Proton spectroscopy of 86, 88Sr VIA (3He,d)

Ii.E.I:2.GI I

Nuclear Physics A246 (1975) 156--172; ~ ) North-Holland Publishing Co., Amsterdam

I

Not to be reproduced by photoprint or microfilm without written permission from the publisher

PROTON SPECTROSCOPY OF se'SSSr VIA (3He, d) t M. J. S C H N E I D E R , R. E. A N D E R S O N

a n d P. G. B R A B E C K t t

Nuclear Physics Laboratory, Department of Physics and Astrophysics, University of Colorado, Boulder, Colorado 80302, USA Received 18 February 1975 Abstract: The ss. S7Rb(3He ' d)S6. SSSr reactions have been studied at 33.3 MeV incident energy. Angular distributions for eighteen S6Sr levels and ten SSSr levels over an angular range 2.5 ° _--<0~,b __. 45 ° were taken in the University o f Colorado energy-loss spectrometer. Two recent prescriptions for (aHe, d) D W B A calculations were compared with the data. Whichever prescription is used, qualitative results are unchanged: the STRb ground state has less than 0.5 f-holes and about 2 p-holes for protons, while SSRb has about 1 p-hole and 2 f-holes, and hence is not well described as a single-proton hole. This indicates that the two g~. neutron holes in SSRb prevent good closure of the If proton shell, in spite of the fact that in this nucleus neutron excitations do not mix appreciably with proton excitations.

E

N U C L E A R R E A C T I O N S sS. STRb(ZHe, d), E = 33.3 MeV; measured 0(0). S6Sr deduced levels, /, s, J, ~r; s SSr levels deduced/, s, J, n. Natural and enriched targets, magnetic spectrometer.

[

I

1. Introduction There is much interest in the proton structure of nuclei near mass 90. This region is worthy of investigation because N = 50 doses the g~ neutron shell and there is still conflicting evidence on how well Z = 38 doses the f~ and pi proton shells. Evidence in favor of good closure is given by the (3He, d) reactions on a6Sr [ref. 1)] and SSSr [ref. 2)], which show that the p~ and f~ shells are well filled and the p, and g~ shells are nearly empty in both of these isotopes. This conclusion has been recently challenged by a comparison of (3He, d) and (d, 3He)normalized spectroscopic factors for s6, 8SSr targets 3), which indicates that the occupation probabilities, V~, are no greater than about 0.8 for the f~ and p~ levels, and no less than 0.26 and 0.08 for the p~ and g~ levels, respectively, in the a6Sr ground state. This study concluded that SaSr, where these probabilities are 0.9, 0.84, 0.2 and 0.0 for the four orbitals mentioned, appears more like a dosed proton shell nucleus. The present a s. s 7Rb(aHe ' d) experiments were undertaken to shed more light on whether Z = 38 constitutes a good dosed shell. If it does, the Rb isotopes (Z = 37) should have ground states describable as single-proton hole configurations. Another motivation for the present study is the scarcity of information available on proton excitations in S6Sr. In this region the f~, p~, p~ and g~ single-particle t Research supported in part by the US Energy Research and Development Administration. tt Present address: Box 893, Homer, Alaska, USA. 156

ss. STRb(3He' d)

157

energies are extremely close. (The ~-, ½-, (½)- and (~)- states of SSRb all lie below 0.525 MeV excitation.) Therefore proton excitations should have energies comparable to neutron excitations in S6Sr, and should have energies lower than neutron excitations in SSSr, since the latter excitations can come only from promotions to the distant d~ shell. In spite of this straightforward prediction, the strengths (in the (p, d) reaction) and excitation energies of the 0.0, 1.077, 2.230, 2.855 and 2.955 MeV states of s 6Sr can be explained by the assumption that they are members of a vg~- 2 multiplet with 0 _<_J < 8 [ref. 4)]. Furthermore, excitation energies of four of the five S6Sr states below 2.4 MeV are well predicted by a shell model calculation which uses only the lg~ and 2pt neutron shells 5). One therefore wonders why s 6Sr has no lower excited states formed by proton promotion within the three close lying levels of the f-p shell, and one questions what role proton excitations play in the ostensibly vg~-2 excited states. It is a goal of this work to address these questions. The inverses of the as, SVRb(3He' d) reactions have been studied previously 3, 6) and we can therefore compare (3He, d) and (d, 3He) results for further information on the questions of shell closure and Rb ground state structure. The STRb(3He, d) reaction has also been previously studied 7), and hence the emphasis of this work will be on s 5Rb(3He ' d), although comparison of the structures of the final nuclei, differing only by two g~ neutrons, is of interest as noted above and will also be discussed.

