Reorientation measurements in the even nickel isotopes

Nuclear

Physics A223 (1974) 563 - 576; @

Not to be reproduced

REORIENTATION

North-K~lIand

Publishing

Co., Amsterdam

or microfilm without written permission from the publisher

by photoprint

MEASUREMENTS

IN THE EVEN

NICKEL

ISOTOPES

P. M. S. LESSER t, D. CLINE, C. KALBACH-CLINE Nuclear

Structwe

Research

Laboratory,

Uniuersity

and A. BAHNSEN tt qf Rochester, Rochester, New York tff

Received 19 March 1973 (Revised 31 December 1973) The reorientation effect in Coulomb excitation was used to measure the static electric quadrupole moments, Qz + , of the first excited (2, +) states in SsNi and 60Ni. A 70 MeV beam of 32S ions was used to excite the 2rf states and the de-excitation y-rays were observed in coincidence with scattered particles, using a multiple detector system. The results of these ~leasurements are in excellent agreement with two previous Rochester measurements which employed different experimental techniques. A weighted average of all Rochester measurements gives: Q2+(5sNi) = --0.10&0.06 e. b and Qz+(60Ni) = +0.03f0.05 e. b, ignoring the possible effects of higher excited 2+ states in both cases. The experimental results are compared with shell model calculations assuming an inert “6Ni core with valence neutrons in the p+, 4, and p) orbitals.

Abstract:

E

I

NUCLEAR

REACTIONS ssNi(32S, 32Sy),60Ni(32S, 32Sy), E = 70 MeV; measured o(E,. , @32s >eszs,.). 58Ni, 60Ni deduced Qz c .

1. Introduction The present paper describes measurements of the static electric quadrupole moments of the first excited (2:) states in 58Ni and 60Ni. This work completes a series of measurements of quadrupole moments in the even nickel isotopes, employing a variety of experimental techniques. All of the techniques utilized the reorientation effect in Coulomb excitation, but a comparison of the results provided a safeguard against certain kinds of systematic errors. In fact, the results of the present measurement are in excellent agreement with the previous results I7“) which inspires greater confidence in the use of the reorientation effect to measure static quadrupole moments of excited nuclear states. This work is also part of a larger program, in progress at the University of Rochester Nuclear Structure Research Laboratory, to measure electric quadrupole moments for doubly even nuclei in the If-2p shell. The low lying Ievels of the even nickel isotopes exhibit many features characteristic of the simplest har~lonic vibrator model. The Iarge static quadrupole moments “) that have been found in supposedly spherical vibrational nuclei in the region of the rare earth deformed nuclei motivated us to investigate quadrupole moments in the even nickel isotopes. The combined results of the present and our previous measure? Present address: Physics Dept., Brooklyn College, CUNY, Brooklyn, New York. +t Present address: Danish Space Research Institute, Lundtoftevej ttt Work supported by the National Science Foundation. 563

7, 2800 Lyngby, Denmark.

564

P. M. S. LESSER

et al.

