Level structure of 28Si by the 27Al(3He, d)28Si reaction

Nuclear Physics A376 (1982) 61-80 © North-Holland Publishing Company

LEVEL STRUCTURE OF 28Si BY THE 2'Al(3 He, d)~Si REACTION H. NANN* Cyclotron Laboratory, Michigan State University, East Lansing, Michigan 48824, USA and Department of Physics, Northwestern University, Evanston, Illinois 60201, USA Received 26 August 1981 Abstract: The level structure of ~Si up to an excitation energy of 15 .5 MeV has been studied by the z'AI(3He, d) zs Si reaction at 35 MeV bombarding energy. The experimental angular distributions were analyzed with distorted-wave Born approximation calculations . Values of the transferred orbital angular moments / and spectroscopic factors were obtained for about sixty levels. Strong transitions to about twenty odd-parity states up to 15 .5 MeV excitation were observed and identified with the (ldsjzlf~~z) and (ldsjz2ps~z .r~z) configurations . Tentative isospin assignments were made by wmparison with zsAl levels . E

NUCLEAR REACTIONS z'Al('He, d), E = 35 MeV; measured Q(Ed, B), levels, l, -rr, T, spectroscopic factors ; DWBA analysis.

zs Si deduced

1. Introduction

In the simplest shell-model picture, the 1dSiZ subshell is filled at ZBSi. The one-particle, one-hole aspects of the ZBSi level structure can be studied by singlenucleon transfer reactions on the adjacent nuclei Z'Al and Z9 Si. However, this is only true to the extent that the ground states of Z'Al and Z9Si can be described as a pure 1d5~ Z proton hole or a pure 2s r iZ neutron particle with respect to a ZBSi core, respectively, and that the single-nucleon transfer mechanism does not excite the core appreciably. In the present paper we report on the single-proton transfer reaction Z'Al(3He, d)ZBSi. In this reaction one should expect the excitation of simple (dsiZ) -t (2stiZ, ld3 ~Z, .lf,iZ, 2p3iZ,tiZ) proton particle-hole configurations in ZBSi. Some of these configuration states have been studied by Barnard and Jones r) and by Kalifa et al . Z) via the Z'Al( 3He, d)ZBSi reaction and by Bohne et al. s) via the Z'Al(d, n)ZBSi reâction . The aim of the present work is to extend the knowledge of the Z'Al(3He, d)ZBSi reaction to levels above 10 MeV, and especially to look for the 1= 3 strength which is carried by a few levels (with spin J~ = 3-, 4-, 5-, and 6-) strongly populated in the ZBSi(p, p') reaction 4) at 135 MeV bombarding energy . This includes proton-unbound levels above Ex = 11 .585 MeV. It was possible to identify the levels observed in the present Z'Al( 3He, d)ZB Si experiment with * Present address: Physics Department, Indiana University, Bloomington, Indiana 47405, USA. 61

H. Nann / ~Si i: ~f

LZ'9

N

v

M Q

N

68'9 + 88'9

a~

M (p ~ n

_O W m 68'8

-~

"

"

9._ L

" (00'0) 3~y

Z6'Ogp68'01

Lß'I I 68'I I

~Q~ wn

aL~ll

9£'bh

6b'ß I

~

-

v x

â

eo w ß0'S I ZI'ßl -

~

..

01 = £L'01~

Eb'II~

_

i

_

"""

8

~3NNVFPJ 2i3d S1f~100

H. Nann / Ze Si

63

resonance levels seen in proton and/or alpha capture reactions S'6). Tentative isospin assignments to some levels in ZeSi were made by comparing the spectroscopic factors obtained from the Z'Al(3He, d)ZB Si reaction to those from the Z'Al(d, p)ZeAI reaçtion . 2. Experimental procedare and resalts A 35 MeV 3He beam from the Michigan State University cyclotron was used for the present experiment . The target consisted of a self-supporting aluminum foil of about 180 Wg/cmZ thickness and was made by the evaporation technique. The reaction products were momentum analyzed in an Enge split-pole magnetic spectrograph and detected in the focal plane by a position-sensitive proportional counter with delay-line readout, backed by a plastic scintillator . This detector system provided excellent spatial resolution and particle identification. An overall resolution between 25 and 30 keV was obtained . Data were taken in 4° steps from 6° to 34° and then in 5° steps to 59 °. A deuteron spectrum obtained at 6° is shown in fig. 1 . Groups belonging to levels in ZBSi are labeled by their excitation energy . Contaminant groups due to the (3He, d) reaction on 1ZC and 160 are shaded . The spectra were analyzed by a peak-fitting program. The excitation energies of the levels observed in the present experiment are given in tables 1 and 2. They have been obtained by using a least square fit to several calibration lines involving the impurities 1ZC and 160 and some levels of ZaSi, the excitation energies of which are accurately known from other experiments. Included in tables 1 and 2 are data from the recent compilation of Endt and Van der Leun') . Angular distributions were extracted for about 60 transitions up to 15.5 MeV in excitation . They are displayed in figs. 2-6 according to the exhibited orbital angular momentum transfer. In order to normalize the relative cross sections at different angles, the beam on target was monitored by recording, with a NaI scintillation counter, the 3He particles elastically scattered at 90° from the target material . The relative cross sections are estimated to be accurate to t5% . The error in the absolute cross sections due to uncertainties in the determination of the target thickness, the solid angle and the beam integration is estimated to be smaller than 15%. 3. Distorted-wave analysis A distorted-wave Born approximation (DWBA) analysis of the experimental data was performed using the code DWUCK s). The optical-model parameters used were taken from the work of Barnard and Jones 1) and are listed in table 3 . Finite range and nonlocality corrections were not included, since they improved

