New reaction chamber for transient field g-factor measurements with radioactive ion beams

Nuclear Instruments and Methods in Physics Research A 785 (2015) 47–54

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Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima

New reaction chamber for transient field g-factor measurements with radioactive ion beams A. Illana n, A. Perea, E. Nácher, R. Orlandi 1, A. Jungclaus Instituto de Estructura de la Materia, CSIC, E-28006 Madrid, Spain

art ic l e i nf o

a b s t r a c t

Article history: Received 22 December 2014 Received in revised form 24 February 2015 Accepted 25 February 2015 Available online 5 March 2015

A new reaction chamber has been designed and constructed to measure g-factors of short-lived excited states using the Transient Field technique in combination with Coulomb excitation in inverse kinematics. In this paper we will discuss several important aspects which have to be considered in order to successfully carry out this type of measurement with radioactive ion beams, instead of the stable beams used in a wide range of experiments in the past. The technical solutions to the problems arising from the use of such radioactive beams will be exposed in detail and the first successful experiment using the new chamber in combination with MINIBALL cluster detectors at REX-ISOLDE (CERN) will be reported on. & 2015 Elsevier B.V. All rights reserved.

Keywords: g-factor Radioactive beams Coulomb excitation Transient Field (TF) technique

Contents 1. 2. 3.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Special requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Design and construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. General design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. The targets for TF experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. Magnetic field and cooling system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4. Particle detector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5. Activity and shielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Experimental test: 72Zn g-factor measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Preparation of the data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3. Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Summary and outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1. Introduction For many years, magnetic moment measurements with stable ion beams have been essential to discriminate between different nuclear models. Nuclear magnetic moments are a very sensitive probe for the contributions of the valence protons and/or neutrons to the wave n

Corresponding author. E-mail address: [email protected] (A. Illana). 1 Present address: Advanced Science Research Centre, Japan Atomic Energy Agency, Tokai-mura 319-1195, Japan. http://dx.doi.org/10.1016/j.nima.2015.02.060 0168-9002/& 2015 Elsevier B.V. All rights reserved.

47 48 48 49 49 50 50 50 51 51 52 52 53 54 54

function of the state of interest, especially in the vicinity of shell closures. A list of all techniques and measurements performed so far has been compiled by Stone in Ref. [1]. Therefore now, with the advent of Radioactive Ion Beam (RIB) facilities providing beams of a wide range of exotic nuclei with sufficient intensities to allow for the measurement of magnetic moments, it is time to adapt the techniques well established over the years with stable ion beams to the peculiarities of RIBs. Three different methods seem to be suitable for measuring magnetic moments of short-lived excited states with RIBs: Recoil In Vacuum (RIV) [2] and the Transient Field (TF) technique with low-velocity ISOL [3] or

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high-velocity fragment beams (HVTF) [4]. The present work focuses on one of the first applications of the TF technique at ISOL facilities which provide beams with energies in the range 2–6 MeV/u. The TF technique in combination with Coulomb excitation in inverse kinematics has been successfully applied in a large number of stable ion beam experiments to measure g factors [5,6]. A low-velocity beam of the nucleus of interest impinges on a multilayer target. The projectile and the recoiling target ion are scattered in the forward direction crossing the remaining layers of the target. One of the layers is made of a ferromagnetic material in which the excited projectile experiences the TF. The TF occurs when an ion traverses a ferromagnetic material, which is magnetized by an external magnetic field, at a certain velocity, v. The moving nucleus experiences a strong internal hyperfine field with magnitude of kT, depending on the charge of the ion, Z, and the velocity of the ion, v. Transient fields arise from a spin exchange between the inner electrons of the moving ion and the aligned electrons of the ferromagnet, which causes a polarization of the spins of the unpaired electrons in the s shell of the moving ion. The use of the TF technique is indicated when the lifetime of the excited state of interest is in the order of a few ps. For such short lifetimes, external or static hyperfine fields are not strong enough to induce a measurable effect during the short interaction time [5,6]. Coulomb excitation in inverse kinematics is used to excite lowlying states in exotic nuclei with a large alignment, and therefore large anisotropy of the angular correlation of the decay radiation, and with high statistics. When exposed to a magnetic field, B, the spin of the nucleus in an excited state with lifetime τ experiences a torque due to the magnetic force, resulting in a precession, Φ, with the Larmor frequency ωL , as it is shown in the following equation [7]:

Φ ¼ ωL  τ ¼  g  τ

μN ℏ

B

ð1Þ

where μN is the nuclear magneton and ℏ is the reduced Planck constant. In TF experiments the gamma detectors are usually placed close to the horizontal plane. The external magnetic field is applied in vertical direction and its direction reversed periodically. The precession can then be deduced experimentally from the ratio of the photopeak intensities measured for the two different directions of the magnetic field and the slope of the perturbed angular correlation for each detection angle. Moreover, the ratio is extracted from the number of γ-rays, N(θ), detected in a pair of detectors positioned at angles 7 θ with respect to the beam line. Finally, the g-factor of the state of interest can be determined from the experimental precession angle, Φ, as described in Ref. [5]: Z t out μ Φ ¼ g  N  BTF ðvion ðtÞÞ  e  t=τ dt ð2Þ ℏ t in where BTF(t) is the transient field strength and tin and tout are the times when the ion enters and leaves the ferromagnetic layer, respectively. In order to extend this technique to measure magnetic moments of short-lived excited states with RIBs, some considerations must be taken into account. So far, only a few experiments have been performed employing this technique in conjunction with RIBs [3,8,9]. In 2011, an experiment aiming at measuring the magnetic moment of the first excited 2 þ state of 72Zn using the TF technique was successfully carried out at REX-ISOLDE (CERN) [10]. Note that the same case has recently also been studied using HVTF technique at GANIL [11]. The main aim of the present work was to investigate the feasibility of TF experiments for more exotic and consequently shorter-lived isotopes. Due to the use of thick targets, severe problems due to the accumulation of activity in the target region are expected when using shortlived radioactive beams. To minimize these problems, a new reaction chamber was designed and constructed prior to the experiment in

2011. In this work we report on the new design, which avoids as much as possible the implantation of radioactive ions close to the target area, mostly due to the straggling of the beam, and therefore minimizing the γ-ray background produced in the angular acceptance of the Ge detectors. Summarizing, we present here the features of a new reaction chamber for TF experiments and some results obtained in the first experiment performed with this novel design. As a first point, we discuss the special requirements fulfilled by the new reaction chamber. We then continue with the design section and explain in detail all the different parts of the reaction chamber. In the following, the problem of activation will be discussed and some solutions will be presented. In Section 4, the results of the first experiment performed with this chamber are presented and in particular an alternative analysis procedure [12] will be compared with the standard one reported in Ref. [10]. The paper ends up with some conclusions about the new chamber and the experiment.

2. Special requirements The TF technique is characterized by the necessity of employing multilayer targets, which are much thicker than the targets used in standard Coulomb excitation experiments. This aspect is crucial for magnetic moment measurements with radioactive beams. As it is explained in several papers, e.g. Refs. [5,6] and references therein, the classical multilayer target is basically composed of three different layers. In the first layer the Coulomb excitation of the beam takes place. It is followed by a ferromagnetic layer in which the excited nuclei experience the transient magnetic field. Finally, the last layer is a stopper made out of a non-magnetic material, usually copper. The large thickness of the target leads to a significant straggling of the beam, and, as a consequence, to an activity build-up in the target area when using the TF technique with RIBs. In order to avoid this problem, the reaction chamber must be designed in such a way that the least number of radioactive beam ions going through the target is implanted close to the target area. A second important consideration when using this technique is the necessity to produce an external magnetic field which focuses as many field lines as possible in the target, to polarize the ferromagnetic target layer. Traditionally, iron was used as a ferromagnetic material but more recent works [5,6,13] show that gadolinium produces stronger transient fields than iron. However, gadolinium has an important disadvantage: its Curie temperature is close to room temperature. Therefore, a cooling system in close contact with the target is necessary to decrease the temperature of this layer and keep it constant at around 100 K. The solution adopted for our chamber design will be described in the next section. The third requirement when using Coulomb excitation in inverse kinematics comes from the necessity to detect the target recoils in order to tag the Coulomb excitation events. This implies the use of particle detectors placed in forward direction, where the Coulomb cross-section is peaked in inverse kinematics, but as far as possible from the trajectory of the beam suffering from straggling in the target. A detailed description of these ancillary detectors and support will be given later in the text. Finally, the composition and the thickness of the chamber has to be chosen in order to minimize as much as possible the absorption of the γ-rays of interest, so that the γ-ray detection efficiency is maximized.

