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Shape transition in neutron deficient Pt isotopes
Volume 217, number 4
PHYSICS LETTERS B
2 February 1989
SHAPE TRANSITION IN NEUTRON DEFICIENT Pt ISOTOPES
H.T. DUONG, J. PINARD, S. L I B E R M A N Laboratoire Aim( Cotton, CNRS I1, F-91405 Orsay, France
G. SAVARD, J.K.P. LEE, J.E. CRAWFORD, G. T H E K K A D A T H Foster Radiation Laboratory, McGill University, Montreal, Quebec, Canada H3A 2B2
F. LE BLANC, P. K I L C H E R , J. OBERT, J. OMS, J.C. P U T A U X , B. ROUSSII~RE, J. SAUVAGE and the ISOCELE Collaboration Institute de Physique NuclOaire, F-91405 Orsay, France
Received 27 September 1988
Isotope shift (IS) and hyperfine structure (HFS) measurements have been performed for 185A87"IS9"IgI'IqSPtusing the PILLS (Post ISOCELE Laser Isobar Separation) apparatus installed at the ISOCELE facility. Magnetic and quadrupole moments have been deduced from the HFS results. The change radius changes determined for these odd nuclei from the IS results, added to the (r 2) values of the even-A nuclei, are compared to the results of lattice Hartree-Fock + BCS calculations for asymmetric solutions. 18~Ptis confirmed to be prolate shaped whereas 187,~9.~9~Ptare likely triaxial in their ground states.
In the transitional region between the well-deformed rare-earth nuclei and the spherical doubly magic nucleus 2°Spb, shape coexistence p h e n o m e n a and related ground-state shape transitions have been observed; this has provided the motivation for a large n u m b e r of e x p e r i m e n t a l and theoretical studies. The m e a s u r e m e n t o f isotopic shifts ( I S ) , which gives inf o r m a t i o n about the v a r i a t i o n o f the nuclear charge radius for neighbouring isotopes, is the most modeli n d e p e n d e n t signature o f a shape transition. Thus the shape coexistence o f Hg nuclei has been observed as an o d d - e v e n charge radius staggering in the light Hg isotopes [ 1 ] ; the even-A Hg ground states continue to be weakly-deformed oblate, whereas the odd-A ones become well-deformed prolate when A decreases. Shape coexistence in Au nuclei resulting in a groundstate shape transition is observed as a very sharp increase o f the charge radius between A = 187 and A = 186 [2,3 ]. In the p l a t i n u m nuclei, nuclear structure m e a s u r e m e n t s indicate the presence o f shape coexistence at low energy in the even-A isotopes between A = 176 a n d A = 190 [ 4 - 6 ] , and in the odd-A
isotopes, at least in 187pt [ 7 - 9 ]. In even-A isotopes, the relative position o f the 2 f and 4 + excited states suggests that a ground-state transition occurs between A - 1 8 8 and A = 1 8 6 [ I 0 ] . However, even though our recent IS m e a s u r e m e n t s have shown a sharp change o f the charge-radius differences between even-A isotopes which supports a transition between A = 188 and A - - 186 [ 1 1,12 ] there is no evident discontinuity o f the charge radius similar to that observed in Au and Hg isotopes. In the odd-A nuclei, studies o f the Yrast bands observed in (HI, xn7) reactions indicate clearly that the shape o f the nucleus in high-spin states changes between A = 187 and A = 185 [ 13 ]. This implies that the I ~= 9 / 2 + groundstate o f lssPt corresponds to a prolate nuclear shape. However, it is much more difficult to d e t e r m i n e the shape o f the 3 / 2 - ground states o f heavier odd-A p l a t i n u m nuclei, especially in 187pt [ 7,9 ]. Therefore the exact location o f the ground-state shape transition is still an open question. It should be noted that theoretical calculations have predicted that in the region of the shape transition the p l a t i n u m nucleus
