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The microscopic structure of the M1 mode in 164Dy
Volume 222, number 3,4
PHYSICS LETTERS B
25 May 1989
T H E M I C R O S C O P I C S T R U C T U R E O F T H E M1 M O D E I N 164Dy S.J. F R E E M A N , R. C H A P M A N , J.L. D U R E L L , M.A.C. H O T C H K I S , F. KHAZAIE, J.C. LISLE, J.N. M O Schuster Laboratory, Department of Physics, The University, ManchesterM I 3 9PL, UK
A.M. BRUCE, R.A. C U N N I N G H A M , P.V. D R U M M , D.D. W A R N E R Daresbury Laboratory, SERC, Warrington, Cheshire, WA4 4AD, UK
and J.D. G A R R E T T 1 The Niels Bohr Institute, Universityof Copenhagen, DK-2100 Copenhagen, Denmark
Received 6 February 1989
The microscopic structure of the M 1 mode in t 64Dy (in which the M 1 strength is fragmented over several 1÷ states) has been investigated using the 165Ho(t,Ix)t64Dyreaction. The 3+-8 ÷ members of a proposed KS= 1÷ rotational band with a band head energy of 2.557 + 0.015 MeV were observed to be strongly populated in 1= 5 proton transfer. These results are not consistent with a collective interpretation of this state.
Considerable interest has been generated by the recent discovery [ 1 ] in inelastic electron scattering experiments on heavy deformed nuclei of a new class of I ~ = 1 ÷ states with excitation energies in the range 2 3 MeV and B(M1 ) values o f the order o f 1/z2. Subsequent measurements have resulted in the identification of similar 1 ÷ states in a range o f nuclei from 46Ti to 238U [2 ]. This mode of excitation has also been observed in nuclear resonance fluorescence experiments [ 3 ]. The prediction that a new collective M1 mode should exist was first proposed within the context of a two-rotor model by Lo Iudice and Palumbo [ 4 ]. In this model the proton and neutron fluids rotate collectively with a fixed angular displacement between their axes of symmetry, and the large M1 strength arises from the orbital motion of protons with respect to neutrons. Following the experimental discovery, a considerable number o f additional theoretPresent address: Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA. 0 3 7 0 - 2 6 9 3 / 8 9 / $ 03.50 © Elsevier Science Publishers B.V. ( North-Holland Physics Publishing Division )
ical models have been used in descriptions o f the mode [ 5 ]. Although the picture normally proposed is that o f a collective mode of excitation, there are alternative microscopic descriptions such as that o f H a m a m o t o et al. [ 6 ] based on a quasiparticle RPA model. Such calculations indicate that large magnetic dipole strength ( ~ 1/1~ ) can be associated with the convection currents of only a few protons moving in specific high-j orbitals. In particular, the 1 ÷ states identified in rare-earth nuclei are suggested to have wavefunctions dominated by typically one or two quasiproton configurations which in terms of a spherical basis have large (h11/2) 2 amplitudes. This result is obviously inconsistent with a description o f the 1 + states in terms of collective degrees of freedom. The resolution of the fundamental questions discussed above concerning the microscopic origins o f the M 1 mode clearly requires information on the single-particle structure o f the 1 + states in question. Here, in the first experimental investigation o f this kind, we present evidence that in 164Dy the wavefunction o f a particular 1 + state, identified both in 347
Volume 222, number 3,4
PHYSICS LETTERS B
