Magnetic rotation past, present and future

Transcription

1 PRAMANA c Indian Academy of Sciences Vol. 75, No. 1 journal of July 2010 physics pp Magnetic rotation past, present and future A K JAIN and DEEPIKA CHOUDHURY Department of Physics, Indian Institute of Technology, Roorkee , India Corresponding author. ashkumarjain@yahoo.com Abstract. Magnetic-dipole rotational (MR) bands were discovered about 15 years ago without any theoretical prediction in contrast to the super-deformed (SD) bands which were predicted long ago. First identification of a quasirotational structure as MR band occurred around 1992 although Kr isotopes probably have the first set of data having the signatures of MR bands as shown by us. Our first compilation of MR bands listed 120 MR bands in 56 nuclides which have now grown to more than 180 bands in 80 nuclides. We have observed new MR bands in the A = 130 mass region in 137 Pr, 139 Nd and 135 Ba nuclei. This led to the observation of the smallest MR bands in 137 Pr, multiple minima in the γ deformation in 135 Ba, coexistence of band structure based on these minima and band crossing of MR bands in A = 130 region. Some of these results have been reviewed in this paper along with theoretical calculations. There are still a number of questions related to MR bands which have not been fully resolved. The role of neutrons/protons in magnetic rotation still needs to be delineated. Do the MR bands follow the I(I + 1) behaviour? Are these structures as regular as normal rotational bands? How important is the existence of deformation for MR bands? We address some of these questions in this paper. Keywords. Magnetic rotation; shears mechanism; band crossing; back bending; signature splitting. PACS Nos Ev; Lv 1. Introduction Regular cascades of dipole γ-rays were, unexpectedly, observed in the nearly spherical Pb [1,2] isotopes in the early 1990s. Subsequent angular distribution, linear polarization and lifetime measurements showed that these γ-rays were strongly enhanced magnetic dipole (M 1) I = 1 transitions, in contrast to strongly enhanced electric quadrupole (E2) transitions as seen in deformed nuclei. Frauendorf [3,4] proposed that regular cascades of such γ-rays found in nearly spherical nuclei such as Pb isotopes were due to a new mode of nuclear excitation termed as magnetic rotation or shears. The sequences of such levels, which look like rotational bands, have been labelled in the literature as magnetic rotational dipole bands (MR) or shears bands. These bands are generally observed in nuclei that are weakly deformed and are close to the proton magic numbers; only few particles/holes play an important role in generating angular momenta for these bands. Nearly all the MR bands are 51

2 A K Jain and Deepika Choudhury known to be connected to low-lying states, and therefore, the spins, parities and excitation energies of these bands are established with greater certainty. This topic was covered by us in 2001 when the concept of magnetic rotation was still new and widely debated [5]. A considerable amount of new work, both theoretical and experimental, has been added to the area since then. Our aim is to discuss the new developments keeping in mind the earlier understanding and expectations. Are these bands as regular as the normal rotational bands? How important is the presence of deformation for the MR bands? What is the behaviour of moment of inertia vs. spin for these bands as compared to the normal rotational bands? How closely do they follow the I(I + 1) law? How common is the signature splitting in MR bands? These and similar other questions will be addressed in this paper. Since the first observation of MR bands in Pb isotopes, MR bands have been identified in the mass regions 80, 110, 135 and 195. The data table prepared by Jain and co-workers [6] lists 178 MR bands in 76 nuclides. The table contains 11 bands in A = 80 mass region, 39 in A = 110 region, 49 in A = 135 mass region and 79 in the A = 195 mass region [6]. This is a marked improvement over the 2001 data table where only 120 bands were listed. Besides the γ-ray spectroscopy, several lifetime measurements have also been carried out to confirm the nature of these bands. The number of papers published in this area has remained steady since 2000 at the rate of about 8 10 papers per year. 2. General features of MR bands 1. The level energies in a band nearly follow the I(I + 1) behaviour (ignoring the band crossings and the signature splitting). It has been suggested that they follow the pattern of E(I) E 0 A(I I 0 ) 2 [7]. 2. The intraband transitions are I = 1 magnetic dipole (M1) in nature and the cross-over E2 transitions are either weak or absent implying relatively large B(M1) values and small B(E2) values. The B(M1) values are generally of the order of 1 10µ 2 n and B(E2) values lie in the range of (eb) 2 or less. 3. The B(M1)/B(E2) ratios are quite large ( 20µ 2 /(eb) 2 ) and decrease with increasing angular momentum. 4. The B(M 1) values decrease with increasing angular momentum in a given MR band and this is taken as the strongest signature of an MR band. 5. The band-head excitation energies and the spins are relatively high. Thus most bands have been discovered in high-spin structure studies. The minimum spin noticed is 13/2. 6. These have a multi-quasiparticle configuration which consists of high-j protons and neutrons, and correspond to small quadrupole deformations (ɛ < 0.15). 7. The dynamical moment of inertia is small, of the order of I = 10 to 25 h 2 MeV 1 ; correspondingly, the ratio I/B(E2) is larger than 150 h 2 MeV 1 (eb) 2 compared with well-deformed [ 10 h 2 MeV 1 (eb) 2 ] or superdeformed [ 5 h 2 MeV 1 (eb) 2 ] structures. 52 Pramana J. Phys., Vol. 75, No. 1, July 2010