Fig. 2 . Experimental angular distributions for predominant l = 0 transitions of the 2 'Al( 3 He, d) ZSSi reaction . The solid curves shown are fits to the data in the angular range from 6° to 40°. The dotted curves show the amount of each individual component.

Fig . 3 . Experimental angular distributions for predominant 1= 2 transitions of the Z 'Al( 3 He, d) 2sSi reaction . The solid curves shown are fits to the data .

w E v

bv

ec.m .

Fig. 4. Experimental angular distributions for transitions to negative-parity states in ZsSi. The solid curves shown are fits to the data in the angular range from 6° to 40°. The dotted curves show the amount of each individual component.

ec. m .

Fig . 5 . Experimental angular distributions of the Z~AI(3 He, d)ZB Si reaction for transitions with ambiguous l~ecomposition .

ec.m . Fig. 6. Experimental angular distributions of the Z'Al(3He, d)ZB Si reaction leading to proton-unbound states . The curves are DWBA predictions for the indicated l-values.

Fig. 6 (continued)

H. Nann

70

/ 28Si

TABLE 1

Spectroscopic information on bound states in 28Si from the Z~AI( 3He, d)~Si reaction, compared to various data Level no.

(',ompilation'~ Ex (keV)

1' ; T

Present experiment IP

(2l+1)Sp

ref . 1 )

2 0+2

0 .67 1 .58, 2 .83

0 .6 1 .7, 0.8

Ex (keV)

3 4 S 6 7 8 9 10 11 12 13 14 15 16 17 18

4979 .1 6276 .3 6691 .4 6878 .E 6888 .8 7380.7 7417 .3 7798 .8 7933 .4 8259 .4 8328 .3 8413 .3 8542 .9 8588 .9 8903 .7 8944 .8

0+ 3+ 0+ 3+ ~ 4 2+ 2+ 3+ 2+ 2+ 1+ 46+ 3+ 1(4 + ,5 -)

4980 6273

20 21 22

9315 .9 9380.5 9418 .1

23 24 25 26 27 28 29 30 31

9479 .9 9497 .3 9702 .0 9762 .8 9794 .2 9929 .2 10179 .9 10210 .0 10272 .3

32 33

10312 .1 10376 .0

3 + ; T=1 2 + ; T=1 (2 + ,3 -, 4+) 2+ (1, 2 + ) S(2, 3)(2-4+ ) (1, 2)3(2 + -4 + ) (0, 1)' ; T=1 (2 + -4 + ) 3~ ; T=1

36 37

10540 .3 10597 .3

38 39

10668 .E 10724 .7

42 43

10901 .0 10915 .8

(2l+1)S ;

0.6 1 .6, 0.9

7382 7419 7802 793E 8262 8332 8414 8588 8899 8942

0+2 1 +3 2

3 .67, 4 .41 0.09, 0 .04 0 .23

9313 9378

0+2 0+2

4 .84, 1 .28 2 .38, 2 .45

9488

0+2

0 .16, 2 .54

9698 9758

3 1+3

2.6E 0 .70, 0 .22

0 .6

9928 10178

1 +3 1 +3

0.10, 0 .24 0.41, 0 .50

0.3 0.3

10268

2

0 .18

10309 10374

2 0+2

0 .38 0.81, 5 .38

(1 - -4 - ) 1+ ; T=0+1 3+ 1+ ; T=0+1

10535 10594

1+3 2

0.20,0 .22 0 .61

10665 1072E

0+2 2

0.92, 0 .1E 0 .12

1 + ; T=1 a=nat ; T=0

10893 10917

2 0+2

1 .17 1 .04, 1 .35

6 .0

5 .5

2 .0, 2 .2 <0 .08 0 .28, 3 .0 4 .0

ref . 3)

