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The Recoil Distance Transient Field method: Target chamber development and test experiment
Nuclear Instruments and Methods in Physics Research A 418 (1998) 365—373
The Recoil Distance Transient Field method: Target chamber development and test experiment C. Teich*, A. Jungclaus, K.P. Lieb II. Physikalisches Institut, Georg-August-Universita( t Go( ttingen, Bunsenstrasse 7-9, D-37073 Go( ttingen, Germany Received 19 December 1997; received in revised form 2 April 1998
Abstract We report on the design and test of a plunger device suited for the determination of g-factors of short-lived high-spin states via the Recoil Distance Transient Field method. A first successful application of the device in combination with five EUROBALL cluster detectors is presented for the case of the 2491 keV 21/2> state in Nb. 1998 Elsevier Science B.V. All rights reserved. PACS: 21.10.Ky; 23.20.En; 27.50; #e Keywords: g-factors; Recoil Distance Transient Field method; EUROBALL cluster detector
1. Introduction The measurement of magnetic moments of picosecond high-spin states populated in heavy-ion fusion reactions entails rather severe experimental difficulties. Due to the short lifetime, one has to employ very large magnetic fields in order to induce measurable Larmor precessions. Sufficient field strengths acting during the passage of fast ions through ferromagnetic foils are available by utilizing transient magnetic hyperfine fields. Due to the statistical nature of the particle and c-ray emission from the compound nucleus and the evaporation residues, a very large time spread in the population
* Corresponding author. Tel.: #490 551 39 7669; #490 551 39 4493; e-mail: [email protected].
fax:
of discrete high-spin states is observed in heavy-ion fusion reactions. This situation is contrary to that in fast single-step processes like Coulomb excitation where the excited state is populated immediately during the collision. The statistical feeding in compound nuclear reactions makes the assignment of the observed precession to a particular nuclear state in the cascade extremely difficult. To deduce the individual contributions of different states to the measured effect, it is necessary to simulate the complete, but partially unknown c-flux through the nucleus, including all the transition intensities, level lifetimes, magnetic moments and sidefeeding intensities and times. In order to avoid these problems, the Recoil Distance Transient Field (RDTF) method has been proposed [1,2]. This method allows to measure the precession induced by the interaction of a single
0168-9002/98/$19.00 1998 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 9 8 ) 0 0 9 2 8 - 0
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discrete high-spin state with the transient field by separating the ferromagnetic foil from the target foil by an appropriate vacuum flight distance d. Fig. 1 illustrates the principle of the RDTF technique. When the nucleus enters the ferromagnetic layer with a recoil velocity v after the flight time t "d/v , it senses the transient field B (v) and 2$ experiences an integral Larmor-precession
l R *U"!g L B (v)e\R O dt, (1) 2$
R before it comes to rest in the non-ferromagnetic backing. The times t and t mark the entry into and exit from the ferromagnetic layer and q denotes the lifetime of the exited state. By introducing the flight path d, the state of interest can be selected by setting a coincidence gate on the Doppler-shifted component c of the feeding transition, thus ensur ing that the level of interest has been populated before the nucleus enters the ferromagnetic foil. Then the Larmor precession of the stopped component c of the c-ray depopulating the state in this coincidence spectrum is a measure of the magnetic moment of this single state. The experimental setup can easily be optimized for the investigation of different states by variation of the delay time, that is change of the flight distance d. To achieve reasonable accuracy in the determination of the small precession angles (in the order of tens of mrad), highly efficient c-ray detectors, which are now available in the new generation of c-ray spectrometers like EUROBALL [3] or GAMMASPHERE [4], have to be used.
Fig. 1. Sketch illustrating the RDTF method: (a) target, (b) ferromagnetic layer and (c) non-ferromagnetic backing.
In Section 2 we describe the RDTF device while in Section 3 we report on the first successful experiment to measure the magnetic moment of the 2491 keV 21/2> state in Nb [6,7] excited in the reaction Ni(S,3p)Nb.
2. Design and construction of the RDTF target chamber Considering the description of the RDTF technique given above, it is obvious that the target chamber has to meet the following requirements: 1. The flight distance between the target and the stopper foil has to be adjustable, with a lower limit of a few lm in order to allow the investigation of ps high-spin states. 2. In order to use gadolinium as the ferromagnetic layer, the stopper foil has to be cooled down to well below its Curie temperature, ¹ "290 K. ! 3. The mechanical supports of the stretched target and stopper foils have to be designed in such a way that precise parallel alignment of both foils is preserved after the evacuation of the chamber and the cooling of the stopper. This requires a good temperature stability of the apparatus. 4. To calibrate and monitor the distance during the experiment, the capacity of the target-stopper system has to be recorded continuously. 5. The periodic change of the polarizing magnetic field direction has to be simple and reliable. 6. The absorption of c-rays in the chamber should be kept as low as possible, especially in those directions in the plane perpendicular to the magnetic field where the logarithmic slope of the angular distribution is largest and therefore the detectors are positioned (around $55° resp. $125° for E2 transitions, within aligned nuclei). The RDTF chamber sketched in Fig. 2 and illustrated in the photograph shown in Fig. 3 meets these requirements. The beam enters the target chamber from the left and hits the target foil which is glued to a 16 mm diameter DURAL (95% Al/4% Cu/1% Mg) ring and stretched over a 20 mm long DURAL cylinder. DURAL was chosen because of its low c-ray absorption. This
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Fig. 2. Sectional view of the RDTF target chamber: (1) aperture, (2) screws used to stretch the target foil, (3) target cylinder, (4) adjustable holder, (5) adjusting screws, (6) micrometer screw, (7) ball bearing for magnets, (8) gearwheel, (9) NdFeB permanent magnets, (10) stopper cylinder, (11) stretched stopper foil, (12) part of the Cu-coldfinger connection, (13) mechanical mounting of the stopper cylinder, (14) mini motor with gearbox, (15) movable sledge, (16) magnetic transducer.