401
Volume 217, number 4
PHYSICS LETTERS B
passes through a triaxial shape and may exhibit 7softness [ 14,15 ]. In order to provide new information about the ground-state shape transition in the platinum isotopes we have performed IS and hyperfine structure (HFS) measurements in the 185'187"189'191'195ptisotopes that we present here. Radioactive Au isotopes are produced by (p, xn) reactions on a Pt-B molten target [ 16 ] placed inside the ISOCELE mass separator [ 17 ] ion source. The 45 keV radioactive ion beam extracted from the source is mass separated and slowed to 0.5 keV before being implanted in a graphite support. The graphite sample which is mounted on an insulating tape transport system is then moved from the high-voltage decelerating region to the input of an electrostatic time-of-flight system. The gold ions decay to the platinum daughter nuclei and are then desorbed by a heating pulse from a Nd: Yag laser. The desorbed Pt atoms are selectively ionized via a resonant ionization spectroscopy (RIS) process by three synchronized laser pulses, and the ions created are detected by a microchannel plate after time-of-flight mass identification. The high-resolution laser spectroscopy is performed on the first excitation step (at 266 rim) of the RIS process. For this, a single-mode continuously tunable pulsed dye laser system is used [ 18 ]. The laser pulses delivered by this system are frequency doubled in a K D P crystal to obtain the 266 nm UV wavelength. Relative and absolute frequency calibrations are obtained by a Fabry-Perot etalon and an iodine absorption cell. The second and third steps at 676 nm and 500 nm are excited by two pulsed dye lasers pumped by the same excimer laser. In the configuration used for these experiments, the apparatus PILIS [19] has an efficiency of about 10 -5 with a resolution of 600 MHz. More details on the experimental technique can be found in refs. [ 11,19 ]. The HFS and IS of lss"lsT'189"191'195pt obtained from 266 nm (5d96s 3D3-* 5d96p 7 4) resonant transition are shown in fig. 1, together with even-A results previously obtained [ 12 ]. The magnetic moments p~ are obtained from the magnetic HFS coupling constant A, and the known value of #~95 from JZi = ( A i / A195 ) JA195 ,
where the precision of the extraction procedure is limited only by the hyperfine anomaly. The spectroscopic quadrupole moments are obtained from the 402
2 February 1989
------~---
--
198 10GNz 196 195 194
_ -2i
192 191 190 189 188
187 .......
i, ~,~ j
....
)
_ _
186 185
FREQUENCY
Fig. 1. Measured relative frequencies and intensities of Pt isotopes from A = 185 to 198.
measured quadrupole HFS coupling constant B through a semi-empirical calculation of the electric field gradient at the nucleus from the fine structure splitting of the 3D configuration. The Qs values are not corrected for the Sternheimer effect since no calculations are available in this mass region. We estimate from values calculated for similar configurations that such an effect could decrease the absolute Qs values by about 30%; the relative values are however still very reliable. The nuclear magnetic dipole and electric quadrupole moments deduced from the HFS are compiled in table 1. They are in agreement with the NICOLE