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Rotational bands in O16
7~!~
12, m l m ~ r ~
PHYSICS
ROTATIONAL
LETTERS
1 October 1964
B A N D S I N 0 16
J. BORYSOWICZ * and R. I~ ~HELINE ** Instttut~ fo~ Theoretical l~kyn~c~, University of Copenhagen~ Denmark Received 28 August 19£4 Theprob~ble e ~ m n c e 1) of rotational bands in 016 h a s been recognized f o r s o m e time. Howe v e r , it wan not untll the r e c e n t dofi~i~ve e x p o r i m e n t s 2) of Gorodetz~y e t a l . and of C a r t e r nt al. that the extent ~ band formation w a s fuily realized, In view of the important implication that the f i r s t excRed state of the double closed shell anclens 016 is a l r e a d y dstormed, it seem~ imp~jrtant to an~yze the empirical bands observed in terms of the theoretical conflgur~tlons and eiruchtres to be expected, A powerful method f o r investigatlen of the collective motions in nuclei based on SU3 s y m m e t r y grOu.p ~ been given by Elllott 3). Applying this s c h e m e Brin~ and Nash ~ anstgned ~42) ~ 3 s+ymmerry for the bamls l~sed on the O ~o s t a t e s . 0 at 6.06 MeV and 2+ at 9.84 MeV. Engeiznd S), a s suming f o r h~w lying s ~ t e s in 0 16 and O ! 8 e o r r e epondLngly (42) and (82) SU3 s y m m e t r ! e s , obtained the l a r g e transition probabilities demanded by e x perlmenf, and good a~reement with th e experi~,, mental spectrum in O ~e. A recent calculation ol by one o~ us (J.B.) e o r J i r m s the existence of r o tational bands for even p a r i t y s t a t e s in 016 , and to s o m e extent the validity M the SU3 s c h e m e . In the calcwiafion all.even p a r i t y one p a r t i c l e - o n e hole ~ d two particle - two hole states with 2 ~ e ~ ttation and [4444] W i ~ m r supermuitiplet symmetry have been taken into account. The calculated s p e c t r u m m u s t be shifted about 17 M e V to fit ~ e experimental ,0+ state at 6,06 MeV. The expianatton of t h i s discrepancy m a y be found at l e a s t in p a r t in the simplified F~tllio-Kolltveit potential 7) and in th e too large oucfllator shell spacing used in the calcuIRflon. M o r e detailed * On leave from h ~ T~etttote for:Nuclear ResearCh, Warsaw. Poland, Supported by a grant from tim~ Ford F ~ m . ** ~zpported by the U.S. Ahnntc E n e r ~ Commissiun No. AT - (40-1) ,-2434j~ by the Guggunhetm Memorial Foundation, and by the:Institute for Theoreticat Phynios, Cc,gunlmgen, Perm~unt address: Nuclear Rssearoh Bldg., Florida State University, T~Em, Florkla.
discussion of these points will be given 6). The comparison between experiment and the preliminary resalts of the calculation are shown in fig. 1. T h e a g r e e m e n t is quite satisgnctory. In p a r t i c uinr the (42), (04) and (31) SU 3 desi~tions are clearly ~¢apresented a s well devalop~i rotational bands with con~Iderable.SU 8 content in the states. Even more gratffy~ is the fact th~t~the calc~daflons give upproxlmately the experimental, moments of inertia and the observed relative positions of the bands. R is also Interest~g to note that all experhnentally observed evan p~rity states up to an energy of 14,8 MeV, with the ex.ception of the 2+ state at 13.1 MeV, have been used in the experimental interpremtlon presented. The SU 3 deslg~mtion seems appropr .intesince the overlaps between the calculated and pure SU~ wave functions a r e v e r y l a r g e for the band heads (~ 0.9o) d i m i n i s h i ~ semewhat (~ o.so) t o t the intermediate m e m b e r of R e bands. Unnatural p a r r y states and high spin members usu~lly have h i g h e r o v e r l a p s again. The comparison between the eape~imental ~ J calculated (42) bands shows clearly the existence of K = 0 a n d K = 2hands. In bet~ c a s e s the cal~ culatod m o m e n t s of i n e r t i a are ~omewhat l a r g e r than the experimentally observed ones. P e r h a p s the m o s t interesting feature of the (04) band is the fact thor the SU3 deslg~mtion ~ g g e s t s that i t should have an oblate d e f o r m e d . The 0 + band head calculated at I0.05 M e V has a large (0.83) overlap