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The physics of Cu nuclei from A = 56 to 78 with particular reference to ground state magnetic moments. N.J.Stone Oxford University and University of Tennessee, Knoxville Russbach Workshop 2009 Outline of Talk Elements of Nuclear Theory - brief! Nuclear magnetic moments Moments close to 68Ni shell closure Moments close to 56Ni shell closure Towards 78Ni shell closure Nuclear astrophysics concerns, among other things, the physics of nuclei which lie along the several paths towards formation of the elements of the universe. For the r-process in particular, experimental access to the isotopes of importance is difficult. Discussion of the details of the sequence, in particular of the 'waiting point' nuclei, requires specific knowledge of the properties of the relevant isotopes which often cannot be measured experimentally. Thus we depend upon extrapolations from accessible nuclei, using methods or models which incorporate whatever degree of understanding we have. Extrapolations from 'known' territory is notoriously unreliable in nuclear physics - mass models are a well known example. One of the interesting 'waiting points' in the r-process is the region of 78Ni. This talk explores what we know of nuclei of Cu isotopes, far from and closer to, 78Ni, to see how well we can say we understand them and thus how reliably we may hope to make the necessary extrapolations. (Very) Basic Nuclear Theory • • • • • • Nucleons move in an average potential produced by interaction with the other nucleons. This leads to a sequence of single particle levels with quantum numbers associated with their orbital and spin angular momenta and parity. The strongest term in their interaction after this is the spin-orbit which produces splitting between levels of j = l + s and gives quantum labels e.g 1f5/2, 1f7/2 with the higher j lying lower. The larger energy gaps between states of higher l produce the magic numbers and the idea of closed shell nuclei. The next strongest term is the pairing interaction which acts between like nucleons and leads to pairs in the same j state coupling to zero angular momentum in their ground states. What remains after these terms is called the 'residual interaction' and acts between both like and unlike nucleons. Evidence for its nature is elusive….. The Residual Interaction We do not have an analytic understanding, or form, for the interaction between nucleons in nuclei. Simple effective potentials are used to construct a general scheme of energies of nucleon states in terms of their (spherical) quantum numbers, with an additional spin-orbit interation, e.g. 1f5/2. Then there is the pairing interaction between like nucleons All other parts of the interaction are called 'residual' and described by a multipole expansion with monopole, [no dipole - C of M], quadrupole etc terms, connected to the shape of the nucleus. This is merely a DESCRIPTION, not an UNDERSTANDING of the origin or magnitude of the terms in the residual interaction. It is a language to describe what is observed. In the absence of the residual interaction Energies of single nucleons are independent of the occupation numbers of the same or other nucleon states, with the clear exception of the phenomenon of Pairing, whereby two nucleons with the same (spherical) potential quantum numbers combine to form a state of total angular momentum zero. As early as the 1960's examples were known where this situation did not apply: Example: Proton ground states in Sb isotopes As the neutron h11/2 shell fills the single proton ground state changes from d5/2 [in lighter] to g7/2 [in heavier] Sb's. Since these nuclei are not deformed, i.e. their potentials have little or no quadrupole or higher terms, the effect which was seen as responsible for the dependence of the occupancy of the neutron h11/2 orbital was called the 'monopole' shift term in the residual interaction. Kisslinger and Sorensen, Pairing + Quadrupole Model [RMP 35 853 1963] Knowledge of local behaviour of the residual interaction is needed to give nuclear models predictive power. Nuclear states • Extreme single particle. • Extreme collective: vibrations and rotations of the nucleus as a single entity. • Limited 'collective': states