The magnetic moment of $^{11}$Be was measured by detecting nuclear magnetic resonance signals in a beryllium crystal lattice. The experimental technique applied to a $^{11}$Be$^+$ ion beam from a laser ion source includes in-beam optical polarization, implantation into a metallic single crystal and observation of rf resonances in the asymmetric angular distribution of the $\beta$-decay ($\beta$-NMR). The nuclear magnetic moment $\mu(^{11}{\rm Be}) = -1.6816(8)\,\mu_N$ provides a stringent test for theoretical models describing the structure of the 1/2$^+$ neutron halo state

Fedosseev, V

Geithner, W

Kappertz, S

Keim, M

Köster, U

Lievens, P

Mishin, V I

Neugart, R

Sebastian, V

Vermeeren, L

Wilbert, S

CERN Document Server

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCHCERN-EP/99-739 June 1999Measurement of the magnetic moment of the one-neutron halo nucleus 11BeW. Geithner, S. Kappertz, R. Neugart, S. Wilbert, V. SebastianInstitut fu¨r Physik, Universita¨t Mainz, D-55099 Mainz, GermanyM. Keim, the ISOLDE CollaborationEP Division, CERN, CH-1211 Geneva 23, Switzerland.P. Lievens,Laboratorium voor Vaste-Stoffysica en Magnetisme, K.U. Leuven, B-3001 Leuven, BelgiumL. Vermeeren,Instituut voor Kern- en Stralingsfysica, K.U. Leuven, B-3001 Leuven, BelgiumV.N. Fedoseyev, V.I. MishinInstitute of Spectroscopy, Russian Academy of Sciences, RUS-142092 Troitsk, RussiaU. Ko¨sterPhysik-Department, Technische Universita¨t Mu¨nchen, D-85748 Garching, GermanyAbstractThe magnetic moment of 11Be was measured by detecting nuclear magnetic resonance sig-nals in a beryllium crystal lattice. The experimental technique applied to a 11Be+ ion beamfrom a laser ion source includes in-beam optical polarization, implantation into a metallicsingle crystal and observation of rf resonances in the asymmetric angular distribution of theβ-decay (β-NMR). The nuclear magnetic moment µ(11Be) = −1.6816(8)µN provides astringent test for theoretical models describing the structure of the 1/2+ neutron halo state.IS 304(Submitted to Physical Review Letters)Halo nuclei are weakly bound nuclear systems with an extreme N/Z ratio, which havea neutron (or proton) density that extends far beyond the core of the nucleus. 11Be is the bestknown case of a one-neutron halo nucleus and it has been studied quite extensively, mainlyusing reactions induced by radioactive ion beams.From interaction cross-sections of 790 A MeV 11Be nuclei with different targets a largerms matter radius for 11Be was deduced using a Glauber-model calculation [1]. This was takenas an indication for either a neutron halo or a large deformation. Additional information fromreaction studies of a 33  A MeV 11Be beam yielded the density distribution of the 11Be nu-cleus [2] showing an extended low-density tail which could not be explained by deformation,but clearly shows the existence of a neutron halo. Also the angular distribution of neutrons indissociation reactions of 11Be supports the assumption of a halo [3].11Be has two bound states (1/2+ and 1/2−), both presenting a halo structure, which areconnected by a very strong E1 transition [4]. Contrary to what one would expect from the stan-dard shell model, the ground state is not p1/2 but a 1/2+ intruder state from the sd shell. Varioustheoretical approaches have been proposed trying to reproduce these peculiar properties. Large-basis shell-model calculations [5, 6, 7, 8, 9, 10, 11, 12] do not invariably reproduce the parityinversion ascribed to a combined effect of core excitation to the first 2+ state, pairing block-ing and proton-neutron monopole interaction [9]. Realistic spatially extended wave functionsof both the 1/2+ and 1/2− states are needed to explain the strong E1 transition [6]. The vari-ational shell model [10], proposed to describe nuclei containing loosely bound nucleons, givesthe correct level ordering and the halo structure, but fails to reproduce the E1 strength. A gooddescription of all these aspects was recently obtained in a microscopic cluster