collaboration values [ 20 ] and with the results already known for 189'191pt [21 ]. The experimental IS (relative to ~9spt) are given in table 2, together with even-A results previously obtained [ 12 ]. The IS consists of a mass shift and a field shift [23 ]. For heavy elements, the mass shift contribution is small. We have corrected our results for the easily calculated normal shift. On the other hand, the specific mass shift cannot be reliably evaluated, but from empirical estimates for similar atomic transiTable 1 Experimental magnetic dipole and electric quadrupole m o m e n t s for 185j87,189191p[
A(P)
~(nN)
0s(b)
185(9/2 + ) 187(3/2 ) 189(3/2 ) 191(3/2-)
-0.83(1) -0.397(5) -0.421(5) --0.501(5)
+4.3(5) -1.13(5) -1.03(5) --0.98(5)
Volume 217, number 4
PHYSICS LETTERS B
2 February1989
Table 2 Experimental results, deduced nuclear parameter 2 and 6( r 2) values, and deformation parameter fl values, A
z~v198,t (GHz)
AI98,.I (Fm 2)
6
d(fl 2)
(f12) i/2
198 196 195 194 192 191 190 189 188 187 186 185
0 1.55(4) 2.05(7) 2.97(6) 4.20(5) 5.65(6) 5.41(4) 6,47(6) 6.49(3) 6.44(3) 6,94(8) 4.50(10)
0 -0.059(3) -0.078(6) -0.113(9) -0.160(8) -0.215(12) -0.206(10) -0.246(11) -0.247(9) -0.245(8) -0.264(10) -0.171(13)
0 -0.0628(3) -0.081(6) -0.118(9) -0.167(8) -0.226(13) -0.215(10) -0.257(12) -0.257(9) -0.254(9) -0.273(11) -0.171(14)
0 0.0037(3) 0.0065(5) 0.0079(8) 0.0126(7) 0.0121(10) 0.0175(9) 0.0184(10) 0.0228(8) 0.0275(8) 0.0304(9) 0.0436(13)
0. ll al 0.12 0.14 0.14 0.16 0.16 0.17 0.17 0.19 0.20 0.21 0.24
"~ Ref. [22].
tions [23] we can assume it to be negligible. The nuclear p a r a m e t e r 2 is extracted from the remaining field shift 6v~fl ' using 8 pA~4' = F266) A,A' ----F26615 ( r2>d'A' @ ( C 2 / C 1 ) 6 (r4> 4"4' Jr- ( C 3 / C 1 )6~
G H z / f m 2 is the electronic factor for the transition evaluated from a c o m p a r i s o n of our even-A results [ 12 ] with those t a b u l a t e d on the stable p l a t i n u m isotopes for other a t o m i c transitions [23 ]. The errors quoted in table 2 include only statistical uncertainties; the extraction of,~ A'A' from the field shift can introduce a small a d d i t i o n a l scaling error which would, however, not change the general aspect o f fig. 2. The changes in m e a n - s q u a r e charge radius 6
plies the same sign for both spectroscopic and intrinsic q u a d r u p o l e moments. The nature o f the shapes o f Pt nuclei with 186 ~
02
A
.
7BP t
......-f"
^o % V
-0.2
-o.L
'4o'
'
'
'+'
'
' A
~
202
Fig. 2. Experimental change in mean-square charge radius (relative to ~98pt) compared with the results obtained from lattice Hartree-Fock+BCS calculations [28] (see text). 403
Volume 217, number 4
PHYSICS LETTERS B
2 February 1989
Table 3 Experimental magnetic dipole moments #~o and theoretical values #~hobtained from two axially symmetric approaches (see text). The gR and g~ values are Z / A and 0 respectively.The calculations reported in column 4 have been performed for q=4 or r/= -4; those in columns 5 and 6 with core deformations f12(~84pt)= +0.27, f12(186pt)= +0.26 or -0.24, fie(~ssPt)=-0.24, f12(19°Pt)=-0.22, and ]]2(t92Pt) = -0.20. A
State
Peep
]/th a )
# t h b)
g~.f~e~ (0.6 g~s~¢e)
191 189 187 185 ") Ref. [31].
3/2-[532] 3/2-[532] 3/2-[5321 9/2+[624]
-0.48(1) -0.40(1) -0.41(3) -0.83(1)
+0.48(+0.39) +0.48(+0.39) +0.48(+0.39) -0.97(-0.45)
gs,free
A+IPt+ 1 qp (0.6 gs.rr~)
+0.39(+0.31) +0.53(+0.39) +0.71(+0.53) -1.3(-0.73)
+0.19(+0.19) +0.39(+0.31) +0.53(+0.39) -1.4(-0.79)
b) Rev.[32].