3. Design and construction In order to satisfy these requirements, a new reaction chamber for magnetic moment measurements was designed. In this section,

A. Illana et al. / Nuclear Instruments and Methods in Physics Research A 785 (2015) 47–54

the design of the chamber and its principal components will be explained in detail, and the specific solutions adapted to fulfill the requirements will be presented. 3.1. General design Following the previous designs for this kind of reaction chamber [13,14], a cylinder of 2 mm thick aluminum was selected. For TF experiments it is necessary to place the γ-ray detectors in a plane perpendicular to the external magnetic field and therefore the cylindrical shape has the appropriate symmetry. Furthermore, compared to the spherical shape, it has some advantages: first, it allows for an easy positioning of the ancillary silicon detectors as well as the magnetic circuit and the cooling system and, second, the flat surface at the top lid allows for the use of a Printed Circuit Board (PCB) to pass through the chamber and transmit the signals from the detectors in vacuum to the data acquisition system in air. This can be seen in Fig. 1.The design of both the chamber and the elements that it contains is optimized to reduce the amount of material between the detection zone and the target holder. In TF experiments one must take care of the straggling of the beam as it passes through the target material. This effect is one of the most important handicaps and perhaps the most difficult to avoid. In order to minimize it, the exit pipe of the chamber must be designed such that the beam stops as far as possible from the target area thus reducing the implantation of radioactive ions in the elements of the chamber and consequently minimizing the γ-ray background radiation produced by their decays. We adopted a solution based on a very wide beam pipe at the exit port of the reaction chamber (see Fig. 1). To further reduce the γ-ray background originating from the ions implanted in the section of this beam pipe, which is still close to the chamber, a shielding made of lead foils was used. 3.2. The targets for TF experiments As mentioned before the key ingredient of this type of experiments is the multilayer target. The different composition of the layers of the target produces extra difficulties to carry out an experiment. In the design of the target some different aspects have to be considered: a low

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Z material with respect to the projectile is necessary to produce Coulomb excitation in inverse kinematics. Traditionally, this layer is made of natural carbon, magnesium or aluminum, depending on the Z of the projectile and the assumed compromise between the total crosssection of the reaction and the low stopping power, to allow the target recoils to pass through the target [5]. The thickness of this layer is usually between 0.5 and 1 mg/cm2. For the second, the ferromagnetic layer, there are some different options: iron, gadolinium and nickel. The most commonly used in the past was iron, but as it was mentioned before, gadolinium produces a stronger transient field than iron or nickel. On the other hand, gadolinium has the disadvantage that its Curie temperature is close to room temperature, therefore a cooling system has to be developed. The classical targets have a last layer called stopper. It is usually made of copper and its purpose is to stop all the ions which experienced Coulomb excitation and traversed the ferromagnetic layer in a field-free environment. The production of these multilayer targets is discussed in detail by Maier-Komor et al. in Ref. [15]. However, when applying the TF technique to short-lived radioactive beams, the use of such “standard targets” may not be the best choice. Substituting the copper backing by a thicker layer of the ferromagnetic material allows to maximize the precession effect, however at the cost that the nucleus stopped in this layer will experiences a static hyperfine field whose strength is not well controlled [16]. Even so, in many cases this uncertainty may be negligible as compared to the statistical uncertainties when exotic radioactive beams are used. For the present case the contribution of the static hyperfine field was estimated in Ref. [10]. A second option is to simply remove the copper backing and allow the excited ions to leave the target. In this case the γ-rays of interest are emitted during the recoil in vacuum which has two consequences. First, the anisotropy of the angular correlation may be reduced due to Recoil In Vacuum (RIV) effects and, second, a Doppler correction has to be applied. On the other hand, the reduced total target thickness will significantly reduce the beam straggling and consequently the γ-ray background due to the implantation of radioactive nuclei close to the target area. A priori it is not obvious which of these two options is the better one and most probably this really depends on each individual case. In the experiment discussed below we therefore compared both options. The thick target, called Target I in the following, consisted of 0.45 mg/cm2 natural carbon, 11.8 mg/cm2 Gd and 1.0 mg/cm2 Ta, the latter being necessary in the production