3 Magnetic rotation Figure 1. The observed cases of MR bands are shown by crosses. See the text for more details. 3. Shears mechanism and regions of magnetic rotation The shears mechanism emerges from a nearly perpendicular coupling of high-j proton and neutron angular momenta. Thus, if one angular momentum is pointing towards the symmetry axis, the other should be aligned perpendicular to it. Therefore, one kind of particles should be particles (holes) in high-ω orbitals whereas the other kind of particles should be holes (particles) in low-ω orbitals. It can be argued that any other type of combination of particles and holes among the neutrons and protons does not lead to shears mechanism. With these considerations, it is possible to predict the possible regions in the periodic table where magnetic rotational excitations can occur. The predicted regions are those where N and/or Z are close to the magic numbers, and the quadrupole deformation is generally less than Figure 1 shows the observed most likely cases of MR bands as listed in ref. [6]. All of them are observed to lie close to the magic numbers and the points of intersection of high-j particles (holes) of one type (either neutron or proton) with high-j holes (particles) of another type. The figure shows the high-j particles by solid lines and high-j holes by dashed lines. Figures 2 and 3 exhibit the number of MR bands observed as a function of proton number (Z) and neutron number (N). Most bands are seen near magic or semi-magic proton numbers Z = 80 83, 55 64, and Same is true for neutrons also where MR bands are seen near N = , 75 82, and The largest number of MR bands has been identified in the Pb isotopes. Pramana J. Phys., Vol. 75, No. 1, July

4 A K Jain and Deepika Choudhury Figure 2. MR bands as a function of proton number. Figure 3. MR bands as a function of neutron number. 4. Tilted-axis cranking model To account for the features observed in MR bands in nearly spherical nuclei, Frauendorf proposed a three-dimensional cranking model, better known as the tilted-axis cranking (TAC) model as it includes the possibility of rotation about an axis other than the principal axes. A complete description of the TAC model (h TAC = h def ω j) developed by Frauendorf and collaborators can be found in [4] and the hybrid version of TAC in [8]; the latter combines the best of the single-particle potentials based on the Woods Saxon and the modified oscillator 54 Pramana J. Phys., Vol. 75, No. 1, July 2010

5 Magnetic rotation potentials (Nilsson model). This approximation has the advantage of using a realistic flat bottom potential along with the coupling between the oscillator shells taken into account. The hybrid version of TAC has been shown to work well in the A = 80 mass region in explaining various features of MR bands in odd-a Rb isotopes [9]. 5. First MR band in the literature 83 Kr The hybrid version [8] of TAC was used by us to understand the observed features of negative parity I = 1 bands in three odd-a Kr isotopes [10]. The experimental data on Kr isotopes existed since 1986 [11 13] without complete understanding. Our calculations pointed out that 83 Kr is the best candidate of magnetic rotation among the three, and is probably a good example of magnetic rotation band based on a shape mixing configuration. The three-quasiparticle configuration chosen for the calculations was π[g 9/2 (fp) 1 ] ν(g 9/2 ). The calculations were performed for two sets of deformation parameters ɛ 2 where minima were obtained. Deformation parameters obtained were ɛ 2 = 0.189, ɛ 4 = and γ = 60. However, we found a second minimum also at a smaller deformation ɛ 2 = and γ = 59. The value of γ is nearly 60 which represents an oblate shape, which is in contrast with most of the other nuclei in A = 80 and 130 mass regions where we get a tri-axial or, a near prolate shape. The results of the calculations for both the calculated deformations along with experimental results for the 83 Kr are shown in figure 4. It is found that the observed energies are more consistent with the calculated band based on larger deformation. We may emphasize that this appears to be the very first case of MR band reported in literature, although characterized as an MR band only now. The comparison of the experimental and the calculated B(M 1) values for both the deformation parameters is shown in figure 5. The Figure 4. Comparison of experimental values with the calculated values in 83 Kr. Pramana J. Phys., Vol. 75, No. 1, July