which have been inferred to have weakly oblate shapes [1,251. Several theoretical approaches have been used to calculate the potential energy surfaces of the platin u m nuclei, either assuming axial symmetry or taking into account the 7 degree of freedom [ 15,26 ]. I n all cases the deformation of the e q u i l i b r i u m solutions are similar, which can explain why the change of ( r 2 ) is smaller than that observed for the Au a n d Hg isotopes. Lattice H a r t r e e - F o c k + B C S calculations for axially asymmetric solutions using the method described in ref. [27] have been performed for platin u m isotopes, they predict a prolate shape for IS6.l S8pt, a triaxial shape for 190.~92,194pt and an oblate shape for the heavier isotopes and are able to reproduce the general trend of the experimental ~ ( r e ) (see fig. 2) [ 14,28 ]. Dynamical effects which are not taken into account in these calculations can play a role because of the softness of the potential energy surface found for the p l a t i n u m isotopes [14,29,30], and might be responsible for the differences between experimental a n d theoretical results. Assuming axial symmetry, theoretical ~ti values have been calculated using the Nilsson model [ 31 ] and a r o t o r + q u a s i p a r t i c l e model which takes into account the Coriolis effect [32] (see table 3). The 187.189.~9~pt are not prolate; thus we compare the ]2ex p values of their ground states to those calculated assuming oblate-shaped nuclei. Unfortunately the signs are not reproduced correctly. It is worth noting that it is difficult to represent the spectroscopic properties of the oblate-shaped nuclei in this mass region [ 33 ]. O n the other hand, in the case of lsspt for both cal404
"~-tPt+ 1 qp gs,free (0.6 gs.free)
culations, ~texpis in good agreement with the #,~ value calculated with the prolate-shaped core. These results, added to the above IS results, allow us to conclude that the shape transition from an oblate (or more likely triaxial) shape to a prolate shape takes place between A-- 186 and A = 18 5. We sincerely t h a n k Dr. M. Meyer and J. Libert for fruitful discussions.
References
[1] G. Ulm et al., Z. Phys. A 325 (1986) 247, and references therein. [2 ] K. Wallmeroth et al., Phys. Rev. Len. 58 ( 1987) 1516. [3] J.K.P. Lee et al., Fifth Intern. Conf. on Nuclei far from Stabilitily (Rosseau Lake), AIP Conf. Proc., Vol. 164 (AIP, New York, 1988) p.205. [4 ] G.D. Dracoulis et al., J. Phys. G 12 ( 1986) L97. [ 5] J.L. Wood, in: Lasers in nucler physics,Nucl. Sci. Res. Conf. Series (Harwood Academic,New York, 1982) p. 481. [6] G. Hebbinghaus et al., Z. Phys. A 328 (1987) 387. [7] A. Ben Braham et al., Nucl. Phys. A 332 (1979) 397. [8] B.E. Gnade, R.W. Fink and J.L. Wood, Nucl. Phys. A 406 (1983) 29. [9 ] B. Roussi~re, Th6se, Orsay ( 1986). [10] K. Kumar, Phys. Rev. C 1 (1970) 369; M. Finger et al., Nucl. Phys. A 188 (1972) 369. [ 111 J.K.P. Lee et al., Proc. XXVI Intern. Conf. on Nuclear physics (Bormio,Italy, 1988) p. 523, and referencestherein. [ 12] J.K.P. Lee et al., Phys. Rev. C, Rapid Comm. ( 1988), to be published. [ 13] M.A. Deleplanque et al., J. Phys. (Paris) 36, C5 ( 1975) 97.
