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Incipient octupole and 26-pole deformation in the mass region 220 < A < 230
Ve;ume 175, number 3
PHYSICS LETTERS B
7 Augus'; i986
I N C I P I E N T O C T U P O L E AND 2%POLE D E F O R M A T I O N ~N T H E M A S S R E G I O N 220 < A < 230 R.R. C H A S M A N Physics Division, Argonne National Laborato~'y I, AtNo~m; 1L 60439-4843, USA Received 30 March 1986; revised manuscript received 9 May t986
~ . e m~ease i~ caicutaled bmdhag energies of nuclides in the mass reNo~ 220 < A < 230 due to varying the 26.-~1e deformation pa~meter is found ~o be ~1.0 NoV. The !mpgcations ef this fk~ding fox oc~upole defo~matio~ are discussed.
Since the prediction [I ] of parity doublets and octupoie de~%rm~tion in ~.:helight actinides, the experiments and theoretical study of the mass region 220 < A < 230 has become an area of considerable research activity. Subsequent experimental studies [2~ of 229pa and studies [3 i of 227Ac have shown this description of odd-mass nuclides to be quite ace'.'rate. This description utilizes a mar.~y-body treatment of octupole correIations and si.ngle-particle energy level spacings based on experimentai studies of the heavier actinides In these calculations one finds that there are states with both strong and weak octupo]e correlations in the saw'e nuclide. This indicates an incipient octupoie deformation, dependent on specifi.c configurations. A different way to study octupoie deformation is the Strutinsky procedure [4]. In such catcuiations, one introduces [5,6] octupole deformation directly into a single-particle potentiai and minimizes the erie> gy (!iquid-drop pius shell corrections and pairing corrections) as a function of the deformation parameters. These calculations, using a folded Yukawa single-pa> ticie potentiai~ give values of the octupole deforma~ tien parameter, e3, as large as 0.10 in the mass region 220 < A < 230. These calculations also show that octupole deformation gives an increase in the binding energy o f ' ~ l . 3 MeV for nuclides in the vicinity of 222Ra, relative to the binding energies calculated when Work supported by the US Department of Energy, Nuclear Physics Division, u~der contract W-3 ~~109-ENG-38.
254
the nuclear shapes are constrained to be reflection symmetric. Calculations [7] using a Woods-.-.Saxon potential show similar effects. Ano/;her calculation utilizing a Woods-Saxon potentiai [8] shows significantly smalier Ncreases in the binding energy near 222Ra arising from octupoie de%traction. Here the increases are ~0.6 MeVo The differences with the folded Yukawa calculations are attributed primarily [8] to differences in the spacing between leveis in the proton single@article spectrum° A large increase in binding energy is needed to remove the discrepancy between known masses and the calculations of Moller and Nix [9i, who found bmdkng energy discrepancies as large as 1.8 MeV i~ this mass region when considering only reflection symmetric deformation modes. Some questions as to the validity of the Strutinsky calculations arise from recent analyses of experimental studies in this mass region. One proton transfer reaction studies [t0], populatir..g levels of 227Ac, indicate that the octupole deformation parameter is quite smail in this nuclide, in contrast to the predicted values of 0.09. The popu!ation of the lowest 13/2 + level rules out a Iarge octupoie deformation. An ana° lysis [I 1] of coriolJ.s matrix elements a~.d decoupiing parameters in 225 Ra shows large deviations from the equal values predicted in the octupole deformatio_~ limit. Analyses of rotational frequencies in 222Th and 22°Ra indicate [12,! 3] that the low-spin positive-parity states are far from the octupo!e deformation iimit in these nuclei. A very recent study of 223Ra also shews [14.] a substantial difference in the i/2 + and 0370-2693/86/$ 03.50 © Elsevier Science Publishers B.V. (NorthoHoiland Physics Publishing Division)
Vc!ume 1"15,number 3
PHYSICS LETTERS B