6 A K Jain and Deepika Choudhury Figure 5. Comparison of the measured B(M1) values with the calculated results in 83 Kr. B(M 1) values calculated for the smaller deformation are small and fairly close to the measured values at higher rotational frequency; however, the B(M 1)s obtained from the larger deformation are quite large and match with the experimental values at smaller rotational frequency. In both the calculated results for 83 Kr there is a sharp decrease in B(M 1) values with the increasing rotational frequency. The complete behaviour can be understood as a mixing of two bands based on the large and the small deformation minima. The MR band in 83 Kr thus appears to originate from a shape mixing configuration. 6. Do they follow the I(I + 1) behaviour? One question often raised is how closely the MR bands follow the I(I + 1) type of behaviour? This question is not easy to answer because the normal rotational bands also deviate from the I(I + 1) behaviour due to many reasons. The best examples of rotational bands are the superdeformed (SD) bands. Their behaviour in the A = 190 mass region, where best examples of SD bands are observed, is shown in figure 6. Also, shown in figure 7 is the behaviour of MR bands in A = 190 mass region again. Here also the best examples of MR bands are found in the Pb isotopes. We show two examples, one from Pb and the other from Bi isotopes. An ideal rotational band will exhibit a linear behaviour for the angular momentum (I) vs. γ-ray energy (E γ ) plot. The SD bands are quite close to it but so are the MR bands shown in figure 7. We, therefore, conclude that no significant difference between the behaviour of SD bands and MR bands in the Pb region can be made out (if we ignore the bands with back bending and signature splitting). 56 Pramana J. Phys., Vol. 75, No. 1, July 2010

7 Magnetic rotation I (h) E (I γ I-2) (kev) Figure 6. Plots of angular momentum I vs. γ-ray energies of SD bands in A = 190 region. 7. Shape coexistence, shape change and PAC-to-TAC transition Shape coexistence has also been observed in some of the isotopes in A = 135 mass region. The deformation parameter β 2 is in general larger in the A = 135 region than that for Pb nuclei in A = 190 region. Some of these bands, therefore, appear to be intermediate between the magnetic rotation and the normal collective rotational bands. This character has also been confirmed by Dimitrov et al [8] for the I = 1 band in 128 Ba by using the hybrid TAC model. The deformation parameters in this case were found to be β = 0.20 and γ = 0. A I = 1 band observed in 136 Ce [14] and interpreted as MR band, exhibits B(M1)/B(E2) values, which are quite small at the lower spins but large at higher spins (I = 18) and then fall again. Calculations based on PAC and TAC suggest that a transition from the PAC regime to TAC regime is taking place, which is induced by a shape change from a triaxial (γ = 21 ) to oblate shape. Another I = 1 band observed in 134 Ce [15], which exhibits large B(M1) values yet a nearly constant B(M 1)/B(E2) ratio with increasing rotational frequency, was explained in terms of two close-lying configurations: (A) π(g7/2 2 ) ν(h 11/2d 3/2 ) and (B) π(h 2 11/2 ) ν(h 11/2d 3/2 ) which have a small and a moderate deformation, respectively. The TAC calculations suggest that the configuration B crosses the configuration A with a small alignment gain and mixing between the two may be needed to explain the observed features. These results suggest that the TAC regime may often get mixed with other modes arising from shape changes with rotational frequency. Pramana J. Phys., Vol. 75, No. 1, July

8 A K Jain and Deepika Choudhury Figure 7. Plots of I vs. γ-ray energies E γ of MR bands in 200 Pb and 202 Bi. Figure 8. Band 4 of 196 Pb fitted by the crossing of two MR bands. 58 Pramana J. Phys., Vol. 75, No. 1, July 2010