(7, 7' ) [ 3 ] and in inelastic electron scattering [ 7 ] as one of several states with a large M 1 strength and described in terms of a collective M1 excitation, is dominated by an (hi 1/2) 2 two-quasiproton configuration. The 1 ÷ state discussed here can therefore not be described in terms of the collective M1 mode. In the present work, states of ~64Dy were populated using the 165Ho(t, ct)164Dyreaction. 165Ho is the only stable odd-Z nucleus with the odd proton in an hi 1/2 orbit ( 7 / 2 - [ 5 2 3 ] ). Proton pickup from the target can therefore lead to population of two-quasiproton configurations of the type discussed by H a m a m o t o et al. [6]. The (t, ct) reaction was chosen because, as a consequence of the angular-momentum mismatch in the entrance and exit channels, it enhances large l transfers, e.g. the l = 5 associated with h 11/2 proton pickup. A beam of tritons of energy 37.3 MeV delivered by the Daresbury Laboratory Tandem Accelerator was used to bombard a target of 165Ho o f approximate thickness 100 ~tg cm -2 and backed with carbon of thickness 10 ~tg c m - 2 . Beam currents in the range from 20 pnA to 200 pnA were used. Reaction products were analysed in a Q M G / 2 magnetic spectrometer, operating with a solid angle of 10 msr and an
EXCI TATIOENERGY N (keY) ~.000 3000
angular acceptance in the reaction plane of 6 °. Measurements were made at 4 ° angular steps over the angular range 8°-36 °. At the focal plane a multi-element gas-filled counter [8] was used to detect the analysed ions. The energy-loss and the total energy signals from the detector were used to provide clean separation of a-particles from other reaction products. A position spectrum from the 165Ho(t, ct)J64Dy reaction is shown in fig. 1. The a-particle energy resolution is 15 keV FWHM. In order to establish the shapes of ct-particle angular distributions corresponding to known/-transfers, the reaction 166Er(t, ct)165Ho was measured under the same conditions as for the reaction of interest. This reaction has previously been studied [ 9 ] and l= 2, 4 and 5 proton transfers have been identified. Here we have chosen to make assignments of the orbital angular-momentum quantum number l of the transferred proton on the basis of measurements of the angular dependence of the ratio (R) of or-particle yield of the transition of interest to that to the l= 5 "groundstate" group. Experimentally, l= 2 transfers are easily identified while the most difficult angular-momentum transfers to distinguish are those corresponding to l = 4 and l--5. We therefore restrict the
2000 5-
t
K~'__1+
8
25 May 1989
K':5-
1000
0
165Ho(3H,~'Hel~6L'Dy E =373HEY 0:26°
I
K"'=0*
* ;*74
200
K~2-
I
I~
I
100 ° U 600
800
1000
1200
I~.00
POSITION ALONG FOCAL PLANE Fig. 1. A position spectrum of or-particles from the 165Ho(t,0t)164Dyreaction measured at a laboratory angle of 26 °. Peaks are labelled with the spin and parity, I t, of the populated state and the proposed K ~ value of the rotational band.
348
Volume 222, number 3,4
PHYSICS LETTERSB
following discussion to these latter/-values. The form of the yield ratios, R(O), for l = 4 and 5 was established from the concurrent measurements of the 166Er(t, Ix) 165Ho reaction. The sum of Ix-particle yields to the known 94.7 keV ( U = 9 / 2 - ) and 209.8 keY ( U = 1 1 / 2 - ) states of 165Ho was taken as the l = 5 "ground state" yield, I ( l = 5 ). Intensities I' (l= 4) and I' (l= 5 ) corresponding to l= 4 and 5 transfers to excited states were measured for u-particle groups corresponding to excitation energies of 491.0 ( U = 7/ 2÷), 589.8 ( U = 7 / 2 + ) , 715.3 keV ( U = 7 / 2 +) and 1674 keV ( U = 1 1 / 2 - ) respectively. Fig. 2 shows the resulting yield ratios, R [ I ' ( l = 4 ) / I ( l = 5 ) ] and R [I' (l = 5 )/I( l = 5 ) ] as a function of centre of mass angle. It can be seen that the shapes of the relative angular distributions are/-dependent. The non-isotropic angular dependence of the yield ratio R[I'(1=5)/1(l=5)] reflects the Q-value dependence of the I= 5 angular distributions. /-value assignments for transitions to states of 164Dy populated in the 165Ho(t, ix) reaction were based on a comparison of the angular dependence of the yield ratios with
~0'6
~0~ cY >-
0
Ù'E
16t'Dy K%1* BANDR[I'/I(I=5)]
°1