ments for the even nickel isotopes permit rather precise determinations of Q2 and B(E2; 0: + 2:) for 58, 6o*62Ni. These results can be compared with the predictions of microscopic (shell model) calculations based on the assumption of an inert 56Ni core, with valence neutrons in the 4, p* and pt. orbitals. In an earlier publication “) we compared our previous results with shell model calculations as performed using various two body interactions. The agreement between theory and experiment was not very good, especially for 58Ni, indicating that the model space used in the shell model calculations is too restricted. On the other hand, it was possible to obtain a qualitative understanding of deformation in the even nickel isotopes; that is, the dependence of Q,+ on neutron number. The present results are compared with the recent shell model calculations of Glaudemans et al. “) which are generally more successful in reproducing the data than prior calculations. 2. Experimental method The multiple particle, y-ray coincidence technique used for the present measurements has been described in detail previously 4*‘). Scattered projectiles and recoiling nuclei were detected by three surface barrier detectors at angles of 30”, 50“, 90” and an annular detector at 180”. Coincident deexcitation y-rays were detected by four 7.6 cm x 7.6 cm NaI scintillators. Incident 32S ions were Coulomb scattered nickel targets. from thin (300 pg/crn’ 6oNi, and 100 pg/cm’ ‘* Ni), self-supporting The targets were prepared by vacuum evaporation of isotopically enriched nickel onto a copper substrate, with subsequent removal of the copper backing by standard techniques “). Evidence was found (see later) for some copper contamination in the “Ni target, but this did not interfere significantly with the measurement. The University of Rochester model MP tandem Van de Graaff accelerator was used to provide incident 32S ions at a nominal energy of 70 MeV. At this projectile energy, the separation distance between nuclear surfaces, for a head-on collision, was w 5.5 fm, where the nuclear radius is taken to be R = 1.25 A* fm. On the basis of previous measurements r* 4), this separation ensures that contributions to the inelastic scattering from nuclear, rather than purely Coulomb, effects are negligible (g 0.5 ‘A). The incident beam energies used in Coulomb excitation calculations for these experiments were corrected for energy loss in the target. 3. Data reduction and results The three-dimensional event-by-event data, that is, particle energy, y-ray energy and time information were stored on magnetic tape and scanned off-line to extract particle, y-ray coincidence yields. Digital windows were set on particle energy and time of flight (TAC) spectra, and the resulting projected y-ray spectra were peeled. Representative spectra are shown in figs. I and 2. The combined particle energy resolution and time of flight resolution (1.3 ns FWHM) were sufficient to separate

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MEASUREMENTS

565

cleanly the particle groups of interest. For the forward angle detectors, this meant separating the scattered 32S projectiles from the recoil Ni nuclei, while for the 180” annular detector the problem was to separate scattered projectiles from light particles produced in reactions on light target contaminants. The appearance of a 962 keV line in the y-ray spectra (fig. 2) indicated the present: of copper in the “Ni target. This was not unreasonable, due to the method of target preparation, although no evidence for copper contamination was found in the 60Ni target. From the known B(E2) in Cu and Ni isotopes, and from the measured ratio of y-ray intensities, it was possible to determine that the copper contamination in the ‘sNi target was x 7 %. This introduced a correction of ,N (10+2) % to the mea-

Particle

i

Particle Spectrum 58f.~j( 32s.32~) 38Nj*

103

E, = 70MeV

k

: :

e Lab

= I75”(annular)

Spectrum

5*Ni ( 32S,32S) “Ni”

i03i

E,

= i’0MeV

e Ld,

i

= 30”

38Nj 102

(light F

particles)

.” r,.’.“‘i‘.,&/-; ;’

896

632

0

r

Time Spectrum

32s

1022

960

Time Spectrum 58Ni(

32s

32s)

58Ni”

E, =76MuleV e L&=30*

58Ni

fwhm = 1.3ns

I

832

,

896

Channel Number Fig. i. Sample coincidence spectra, taken with a sSNi target. The upper figures show particles in coincidence with the full energy peak y-rays (1.454 MeV) only. The lower figures show the corresponding time-of-flight spectra.

566

P. M. S. LESSER

t ;

Gamma-Ray 5BNi

103 L

(32s.

et al.

Spectrum 32s)

5eNi*

E, =70MeV

960

696

632

Channel

Number

y-rays in Fig. 2. Sample coincidence spectrum taken with a 58Ni target, showing the de-excitation ?S projectiles. In addition to the 1.454 MeV peak from decoincidence with inelastically scattered a peak is seen at 0.962 MeV which has been excitation of the first excited (2+) state in “Ni, identified as coming from copper contamination of the target.

sured 58Ni 1454 keV line, due to the unresolved lines at 1323 keV (63Cu) and 1482 keV (6sCu). The calculations for these corrections included angular correlation effects. Coulomb excitation calculations required for reduction of the data were performed using the De Boer-Winther coupled channels computer code ‘). The calculational procedure, including recoil corrections to the angular distribution of de-excition y-rays, has been described previously 4, ‘). Attenuation of the angular distribution due to deorientation effects “) was measured directly, but the attenuation was measurably large only for the case of backscattered projectiles. The results of this measurement are given in table 1, where /3 = (recoil velocity)/c and G, is the measured attenuation coefficient for the Y, terms in the angular distribution of de-excitation y-rays. As discussed in a previous paper “) we TABLE 1 Measured Nucleus 58Ni 60Ni

values

of the deorientation ._

parameter,

r(ps)

