Shears bands in the Pb region
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Z. Phys. A 358, 237–238 (1997) ZEITSCHRIFT F ¨ UR PHYSIK A c Springer-Verlag 1997 Shears bands in the Pb region H. H ¨ ubel 1 , G. Baldsiefen 1 , R.M. Clark 2 , S.J. Asztalos 2 , J.A. Becker 3 , L. Bernstein 3 , M.A. Deleplanque 2 , R.M. Diamond 2 , P. Fallon 2 , I.M. Hibbert 4 , R. Kr¨ ucken 2 , I.Y. Lee 2 , A.O. Macchiavelli 2 , R.W. MacLeod 2 , G. Schmid 2 , F.S. Stephens 2 , K. Vetter 2 , R. Wadsworth 4 1 Institut f¨ ur Strahlen- und Kernphysik, Universit¨ at Bonn, Nussallee 14-16, D-53115 Bonn, Germany 2 Lawrence Berkeley Laboratory, Berkeley, CA 94720, USA 3 Lawrence Livermore National Laboratory, Livermore, CA 94550, USA 4 Department of Physics, University of York, Heslington, York Y015DD, UK Received: 9 August 1996 Communicated by B. Herskind Abstract. The properties of the M1 bands in the Pb region are reviewed. They can be explained by ‘magnetic rotation’ which is a new concept in nuclear excitations. Spin and ex- citation energy along the bands are increased by the shears effect, a step–by–step alignment of large proton–particle and large neutron–hole spins into the direction of the total angular momentum. First evidence is presented for band termination connected with the closing of the shears. PACS: 23.20.Lv; 27.80.+w A large number of long regular cascades of magnetic dipole transitions are known in the Pb region [1]. Their properties are extremely unusual: (i) They form regular I(I+1)–bands over many states despite very low deformations (β ≤ 0.1). (ii) The ratios of reduced transition probabilities B(M1)/B(E2) are very large (≈15–40(μ n /eb) 2 ). (iii) The M1 transitions are strongly enhanced (B(M1) ≈ 4μ 2 n ) [2,3]. (iv) The ratios of mo- ment of inertia over B(E2) lie about an order of magnitude higher than for deformed rotational bands. For many bands the connection to the normal states has been established, fixing their spins and excitation energies [1,4-9]. These investigations show that the band heads can be explained as high–spin proton–particle excitations across the Z = 82 shell gap coupled to one or more neutron i 13/2 hole states. The particle–hole interaction favours a perpendicular coupling of proton and neutron orbitals which explains the band–head spins. Along the bands angular momentum and excitation energy are increased by a step–by–step alignment of the proton–particle and neutron–hole spins into the direction of the total spin [9,10]. Since this resembles the closing of the blades of a pair of shears, the M1 bands have been called ‘shears bands’. An adequate description of the underlying physics is pro- vided by the Tilted–Axis–Cranking (TAC) model [10] which considers uniform rotation about an axis that is not one of the principal axes of the nucleus. A slightly oblate deformed mean field is used in which the protons are aligned along the symmetry axis and the neutrons are aligned perpendicular to that axis. Solutions of the Hamiltonian are then calculated for cranking around the total angular momentum, which does not coincide with one of the principal axes of the nucleus. The calculations show [9,10] that the tilting angle of the total spin with respect to the symmetry axis remains almost fixed along the bands, as expected for the shears mechanism described above. Good agreement with experiment is obtained for the excitation energies and the spins of the bands. A consequence of the large angle between proton and neu- tron spin is that there exists a large component of the mag- netic dipole moment perpendicular to the total nuclear spin. This transversal dipole moment specifies an orientation and the system may change by rotation around the nuclear spin. The rotating magnetic dipole emits the magnetic dipole radia- tion. The quantized states of this motion, which may be called ‘magnetic rotation’, form the rotational bands [11]. The perpendicular component of the magnetic dipole mo- ment decreases with increasing spin along the bands (closing of the shears). Therefore, the B(M1) rates should also de- crease. Previous experiments [2] were not sufficiently accurate to check this prediction, but a recent measurement [3] using the Gammasphere spectrometer at Berkeley clearly shows the predicted decrease of the B(M1) values for two bands each in 198 Pb and 199 Pb. Moreover, there is quantitative agreement with TAC calculations of the B(M1) values. Shears bands with a different number of decoupled i 13/2 neutron quasiparticles may cross, similar to the band cross- ings observed for normal rotational bands. Here the ques- tion is what happens when no further energetically favourable