2. Experimental procedures The ss, STRb(3He' d)S6, SSSr reactions were studied using the 33.3 MeV 3He beam from the University of Colorado 1.3 m AVF cyclotron. Angular distributions were taken for 2.5 ° =< 01ab _~ 45 °, a range sufficient to identify/-values, in the energy-loss spectrometer s). The far forward angle data were extremely useful in tracing out the contour of the forward peak in l = 1 angular distributions (thereby increasing the accuracy of calculated spectroscopic factors), and in discovering some surprising l = 0 strength in a region many nucleons from any s-orbit, The focal plane detector of the spectrometer was a helical cathode proportional counter backed by a plastic scintillator. Deuterons were distinguished from tritons and uncharged radiation impinging on the detector by the scintillator E and proportional counter anode A E signals. The deuteron signature in the scintillator was unambiguous and complete separation from background was achieved. Particle positions along the focal plane were given by the time delay between arrival of cathode signals at either end of the detector 9). Several targets of ~ 100/tg/cm 2 thickness evaporated on carbon backings were used, viz. 87RbCO3, s s, s 7RbC1' and metallic natural Rb (handled in an argon atmosphere and stored in vacuum). Many angles were taken with several targets, so that normalization of data using different targets was not a problem. Most data herein were taken with the chloride targets.

158

M.J. SCHNEIDER

et al.

The strong argon peaks in the chloride targets and the presence of two rubidium isotopes in the metallic targets both caused some regions of their respective spectra to be obscured, but with few exceptions no region was obscured with both types of targets. Peaks in the region of high level density were identified using well known excitation energies of levels populated in the 35'37C1(3He, d)36'3SAr and 13C(3He, d)t4N reactions. Absolute cross sections were determined by comparing elastic scattering on natural Rb and SSRbC1 targets to !optical model predictions using parameters describedbelow, and are estimatedto be accurate to + 20 %. Efficiency along the detector, which varied + l0 % due to spectrometer optics and variations of the scintillator signals, was measured during each data-taking session by observing the yield of the stronger deuteron peaks as they were moved along the focal plane. Oxygen coatings,

I I I I I I I i [ I I I~/-I

I I I I I f I I Ir~ t,D

I I I I [ I I I I I I I i I J I I I I I I I I i [ i i i i i f i i

i

o ~ ~°2. ,,5 ~ ~o ~

-

85Rb CI(3He

o d

L

d}

0=7.5"

Iooo J

_oo-

D ~° ~N u2 r4 B_ i ro

-

r-co

~o. z NOJ~-

N

I00

(5°

m

•

n

0 0

2-

°

o

__

Jo

1

__1

I I

I

DISTANCE

ALONG

FOCAL

I

I I I I I

I I

I

PLANE

Fig. 1. S p e c t r u m t a k e n a t 7.5 ° u s i n g a S S R b C l t a r g e t .

which accumulated as the metallic Rb was allowed to oxidize slowly, did not affect targets or resolution, which typically was about 35 keV. Deuteron yields were normalized to charge collected in a Faraday cup and, at low angles, a graphite plate. Normalization of plate to cup runs was achieved by taking data at several angles several times with both methods in succession, and led to small ( ~ 20 %) correction factors due to greater electron losses from the plate. The far forward angle data were normalized to the elastic peak in a cooled Si(Li) monitor detector at 0 = 50°. Fig. 1 shows the 7.5 ° spectrum using a SSRbCl target.

as. STRb(3He' d)

159

3. DWBA calculations

All DWBA calculations were performed with the program DWUCK4 lo). For the (3He, d) reaction, absolute cross sections are related to the output of DWUCK4 by the equation da = 4.42 2JB+ 1 C2 S O'DW fm2/sr, dl2 2JA+ 1 2J+ 1

(1)

where subscript B(A) refers to the final (initial) nucleus, J is the total angular momentum transferred, S is the spectroscopic factor for the transition, C is the isospin Clebsch-Gordan coefficient, and now is the output of DWUCK4. There exist several prescriptions for the proper way to do proton transfer DWBA calculations. Harrison and Hiebert 6) (HH) discuss these and conclude that a local zero-range calculation with the bound state spin-orbit radius 0.9 times the WoodsSaxon well radius gives the best agreement between stripping and pickup calculations. Comfort et aL 3), on the other hand, use finite-range and non-locality corrections, which tend to reduce spectroscopic factors, and further find it necessary to use a bound state well radius coefficient 1.25 fm and diffusivity a = 0.70 fm [compared to the values 1.17 and 0.75, respectively, from the global fit of Becchetti and Greenlees 1~)] in order to obtain good agreement (generally within ~ 10 ~ ) between stripping and pickup calculations. Angular distribution shapes for Rb(aHe, d) predicted by these two prescriptions are very similar over the range of angles observed in the present experiment in spite of rather large differences between the bombarding energies at which the optical parameters were determined. The Comfort prescription, however, gives curves that are slightly steeper overall, and 25 to 50 ~ higher in absolute magnitude than the H H prescription. Brief tests were made with other optical parameters 12,13) and it was found that these had little effect on angular distribution shapes, but could vary magnitudes as much as ___ 50 ~ from the values predicted by the Comfort prescription. For purposes of comparison with the inverse reactions 3, 6) of those studied here, complete (3He, d) calculations were done using both sets of parameters and prescriptions discussed above for excitation energies of 0 and 3 MeV in arSr. Predicted level strengths increased as much as 75 ~ (for p~ transfer) when going from 0 to 3 MeV excitation. The optical parameters used are given in table 1. 4. The 86Sr nucleus