Fig. 1. Lateral (left) and inside view (right) of the chamber constructed and tested in the experiment at the ISOLDE facility. The main elements are: (a) ISOLDE beam in and out, (b) beam collimator, (c) chamber, (d) beam pipe out, (e) MINIBALL crystals, (f) feed-through for the cooling system, (g) coils, (h) yoke of the magnetic circuit, (i) flange, (j) piece of the yoke inside the chamber, (k) internal cooling circuit, (l) H-shaped copper piece, (m) PT-100 and cable conexion to PCB, (n) PCB, (o) DSSD, (p) DSSD support structure, (q) rails support structure (r) DSSD cables, (s) absorbers, and (t) target. The red arrow indicates the direction of the beam. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)

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process of the target [15]. The thin target (Target II), on the other hand, was composed of 1.0 mg/cm2 natural carbon, 6.7 mg/cm2 Gd and 1.0 mg/cm2 Ta.

3.3. Magnetic field and cooling system The target is fixed on an H-shaped copper piece. Soldered to this piece, in good thermal contact, there is a brass pipe through which a constant flow of liquid nitrogen is circulating. The flux is produced by a standard pumping system, placed outside the chamber, which pumps liquid nitrogen out of a Dewar tank and makes it circulate through the chamber. The flux was regulated using a vent connected to the pump. This system produces a constant cooling of the target area. The temperature is monitored by a PT-100 resistors attached to the H-shaped piece. During the experiment an average temperature of 110 K was measured. Since the Curie temperature of gadolinium is equal to 294 K, this temperature is sufficient to keep it in a stable ferromagnetic state [17,18]. The evolution of the magnetization respect to the temperature of a typical Gd foil is shown in Fig. 2. In addition to that, an external magnetic field is necessary to polarize the ferromagnetic target layer. With this aim, a magnetic circuit made by an iron yoke was constructed and set in place. As it is shown in Fig. 1, the parts close to the target (marked j in the picture) have a sharp end in order to focus, as much as possible, all the magnetic field lines. For the magnetic-field production two different coils were wrapped around the iron bars of the yoke. One copper coil with N  2000 turns of a wire with diameter d¼ 0.4 mm and a second one with N  4000 turns of a wire with diameter d¼ 0.71 mm were placed on top and bottom of the chamber, respectively. The coils were connected in parallel circuit to a power supply of 30 V. The magnetic field was measured using a Hall probe at different points, giving a value of 0.1 T in the gap between the pole tips in which the target is placed. The effect of this magnetic field on the incident beam was estimated to amount to less than 1 mrad of deviation and has therefore been neglected in the following. A complete view of these parts is shown in Fig. 1.

Magnetization [T]

0.2

0.15

0.1

0.05

0

50

100

150

200

250

Temperature [K] Fig. 2. Measured magnetization at different temperatures of a typical rolled Gd foil extracted from Ref. [19]. The red line is drawn to guide the eye and the error bars represent the uncertainty in the absolute magnetization. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)