Fig. 3. Photograph of the plunger apparatus. Numbering according to Fig. 2.
electrically insulated cylinder is mounted on the adjustable holder (4), which allows to align the target and the stopper foils parallel to each other. The holder is made from the temperature stable Fe—Ni alloy INVAR (64% Fe/32% Ni). The trilayer stopper foil is mounted onto a similar holder as the target foil. However, a carbon ring was used instead of DURAL to keep the Gd foil stretched when the stopper cylinder is cooled down. Because of the higher thermal expansion coefficient of DURAL (j "22.5;10\ K\) as compared "30 *
to Gd (j "6.4;10\ K\), the Gd foil gets wavy % when glued onto a DURAL ring. The stopper cylinder is fixed to the base of the chamber by the INVAR support (13). To enable the cooling of the stopper foil, the cylinder is connected via a copper plait to a cold finger (10 mm diameter Cu) kept at liquid nitrogen temperature. The temperature at the carbon ring is measured by an iron-constantan-thermocouple. With a 110 MeV S beam of 1.5 pnA on the target, the stable equilibrium temperature of 200(3) K is reached some 45 min. after the beginning of the cooling. The temperature stability leads to a distance stability of typically 1 lm at the distance d"20 lm. The distance between the target and the stopper foil can be adjusted using the micrometer screw (6). The translation is monitored by the magnetic transducer (16). In order to obtain an absolute distance calibration, the capacity of the target-stopper system is measured, with both foils being electrically insulated. Such a calibration curve is shown in Fig. 4. The inverse capacity C\ increases linearly with increasing d until the two foils get into electrical contact. The “zero” distance, derived from extrapolation of the inverse capacity C\, is a measure of the quality of the parallel alignment of the two foils and their surface roughness. The offset of only
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2491 keV 21/2> state in Nb. The target foil consisted of 1.0 mg/cm Ni with an enrichment of 99.8%. The five cluster detectors were positioned at 0°, $55° and $125° with respect to the beam, in the horizontal plane. The distance between the cluster front face and the target was 25.4 cm for the 0° cluster and 24 cm for the others. A distance d&25 lm, corresponding to a flight time of about 3 ps was adjusted. In order to prevent local heating in the Gd layer due to the energy deposition of the beam it was slightly defocussed and restricted to 1.5 pnA. The magnetic field direction was reversed periodically every 30 min. Fig. 4. Distance calibration obtained using two 10 lm Ta foils as target and stopper. The difference between the electrical and the extrapolated contact is only 4.1 lm.
4 lm in the calibration curve demonstrates that a very good alignment can be achieved with our device. The capacity is measured and recorded during the experiment so that unintentional displacements, e.g. due to variations of the beam intensity and instabilities of the cooling of the stopper foil, can be monitored. The external magnetic field necessary to polarize the ferromagnetic stopper foil is provided by two NdFeB permanent magnets (9), mounted at a distance of 2 cm from each other. The resulting field strength of 125 mT at the beam spot is sufficient to saturate the magnetization of the Gd foil. To allow a simple change of the field direction, the magnets are mounted in a rotating frame on ball bearings and can be rotated with the help of a high-vacuum mini motor (14). 3. The RDTF test experiment in Nb 3.1. Set-up A first experiment using the new RDTF device was performed at the tandem accelerator of the Max Planck Institute Heidelberg. Using five EUROBALL cluster detectors [5] and the reaction Ni(S,3p)Nb at 110 MeV beam energy, we measured g-factors in Nb [6,7]. Here, we report on the test of the chamber and method for the
3.2. Preparation of the multilayer stopper foils The stopper trilayer used in the experiment consisted of 2.9 mg/cm Gd, 0.07 mg/cm In and 27.8 mg/cm Au. Gd was chosen as the ferromagnetic host because compared to iron the transient field in Gd is stronger by a factor of 1.4 [8] and the stopping power smaller by a factor of 2 [9], leading to a higher integral TF strength. The flight time within the Gd layer of 2.8 mg/cm thickness is about 1 ps. A disadvantage of Gd, besides its low Curie temperature (¹ "290 K), is the fact that Gd ! is quite an effective hydrogen getter and oxidizes nearly spontaneously in atmosphere. This fact complicates the preparation and stretching of the stopper foil considerably. The thickness of the Gd foil was chosen such that the reaction residues can leave the Gd and come to rest in the non-ferromagnetic Au backing. Fig. 5 shows the range distribution of the recoiling Nb nuclei entering the stopper with an average energy of 28 MeV, as obtained in a Monte Carlo simulation using the code TRIM95 [10,11]. Only 11% of the recoiling nuclei are stopped in the ferromagnetic layer so that contributions to the measured precessions due to the interaction of the stopped nuclei with the static hyperfine field are small and can be neglected in the analysis. Gold was chosen as backing material because of its large stopping power in combination with a high thermal conductivity, advantageous for efficient cooling. The Gd foil was annealed in vacuum (5;10\mbar) for 20 min at 1073 K to remove lattice defects. To stick the Gd and Au layers
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Fig. 5. Monte-Carlo simulation of the range distribution of recoiling Nb nuclei in the stopper trilayer. 89% of the recoils leave the Gd and come to rest in the non-ferromagnetic Au backing.