4.1. PREVIOUS EXPERIMENTS Most of our knowledge of the 86Sr level scheme comes from S r y beta decay and neutron transfer studies. A 1971 data compilation ~4) shows no proton transfer reactions leading to S6Sr. Extensive investigation of the fl-decay of the 86y ground state 15) led to spin assignments or suggestions for 21 levels below 4 MeV excitation, but yielded little structure information. The decay of the S6y 218 keV isomer has

M. I. S C H N E I D E R et al.

160

TABLE Woods-Saxon optical model parameters Channel

Source (ref.)

Vo

ro

a

4 Ivs

IV,

Rb.3He Rb.3He Sr-d Sr-d bound bound

3) 6) 3) 6) 3) 6)

170.0 177.3 100.0 98.5 a) a)

1.14 1.14 1.10 1.10 1.25 1.24

0.75 0.729 0.80 0.83 0.70 0.65

0 0 49.9 62.2

18.0 17.2 0 0

All well depths are in MeV, and radii and diffusivities in fm. W, is the surface imaginary potential and channels in code DWUCK4. a) Dependent upon separation energy of bound state.

also been investigated t 6) giving insight into the 8+-0 + vg~ -2 multiplet discussed in the introduction. A (p, t) experiment ~7) has also given level spin information. 4.2. (SHe, d) 1 A N D jTr ASSIGNMENTS

Fig. 2 shows the experimental 8SRb(3He, d)angular distributions grouped by assigned/-value. Excitation energies are from refs. ~5, ~7) except for the 3.396 MeV state. The accompanying calculations use the Comfort prescription. In general, agreement with data is quite satisfactory, as is typical in (3He, d)reactions at these energies. The calculations show only small differences between the j = l -4- ½ shapes and our angular distributions do not go to far backward angles, hence no search for j-dependent shapes was made. Most assigned/-values in the present experiment are consistent with previous spin assignments. In the discussion below, the J~ assignments are those of Ramayya i s) unless otherwise noted. Some features of (3He, d)/-assignments and level strengths should be pointed out: the 2 + assignments for the 1.077 MeV and 1.854 MeV levels put no restriction on j of the l = 1 (3He, d) transitions, but the large difference in (3He, d) strengths of these two levels favors the hypothesized 4,a6) pure vg~-2 nature of the former. It is surprising to find an unambiguous s½ transfer component for the 2.482 MeV 3state along with the more likely g-transfer since the 3s~ orbital closes the next major shell at Z = 82! The low yield to this state is consistent with its possible core-excited nature ~s), but it is curious that the 3- state at 2.997 MeV, hypothesized to have quite different structure is), is also very weak here. If it is due to proton excitations t 5), these must have little overlap with SSRb (g.s.) + 7rg~. At 2.860 MeV, we do not see the vg~-2 6 + level reported by several experimenters [refs. 4, 26, 17)]. The transition to the nearby 2.878 MeV 3 + or 4 + state is apparently pure l = 1, with an estimated upper limit of 0.012 particles to any possible 1 = 3 component. The absence of the 6 + state in this experiment supports the fullness of the f~ orbit in 8SRb, since we must strip an f~ proton into our ~- target to populate

a s . STRb(aHe ' d)

161

1

used in D W B A calculations ri

ai

Vs.o.

rs.o.

rc

PNLOC

FNRNG

1.60 1.56 1.27 1.35

0.80 0.799 0.844 0.674

0 0 14.4 14.5 3. = 18 3. = 25

0 0 1.10 1.10 1.25 1.12

1.4 1.4 1.3 1.3 1.25 1.25

0.25 0 0.54 0 0 0

0.77 0 0.77 0 0 0

IV, is t h e v o l u m e i m a g i n a r y potential. P N L O C a n d F N R N G

are p a r a m e t e r s for entrance a n d exit

it. The 3- state at 2.997 MeV is populated rather weakly in this experiment with uncertain /-transfer. The 3- assignment makes g~ most likely, but l = 4 fits the (3He, d) angular distribution only if accompanied by l = 1 to reproduce the forward angle strength. This suggests the presence of a doublet at this energy. A peak near the 3.185 MeV state, assigned (3)-, is populated b y / = 1, yielding 1 + __
The ~- ground state spin of SSRb puts rather weak limits on spins of final states and therefore leaves much uncertainty in spectroscopic factors. However, the quantity ((2J r + 1)/(2J i + 1)) CZS, the number of holes filled in a given transition, is easily determined using eq. (1). For l = 3 transitions we assumej = ~ since the f~ shell is probably well filled in 8SRb. For l = 1 transitions the quantity ((2Jr+ l)/(2Ji+ 1)) C2S is not very different for j = ½ or ~. This is because the spin-orbit coupling in the

162

M . J . S C H N E I D E R e t al.