those established from the 166Er(t, Ix)165H0 reaction. In this case the sum of transfer yields to the 2+-8 + members of the ground-state rotational band was taken as the l= 5 "ground-state" yield, I(l= 5 ). Some of the low-lying states and associated band structures can be identified by reference to previous spectroscopic studies of ]64By [ 10]. Here we do not wish to discuss in detail the spectroscopy of 164Dybut rather to concentrate attention on one particular feature of the data, namely the identification of six members of a new band populated strongly through l= 5 proton pickup. This band is labelled K~= 1÷ in fig. 1 and the corresponding yield ratios are presented in fig. 2; l= 5 transfer is assigned on the basis of these data. The discussion which follows is centred around the l= 5 transfer strength. The six band members identified with l= 5 strength correspond to the Ix groups lying in the range from channel 700 to channel 900 in the spectrum of fig. 1. No other l= 5 strength could be identified, and no l= 4 strength was observed. We associate the six states with the U = 3 ÷-8 ÷ members of a proposed K ~= 1 + rotational band with a configuration 7 / 2 - [ 5 2 3 ] × 5 / 2 - [ 532 ]. Both Nilsson orbitals in a spherical basis are dominated by the hi 1/2 intruder shell. The identification o f l = 5 proton pickup from the 5 / 2 - [ 532 ] orbital is further strengthened by a comparison of the relative transfer yields with the square of the ClebschGo rdan coefficients, ( 7/2 7/2 11/2 - 5/211 1 ). Fig. 3 presents this latter comparison which also serves to explain the lack of a positive identification of the 2 + and 9 ÷ members of the band. The ability to reproduce the data using the usual I(I+ 1 ) expansion of excitation energies further confirms that the six states may be considered as members of a rotational band. A least-squares fit to the experimental data yields
E=2.528+0.01396I(I+ 1 ) +0.0000188[•(•+
0-
8
16
2/-,
32
0°m.
Fig. 2. The yield ratios for known l= 4 and 1= 5 transitions from the reaction 166Er(t, 1~)165Ho(upper two data sets) and for the transition leading to members of the proposed K~= 1+ band in t64Dypopulated in the ~6SHo(t,ct) reaction (bottom data set). The smooth curves are to guide the eye. See text for details.
25 May 1989
1 ) ]z M e V .
The corresponding band head ( U = 1 ÷ ) energy is 2.557 + 0.015 MeV, and the rotational parameter (h2/ 2 J = 14.0 keV) is close to that observed in the ground state band (h2/2J = 12.5 keV). An important question relates to the amplitude of the h11/2 two-quasiproton component in the intrinsic wavefunction of the K~= 1÷ band. The measured total l= 5 transfer yields to the two rotational bands in 349
Volume 222, number 3,4
PHYSICS LETTERS B
RELATIVE POPULATIONOF MEMBERSOF K'r:1 + ROTATIONAL BAND ~m
,
03
DATA.
,(7/2 Z'2 11/2- 5/2111~
02
01
0 1
2
3
/,
5
6
7
B
9
I Fig. 3. Comparison of the relative population of members of the proposed K"= 1+ rotational band and a comparison with the square of the Clebsch-Gordan coefficients (7/2 7/2 1 1/2 - 5 / 2111). 164Dy were corrected for the effects of Q-value differences using the results of zero-range DWBA calculations in which cross sections were the averages of those calculated using the t and a-particle optical model parameters taken from refs. [ 11-13 ] and refs. [14-16 ] respectively and the bound state WoodsSaxon potential parameters were ro= 1.35 fm and a = 0.64 fm. With this choice of parameters and a (t, a) normalization factor of 21 × 104 MeV 2 fm 3 the calculations were able to reproduce the 165Ho(t, a ) cross section measurements for the 164Dy ground state band made by Zybert et al. [17] at E=37.3 MeV. After correction for Q-value effects the resulting ratio of total l = 5 transfer strength to members of the K " = 1 + band (which includes small estimated contributions from the unobserved 2 + and 9 + members) compared to that to the ground band is 1.I1 +0.09. For pure h~/2 configurations the predicted ratio of transfer strength to the two bands is equal t o V2/211U2/2 , where V2/2 and U2/2 represent the BCS pair occupation probabilities of the 5/ 2 - [ 532 ] and 7 / 2 - [ 523 ] Nilsson orbits in the ground state o f 16Silo and 164Dy, respectively. The measured yield ratio compares closely to that calculated ( 1.25 ) for unfragmented l= 5 strength to the K " = 1 + band when occupation probabilities calculated from pairing theory are used [ 18 ] and implies that the square