associated with excitations of 'valence' nucleons outside a close shell 'core'. • Clearly a complex system! Nuclear magnetic moments. Nuclear magnetism has contributions from all angular motion with unit the nuclear magneton (n.m.) Orbital angular momentum: Single particle - proton charge 1 neutron charge 0 Collective - whole nucleus charge Z/A valence nucleons - variable Spin angular momentum Single particle - proton s1/2 moment + 2.79 n.m. neutron s1/2 moment -1.91 n.m. A sensitive measure of the state wavefunction Cu isotope magnetic moments close to 68Ni In the range between N,Z = 28 and 40 both protons and neutrons are filling states p3/2, f5/2 and p1/2 (all negative parity). Cu isotopes have a single proton outside the Z = 28 shell closure Between N = 28 (57Cu) and N = 40 (69Cu) the ground state spin/parity of the odd-A copper isotopes is 3/2- the p3/2 state. The ground states and excitations of these nuclei are expected to provide a good laboratory for nuclear theory since the proton states are relatively simple. Pre 1998 Known Odd-A Cu Magnetic Moments circa 1998 Nuclear Magnetons 4 Schmidt limit 3.5 3 2.5 2 60 61 62 63 64 65 66 Mass number Only three, mid-shell, values known: isotopes 63,65Cu are stable 1999 Cu Laser ion source at ISOLDE : 67,69Cu moments measured by NMR/ON at NICOLE on-line nuclear orientation facility, ISOLDE, CERN using the new laser Cu ion source. Odd-A Cu Magnetic Moments to N = 40 Magnetic moment 69Cu(3/2-) Starting from extreme single particle (Schmidt limit) and based on full treatment of moment operator, including meson exchange, gave value 2.85 n.m. J. Rikovska-Stone et al. PRL 85 1392 (2000) Nuclear Magnetons = 2.84(1) n.m. 4 Schmidt limit 3.5 3 2.5 2 60 62 64 66 Mass number At 28,40 double shell closure: Full agreement with best shell model theory [calculations by Ian Towner] [J.Rikovska et al. PRL 85 1392 (2000)] 68 70 Down to shell closure at N = 28 59Cu measured by Leuven group at NICOLE by NMR/ON μ(59Cu, 3/2-) = 1.891(9) n.m. [V.V.Golovko et al. PR C70 014312 (2004)] 57Cu measured by β−NMR at MSU fragment separator μ(57Cu, 3/2-) = 2.00(5) n.m [K.Minamisono et al. PRL 98 103508 (2006)] N.B. Narrow resonance p3/2 proton moments across full sub-shell N = 28 - 40 Odd-A Cu Magnetic Moments N = 28 - 40 First complete shell - shell sequence BUT 57Cu result shows little sign of predicted return to close to the value found for 69Cu Nuclear Magnetons 4 3.5 Schmidt limit 3 2.5 2 1.5 1 56 58 60 62 64 66 68 Mass number Major discrepancy with shell model theory. Is 56Ni truly double magic? 70 On-Line Laser spectroscopy Collinear and In-Source Methods In Source, Doppler width resolution ~ 250 MHz 68Cu Collinear Concept - add constant energy to ions ΔE=const=δ(1/2mv2)≈mvδv Resolution ~ MHz, resulting from the velocity compression of the line shape through energy increase. In Cu+ ion, electron states involved are s1/2 and p1/2. With nuclear spin I these each form a doublet with F (= I + J) = I +1/2 and I - 1/2. Transitions between these doublets give four lines in two pairs with related splittings. - can be fitted with poor resolution only for the A (magnetic dipole) splitting and in good resolution, for both A and B (electric quadrupole splitting) PR C77 067302 (2008) 63Cu μ = 2.22(9) n.m. [Ref 2.23] 59Cu μ = 1.84(3) n.m. [Ref. 1.89] 58Cu μ = 0.52(8) n.m. Measurement of moment of 58Cu (I = 1) at ISOLDE: Established fitting parameters using data on 63Cu, confirmed by 59 Cu fit agreement with previous NMR/ON result. 58Cu [odd-odd] predictions - based on shell model 57Cu 0.68(1) n.m. - based on MSU 57Cu result 0.40(2) n.m. Nature not kind: experimental result 0.52(8) n.m. no decisive answer. Situation at 28,28 double shell closure Failure of experimental magnetic moment of 57Cu to move strongly towards value found for 59Cu suggests a serious problem for detailed shell model calculations M. Honma et al. PR C69 034335 (2004) Cu isotopes across the N = 40 shell closure. Between N = 28 and N = 40, as we have seen, the ground state of Cu isotopes is 3/2Both the proton and neutron subshells in this range are p3/2, f5/2 and p1/2 [with increasing energy - all negative parity] Above N = 40, the neutron filling subshell becomes positive parity g9/2. We can see influence of this