A study of levels in 141Nd with the (d, t) AND (3He, α) reactions

NuclearPhyatca A280 (1977) 1-d2 ; © Nortk-Bollard Publfahing Co., Anlsttrdasi Not to be e+eprodooed bY P>~~ ~ mlao8lm ~~ ~~ P ~m tbe Du

A STUDY OF LEVEIS YN 1~iNd WITH THE (d, t) AND (aHe, a) REACTIONS

S. El-KA77A7.f~ J, R, LIEN and G. LGJVHPlIDEN Institute ojPhysics, Unlutrstty of Bugen, Bugen, Norway P. KLElI1IiEiNZ Institut fQr %dnphysik, %FA JWich, D-SI70 Jfllkh, F.R. Germany C. ELLEGAARD, J. BJERREGAARD ând P. KNUDSBN Nltlr Bohr Institute, Univtrsity of Copenhagen, Copenhagen, Denmark and J. REKSTAD Instituts of Physics, Univtrsity of Oslo, Oslo, Norway Received 8 December 1976

Abs4xd : The level structure of' 41 Nd up to 4 MeV excitation has been investigated by the (d, t) and ('He, a) reactions with beams of 17 MeV deuterons and 24 MeV 3He particles The arFgutar distributions have been analyzed with standard DWHA calculations and spectroscopic factors are deduced. The lg~ 1 and lh~ 1 states are severely fragmented in this N~ 81 nucleus. E

NUCLEAR REACTIONS ' 4sNd(d, t), E = 17 MtV; measured o(E ~.'~Nd(sHe, a), E = 24.0 MeV; measured a(Ea, B) . "1 Nd dedl}ced levels, L, S. Enriched targets.

1. Introdaction Single neutron hole excitations of the N = 81 nucleus have been studied recentl~r with both the (p, d) and (d, t) reactions l' 2). Essentially pure 2d .ß 1, 3sß 1 and lh~.l single neutron hole states were found below 1 MeV of excitation energy . Fragme~tation into several levels with excitation energies between 1 and 3.5 MeV was reported for the 2d} 1 and lg~ 1 strengths. However the spectroscopic factors for 1= 4 and. 5 transitions deduced l' s) from the (p, d) and (d, t) reactions differ by a factor of two. Comparison for the lg~ l and lh~l strengths with existing nuclear model predictions for N = 8.1 nuclei 3) therefore remains difficult. The aim ôf the present study is to resolve this disc>"epancy through further measuréments of the states populated with high-I transfer using ,the (3He, ac)[eaçtiQn wl}ich preferably populates the states with high 1. Unfortunately, the absolute magnitude of the (3He, a) cross section is difficult to predict since the DWHA normalization constant for that reaction is not well known. We have therefore also studied la1Nd t Permanent address: Cairn University, Faculty of Science, Physics Dépt:, ~Gizâ; Egypt.

April 1977

2

3. BIrR.A~~A3 et al.

m

Y Z

W

t~

ww ~~i ~3d s1Nno~

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Û X W

LEVELS 1N l'1Nd

d

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b

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.. s

O a i.i Ô

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h s ^ a O

v

^ a û

3

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G C .. .-, Ô

ri

.,

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en ~O O~ v~ ~ h N .: ~ .: ri Ô Ô Ô

.-.

.-. .~

r, r, ^ ^ ^ .~ ^ ^ .~ ~.

b

v ~ vv ~ v v*v ~ v vv

d

v^ ~ ^ e .. ., ..

r

'S

N O h N ~ N N

V z ..

v °~ v v~

N a

â v~ v N vN h v~ vh v~

y

v~ v

vv

0

a

3 c.x b

ôô ., ..

.. û i + ~

v

e~ ., ~ aô M

h

e

â ..

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..