model [13].Concerning the structure of the lowered 1/2+ state all the model approaches have incommon that the main component of the wave function is j(10Be)0+  ν2s1/2i, whereas thepredicted admixture of the core excited j(10Be)2+  ν1d5/2i state ranges from 10 % to 40 %.The magnetic moment should be particularly sensitive to the relative amplitudes of these twocomponents. Thus, in combination with a theoretical analysis, a measurement of the magneticmoment of 11Be would give detailed information about the wave function of the halo neutron.In this letter we report on the measurement of the magnetic moment of 11Be [*], per-formed by β-NMR spectroscopy on implanted polarized nuclei. The experimental technique isclosely related to the one employed for measurements of the nuclear spin and electromagneticmoments of 11Li [14, 15] and of the quadrupole moments of Na isotopes [16]. An isotope-separated 60 keV beam is polarized by optical pumping and implanted into a crystal lattice,where nuclear magnetic resonance signals are observed in the asymmetric angular distributionof the β-decay (β-NMR).The present experiment involves some novel features. (i) An efficient source of radioac-tive Be+ beams emerged from the development of laser ionization schemes [17] now beingwidely used at ISOLDE. (ii) The 11Be case constitutes the first application of optical polariza-tion to an ion beam instead of a neutralized beam, necessitating efficient optical pumping in theultraviolet resonance line with the low output power of a frequency-doubled cw dye laser. Inaddition to that, the first-forbidden β-decay to 11B allows no safe prediction of the asymmetrysignal to be expected. (iii) The magnetic field at the site of the 11Be sample may be calibratedby performing a similar experiment on a 8Li beam obtained from the same target and surface-ionized at the hot walls of the ion source.The experiment was performed at the ISOLDE facility at CERN. Beryllium isotopes wereproduced by fragmentation of uranium in a heated UC2 target exposed to the pulsed 1 GeVproton beam from the PS-Booster synchrotron. They diffused into a tungsten cavity in whichresonant laser ionization from the 2s2 1S0 atomic ground state via 2s2p 1P1 to an auto-ionizing1state took place [17]. The laser beams used for the two-step ionization process were obtainedfrom copper-vapor-laser pumped dye lasers combined with respectively frequency tripling andfrequency doubling. The ions were extracted electrostatically out of the cavity, accelerated to60 keV, mass-separated and guided to the experiment.For optical excitation the ion beam was propagating collinearly with a cw laser beamwhose wavelength was tuned to the (Doppler-shifted) BeII transition 2s 2S1/2 ! 2p 2P1/2.About 1 mW of 313 nm laser light was obtained by intra-cavity frequency doubling of anAr+-laser pumped dye laser running on Sulforhodamine B dye. In a preparatory experiment,fluorescence detection of resonant optical excitation was used to measure the isotope shift andhyperfine structure (hfs) for 7,9,10Be produced copiously from a carbon target. These measure-ments yield the previously unknown magnetic moment of 7Be [18] and in particular the mag-nitude of the specific mass shift [18], facilitating considerably the search of 11Be resonancefrequencies. Beam intensities over 109 atoms per second were available for these long-lived orstable isotopes, whereas the 11Be yield was only a few 106 atoms per second.The half-life of 13.8 s is just sufficiently short for a β-NMR experiment which requiresthe decay of implanted polarized nuclei within the spin-lattice relaxation time. This techniqueis by far more sensitive than fluorescence detection of optical excitation. Furthermore, a directNMR measurement of the nuclear g-factor is expected to be at least an order of magnitude moreaccurate than an optical hfs measurement.Circularly polarized (σ+) light was used to polarize the Be+ beam, and a weak longitudi-nal magnetic field was applied to the optical pumping section of 