B 0.0480 0.0469

0.9 1.0

G2, as a function

of B GZ

0.93 fO.10 0.982_10.032

think it reasonable to assume a relation between G, and G, expected from a randomly fluctuating magnetic hyperfine interaction: G,=-,

3Gz IO-7G2

REORIENTATION

MEASUREMENTS

567

and this relation was assumed in analyzing the present data. Furthermore, since the velocity dependence of the hyperfine interaction could not be measured reliably in the present experiment, we have assumed the same velocity dependence for Ni as 56Fe. That is, we have used the value x = 0.66+0.13 from ref. “) in for 48Ti and the expression: l-G2 = KrZ2(/?)2”. (2) G2

Here K is a constant, z is the mean lifetime of the 2, + state, and Z is the charge of the recoil nucleus. The values of the static quadrupole moments, extracted from the data, were quite insensitive to the assumed deorientation effect parameters. This follows from the fact that the angular correlation depends very weakly an the static quadrupole moment and from the small magnitude of the deorientation effect for these short-lived (5 1 ps) states. Experimental values for the static electric quadrupole moments, Q2, were extracted from the dependence of the cross section on c.m. scattering angle. Presentation of the data is facilitated by using the fact that to a first approximation the reorientation effect depends linearly on the quadrupole moment; linear least squares fits to the data are shown in figs. 3 and 4. The experimental value of the quadrupole moment is determined to a first approximation by the slope of the fitted (dashed) line. For comparison, the effect of an assumed “rotational” quadrupole moment, QR, is also shown (solid line), where QR = +&&nB(E2; The experimental

values determined

0+ + 2+).

from the analysis

(3)

are the following:

Q2(58Ni)

= -O.lO+O.lO

e. b,

Q2(60Ni)

= +0.09f0.08

e * b.

The errors quoted above are the statistical errors obtained from the fits to the data. Errors arising from uncertainties in various experimental parameters, such as mean detector angles, relative solid angles, etc., were negligible by comparison. The only significant corrections to the results which we anticipate come from the effects of higher excited states. Figs. 5 and 6 show the known level information for the low-lying excited states of 58Ni and 60Ni respectively. This information was used to calculate the effects due to virtual excitation of the 2:, 4:, 2: and 2: states. The reduced E2 transition matrix elements used in the calculations for ‘*Ni and 60Ni are given in tables 2 and 3 respectively. Matrix elements for the higher excited 2+ states in 58Ni were taken from the work of Bertin et al. lo). It should be noted that recent measurements il) of the radiative widths of the 23+ and 24+ states give results which are % 20 oA smaller than those of Bertin lo). Thus, the effects of these two states may have been overestimated in the present calculations. The measured lifetime of the 4: state gives an

.._ 58Ni

1

Run I 1.6 -

._ v z

.-

0.6 -

1 0e40

2

4I

64

8I

IO I

I4I

12 I

1

16 1

18 I

20t

22

20

22

24

‘*Ni Run 2

il:

1.2 ~

1---

0.8 -

0.6 -

l

0

I

/

I

f

I

I

L

I

t

2

4

6

8

IO

12

I4

16

I6

I

II

24

bi ~%) Fig. 3. The reorientation effect in 5*Ni, showing the best fits (dashed lines) to the experimental data. Data from two separate runs, taken with different sets of detector angles, are shown. The ordinate is the ratio of measured to calculated cross section, assuming Q = 0 and arbitrarily normalized to unity at bt = 0. The abscissa, b,, measures sensitivity of each data point to the static quadrupole moment, Qz +. For comparison, the effect of an assumed “rotational” quadrupole moment Qa, is shown (solid iine). Note that the experimentally measured quadrupole moment is determined by the slope of the dashed line.