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PHYSICS LETTERS B
I14] P. Quentin, Proc. 4eme Colloq. Franco-Japonais (Seillac, 1986), report CEN Saclay 87-022 (DOC, CEN Saclay, I987) p. 83; N. Redon, Thbse, Lyon (1987). [15] R. Bengtson et al., Phys. Lett. B 183 (1987) 1. [ 161 J.C. Putaux et al., Nucl. Instrum. Methods 186 ( 1981 ) 321. [ 17 ] P. Paris et al., Nucl. Instrum. Methods 186 ( 1981 ) 91. [ 18 ] J. Pinard and S. Libermam Opt. Commun. 20 (1977) 344. [ 19 ] J.K.P. Lee et al., Nucl. Instrum. Methods B 34 ( 1988 ) 252, and references therein. [20] NICOLE Collab., ISOLDE, private communication; and Workshop on On-line nuclear orientation and related topics (Oxford, September 1988 ) Hyp. lnt., to be published. [21] R. Eder, E. Hagn and E. Zech, Phys. Lett. B 158 (1985) 371. [22] P, M6ller, J. Nix, At. Data Nucl. Tables 26 ( 1981 ) 165.
2 February 1989
[23] P. Aufmutb, K. Heilig and A. Steudel, At. Data Nucl. Tables 37 (1987) 455. [24] B. Roussibre et al., Nucl. Phys. A 438 ( 1985 ) 93. [25] K. Heyde et al., Phys. Rep. 102 (1983) 291. [26] N. Redon et al., Phys. Lett. B 181 (1986) 223. [27] P. Bonche et al., Nucl. Phys. A 443 (1985) 39. [28] H. Flocard, P. Bonche, P.H. Heenen, M. Weiss, S. Krieger, N. Redon, M. Meyer, J. Meyer and P. Quentin, to be published. [29] M. Veskovic, M.K. Harder, K. Kumar and W.D. Hamilton, J. Phys. G 13 (1987) L155. [ 30 ] L. Bennour, Th6se, Orsay (1987). [31 ] S.G. Nilsson, Dan Mat. Fys. Medd. 29 no. 16 (1955). [ 32 ] J. Libert, M. Meyer and P. Quentin, Phys. Rev. C 25 ( 1982 ) 586. [33] M.G. Porquet, J. Sauvage, M. Meyer and P. Quentin, Nucl. Phys. A 451 (1986) 365.
405
PHYSICS LETTERS B
2 February 1989
SHAPE TRANSITION IN NEUTRON DEFICIENT Pt ISOTOPES
H.T. DUONG, J. PINARD, S. L I B E R M A N Laboratoire Aim( Cotton, CNRS I1, F-91405 Orsay, France
G. SAVARD, J.K.P. LEE, J.E. CRAWFORD, G. T H E K K A D A T H Foster Radiation Laboratory, McGill University, Montreal, Quebec, Canada H3A 2B2
F. LE BLANC, P. K I L C H E R , J. OBERT, J. OMS, J.C. P U T A U X , B. ROUSSII~RE, J. SAUVAGE and the ISOCELE Collaboration Institute de Physique NuclOaire, F-91405 Orsay, France
Received 27 September 1988
Isotope shift (IS) and hyperfine structure (HFS) measurements have been performed for 185A87"IS9"IgI'IqSPtusing the PILLS (Post ISOCELE Laser Isobar Separation) apparatus installed at the ISOCELE facility. Magnetic and quadrupole moments have been deduced from the HFS results. The change radius changes determined for these odd nuclei from the IS results, added to the (r 2) values of the even-A nuclei, are compared to the results of lattice Hartree-Fock + BCS calculations for asymmetric solutions. 18~Ptis confirmed to be prolate shaped whereas 187,~9.~9~Ptare likely triaxial in their ground states.