350
25 May 1989
of the amplitude of the ( h t l / 2 ) 2 component in the wavefunction of the 1+ state is approximately 0.9. An experimental limit of ~<5% of the intensity of the observed 7 / 2 - [ 5 2 3 ] X 5 / 2 - [ 5 3 2 ] 1 + band can be placed on any other candidate for such a configuration. Our data are therefore consistent with the identification of the U = 3+-8 + members o f a K " = 1 + band in 164Dy with an extrapolation leading to a band head energy of 2.557 + 0.015 MeV, and having a relatively pure two-quasiproton 7 / 2 - [523] X 5 / 2 - [532] intrinsic configuration. Two groups of 1 + states have been identified in J64Dy at excitation energies near 2.5 MeV (2.530, 2.539, 2.578 and 2.694 MeV) and 3.1 MeV (3.112, 3.159 and 3.173 MeV) in (e, e ' ) [ 7 ] and nuclear resonance fluorescence, (y, V' ), experiments [ 3 ]. Since these two groups of states carry large M1 strength (1.67# 2 and 3.15/~ 2, respectively), they have been described as the collective M 1 mode although the reason for the fragmentation of the strength over such a wide region of excitation energies in this nucleus is not understood. The band head of the state populated in the (t, a) reaction probably corresponds either to the 1+ state observed in (7, V' ) at 2.539 MeV or that at 2.578 MeV with B ( M 1 ) = 0 . 3 0 # 2, and 0.36# 2, respectively. These states lie within about 1.5 standard deviations of the measured band head energy. The observed M1 strength of either band head candidate is much less than predicted [ 19 ] for the 7 / 2 - [ 523 ] X 5 / 2 - [ 532 ] configuration, ~ 1.36#~. The wavefunction of the group of 1 + states strongly populated in (e, e' ) and (?, y' ) at 3.1 MeV do not contain significant components of 7 / 2 - [523] × 5 / 2 - [532]. The structure of these states and the remaining 1+ states near 2.5 MeV may involve quasiproton configurations associated with large M1 strength, but not accessible in the (t, a) reaction (e.g. 7 / 2 - [ 5 2 3 ] × 9 / 2 - [ 5 1 4 ] , 5/ 2 - [ 5 3 2 ] × 3 / 2 - [ 5 3 2 ] or 3 / 2 - [ 5 3 2 ] X 1 / 2 - [ 5 4 1 ] , see ref. [ 20 ] ), or a collective M 1 interpretation may be appropriate. Clearly the microscopic structure of the remaining 1 + states is a matter of considerable interest. This work was supported by the U K Science and Engineering Research Council and the Danish Natural Science Research Council. One of us (S.J.F.) wishes to acknowledge receipt of an SERC student-
Volume 222, number 3,4
PHYSICS LETTERS B
ship. V a l u a b l e d i s c u s s i o n s w i t h I. H a m a m o t o gratefully acknowledged.
are
References [ 1 ] D. Bohle, A. Richter, W. Steffen, A.E.L. Dieperink, N. Lo Iudice, F. Palumbo and O. Scholten, Phys. Lett. B 137 (1984) 27. [2]A. Richter, in: The variety of nuclear shapes, eds. J.D. Garrett, C.A. Kalfas, G. Anagnostatos, E. Kossionides and R. Vlastou (World Scientific, Singapore, 1987) p. 54. [3] C. Wesselborg, P. Von Brentano, K.O. Zell, R.D. Heil, H.H. Pritz, U.E.P. Berg, U. Kneissl, S. Lindenstruth, U. Seemann and R. Stock, Phys. Lett. B 207 (1988) 22. [4] N. Lo Iudice and F. Palumbo, Phys. Rev. Lett. 41 (1978) 1532; Nucl. Phys. A 326 (1979) 193. [ 5 ] A. Richter, in: Nuclear structure 1985, eds. R. Broglia, G.B. Hagemann and B. Herskind (North-Holland, Amsterdam, 1985) p. 469. [6] I. Hamamoto and S. •berg, Phys. Lett. B 145 (1984) 163; Phys. Scr. 34 (1986) 697; I. Hamamoto and C. R6nstr6m, Phys. Lett. B 194 (1987) 6.