REORIENTATION

569

MEASUREMENTS

-7

‘..+O7

60Ni

! I

I

1.30

I ___/

.- l.iO Y 5

---

-~

i

0.90

0.80

L

0

2

Fig. 4, The reorientation

4

6

6

IO

12

14

16

18

20

24

effect in 60Ni , showing the best fit (dashed line) to the experimentai Explanation as in fig. 3.

data.

upper limit for the reduced matrix element which is unreasonably large, i.e. in excess of the value predicted by the harmonic vibrator model. The actual value of this matrix element can reasonably be expected to lie somewhere between the values predicted by the harmonic vibrator and spheriodal rotor models, where: ( 4: j I E21 12:

9

( 2: I I =I

+? rotor

IO:

vibrator

(4)

The value quoted in table 2 represents the vibrational limit. Similarly, the vibrational limit was used for the 4: -+ 2: transition in 60Ni. The treatment of higher excited states in 6oNi here parallels that given in ref. ‘), where a more complete discussion is given. Since the effects are larger for 32S projectiles than for 160, and since the

3.2635

2+ 4 gy-

I- = 0.04ps

56

~=O.O6ps

, 4

2f

96

r-0.55ps

- 100

4+-

I->

T=o.spS

2+- I

o+

&_l

Fig. 5. Energy level diagram,

1.4ps

0.0

showing the known electromagnetic states in 58Ni.

1”

Fig. 6. Energy level diagram showing the known electromagnetic in 60Ni.

decay properties

1.3325

of low-lying

T

<5ps

T

>2ps

r

= ,.ops

decay properties of low-lying states

REORIENTATION

571

MEASUREMENTS

TABLE2 L eve1 information Level index n 1 2 3 4 5 6

and reduced E2 matrix elements, M,, (in units of e . b), used in the analysis of the 58Ni data

Excitation energy (MeV) 0.0 1.454 2.459 2.775 3.038 3.264

Spin, parity

0+ 2+ 4+ 2+ 2+ 2+

M,,

0 0.270 0 10.013 10.110 ho.138

Mnz

Mns

0.270

0 0.512 0 0 0 0

M22

0.512 0.316 0.114 0.265

M”4

f0.013 0.316 0 0 0 0

MlZ5

*to.110 0.114 0 0 0 0

M”6

*0.138 0.265 0 0 0 0

TABLE3 Level information Level index n

and reduced E2 matrix elements, M,, (in units of P. b), used in the analysis of the 60Ni data

Excitation energy (MeW

Spin, parity

1

0.0

0+

2 3 4 5 6

1.3325 2.158 2.506 3.124 3.269

2+ 2+ 4+ 2+ 2+

MI

0

0.305 &0.025 0 5 0.040 *0.090

M”Z

Mn3

M”4

0.305

*0.025 0.398 0 0 0 0

0 0.580 0 0 0 0

M,,

0.398 0.580 0.093 0.311

KS

hO.040 0.093 0 0 0 0

M”6

&to.090 0.311 0 0 0 0

160 data dominated the results quoted in reference ‘), the effects of higher excited states were somewhat greater in the present experiment. In particular, the 4: state had a negligible effect in the previous measurement but a non-negligible effect in the present one. The matrix elements for the 2: state at 3.124 MeV excitation were taken from Metzger 11) an d are considerably smaller than those assumed earlier I), thereby greatly reducing the importance of this state. However, an additional state not included in the previous analysis, the 24’ state at 3.269 MeV excitation, was found to be important here. The measured width of this state 11) gives only an upper limit on the transition strength, and the mixing ratio for the 2: + 2: transition has not been measured. Because of the strong similarity between the structures of 58Ni and ‘joNi, it seemed reasonable to assume a mixing ratio of 6 = -0.67 obtained from the corresponding transition in 58Ni . The effects of the 0: state at 2.286 MeV and the 3: state at 2.625 MeV were negligibly small. The calculated effects of higher excited states, in terms of how they alter the measured static quadrupole moment of the 2: state, are presented in tables 4 and 5 for ‘*Ni and 60Ni respectively. Since the effects of higher excited 4+ states involve no ambiguity in sign, they can be included as corrections to the final experimental results.