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a~ ~ w 8

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s

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3.'~K ~-~~~~ st âl.

through the (d,~t) reaction where the DWBA . norn~alization . i$ : more reliable . From comparison of the two sets of data we derived an empirical (~He, a) normalization constant, pertinent for the particular DWBA analysis employed here. 2. Faperi~hl'detaüa anä rewlta The experimçnts were performed with 17 MeV, deuteron and 24 MeV 31?TTe beams from the Niels ~ohr'Ynstit~u,~e : Taâdgm Vex de Graaff a~lerator; Thë. reaction products were anal3+zed in the Elbak-type multiangle spectrograph ~) aâd detected with nuclear emnlsiôns, which have been scanned on the Bergen Univérsity automatic plate scanner s~. The 142Nd . targets .were, .made from enriched .(> 95 ~~) Nd203 reduced to Nd mëtaI and evaporated onto carbon~backings. The târgât thicknesses were ~ 175 pg~pm2 for the (3He, a) reaction and ~ 50 ~gfcm2 for the (d,t) :measurements. , Cross-sectiog normalization was obtained thrôugh comparison pf the measured yield of elastic~Wy scattered particles to the elastic scattering cro8s sectiôn calculated from the ~V~HA described below. The elastic,scattering yield was measured in separate short eXpos~tces; long and ~sh~t exposures wére normalized dvith a Si detector at fixed geometry recording elastically scattered particles. The reaction producfà were recôrded at twelve angles . between 7.5° and .77.5° for the (3He, a) reaction, and:at eleven angles between.7.5° and b2:5° for that (d, t} re-

u~ m z 0 H U W U7 [J~ O U U

Fig. ~. -Anaulac :djstributiona for the (d, t) reaction. the solid Çurvea. #eaylr-irom DWHA calca]afions and the pointa reprnaerif:experimöd~tal âgta:' , .' .

LEVELS IN 1 siNd. i o~

vo-~

zo

4o

io-=

so eo

~ o-=

20

40

60

60

io-~i . , I0 - ~

20 ~ 40 ~ 60 ~ 60

~ io-~ I0 - ~

20

40

60

60

20

40

60

60

20

40

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60

10 - =

20

0

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60

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0

io-~

20

40

60

60

io-m .

.v io -~i .,

C~M~RN L

1 20 ~ 40 ~ 60 " 80

.v , o . .

Fig 3. Angular distributions for the (sHe, a) reaction. The solid carves result from DWHA calculations and the points represent experimental data .The angulardietdbution labelled 3.800 represents the background counts from 3.3 MeV to 4.1 MeV of excitatott .energy fitted wlth .an 1.= 4 sad S DWBA curve calculated for the average eaccitation energy of 3.81)0 MeV.

$, F,UKA77A7 et al.

6

Teats 2 Optical model parameters used in the DWBA calculations Part.

Ya

d

.

Wi

-106 .63 1.100 0.820

t 'He a

ae

ra

bound n

rI

o,

Wn

Y....

r....

4 .0 .

1 .249 0.818 63 .6 -11.26 0.980 1.00 1.30

-133 .00 1.240 0.700 -16.42 1.420 0.890 -136.00 1.200 0.720 -40.00 1 .430 0.840 -168 .70 1.378 0.317 -21.60 1.378 0.317 ')

r.

1.230 0.630

1.23 1.40 1 .30

.i=30

Potential atrongths in MeV, lengths in fm. ') Adjusted by the computer program to ßt the neutron separation energy. The analytical expression of the potential is Y ~ Yc-i-Y~j(r, R,i, W~-~ Y, ., . ~ ~!~(r.1i!. .... W...)L . S-I-iwj(r. R~. ai)+iWp ~j(r, Ri . wh~e j(r, Rr, a~)

(1-f-exp((r-Rw)/~M))-1 . x =(r-Rr)/~v . RN = rNA }; N = R, I, s.o .

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10

Qi).

20

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40 e C.M .

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50

60

70

BO

0 e C.M.

Fig. 4. Calculated (d, t) (left) sad ('He, a) (right) angular distributions for. I-trander valses of the 30 < N < 82 shell. The earvas are calculated for ¢values corresponding to as excitation energy in 1`~Nd of 1 MeV.