together, very thin In layers (0.035 mg/cm) were evaporated on both metal foils. Then they were rolled together after being heated up to the melting temperature of In (430 K). The trilayer was finally glued to the carbon ring using epoxy resin and stretched over the stopper cylinder. Despite the very different thermal expansion coefficients of Gd (j "6.4;10\ K\) and Au (j "14.1; % 10\ K\), the foils did not come apart, even when cooled down to 200 K and heated up again several times. Fig. 6 shows the measured magnetization of the trilayer as a function of the external polarizing field at a temperature of 250 K. It is evident that the polarizing field of 125 mT saturates the magnetization of the Gd. Taking into account the known temperature dependence of the magnetization M(T) [12,13], 73% of the 0 K-magnetization is reached. 3.3. Data analysis 3.3.1. Preparation of the data As mentioned before, our set-up consisted of five EUROBALL cluster detectors arranged in a plane. Fig. 7 shows a front view of such a cluster detector with the 7 individual Ge-crystals. For each cluster, the crystals C2/3, C1/4/7 and C5/6 form groups with the same angle H with respect to the beam. Altogether, the crystals can be divided in 15 groups: three crystals at 0°, two at $14°, two at $42°, three at $55°, two at $68°, two at $112°, three at $125° and two at $138°. During 80 h beam
369
Fig. 6. Magnetization of the Gd/In/Au trilayer measured at 250 K as function of the polarizing field. The applied field strength of the polarizing field of 125 mT is indicated by a vertical line.
Fig. 7. Front view on a cluster detector. The seven individual Ge capsules are numbered.
on the target, we collected 1.2;10 cc-events that were sorted into 60 different E —E matrices for c c each direction of the polarizing field. For each of the 15 groups of crystals, four different matrices were produced containing coincidence events between a crystal of this group and one of the four remaining clusters. 3.3.2. The situation in Nb Fig. 8 shows the relevant part of the level scheme of Nb [6] and two coincidence spectra gated on the 781 keV line in all forward and backward detectors, respectively. One notes that all transitions above the 2491 keV 21/2> state are partly or completely Doppler-shifted, while the depopulating
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Fig. 9. Angular correlation function of the 754, 953 and 781 keV transitions deduced when gating on the flight component of the 729 keV transition. Fig. 8. Relevant part of the level scheme of Nb and two coincidence spectra taken at forward (full line) and backward angles (dotted line) with a gate set on the 781 keV transition.
transitions below the 21/2> state show only unshifted photopeaks. The 21/2> state therefore meets the requirements of deducing its magnetic moment via the RDTF method. In a first step, gates were set on the shifted components of the populating 729 keV transition to deduce the angular correlations and, later on, the rotations *U of the unshifted depopulating transitions. Unfortunately, the 955 keV transition could not be used in the analysis because of its contamination by the much stronger 953 keV 17/2>P13/2> transition. 3.3.3. Angular correlation functions For the determination of the precession angle *UH of the depopulating transition c in a conven tional analysis, the angular correlation function W(H) has to be known. To deduce W(H) from our data, the individual coincidence spectra for the two field directions were summed up. The peak areas were corrected for the different relative efficiencies of the individual Ge crystals, known from calibrations. An absolute normalization was performed by comparing the photopeak intensities of transitions following the b-decays of Nb, Y and Y in the coincidence gate on the 511 keV annihilation line. By gating in each of the five clusters, five sets of angular correlation functions are obtained for each transition, which are then combined to determine the a and a angular correlation coeffi cients. Under the assumption that the 3220 keV
23/2> initial state is well aligned, the three depopulating E2 transitions 754, 953 and 781 keV should have identical angular correlations [14,15]. Fig. 9 shows the resulting angular correlation function of the three transitions deduced by gating on the flight component of the 729 keV transition. The resulting coefficients are a "0.40(2) and a "!0.03(2). 3.3.4. Precession angles In order to deduce the Larmor precession of the 21/2> state, counting rate ratios Nj(H ,H ) , R(H ,H )" Ni(H ,H ) H 3+$42°,$55°,$68°,$112°,$125°, $138°,
(2)
H 3+0°,$55°,$125°,, were calculated, where Nj(H ,H ) refers to the intensity of the unshifted peak of the depopulating c-ray observed in the detector at H gated with the populating flight peak c (here the 729 keV transition) in the detector positioned at H , for the field direction “up”. Defining I(H )"
H H +H H
R(H ,H )
(3)
A !°, we can deduce the geometrical mean value
. H"
I(#H) I(#H!180°) , I(!H) I(!H#180°)
H3+42°,55°,68°,,
(4)
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for the groups of crystals placed symmetrically at angles $H and 180°$H with respect to the beam axis. These quantities . H are independent of the detector efficiencies and the integral beam current. From these values . H the precession angles
1 . H!1 *UH" , S(H) . H#1
(5)
can be deduced taking into account the logarithmic slope S(H)"1/¼d¼/dH of the angular correlation function W(H). The three independent rotations *U °, *U ° and *U ° for each depopula ting transition are shown in Fig. 10. The average value of the deduced rotations is *U" !20.0(55) mrad. The parametrization of the acting TF implies the largest uncertainty in the analysis. The question of the correct parametrization is strongly related to the preparation technique of the Gd foil. Similar to [16], we used Gd as a foil instead of evaporating it on the non-ferromagnetic backing. We used the “Chalk River” parametrization of the transient field [16] B"(a Zv/v ) exp(!0.135v/v ), (6) !0 with Z being the proton number of the nucleus recoiling at the velocity v/v in units of the Bohr velocity v and a "22.3(14) T for Gd at 200 K. !0 Fig. 11 shows the calculated transient field and expected rotation of Nb, entering the Gd-foil at the initial energy of 28 MeV and being stopped according to the ZBL formula [10]. The resulting g-factor of the 2491 keV 21/2> state in Nb g(21/2>)" #0.36(11) corresponds well to the value of g"#0.41(13) measured in a recent IMPAD experiment [17]. The problem of possible systematic errors as a consequence of the parametrization used for the acting field can be tackled by measuring g-factors that have been determined with other methods. However, the meaning of such comparisons is often limited by the quite large experimental uncertainties. For comparison, we have also used the Rutgers parametrization [18] of the TF strength, B"a Z ! (v/v ) ! , (7) 0 (see Fig. 11 dotted lines) with a "13.00(65) T 0 which leads to g(21/2>)"#0.45(36) and, there-
Fig. 10. Precession angles *U ° (䉱), *U ° (䉬) and *U ° (䊉) for the depopulating 754 953 and 781 keV transitions. The mean value of *U"!20.0(55) mrad is underlayed in gray.
