The first fully on-line use of the angular distribution of $\beta$ - emission in detection of NMR of nuclei oriented at low temperatures is reported. The magnetic moments of the single valence particle, intermediate mass, isotopes $^{67}$Ni($\nu{p}^{-1}_{1/2}$; 1/2$^{-}$) and $^{69}$Cu($\pi{p}^{+1}_{ 3/2}$; 3/2$^{-}$) are measured to be +0.601(5)$\mu_{N}$ and +2.84(1)$\mu_{N}$ respectively, revealing only a small deviation from the neutron $p_{1/2}$ single-particle value in the former and a large deviation from the proton $p_{3/2}$ single-particle value in the latter. Quantitative interpretation is given in terms of core polarization and meson-exchange currents

Fedosseev, V

Giles, T

Köster, U

Mantica, P F

Mishin, V I

Morrissey, D J

Prisciandaro, J I

Ríkovská, J

Stone, N J

Towner, I S

Van Esbroeck, K

Veskovic, M

Walters, W B

White, G

Wöhr, A

CERN Document Server

VOLUME 85, NUMBER 7 P H Y S I C A L R E V I E W L E T T E R S 14 AUGUST 2000139First On-Line Beta-NMR on Oriented Nuclei: Magnetic Dipole Momentsof the np1221 122 Ground State in 67Ni and pp3211 322 Ground State in 69CuJ. Rikovska,* T. Giles, N. J. Stone, K. van Esbroeck,† G. White, and A. WöhrDepartment of Physics, Oxford University, Parks Road, OX1 3PU Oxford, United KingdomM. VeskovicDepartment of Physics, University of Novi Sad, Novi Sad, YugoslaviaI. S. TownerPhysics Department, Queen’s University, Kingston, Ontario, K7L 3N6, CanadaP. F. Mantica, J. I. Prisciandaro, and D. J. MorrisseyDepartment of Chemistry, Michigan State University, East Lansing, Michigan 48824V. N. Fedoseyev and V. I. MishinInstitute of Spectroscopy, Russian Academy of Sciences, 142092 Troitsk, RussiaU. KösterEP Division, CERN, CH 1211 Geneva 23, SwitzerlandW. B. WaltersDepartment of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742and the NICOLE and ISOLDE Collaboration(Received 17 April 2000)The first fully on-line use of the angular distribution of beta emission in detection of NMR of nucleioriented at low temperatures is reported. The magnetic moments of the single valence particle, interme-diate mass, isotopes 67Ninp2112; 122 and 69Cupp132; 322 are measured to be 10.6015 mN and12.841 mN , respectively, revealing only a small deviation from the neutron p12 single-particle valuein the former and a large deviation from the proton p32 single-particle value in the latter. Quantitativeinterpretation is given in terms of core polarization and meson-exchange currents.PACS numbers: 21.10.Ky, 21.60.–n, 23.20.En, 27.60.+ jMagnetic moments in odd-mass heavy nuclei differ sig-nificantly from their single-particle (Schmidt) values. Thiseffect occurs because, in heavy nuclei, the shell closuresare such that an orbital with j.  l 1 12 may be fullyoccupied while the spin-orbit partner orbital with j, l 2 12 may be unoccupied. Here j is the total angu-lar momentum of the orbital and l its orbital angular mo-mentum. In this situation, there is a large correction tothe single-particle magnetic moment coming from the ex-citation in the closed-shell core of the particle-hole statej,, j21. 11 made from the particle in orbital j, couplingto a hole in orbital j. with resultant angular momentum11, the multipolarity of the magnetic moment operator.This correction is generally known as core polarization.For example, at the 208Pb closed shell, magnetic momentsof eight orbitals have been directly measured [1] or in-ferred. In seven of the cases (see Table I) the correc-tion to the single-particle estimate is large, between 0.4and 1.5mN . In the eighth case, that of a neutron p12 or-bital, the correction is very small, 0.05mN . Why, then,2 0031-90070085(7)1392(4)$15.00is the correction small for the p12 orbital and large forall others?TABLE I. Experimental magnetic moments mexpt and single-particle values msp and their difference Dm for odd-proton (p)and odd-neutron (n) nuclei in the Pb region.mexpt msp Dm209Bi ph92 4.11 2.62 1.49209Bi pi132 2.78(10)a 3.56 20.78207Tl ps2112 1.87 2.79 20.92207Tl pd2132 0.76(19)b 0.12 0.64209Pb ng92 21.47 21.91 0.44207Pb np2112 0.59 0.64 20.05207Pb nf2152 0.79(3) 1.37 20.58207Pb ni21132 21.013c 21.91 0.90aDeduced from the magnetic moment of the 112 state in 210Po.bDeduced from the magnetic moment of the 321 state in 205Tl.cDeduced from the magnetic moment of the 121 state in 206Pb.