with the (04) SU 3 state. The next caleuinted 2+ state at 10.46 M c V corre~oed~ g to the e~porimentally observed state at 11.5t MeV h a s ~ s m a l l overlap (0.13). Although eeorgefically i t rite into the band, the overlap indiCates i t s foreign nature. The second 3 ~ state calenlated a t 14.3 M e V , and e ~ e r h n e n t a l I y o b s e r v ed a t 14,72 o r 15.25 MeV l ~ s a ~ overlap (0.88):consistent with the (04) SU3 interpretation. S i m i l a r statements :apply with r e g a r d to the 4 + state e ~ i m e n t h l l y observed at 16.8 MeV and calcnlated at 14.86 MeW It i s interesting to 219
Volume 12, number 3
PHYSICS L E T T E R S
10eto&er 1964
C
£
fi~__
I
15
(b)
, ~,
;4 2)
~4 2)
(0 4)
(3 ~)
Fig. 1. E~perimental andl~alculatedeven parity levels in 016. a). Experimental levele and spin a~ignmen~ 2,1 ). All even parity levels are given up to 14,8 ICmVexcept tim 13.1 MeV level which recent m e a s a r e m ~ 2) have elmw~ to have spin*parity 2+ in addition to the previous l-asslgnment; b. Theoretical levels. Thsee levels are eblftod down 17 MeV, The dornln~t SUz configurations are given below the apprc~pr~e basis. that only these assignments of the (04) band have large experimental alplm widths. Both the overlaps with SU3 states and the energy agreement between the calculated spectrum and the experimentally observed spectrum indicate that the 1+ state at 13.65 MeV with ~uperimposed rotational band (3÷ member missing) and the 1+ state at 18.21 MeV are the two (81) configurations expected. It would be particularly worthwhile to observe experimentally the expected 5 ÷ member of the (42) band mud the 3+ member of the (31) band. These states are expected at ~ 19 and ~ 15 MeV r e s p e c tively. The negative parity states in 016 obviously fit empirically into rotational bands. However, the theoretical interpretatior of these states i s much more ambi~aous. Gillet ~nd vtnk-Mau 8) and more recently Erikson 9, have Lutorpreted the lowest lying 3-, 1" states as essentially one partiele - one hole states. (Although the strong E2 between them indicates three p~rticle - three hole admixture. ) The most deformed ~J3 eoatiguration for 3~w excitation is (~3) which could be the band begir~uing with ~pin 1" ~ 9.58 MeV. This b~_nd utilizes the 2- state at 8.88 M e V which does not fit well i~to band energy systematics. An alternative e ~ l a n a t i o n would involve the (52) configuration which may ~e rea~Azed from both ~ o particle - two hole and three particle th~°ee hole excitations. This provides naturally the 1-, 8% 5- and 7" spin sequence (K = 0) and the K = 2 band beg'~r,~g at 12.52 MeV. ~20
R has eormnonly been a~sumed that the rotational bands In the same deformed r]ucleus have approximately the same character. In c~ntradlstinction to this, Mcttelson and Nllsson 10) have suggested that in the region of approximately 90 neutrons quite different prelate deformations may occur within the same nucleus. The interpretation presented here suggests that one may general. ly expect to find spherical, prelate and oblate shapes in the same nucleus. The energetic t h r e s hold for the appearance of these states will v a r y from nucleus to nucleus, making a s e r i e s of complex surfaces on a three dimensional plot of neutron number, proton nunther and energy. In 016, for example, the threshold for prelate deformation is 6.06 M e V while the threshold for oblate deformation i s 11.25 MeV. Thus, it ~eems quite rear~n~hle that one will e:~pect to see not only nuclei with spherical ground states giving r i s e to proLute and oblate excited shapes and states, but also nuclei with deformed ground states containing ~pherical excited states. The authors are e~:iremely grateful for the hospitality exteeded by the Institute for Theoretical Physics and for in~,~piration and guidance from P r o f e s s o r s Bohr, Brovm, itecht and Mottelson, ~nd Dr.David Brink, which have contributed importantly to this research. In particular, one. of us (J.B.) wishes to thank Prof. G,E. Brown for suggesting the calculation.