i / 2 - decoupling parameters in this nuciide. Using the three lowest levels assigned to the 1/2 + band (i/2 +, 5/2 + and 7/2+), we extract h;/2I = 8.59 keV and = ! A8. For the negative-parity t / 2 - band, we get h2/2I = 6.0"-,' and a = - 2 . 1 3 using the iowest three levels assigned to this band. These values differ slightI}, from the values given in ref. [t4I where higher lying levels were used in the ar, atysis. In this letter, we present a new calculation of bi'nding energies using the Strutinsky procedure. We find that reflection asymmetric deformations play a smaller role than had been previously thought° Our calcu!ation differs from the earlier ones in that we a_~iow variations in the 26-pole deformation mode, rather than fixing the value o f this deformation parameter as has been done previously, in the earlier studies [5-71 of hue dear binding energies uti~zing the Strutinsky procedure, the magnitude of the 2°-pole deformation parameter was fixed using the relation e 6 = - e 4 ( e 2 + 0.i0),
(1)
where e 2 and e 4 are the quadr'apole and hexadecapole deformation parameters. TMs choice for the magnitude of the e 6 parameter gives an optimal binding energy for the liquid-drop term of the Strutinsky procedure. However, it is made without regard to the shell~ correction term. The equivalent parameter ~6 was fixed to optimize the liquid-drop e~ergy in the studies o f ref° [g]. The motivation for so fixing either ~6 or e 6 is tt~at the Strutinsky calculations become increasingly expensive with the addition of each dimension in deformation space. The prescription o f eq. (1) gives values of 0 . 0 I - 0 . 0 0 1 for e 6 in this mass region as the equilibrium value o r e 2 is 0 . i 0 - 0 . i 5 and the equiiibri~am value of e 4 is ~ - 0 . 0 6 . Our major finding is that the binding energy associated with reflection symmetric shapes is increased by ~1.0 M e V for the nuclides with 134 and 136 neutrons whe~. e 6 is not co~.strained. This result can be easily understood quMitatively. The three ~.eutron orbitals 5 / 2 - [752], 5/2 + [6331 and 3/2 + [63 t ], which lie above N = 136 ai the equilibrium deformations of the nuclides in this region, all move up and away from the Fermi level as e 6 becomes more negative. Our single-particle potential is a W o o d s Saxon potentiai with the single particle spacings shown in figs. 3 and 4 o f ref. fl51. We vary e 2 from 0.07 to 0.I7; e 3 from 0 to 0°09; e4 from - 0 . 0 7 to - 0 . 0 3 ; and e 6 was calcuiated for values between 0
7 Aug*ast t986
and - 0 . 0 2 4 in addition to the value given by eqo (!). The she!! corrections are calculated with an eighthorder Her.mite poiynomiai and a smoothing width of 10 MeV. We use a sharp-surface [i6] liquid-drop model in our calculations as there is some question regarding the diffuse-surface liquid-drop model in dealing with Mgh-order multipole deformations. The effect o f a diffuse-surface iiq,aid-drop model would be to give even Iarger increases in binding energy associated with 26-pole deformations. We also eMcuiate the effects of octapole deformation on the binding energy. We find a substantial reduction in the mag~io rude ofoctupole deformation effects. In tabIe i, we present resMts for several nuclides in the mass reg::o~. 220 < A < 230. We give the difference between the experimentM binding energies and the va!ues caicuIated by Moller and Nix [91 when the mass is known; the increase that we calculate in binding energy for 26 -pole deformation for reflection symmetric shapes, obtained by using a sb.arpos~.rfaee iiqu::d-drop mode1 for minimization calculations both with and without the constraints of eqo (i); the additional ino crease in binding energy that we calcuiate relative to i n s minimum associated with variations of tke octupole deformat::on parameter e 3; the difference between the experimental bkr~ding energy and a va!ae that we estimate hy sub*ract~-g (~.,B E ) , and &B E p from "the values of ref. [9] ; and finallythe equilibrium values of the deformation parameters. The corrections that we !ist are rounded off to 0.05 MeV. The uncertainties in the shell corrections caicuiated with the Strutinsky method are ~100 keV. The equilf~rNm values of the deformation parameters e 2 and e~ that we obtain: are very close to the values obtained in refo [6]. SmaIi variations in e 5 do not give o~.