25 May 1989
[7] D. Bohle, G. Kilgus, A. Richter, C.W. de Jager and H. de Vries, Phys. Lett. B 195 (1987) 326. [8] R.A. Cunningham, N.E. Sanderson, W.N.J. Snodgrass, D.W. Banes, S.D. Hoath and J.N. Mo, Nucl. Instrum. Methods A 234 (1985) 67. [9] G. Lovhoiden, D.G. Burke, C.R. Hirning, E.R. Flynn and J.W. Sunier, Nucl. Phys. A 303 (1978) 1; L.K. Wagner, D.G. Burke, H.C. Cheung, P. Kleinheinz and R.K. Sheline, Nacl. Phys. A 246 (1975) 43. [ 10] Nucl. Data Sheets 47 (1986) 433. [ 11 ] F.T. Baker and R. Tickle, Phys. Lett. B 32 (1970) 47. [ 12] F.T. Baker and R. Tickle, Phys. Rev. C 5 (1972) 182. [ 13 ] J.H. Barker and J.C. Hiebert, Phys. Rev. C 4 ( 1971 ) 2256. [14] D. Burke and J. Waddington, Nucl. Phys. A 193 (1972) 271. [ 15] E.R. Flynn, D.D. Armstrong, J.G. Beery and A.G. Blair, Phys. Rev. 182 (1969) 1113. [ 16 ] J.B.A. England, Nucl. Phys. A 475 ( 1987 ) 422. [ 17 ] L. Zybert, private communication. [ 18 ] L. Kisslinger and B. Sorensen, Revs. Mod. Phys. 35 ( 1963 ) 853; B. Elbek and P.O. Tjom, Adv. Nucl. Phys. 3 (1970) 259. [ 19 ] I. Hamamoto, private communication. [20] O. Civitarese, A. Faessler and R~ Nojarov, Phys. Rev. C 35 (1987) 2310.
351
PHYSICS LETTERS B
25 May 1989
T H E M I C R O S C O P I C S T R U C T U R E O F T H E M1 M O D E I N 164Dy S.J. F R E E M A N , R. C H A P M A N , J.L. D U R E L L , M.A.C. H O T C H K I S , F. KHAZAIE, J.C. LISLE, J.N. M O Schuster Laboratory, Department of Physics, The University, ManchesterM I 3 9PL, UK
A.M. BRUCE, R.A. C U N N I N G H A M , P.V. D R U M M , D.D. W A R N E R Daresbury Laboratory, SERC, Warrington, Cheshire, WA4 4AD, UK
and J.D. G A R R E T T 1 The Niels Bohr Institute, Universityof Copenhagen, DK-2100 Copenhagen, Denmark
Received 6 February 1989
The microscopic structure of the M 1 mode in t 64Dy (in which the M 1 strength is fragmented over several 1÷ states) has been investigated using the 165Ho(t,Ix)t64Dyreaction. The 3+-8 ÷ members of a proposed KS= 1÷ rotational band with a band head energy of 2.557 + 0.015 MeV were observed to be strongly populated in 1= 5 proton transfer. These results are not consistent with a collective interpretation of this state.
Considerable interest has been generated by the recent discovery [ 1 ] in inelastic electron scattering experiments on heavy deformed nuclei of a new class of I ~ = 1 ÷ states with excitation energies in the range 2 3 MeV and B(M1 ) values o f the order o f 1/z2. Subsequent measurements have resulted in the identification of similar 1 ÷ states in a range o f nuclei from 46Ti to 238U [2 ]. This mode of excitation has also been observed in nuclear resonance fluorescence experiments [ 3 ]. The prediction that a new collective M1 mode should exist was first proposed within the context of a two-rotor model by Lo Iudice and Palumbo [ 4 ]. In this model the proton and neutron fluids rotate collectively with a fixed angular displacement between their axes of symmetry, and the large M1 strength arises from the orbital motion of protons with respect to neutrons. Following the experimental discovery, a considerable number o f additional theoretPresent address: Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA. 0 3 7 0 - 2 6 9 3 / 8 9 / $ 03.50 © Elsevier Science Publishers B.V. ( North-Holland Physics Publishing Division )