P. M. S. LESSER et a[.

572

TABLE4 The reorientation Level energy (MeV)

Spin, parity

1.454

2f

2.459 2.7753

4+ 2+

3.0378

2+

3.2635

2+

effect in 58Ni and some calculated effects of higher excited states Transition, multipolarity

E2 moment (exp) rotational E2 moment E2to2,+ E2 to g.s. and 21 + E2 to gs. and 21 + E2 to g.s. and 2r +

Calculated effect (A)

(e”;)

- 8.3 k20.2 + 1.9 I-t 0.8

Q = -0.10~0.10 QR = &0.244 -0.023 “) *0.010

+ 1.5

*0.018

* 3.9

kO.047

“) Upper limit for magnitude. TABLE5 The reorientation Level energy (MeV)

Spin, parity

1.3325

2f

2.158

2+

2.506 3.124

4+ 2+

3.269

2f

effect in 60Ni and some calculated effects of higher excited states Transition, multipolarity

E2 moment (exp) rotational E2 moment E2 to g.s. and 2r+ E2t021+ E2 to gs. and 21+ E2 to g.s. and 2, +

Calculated effect (A)

(Z)

+ 6.8 +21.7 f 1.7

Q = +0.087&0.082 Qrr = 10.276 hO.022

+ 2.2 + 0.3

-0.028 “) +0.004

+ 2.4

&to.030

“) Upper limit for magnitude.

For this purpose, however, we have chosen to use the rotor limit rather than the vibrational limit [eq. (4)] for the 4: -+ 2: transition. This limit gives better agreement with experiment for neighboring nuclei in which the 4: -+ 2: transition has been measured. With these corrections, then, we obtain the results: Q2(‘*Ni)

= -0.12+0.10

e - b,

Q2(60Ni)

= +0.07f0.08

e * b.

The effects of higher excited 2+ states involve an ambiguity in sign, as discussed more fully in previous publications ‘I ‘, ‘). Thus, a rather large uncertainty in the measured quadrupole moments of ‘*Ni and 60Ni arises from the possible effects of the 2:, 2: and 24’ states. If the effects of these three states add coherently, i.e. with the same

REORIENTATION

MEASUREMENTS

573

sign, then the static quadrupole moments are altered by ItO. e * b for 58Ni and +O.O% e - b for 6oNi. These numbers should, perhaps, be regarded as upper limits on the possible effects of higher excited 2’ states, with the probable effect being significantly smaller in magnitude. 4. Comparisons with previous measurements Two previous measurements I3“) of static electric quadrupole moments in the even nickel isotopes were made at Rochester. Since rather different experimental techniques were employed, it is particularly interesting to compare the results. The relative merits of the various techniques will also be mentioned. The absolute static quadrupole moment of the 2: state of 6oNi, as well as the B(E2; Of + 2:), was determined from a measurement of the ratio of inelastic to elastic scattering as a function of scattering angle, for both I60 and 32S projectile beams “). Position-sensitive detectors in the focal plane of a magnetic spectrometer were used to obtain the necessary high resolution. This technique has the advantage of being straightforward and relatively simple in terms of both the actual measurements and the calculations used in analyzing the data. It avoids the complications and possible uncertainties introduced by the particle y-ray angular correlation. However, it is necessary to measure precisely the improbable inelastic events in the presence of a very strong elastic peak. Difficulties are encountered when the excitation probability is very small (6 0.01) since then elastic scattering from very small amounts of target contaminants may be comparable to the inelastic scattering from the target. This was a major source of error in the 60Ni measurement ‘). The result of this measurement, ignoring the effects of higher excited states is presented in table 6 and agrees very well with the present results. Another technique, useful for obtaining precise measurements of relative quadrupole moments [as well as relative B(E2)], was developed at Rochester “). The relative de-excitation y-ray yields for 58,60962Ni, following Coulomb excitation of a thick natural nickel target, were measured using a Ge(Li) detector. Sensitivity to the relative quadrupole moments was obtained by using several different projectiles: Comparison

TALE 6 of the measured static electric quadrupole moments of the first 2 + states in 58Ni and 60Ni Ref. ..“_

Cline et al. (1969) ‘) Lesser et af. (1969) *f Present work (1973) Weighted mean of Rochester Charbonneau (1971) 14)

58Ni 1.454 MeV

--

“ONi 1.3325 MeV Oh 8

work

-121 4”) -12110 -1Of 6 - 14110

The effects of higher excited 2+ states are ignored. Units are e. fm*. “) Result assuming Q2+ =i 0 for 60Ni.