1.5 m length, kept at a variableelectrical potential for tuning the Doppler-shifted laser frequency into resonance. Polarizationof the total (electronic and nuclear) spin system was created in several cycles of excitation anddecay. A gradually increasing guiding field was used to rotate and then decouple the spins adi-abatically while entering the transverse field of the NMR magnet (about 0.3 T). The ions wereimplanted into a beryllium single crystal placed in the center of this magnet. Electrostatic de-flectors were used to compensate the magnetic force. The β-decay of the polarized nuclei wasdetected by two scintillation counter telescopes placed between the thin windows of the vacuumchamber and the magnet pole faces. The host crystal was cooled to about 50 K to slow downthe relaxation (T1 = 2.5 s at 300 K) by a factor of 5.The β-decay asymmetry reached about 1 % for optical pumping in the strongest hfs com-ponent. In principle this scheme should provide complete nuclear polarization, but the powerdensity of the ultraviolet laser beam was far below saturation. Taking this into account as wellas the relaxation losses we estimate the β-decay asymmetry parameter (averaged over all decaychannels and β-ray energies) to be at least 20 %.Now the complete hfs pattern was recorded by applying a voltage sweep to the opticalpumping section. The hfs splitting already gives a rough value for the magnetic moment, andin addition it gives the sign which of course is expected to be negative for the 1/2+ neutronstate. With this preliminary information the frequency scanning range for detecting the Larmorresonance (around 7.5 MHz) could be restricted to about 5 %.In the NMR experiment the β-decay asymmetry is destroyed by coupling the nuclearZeeman levels through rf irradiation at the Larmor frequency. Well-saturated NMR signalswere observed and finally narrowed to about 10 kHz by reducing the rf power (Fig. 1). Theexperimental line shapes are influenced by non-statistical fluctuations of the asymmetry signalmainly caused by power instabilities of the two laser systems: (i) Changes in the output of thefrequency-doubled dye laser used for optical pumping directly translate into changes of nuclearpolarization, whereas (ii) fluctuations in the ion source efficiency interfere with the timing ofthe scan (about one 11Be half-life integration time per channel) via the exponential radioactive27.82 7.83 7.84 7.85 7.86 7.87 7.880.51.01.52.0β-asymmetry[%]rf[MHz]0.40.60.81.00.40.60.81.0Figure 1: β-NMR signals of 11Be nuclei in a beryllium host crystal.decay and the relaxation. Apart from these fluctuations the NMR spectra at low rf power turnedout to be well described by a single Gaussian. In order to avoid uncontrolled errors in the deter-mination of the resonance frequency we took seven independent spectra and used the deviationsfrom the mean value together with the fitting results for evaluating a realistic error. This analysisyields the Larmor frequency of 7.8508(6) MHz.For an evaluation of the nuclear g-factor it is necessary to calibrate the magnetic fieldat the position of the implanted sample. This could be done in an elegant way by measuringthe Larmor frequency of 8Li [14] in the identical NMR setup, using a beam from the sametarget produced by surface ionization. The technique is similar to the one described for 11Be,but optical pumping of lithium requires some modification of the apparatus, to be achievedwithin a few hours. A beam of neutral lithium atoms was obtained by charge exchange onsodium vapor produced in a heated cell to which the Doppler-tuning potential was applied. Thelaser (operated on DCM dye) was tuned to the 2s 2S1/2 ! 