neutron–hole states are available and the proton and neutron spins are fully aligned. In other words: Do the bands terminate when the shears are closed? We have reinvestigated the bands in 199 Pb using the Gam- masphere spectrometer array which at the time of this exper- iment consisted of 60 Ge detectors. High–spin states were populated using the 186 W( 18 O,5n) reaction at 104MeV. A 12.2 mg/cm 2 thick 186 W target was used in which the reac- tion products were stopped. A total of 4.7 × 10 8 four– and higher–fold coincidence events were collected. The coincidence events were unpacked and sorted into an E γ –E γ –E γ cube and into gated DCO matrices. Coincidence spectra were obtained by setting combinations of two gates on transitions within the bands known in 199 Pb from previous work [9]. The data allowed to extend these bands considerably. The two strongly populated bands (bands 1 and 2) are shown
Transcript of Shears bands in the Pb region
Z. Phys. A 358, 237–238 (1997) ZEITSCHRIFTFUR PHYSIK Ac© Springer-Verlag 1997
Shears bands in the Pb region
H. Hubel1, G. Baldsiefen1, R.M. Clark 2, S.J. Asztalos2, J.A. Becker3, L. Bernstein3, M.A. Deleplanque2, R.M. Diamond2,P. Fallon2, I.M. Hibbert 4, R. Kr ucken2, I.Y. Lee2, A.O. Macchiavelli2, R.W. MacLeod2, G. Schmid2, F.S. Stephens2,K. Vetter 2, R. Wadsworth4
1 Institut fur Strahlen- und Kernphysik, Universit¨at Bonn, Nussallee 14-16, D-53115 Bonn, Germany2 Lawrence Berkeley Laboratory, Berkeley, CA 94720, USA3 Lawrence Livermore National Laboratory, Livermore, CA 94550, USA4 Department of Physics, University of York, Heslington, York Y015DD, UK
Received: 9 August 1996Communicated by B. Herskind
Abstract. The properties of the M1 bands in the Pb regionare reviewed. They can be explained by ‘magnetic rotation’which is a new concept in nuclear excitations. Spin and ex-citation energy along the bands are increased by the shearseffect, a step–by–step alignment of large proton–particle andlarge neutron–hole spins into the direction of the total angularmomentum. First evidence is presented for band terminationconnected with the closing of the shears.
PACS: 23.20.Lv; 27.80.+w
A large number of long regular cascades of magnetic dipoletransitions are known in the Pb region [1]. Their propertiesare extremely unusual: (i) They form regular I(I+1)–bandsover many states despite very low deformations (β≤ 0.1). (ii)The ratios of reduced transition probabilities B(M1)/B(E2)are very large (≈15–40(µn/eb)2). (iii) The M1 transitions arestrongly enhanced (B(M1)≈ 4µ2
n) [2,3]. (iv) The ratios of mo-ment of inertia over B(E2) lie about an order of magnitudehigher than for deformed rotational bands.
For many bands the connection to the normal states hasbeen established, fixing their spins and excitation energies[1,4-9]. These investigations show that the band heads can beexplained as high–spin proton–particle excitations across theZ = 82 shell gap coupled to one or more neutron i13/2 holestates. The particle–hole interaction favours a perpendicularcoupling of proton and neutron orbitals which explains theband–head spins. Along the bands angular momentum andexcitation energy are increased by a step–by–step alignment ofthe proton–particle and neutron–hole spins into the directionof the total spin [9,10]. Since this resembles the closing ofthe blades of a pair of shears, the M1 bands have been called‘shears bands’.
An adequate description of the underlying physics is pro-vided by the Tilted–Axis–Cranking (TAC) model [10] whichconsiders uniform rotation about an axis that is not one ofthe principal axes of the nucleus. A slightly oblate deformedmean field is used in which the protons are aligned along thesymmetry axis and the neutrons are aligned perpendicular tothat axis. Solutions of the Hamiltonian are then calculated forcranking around the total angular momentum, which does notcoincide with one of the principal axes of the nucleus. The
calculations show [9,10] that the tilting angle of the total spinwith respect to the symmetry axis remains almost fixed alongthe bands, as expected for the shears mechanism describedabove. Good agreement with experiment is obtained for theexcitation energies and the spins of the bands.
A consequence of the large angle between proton and neu-tron spin is that there exists a large component of the mag-netic dipole moment perpendicular to the total nuclear spin.This transversal dipole moment specifies an orientation andthe system may change by rotation around the nuclear spin.The rotating magnetic dipole emits the magnetic dipole radia-tion. The quantized states of this motion, which may be called‘magnetic rotation’, form the rotational bands [11].