ical models have been used in descriptions o f the mode [ 5 ]. Although the picture normally proposed is that o f a collective mode of excitation, there are alternative microscopic descriptions such as that o f H a m a m o t o et al. [ 6 ] based on a quasiparticle RPA model. Such calculations indicate that large magnetic dipole strength ( ~ 1/1~ ) can be associated with the convection currents of only a few protons moving in specific high-j orbitals. In particular, the 1 ÷ states identified in rare-earth nuclei are suggested to have wavefunctions dominated by typically one or two quasiproton configurations which in terms of a spherical basis have large (h11/2) 2 amplitudes. This result is obviously inconsistent with a description o f the 1 + states in terms of collective degrees of freedom. The resolution of the fundamental questions discussed above concerning the microscopic origins o f the M 1 mode clearly requires information on the single-particle structure o f the 1 + states in question. Here, in the first experimental investigation o f this kind, we present evidence that in 164Dy the wavefunction o f a particular 1 + state, identified both in 347
Volume 222, number 3,4
PHYSICS LETTERS B
(7, 7' ) [ 3 ] and in inelastic electron scattering [ 7 ] as one of several states with a large M 1 strength and described in terms of a collective M1 excitation, is dominated by an (hi 1/2) 2 two-quasiproton configuration. The 1 ÷ state discussed here can therefore not be described in terms of the collective M1 mode. In the present work, states of ~64Dy were populated using the 165Ho(t, ct)164Dyreaction. 165Ho is the only stable odd-Z nucleus with the odd proton in an hi 1/2 orbit ( 7 / 2 - [ 5 2 3 ] ). Proton pickup from the target can therefore lead to population of two-quasiproton configurations of the type discussed by H a m a m o t o et al. [6]. The (t, ct) reaction was chosen because, as a consequence of the angular-momentum mismatch in the entrance and exit channels, it enhances large l transfers, e.g. the l = 5 associated with h 11/2 proton pickup. A beam of tritons of energy 37.3 MeV delivered by the Daresbury Laboratory Tandem Accelerator was used to bombard a target of 165Ho o f approximate thickness 100 ~tg cm -2 and backed with carbon of thickness 10 ~tg c m - 2 . Beam currents in the range from 20 pnA to 200 pnA were used. Reaction products were analysed in a Q M G / 2 magnetic spectrometer, operating with a solid angle of 10 msr and an
EXCI TATIOENERGY N (keY) ~.000 3000
angular acceptance in the reaction plane of 6 °. Measurements were made at 4 ° angular steps over the angular range 8°-36 °. At the focal plane a multi-element gas-filled counter [8] was used to detect the analysed ions. The energy-loss and the total energy signals from the detector were used to provide clean separation of a-particles from other reaction products. A position spectrum from the 165Ho(t, ct)J64Dy reaction is shown in fig. 1. The a-particle energy resolution is 15 keV FWHM. In order to establish the shapes of ct-particle angular distributions corresponding to known/-transfers, the reaction 166Er(t, ct)165Ho was measured under the same conditions as for the reaction of interest. This reaction has previously been studied [ 9 ] and l= 2, 4 and 5 proton transfers have been identified. Here we have chosen to make assignments of the orbital angular-momentum quantum number l of the transferred proton on the basis of measurements of the angular dependence of the ratio (R) of or-particle yield of the transition of interest to that to the l= 5 "groundstate" group. Experimentally, l= 2 transfers are easily identified while the most difficult angular-momentum transfers to distinguish are those corresponding to l = 4 and l--5. We therefore restrict the
2000 5-
t
K~'__1+
8
25 May 1989
K':5-
1000
0
165Ho(3H,~'Hel~6L'Dy E =373HEY 0:26°
I
K"'=0*
* ;*74
200
K~2-
I
I~
I
100 ° U 600
800
1000
1200
I~.00
POSITION ALONG FOCAL PLANE Fig. 1. A position spectrum of or-particles from the 165Ho(t,0t)164Dyreaction measured at a laboratory angle of 26 °. Peaks are labelled with the spin and parity, I t, of the populated state and the proposed K ~ value of the rotational band.