Volunm 12, nember 3
PHY8ICS LETTERS
I October 1964
4) D. M,Brink and G, F, Eash, NucL Phys, 40 (1963) I) H, Morhmga, Phys. Rev. I01 (1955) 254; K~ Wildermuth and T. Ksmmllopouloe, CERN Report SS-~, lSS9 (u~pubRohel); R.K.8~leline and K,Wildormuth, Nuel, Phys. 21 (1~1) 196. 2) S,Gorodetzky at al. ,Physics Letters I (1962) 14; E.B, Carter, G.E,Mitcbell and R,H.Devls, Phys, Roe. 133B (1964) 1421~ G,E,Mitohell, E.B.Carter ned R.H,Davin, Phys.
Rev. 133B 0964) 1434. 3) J.P.Elliott~ Proc~ Roy. See. 245 (1958) 128,562.
K-CAPTURE
EFFECTS ON IN G A S E O U S
608,
5) T, Engelaud, to be published in Nuc]. P.hys. ; See also G.E'.Brown, Prec. of ~t. Conf.on NucL Phys., Parts, 1964, 5) J,'Borysowic~, to be published. 7) A.Kallio and K.Kolltveit, NucL Phys; S3 (1964) 87. 5) V.Gllletand N.Vin-Mau, Nuel. Phys. 54 (1964) 321 9) T . E r ~ o n , Nuof. Phys. 55 (1964) 497. 10) B.R.Mottelson and S.G~Nflss0n, Met. Fys. ~ r . Dan. Vld. Selsk. 1 (1959) No. 8. I1) F.Ajzm~borg-Selove and T. Laurlinen,NucL pl~s. 11 (1959) 1,
ANGULAR SOURCES*
CORRELATIONS
H.J. LE~I Ba~oZ Research Foundation of the Franklfn Institute, Swavthmore, Pennsylvan~e
R~eived 17 August 1964 This report is concerned with angular correlation studies using monoatomie gaseous sources. Such a source environment is particularly attractive from the point el view of studying the hyperfine interactionof excited nuclear slates. h' the gas pressure is kept small enough, such thaf there a r e no atomic collisions during the nuclear decay p r o c e s s , the decaying s y s t e m i s completely f r e e f r o m interactions iwith the environment. The only extranuctear interaction by which an angular correlation can be perturbed i~ a gaseous source of low pressure is the leotropic hyperfine interaction, which is theoretically fully understood 1). In cases where this interaction is time-independent during the lifetime of the intermediate state of a garnma-gamma cascade information on nuclear moments of excited states m a y be obtained from the perturbation of the angular correlation P'). One way of creating a hyperfine interactiontu a gaseous source is to select a g a m m a cascade which is preceded by a K-capture decay. R is well known that the rearrangement of the electron shell following K-capture (or internal conversinn) results in the formation of highly ionized atoms ~-~, which, in general, must give r~se to a hyperfine coupling between the atomic shell and ~he nucleus. * Supportedby the Atomic Energy Commlssion~
The g a m m a - g a m m a angul~ correlatlons of the 172-203 knV caso~de in iI27and the S5-188 keV cascade in 1125 were measured with gaseous sources of Xe 127 and X e 125 at totalpressure~ vPxying between I and 4 nun Hg and With xenon carrier pressures between 0.5 aud I m m llg. The mean coUislon times, re, of the active ions after K-capture are estimated to be T C ~ 2 : 4 × 10.9 sec for Xe 127 and Xe 125, respectively. Based on Coulomb excitation measurements of Davis et al. on the 203 keV and 375 keV states in 1127 and assuming the m~me re~ duced g a m m a transitionpro~bilities for the corresponding l~vels 5) in 1125 w