LEVELS IN i4iNd

7

action. Energy resolutions of 12 keV in the triton spectra and of 30 keV in the aparticle spectra were obtained. Representative spectra for each of these reactions are shown in fig. 1, where the data are plotted on a common excitation energy scale to facilitate comparison. Eight levels up to an excitation energy of 1.9 MeV won observed inthe (d, t) reaction ; in the (3He, a) processfifteen levels upto 3.5 MeV wen located. The maximum cross section and the energies averaged from all angles an presented in table 1 for each reaction . The estimated uncertainty for the excitation energies in table 1 is f 10 keV and t 5 keV for the (3 He, a) and (d, t) reactions, respectively. The uncertainties in the relative cross sections are of statistical nature only; the uncertainty in the absolute cross sections is estimated to be t 15 ~. The measured angular distributions for the states populated in the (d, t) and (3He, a) reactions an shown in figs . 2 and 3, when they are compared with the angular distributions calculated from the DWBA. 3. DWBA calculations The calculations were performed with the DWBA code DWUCK 6). The (d, t) angular distributions were evaluated with the inclusion of a finite range correction and . aon-local potential corrections in the entrance and exit channels but not for the bound neutron. The optical parameters were those by Childs et al. ~) for the deuteron channel and those given by Flynn et al. s) for the tritons. For the bound neutron a real potential well radius of 1 .25 A} fm and a diffuseness of 0.65 fm was used. The depth of the potential well was adjusted to reproduce the experimental binding energy . The 3 He parameters of Becchetti and Greenless 9) and the a-parameters given by McFadden 1° ) were employed for the ( 3 He, a) DWBA calculations . They were performed in the zero-range approximation. The optical model parameters are summarized in table 2. Calculated angular distributions for both reactions and all 1-values of the 50 < N < 82 shell are shown in fig. 4. 4. The l-tramfer valses and spectroscopic factors Spectroscopic factors 5,f wen computed from a least squares fit of the calculated angular distributions to the data points. The spectroscopic factors are given by the relation %_da 1 \dDl e:p where v°~ = op~c=/(2j+ 1). The normalization factor N = 3.33 is used for the (d, t) reaction. The normalization factor for the ( 3 He, a) reaction is not well known and values ranging from 17-50 have bean reported 11 ). The value N(3He, a) = 16.6 was determined from our data by comparing the (d, t) and ( 3 He, a) cross sections to the states at 0, 757, 1226 and 1343 keV which an strongly populated is both reactions and are considered to be the best understood levels in 1°1Nd.

"8

S. F.YrKA7.7.A7. 'at pJ.

~: . An inspection of the (3He,. a) .angular distributions show that the data are well described by the DOHA predictions, and that angular distributions with low 1-values are quite different from transfers of 4 and 3 units of angular momentum. It is, however, rather difficult to distinguish between I = 4 and 1= 5 angular distributions although there is a tendency for the latter to fall off faster at backward " angles . The (d, t) angular distributions were of great value for the determination of the l-values .for the low-spin states which " often are weakly populated in (3He, a). In particular, the 1= 0 transitions exhibit a characteristic peaking at forward angles, which..provides an unambiguous ~}+ assignment from the (d, t) data . An independent -assignment is obtained from comparison of the (3He, a) to.the (d, t) cross sections populating the same level. However, due to. the large negative Q-value of the (d, t) reaction, the triton spectrum could only be measured up to 1.9 MeV excitation where the elastically scattered deuterons are focussed on the nuclear emulsions. All information on the higher lying levels therefore is obtained from the (3He, a) data alone.

4 .1 . TRANSITIUNS WITH l = 0

A transition to the 194 keV level was observed both in the (d, t) and (3He, a) reactions showing the characteristic behaviour of zero angular momentum transfer (figs. 2 and 3). The previous studies l' ~) have reported a state with spin ~+ at an excitation of 1.9 MeV. In the present (d, t) experiment this level is partly obscured by elastically scattered deuteron groups and a complete angular distribution could therefore not be measured. The strength of the state is too weak to be seen in (3He, a). I7n the (3 He, a) reaction these éxists a severe mismatch for 1= 0 transfer. This rxplains the large difference in the spectroscopic factors deduced from the (3He, a) and (d; t) reâctions for the ~+ level at 194 keV. 4.2. TRANSTTIONS WITH 1= 2

The transitions to the levels at 0, 1223, 1565, -1820, 2071 and 3402 keV all have angular distributions characteristic of 1= 2 transfer and these states thus have spin and parities ~* or ~+ . The i4iNd ground state is known is) to be ~+ and the large spectroscopic factor indicates a fairly pure 2dß neutron-hole configuration for that level The strongly populated level at 1223 keV as well as the four higher lying more weakly populated 1= 2 states have been assigned .as ~+ in ref. 1). These authors give detailed arguments, principally based upon the transition strengths and on the level energy systematics in the N = 81 isotones. These same arguments fully apply for our results. Foster et al. 2) observed s marked~difference at B = 40° in the (d, t) angular distributions for the ground state (~+,) and 1226 keV level (~+) which they attributed to a possible }-dependençe, Such a dependence is not apparent in our (d, t) data (cf. fib. 2).