2p 2P1/2 resonance line at 671nm. The 8Li resonance (Fig. 2) was found to be essentially Gaussian with a width of 3 kHz. Thededuced Larmor frequency of 1.9301(5) MHz includes an error accounting for possible shifts ofthe resonance center by the unknown quadrupole interaction of 8Li in the beryllium lattice. Thisinfluence was estimated from simulations of the line shape in comparison with the experimentalcurve.Different positions of the implanted spot on the crystal could involve slight differencesbetween the magnetic fields used for 11Be and for 8Li. Field inhomogeneities over the 12 mmdiameter of the crystal were measured with an NMR probe to be smaller than 10−4. On-line31.920 1.925 1.930 1.935 1.9405.05.56.06.57.07.58.0β-asymmetry[%]rf[MHz]Figure 2: β-NMR signal of 8Li nuclei in beryllium serving for calibration of the magnetic field.checks were performed during the 11Be experiment by moving the 5 mm ion beam spot over thecrystal with no measurable effect on the Larmor frequency. Field drifts of the order 5  10−5occurred during the two days of data taking. These drifts were monitored with a Hall probe.Apart from the time of changeover from the original to the calibration setup their influenceon the resonance position is largely included already in the averaging over the results of theindividual measurements.Using the reference value for the magnetic moment of 8Li [19], µ(8Li) = 1.653560(18)µN ,we obtain the magnetic moment of 11Be, µ(11Be) = −1.6816(8)µN . The difference in the dia-magnetic corrections for Be and Li, though practically negligible, has been taken into account.The quoted error includes an uncertainty from the Knight shift. This shift is known to be verysmall for Be in beryllium [20], and it can be estimated for Li in beryllium to be less than2  10−4 from the systematics of results for the 8Li spin-lattice relaxation obtained in similarsystems [21].The magnetic moment should reflect the composition of the 11Be ground-state wave func-tion. Most experimental information [1, 2, 3, 22] has been found to be consistent with theassumption of a well developed one-neutron halo state of essentially s1/2 nature. The large vari-ation in theoretically calculated amplitudes of the j(10Be)2+  ν1d5/2i admixture [5, 6, 7, 8,9, 10, 11, 12] must be due to particularities of the models, e. g. in the construction of a p -sdcross-shell interaction or in the ways of incorporating the features of weakly bound halo struc-tures. Nevertheless, the predictions for the magnetic moment are generally close to −1.5µN[10, 11, 23].Using recent empirical interactions for the p -sd region [8] and free-nucleon g-factorsBrown [23] obtained −1.58µN with the WBP interaction and −1.49µN with the WBT interac-tion. In both calculations the j2+  d5/2i component contributes about 20 % to the ground-statewave function. The calculated moments, being already smaller than the experimental value, arefurther reduced to about −1.2µN by taking an effective value of 0.78gsfree for the gs-factor of4the neutron as obtained from a fit to 13 magnetic moments of p -sd-shell nuclei [y]. In compar-ing this with the experimental value one may conclude that the 1/2+ halo state is of even purers1/2 character (with a Schmidt value of −1.91µN ) than the particular interactions predict. Aprevious shell-model calculation by Millener [24] based on the MK interaction [5, 6] and usingthe free-neutron gs-factor gave −1.71µN , a value which is very close to the experimental re-sult. Compared to other calculations the enhanced value of the magnetic moment can be tracedto a larger j0+  s1/2i parentage in the wave function. However, as long as the quenching ofgs for halo states cannot be calculated reliably (see below), the agreement may be regarded asfortuitous.Suzuki et al. [25] based their prediction for the magnetic moment on variable relativeamplitudes of the j0+s1/2i and j2+d5/2i components, and they included corrections for theinfluence of meson-exchange currents. By analyzing the situation in 15C they assumed gseff =0.85 gsfree. The prediction of −1.5µN for a 40 % component of j2+  d5/2i is then consistentwith the situation suggested by the variational shell model. However, the experimental valueof −1.68µN is incompatible with the range of predictions reaching the maximum (negative)value of −1.62µN for a pure s1/2 configuration. On the