1-71 g +3z!c 5 1-l-410

I_.-

sg iJug”oddns aDuap!Aa Iwuau.+adxg .puno~8 aimas hah uo aq 01 leadde pInoM sluawa,nwaur uopawyoa~ 8u!zQlaua ut pasn hoayl uopel!Dxa qwoIno3 ayJ ‘9 aIqe$ u! uMoys se slInsa1 Ino ~I!M luatuaa& lualIaDxa ul s)uauow paugqo pue suoi o9 I p aJaw3s AIIsDgsvIauy30 uognqgsyp 3epCkra ay3 &3a;r!p paritseatu XayA *(,% -1~za n~auuoq~~q~ Lq apew uaaq aAey IN_ put2 :NZs ayl30 s)uaura_wseaK ‘!Nos ‘!Nss us sa$w +z JS.I~ayT30 swauxotu aIdnJpwtb c~;i)t?)s .~aIIeurs a.w spaBa aIqvqoxd ayi yiinoyyt! ‘!Nos 10~ tab . a 9’S T puv JN~$ 103 Z~3 . J S-L rp SBy3nr.u SCdq swauror_u aIodnlpenb paJnseauI ayl .ta)I~ UBDslDaaa asayL .rllaag -Dadsa S pue * sa1qv cuol3 uayw aq dw.u !Nos pug !Nss u! saws +z pa)!axa .Iay+y 30 spaga aIq:ssod ayL *adt;2ys~!supw~ Iep~osd~IIa awIqo Lpy8gs E 0% spuodsano3 a)t?Io”d ~I~u~~~~opa~d B 05 Pu” % (81 TOI) sI 2uawow INos ay$ a[gM ad;eys D!SLI_I.I).U~ spuodsaJlo3 puv % (fZT 1~) SFluatuour g& ayl ‘s~!uuI JOJO~p!%y ayl 30 sunal UI ‘eu3 . a S +f + = (!N,,)Zi3 ‘$uJ *2 9fOI - = (INss)Za :slInsaJ %u!~o1Io3ayl San!%swaura.uwaw .xalsatpo~ ay* jo ak?waAEpal@aM p2uy v -aJay paqpasap sluauralnssatu uoyewapoal ayl Ip2 0~ uounuo~ a.w slolla yseua~s6s alq!ssod auras ‘JaAaMoH yt$@ucaur paapur ala swaw -a.uweaua uoywa!loal wyl jagaq ayi 01 lloddns spuaI 11 y~a~yy_~~~sput? flugsala$ur Qy3adsa aq 0) $yilnoy$ st $uauraa.& sy$ ‘palEo[dwa sanbyuyDa$I~$uaur~.radxa)uaJagp ciaylw ays 30 Ma!AUI *poo%iclan aq 0~ ‘9 aiqw us ‘uaas s! !Nos pur! !Nss u! sluauI0t.u aIodnlpgnb D!WJS30 sluauractnseanr sno!;rt?h asay uaawaq watuaaA?tr IIwaho ayl xG?.I-Xuoga)i3xa-ap 30 uognqgs!p .wIn8uv ayy uo $aaga vnwodr,ul ue w!y qcq~ ‘uoyw~~xa qwoIno3 SuyoII03 uogeluapoap leaI3nu ~03 apvtu aq lsnw aDushzoIp loy~ 73~23 ay$ si ‘s+.Io.?paIa pawgdmo3 rayw sanIo.“u! 7~]wg JX?Jayl ~033 vodt? ‘anbyyw ay) JO aZk)uehpwp .IO[WIIayA *(12 +- :O :zz)g (pawnsw) aq$ JO wapuadapu! ilI@guassa aJa sgnsar ay$ pur! ‘paure$qo a_wstuanrotu aIodn.Ipenb D~EZS 30 s~uaura.nw~acualnIosqv (un) fanb!uy3al Z@unsuoa-auy ssaI puv wa!Dy3a UE s! $1 acway pua saI%ut?8ugalws ‘~3 30 Jaquntu a8.y B Ie @noauwIntu!s uaq’trl aq ~83 s$uauIamseaur (u) fs$uaAa yaIa urog pawedas LIueaI:, CUBswaaa ysoIaut (f) :al’E Sa%?$UeApX? ayl30 aI.uos *sanbyuy3ai 0~) ray10 ay$ lane s&?uIE?A~~?w~~s~p uylacr slaBo s~ua~a~n~a~ IuasaJd ay% 303 pasn $uampadxa a~uap~~u~o3A-aIcg”vd ay& .palou%f uaaq ah-ey saws payDxa .ta+!y 30 spaBa ay? u@e a3uo alayM c$u3 * a 17TZI - = (!No$a