© 2000 The American Physical SocietyVOLUME 85, NUMBER 7 P H Y S I C A L R E V I E W L E T T E R S 14 AUGUST 2000This question has a long history. It was first raised, webelieve, in Blin-Stoyle’s monograph [2] of 1957, and aquantitative response was given by Arima and colleagues[3]. One difficulty with answering this question is thatthere are very few examples of odd-mass heavy nuclei,with ground state spin parity of 122, whose magneticmoments have been measured. Here we report the firstmeasurement of the magnetic moment of 67Ni 122,and of the neighboring nucleus 69Cu 322. This pair ofnuclei provides a unique opportunity to explore the gen-erality of the findings in the Pb region, namely that thecorrection to the magnetic moment of the proton p32 or-bital is large, 1.0mN , while in the neutron p12 orbital itis small, 0.05mN .New techniques of fully on-line nuclear magnetic reso-nance on oriented nuclei (NMRON) make it possible todetermine precisely ground and isomeric state magneticdipole moments far from stability [4,5]. So far, the reso-nance effect was detected by a change in the angularanisotropy of gamma-ray emission. This method does notallow study of states with Ip  122 for which, however,the change in the asymmetric emission of parity noncon-serving beta decay can be used as a resonance detectionsignal. All except pure s-wave Fermi allowed beta de-cays from polarized nuclei exhibit appreciable forward-backwards asymmetry with respect to the polarization axis[6]. This method has been only seldom used in the past,as it requires that beta detectors be operated within thecryostat, at temperatures close to 4 K, coupled with thedifficulty of separating the various overlapping beta com-ponents in a typical decay spectrum. However, in connec-tion with on-line experiments aimed at nuclear momentmeasurements there is little need to analyze the observedbeta spectrum quantitatively— it suffices that the isotopeunder study contributes a considerable component to theobserved beta asymmetry. Moreover, far from stability,Qb is often at least several MeV so that beta detectorsmounted outside the cryostat can be used, accepting thescattering and energy loss produced by thin cryostat win-dows between source and detector [7]. Beta-NMR offersadvantages for modest degrees of nuclear orientation, sincebeta asymmetries are proportional to the first power ofthe ratio mBkT , where m is the nuclear dipole momentof the oriented isotope, B the hyperfine field, and T thesample temperature, whereas the gamma anisotropy is pro-portional to the square of this quantity. Thus beta asym-metries are often larger than gamma anisotropies, so that areadily measurable resonance signal can be produced in awider range of isotopes using beta asymmetry, especiallyfor isotopes—often odd-neutron—with smaller magneticmoments.Both 67Ni T12  21 s and 69Cu T12  2.85 mwere produced at ISOLDE (CERN) in far asymmetricfission of 238U induced by 1 GeV protons from the PSBooster. The standard uranium carbide/graphite target(50 gcm22) was coupled to the resonance ionizationlaser ion source giving enhanced element sensitivity.The yields were 7 3 105 per mC of incident protonsfor 67Ni and 1.8 3 108 per mC for 69Cu, respectively[8]. The resulting mass-separated beams, which showedexcellent stability, were implanted at 60 keV into rolled,polished, and annealed 99.99% pure Fe foils solderedto the cold finger of the NICOLE dilution refrigerator.The refrigerator was maintained at a temperature between11–12 mK, measured using a 54MnNi nuclear orientationthermometer. The NICOLE cryostat is constructed withthin foil windows of less than 2 mm aluminum betweenthe sample and room temperature. Beta spectra wereobservable using plastic scintillator detectors, consistingof 2.5 cm diameter discs of scintillator optically coupledto 25 mm square silicon PIN detectors, placed outside thecryostat, at room temperature, at angles of 0± and 180± tothe orientation axis defined by magnetization of the ironfoil in the external applied field Bapplied.The beta spectrum of 67Ni above 600 keV is dominatedby the 98% direct ground-state–ground-state, 122-322,Gamow-Teller allowed transition with end point 3.56 MeV.The beta spectrum of 69Cu has two major components,a 51% ground-state–ground-state, 322-122, Gamow-Teller allowed beta decay with end point 2.68 MeV anda 24% ground-state to 1007.66 keV, 322-122, 322,Gamow-Teller allowed transition, with a possible Fermiadmixture, having end point 1.67 MeV.The presence of substantial beta asymmetry, defined as N0N180 mKN0N180 1 K 2 1 3 100% was established bycomparison of the count rate N0N180 from samples atmillikelvin and 1 K temperatures. Nuclear magnetic reso-nance was detected and the nuclear Zeeman splittingmeasured by observing the variation of the asymmetry atconstant millikelvin temperature as the applied rf fieldfrequency was varied. The resulting asymmetry changesfor 67Ni are shown in Fig. 1. A fit to the center frequencyn0 yields the magnetic moment of the oriented statethrough the resonance conditionhn0 jmjIBhf 1 Bapplied . (1)206 208 210 212 214 216 218 220Frequency  [MHz]0102030Destruction of asymmetry [%]67NiFIG. 