change by comparing the magnetic moments of 69Cu and 71Cu. [N.J. Stone et al. PR C77 014315 (2008)] There is clearly a difference between 69,71Cu (results joined by solid line), which is to be associated with the fact that residual interactions exist between the unlike nucleons which are not fully described by the Honma et al. shell model calculations. Configuration mixing depends upon the states available. Spectroscopic study of decay of Ni isotopes above 68Ni. Work of Leuven group at LISOL S. Franchoo et al. PRL 81 3100 (1998) S. Franchoo et al. Phys. Rev. C64 054308 (2001) Odd neutron ground states g9/2 - no allowed beta decay to p3/2 or f5/2. Decay of beta fed states revealed a state at 534 keV in 71Cu and at 166 keV in 73Cu - no electron conversion or angular correlation information - identified as likely (5/2-) SOME model calculations gave support to this assignment Sinatkas et al - shell model with S3V' interaction - J.Phys.G18 1377 (1992) Ji and Wildenthal Phys Rev C40 389 (1989) Both placed f5/2 below p3/2 in context of 79Cu Oros-Peusquens and Mantica Nucl Phys A669 81 (2000) Placed f5/2 2 MeV below p3/2 in 78Ni in PCM Suggestive of monopole interaction between πf5/2 and νg9/2 [N.B. not πf7/2 - νg9/2 as mentioned yesterday from Tensor term] •5/2- level associated with the π(f5/2) orbital E(keV) 1000 1/25/2- ? 57 59 61 63 65 67 69 71 73 75 Mass number S. Franchoo et al. Phys. Rev. C 64 054308 I. Stefanescu Phys. Rev. Lett 100 (2008) A.F. Lisetskiy et al. Eur. Phys. J. A, 25:95, 2005 N.A. Smirnova et al. Phys. Rev. C, 69:044306, 2004 I=5/2- level: •Remains static between 57-69Cu at ~1MeV •Systematically drops in energy as the ν(g9/2) shell begins to fill •Predictions on the inversion of the ground state lie between 73Cu and 79Cu. •Experimental evidence for the inversion to occur at 75Cu. From Kieren Flanagan Magnetic moments A > 70 71Cu 73Cu NMR/ON I = 3/2 μ = 2.28(1) n.m. collinear laser I = 3/2 μ = 1.748(1) n.m. [Isolde laser group, unpublished] The relative intensity of the two (unresolved doublet) peaks in the In-Source method is related to the nuclear spin through the statistical weight (2F + 1) Fitted data for 77Cu for I = 3/2 and I = 5/'2 - clearly favours 5/2 assignment. N.B. peaks well resolved Magnetic moments A > 70 71Cu 73Cu 77Cu NMR/ON I = 3/2 μ = 2.28(1) n.m. collinear laser I = 3/2 μ = 1.748(1) n.m. [Isolde laser group, unpublished] in-source laser I = 5/2 μ = 1.75(5) n.m. [in-source laser group, unpublished] In source laser data, 75Cu, fits for I = 3/2,5/2 Peaks barely resolved, but clear preference for spin 5/2 Moment of 75Cu(I = 5/2) μ = 0.99(4) n.m. [Aug 2008] Confirmed during collinear run, later Aug 08, which used the in-source moment to set line search frequencies. A > 71 71Cu 73Cu 75Cu 77Cu NMR/ON I = 3/2 μ = 2.28(1) n.m. collinear laser I = 3/2 μ = 1.748(1)* n.m. [Isolde laser group, to be published] in-source laser I = 5/2 μ = 1.005(1)* n.m. and collinear laser [combined group, to be published] in-source laser I = 5/2 μ = 1.75(5)* n.m. [in-source laser group, to be published] * preliminary values Overall situation: ground state spin change positively identified at A = 75 Odd-A Cu Magnetic Moments towards N = 50 Nuclear Magnetons 4 3.5 spin 3/2 Schmidt limit p3/2 spin 5/2 3 2.5 2 1.5 1 60 65 70 Mass number Schmidt limit for f5/2 is at +0.8 n.m. 75 STOP PRESS UPDATE!!! Isolde Feb 16th MSU result for 57Cu is WRONG. New data from Leuven show resonance at higher frequency. New [est N.J.S.] value 57Cu μ = 2.6(1) n.m. [Cocolios, Van Duppen et al. to be published] The Final Picture Odd-A Cu Magnetic Moments towards N = 50 Nuclear Magnetons 4 3.5 spin 3/2 Schmidt limit p3/2 spin 5/2 3 2.5 2 1.5 1 60 65 70 Mass number 75 Conclusions 1. Shell model has managed to calculate odd-A magnetic moments at N = 28, 40 very well and between them adequately. 2. Now that shift of the f5/2 state has been identified, magnetic moments of 75,77Cu should be calculated reasonably well. This residual interaction effect is established. 3. Models which give these results successfully may be expected to give useful predictions concerning the A = 78 shell closure. Others which fail to reproduce these may not be trusted in other predictions. The magnetic moments are a valuable constraint. Thank You