In the transitional region between the well-deformed rare-earth nuclei and the spherical doubly magic nucleus 2°Spb, shape coexistence p h e n o m e n a and related ground-state shape transitions have been observed; this has provided the motivation for a large n u m b e r of e x p e r i m e n t a l and theoretical studies. The m e a s u r e m e n t o f isotopic shifts ( I S ) , which gives inf o r m a t i o n about the v a r i a t i o n o f the nuclear charge radius for neighbouring isotopes, is the most modeli n d e p e n d e n t signature o f a shape transition. Thus the shape coexistence o f Hg nuclei has been observed as an o d d - e v e n charge radius staggering in the light Hg isotopes [ 1 ] ; the even-A Hg ground states continue to be weakly-deformed oblate, whereas the odd-A ones become well-deformed prolate when A decreases. Shape coexistence in Au nuclei resulting in a groundstate shape transition is observed as a very sharp increase o f the charge radius between A = 187 and A = 186 [2,3 ]. In the p l a t i n u m nuclei, nuclear structure m e a s u r e m e n t s indicate the presence o f shape coexistence at low energy in the even-A isotopes between A = 176 a n d A = 190 [ 4 - 6 ] , and in the odd-A
isotopes, at least in 187pt [ 7 - 9 ]. In even-A isotopes, the relative position o f the 2 f and 4 + excited states suggests that a ground-state transition occurs between A - 1 8 8 and A = 1 8 6 [ I 0 ] . However, even though our recent IS m e a s u r e m e n t s have shown a sharp change o f the charge-radius differences between even-A isotopes which supports a transition between A = 188 and A - - 186 [ 1 1,12 ] there is no evident discontinuity o f the charge radius similar to that observed in Au and Hg isotopes. In the odd-A nuclei, studies o f the Yrast bands observed in (HI, xn7) reactions indicate clearly that the shape o f the nucleus in high-spin states changes between A = 187 and A = 185 [ 13 ]. This implies that the I ~= 9 / 2 + groundstate o f lssPt corresponds to a prolate nuclear shape. However, it is much more difficult to d e t e r m i n e the shape o f the 3 / 2 - ground states o f heavier odd-A p l a t i n u m nuclei, especially in 187pt [ 7,9 ]. Therefore the exact location o f the ground-state shape transition is still an open question. It should be noted that theoretical calculations have predicted that in the region of the shape transition the p l a t i n u m nucleus
401
Volume 217, number 4
PHYSICS LETTERS B
passes through a triaxial shape and may exhibit 7softness [ 14,15 ]. In order to provide new information about the ground-state shape transition in the platinum isotopes we have performed IS and hyperfine structure (HFS) measurements in the 185'187"189'191'195ptisotopes that we present here. Radioactive Au isotopes are produced by (p, xn) reactions on a Pt-B molten target [ 16 ] placed inside the ISOCELE mass separator [ 17 ] ion source. The 45 keV radioactive ion beam extracted from the source is mass separated and slowed to 0.5 keV before being implanted in a graphite support. The graphite sample which is mounted on an insulating tape transport system is then moved from the high-voltage decelerating region to the input of an electrostatic time-of-flight system. The gold ions decay to the platinum daughter nuclei and are then desorbed by a heating pulse from a Nd: Yag laser. The desorbed Pt atoms are selectively ionized via a resonant ionization spectroscopy (RIS) process by three synchronized laser pulses, and the ions created are detected by a microchannel plate after time-of-flight mass identification. The high-resolution laser spectroscopy is performed on the first excitation step (at 266 rim) of the RIS process. For this, a single-mode continuously tunable pulsed dye laser system is used [ 18 ]. The laser pulses delivered by this system are frequency doubled in a K D P crystal to obtain the 266 nm UV wavelength. Relative and absolute frequency calibrations are obtained by a Fabry-Perot etalon and an iodine absorption cell. The second and third steps at 676 nm and 500 nm are excited by two pulsed dye lasers pumped by the same excimer laser. In the configuration used for these experiments, the apparatus PILIS [19] has an efficiency of about 10 -5 with a resolution of 600 MHz. More details on the experimental technique can be found in refs. [ 11,19 ]. The HFS and IS of lss"lsT'189"191'195pt obtained from 266 nm (5d96s 3D3-* 5d96p 7 4) resonant transition are shown in fig. 1, together with even-A results previously obtained [ 12 ]. The magnetic moments p~ are obtained from the magnetic HFS coupling constant A, and the known value of #~95 from JZi = ( A i / A195 ) JA195 ,
where the precision of the extraction procedure is limited only by the hyperfine anomaly. The spectroscopic quadrupole moments are obtained from the 402
2 February 1989
------~---
--
198 10GNz 196 195 194
_ -2i
192 191 190 189 188
187 .......
i, ~,~ j
....