1. Beta-NMRON for 67NiFe.1393VOLUME 85, NUMBER 7 P H Y S I C A L R E V I E W L E T T E R S 14 AUGUST 2000The present data give center frequency 213.40(15) MHzand, integrating over the resonance line, destruction of ap-proximately 60% of the beta asymmetry. The integratedstrength of the resonance reflects the excellent implanta-tion properties of Ni in iron. The hyperfine field of Ni inFe is known to be 223.42 T [9]. After allowing for theapplied field Bapplied  10.1 T and incorporating the er-ror in the hyperfine field, the magnetic moment of 67Ni ism67Ni  10.6015mN , (2)where the positive sign of the moment is given by the signof the beta asymmetry.The results for 69Cu are shown in Fig. 2. The reso-nance was fitted with center frequency 311.7(1) MHz andintegrated destruction of approximately 40% of the betaasymmetry. The hyperfine field of Cu in Fe is measuredas221.81 T [10], and after allowing for the applied fieldof 0.2 T the nuclear magnetic moment of 69Cu is given asm69Cu  12.841mN . (3)When these results are compared with the correspondingSchmidt limits we find the deviations between experimen-tal moments and the free nucleon approximation to benp1267Ni, Dmnp12  20.0375 , (4)pp3269Cu, Dmpp32  20.951 . (5)We reiterate that these results are for isotopes havingmajor configurations closed subshell 2 1 67Ni andclosed subshell 1 1 69Cu. Only for such simple con-figurations can the detailed theoretical analysis presentedbelow be carried through with confidence.It is convenient to discuss the calculated results thatfollow in terms of an effective one-body magnetic momentoperator:meff  gl,effl 1 gs,effs 1 gp,effY2, s , (6)where gx,eff  gx 1 dgx, with x  l, s, or p [11,12].Here gx is the single-particle g factor and dgx the cor-rection to it. Note that in the effective operator there is anadditional term involving a spherical harmonic of rank 2coupled to a spin operator to give a tensor of multipolarity1. One reason why the correction for a p12 single-particle305 307 309 311 313 315 317Frequency [MHz]051015Destruction of asymmetry [%]69CuFIG. 2. Beta-NMRON for 69CuFe.1394magnetic moment is so small, is that the core-polarizationcorrection from the 11 particle-hole states mentioned inthe introduction is small. This was demonstrated by Arimaet al. [3,13]. In the limit that core polarization is calculatedwith zero-range effective interactions a closed expressionis obtained for the correction, namelydgl  0, dgp  2122p12dgs . (7)This relationship between dgs and dgp is such that forp12 orbitals the correction to the magnetic moment isidentically zero. This result is exact, not just to first-ordercore polarization, but to all orders in the random phaseapproximation (RPA) theory for 11 particle-hole states.However, with finite-range effective interactions the rela-tionships are only approximately true. Nevertheless, thecore-polarization RPA correction, CP(RPA), of Table II,remains small for the p12 neutron state, 20.15mN , com-pared to 20.49mN for the p32 proton state.The CP(RPA) is not the only correction to consider. Insecond and higher orders there are further core-polarizationcorrections that are not part of the RPA series [11–13].These are difficult to compute because the intermediate-state summations are slow to converge. Thus we have onlycomputed the second-order graphs, CP(2nd), in a harmonicoscillator basis, and taken the intermediate-state summa-tions up to 12h¯v excitation energy, and extrapolated be-yond that.Another class of corrections are meson-exchange cur-rents (MEC) described more fully in [11,12,14]. Theseproduce a large positive correction for the proton p32orbital, but only a small negative correction for the neu-tron p12 orbital. The reason is that the dgl and dgsvalues are of the same sign, giving in-phase contributionsto j  l 1 12 orbits and out of phase contributions toj  l 2 12 orbits. A further mesonic correction to beconsidered is that in which the meson prompts the nucleonto be raised to an excited state, the D resonance, whichis then de-excited by the electromagnetic field. Theseisobar currents give only a small correction to the mag-netic moment. A more important mesonic contribution isa first-order core-polarization correction to the two-bodyMEC operator, MEC-CP. These terms are fourth order inmeson-nucleon couplings, as are the CP(2nd) contribu-tions, and like the CP(2nd) terms they are difficult to com-pute because the intermediate-state summations are slowto converge. Again we took the summation to 12h¯v exci-tation energy and extrapolated beyond that. Note that theCP(2nd) and MEC-CP contributions are of