3.4. Particle detector After Coulomb excitation in inverse kinematics both particles are scattered in the forward direction, the excited beam ion and the target recoil. As a consequence of this mechanism a high spin alignment is observed, the velocity of the excited projectiles is maximized and the number of detected recoil particles close to 01 is increased, which improves the probability to detect coincident particle-γ events [5]. In contrast to the g-factor measurements with stable beams, the scattered beam cannot be simply stopped behind the target in a Ta foil, because this would adversely affect in the γ-ray detection increasing the background, as it was discussed in [5,6,14] and references therein. For this reason particle detection using a circular Si detector in the forward direction is not an option when measuring with radioactive beams. Instead two small Double-sided Silicon Strip Detectors (DSSD) were used at forward angles, fixed on an aluminum structure above and below the beam axis. This geometry selects the reactions with largest spin alignment perpendicular to the beam trajectory [5,14]. The two DSSD have 16  16 strips in a square piece of silicon with dimensions 2  2 cm2. The total surface of one DSSD, including the PCB support, is 4  5 cm2. The DSSD support structure was designed with some degrees of freedom to allow for changes in the geometry (angular coverage) during the experiment. The vertical distance of the Si from the beam axis can be changed. Moreover, the support is mounted over two rails, which are fixed to the flange, giving us the possibility to move the detectors in the direction of the beam axis. 3.5. Activity and shielding One of the main problems of this technique, as already mentioned in the previous section, is the implantation of radioactive ions in the surroundings of the target, leading to a high γ-ray background rate produced following beta decays. The distribution of radioactive ions behind the target and the subsequent γ-ray background should be studied in detail in order to keep it as low as possible. With this aim, a Monte Carlo simulation using the Geant4 and SRIM codes [21,20] was performed to estimate and prevent the effects of the γ-ray background in the MINIBALL clusters. In all performed simulations, the two different targets specified in Section 3.2. were considered. The composition of the targets and the position of all the chamber elements described above were implemented in the simulation as they were used in the experiment, described in detail in Section 4.1. The straggling of the beam produced by the target is mainly due to multiple scattering of the beam particles by the target atoms. The results of the Monte Carlo simulation are shown in Fig. 3. The upper panel shows the angular distribution of the particles emerging from the target. One can see how the thick Target I produces, as expected, far more straggling of the ion beam (red histogram) than the thinner Target II (blue histogram). In the lower panel of the same figure we have represented the integral angular distribution, that is, for each angle θ we have plotted the fraction of particles emitted within the range 01–θ. To illustrate the difference between the two targets with respect to the straggling, let us determine the angle at which the integral angular distribution reaches 99%. This would correspond to a fraction of 1% of the beam implanted in the chamber. In other words, requiring that 99% of the particles leave the chamber without touching any wall or material inside, we can use the graph in the lower panel of Fig. 3 to estimate the minimum angle to design the beamout port of the chamber and for setting up any detector or support whatsoever. The vertical dashed lines in the figure show these angles for each target, being 441 for Target I and 181 for Target II. The angular distribution of the Coulomb excitation cross-section is calculated using the CLX code [22], which is based on the original Winther and de Boer code [23]. For the reaction used in this work, the maximum of the cross-section is located around 151. Therefore, while placing the Si detectors at angles larger than 181 seems still acceptable, it is

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and cooled by liquid nitrogen to far below the Curie temperature of Gd (294 K). The scattered carbon target ions were detected in two square segmented Si detectors, as described in Section 3.4. They were positioned 3.0 cm downstream from the target 1.1 cm above and

3

10

Counts / 0.1 deg

51

102

10

1 100

Integral (%)

80

60

40

20

0 0

10

20

30

40

50

60

70

80

90

100

Theta (deg) Fig. 3. Monte Carlo simulation of the ion beam passing through the target and undergoing only multiple scattering. In both panels red and blue correspond to the thick (Target I) and thin (Target II) targets, respectively. Top: Angular distribution of particles emerging from the target. Bottom: Integrals of the previous histograms normalized to 100. The vertical dashed lines mark the angle covering 99% of the emitted particles. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)

certainly not reasonable to move them out much further. Already this simple estimate shows how severe the problem of activation really is using thick multilayer targets. Once we have designed the chamber and set up the detectors constrained by the angle calculated before (angular coverage 201‐451, see Section 4.1. for details), one can also estimate from the Monte Carlo simulation how the implantation is distributed over the different elements of the chamber and the beam pipe. Again two simulations were performed, one for each target, considering all the elements contained in the reaction chamber as they were described above. The results of these simulations are shown in Fig. 4. Looking at this figure one again observes huge differences between the two targets with respect to the fraction of ions implanted in the different parts of the chamber. For example, using the thick Target I about 5% of the beam ions are stopped in the Ta absorber foils mounted in front of the Si detectors while this number decreases to 0.3% when the thin Target II is employed.

4. Experimental test:

72

Fig. 4. Histogram of the fraction of ions implanted in the most relevant parts of the chamber. The upper panel corresponds to Target I (thick) and the lower panel to Target II (thin). The simulation was performed with 500,000 particles impinging on each target.

