Cederkäll, J

Fästermann, T

Gerber, J P

Gerl, J

Gernhäuser, R

Habs, D

Jolie, J

Kenn, O

Kröll, T

Krücken, R

Leske, J

Mahgoub, M

Maier-Komor, P

Mandal, S K

Scherillo, A

Schielke, S

Schwerdtfeger, W

Speidel, K H

Thirolf, P G

Warr, N

Wollersheim, H J

CERN Document Server

CERN-INTC-2003-003 and INTC-P-166Proposal to the INTC CommitteeMagnetic Moments of Coulomb Excited 2+1States for RadioactiveBeams of132;134;136Te and138Xe Isotopes at REX-ISOLDEK.-H. Speidel1, J. Leske1, O. Kenn1, S. Schielke1, J. Gerber2, D. Habs3, P. Thirolf3,W. Schwerdtfeger3, R. Krucken4, T. Kroll4, M. Mahgoub4, T. Faestermann4,R. Gernhauser4, P. Maier-Komor4, J. Jolie5, N. Warr5, A. Scherillo5, S. K. Mandal6,H.-J. Wollersheim6, J. Gerl61University of Bonn, Germany,2IReS Strasbourg, France,3LMU Munchen, Germany,4TUMunchen, Germany,5University at Koln, Germany,6GSI Darmstadt, Germany, and theREX-ISOLDE collaborationSpokesperson: K.-H. SpeidelContact person: J. Cederkall1 IntroductionMagnetic moments are an indispensable source of information on the microscopic structureof atomic nuclei. It results from the fundamental dierence of the spin g factors of protonsand neutrons, in sign and magnitude, gS()= +5.586 and gS()= {3.826, which enables todetermine the nucleonic components of the wave functions of nuclear states. This behaviourwas clearly demonstrated in recent experiments on low-spin states of stable even-A Xenonisotopes for which the well-established increase of g(2+1) values with increasing neutronnumber, approaching the N = 82 shell closure, exhibits the transition from collective tosingle particle degrees of freedom with a dominant 1g7=2proton conguration for136Xe [1].It is a general feature, that nuclei near closed shells, in particular with magic neutronand proton numbers, are characterized by specic single particle components in the wavefunctions which changes into collective structures when departing from shell closures. Thecompetition between single particle and collective degrees of freedom is sensitively probedby magnetic moments as well as E2 transition rates.For ps lifetimes of nuclear states, there is at present only the technique of transientmagnetic elds (TF ) which provides the necessary eld strengths of several kTesla, to ob-serve spin precessions with perturbed -angular correlations (PAC). The TF are hyperneelds of the Fermi contact type, which are experienced in fast moving ions during theirpassage through ferromagnetic materials [2], among which Gd provides the best propertiesin terms of the polarization of the ions. Its Curie temperature of 298 K, however, requirescooling of the target to liquid nitrogen temperature.TF have been well studied and described by empirical parametrizations [3] at interme-diate ion velocities vion Zv0(v0= e2=h), whereby the eld strength generally increaseswith velocity reaching a maximum at vion= Zv0for single electron ions with its maximumfraction at the 1s electron Bohr velocity [3]. Beyond this velocity the eld strength de-creases towards zero as the ions become fully stripped [4]. Among the eld parametrizationsthe `linear' (Blin) and the Rutgers `rut' (Brut) are the most frequently used parametriza-tions providing the most reliable g factor results [3].2 Nuclear structure motivation and expectationIn comparison to the stable even-A Te isotopes120 130Te, which are collective of vibrationalnature with E(4+1)=E(2+1) ' 2:0, the structure of the unstable neutron-rich isotopes132Te,134Te and136Te is strongly inuenced by the N = 82 shell closure and the two protonsoutside the magic Z = 50 shell. This feature becomes evident already from their 2+1excitation energies (Fig. 1a and Fig. 2).It is also determined by their proximity to doubly-magic132Sn (Z=50, N=82) anddirectly relates to neighbouring isotones134Xe,136Xe and138Xe, respectively (Fig. 1b).For stable134Xe and136Xe g factors were recently determined for the 2+1and 4+1statesclearly exhibiting single proton excitations with dominant 1g7=2conguration [1]:134Xe : g(2+1) = +0.354(7)136Xe : g(2+1) = +0.766(45)g(4+1) = +0.80(15) g(4+1) = +0.83(14)It is the large and positive g factor of both states in136Xe and of the 4+1state in134Xe whichunambiguously shows the dominant proton nature whereas the smaller g(2+1) value in134Xeimplies additional neutron hole congurations mainly in the h11=2orbit (with its negativeSchmidt value, g(h11=2) =  0:348). This structure is well conrmed by shell modelcalculations which in addition yield small admixtures of congurations of neighbouringsingle particle orbits.For the isotones132Te and134Te we expect for the rst 2+states similar g factorsalthough the number of protons in the 1g7=2orbit is reduced. For136Te where the 