P6’0- (!Nsr)za : SBM

~uaura.utst?aui sg$ ~11033 pautwqo SiuamouI aiodnlpgttb ogs~s !Nos ,85 aMy?fa.I ay$ JO anpA aqA .s~ua~a3ns~a~ a$nIosqt? uyqo 0~ pasn aq 2ouurr~ p0ylau.t sg ‘aslno3 30 ‘XIIW!J *pauapeoJq raIddoa @?aAtl aJaM tsala$u! 30 syvad ay$ ac?u>u!s ‘uo!s!3a_rd lua!D -yClns~J!M ewads (!?)a9 ay$ Iaad 01 paJ!nbal OSI’!SBMLtoga aIqvJap!suo3 ‘6y@ual 6laura3$xa 33~ wp ay) azAIeu~ 01 pasjnbal spIa!L la%n) yq~ 30 suoyyn5Ie3 ayl ‘dyyduy Iwtacupadxa 30 Iapow t! s! anb!uyDa) sg y8noytIv *sZc puz! ogr ‘szr

REORIENTATION

MEASUREMENTS

515

statement is exemplified by the impressive agreement between the Coulomb excitation measurement ‘) of B(E2; 0: -P 2:) for 6 ‘Ni and a recent measurement of the same transition probability using the method of resonance fluorescence I’). The results obtained by these two different methods are 928 +20 e* - fm4 and 938+20 e* - fm4 respectively, where the Coulomb excitation result has been corrected slightly i3) to include the effects of vacuum polarization and atomic screening, not included in the published result ‘). 5. Discussion A comparison of theoretical and experimental results for the even nickel isotopes, 58*6o*62Ni, has been presented in a previous paper ‘). The conclusions reached then are not altered by the present experimental results. However, for completeness we summarize the results of various shell model calculations, as well as the corresponding experimental numbers, in table 7. All of the calculations assumed an inert :iNi core with valence neutrons in the pq, f+ and p& orbitals. They differ in the choice of two-body matrix elements used to describe the effective residual interaction. The first four of these: Kuo A [ref. “)I ( unrenormalized), Kuo B (renormalized), Cohen et al. 16), and Auerbach 17), were presented and discussed in ref. ‘). In addition, we have included here the recent calculations of Glaudemans et al. 3), who used a modiTABLE 7

A comparison

of shell model

Nucleus

Ref.

calculations moments

B(E2;

e, ___-._.__ s8Ni

1.90

60Ni

1.65

62Ni

1.45

Experiment Kuo A Kuo B Cohen et al. Auerbach Glaudemans et al. Experiment Kuo A Kuo B Cohen et al. Auerbach Glaudemans et al. Experiment Kuo A Kuo B Cohen et al. Auerbach Glaudemans et al.

The five sets of shell model calculations assumed an inert indicated.

with experimental in the even nickel

2r+ + Or+) e* . fm4 145&4 137 129 151 153 162 186f4 89 111 195 204 203 179&6 64 104 183 196 183

B(E2;

results for E2 transition isotopes

22+ -for+) ez . fm4

0.36kO.14 26 42 20 20 5 < 1.5 42 50 12.5 6.3 2.7 7.1+2.2 0.33 4.0 3.2 2.3 4.2

rates and static

B(E2;

22+ + O,+)

B(E2;

22+ + 2i+)

(1.9+0.5) >: 1o-3 0.3 0.5 35 56 (4.01%) s 10-3 8.7 2.7 0.049 0.023 0.01 0.065rtO.030 0.013 6.4 0.026 0.076 0.02