)
_ _
186 185
FREQUENCY
Fig. 1. Measured relative frequencies and intensities of Pt isotopes from A = 185 to 198.
measured quadrupole HFS coupling constant B through a semi-empirical calculation of the electric field gradient at the nucleus from the fine structure splitting of the 3D configuration. The Qs values are not corrected for the Sternheimer effect since no calculations are available in this mass region. We estimate from values calculated for similar configurations that such an effect could decrease the absolute Qs values by about 30%; the relative values are however still very reliable. The nuclear magnetic dipole and electric quadrupole moments deduced from the HFS are compiled in table 1. They are in agreement with the NICOLE collaboration values [ 20 ] and with the results already known for 189'191pt [21 ]. The experimental IS (relative to ~9spt) are given in table 2, together with even-A results previously obtained [ 12 ]. The IS consists of a mass shift and a field shift [23 ]. For heavy elements, the mass shift contribution is small. We have corrected our results for the easily calculated normal shift. On the other hand, the specific mass shift cannot be reliably evaluated, but from empirical estimates for similar atomic transiTable 1 Experimental magnetic dipole and electric quadrupole m o m e n t s for 185j87,189191p[
A(P)
~(nN)
0s(b)
185(9/2 + ) 187(3/2 ) 189(3/2 ) 191(3/2-)
-0.83(1) -0.397(5) -0.421(5) --0.501(5)
+4.3(5) -1.13(5) -1.03(5) --0.98(5)
Volume 217, number 4
PHYSICS LETTERS B
2 February1989
Table 2 Experimental results, deduced nuclear parameter 2 and 6( r 2) values, and deformation parameter fl values, A
z~v198,t (GHz)
AI98,.I (Fm 2)
6
d(fl 2)
(f12) i/2
198 196 195 194 192 191 190 189 188 187 186 185
0 1.55(4) 2.05(7) 2.97(6) 4.20(5) 5.65(6) 5.41(4) 6,47(6) 6.49(3) 6.44(3) 6,94(8) 4.50(10)
0 -0.059(3) -0.078(6) -0.113(9) -0.160(8) -0.215(12) -0.206(10) -0.246(11) -0.247(9) -0.245(8) -0.264(10) -0.171(13)
0 -0.0628(3) -0.081(6) -0.118(9) -0.167(8) -0.226(13) -0.215(10) -0.257(12) -0.257(9) -0.254(9) -0.273(11) -0.171(14)
0 0.0037(3) 0.0065(5) 0.0079(8) 0.0126(7) 0.0121(10) 0.0175(9) 0.0184(10) 0.0228(8) 0.0275(8) 0.0304(9) 0.0436(13)
0. ll al 0.12 0.14 0.14 0.16 0.16 0.17 0.17 0.19 0.20 0.21 0.24
"~ Ref. [22].
tions [23] we can assume it to be negligible. The nuclear p a r a m e t e r 2 is extracted from the remaining field shift 6v~fl ' using 8 pA~4' = F266) A,A' ----F26615 ( r2>d'A' @ ( C 2 / C 1 ) 6 (r4> 4"4' Jr- ( C 3 / C 1 )6~
G H z / f m 2 is the electronic factor for the transition evaluated from a c o m p a r i s o n of our even-A results [ 12 ] with those t a b u l a t e d on the stable p l a t i n u m isotopes for other a t o m i c transitions [23 ]. The errors quoted in table 2 include only statistical uncertainties; the extraction of,~ A'A' from the field shift can introduce a small a d d i t i o n a l scaling error which would, however, not change the general aspect o f fig. 2. The changes in m e a n - s q u a r e charge radius 6
plies the same sign for both spectroscopic and intrinsic q u a d r u p o l e moments. The nature o f the shapes o f Pt nuclei with 186 ~
02
A
.