2f7=2orbit is occupied by neutrons, its 2+1g factor should be smaller than that of neighbouringsemi-magic134Te. The same behaviour is expected for138Xe with two neutrons beyondthe magic N = 82 shell. Shell model calculations predict for136Te an even negativevalue emphasizing a dominant neutron component in the nuclear wave function [5]. Thisscenario is accompanied by an anomalous behaviour of the B(E2) values which consistsin an unexpectedly small value for136Te in comparison to132Te [6]. In fact its B(E2) isalmost equal to that of134Te (Fig. 2). A measurement of the g factor may shed more lighton this unusual behaviour. Terasaki et al. [5] suggested that the origin of this behaviour isrelated with a reduced neutron pairing gap at136Te which would cause an increase of theneutron and a decrease of the proton amplitudes in the wave function. On these grounds2τ [ps] τ [ps]τ [ps]21642.701.2448T1 2/ = 17,5 sT1 2/ = 41.8 minT1 2/ = 3.204 d2+52Te136 842+52 80132Te4+52 82134Te2+4+E level[MeV]120+ 0+ 0+697 2974+97460642312790.521900τ [ps] τ [ps]τ [ps]3.03.221stable stable T1/2=14.08 min54 80134Xe2+2+24+2+0+54 82136Xe13134+3812+E level[MeV]120+84716147678840+54 84138Xe5894844+a)b)Figure 1: Low-lying states with relevant  transitions of even-A (a) unstable Te isotopesand (b) corresponding Xe isotopes. The lifetime quoted for138Xe(2+1) corresponds to thecalculated B(E2) value [5]an even negative g(2+) value is expected for136Te which makes the g factor measurementso important (Fig. 2). The same calculations predict for138Xe a positive but denitelyreduced g-factor compared to semi-magic136Xe.3Te80132Te82134(2  )+1(2  )+1Te841360 0.5 00.51.01.550B(E2;2       0  )  [W.u.]− 0.5+1+1 E       [MeV]g    Figure2:ExperimentalE(2+1)excitationenergiesandB(E2)valuesinWeisskopfunitsaswellascalculatedgfactorsofthe2+1statesfor132;134;136Teisotopes.3ExperimentaldetailsThetechniqueusedforthenuclearstatesofinterest,withemphasisonthe2+1states(Fig.1),isprojectileCoulombexcitationininversekinematicsincombinationwithTFinferromagneticgadolinium.Thetargetconsistsof(Fig.3):1.0mg/cm248Ti+7.0mg/cm2Gd+1.0mg/cm2Ta+4.0mg/cm2Cu,wherebythe132;134;136Teand138Xeprojectilesareexcitedatenergiesof3.1MeV/Aincollisionswiththelayerof48TinucleiandexperienceprecessionsinthesubsequentGd4BTF γtransient fieldAγΘγbeam−ionΦ2Gd Ta CuTa − shield Si −detectortarget−ionFaraday−cupTi3.1 MeV/ATe−beam−detectorsFigure 3: Schematic view of target composition with the arrangement of particle detectorand two pairs of MINIBALL  detectors. Rotations of anisotropic -angular correlationsfor opposite directions of the TF are indicated. Trajectories of beam and target ions aredisplayed.layer which is magnetized by an external eld of 0.05 Tesla. The copper backing servesas stopper for the excited nuclei providing a hyperne interaction-free environment. De-excitation  rays are measured with MINIBALL detectors in coincidence with forwardscattered titanium ions which are detected in an annular Si detector at acceptance anglesbetween 22Æand 35Ærelative to the beam axis. The radioactive beam ions are steeredthrough the centre hole of the detector and are stopped in a downstream Faraday cup.The particle detector is covered with a thin Ta foil to stop beam ions from large anglescattering in the target in order to avoid radioactive contamination of the detector. Thistarget-detector arrangement (Fig. 3) has been tested in recent measurements using a stable550Ti beam [7]. It is noteworthy that the Doppler-shifted and broadened  rays, emitted inight from the also excited48Ti target nuclei, should not interfere with the  lines fromthe excited projectiles of all three Te isotopes. Because of this relevant aspect isotopicallypure48Ti is favoured over a natural Ta layer as target, although the other Ti isotopes mayalso not cause severe disturbances in the spectra in the energy region of interest. In fact,this situation has been veried by the measurements on neighbouring xenon isotopes [1].The technique described ensures high detection eÆciency of coincident  rays due tokinematic focussing of the target ions in the beam direction and provides high spin align-ment of the excited states followed by strongly anisotropic -angular correlations. Thelatter is a prerequisite to be sensitive to the spin precessions in the TF . Furthermore, theinverse kinematics implies high velocities of the Te ions with which large TF strengths areassociated. This property has been shown in many previous experiments [3].Four clusters of the MINIBALL detector array will be placed in pairs symmetric to thebeam axis in the plane perpendicular to the applied magnetic eld at angles , wherethe -angular correlations have their maximum slopes, S() = 1=W ()dW ()=d(Fig. 3). This experimental design has been used in many former measurements with theexception of the annular structure of the particle detector at forward angles: its eect on theanisotropy of the -angular correlation has been studied in detail in the above-mentionedtest experiment [7].For the (2+1! 