~yme, ease in binding energy and we have set it equal to zero. From rabid I, we see that the variation of e 6 gives rise to me creases o f ~ 1 MeV for many of the nuciides we consider° The inclusion of these variations in e 6 affects the estimates of oetupo!e deformation substantially° Typically, the values are reduced substantially from the value of 0°09 found [6,7] previously. More signi~cantly, the binding energy gains associated with ref!ection asymmetric deformation are cow < 0 . 6 MeV for the nuclides having more than t32 neutrons. Altho~gh it is not fully coa~stent to subtract the values of (&B.E.)p. and (&B.E.)~. from the binding energy discrepancies from ref. [9~, it is a reasonable 255
Vok:me 175, number 3
PHYSICS LETTERS B
7 August t986
Table t Binding energies of even-even nuclides 220 ~ A < 230. Nuciide
zB.E.)expt:
(AB.E.)p6
(Z~B.Eo)p3
- (B-EJMoller-Nix
(KE.)exptL (B.E.)Moller_N:; x
62
e3
¢4
e6
0.20 0A5 -
0.09 0.12 0.i2 0.15
0.06 0.03 0.00 0.03
-0,03 -0.045 -0.06 -0.045
-0.0!2 -0.0t8 -0.0i8 -0.009
0.15 0.35 0.00 -0.25 0.I0
0.09 0.12 0.i2 0.15 0.15
0,07 0.07 0.09 0.07 0.03
-0.04 -0.04 -0°04 -0.045 -0.045
-0.009 -0.006 -O.000 -0.003 -0.009
0.00 0.20 -0.10 0.10
0.!2 0.12 0,15 0.!6
0.06 0.07 0.03 0.03
-0.035 -0.045 -0,06 -0.065
-0.0i2 -0.009 -0.0i5 -0.012
0.t2 0.15 0.17
0.06 0.00 0.00
-0.045 -0.06 -0.06
--0.006 -0,015 -0.012
-
- (~.B.EjI; a
2~Rn~a6 292~Rn!38 2~Rn~4o
1.5 ! i.24-
1.00 1.10 0.70
0.30 000 0.10
220
~ ~a-..32 2~Ra!34 224~ggtva136 2~Ralaa
1.75 i.81 !.05
0.60 0.90 0.90 0°70
1.0 0.55 0.55 0.60
228
0.54
0.15
0.30
aa~a,.4O
224m" 90 -':11134 9o~n~a6 ~0, :~38
1.43
1.54
0.70
o85
~ al
1.00
0.20
~.I~
-
-
-
228 '-c~
0.88
1.I0 0.70
0.15 0.10
2,g4: t
0.99 0.70
0.45 0.90 1.I0
0.40 0.00
9~ ui32 I~4 228,,t 92wlaa 226 9~U
0.00
procedure and gives good estimates o f k n o w n binding energies. This procedure gives estimates o f the binding ~, I energies o f n u t"! i c~e s 220 ~ u , z26 ~ Rn and 224 U., Ou~~-ca,cuia~ions o f the bin4ing energy increases associated w i t h o c t u p o i e d e % r m a t i o n and 26-poie d e f o r m a t i o n are N d e p e n d e n t o f t N s procedure. tn summary, we have found that the sheil corrections associated w i t h Y6(cos ~) deformations are large in the mass region 220 < A < 230 and give rise to values o f e 6 opposite N sign from the vatues suggested by iiquid-drop considerations. The existence o f b o t h incipient o e t u p o t e and 26-po!e d e f o r m a t i o n s in this mass region shouid make it a particularly interesting one % r deta::led study° k is a pleas~are to acknowledge usefuI discussions on various aspects o f this w o r k w i t h [. Abroad, R. Pipenbring, Ho Martz, Go Struble, D. Burke and G. Leander.
256
-
0.I0 -0.40
References [ i I R°R. Chasman, Phys. Lett. 69 B (1980) 7. i2] I. Abroad etaL, Phys~ Rev. Left. 49 (1982) 1758. [3} R.K. SheEne and G.A. Leander, Phys. Roy. Le~t. 5 i (1983) 359. [4] V.M= StrutL~sky, NucL Phys. A95 (1967) 420. [5! P. Moller and J.R. Nix, NucL Phys. A36I (198i) tt7. [6! G.A. Leander et al.,NucL Phys. A388 (1982) 452. [71 R.R. Chasman, Jo Phys. (Paris) C6 (1984) 167. [81 W. Nazarewicz etaL, N~cL Phys. A429 (1984) 269. [9] Po Moiler and LRo Nix, At. Data NucL Data Tables 26 (t981) 165. [ !0] H. Martz etaL, Abstract A.C.S. Division of Nuclear Chemistry ~ d Technology Phi!adelphia Meeting (August 1984). [i ii R. Piepenbring, J. Phys. (Paris) Let',,. 45 (t984) L-I023. [12 i W. Nazarewicz etaL, Phys. Rev. Le,t. 52 (I984) 1272. [13) A. Celler et aL, NucL Phys~ A432 (i985) 42I. [t41 R.Ko SheIine, Phys. Lett. t~ t66 (1986) 269. [I5] R.R. Chapman, 1. Abroad, A.M. Friedman and J.R. Erskine, Roy. Mod. Phys. 49 (!977) 833. [t6] P.A. Seeger and R.C. Perishe, LASL Report LA-375 t (1967).