7BP t
......-f"
^o % V
-0.2
-o.L
'4o'
'
'
'+'
'
' A
~
202
Fig. 2. Experimental change in mean-square charge radius (relative to ~98pt) compared with the results obtained from lattice Hartree-Fock+BCS calculations [28] (see text). 403
Volume 217, number 4
PHYSICS LETTERS B
2 February 1989
Table 3 Experimental magnetic dipole moments #~o and theoretical values #~hobtained from two axially symmetric approaches (see text). The gR and g~ values are Z / A and 0 respectively.The calculations reported in column 4 have been performed for q=4 or r/= -4; those in columns 5 and 6 with core deformations f12(~84pt)= +0.27, f12(186pt)= +0.26 or -0.24, fie(~ssPt)=-0.24, f12(19°Pt)=-0.22, and ]]2(t92Pt) = -0.20. A
State
Peep
]/th a )
# t h b)
g~.f~e~ (0.6 g~s~¢e)
191 189 187 185 ") Ref. [31].
3/2-[532] 3/2-[532] 3/2-[5321 9/2+[624]
-0.48(1) -0.40(1) -0.41(3) -0.83(1)
+0.48(+0.39) +0.48(+0.39) +0.48(+0.39) -0.97(-0.45)
gs,free
A+IPt+ 1 qp (0.6 gs.rr~)
+0.39(+0.31) +0.53(+0.39) +0.71(+0.53) -1.3(-0.73)
+0.19(+0.19) +0.39(+0.31) +0.53(+0.39) -1.4(-0.79)
b) Rev.[32].
which have been inferred to have weakly oblate shapes [1,251. Several theoretical approaches have been used to calculate the potential energy surfaces of the platin u m nuclei, either assuming axial symmetry or taking into account the 7 degree of freedom [ 15,26 ]. I n all cases the deformation of the e q u i l i b r i u m solutions are similar, which can explain why the change of ( r 2 ) is smaller than that observed for the Au a n d Hg isotopes. Lattice H a r t r e e - F o c k + B C S calculations for axially asymmetric solutions using the method described in ref. [27] have been performed for platin u m isotopes, they predict a prolate shape for IS6.l S8pt, a triaxial shape for 190.~92,194pt and an oblate shape for the heavier isotopes and are able to reproduce the general trend of the experimental ~ ( r e ) (see fig. 2) [ 14,28 ]. Dynamical effects which are not taken into account in these calculations can play a role because of the softness of the potential energy surface found for the p l a t i n u m isotopes [14,29,30], and might be responsible for the differences between experimental a n d theoretical results. Assuming axial symmetry, theoretical ~ti values have been calculated using the Nilsson model [ 31 ] and a r o t o r + q u a s i p a r t i c l e model which takes into account the Coriolis effect [32] (see table 3). The 187.189.~9~pt are not prolate; thus we compare the ]2ex p values of their ground states to those calculated assuming oblate-shaped nuclei. Unfortunately the signs are not reproduced correctly. It is worth noting that it is difficult to represent the spectroscopic properties of the oblate-shaped nuclei in this mass region [ 33 ]. O n the other hand, in the case of lsspt for both cal404
"~-tPt+ 1 qp gs,free (0.6 gs.free)
culations, ~texpis in good agreement with the #,~ value calculated with the prolate-shaped core. These results, added to the above IS results, allow us to conclude that the shape transition from an oblate (or more likely triaxial) shape to a prolate shape takes place between A-- 186 and A = 18 5. We sincerely t h a n k Dr. M. Meyer and J. Libert for fruitful discussions.
References
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PHYSICS LETTERS B
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2 February 1989
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