e conelud~ ~h~i the totaldecay time for both cascades is mush smaller than the mean coUislon time ~c and therefore, the dccay~.ngatoms are completely free from interactionswith the enviroRment. The Xe 127 - artiTitywas prepared by irradiating KI with protons in the 86-in. cyclotron at th~ C~k Ridge Natlonal Laboratory. The active ~:enon was extracted from the targets and purlfi!ed~y.;m residual gases by a method shnilar to the one described by Balestrini6). The X 1~'~ ~ activitywas obtained by irradlntingr ~ - a l xenon gas, enclosed in a quartz ampoule, in the Oak Ridge Research Reactor, In order to ~ei~a~ ~te off the activities produced in the quart~ ~h~ irradiated ampoule WaS broken under vacu,.m~
12, m l m ~ r ~
PHYSICS
ROTATIONAL
LETTERS
1 October 1964
B A N D S I N 0 16
J. BORYSOWICZ * and R. I~ ~HELINE ** Instttut~ fo~ Theoretical l~kyn~c~, University of Copenhagen~ Denmark Received 28 August 19£4 Theprob~ble e ~ m n c e 1) of rotational bands in 016 h a s been recognized f o r s o m e time. Howe v e r , it wan not untll the r e c e n t dofi~i~ve e x p o r i m e n t s 2) of Gorodetz~y e t a l . and of C a r t e r nt al. that the extent ~ band formation w a s fuily realized, In view of the important implication that the f i r s t excRed state of the double closed shell anclens 016 is a l r e a d y dstormed, it seem~ imp~jrtant to an~yze the empirical bands observed in terms of the theoretical conflgur~tlons and eiruchtres to be expected, A powerful method f o r investigatlen of the collective motions in nuclei based on SU3 s y m m e t r y grOu.p ~ been given by Elllott 3). Applying this s c h e m e Brin~ and Nash ~ anstgned ~42) ~ 3 s+ymmerry for the bamls l~sed on the O ~o s t a t e s . 0 at 6.06 MeV and 2+ at 9.84 MeV. Engeiznd S), a s suming f o r h~w lying s ~ t e s in 0 16 and O ! 8 e o r r e epondLngly (42) and (82) SU3 s y m m e t r ! e s , obtained the l a r g e transition probabilities demanded by e x perlmenf, and good a~reement with th e experi~,, mental spectrum in O ~e. A recent calculation ol by one o~ us (J.B.) e o r J i r m s the existence of r o tational bands for even p a r i t y s t a t e s in 016 , and to s o m e extent the validity M the SU3 s c h e m e . In the calcwiafion all.even p a r i t y one p a r t i c l e - o n e hole ~ d two particle - two hole states with 2 ~ e ~ ttation and [4444] W i ~ m r supermuitiplet symmetry have been taken into account. The calculated s p e c t r u m m u s t be shifted about 17 M e V to fit ~ e experimental ,0+ state at 6,06 MeV. The expianatton of t h i s discrepancy m a y be found at l e a s t in p a r t in the simplified F~tllio-Kolltveit potential 7) and in th e too large oucfllator shell spacing used in the calcuIRflon. M o r e detailed * On leave from h ~ T~etttote for:Nuclear ResearCh, Warsaw. Poland, Supported by a grant from tim~ Ford F ~ m . ** ~zpported by the U.S. Ahnntc E n e r ~ Commissiun No. AT - (40-1) ,-2434j~ by the Guggunhetm Memorial Foundation, and by the:Institute for Theoreticat Phynios, Cc,gunlmgen, Perm~unt address: Nuclear Rssearoh Bldg., Florida State University, T~Em, Florkla.