348
Volume 222, number 3,4
PHYSICS LETTERSB
following discussion to these latter/-values. The form of the yield ratios, R(O), for l = 4 and 5 was established from the concurrent measurements of the 166Er(t, Ix) 165Ho reaction. The sum of Ix-particle yields to the known 94.7 keV ( U = 9 / 2 - ) and 209.8 keY ( U = 1 1 / 2 - ) states of 165Ho was taken as the l = 5 "ground state" yield, I ( l = 5 ). Intensities I' (l= 4) and I' (l= 5 ) corresponding to l= 4 and 5 transfers to excited states were measured for u-particle groups corresponding to excitation energies of 491.0 ( U = 7/ 2÷), 589.8 ( U = 7 / 2 + ) , 715.3 keV ( U = 7 / 2 +) and 1674 keV ( U = 1 1 / 2 - ) respectively. Fig. 2 shows the resulting yield ratios, R [ I ' ( l = 4 ) / I ( l = 5 ) ] and R [I' (l = 5 )/I( l = 5 ) ] as a function of centre of mass angle. It can be seen that the shapes of the relative angular distributions are/-dependent. The non-isotropic angular dependence of the yield ratio R[I'(1=5)/1(l=5)] reflects the Q-value dependence of the I= 5 angular distributions. /-value assignments for transitions to states of 164Dy populated in the 165Ho(t, ix) reaction were based on a comparison of the angular dependence of the yield ratios with
~0'6
~0~ cY >-
0
Ù'E
16t'Dy K%1* BANDR[I'/I(I=5)]
°1
those established from the 166Er(t, Ix)165H0 reaction. In this case the sum of transfer yields to the 2+-8 + members of the ground-state rotational band was taken as the l= 5 "ground-state" yield, I(l= 5 ). Some of the low-lying states and associated band structures can be identified by reference to previous spectroscopic studies of ]64By [ 10]. Here we do not wish to discuss in detail the spectroscopy of 164Dybut rather to concentrate attention on one particular feature of the data, namely the identification of six members of a new band populated strongly through l= 5 proton pickup. This band is labelled K~= 1÷ in fig. 1 and the corresponding yield ratios are presented in fig. 2; l= 5 transfer is assigned on the basis of these data. The discussion which follows is centred around the l= 5 transfer strength. The six band members identified with l= 5 strength correspond to the Ix groups lying in the range from channel 700 to channel 900 in the spectrum of fig. 1. No other l= 5 strength could be identified, and no l= 4 strength was observed. We associate the six states with the U = 3 ÷-8 ÷ members of a proposed K ~= 1 + rotational band with a configuration 7 / 2 - [ 5 2 3 ] × 5 / 2 - [ 532 ]. Both Nilsson orbitals in a spherical basis are dominated by the hi 1/2 intruder shell. The identification o f l = 5 proton pickup from the 5 / 2 - [ 532 ] orbital is further strengthened by a comparison of the relative transfer yields with the square of the ClebschGo rdan coefficients, ( 7/2 7/2 11/2 - 5/211 1 ). Fig. 3 presents this latter comparison which also serves to explain the lack of a positive identification of the 2 + and 9 ÷ members of the band. The ability to reproduce the data using the usual I(I+ 1 ) expansion of excitation energies further confirms that the six states may be considered as members of a rotational band. A least-squares fit to the experimental data yields
E=2.528+0.01396I(I+ 1 ) +0.0000188[•(•+
0-
8
16
2/-,
32
0°m.
Fig. 2. The yield ratios for known l= 4 and 1= 5 transitions from the reaction 166Er(t, 1~)165Ho(upper two data sets) and for the transition leading to members of the proposed K~= 1+ band in t64Dypopulated in the ~6SHo(t,ct) reaction (bottom data set). The smooth curves are to guide the eye. See text for details.
25 May 1989
1 ) ]z M e V .
The corresponding band head ( U = 1 ÷ ) energy is 2.557 + 0.015 MeV, and the rotational parameter (h2/ 2 J = 14.0 keV) is close to that observed in the ground state band (h2/2J = 12.5 keV). An important question relates to the amplitude of the h11/2 two-quasiproton component in the intrinsic wavefunction of the K~= 1÷ band. The measured total l= 5 transfer yields to the two rotational bands in 349
Volume 222, number 3,4
PHYSICS LETTERS B
RELATIVE POPULATIONOF MEMBERSOF K'r:1 + ROTATIONAL BAND ~m
,
03
DATA.