~'

85Rb(3He, d) 86Sr

I00! ~ s i

!~

i

1.854

io

_ i

'/++ +

'° ~

7

7

2.230

3,~s

• 42

,°E 1

I0

I

20

I

30

!

40 ~c.m.

I

50

r

60

I

I0

I

20

_k~

30

I

40

f

50

60

~¢.rn.

Fig. 2a. Angular distributions for the SSRb(aHe, d)a6Sr reaction which are assigned 1 = 1. The solid lines in figs. 2 and 4 are the results of the D W B A calculations discussed in the text.

bound state does not change the predicted p~-p~ cross-section ratio much from (2j> + 1)/(2j< + 1) = 2.0. Using these guides, the right hand columns of table 2 were generated. Linear interpolation between DWBA calculations at 0.0 and 3.0 MeV was used to determine predicted strengths of all levels.

: [ _

~

,00 ~ _ ~

i

J

I

85Rb{?:'/) 86Sr I

F T"

/

I

I

~

i

I

8SRb (~He, d) e6Sr

I~I'N

GROUND

EVEN AND MIXED t VALUES

I00

t~÷ I0 l

l

#/'~+

V\\ t\;

100

2.100 MeV

+ L'%";v ! / i % / iX ÷ . . . .

- .~'/ ~. ~ J - ! = o

2.673 ~=4 .m =L

,oo . ~

" toc

-

3.056

iooi

~

D , O~

7

~ ~=2+4

io ~--

Fig.

2b.

I

I0

I

20

Angular

I

I

30 40 ~c.m.

I

50

distributions

f io

I

60 for

the

SSRb(3He, d) 8 6 Sr reaction assigned l = 3.

r zo

I so

I 40

q 50

I so

0c.m. Fig. 2c. Angular distributions for the aSRb(3He,d)a6Srreactionassignedevenor mixed/-transfers.

164

M. J. SCHNEIDER et aL TABLE2 Summary of results of the aSRb(aHe, d) experiment

Ez (MeV)

i

j~r

Source (ref.)

0.0

3 0+ xs) [1 2+ is) 1.077 ~-' 1.854 1 2+ is) 2.100 3 0+ 17) 2.230 1 4+ I s) I'0 3I s) 2.482 [4 2.642 1 (2) + is) 2.673 4 5is) 2.788 1 2+ 17) 2.878 1 3 +, 4 + is) 2.997 (4) 3is) 3.056 4 (4, 5)iT) 3.185 1 1+--4+ present work 3.291 4 2--7present work 3.396 1 1+-4 + present work 3.500 3 0+-5 + present work 3.556 3 0+-5 + present work 3.687 3 3 +, 4 + is) Number of proton holes filled Total proton holes filled ~ 4.75

C2S

P 2.9 0.059 0.12 0.20 0.40 0.0028

((2Jr+ 1)/(2Ji + 1))CzS f g 0.49

0.049 0.098 0.16 0.067 0.004 0.0042

0.0036

0.028 0.043 0.037 0.072 0.038-0.049 0.037 0.38 0.008-0.025 0.44--1.3 0.38-1.1 0.22-2.4 0.13-1.4 0.49-0.63

0.033 0.036 0.069 0.060 0.057 0.043 0.57 0.013 1.11 0.57 0.41 0.23 0.74 0.95

~ 2.0

..~ 1.8

~ 0.0042

4.4. THE GROUND STATE OF SSRb The ground-state to ground-state transition has a spectroscopic factor S = 3.2 in g o o d agreement with the value 3.1 determined by C o m f o r t e t al. a) in the inverse reaction. Table 2 shows that in the (3He, d) reaction a b o u t one particle is stripped into the p-shell and, more importantly, a b o u t two particles are stripped into the f-shell. This comes very close to exhausting the sum rule limit, which is three holes in the f-p shell (assuming the g~ orbit is empty). It is unlikely that m u c h more ptransfer strength lies above 3.7 M e V excitation. This is because the p r o t o n configurations likely to be f o u n d in the 8SRb g r o u n d state, f - 1 p t - 2 , fg.-lp/r-2 ' and f - a , (written with respect to a filled f-p shell) have unperturbed energies below 1 MeV. In arty event, the presence o f at least one p-hole and two f-holes in the g r o u n d state o f aSRb contradicts the simple picture o f a single p r o t o n hole Z = 37 nucleus, and therefore o f Z = 38 as a g o o d closed shell. In the (aHe, d) reaction, a total o f a b o u t 4.8 particles are stripped into the SSRb nucleus below 3.7 MeV excitation, populating 18 levels. 90 % o f this strength feeds only eight a 6Sr levels and these deserve closer attention: the simplest picture o f s SRb ' 7rf~-lp~-2vg~ -2, mandates that the lowest states (3He, d) populates are (i) the 0 + g r o u n d state o f 868r by f÷ stripping, (ii) a 2 + and 3 + state by p , stripping, and (iii) 2 - - 7 - states by g~ stripping. The g r o u n d state is indeed populated strongly, and so

as. aTRb(aHe' d)