opposite sign,providing some cancellation as has been pointed out byArima et al. [13].Last, there is a relativistic correction to the single-particle magnetic moment operator obtained when evalu-ating the operator to order pM3, where p is a typicalnucleon momentum and M its mass. This correction hasbeen estimated using harmonic oscillator wave functions.VOLUME 85, NUMBER 7 P H Y S I C A L R E V I E W L E T T E R S 14 AUGUST 2000TABLE II. Contributions to the calculated effective magnetic moment operator for a p12 neutron in 67Ni and a p32 proton in 69Cu.Neutron p12 Proton p32dgl dgs dgp dm dgl dgs dgp dmCP(RPA) 20.010 0.371 0.610 20.15 0.000 21.019 0.504 20.49CP(2nd) 0.191 1.150 20.226 20.03 20.225 21.448 0.334 20.94Isobars 0.004 0.293 20.805 0.06 20.002 20.178 0.558 20.07MEC 20.092 20.241 0.051 20.03 0.183 0.368 20.295 0.36CP-MEC 20.091 20.148 20.169 20.01 0.103 0.355 0.393 0.30Relativistic 0.000 0.087 0.000 20.02 20.023 20.143 20.038 20.10Sum 0.001 1.513 20.539 20.18 0.036 22.065 1.456 20.94Expt 20.0375 20.951Although this term is very sensitive to the choice of theradial wave function, depending on its second derivative,the result is small, about a 2.5% reduction to the single-particle value.All corrections have been collated in Table II. For thep32 proton in 69Cu, the calculated correction to the single-particle magnetic moment is large,20.94mN , while for thep12 neutron in 67Ni it is small, 20.18mN . For the former,the result is in good agreement with experiment, while forthe latter, the correction, although small, is a factor of 4larger than required by experiment. The same phenomenonis found in the Pb region, where for the neutron p12 statethe calculated [12,14,15] correction is of order 0.2mN ,compared with the experimental value of 0.05mN . Thesmall changes observed for p12 nuclei are related to theabsence of nearby low angular momentum negative parityorbitals. The fact that, in 67Ni, even this small correctionis overestimated, provides evidence for the strength of thesubshell closure at N  40 in 68Ni.In conclusion, these critical measurements result fromthe first fully on-line experiment by the beta-NMRONtechnique, and also the first experiment to use detectors ex-ternal to the cryostat in the study of an isotope for which noprevious data existed. Such external detection is restrictedto high energy [more than 1.5 MeV] beta decay.The results show conclusively the need to include bothmeson exchange current effects and core polarization inthe description of deviations from single-particle Schmidtlimits.The research was supported by UK EPSRC, U.S. DOEGrant No. DE-FG02-94ER40834, and NSF Grant No. 95-28844.*Also at Department of Chemistry, University of Maryland,College Park, Maryland 20742.†Visiting scientist from University of Leuven, Celestijnen-laan 200D, B3030 Leuven, Belgium.[1] P. Raghavan, At. Data Nucl. Data Tables 42, 189 (1989).[2] R. J. Blin-Stoyle, Theories of Nuclear Moments (OxfordUniversity Press, Oxford, 1957).[3] H. Noya, A. Arima, and H. Horie, Suppl. Prog. Theor.Phys. 8, 33 (1959); A. Arima and L. J. Huang-Lin, Phys.Lett. B 41, 429 (1972); 41, 435 (1972).[4] N. J. Stone, D. Doran, M. Lindroos, J. Rikovska, M.Veskovic, G. White, D. A. Williams, B. Fogelberg, L.Jacobsson, I. S. Towner, and K. Heyde, Phys. Rev. Lett.78, 820 (1997).[5] G. White, J. Rikovska, N. J. Stone, J. Copnell, I. S. Towner,A. M. Oros, K. Heyde, B. Fogelberg, L. Jacobsson, andF. Gustavsson, Nucl. Phys. A640, 322 (1998).[6] L. Vanneste, in Low Temperature Nuclear Orientation,edited by N. J. Stone and H. Postma (North-Holland,Amsterdam, 1986), Chap. 3.[7] P. F. Mantica, B. D. Kern, B. E. Zimmerman, W. B. Walters,J. Rikovska, and N. J. Stone, Hyperfine Interact. 75, 415(1992).[8] A. Jokinen et al., Nucl. Instrum. Methods B 126, 95 (1997);U. Köster et al., Nucl. Instrum. Methods B (to be pub-lished).[9] K. S. Krane, Hyperfine Interact. 15/16, 1069 (1983).[10] Le Dang Khoi, P. Veillet, and I. A. Campbell, J. Phys. F5,2184 (1975); error from I. A. Campbell (private communi-cation).[11] B. Castel and I. S. Towner, Modern Theories of NuclearMoments (Clarendon Press, Oxford, 1990).[12] I. S. Towner, Phys. Rep. 155, 263 (1987).[13] A. Arima and H. Hyuga, in Mesons in Nuclei, edited byD. H. Wilkinson and M. Rho (North-Holland, Amsterdam,1979), p. 685; H. Hyuga, A. Arima, and K. Shimizu, Nucl.Phys. A336, 363 (1980).[14] A. Arima, K. Shimizu, W. Bentz, and H. Hyuga, Adv. Nucl.Phys. 18, 1 (1987).[15] I. S. Towner, in Proceedings of the International Sympo-sium on Non-Nucleonic Degrees of Freedom Detected inNucleus, Osaka, Japan, 1996, edited by T. Minamisono,Y. Nojiri, T. Sato, and K. Matsuta (World Scientific,Singapore, 1997), pp. 33–42.1395