,(7/2 Z'2 11/2- 5/2111~
02
01
0 1
2
3
/,
5
6
7
B
9
I Fig. 3. Comparison of the relative population of members of the proposed K"= 1+ rotational band and a comparison with the square of the Clebsch-Gordan coefficients (7/2 7/2 1 1/2 - 5 / 2111). 164Dy were corrected for the effects of Q-value differences using the results of zero-range DWBA calculations in which cross sections were the averages of those calculated using the t and a-particle optical model parameters taken from refs. [ 11-13 ] and refs. [14-16 ] respectively and the bound state WoodsSaxon potential parameters were ro= 1.35 fm and a = 0.64 fm. With this choice of parameters and a (t, a) normalization factor of 21 × 104 MeV 2 fm 3 the calculations were able to reproduce the 165Ho(t, a ) cross section measurements for the 164Dy ground state band made by Zybert et al. [17] at E=37.3 MeV. After correction for Q-value effects the resulting ratio of total l = 5 transfer strength to members of the K " = 1 + band (which includes small estimated contributions from the unobserved 2 + and 9 + members) compared to that to the ground band is 1.I1 +0.09. For pure h~/2 configurations the predicted ratio of transfer strength to the two bands is equal t o V2/211U2/2 , where V2/2 and U2/2 represent the BCS pair occupation probabilities of the 5/ 2 - [ 532 ] and 7 / 2 - [ 523 ] Nilsson orbits in the ground state o f 16Silo and 164Dy, respectively. The measured yield ratio compares closely to that calculated ( 1.25 ) for unfragmented l= 5 strength to the K " = 1 + band when occupation probabilities calculated from pairing theory are used [ 18 ] and implies that the square
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of the amplitude of the ( h t l / 2 ) 2 component in the wavefunction of the 1+ state is approximately 0.9. An experimental limit of ~<5% of the intensity of the observed 7 / 2 - [ 5 2 3 ] X 5 / 2 - [ 5 3 2 ] 1 + band can be placed on any other candidate for such a configuration. Our data are therefore consistent with the identification of the U = 3+-8 + members o f a K " = 1 + band in 164Dy with an extrapolation leading to a band head energy of 2.557 + 0.015 MeV, and having a relatively pure two-quasiproton 7 / 2 - [523] X 5 / 2 - [532] intrinsic configuration. Two groups of 1 + states have been identified in J64Dy at excitation energies near 2.5 MeV (2.530, 2.539, 2.578 and 2.694 MeV) and 3.1 MeV (3.112, 3.159 and 3.173 MeV) in (e, e ' ) [ 7 ] and nuclear resonance fluorescence, (y, V' ), experiments [ 3 ]. Since these two groups of states carry large M1 strength (1.67# 2 and 3.15/~ 2, respectively), they have been described as the collective M 1 mode although the reason for the fragmentation of the strength over such a wide region of excitation energies in this nucleus is not understood. The band head of the state populated in the (t, a) reaction probably corresponds either to the 1+ state observed in (7, V' ) at 2.539 MeV or that at 2.578 MeV with B ( M 1 ) = 0 . 3 0 # 2, and 0.36# 2, respectively. These states lie within about 1.5 standard deviations of the measured band head energy. The observed M1 strength of either band head candidate is much less than predicted [ 19 ] for the 7 / 2 - [ 523 ] X 5 / 2 - [ 532 ] configuration, ~ 1.36#~. The wavefunction of the group of 1 + states strongly populated in (e, e' ) and (?, y' ) at 3.1 MeV do not contain significant components of 7 / 2 - [523] × 5 / 2 - [532]. The structure of these states and the remaining 1+ states near 2.5 MeV may involve quasiproton configurations associated with large M1 strength, but not accessible in the (t, a) reaction (e.g. 7 / 2 - [ 5 2 3 ] × 9 / 2 - [ 5 1 4 ] , 5/ 2 - [ 5 3 2 ] × 3 / 2 - [ 5 3 2 ] or 3 / 2 - [ 5 3 2 ] X 1 / 2 - [ 5 4 1 ] , see ref. [ 20 ] ), or a collective M 1 interpretation may be appropriate. Clearly the microscopic structure of the remaining 1 + states is a matter of considerable interest. This work was supported by the U K Science and Engineering Research Council and the Danish Natural Science Research Council. One of us (S.J.F.) wishes to acknowledge receipt of an SERC student-
Volume 222, number 3,4
PHYSICS LETTERS B
ship. V a l u a b l e d i s c u s s i o n s w i t h I. H a m a m o t o gratefully acknowledged.
are
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