9 Magnetic rotation Figure 9. Fall in the B(M1) values followed by a rise and again a fall suggesting closing, opening and again closing of p n blades. Also plotted is the shears angle θ as a function of spin I. 8. Back bending and band crossing in MR bands A number of MR bands have been observed to display band crossing and backbending phenomena. As an example, we show in figure 8 the band crossing and the consequent back-bending behaviour of the MR band in 196 Pb. The solid points are the experimental data which are fitted by two polynomials; this clearly indicates the crossing of two bands. The observed behaviour of the B(M1) values for the two bands is shown in figure 9. We find that the B(M1) values decrease for Band 1, as they should for an MR band. But there is a sudden jump in the value around I = 22, just where the crossing occurs. The crossing point matches with that in figure 8. The B(M 1) values again fall afterwards, suggesting an MR behaviour again. We have fitted this behaviour in the semiclassical model of Macchiavelli et al [16,17] by using the configurations π(i 13/2 h 9/2 )K = 11 ν(i 13/2 ) 2 before and π(i 13/2 h 9/2 )K = 11 ν(i 13/2 ) 4 after the crossing, suggesting the transition from a three-quasiparticle to a five-quasiparticle configuration. The closing neutron proton blades open up again near I = 22 and a new MR band, having two more neutrons, crosses it. The shears angle exhibits a change which closely follows the B(M 1) behaviour. The neutron proton blades, which were perpendicular to each other at the band head, again open up and start closing after the crossing [18]. Our group has also discovered a number of MR bands in A = 135 mass region in 137 Pr [19], 139 Nd [20] and 135 Ba [21]. An example of band crossing of two MR bands in A = 135 mass region, which leads to back bending, is shown in figure 10. The negative parity part of the level scheme of 137 Pr studied by us, consisting of the MR band (Band 2) is shown here [19]. We plot (figure 11) the experimental energy E vs. I for Band 2, which exhibits a band crossing around spin 17.5; this is explained by the TAC calculations (shown by solid and dashed lines) as a crossing Pramana J. Phys., Vol. 75, No. 1, July

10 A K Jain and Deepika Choudhury Figure 10. A part of the negative parity levels showing the MR band (left hand) which has a crossing of a 3qp and a 5qp MR band in 137 Pr. of a 3qp band π(h 11/2 ) ν(h 11/2 ) 2 and a 5qp band π(h 11/2 g 7/2 2 ) ν(h 11/2 ) 2. The B(M 1) values, both theoretical and measured, confirm this interpretation where we see the typical fall, rise and again fall in the B(M1) values. 9. Signature splitting in MR bands Symmetry considerations suggest that the MR bands do not have signature as a good quantum number and one expects a I = 1 band structure in MR bands. It basically means that good MR bands must not exhibit any signature splitting. We do, however, find a large number of MR bands in all the mass regions which display large to small signature splitting [5,6]. We note that the large signature splitting is an effect of relatively smaller deformation as it increases the Coriolis mixing [22] among the high-j orbitals. A deformation thus appears to be present in all the 60 Pramana J. Phys., Vol. 75, No. 1, July 2010

11 Magnetic rotation Figure 11. The calculated energies of the 3qp and 5qp MR bands are compared with the experimental data in 137 Pr. nuclei with MR band and Coriolis mixing appears to play a significant role in the signature splitting as well as in the closing of the neuron and proton blades [22]. 10. Conclusions To summarize, we have discussed the salient features of the magnetic rotation phenomenon and the MR bands. Some of the observed features like signature splitting and I(I + 1)-type behaviour highlight the importance of deformation in MR bands. The behaviour of kinematic moment of inertia also supports this [18]. Some of the questions remaining unanswered relate to the role of neutrons vs. protons in MR phenomenon and the exact nature of increase in excitation energy in MR bands. References [1] H Hübel et al, Prog. Part. Nucl. Phys. 28, 427 (1992) [2] R M Clark et al, Phys. Lett. B275, 247 (1992) [3] S Frauendorf, Nucl. Phys. A557, 259c (1993) [4] S Frauendorf, Nucl. Phys. A677, 115 (2000) [5] A K Jain and Amita, Pramana J. Phys. 57, 611 (2001) [6] Amita, A K Jain and Balraj Singh, At. Nucl. Data Tables 69, 239 (1998); (2006) [7] R M Clark and A O Macchiavelli, Annu. Rev. Nucl. Part. Sci. 50, 1 (2000) [8] V I Dimitrov, F Dönau and S G Frauendorf, Phys. Rev. C62, (2000) [9] Amita, A K Jain, V I Dimitrov and S G Frauendorf, Phys. Rev. C64, (2001) [10] S S Malik, P Agarwal and A K Jain, Nucl. Phys. A732, 13 (2004) Pramana J. Phys., Vol. 75, No. 1, July

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