PHYSICS LETTERS B
7 Augus'; i986
I N C I P I E N T O C T U P O L E AND 2%POLE D E F O R M A T I O N ~N T H E M A S S R E G I O N 220 < A < 230 R.R. C H A S M A N Physics Division, Argonne National Laborato~'y I, AtNo~m; 1L 60439-4843, USA Received 30 March 1986; revised manuscript received 9 May t986
~ . e m~ease i~ caicutaled bmdhag energies of nuclides in the mass reNo~ 220 < A < 230 due to varying the 26.-~1e deformation pa~meter is found ~o be ~1.0 NoV. The !mpgcations ef this fk~ding fox oc~upole defo~matio~ are discussed.
Since the prediction [I ] of parity doublets and octupoie de~%rm~tion in ~.:helight actinides, the experiments and theoretical study of the mass region 220 < A < 230 has become an area of considerable research activity. Subsequent experimental studies [2~ of 229pa and studies [3 i of 227Ac have shown this description of odd-mass nuclides to be quite ace'.'rate. This description utilizes a mar.~y-body treatment of octupole correIations and si.ngle-particle energy level spacings based on experimentai studies of the heavier actinides In these calculations one finds that there are states with both strong and weak octupo]e correlations in the saw'e nuclide. This indicates an incipient octupoie deformation, dependent on specifi.c configurations. A different way to study octupoie deformation is the Strutinsky procedure [4]. In such catcuiations, one introduces [5,6] octupole deformation directly into a single-particle potentiai and minimizes the erie> gy (!iquid-drop pius shell corrections and pairing corrections) as a function of the deformation parameters. These calculations, using a folded Yukawa single-pa> ticie potentiai~ give values of the octupole deforma~ tien parameter, e3, as large as 0.10 in the mass region 220 < A < 230. These calculations also show that octupole deformation gives an increase in the binding energy o f ' ~ l . 3 MeV for nuclides in the vicinity of 222Ra, relative to the binding energies calculated when Work supported by the US Department of Energy, Nuclear Physics Division, u~der contract W-3 ~~109-ENG-38.
254
the nuclear shapes are constrained to be reflection symmetric. Calculations [7] using a Woods-.-.Saxon potential show similar effects. Ano/;her calculation utilizing a Woods-Saxon potentiai [8] shows significantly smalier Ncreases in the binding energy near 222Ra arising from octupoie de%traction. Here the increases are ~0.6 MeVo The differences with the folded Yukawa calculations are attributed primarily [8] to differences in the spacing between leveis in the proton single@article spectrum° A large increase in binding energy is needed to remove the discrepancy between known masses and the calculations of Moller and Nix [9i, who found bmdkng energy discrepancies as large as 1.8 MeV i~ this mass region when considering only reflection symmetric deformation modes. Some questions as to the validity of the Strutinsky calculations arise from recent analyses of experimental studies in this mass region. One proton transfer reaction studies [t0], populatir..g levels of 227Ac, indicate that the octupole deformation parameter is quite smail in this nuclide, in contrast to the predicted values of 0.09. The popu!ation of the lowest 13/2 + level rules out a Iarge octupoie deformation. An ana° lysis [I 1] of coriolJ.s matrix elements a~.d decoupiing parameters in 225 Ra shows large deviations from the equal values predicted in the octupole deformatio_~ limit. Analyses of rotational frequencies in 222Th and 22°Ra indicate [12,! 3] that the low-spin positive-parity states are far from the octupo!e deformation iimit in these nuclei. A very recent study of 223Ra also shews [14.] a substantial difference in the i/2 + and 0370-2693/86/$ 03.50 © Elsevier Science Publishers B.V. (NorthoHoiland Physics Publishing Division)
Vc!ume 1"15,number 3
PHYSICS LETTERS B