Fig. 11. (a) Calculated transient field strength B for Gd at 2$ 200 K and (b) deduced integral rotation *U/g as a function of the penetration depth in the Gd layer. The curves refer to the Chalk River parametrization (full lines), B "(a Zv/v ) 2$ !0 exp(!0.135v/v ) with a "22.3(14) T and the Rutgers par !0 ametrization (dotted lines), B "a Z ! (v/v ) ! 2$ 0 with a "13.00(65) T. The upper and lower lines of each type 0 represent the errors of the different parametrizations.
fore, still in agreement with the previous IMPAD value [17]. The upper and lower limits in Fig. 11 represent the errors taking into account the uncertainties in the constants a , a and the two expo!0 0 nents in the Rutgers parametrization.
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3.3.5. Checks Systematic effects that might influence the measured rotations can be tracked down by calculating . the “check ratios” . H
. H"
I(#H) I(!H) . I(!H#180°) I(#H!180°)
(8)
The difference between . H and . H is the fact that the latter is a product of diametral detector pairs and the resulting ratio should be equal to unity. The average “check ratio” . "0.9992(17) of 40 evaluated transitions is in perfect agreement with this expectation (see Fig. 12a). Another possibility to look for systematic effects is to deduce the rotations *UH of flight peaks, e.g. for c-rays which have been emitted before the nuclei were exposed to the TF. These c-rays should not exhibit any rotation. Fig. 12b shows the precession angles *U of various flight peaks in different gates. The average rotation of 0.2(27) mrad is in very good agreement with the expected zero rotation.
4. Summary and outlook The present RDTF test experiment for the 2491 keV 21/2> state in Nb (q"20(1) ps) have
Fig. 12. (a) Check ratios . H of 40 evaluated transitions. The mean value of . "0.9992(17) underlayed in gray. (b) Precession angles *U of 12 flight peaks in different gates. The mean value of *U"0.2(27) mrad underlayed in gray agrees with the expected zero effect.
shown first evidence, that the highly efficient Ge arrays or a set-up of EUROBALL cluster detectors can solve the old problem of measuring magnetic moments of short-lived high-spin states populated in heavy ion fusion reactions. Based on the present experiences we have now started to design a new target chamber suitable for the full EUROBALL array. Besides its more compact construction and direct liquid nitrogen cooling, the major difference, is the distance setting via remote-control.
Acknowledgements We would like to thank J. Billowes for the measurement of the magnetization of the Gd foils and many useful suggestions concerning the chamber construction and R. Repnow and the crew of the Heidelberg tandem accelerator for their friendly and efficient cooperation. T. Ha¨rtlein’s advice concerning the angular correlations is appreciated. The EUROBALL project is funded by Deutsches Bundesministerium fu¨r Bildung, Wissenschaft, Forschung und Technologie (BMBF).
References [1] E. Lubkiewicz, H. Emling, H. Grein, R. Kulessa, R.S. Simon, H.J. Wollersheim, C. Ender, J. Gerl, D. Habs, D. Schwalm, Z. Phys. A 335 (1990) 369. [2] U. Birkental, A.P. Byrne, S. Heppner, H. Hu¨bel, W. Schmitz, Nucl. Phys. A 555 (1993) 643. [3] C.W. Beausang, J. Simpson, Nucl. Part. Phys. 22 (1996) 527. [4] I-Yang Lee, Nucl. Phys. A 520 (1990) 641c. [5] J. Eberth, H.G. Thomas, P.v. Brentano, R.M. Lieder, H.M. Ja¨ger, H. Ka¨mmerling, M. Berst, D. Gutknecht, R. Henck, Nucl. Instr. Meth. A 369 (1996) 135. [6] A. Jungclaus, K.P. Lieb, C.J. Gross, J. Heese, D. Rudolph, D.J. Blumenthal, P. Chowdhury, P.J. Ennis, C.J. Lister, C. Winter, J. Eberth, S. Skoda, M.A. Bentley, W. Gelletly, B.J. Varley, Z. Phys. A 340 (1991) 125. [7] A. Jungclaus, C. Teich, V. Fischer, D. Kast, K.P. Lieb, C. Lingk, C. Ender, T. Ha¨rtlein, F. Ko¨ck, D. Schwalm, J. Billowes, J. Eberth, H.G. Thomas, Phys. Rev. Lett. 80 (1998) 2793. [8] K.H. Speidel, H. Busch, G. Jakob, J. Cub, S. Kremeyer, U. Grabowy, A. Gohla, J. Gerber, A. Meens, P. MeierKomor, C. Rezny, M. Behr, P. Padberg, 10th Int. Conf. on Hyp. Int. Leuven, 1995.
