for the non-stretched E1-transitions,yields the valuesB(E1)[2 − → + ] = 0 . (cid:0) . . (cid:1) W.u.B(E2)[4 − → + ] = 1 . (cid:0) . . (cid:1) W.u.,whereas for the stretched E2-transition,B(E2)[4 − → − ] = 1 . × (cid:0) . . (cid:1) W.u.4
881 882 883 884 885 886 887 0 1000 2000 3000 4000 5000
Lifetime (fs)
50 100 150 200 250 300 350-20 -15 -10 -5 0 5 10 15 20
E-1180311 (eV)
Exp. dataLifetime fitinstr. resp C oun t s Fig.
4: The upper part shows the Doppler broadened line-shape of the 1180 keV transition depopulating the 4 − state.The lower part shows the χ ( τ LOI ) curves obtained for differ-ent E s , τ s combinations. The horizontal dashed lines indicatethe values of χ ( τ LOI ) min and χ ( τ LOI ) min + 1 allowing tofind the most probable lifetime and to extract the error bar,respectively. The deduced quadrupole moment of the even-spinnegative-parity band is Q = 13 . (cid:0) . (cid:1) b.The most surprising result here is certainly the extraor-dinarily large B(E2)[4 − → − ], which lies half way be-tween the the B(E2) values obtained for normal deformedand super deformed structures, sign of high collectivity,for which at present we have no clear interpretation. Itis worth mentioning that the present values of the life-times and the resulting branchings are still preliminary,since the evaluation of the EXILL data is not yet finished.However, since the EXILL data impact only the amountof known feeding the further evaluation will most likelyonly affect the error bars and not shift the numbers of theextracted values. In this sense, it seems to be already clearthat the difference of quadrupole moment of the odd andeven spin negative parity bands indicates that these bothbands should not be considered to be signature partners.Since the odd spin band is showing a quadrupole momentcomparable with the ground state band ( Q = 6 . References [1] Li X and Dudek J 1994
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