165

are two g~ states. However, just one strong l = 1 transition and five strong l = 3 transitions are seen. A more complicated a 5Rb proton wave function seems necessary therefore, and inclusion of the configurations mentioned in the above paragraph yields the following positive parity states: 0 +, 2 +, 3 + from the first configuration as described above; 0 + and 1+-4 + by l = 3 and 1 stripping, respectively, into the second configuration; and 0 +, 2 +, 4 + by l = 3 transfer into the third configuration. Thus a plausible explanation for the five l = 3 transitions is provided. However, the absence of substantial l = 1 (3He, d) strength suggests that the f - 3 component may be large compared to the other two. Because the optical parameters of Comfort et al. 3) are for projectiles of substantially different energies from the present experiment, spectroscopic factors were recalculated using the Harrison and Hiebert 6) parameters (and DWBA prescription). With this calculational mode the numbers of p-, f-, and g-protons stripped into 85Rb are ~ 1.4, ~ 2.8, and ,~ 2.4 respectively. Hence our qualitative conclusions are u n c h a n g e d - i n fact SSRb looks less like a single ft proton hole n u c l e u s - i f this formalism is followed. 4.5. LEVELS OF SrSr Previous experiments 5) have identified eight 86Sr states below 3.2 MeV excitation as arising from two neutron holes in the g~ and p½ orbits, as indicated in fig. 3. This identification is strengthened by the present experiment, which transfers a total of only 0.20 protons into these states (excluding the ground state). In fig. 3 levels are labeled "strong" or "weak" depending on whether they are populated in (SHe, d) by transfer of more than 0.5 protons. The ground and 1.854 MeV states are the only strong states below 3 MeV. Hence in spite of the close spacing of the p,, p t and f~ proton orbits suggested by levels of 8SRb (and aVRb), proton excitations do not mix substantially with low-lying neutron excitations and play little role in 86Sr below 3 MeV excitation: 3.6 protons are transferred into 7 levels above 3 MeV, but only 1.2 protons are transferred to 11 levels below 3 MeV. It is curious that two g÷ neutron holes can strongly affect proton configurations (in that the valence orbit and proton distributions are different in 8SRb and 87Rb as demonstrated below) but do not mix with them. We have no explanation for this phenomenon. 5. The aSSr nucleus

5.1. PREVIOUS EXPERIMENTS Early studies of the inelastic scattering of various projectiles from s 8Sr [refs. 2,1s )] gave some J~ assignments and concluded that this nucleus is not well described as collective. Neutron capture experiments x9) suggested some J~ values, and studies of SSRb t-decay and comparisons with other experiments 2o) have given more J~ and structure information. The irrelevance of neutron excitations to low-lying states of 88Sr was demonstrated by the 87Sr(d, p) experiment 2~), which populated states below

166

M.J. SCHNEIDER STRONG

3.687

"

3.556 3,500 :3.396 .3.29 I

,, ,, . WEAK

5.056 2.997 2.955 2.878 2.855 2.788

It

,,

2.642 2.675

"

2.482

. ,, STRONG

WEAK

p;J2g;~2 4--~

5.185

STRONG WEAK WEAK WEAK

et aL

-2 g9/2 -

g922

~ 8+ 6+

PlY2 g9112 5

-2: g9/2

2.2130

4+

o o~3

0.0 0.0 0.069

0.004 0.067

2.100

1.854

i

1

1.077

g-gz/2 2 +

0.050

I

0.205

!

i I

STRONG

0.0

Fig. 3. Levels of S6Sr. Strength in the (aHe, d) reaction (as defined in the text) is listed at the left. Neutron excited states' excitation energies are listed separately from those of proton excited states. Assigned neutron configurations 5) and number of protons transferred in (3He, d) are listed at the right.