Zn g-factor measurement

4.1. Experimental setup The experiment was performed in November 2011 at the REXISOLDE facility at CERN. A UCx primary target was bombarded with a proton beam at energy 1.4 GeV produced by the PS-Booster. A radioactive 72Zn beam ðT 1=2 ¼ 46:5 hÞ was selected by the combination of the Resonant Ionisation Laser Ion Source (RILIS) and the General Purpose Separator (GPS) of the ISOLDE facility. The beam was postaccelerated to an energy of 2.94 MeV/u with a maximum beam intensity of 9  106 ions=s by the REX-ISOLDE linear accelerator, and impinged on two different multilayer targets (see Section 3.2.). These targets were magnetized by an external magnetic field of about 0.1 T

Fig. 5. Sketch of the MINIBALL cluster dispositions used in the experiment. The center of each cluster was positioned at a distance of 9.7 cm from the center of the target at angles of 7 601 and 71201 with respect to the beam axis and 751 with respect to the horizontal plane.

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below the beam axis, respectively, covering an angular range from 201 to 451 (see Fig. 1). The geometry and position of the DSSD detectors were chosen as a compromise between the fraction of radioactive beam ions implanted in the absorber foils mounted in front of the detectors and the coverage of a reasonable fraction of the Coulomb excitation cross-section. The de-excitation γ-rays were detected, in coincidence with the carbon ions, by four MINIBALL Cluster detectors positioned at 7601 and 71201 with respect to the beam axis and close to the horizontal plane. All of them were situated at a distance of 9.7 cm from the target (see Fig. 5). For a description of the MINIBALL Clusters as well as the associated electronics the reader is referred to Ref. [24]. More details with respect to the setup used in the present experiment are given in Ref. [10]. Even though the new reaction chamber was designed to be used in combination with the MINIBALL clusters at ISOLDE-CERN, it can of course also be used at other facilities and in combination with other detectors. 4.2. Preparation of the data The energy calibration of the DSSD was performed using a quadruple α source containing 148Gd, 239Pu, 241Am and 244Cm. For our purpose, this calibration is good enough since a precise knowledge of the energy of the particle is not critical in our analysis. On the other hand, for the MINIBALL crystals, an energy and efficiency calibration was carried out using a 152Eu γ-ray source placed in the

target support. The efficiency calibration procedure is described in Ref. [24]. The polar angle θ of each element of detection has to be known exactly in order to determine the angular correlation coefficients. For this purpose, a stable 22Ne beam at 2.94 MeV/u was provided by the REX-ISOLDE facility, bombarding a 1.0 mg/cm2 deuterated polyethylene (DPE) target which was mounted on the target support. The angle θ could be extracted from the observed Doppler-shift of the 1017-keV γ-ray emitted in the decay of the first excited state in 23Ne populated in the dð22 Ne; 22 NeÞp neutron pick-up reaction. 4.3. Data analysis The spectra of γ-rays detected in prompt coincidence with the carbon ions for the two different targets are shown in Fig. 6. In the case of Target II, the γ-rays of interest were emitted in flight, hence both a Doppler-shift correction of the energy as well as a transformation of the angles and counting rates from the laboratory to the rest frame of the nucleus were required as it was discussed in detail in Ref. [25]. Besides the most intense γ-rays corresponding to the 21þ -01þ and 41þ -21þ transitions in 72Zn with energies of 652.7 keV and 846.7 keV, respectively, additional lines were observed. The γ-rays with energies of 613.7, 889.1, 1043.9 and 884.9 keV can be identified as the 21þ -01þ , 41þ -21þ , 61þ -41þ and 02þ -21þ transitions in 78Se. The most plausible explanation for the presence of 78Se is that it is produced by an incomplete fusion reaction between the 12C target ions and the 72Zn beam. On the other hand, the states in 81 Br are populated via a fusion-evaporation reaction (see Ref. [10] for a more detailed discussion). The transition of interest here, the 21þ -01þ transition with an energy of 652.7 keV, is clearly visible in both spectra shown in Fig. 6. A total of 1940 and 11450 counts were measured for the 652.7-keV transition in the two runs using the Targets I and II, respectively. The intensity of the 846.7-keV line, which feeds the 21þ state, was determined to be as low as 5% compared to that of the 652.7-keV transition depopulating this state. The experimental angular correlations were obtained from the γ-ray intensity measured at each angle, θ, once corrected for the detector efficiency. A fit was made to the data using Eq. (3), where P k ð cos ðθÞÞ are the Legendre polynomials of order k:   WðθÞ ¼ a0 1 þ a2 P 2 ð cos ðθÞÞ þ a4 P 4 ð cos ðθÞÞ ð3Þ From this fit one can determine the angular coefficients a2 and a4. The resulting angular coefficients for each target are shown in Table 1. The first step to quantify the perturbation in the gamma emission, caused by the interaction between the spin and the external magnetic field, is to calculate the single or double ratios:

Fig. 6. Prompt γ-ray spectra (sum of all segments) for Target I (top) and the Target II (bottom). The different transitions populated during the experiment are shown.

ρSR ðθÞ ¼

N↑ð 7 θÞ F N↓ð 7 θÞ

ρDR ðθÞ ¼

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi N↑ð þ θÞ  N↓ð  θÞ N↓ð þ θÞ  N↑ð  θÞ

ð4Þ

ð5Þ

where N↑; ↓ð 7 θÞ are the number of counts measured for the transition of interest at angles 7 θ for the vertical field directions

Table 1 Angular correlation coefficients a2 and a4, precession angles, ΔΦexp , the calculated precession angle per unit of g factor for the linear parametrization and the deduced g factor for the transition 21þ -01þ in

72

Zn for the two different targets.

Target

a2

a4

ΔΦdiff (mrad)

ΔΦexp (mrad)a

ΔΦ=g (mrad)

gð21þ Þ

gð21þ Þa

I II

0.52(26) 0.61(25)

 0.53(30)  0.32(27)

 77 (26)  32 (13)

 71 (20)  30 (10)

 144 (16)  61 (9)

þ 0.53 (19) þ 0.52 (23)

þ 0.48 (12) þ 0.51 (17)

a

Ref. [10].

A. Illana et al. / Nuclear Instruments and Methods in Physics Research A 785 (2015) 47–54

“Up” or “Down”, respectively, and F is a statistical factor correcting for small differences in the integral number of beam ions for the two field directions. The double ratio is symmetric with respect to the beam axis and independent from other experimental factors such us the measuring time for each field direction, the integral beam currents or the detector efficiencies. For the γ-ray transition of interest, the measured effect, ϵðθÞ, is deduced directly from ρ:

ϵðθÞ ¼

ρ1 : ρþ1

ð6Þ

Finally, the precession angle can be calculated from the measured effect, ϵðθÞ, and the logarithmic slope, SðθÞ:

ΔΦðθÞ ¼

ϵðθÞ SðθÞ

ð7Þ

where the logarithmic slope SðθÞ ¼ ð1=WðθÞÞðdWðθÞ=dθÞ is calculated using Eq. (3) and the angular correlation coefficients, a2 and a4, deduced from the fit to the experimental values. On the other hand, an alternative approach referred to as differential method is to use a single ratio which allows to determine the precession angle for each crystal. Following Ref. [12]:

ΔΦdiff ðθÞ ¼

1 Ntot ↑ðθÞ  Ntot ↓ðθÞ SðθÞ N↑ðθÞ þ N↓ðθÞ

ð8Þ

where N tot ↑; ↓ðθÞ are the total number of counts measured for the transition of interest at angle θ, without subtracting background (the background is naturally removed in the subtraction). The quantities SðθÞ and N↑; ↓ðθÞ are the same as in the traditional procedure explained before. An example of the different spectra obtained for the numerator and denominator are shown in Fig. 7. This procedure, in contrast to the traditional one, provides a check of the background subtraction which is crucial for the calculation of the precession angle.