C. Teich et al. /Nucl. Instr. and Meth. in Phys. Res. A 418 (1998) 365—373 [9] L.C. Northcliffe, R.F. Schilling, Nucl. Data Tables A 7 (1970) 233. [10] J.F. Ziegler, J.P. Biersack, U. Littmark, The Stopping and Range of Ions in Matter, Pergamon Press, New York, 1977—1985, pp. 2—6. [11] J.P. Biersack, L. Haggmark, Nucl. Instr. Meth. 174 (1980) 257. [12] H.E. Nigh, S. Legvold, F.H. Spedding, Phys. Rev. 132 (1963) 1092. [13] N. Benczer-Koller, D.C. Ballon, A. Pakou, Hyp. Int. 33 (1987) 37.
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[14] R. Bauer, Phys. Rev. C 19 (1979) 399. [15] D. Pelte, D. Schwalm, in: R. Bock (Ed.), Heavy Ion Collisions, vol. 3, North-Holland, Amsterdam, 1982, p. 1. [16] O. Ha¨usser, H.R. Andrews, D. Ward, N. Rud, P. Taras, R. Nicole, J. Keinonen, P. Skensved, C.V. Stager, Nucl. Phys. A 406 (1983) 339. [17] M. Weiszflog, J. Billowes, J. Eberth, C.J. Gross, M.K. Kabadiyski, K.P. Lieb, T. Mylaeus, D. Rudolph, Nucl. Phys. A 584 (1995) 133. [18] N.K.N. Shu, D. Melnik, J.M. Brennan, W. Semmler, N. Benczer-Koller, Phys. Rev. C 21 (1980) 1828.
The Recoil Distance Transient Field method: Target chamber development and test experiment C. Teich*, A. Jungclaus, K.P. Lieb II. Physikalisches Institut, Georg-August-Universita( t Go( ttingen, Bunsenstrasse 7-9, D-37073 Go( ttingen, Germany Received 19 December 1997; received in revised form 2 April 1998
Abstract We report on the design and test of a plunger device suited for the determination of g-factors of short-lived high-spin states via the Recoil Distance Transient Field method. A first successful application of the device in combination with five EUROBALL cluster detectors is presented for the case of the 2491 keV 21/2> state in Nb. 1998 Elsevier Science B.V. All rights reserved. PACS: 21.10.Ky; 23.20.En; 27.50; #e Keywords: g-factors; Recoil Distance Transient Field method; EUROBALL cluster detector
1. Introduction The measurement of magnetic moments of picosecond high-spin states populated in heavy-ion fusion reactions entails rather severe experimental difficulties. Due to the short lifetime, one has to employ very large magnetic fields in order to induce measurable Larmor precessions. Sufficient field strengths acting during the passage of fast ions through ferromagnetic foils are available by utilizing transient magnetic hyperfine fields. Due to the statistical nature of the particle and c-ray emission from the compound nucleus and the evaporation residues, a very large time spread in the population
* Corresponding author. Tel.: #490 551 39 7669; #490 551 39 4493; e-mail: [email protected].
fax:
of discrete high-spin states is observed in heavy-ion fusion reactions. This situation is contrary to that in fast single-step processes like Coulomb excitation where the excited state is populated immediately during the collision. The statistical feeding in compound nuclear reactions makes the assignment of the observed precession to a particular nuclear state in the cascade extremely difficult. To deduce the individual contributions of different states to the measured effect, it is necessary to simulate the complete, but partially unknown c-flux through the nucleus, including all the transition intensities, level lifetimes, magnetic moments and sidefeeding intensities and times. In order to avoid these problems, the Recoil Distance Transient Field (RDTF) method has been proposed [1,2]. This method allows to measure the precession induced by the interaction of a single
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discrete high-spin state with the transient field by separating the ferromagnetic foil from the target foil by an appropriate vacuum flight distance d. Fig. 1 illustrates the principle of the RDTF technique. When the nucleus enters the ferromagnetic layer with a recoil velocity v after the flight time t "d/v , it senses the transient field B (v) and 2$ experiences an integral Larmor-precession
l R *U"!g L B (v)e\R O dt, (1) 2$
R before it comes to rest in the non-ferromagnetic backing. The times t and t mark the entry into and exit from the ferromagnetic layer and q denotes the lifetime of the exited state. By introducing the flight path d, the state of interest can be selected by setting a coincidence gate on the Doppler-shifted component c of the feeding transition, thus ensur ing that the level of interest has been populated before the nucleus enters the ferromagnetic foil. Then the Larmor precession of the stopped component c of the c-ray depopulating the state in this coincidence spectrum is a measure of the magnetic moment of this single state. The experimental setup can easily be optimized for the investigation of different states by variation of the delay time, that is change of the flight distance d. To achieve reasonable accuracy in the determination of the small precession angles (in the order of tens of mrad), highly efficient c-ray detectors, which are now available in the new generation of c-ray spectrometers like EUROBALL [3] or GAMMASPHERE [4], have to be used.
Fig. 1. Sketch illustrating the RDTF method: (a) target, (b) ferromagnetic layer and (c) non-ferromagnetic backing.
In Section 2 we describe the RDTF device while in Section 3 we report on the first successful experiment to measure the magnetic moment of the 2491 keV 21/2> state in Nb [6,7] excited in the reaction Ni(S,3p)Nb.