4 MeV very weakly. (3He, d) experiments on 88Sr [ref. 2)] have suggested that it is well described as having a closed Z = 38 shell, but (d, 3He) on 8SSr [refs. 6, 22)] and comparison of normalized spectroscopic factors for (3He, d) and (d, SHe) [ref. 3)] demonstrate that this description is not adequate. Detailed shell model calculations for 88Sr have also been done 7, 23.24) and agree with many of the results of the above experiments. The 87Rb(3He, d) experiment has been previously studied at 21 MeV

ss. STRb(3He ' d)

167

[ref. 7)], but several differences will emerge between the results of that study and the present one. 5.2. T H E a7Rb(aHe, d ) I - A S S I G N M E N T S A N D S P E C T R O S C O P I C F A C T O R S

Fig. 4 shows experimental 87Rb(3He, d) angular distributions along with the appropriate DWBA curves from the SSRb(3He, d)calculations. Excitation energies are from ref. 7). Yields to some of the higher excitation aaSr states were obtained indirectly from peaks in the natural Rb spectra due to overlapping 86Sr and SSSr states. The uncertainty in this procedure appears to have been underestimated, as the angular distributions differ more from DWBA calculations than for s 6Sr states. However,/-values remain unambiguous and the increase in uncertainty of spectroscopic factors is small. The present experiment at 33 MeV bombarding energy populates all states below 4.1 MeV excitation seen at 21 MeV [ref. 7)], with the addition of an l = 1 transition at 3.63 MeV. In all, six l = 1 and four l = 4 transitions are seen. The lower density of states in SSSr, where the g~ neutron shell is dosed, attests to the importance of neutron excitations in 8 6 S r . TABLE 3 S u m m a r y o f results o f t h e S7Rb(aHe, d) experiment E~ (MeV)

l

j~r

0.0 1 0+ 1.836 1 2+ 2.734 4 33.155 1 0+ 3.220 1 2+ 3.489 1 (1 +) 3.587 4 (4-) 3.63 1 (3 + ) 3.955 4 34.020 4 3--6N u m b e r o f p r o t o n holes filled Total p r o t o n holes filled m 4.9

Source (ref.)

C2S

2,18) 2.18) 2,1s) 27) 2, ~s) 7) 7) 7) 20) present work

3.0 0.38 0.55 0.20 0.30 0.32 0.25 0.04 0.37 0.23-0.43

((21r+ l )/(2Jt+ l ))C2S p

f

0.75 0.48

< 0.2

g

0.96 0.050 0.380 0.24

< 0.14 < 0.17

0.072

< 0.02

0.57 0.64 0.75 ,~ 2.0

< 0.53

~ 2.9

N o l = 3 transfer was seen, b u t t h e u p p e r limit to the l = 3 strength present h a s been e s t i m a t e d for t h o s e levels where 1 = 3 is allowed.

The/-values for all levels are identical to those seen at 21 MeV bombarding energy and are consistent with, but add little information to, previous d~ assignments or suggestions. A serious discrepancy with the 21 MeV experiment 7) is apparent from table 3, however. Spectroscopic factors in that experiment are always larger than present ones, with the difference increasing almost uniformly with excitation energy. It may be that those spectroscopic factors fail to take into account the substantial increase in predicted cross section with excitation energy.

168

M . J . S C H N E I D E R et aL

The ground state p~ spectroscopic factor of 3.0 agrees with that of the inverse reaction 3). That this value is ¼ of that expected from a simple rcp~-lp~ -2 model affirms the complexity of this state noted by many investigators 6, 7, 2 o). The spectroscopic factors for the2 + levels at 1.836and 3.220 MeV (0.38 and 0.30 respectively) can be used to test the wave functions of Hughes za) and of Shastry 24) for these states. All that is needed is the wave function for the s 7Rb ground state. This has been calculated by Shreve 7), but the only number given by him is the coefficient 0.92 for the rcp÷-lp~ -2 component. It turns out, however, that under a reasonable assump-

t

I

I

-7-

J

j

i [-

87Rb(3He,

/~

d} 88Sr

i

.e.=l

!-@ , '

i-

GROUND STATE

--

IOOO

q :1

~7 Joo0

- 1

-i

.! _i

oo

I

[

-!

.

,o

~

! 4

1

i i

~ L___I

. tO

_~ 20

! 30

' _ 40 Oc.rn.

L_ 50

.2 60

J I0

20

50

40

50

60

~'C. i"n.

Fig. 4a. Angular distributions for the aTRb(3He, d)SaSr reaction assigned 1 = 1.

as, S T R b ( a H e ' d )

I

L

i~/'~

i

L

169

]-

I

87Rb(3He, d)eaSr

I00

r

I00

.~87

"c

ta %.

~L c:l

55

I00

'7, -1

I [00

0

I0

20

308C.m.40 50 60 I

Fig. 4b. Angular distributions for the aTRb(aHe, d)aSSr reaction assigned l = 4.