discussion of these points will be given 6). The comparison between experiment and the preliminary resalts of the calculation are shown in fig. 1. T h e a g r e e m e n t is quite satisgnctory. In p a r t i c uinr the (42), (04) and (31) SU 3 desi~tions are clearly ~¢apresented a s well devalop~i rotational bands with con~Iderable.SU 8 content in the states. Even more gratffy~ is the fact th~t~the calc~daflons give upproxlmately the experimental, moments of inertia and the observed relative positions of the bands. R is also Interest~g to note that all experhnentally observed evan p~rity states up to an energy of 14,8 MeV, with the ex.ception of the 2+ state at 13.1 MeV, have been used in the experimental interpremtlon presented. The SU 3 deslg~mtion seems appropr .intesince the overlaps between the calculated and pure SU~ wave functions a r e v e r y l a r g e for the band heads (~ 0.9o) d i m i n i s h i ~ semewhat (~ o.so) t o t the intermediate m e m b e r of R e bands. Unnatural p a r r y states and high spin members usu~lly have h i g h e r o v e r l a p s again. The comparison between the eape~imental ~ J calculated (42) bands shows clearly the existence of K = 0 a n d K = 2hands. In bet~ c a s e s the cal~ culatod m o m e n t s of i n e r t i a are ~omewhat l a r g e r than the experimentally observed ones. P e r h a p s the m o s t interesting feature of the (04) band is the fact thor the SU3 deslg~mtion ~ g g e s t s that i t should have an oblate d e f o r m e d . The 0 + band head calculated at I0.05 M e V has a large (0.83) overlap with the (04) SU 3 state. The next caleuinted 2+ state at 10.46 M c V corre~oed~ g to the e~porimentally observed state at 11.5t MeV h a s ~ s m a l l overlap (0.13). Although eeorgefically i t rite into the band, the overlap indiCates i t s foreign nature. The second 3 ~ state calenlated a t 14.3 M e V , and e ~ e r h n e n t a l I y o b s e r v ed a t 14,72 o r 15.25 MeV l ~ s a ~ overlap (0.88):consistent with the (04) SU3 interpretation. S i m i l a r statements :apply with r e g a r d to the 4 + state e ~ i m e n t h l l y observed at 16.8 MeV and calcnlated at 14.86 MeW It i s interesting to 219
Volume 12, number 3
PHYSICS L E T T E R S
10eto&er 1964
C
£
fi~__
I
15
(b)
, ~,
;4 2)
~4 2)
(0 4)
(3 ~)
Fig. 1. E~perimental andl~alculatedeven parity levels in 016. a). Experimental levele and spin a~ignmen~ 2,1 ). All even parity levels are given up to 14,8 ICmVexcept tim 13.1 MeV level which recent m e a s a r e m ~ 2) have elmw~ to have spin*parity 2+ in addition to the previous l-asslgnment; b. Theoretical levels. Thsee levels are eblftod down 17 MeV, The dornln~t SUz configurations are given below the apprc~pr~e basis. that only these assignments of the (04) band have large experimental alplm widths. Both the overlaps with SU3 states and the energy agreement between the calculated spectrum and the experimentally observed spectrum indicate that the 1+ state at 13.65 MeV with ~uperimposed rotational band (3÷ member missing) and the 1+ state at 18.21 MeV are the two (81) configurations expected. It would be particularly worthwhile to observe experimentally the expected 5 ÷ member of the (42) band mud the 3+ member of the (31) band. These states are expected at ~ 19 and ~ 15 MeV r e s p e c tively. The negative parity states in 016 obviously fit empirically into rotational bands. However, the theoretical interpretatior of these states i s much more ambi~aous. Gillet ~nd vtnk-Mau 8) and more recently Erikson 9, have Lutorpreted the lowest lying 3-, 1" states as essentially one partiele - one hole states. (Although the strong E2 between them indicates three p~rticle - three hole admixture. ) The most deformed ~J3 eoatiguration for 3~w excitation is (~3) which could be the band begir~uing with ~pin 1" ~ 9.58 MeV. This b~_nd utilizes the 2- state at 8.88 M e V which does not fit well i~to band energy systematics. An alternative e ~ l a n a t i o n would involve the (52) configuration which may ~e rea~Azed from both ~ o particle - two hole and three particle th~°ee hole excitations. This provides naturally the 1-, 8% 5- and 7" spin sequence (K = 0) and the K = 2 band beg'~r,~g at 12.52 MeV. ~20
R has eormnonly been a~sumed that the rotational bands In the same deformed r]ucleus have approximately the same character. In c~ntradlstinction to this, Mcttelson and Nllsson 10) have suggested that in the region of approximately 90 neutrons quite different prelate deformations may occur within the same nucleus. The interpretation presented here suggests that one may general. ly expect to find spherical, prelate and oblate shapes in the same nucleus. The energetic t h r e s hold for the appearance of these states will v a r y from nucleus to nucleus, making a s e r i e s of complex surfaces on a three dimensional plot of neutron number, proton nunther and energy. In 016, for example, the threshold for prelate deformation is 6.06 M e V while the threshold for oblate deformation i s 11.25 MeV. Thus, it ~eems quite rear~n~hle that one will e:~pect to see not only nuclei with spherical ground states giving r i s e to proLute and oblate excited shapes and states, but also nuclei with deformed ground states containing ~pherical excited states. The authors are e~:iremely grateful for the hospitality exteeded by the Institute for Theoretical Physics and for in~,~piration and guidance from P r o f e s s o r s Bohr, Brovm, itecht and Mottelson, ~nd Dr.David Brink, which have contributed importantly to this research. In particular, one. of us (J.B.) wishes to thank Prof. G,E. Brown for suggesting the calculation.