2. Design and construction of the RDTF target chamber Considering the description of the RDTF technique given above, it is obvious that the target chamber has to meet the following requirements: 1. The flight distance between the target and the stopper foil has to be adjustable, with a lower limit of a few lm in order to allow the investigation of ps high-spin states. 2. In order to use gadolinium as the ferromagnetic layer, the stopper foil has to be cooled down to well below its Curie temperature, ¹ "290 K. ! 3. The mechanical supports of the stretched target and stopper foils have to be designed in such a way that precise parallel alignment of both foils is preserved after the evacuation of the chamber and the cooling of the stopper. This requires a good temperature stability of the apparatus. 4. To calibrate and monitor the distance during the experiment, the capacity of the target-stopper system has to be recorded continuously. 5. The periodic change of the polarizing magnetic field direction has to be simple and reliable. 6. The absorption of c-rays in the chamber should be kept as low as possible, especially in those directions in the plane perpendicular to the magnetic field where the logarithmic slope of the angular distribution is largest and therefore the detectors are positioned (around $55° resp. $125° for E2 transitions, within aligned nuclei). The RDTF chamber sketched in Fig. 2 and illustrated in the photograph shown in Fig. 3 meets these requirements. The beam enters the target chamber from the left and hits the target foil which is glued to a 16 mm diameter DURAL (95% Al/4% Cu/1% Mg) ring and stretched over a 20 mm long DURAL cylinder. DURAL was chosen because of its low c-ray absorption. This
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Fig. 2. Sectional view of the RDTF target chamber: (1) aperture, (2) screws used to stretch the target foil, (3) target cylinder, (4) adjustable holder, (5) adjusting screws, (6) micrometer screw, (7) ball bearing for magnets, (8) gearwheel, (9) NdFeB permanent magnets, (10) stopper cylinder, (11) stretched stopper foil, (12) part of the Cu-coldfinger connection, (13) mechanical mounting of the stopper cylinder, (14) mini motor with gearbox, (15) movable sledge, (16) magnetic transducer.
Fig. 3. Photograph of the plunger apparatus. Numbering according to Fig. 2.
electrically insulated cylinder is mounted on the adjustable holder (4), which allows to align the target and the stopper foils parallel to each other. The holder is made from the temperature stable Fe—Ni alloy INVAR (64% Fe/32% Ni). The trilayer stopper foil is mounted onto a similar holder as the target foil. However, a carbon ring was used instead of DURAL to keep the Gd foil stretched when the stopper cylinder is cooled down. Because of the higher thermal expansion coefficient of DURAL (j "22.5;10\ K\) as compared "30 *
to Gd (j "6.4;10\ K\), the Gd foil gets wavy % when glued onto a DURAL ring. The stopper cylinder is fixed to the base of the chamber by the INVAR support (13). To enable the cooling of the stopper foil, the cylinder is connected via a copper plait to a cold finger (10 mm diameter Cu) kept at liquid nitrogen temperature. The temperature at the carbon ring is measured by an iron-constantan-thermocouple. With a 110 MeV S beam of 1.5 pnA on the target, the stable equilibrium temperature of 200(3) K is reached some 45 min. after the beginning of the cooling. The temperature stability leads to a distance stability of typically 1 lm at the distance d"20 lm. The distance between the target and the stopper foil can be adjusted using the micrometer screw (6). The translation is monitored by the magnetic transducer (16). In order to obtain an absolute distance calibration, the capacity of the target-stopper system is measured, with both foils being electrically insulated. Such a calibration curve is shown in Fig. 4. The inverse capacity C\ increases linearly with increasing d until the two foils get into electrical contact. The “zero” distance, derived from extrapolation of the inverse capacity C\, is a measure of the quality of the parallel alignment of the two foils and their surface roughness. The offset of only
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2491 keV 21/2> state in Nb. The target foil consisted of 1.0 mg/cm Ni with an enrichment of 99.8%. The five cluster detectors were positioned at 0°, $55° and $125° with respect to the beam, in the horizontal plane. The distance between the cluster front face and the target was 25.4 cm for the 0° cluster and 24 cm for the others. A distance d&25 lm, corresponding to a flight time of about 3 ps was adjusted. In order to prevent local heating in the Gd layer due to the energy deposition of the beam it was slightly defocussed and restricted to 1.5 pnA. The magnetic field direction was reversed periodically every 30 min. Fig. 4. Distance calibration obtained using two 10 lm Ta foils as target and stopper. The difference between the electrical and the extrapolated contact is only 4.1 lm.