170

M . J . S C H N E I D E R e t aL

tion, the other amplitudes are unimportant. The assumption is that there are only two other major components in the 87Rb ground state wave function, so that it can be written as ku(s 7Rb(g.s.)) = 0.92 np - l p -2 + c¢~cp -3 + (0.1536- ~2)~lrf~-2p~- 1, outside of a closed 7rf~p~p~vg~ core. The choice of ~least favorableto the Hughes wave functions is ~ = (0.1536- c~2)~ = 0.277. In this case Hughes predicts spectroscopic factors of 0.82 and 0.26 for these two states, while Shastry predicts 0.15 and 0.20. For most other choices of ~, the Hughes wave functions predict spectroscopic factors closer to our experimental results, but the Shastry prediction does not change, since transfer into only the first term in our 87Rb wave function populates 2 + states given by his wave functions. Thus almost independently of ~, Hughes' 88Sr wave functions predict trends and magnitudes of those spectroscopic factors better than those of Shastry. A choice of ~ m o s t favorable to Hughes is ct = - 0.36, yielding spectroscopic factors of 0.31 and 0.23 for these two states. This model wave function for the 87Rb ground state will be discussed further below. The strength of the 3- state at 2.734 MeV speaks against its being strongly collective 2). The experimental spectroscopic factor of 0.55 compares reasonably well with the value 0.78 predicted by Shastry 24). The weakness of the second 0 + state, at 3.155 MeV, shows that it is strongly orthogonal to the 87Rb ground state. If the 3.63 MeV state is truly 3 + [-refs. 7, ~9)]. Here, its presence in this reaction is interesting, since no combination of two p , or p~ holes can combine to 3 +. Hence there must be some f~ hole strength in the s 7Rb ground state, even though this level is populated by l = 1. In fact, the only configuration in the ground state of 87Rb into which a proton can be stripped to populate this 3 + state is rope-~p~-~f~-t. Using our spectroscopic factor and the wave function of Hughes for a 3 + state predicted at 3.81 MeV, we find the amplitude of this component to be 0.103, i.e., a 1 ~ admixture in the ground state of a 7Rb" The negative parity levels at 3.955 and 4.020 MeV have spectroscopic factors TABLE 4 Spectroscopic factors for various states in STRb(3He, d)SSSr Source SSSr: ref. 23) aTRb: ~ p - lp½- zj 8SSr: ref. 23) 87Rb: complex ~ wave function ! experiment

0t +

2x +

02 +

22 +

(11 + )

(3x +)

2.8

0.57

0.90

0.33

1.0

0.0

2.6

0.31 a)

0.39

0.23 a)

0.85

0.0

3.0

0.38

0.20

0.30

0.32

0.04

The complex wave function deduced in sect. 5 is kP(S7Rb g.s.) ~ 0.92ztp~_-lp~-2--0.36ztP~r-3q0.155 f~-Zp~-X with respect to a filled f-p shell core. ~) The a7Rb wave function was deduced by maximizing agreement between calculation and experiment for these two levels.

as, aTRb(aHe ' d)

171

too small to be used in assigning spins. This conclusion contradicts a previous (3He, d) result 7) and a possible reason for the disparity (excitation energy dependence of the calculations) is given above. All possible distributions of two proton holes in the p½, Pt, and f~ orbits produce three 0 +, two 1+, five 2 +, two 3 + and one 4 + levels, compared to the known two 0 +, one (1 +), two 2 +, one (3+), and no 4 + aSSr levels below 4 MeV populated in (3He, d). Hence (3He, d) populates less of each J~ than theoretically possible. If one assumes that 87Rb has a pure 7zp~r-lp~-2 ground state, then the present reaction should populate a 0 +, 1 + and 2 +, all by l = 1, showing that more sophistication is needed. In fact, the sophistication is needed in aTRb, since using the SaSr wave functions of Hughes with a pure 87Rb ground state the predicted spectroscopic factors for the six positive parity levels seen are not satisfactory, as shown in table 4. A more sophisticated 87Rb wave function, the one deduced above, provides some improvement but could be further improved upon, especially for the 1 + level. We note that this state is high enough in excitation to have a v g ~ - l g l component, which would explain the low spectroscopic factor, but more of this neutron particle-hole excitation is needed than was predicted in a recent calculation 25).

6. Conclusion-comparison of SSRb and STRb Overall, three l = 4 protons and two l = 1 protons are stripped into STRb in this experiment. The argument used for S6Sr that there should be little I = 1 strength at higher excitations is applicable here, too. No identifiable l = 3 strength is seen in STRb(aHe, d), and our estimated upper limit to the l = 3 strength that may be present is 0.5 particles. [The absolute upper limit to this strength is 1.5 particles, since in the (t, ¢t) reaction on this nucleus, 4.5 protons are picked up 26).] Hence in (aHe, d) no more than 2.5 particles are stripped into the f-p shell, compared to the sum rule limit of 3.0. We are not able to say how the l = 1 strength is distributed between the P~r and p~ orbits, but it seems reasonable that a substantial portion of it goes to the p~ orbit. Thus we can say that the valence (p~) orbit in SVRb has less than two holes. Our conclusion, then, from comparison of this result with the two valence orbit (f~) holes in SSRb is that the single-hole description is poorer for S5Rb than for S7Rb, and hence Z = 38 forms a better closed shell when N = 50 than when N = 48. This reinforces the conclusions of investigation of the inverse reactions to those studied here 3) and of the (3He, d) reaction on S6Sr [ref. 2)] and SSSr [ref. 1)]. Finally, we restate the enigma that the two neutron holes in SSRb cause a substantial redistribution of protons (compare the two p-holes and < 0.5 f-holes in 87Rb with the one p-hole and two f-holes in 85Rb, and consider the change in the valence orbit from f~ to p~ when the two neutrons are added) but yet there is little mixing of proton- and neutron-excited states in 86Sr. We are grateful to Profs. E. Rost and J. J. Kraushaar for reading this manuscript.