Q21+ e*fm* -lo+6 -19.2 -14.6 -25.5 -26.0 -22 + 3*5 +20.7 +17.2 - 2.9 - 6.2 -17 + 5*12 -15.8 - 18.9 + 4.6 + 4.6 - 9.4

calculations differed in the two-body matrix elements used. All 56Ni core and are renormalized to the effective neutron charge

576

P. M. S. LESSER et al.

fied surface delta interaction to obtain a much better overall fit to the available data than had been obtained previously. The experimental values for static quadrupole moments of ‘*Ni and 6oNi, given in table 7, represent weighted averages of all Rochester measurements but do not include the possible corrections arising from higher excited 2+ states (see sect 3). The static quadrupole moment given for 62Ni is a weighted average of the Lesser et al. “). Charbonneau et al. r4), and Hausser et al. I*) results. Experimental values for B(E2; 2: + 0:) are taken from the Rochester measurements. They differ slightly from those given previously “) due to corrections for vacuum polarization and atomic screening affecting the 60Ni measurement ‘). Data for the “crossover” transitions, B(E2; 2: -+ O:), were taken from refs. ‘**rl). None of the shell model calculations produces very good agreement with the experimental results. Although the calculated quadrupoIe moments and crossover transition rates are quite sensitive to the choice of effective two-body interaction, it does not seem possible, within the framework of the restricted f-p shell model space, to obtain quantitative agreement for all of the even nickel isotopes. The authors wish to thank A. N. Petersen and his crew for efficient operation of the accelerator. The assistance of Dr. R. N. Horoshko and C. W. Towsley in the final stages of this experiment is much appreciated. References 1) D. C&e, H. S. Gertzman, H. E. Gove, P. M. S. Lesser and 5. .I. Schwartz, Nucl. Phys. Al33 (1969) 445 2) P. M. S, Lesser, D. Cline and J. D. Purvis, Proc. Int. Conf. on nuclear structure, Montreal (1969) p. 93; Nucl. Phys. A151 (1970) 257 3) P. W. M. Glaudemans, M. J. A. deVoigt and E. F. M. Steffens, Nucl. Phys. A198 (1972) 609 4) P. M. S. Lesser, D. Cline, P. Goode and R. N. Horoshko, Nucl. Phys. A190 (1972) 597 5) P. M. S. Lesser, thesis, Univ. of Rochester, 1971 6) L. Yaffe, Ann. Rev. Nucl. Sci. 12 (1962) 153 7) A. W&her and J. de Boer, in Coulomb excitation, ed. K. Alder and A. Winther (Academic Press, New York, 1966) p. 303 8) J. de Boer, R. G. Stokstad, G. D. Symons and A. Winther, Phys. Rev. Lett. 14 (1965) 564; A. Christy and 0. Hausser, Nucl. Data Tables 4A (1973) 281 9) I. Ben Zvi, P. Gilad, M. Goldberg, G. Goldring, A. Schwarzschild, A. Sprinzak and Z. Vager, Nucl. Phys. A121 (1968) 592 10) M. C. Bertin, N. Benczer-Koller, G. G. Seaman and J. R. MacDonald, Phys. Rev. 183 (1969) 964 11) F. R. Metzgcr, Nucl. Phys. AX58 (1970) 88 12) F. R. Metzger, Nucl. Phys. A148 (1970) 362 13) D. Cline, Univ. of Rochester reports, UR-NSRL-37 (1970) and UR-NSRL-40 (1971) 14) .I. Charbonneau, N. V de Castro-Faria, J. L. Ecuyer and D. Vitoux, Bull. Am. Phys. Sot. 16 (1971) 625 15) R. D. Lawson, M. H. MacFarlane and T. T. S. Kuo, Phys. Lett. 22 (1966) 168 16) S. Cohen, R. D. Lawson, M. H. MacFarlane, S. P. Pandya and M. Soga, Phys. Rev. 160 (1967) 903 17) N. Auerbach, Phys. Rev. 163 (1967) 1203 18) 0. Hausser, T. K. Alexander, D. Pelte, B. W. Hooton and H. C. Evans, Phys. Rev. Letr. 23 (1969) 320