First on-line $\beta$-NMR on oriented nuclei: magnetic dipole moments of the $\nu{p}^{-1}_{1/2}; 1/2^-$ ground state in $^{67}$Ni and $\pi{p}^{+1}_{3/2}; 3/2^-$ ground state in $^{69}$Cu

First on-line $\beta$ -NMR on oriented nuclei: magnetic dipole moments of the $\nu{p}^{-1}_{1/2}; 1/2^-$ ground state in $^{67}$ Ni and $\pi{p}^{+1}_{3/2}; 3/2^-$ ground state in $^{69}$ Cu

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First on-line β\betaβ-NMR on oriented nuclei: magnetic dipole moments of the νp1/2−1;1/2−\nu{p}^{-1}_{1/2}; 1/2^-νp1/2−1​;1/2− ground state in 67^{67}67Ni and πp3/2+1;3/2−\pi{p}^{+1}_{3/2}; 3/2^-πp3/2+1​;3/2− ground state in 69^{69}69Cu

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First on-line $\beta$ -NMR on oriented nuclei: magnetic dipole moments of the $\nu{p}^{-1}_{1/2}; 1/2^-$ ground state in $^{67}$ Ni and $\pi{p}^{+1}_{3/2}; 3/2^-$ ground state in $^{69}$ Cu