4 lm in the calibration curve demonstrates that a very good alignment can be achieved with our device. The capacity is measured and recorded during the experiment so that unintentional displacements, e.g. due to variations of the beam intensity and instabilities of the cooling of the stopper foil, can be monitored. The external magnetic field necessary to polarize the ferromagnetic stopper foil is provided by two NdFeB permanent magnets (9), mounted at a distance of 2 cm from each other. The resulting field strength of 125 mT at the beam spot is sufficient to saturate the magnetization of the Gd foil. To allow a simple change of the field direction, the magnets are mounted in a rotating frame on ball bearings and can be rotated with the help of a high-vacuum mini motor (14). 3. The RDTF test experiment in Nb 3.1. Set-up A first experiment using the new RDTF device was performed at the tandem accelerator of the Max Planck Institute Heidelberg. Using five EUROBALL cluster detectors [5] and the reaction Ni(S,3p)Nb at 110 MeV beam energy, we measured g-factors in Nb [6,7]. Here, we report on the test of the chamber and method for the
3.2. Preparation of the multilayer stopper foils The stopper trilayer used in the experiment consisted of 2.9 mg/cm Gd, 0.07 mg/cm In and 27.8 mg/cm Au. Gd was chosen as the ferromagnetic host because compared to iron the transient field in Gd is stronger by a factor of 1.4 [8] and the stopping power smaller by a factor of 2 [9], leading to a higher integral TF strength. The flight time within the Gd layer of 2.8 mg/cm thickness is about 1 ps. A disadvantage of Gd, besides its low Curie temperature (¹ "290 K), is the fact that Gd ! is quite an effective hydrogen getter and oxidizes nearly spontaneously in atmosphere. This fact complicates the preparation and stretching of the stopper foil considerably. The thickness of the Gd foil was chosen such that the reaction residues can leave the Gd and come to rest in the non-ferromagnetic Au backing. Fig. 5 shows the range distribution of the recoiling Nb nuclei entering the stopper with an average energy of 28 MeV, as obtained in a Monte Carlo simulation using the code TRIM95 [10,11]. Only 11% of the recoiling nuclei are stopped in the ferromagnetic layer so that contributions to the measured precessions due to the interaction of the stopped nuclei with the static hyperfine field are small and can be neglected in the analysis. Gold was chosen as backing material because of its large stopping power in combination with a high thermal conductivity, advantageous for efficient cooling. The Gd foil was annealed in vacuum (5;10\mbar) for 20 min at 1073 K to remove lattice defects. To stick the Gd and Au layers
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Fig. 5. Monte-Carlo simulation of the range distribution of recoiling Nb nuclei in the stopper trilayer. 89% of the recoils leave the Gd and come to rest in the non-ferromagnetic Au backing.
together, very thin In layers (0.035 mg/cm) were evaporated on both metal foils. Then they were rolled together after being heated up to the melting temperature of In (430 K). The trilayer was finally glued to the carbon ring using epoxy resin and stretched over the stopper cylinder. Despite the very different thermal expansion coefficients of Gd (j "6.4;10\ K\) and Au (j "14.1; % 10\ K\), the foils did not come apart, even when cooled down to 200 K and heated up again several times. Fig. 6 shows the measured magnetization of the trilayer as a function of the external polarizing field at a temperature of 250 K. It is evident that the polarizing field of 125 mT saturates the magnetization of the Gd. Taking into account the known temperature dependence of the magnetization M(T) [12,13], 73% of the 0 K-magnetization is reached. 3.3. Data analysis 3.3.1. Preparation of the data As mentioned before, our set-up consisted of five EUROBALL cluster detectors arranged in a plane. Fig. 7 shows a front view of such a cluster detector with the 7 individual Ge-crystals. For each cluster, the crystals C2/3, C1/4/7 and C5/6 form groups with the same angle H with respect to the beam. Altogether, the crystals can be divided in 15 groups: three crystals at 0°, two at $14°, two at $42°, three at $55°, two at $68°, two at $112°, three at $125° and two at $138°. During 80 h beam
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Fig. 6. Magnetization of the Gd/In/Au trilayer measured at 250 K as function of the polarizing field. The applied field strength of the polarizing field of 125 mT is indicated by a vertical line.
Fig. 7. Front view on a cluster detector. The seven individual Ge capsules are numbered.
on the target, we collected 1.2;10 cc-events that were sorted into 60 different E —E matrices for c c each direction of the polarizing field. For each of the 15 groups of crystals, four different matrices were produced containing coincidence events between a crystal of this group and one of the four remaining clusters. 3.3.2. The situation in Nb Fig. 8 shows the relevant part of the level scheme of Nb [6] and two coincidence spectra gated on the 781 keV line in all forward and backward detectors, respectively. One notes that all transitions above the 2491 keV 21/2> state are partly or completely Doppler-shifted, while the depopulating
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Fig. 9. Angular correlation function of the 754, 953 and 781 keV transitions deduced when gating on the flight component of the 729 keV transition. Fig. 8. Relevant part of the level scheme of Nb and two coincidence spectra taken at forward (full line) and backward angles (dotted line) with a gate set on the 781 keV transition.