LEVELS IN iupd

9

4.3 . TRANSITIONS wiTH I = 4 AND S

Three transitions with l = 5 and five transitions with ! = 4 are located in the (3He, a) spectra. Of these, only the levels at 757 keV (! = S) and 1346 keV (l = 4) lie within the energy range covered in the (d, t) reaction and therefore can be given definite l-assignments. As mentioned before, the similarity between the ! = 4 and 5 angular distributions makes it difficult to distinguish between these I-values ; probably the (p, d) angular distributions t) can distinguish them more clearly. The isomeric state at 757 keV is known t' Z . ' a) to have spin ~- and our data unambiguously give ! = 5 for this state. T~t,s 3 Experimental and theoretical values of the summed spectroscopic strength and centroid energies of neutmn singlo-hok states S~, ~ (exp)

2d~ t

2.8

4

-0.34

1 .4

2

0 0.93

3s~ t 1 h~ t

Theoretical sum rule limit 2J-I-1

>"~ (axp) (MeV)

Orbital

7.0

12

2d# t

3 .3

6

1

3.8

8

g~

1

E~ (theor.) " ) (MeV)

-0.23 0 0 .43

1 .3

1 .1

Z.1

2 .3

') Ref. e) .

The 1346 keV state, which earlier t ) had been assigned as l = (4) can now be given definite 1 = 4 assignment from the (3He, a)/(d, t) cross-section ratio. Our data agree with the previous t ) ! _ (4) assignments for the two rather strongly populated levels at 2313 and 3112 keV. Two additional, more weakly populated states (1968 and 3041 keV) are also best fitted with l = 4. The angular distribution as well as the large (3He, a) cross section to the state at 2924 keV strongly favour an l = 5 assignment, in.contrast to ref. I) where an ! = 2 and 4 doublet is assigned at this energy . 4'.4 . NEUTRON SIIVßLE-HOLE ENERGIES

The centroids EJ of the neutron single hole energies for the different orbitale are calculated according to EJ = ES,~~~su, where 5,f is the experimentally determined spectroscopic factor (table 1) .of the level with excitation energy EJ. The results are given in table 3 zelative to the energy of the 3s} orbital. The theoretical single hale energies sae quoted from ref 3). With the exception of the. lh~t orbital, the agreement is good.

3. Eir~w3-~3 et a~

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3.5

3

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0.5 t.tf tn"_ _ __ % tn" t .e tn" _ . . x~ vx" _ _ 0 utNd uaSm Heyde 8 Brussanrd

predictia~na of Heyde Fig. S. The experimental level scheme of 14'Nd comparod with the theoretical iaa~ lini: sa)l, and Hruaaaard a), and with the experimental level scheme of

5. Diecmrion add caaclaebne

In table 1 the present spectroscopic factors are compared with those deduced in the previous (d, t) and (p, d) measurements. Our results agree well with the (d, t) work by Foster et al. ~), but the spectroscopic factors from the (p, d) measurements') disagree for 1= 4 and 5 transitions by more than a factor of two. A similar discre-