The perpendicular component of the magnetic dipole mo-ment decreases with increasing spin along the bands (closingof the shears). Therefore, the B(M1) rates should also de-crease. Previous experiments [2] were not sufficiently accurateto check this prediction, but a recent measurement [3] usingthe Gammasphere spectrometer at Berkeley clearly shows thepredicted decrease of the B(M1) values for two bands eachin 198Pb and199Pb. Moreover, there is quantitative agreementwith TAC calculations of the B(M1) values.
Shears bands with a different number of decoupled i13/2neutron quasiparticles may cross, similar to the band cross-ings observed for normal rotational bands. Here the ques-tion is what happens when no further energetically favourableneutron–hole states are available and the proton and neutronspins are fully aligned. In other words: Do the bands terminatewhen the shears are closed?
We have reinvestigated the bands in199Pb using the Gam-masphere spectrometer array which at the time of this exper-iment consisted of 60 Ge detectors. High–spin states werepopulated using the186W(18O,5n) reaction at 104 MeV. A12.2 mg/cm2 thick 186W target was used in which the reac-tion products were stopped. A total of 4.7× 108 four– andhigher–fold coincidence events were collected.
The coincidence events were unpacked and sorted into anEγ–Eγ–Eγ cube and into gated DCO matrices. Coincidencespectra were obtained by setting combinations of two gateson transitions within the bands known in199Pb from previouswork [9]. The data allowed to extend these bands considerably.The two strongly populated bands (bands 1 and 2) are shown
238
Fig. 1.Shears bands 1 and 2 of199Pb
in Fig. 1. Band 1 has been extended by two levels at high–spinand the remaining missing∆I = 2 crossover transitions havebeen established. Band 2 was known only up to one of the(59/2+) states. The seven levels above that state as well as theadditional (57/2+) and (59/2+) levels have been added by ourwork.
The different behaviour of the two bands can be seen in aplot of the spin as a function of the M1–transition energy asshown in Fig. 2. While band 1 shows a crossing of the configu-rations A11 and ABC11, band 2 shows a splitting into severalstates around spin (57/2, 59/2). Then a new regular sequence ofdipole transitions emerges at higher spins. The configurationABE11 has been assigned to band 2 (below the irregularity)[9]. The letters A,B,C and D denote neutron quasiparticles ofi13/2 origin, while E and F represent natural–parity orbitalsof p3/2 and f5/2 origin. These neutron states are coupled tothe proton excitation (h9/2 i13/2) with spin 11. In order to es-timate the maximum aligned spin for these configurations wehave to keep in mind that there is also a contribution from col-lective rotation [9,10]. Taking 4 ¯h at the top of the bands forthat part from TAC calculations, we get maximum spin valuesof 63/2 and 57/2, respectively, at which the two bands shouldterminate. For band 1 that is the highest spin observed in exper-iment. At the top of this band the intensity drops sharply andno transitions could be observed to feed into the highest–spinstates. For band 2, on the other hand, the observed irregular-ity occurs just at the calculated maximum spin for the ABE11
0.2 0.4 0.6
15
20
25
30
35
I(h)
0.2 0.4 0.6
Band 1
A11
ABC11
Band 2
ABE11
Eγ (MeV)
Fig. 2. Angular momentum as a function of∆I = 1 transition energies forbands 1 and 2 of199Pb
configuration. It is most likely that at this point the next pair ofi13/2 neutrons (CD) breaks up and aligns, forming the config-uration ABCDE11. The experimental alignment gain of 7 ¯his in agreement with this assumption. In this way the shearsis opened again and a new sequence of M1 transitions can begenerated by magnetic rotation.
In conclusion, the regular M1 bands observed in the Pb(and Bi) isotopes may be understood as magnetic rotationwhich is a new form of nuclear excitation. There is evidencefor band termination when the proton and neutron spins arefully aligned.
This work is supported in part by the U.S. Department of Energy, contract nos.DE-AC03-76SF00098 and W-7405-ENG-48. The work of the Bonn groupwas supported by NATO grant CRG-930496. Funding from the U.K. camefrom the EPSRC.
References
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10. S. Frauendorf, Nucl. Phys.A557, 259c (1993) and contribution to thisconference
11. S. Frauendorf, Proc. Conf. on Phys. from large Detector Arrays, Berkeley(1994), LBL-35687, Vol. 2, 52 and contribution to this conference
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