transitions below the 21/2> state show only unshifted photopeaks. The 21/2> state therefore meets the requirements of deducing its magnetic moment via the RDTF method. In a first step, gates were set on the shifted components of the populating 729 keV transition to deduce the angular correlations and, later on, the rotations *U of the unshifted depopulating transitions. Unfortunately, the 955 keV transition could not be used in the analysis because of its contamination by the much stronger 953 keV 17/2>P13/2> transition. 3.3.3. Angular correlation functions For the determination of the precession angle *UH of the depopulating transition c in a conven tional analysis, the angular correlation function W(H) has to be known. To deduce W(H) from our data, the individual coincidence spectra for the two field directions were summed up. The peak areas were corrected for the different relative efficiencies of the individual Ge crystals, known from calibrations. An absolute normalization was performed by comparing the photopeak intensities of transitions following the b-decays of Nb, Y and Y in the coincidence gate on the 511 keV annihilation line. By gating in each of the five clusters, five sets of angular correlation functions are obtained for each transition, which are then combined to determine the a and a angular correlation coeffi cients. Under the assumption that the 3220 keV
23/2> initial state is well aligned, the three depopulating E2 transitions 754, 953 and 781 keV should have identical angular correlations [14,15]. Fig. 9 shows the resulting angular correlation function of the three transitions deduced by gating on the flight component of the 729 keV transition. The resulting coefficients are a "0.40(2) and a "!0.03(2). 3.3.4. Precession angles In order to deduce the Larmor precession of the 21/2> state, counting rate ratios Nj(H ,H ) , R(H ,H )" Ni(H ,H ) H 3+$42°,$55°,$68°,$112°,$125°, $138°,
(2)
H 3+0°,$55°,$125°,, were calculated, where Nj(H ,H ) refers to the intensity of the unshifted peak of the depopulating c-ray observed in the detector at H gated with the populating flight peak c (here the 729 keV transition) in the detector positioned at H , for the field direction “up”. Defining I(H )"
H H +H H
R(H ,H )
(3)
A !°, we can deduce the geometrical mean value
. H"
I(#H) I(#H!180°) , I(!H) I(!H#180°)
H3+42°,55°,68°,,
(4)
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for the groups of crystals placed symmetrically at angles $H and 180°$H with respect to the beam axis. These quantities . H are independent of the detector efficiencies and the integral beam current. From these values . H the precession angles
1 . H!1 *UH" , S(H) . H#1
(5)
can be deduced taking into account the logarithmic slope S(H)"1/¼d¼/dH of the angular correlation function W(H). The three independent rotations *U °, *U ° and *U ° for each depopula ting transition are shown in Fig. 10. The average value of the deduced rotations is *U" !20.0(55) mrad. The parametrization of the acting TF implies the largest uncertainty in the analysis. The question of the correct parametrization is strongly related to the preparation technique of the Gd foil. Similar to [16], we used Gd as a foil instead of evaporating it on the non-ferromagnetic backing. We used the “Chalk River” parametrization of the transient field [16] B"(a Zv/v ) exp(!0.135v/v ), (6) !0 with Z being the proton number of the nucleus recoiling at the velocity v/v in units of the Bohr velocity v and a "22.3(14) T for Gd at 200 K. !0 Fig. 11 shows the calculated transient field and expected rotation of Nb, entering the Gd-foil at the initial energy of 28 MeV and being stopped according to the ZBL formula [10]. The resulting g-factor of the 2491 keV 21/2> state in Nb g(21/2>)" #0.36(11) corresponds well to the value of g"#0.41(13) measured in a recent IMPAD experiment [17]. The problem of possible systematic errors as a consequence of the parametrization used for the acting field can be tackled by measuring g-factors that have been determined with other methods. However, the meaning of such comparisons is often limited by the quite large experimental uncertainties. For comparison, we have also used the Rutgers parametrization [18] of the TF strength, B"a Z ! (v/v ) ! , (7) 0 (see Fig. 11 dotted lines) with a "13.00(65) T 0 which leads to g(21/2>)"#0.45(36) and, there-
Fig. 10. Precession angles *U ° (䉱), *U ° (䉬) and *U ° (䊉) for the depopulating 754 953 and 781 keV transitions. The mean value of *U"!20.0(55) mrad is underlayed in gray.
Fig. 11. (a) Calculated transient field strength B for Gd at 2$ 200 K and (b) deduced integral rotation *U/g as a function of the penetration depth in the Gd layer. The curves refer to the Chalk River parametrization (full lines), B "(a Zv/v ) 2$ !0 exp(!0.135v/v ) with a "22.3(14) T and the Rutgers par !0 ametrization (dotted lines), B "a Z ! (v/v ) ! 2$ 0 with a "13.00(65) T. The upper and lower lines of each type 0 represent the errors of the different parametrizations.
fore, still in agreement with the previous IMPAD value [17]. The upper and lower limits in Fig. 11 represent the errors taking into account the uncertainties in the constants a , a and the two expo!0 0 nents in the Rutgers parametrization.
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3.3.5. Checks Systematic effects that might influence the measured rotations can be tracked down by calculating . the “check ratios” . H
. H"
I(#H) I(!H) . I(!H#180°) I(#H!180°)
(8)
The difference between . H and . H is the fact that the latter is a product of diametral detector pairs and the resulting ratio should be equal to unity. The average “check ratio” . "0.9992(17) of 40 evaluated transitions is in perfect agreement with this expectation (see Fig. 12a). Another possibility to look for systematic effects is to deduce the rotations *UH of flight peaks, e.g. for c-rays which have been emitted before the nuclei were exposed to the TF. These c-rays should not exhibit any rotation. Fig. 12b shows the precession angles *U of various flight peaks in different gates. The average rotation of 0.2(27) mrad is in very good agreement with the expected zero rotation.
4. Summary and outlook The present RDTF test experiment for the 2491 keV 21/2> state in Nb (q"20(1) ps) have
Fig. 12. (a) Check ratios . H of 40 evaluated transitions. The mean value of . "0.9992(17) underlayed in gray. (b) Precession angles *U of 12 flight peaks in different gates. The mean value of *U"0.2(27) mrad underlayed in gray agrees with the expected zero effect.
shown first evidence, that the highly efficient Ge arrays or a set-up of EUROBALL cluster detectors can solve the old problem of measuring magnetic moments of short-lived high-spin states populated in heavy ion fusion reactions. Based on the present experiences we have now started to design a new target chamber suitable for the full EUROBALL array. Besides its more compact construction and direct liquid nitrogen cooling, the major difference, is the distance setting via remote-control.
Acknowledgements We would like to thank J. Billowes for the measurement of the magnetization of the Gd foils and many useful suggestions concerning the chamber construction and R. Repnow and the crew of the Heidelberg tandem accelerator for their friendly and efficient cooperation. T. Ha¨rtlein’s advice concerning the angular correlations is appreciated. The EUROBALL project is funded by Deutsches Bundesministerium fu¨r Bildung, Wissenschaft, Forschung und Technologie (BMBF).
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