LEVEL~3 IN 'a'Nd

11

panty, but only for 1= 4, has been noted in the (3He, a) [ref. ia)] and (p, d) [ref. 1)] spectroscopic fedora in the isotone ia3Sm . If the spectroscopic factors deduced by Jolly and Kashy 1) are normalized to the value obtained in the present work for the - level at 757 keV there is good agreement for all levels. The spectroscopic information obtained is compared in fig. 5 with the particlevibration calcuations of Heyde and Brussaard 3 ). In this model the collective quadrupole vibrations of up to three phonons of the 1 aZNd core are coupledto the neutron single-bole states . For the low-lying ( < 1 .5 MeV) states which are rather well understood, the agreement between the model and the experimental data is quite good with the exception of the lowest ~- excitation which experiment establishes to be severely more fragmented than predicted in the model calculation. Only half the predicted strength is located in the lowest lh~l excitation, and two additional strong lh~l excitations, at 2205 and2924 keY, were found inour experiment . Thepooragreementof the calculated lh~l excitation with experiment is also apparent in table 3, where the experimental 1h.~1 single-holeenergy lies 500 keV above the value used inthecalculations . A similarlq poor agreement between calculation and measurement has also been noticed ia) for the neighbouring isotone'a3Sm. The most probable reason for the unsatisfactory agreement between theory and experiment is the neglect in the model of odupole vibrations which are expected to dominate the coupling of the h~. opposite parity orbital in the odd nucleus. For the higher-lying levels, the experimental results in general demonstrate stronger fragmentation of the spectroscopic strength than predicted by the model calculation. A ~+ state with a spectroscopic factor of 2.6 predicted at an excitation of 2.5 MeV is not confirmed èxperimentally. Instead, three scattered ~+ levels are located in the region 1.8 to 3.5 MeV with a summed spectroscopic strength of 1.4. For the lg~' state the lowest ~+ level has the spectroscopic factor predicted by the model . The model, however, predicts a strongly populated level at about 2.5 MeV, which is not located experimentally. Instead four weaker peaks that have been assigned (~+) are located in the spectrum above 2 MeV. It is apparent from the results presented in table 3 that appreciable strength is missing for the lg~ 1 and lh~i states, which are preferably populated in (3He, a). The missing strength most likely indicates severe fragmentation of these high-spin states, and one may speculate whether the considerable background always observed in the (3He, a) spectra at excitation energies > 3 MeV, is due to such fragments. In order to test this assumption, the background counts from 3.5 to 4.1 MeV of excitation were summed, and the angular distribution for these particles is consistent with 1= 4 or 5 (see fig. 3). Assuming 1= 4 or 5, spectroscopic strengths of 4.2 and 1 .7 may be deduced, respectively, for the background cross section within this energy range. This portion of the background cross section could thus account for as much as 60 ~ of the available g~ strength or 16 ~ of the h~ strength . It is interesting to compare our results with a recent experimental study 1 a) of

12

S. BIIK.:~~~w7 et àl.

~ta3Sm.($g. 5): In l4~Smmorefragmentationof theltigh-spinstates (lg~1 and lh~l) was also found experimentally than predicted bythemodelof Heydeand Hrussasrd 3 ). Howevei, the experimental level spectra of iaiNd and ia3Sm exhibit striking similarities . Ia the region below 2.3 MeV the levels (with the exception of a very weak ~-.level and~a tentative ~}± level ia .~a3Sm) come in the same order with almost identical spectroscopic factors. In both nuclei there are two strongly popu]ated ~- levels in the region 2.2 to 3 MeV. and several ~* levels with appreciable spectroscopic strength . This surprsingly good agreement between the isotones is obviously not mirrôred in the present s) theory. One of us (S. El-Kazzaz) would like to thank Prof: A. Graus and his colleagues for thoir hospitality during his stay, and is grateful to the NORAD authorities for the fellowship offered to him. Thanks are due to Ms. E. Fotland, H. Helland, K. M. Hovland and L. Olsvik for careful scanning of the nuclear emulsions. 8efereaces 1) 2) 3) 4) S)

R . K. Jolly and E. Keahy, Phys . Rev . C4 (1971) 887 I . L. Fester, O. Diotzech and D . Spalding, Nucl. Phys. Aim (1971) 187 K. Heyde and P. J . Brueaaerd, Z . Phya . 299 (1973) 15 J: H . Bjetre~d; Fys. TidslQitt (1972) no . 2-3, p . 49 A. C~raue, 3. Dines, C~. föstevold and P . Hansen, Scientific Technical Report No. 86, University of Hergen, May 1976 6) P . D . Kunz, DWBA code DWUCK, Version 8, University of Colorado, Boulder, Colorado 7) J. D. Childs, W. W. Daehnick and M. J . 3piaak, Phya. Rev. C10 (1974) 217 8) E. R Flynn, D . D . Armstrong, J. C~ . Heery sad A . C~. Blair, Phya . Rev. 182 (1969) 1113 9) F. D . Hecchetti, Jr. and Q. W. Cireealesa, Annual Report of the J. H. Williams Laboratory of Nuclear Physics, University of Minnesota, 1969 10) . L. McFadden and C~ . R Satchler, Nucl . Phya. 84 (1966) 177 11) T. .K. Lim, Nucl . Phya . A148 (1970) 1 . 12) Nucl. Data Sheets 10 (1973) 151 13) K. Kotayima sad H. Morinaga, Nucl . Phys . A16 (1960) 231 14) E. Friedland, M. Goldschmddt, C. A. Wiedner, J. L . C: Ford, Jr. and S . T. Thornton, Nucl. Phya. A296 (1976) 93