other hand, the variational-shell-modelresults [10] seem to be in accordance with recent preliminary data [26] on the transfer reactionp(11Be, 10Be)d. Spectroscopic factors for the reaction channels to the 0+ ground state and the2+ excited state of 10Be suggest a strong j2+  d5/2i component for 11Be.As we have shown, we may interpret the magnetic moment as compared to the shell-model calculations in support of a pronounced (and relatively pure s1/2) halo state. The halostructure will reduce core polarization compared to equivalent configurations in other nuclei.This also means that shell-model calculations not accounting for the exotic spatial structure ofthe 11Be wave function will implicitly overestimate the quenching of the gs-factor. Presumably,the shell-model predictions of about −1.5µN , compared to the experimental value of −1.68µN ,are influenced by this effect. Thus a coherent description of the 11Be nucleus will depend onfurther theoretical investigations quantifying these arguments.We wish to thank B. A. Brown, P. G. Hansen, D. J. Millener and T. Otsuka for valuablediscussions and comments. We particularly acknowledge the communication of shell-modelresults by B. A. Brown and D. J. Millener, of β-decay calculations by N. Severijns and ofestimates on Knight shifts by P. Heitjans. This work was supported by the German Ministry forEducation and Research (BMBF) under the contract number 06 MZ 866 I and by the BelgianFund for Scientific Research - Flanders (F.W.O.).References[*] A preliminary stage of this experiment was reported at the ENAM 98 Conference at Bel-laire, Michigan (AIP Conf. Proc. 455, p. 110).[y] The fit for the effective g-factor crucially depends on the magnetic moment of 15C used alsoby Suzuki et al. [25] as a representative of a well-bound spherical s1/2 system.[1] I. Tanihata et al., Phys. Lett. B 206, 592 (1988).[2] M. Fukuda et al., Phys. Lett. B 268, 339 (1991).[3] R. Anne et al., Nucl. Phys. A 575, 125 (1994).[4] S. S. Hanna et al., Phys. Rev. C 3, 2198 (1971).[5] D. J. Millener and D. Kurath, Nucl. Phys. A 255, 315 (1975).[6] D. J. Millener et al., Phys. Rev. C 28, 497 (1983).[7] A. G. M. van Hees and P. W. M. Glaudemans, Z. Phys. A 315, 223 (1984).[8] E. K. Warburton and B. A. Brown, Phys. Rev. C 46, 923 (1992).[9] H. Sagawa, B. A. Brown and H. Esbensen, Phys. Lett. B 309, 1 (1993).5[10] T. Otsuka, N. Fukunishi and H. Sagawa, Phys. Rev. Lett. 70, 1385 (1993).[11] N. A. F. M. Poppelier, A. A. Wolters and P. W. M. Glaudemans, Z. Phys. A 346, 11 (1993).[12] H. Esbensen, B. A. Brown and H. Sagawa, Phys. Rev. C 51, 1274 (1995).[13] P. Descouvemont, Nucl. Phys. A 615, 261 (1997).[14] E. Arnold et al., Phys. Lett. B 197, 311 (1987).[15] E. Arnold et al., Phys. Lett. B 281, 16 (1992).[16] M. Keim et al., Hyperfine Interactions 97/98, 543 (1995) and to be published.[17] J. Lettry et al., Rev. Sci. Instr. 69, 761 (1998).[18] S. Kappertz et al., to be published.[19] A. Winnacker et al., Phys. Lett. 67 A, 423 (1978); recalibrated according to P. Raghavan,At. Data Nucl. Data Tables 42, 189 (1989).[20] D. E. Barnaal et al., Phys. Rev. 157, 510 (1967).[21] P. Heitjans et al., J. Phys. (Paris) 41, C8-409 (1980).[22] F. Ajzenberg-Selove, Nucl. Phys. A 506, 1 (1990).[23] B. A. Brown, private communication.[24] D. J. Millener, private communication.[25] T. Suzuki, T. Otsuka and A. Muta, Phys. Lett. B 364, 69 (1995).[26] S. Fortier et al., Proc. 2nd Int. Conf. on Exotic Nuclei and Atomic Masses (ENAM 98),Bellaire, Michigan, USA, 1998, eds. B. M. Sherrill, D. J. Morrisey and C. N. 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Measurement of the magnetic moment of the one-neutron halo nucleus $^{11}$Be

Measurement of the magnetic moment of the one-neutron halo nucleus $^{11}$ Be

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Measurement of the magnetic moment of the one-neutron halo nucleus 11^{11}11Be

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Measurement of the magnetic moment of the one-neutron halo nucleus $^{11}$ Be