172

M . J . S C H N E I D E R et al.

References 1) J. V. Maher, J. R. Comfort and G. C. Morrison, Phys. Rev. C3 (1971) 1162 2) M. M. Stautberg, J. J. Kraushaar and B. W. Ridley, Phys. Rev. 157 (1967) 977; J. Picard and G. Bassani, Nucl. Phys. A131 (1969) 636 3) J. R. Comfort, J. R. Duray and W. J. Braithwaite, Phys. Rev. C8 (1973) 1354 4) J. E. Kitching, W. Darcey, W. G. Davies, W. McLatchie and J. M. Morton, Phys. Lett. 32B (1970) 343, and references therein 5) J. E. Kitching, W. G. Davies, W. J. Darcey, W. McLatchie and J. Morton, Nucl. Phys. A177 (1971) 433 6) J. F. Harrison and J. C. Hiebert, Nucl. Phys. A185 (1972) 385 7) D. C. Shreve, University of Rochester Report UR-NSRL-33 (1970) unpublished 8) B. W. Ridley, D. E. Prull, R. J. Peterson, E. Stoub and R. Emigh, to be published 9) E. W. Stoub and R. A. Ristinen, to be published 10) P. D. Kunz, unpublished 11) F. D. Becchetti, Jr. and G. W. Greenlees, Phys. Rev. 182 (1969) 1190 12) Y. Shamai, D. Ashery, A. I. Yavin, G. Bruge and A. Chameaux, Nucl. Phys. A197 (1972) 211 13) C. R. Bingham and G. T. Fabian, Phys. Rev. C7 (1973) 1509 14) R. L. Auble, Nucl. Data Sheets 135 (1970) 151 15) A. V. Ramayya, B. Van Nooijen, J. W. Ford, D. Krmpoti~ and J. H. Hamilton, Phys. Rev. C2 (1970) 2248, and references therein 16) M. L. Simpson, J. E. Kitching and S. K. Mark, Nucl. Phys. A186 (1972) 171; M. Ishihara, H. Kawakami, N. Yoshikawa, M. Sakai and K. Ishi, Phys. Lett. 35B (1971) 398 17) J. B. Ball, J. J. Pinajian, J. S. Larsen and A. C. Rester, Phys. Rev. C8 (1973) 1438 18) E. W. Hamburger, Nucl. Phys. 39 (1962) 139, and references therein; J. Alster, D. C. Shreve and R. J. Peterson, Phys. Rev. 144 (1966) 999; G. A. Peterson and J. Alster, Phys. Rev. 166 (1968) 1136; J. Picard, O. Beer, A. E1 Behay, P. Lopato, Y. Terrien, G. Vallois and R. Schaeffer, Nucl. Phys. A128 (1969) 481; F. E. Cecil, R. P. Chestnut and R. C. McGrath, Phys. Rev., to be published 19) J. L. Irigaray, G. Y. Petit, P. Carlos, B. Maier, R. Samama and H. Nifenecker, Nncl. Phys. Al13 (1968) 134; H. Schmidt, W. Michaelis, C. Weitkamp and G. Markus, Z. Phys. 194 (1966) 373; H. Lycklama and T. J. Kennett, Nucl. Phys. A139 (1969) 625 20) R. C. Ragaini and R. A. Meyer, Phys. Rev. C5 (1972) 890, and references therein 21) E. R. Cosman and D. C. Slater, Phys. Rev. 172 (1968) 1126 22) C. D. Kavaloski, J. S. Lilley, D. C. Shreve and N. Stein, Phys. Rev. 161 (1967) 1107 23) T. J. Hughes, Phys. Rev. 181 (1969) 1586 24) S. Shastry, Nucl. Phys. A142 (1970) 12 25) F. E. Cecil, T. T. S. Kuo and S. F. Tsai, Phys. Lett. 45B (1973) 217 26) A. B. Tucker, K. E. Apt, J. D. Knight and C. J. Orth, Phys. Rev. C6 (1972) 2075 27) R. C. Ragaini, J. D. Knight and W. T. Leland, Bull. Am. Phys. Soc. 11 (1969) 1238