0+1)  transitions slope values jS(= 65Æj of the angular correlationsin the rest frame of the  emitting nuclei are expected to be between 1.5 and 2.0. This spinalignment ensures large precession eects in counting rates for `up' and `down' directionsof the external magnetic eld. Precession angles, est, have been estimated for the presentconditions of the dierentATe beams and the specics of the target using the computerprogram TRANSI (Table 1). In these calculations the precession angle  is given by [3]: = g NhZtouttinBTF(vion(t))  e tdt (1)where g is the g factor of the state of interest and BTFthe transient eld acting for theeective time teff' (tin  tout) with entrance time tinand exit time toutof the ions in theGd layer; the exponential accounts for the decay of the nuclear state with lifetime  . TheTF strength in the linear parametrization is given by [3]:BTF= BlinGbeam(2)withBlin= a(Gd)  Z vionv0(3)where Gbeamis the attenuation factor of the TF induced by the beam ions and the strengthparameter a(Gd) ' 17 Tesla.For the present experimental conditions (Table 1) one obtains: Blin' 4 kTesla whichgives rise to an eective TF of BTF' 2:8 kTesla where GTe beam' 0:7 [3]. These datacorrespond for the three Te and the Xe isotopes to precession angles as quoted in Table 1.6Table 1: Summary of the mean velocities of the Te and Xe ions traversing the Gd layerof the target, the eective interaction times with the TF and the estimated precessionscalculated from Eqs.(1)-(3) based on the linear parametrization of the TF and g-factorpredictions [5].Isotope g(2+)theor< vion=v0> teff[ps] est[mrad]132Te +0.491 4.6 0.79 +50.134Te +0.695 4.9 0.62 +58.136Te {0.174 4.6 0.93 {21.138Xe +0.291 4.0 1.07 +35.4 Count rates and beam time requestIn the following we give an estimate of the expected count rates and the beam time re-quested for the determination of the angular correlations and precessions aiming for a 10 %accuracy of the 2+1g factors for132;134Te, a 20 % accuracy for136Te and a 10 % accuracyfor138Xe.With intensities of the Te and Xe beams of  4 106ions/s for132;134Te,  4 105ions/sfor136Te and  2  106for138Xe one obtains from Coulomb excitation cross-sections basedon the known B(E2) values (Fig. 2 and [5]) and the48Ti target including the particledetector acceptance, for each of the four detectors in the photopeaks coincident -countrates of:132Te(2+1! 0+1) : 2000 counts/h,134Te(2+1! 0+1) : 2400 counts/h,136Te(2+1! 0+1) : 160 counts/h and138Xe(2+1! 0+1) : 1600 counts/h.With four  detectors in the reaction plane and a 10 % or 20 % accuracy of the g factor onerequires in each detector and eld direction total peak intensities of  4.000 cts, 3.000 cts,6.000 cts for132Te,134Te and136Te, respectively, and  15.000 cts for138Xe. These dataimply a total beam time of 10 days composed of 2 days for both132;134Te, 6 days for136Teand 2 days for138Xe.In addition, we are planning a test experiment at the Cologne tandem acceleratorwith a stable50Ti beam and a carbon target (intead of48Ti) using the MINIBALL for7 ray detection and an annular Si detector for detecting the forward scattered carbonions, in almost identical geometry as for the planned REX-ISOLDE experiment. The maindierence to the earlier test measurement [7] consists in the rst use of MINIBALL fornuclear spin precessions in TF .References[1] G. Jakob et al., Phys. Rev. C 65 (2002) 024316[2] O. Kenn et al., Phys. Rev. C 63 (2000) 021302(R)[3] K.-H. Speidel et al., Prog. Part. Nucl. Phys. 49 (2002) 91[4] G. J. Kumbartzki et al., Hyp. Int. 7 (1979) 253[5] J. Terasaki et al., Phys. Rev. C 66 (2002) 054313[6] D. C. Radford et al., Phys. Rev. Lett. 88 (2002) 222501[7] O. Kenn et al., Nucl. Instr. Meth. in Phys. Res. B 171 (2000) 5898

Magnetic moments of Coulomb excited $2^{+}_{1}$ states for radioactive beams of $^{132,134,136}$Te and $^{138}$Xe isotopes at REX-ISOLDE

Magnetic moments of Coulomb excited $2^{+}_{1}$ states for radioactive beams of $^{132,134,136}$ Te and $^{138}$ Xe isotopes at REX-ISOLDE

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Magnetic moments of Coulomb excited 21+2^{+}_{1}21+​ states for radioactive beams of 132,134,136^{132,134,136}132,134,136Te and 138^{138}138Xe isotopes at REX-ISOLDE

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Magnetic moments of Coulomb excited $2^{+}_{1}$ states for radioactive beams of $^{132,134,136}$ Te and $^{138}$ Xe isotopes at REX-ISOLDE