i / 2 - decoupling parameters in this nuciide. Using the three lowest levels assigned to the 1/2 + band (i/2 +, 5/2 + and 7/2+), we extract h;/2I = 8.59 keV and = ! A8. For the negative-parity t / 2 - band, we get h2/2I = 6.0"-,' and a = - 2 . 1 3 using the iowest three levels assigned to this band. These values differ slightI}, from the values given in ref. [t4I where higher lying levels were used in the ar, atysis. In this letter, we present a new calculation of bi'nding energies using the Strutinsky procedure. We find that reflection asymmetric deformations play a smaller role than had been previously thought° Our calcu!ation differs from the earlier ones in that we a_~iow variations in the 26-pole deformation mode, rather than fixing the value o f this deformation parameter as has been done previously, in the earlier studies [5-71 of hue dear binding energies uti~zing the Strutinsky procedure, the magnitude of the 2°-pole deformation parameter was fixed using the relation e 6 = - e 4 ( e 2 + 0.i0),
(1)
where e 2 and e 4 are the quadr'apole and hexadecapole deformation parameters. TMs choice for the magnitude of the e 6 parameter gives an optimal binding energy for the liquid-drop term of the Strutinsky procedure. However, it is made without regard to the shell~ correction term. The equivalent parameter ~6 was fixed to optimize the liquid-drop e~ergy in the studies o f ref° [g]. The motivation for so fixing either ~6 or e 6 is tt~at the Strutinsky calculations become increasingly expensive with the addition of each dimension in deformation space. The prescription o f eq. (1) gives values of 0 . 0 I - 0 . 0 0 1 for e 6 in this mass region as the equilibrium value o r e 2 is 0 . i 0 - 0 . i 5 and the equiiibri~am value of e 4 is ~ - 0 . 0 6 . Our major finding is that the binding energy associated with reflection symmetric shapes is increased by ~1.0 M e V for the nuclides with 134 and 136 neutrons whe~. e 6 is not co~.strained. This result can be easily understood quMitatively. The three ~.eutron orbitals 5 / 2 - [752], 5/2 + [6331 and 3/2 + [63 t ], which lie above N = 136 ai the equilibrium deformations of the nuclides in this region, all move up and away from the Fermi level as e 6 becomes more negative. Our single-particle potential is a W o o d s Saxon potentiai with the single particle spacings shown in figs. 3 and 4 o f ref. fl51. We vary e 2 from 0.07 to 0.I7; e 3 from 0 to 0°09; e4 from - 0 . 0 7 to - 0 . 0 3 ; and e 6 was calcuiated for values between 0
7 Aug*ast t986
and - 0 . 0 2 4 in addition to the value given by eqo (!). The she!! corrections are calculated with an eighthorder Her.mite poiynomiai and a smoothing width of 10 MeV. We use a sharp-surface [i6] liquid-drop model in our calculations as there is some question regarding the diffuse-surface liquid-drop model in dealing with Mgh-order multipole deformations. The effect o f a diffuse-surface iiq,aid-drop model would be to give even Iarger increases in binding energy associated with 26-pole deformations. We also eMcuiate the effects of octapole deformation on the binding energy. We find a substantial reduction in the mag~io rude ofoctupole deformation effects. In tabIe i, we present resMts for several nuclides in the mass reg::o~. 220 < A < 230. We give the difference between the experimentM binding energies and the va!ues caicuIated by Moller and Nix [91 when the mass is known; the increase that we calculate in binding energy for 26 -pole deformation for reflection symmetric shapes, obtained by using a sb.arpos~.rfaee iiqu::d-drop mode1 for minimization calculations both with and without the constraints of eqo (i); the additional ino crease in binding energy that we calcuiate relative to i n s minimum associated with variations of tke octupole deformat::on parameter e 3; the difference between the experimental bkr~ding energy and a va!ae that we estimate hy sub*ract~-g (~.,B E ) , and &B E p from "the values of ref. [9] ; and finallythe equilibrium values of the deformation parameters. The corrections that we !ist are rounded off to 0.05 MeV. The uncertainties in the shell corrections caicuiated with the Strutinsky method are ~100 keV. The equilf~rNm values of the deformation parameters e 2 and e~ that we obtain: are very close to the values obtained in refo [6]. SmaIi variations in e 5 do not give o~.