53

Following these guidelines, the ΔΦdiff ðθÞ can be calculated for both targets. The results obtained using the differential method, as well as the ones using the traditional procedure (see Ref. [10]) are shown in Table 1. The two values are perfectly compatible within the uncertainties for both targets. For Target II (thin target), in which the thickness of the Gd layer is reduced, the experimental precession angle is smaller by roughly a factor of two as compared to the run with the thick Target I. Also the anisotropy of the angular correlation is reduced in this case due to a partial de-orientation when the ions recoil out of the target into the vacuum. These disadvantages are partially compensated by the fact that when using the thin target a larger beam intensity could be accepted. Finally, in order to determine the precession angle per unit of g factor and deduce the g factor, the integral in Eq. (2) has to be solved. For this purpose, an adequate parametrization of the TF has to be chosen. We have adopted here the linear parametrization BTF ðtÞ ¼ G  a  Z  vðtÞ=v0

ð9Þ

where, a is the field parameter (17 T for Gd), Z is the atomic number of the recoiling ion, vðtÞ=v0 is the velocity of the ion in units of the Bohr velocity and G is an attenuation factor which takes into account the beam-induced reduction of the transient field strength. Values of G¼ 0.9(1) for Target I and G¼0.65(10) for Target II were derived in [10]. Regarding the lifetime, τ, we have considered a value of 17.7(11) ps which is the average of the values reported recently by Niikura et al. [26], τ ¼17.9(18) ps, and Louchart et al. [27], τ ¼17.6(14) ps. Using these parameters the precession angle per unit of g factor can be calculated using Eqs. (2) and (9) and, in turn, the g factor is deduced. The g factors obtained for each of the two runs are listed in Table 1. We comment at this point on alternative TF parametrizations. As discussed in Ref. [10], the use of the Rutgers parametrization instead of the linear one for Target II leads to a slightly larger g-factor value with the difference however being much smaller than the uncertainty. In Ref. [11] the problem of the TF parametrization was avoided by using a known g factor of a neighbour nucleus to calibrate. We can conclude that the results obtained with the two different analysis methods are in good agreement for both targets. The average g-factor for the differential procedure is g diff ð21þ Þ ¼ þ0:53ð15Þ and a value of gð21þ Þ ¼ þ 0:49ð10Þ is obtained in the case of the traditional procedure [10].

5. Summary and outlook

Fig. 7. The upper panel shows the sum (corresponds to the denominator) and and the lower panel is the difference (corresponds to the numerator) spectra for a detector at θ¼ 451 and for the Target I. Windows drawn in both cases refer to the peak of interest.

The main goal of this work was to evaluate the viability of the transient field technique to measure magnetic moments of short-lived excited states using radioactive ion beams. For this purpose a new reaction chamber was designed and built adapted to the requirements of this technique and optimized for its use in conjunction with MINIBALL detectors at REX-ISOLDE and the future HIE-ISOLDE facility. Results of a first experiment performed using this new chamber to measure the magnetic moment of the first excited 2 þ state in 72Zn were presented demonstrating the feasibility of such studies under certain circumstances. Since the straggling of the radioactive-ion beam in the thick multilayer target employed in TF measurements, and consequently the activity built up within the target chamber, is the most crucial aspect with respect to the applicability of this technique with short-lived exotic beams, two different targets were hence employed. Using a thick ferromagnetic layer the precession effect as well as the anisotropy of the angular correlation and therefore the sensitivity are maximized at the cost that only a limited beam intensity is acceptable in order to keep the counting rate in the Ge detector at a reasonable level. On the other hand, the use of a Gd layer thin enough to allow the excited beam ions to leave the multilayer target and decay in vacuum behind the target implies a reduced precession effect and a reduced anisotropy, but allows to accumulate higher statistics to at

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least partially compensate for these disadvantages. The experience gained in the first application of this technique at REX-ISOLDE clearly indicates that in order to perform a successful magnetic-moment measurement using the TF technique, the optimum conditions with respect to target composition as well as Si detector geometry have to be decided case by case. Several parameters ought to be considered in this choice, such as the half-lives of the radioactive beam itself and its decay products, the number of γ-rays emitted in the decay chain, the available beam intensity etc. Acknowledgments This work has been supported by the Spanish Ministerio de Ciencia e Innovación under Contracts FPA2009-13377-C02 and FPA2011-29854C04, and the Spanish MEC Consolider Ingenio 2010, Project No. CDS2007-00042 (CPAN). We would like to thank the mechanics workshops at the IEM-CSIC, the Universidad Autónoma de Madrid and the IFIC-CSIC for their excellent work. References [1] [2] [3] [4]

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