Volunm 12, nember 3
PHY8ICS LETTERS
I October 1964
4) D. M,Brink and G, F, Eash, NucL Phys, 40 (1963) I) H, Morhmga, Phys. Rev. I01 (1955) 254; K~ Wildermuth and T. Ksmmllopouloe, CERN Report SS-~, lSS9 (u~pubRohel); R.K.8~leline and K,Wildormuth, Nuel, Phys. 21 (1~1) 196. 2) S,Gorodetzky at al. ,Physics Letters I (1962) 14; E.B, Carter, G.E,Mitcbell and R,H.Devls, Phys, Roe. 133B (1964) 1421~ G,E,Mitohell, E.B.Carter ned R.H,Davin, Phys.
Rev. 133B 0964) 1434. 3) J.P.Elliott~ Proc~ Roy. See. 245 (1958) 128,562.
K-CAPTURE
EFFECTS ON IN G A S E O U S
608,
5) T, Engelaud, to be published in Nuc]. P.hys. ; See also G.E'.Brown, Prec. of ~t. Conf.on NucL Phys., Parts, 1964, 5) J,'Borysowic~, to be published. 7) A.Kallio and K.Kolltveit, NucL Phys; S3 (1964) 87. 5) V.Gllletand N.Vin-Mau, Nuel. Phys. 54 (1964) 321 9) T . E r ~ o n , Nuof. Phys. 55 (1964) 497. 10) B.R.Mottelson and S.G~Nflss0n, Met. Fys. ~ r . Dan. Vld. Selsk. 1 (1959) No. 8. I1) F.Ajzm~borg-Selove and T. Laurlinen,NucL pl~s. 11 (1959) 1,
ANGULAR SOURCES*
CORRELATIONS
H.J. LE~I Ba~oZ Research Foundation of the Franklfn Institute, Swavthmore, Pennsylvan~e
R~eived 17 August 1964 This report is concerned with angular correlation studies using monoatomie gaseous sources. Such a source environment is particularly attractive from the point el view of studying the hyperfine interactionof excited nuclear slates. h' the gas pressure is kept small enough, such thaf there a r e no atomic collisions during the nuclear decay p r o c e s s , the decaying s y s t e m i s completely f r e e f r o m interactions iwith the environment. The only extranuctear interaction by which an angular correlation can be perturbed i~ a gaseous source of low pressure is the leotropic hyperfine interaction, which is theoretically fully understood 1). In cases where this interaction is time-independent during the lifetime of the intermediate state of a garnma-gamma cascade information on nuclear moments of excited states m a y be obtained from the perturbation of the angular correlation P'). One way of creating a hyperfine interactiontu a gaseous source is to select a g a m m a cascade which is preceded by a K-capture decay. R is well known that the rearrangement of the electron shell following K-capture (or internal conversinn) results in the formation of highly ionized atoms ~-~, which, in general, must give r~se to a hyperfine coupling between the atomic shell and ~he nucleus. * Supportedby the Atomic Energy Commlssion~
The g a m m a - g a m m a angul~ correlatlons of the 172-203 knV caso~de in iI27and the S5-188 keV cascade in 1125 were measured with gaseous sources of Xe 127 and X e 125 at totalpressure~ vPxying between I and 4 nun Hg and With xenon carrier pressures between 0.5 aud I m m llg. The mean coUislon times, re, of the active ions after K-capture are estimated to be T C ~ 2 :