~yme, ease in binding energy and we have set it equal to zero. From rabid I, we see that the variation of e 6 gives rise to me creases o f ~ 1 MeV for many of the nuciides we consider° The inclusion of these variations in e 6 affects the estimates of oetupo!e deformation substantially° Typically, the values are reduced substantially from the value of 0°09 found [6,7] previously. More signi~cantly, the binding energy gains associated with ref!ection asymmetric deformation are cow < 0 . 6 MeV for the nuclides having more than t32 neutrons. Altho~gh it is not fully coa~stent to subtract the values of (&B.E.)p. and (&B.E.)~. from the binding energy discrepancies from ref. [9~, it is a reasonable 255
Vok:me 175, number 3
PHYSICS LETTERS B
7 August t986
Table t Binding energies of even-even nuclides 220 ~ A < 230. Nuciide
zB.E.)expt:
(AB.E.)p6
(Z~B.Eo)p3
- (B-EJMoller-Nix
(KE.)exptL (B.E.)Moller_N:; x
62
e3
¢4
e6
0.20 0A5 -
0.09 0.12 0.i2 0.15
0.06 0.03 0.00 0.03
-0,03 -0.045 -0.06 -0.045
-0.0!2 -0.0t8 -0.0i8 -0.009
0.15 0.35 0.00 -0.25 0.I0
0.09 0.12 0.i2 0.15 0.15
0,07 0.07 0.09 0.07 0.03
-0.04 -0.04 -0°04 -0.045 -0.045
-0.009 -0.006 -O.000 -0.003 -0.009
0.00 0.20 -0.10 0.10
0.!2 0.12 0,15 0.!6
0.06 0.07 0.03 0.03
-0.035 -0.045 -0,06 -0.065
-0.0i2 -0.009 -0.0i5 -0.012
0.t2 0.15 0.17
0.06 0.00 0.00
-0.045 -0.06 -0.06
--0.006 -0,015 -0.012
-
- (~.B.EjI; a
2~Rn~a6 292~Rn!38 2~Rn~4o
1.5 ! i.24-
1.00 1.10 0.70
0.30 000 0.10
220
~ ~a-..32 2~Ra!34 224~ggtva136 2~Ralaa
1.75 i.81 !.05
0.60 0.90 0.90 0°70
1.0 0.55 0.55 0.60
228
0.54
0.15
0.30
aa~a,.4O
224m" 90 -':11134 9o~n~a6 ~0, :~38
1.43
1.54
0.70
o85
~ al
1.00
0.20
~.I~
-
-
-
228 '-c~
0.88
1.I0 0.70
0.15 0.10
2,g4: t
0.99 0.70
0.45 0.90 1.I0
0.40 0.00
9~ ui32 I~4 228,,t 92wlaa 226 9~U
0.00
procedure and gives good estimates o f k n o w n binding energies. This procedure gives estimates o f the binding ~, I energies o f n u t"! i c~e s 220 ~ u , z26 ~ Rn and 224 U., Ou~~-ca,cuia~ions o f the bin4ing energy increases associated w i t h o c t u p o i e d e % r m a t i o n and 26-poie d e f o r m a t i o n are N d e p e n d e n t o f t N s procedure. tn summary, we have found that the sheil corrections associated w i t h Y6(cos ~) deformations are large in the mass region 220 < A < 230 and give rise to values o f e 6 opposite N sign from the vatues suggested by iiquid-drop considerations. The existence o f b o t h incipient o e t u p o t e and 26-po!e d e f o r m a t i o n s in this mass region shouid make it a particularly interesting one % r deta::led study° k is a pleas~are to acknowledge usefuI discussions on various aspects o f this w o r k w i t h [. Abroad, R. Pipenbring, Ho Martz, Go Struble, D. Burke and G. Leander.
256
-
0.I0 -0.40
References [ i I R°R. Chasman, Phys. Lett. 69 B (1980) 7. i2] I. Abroad etaL, Phys~ Rev. Left. 49 (1982) 1758. [3} R.K. SheEne and G.A. Leander, Phys. Roy. Le~t. 5 i (1983) 359. [4] V.M= StrutL~sky, NucL Phys. A95 (1967) 420. [5! P. Moller and J.R. Nix, NucL Phys. A36I (198i) tt7. [6! G.A. Leander et al.,NucL Phys. A388 (1982) 452. [71 R.R. Chasman, Jo Phys. (Paris) C6 (1984) 167. [81 W. Nazarewicz etaL, N~cL Phys. A429 (1984) 269. [9] Po Moiler and LRo Nix, At. Data NucL Data Tables 26 (t981) 165. [ !0] H. Martz etaL, Abstract A.C.S. Division of Nuclear Chemistry ~ d Technology Phi!adelphia Meeting (August 1984). [i ii R. Piepenbring, J. Phys. (Paris) Let',,. 45 (t984) L-I023. [12 i W. Nazarewicz etaL, Phys. Rev. Le,t. 52 (I984) 1272. [13) A. Celler et aL, NucL Phys~ A432 (i985) 42I. [t41 R.Ko SheIine, Phys. Lett. t~ t66 (1986) 269. [I5] R.R. Chapman, 1. Abroad, A.M. Friedman and J.R. Erskine, Roy. Mod. Phys. 49 (!977) 833. [t6] P.A. Seeger and R.C. Perishe, LASL Report LA-375 t (1967).