~ 1 +3 2 0+2 0+2 0+2 0+2 0+2 2 1 +3

6882

0 .22, 1 .4E 5 .49 0.02, 0 .651 0.05, 0 .63 0 .99, 0 .74 0.76, 1 .75 0.07, 2 .11 0 .31 0.09, 1 .67

ref. 2)

(0 .06) 2 .8

1 .4 0 .7, 0 .5 1 .2, 0.8

2 .4, 3 .4

1 .3 1 .0, 0 .6 0 .8, 2 .0 0.06, 2 .4 <0 .5 0 .04, 1 .7

0 .6, 0 .5 0.6, 0.8 (1 .2)

2 .6

2 .8, 3 .8

2 .4, 2 .7 0 .12 (0.4)

3 .4, 3 .4 2 .2, 1 .0

3 .1, 1 .6 1 .5, 1 .2

0.2, 3 .4

71

K. Nann / ZBSi T.~LS 1 (continued)

Level no.

CompdaUOn`~ E~(keV)

1° ;T

Present experiment E=(keV)

lo

(2J+1)Sô

0+2 11075 ~ or 1+3

47

11077.8

52

11296.8

1 -; T = 0

11292

55

11434 .3

56 57 58 59

11434.E 11446.2 11516.7 11576.5

(2, 3)+; (T=1) 4; T=0 1+; T=1 2+ 6-

0+2 11431q{ or 11+3 1151E 11575

3

(2J+1)SP ref. 1)

ref. 2)

ref. s)

1 .01, 1.71 0.76,0.81

3.65, 7.94

1.0, 7.9

2.77,4.6E 6.20

`) Ref. ~). b) ü fitted by ir =0+2+1+3, one gets (2J+1)SP =3 .20, 4.66, 0.56 and 2.41, respectively . The excitation energies of the present experiment have an estimated uncertainty of t8 keV.

the fits to the data only marginally beyond 35 ° . The spectroscopic strengths G,; _ (2Jj + 1)Sy were extracted from the data by minimizing the quantity CZGI' ~ i~ N~J~+1

~nwucrc(e +)

2j+1

-~°xP ( B' ))

d~;

through the adjustment of the coefficients G,; by fitting the DWBA predictions to the experimental angular distributions. Here ~nwucx(B ;) are the numbers output from the program DWUCK, v°xP(9,) are the experimental differential cross sections and dv; are the errors in the experimental numbers. The number of data points n includes all observations at angles up to 40 ° . The quantities J,, J; and j are the final, initial and transferred angular momenta, and 1 is the transferred orbital angular momentum . The quantity C is an isospin Clebsch-Gordan coefficient which, for the ( 3He, d) reaction on a T; = Tz; = z target, gives CZ = z for both possible Tf = 0 and TF =1 states in the final nucleus, N is an overall normalization factor depending on the overlap of the 3 He and deuteron wave functions and has the well stablished value of N = 4.43 [ref. v)] . The relation given above contains an incoherent sum over 1 and j, the transferred orbital and total angular momenta. For odd-A target nuclei, often both j =1 - 'z and j =1 + z can be added vectorially to the target spin to form the (supposedly known) spin of the final state. The j-values actually taken in the analysis are decided by shell-model arguments. In the present analysis, the 1= 0, 1, 2, and 3 curves were calculated assuming 2sä2, 2p3iZ, 1d3î2, and 1f,; 2 transfers, respectively . Since the

72

H. Nann / ~Si TABLE 2 Transitions to unbound levels in ~Si observed in the Zs Si('He, d) 28 Si reaction Compilation') E~ (MeV)

11 .658 11 .779 11 .780 11 .901 11 .977 12 .073 12 .074 12 .195 12 .242 12 .302 12 .489 12 .664 12 .743 12 .803 12 .860 12 .918 12 .990 13 .051 13 .116 13 .189 13 .190 13 .205 13 .247 13 .248 13 .428 13 .484 13 .557 b~ 13 .612 q 13 .616 q 13 .707 q

!~ ; T 2 + ;0 2+ ; 0 (2 +, 3 - , 4+) ; 0 (2 +, 3 - , 4+) ; 0 2 + ;0 2 3 - ;0 q+ ; p } (1 -, 2 + ) ; 0 3-; 0 4- ; 1 3 - ; (1) (3, 4+) (2 +, 3 - , 4+) ; 0 (2, 3) + ; 1 32- ; 1 3; 0 2 + ;0 (2, 3)+ 0 5 - ;1 2 2+ , 3, 4 3-, 4+ 2,3,4 + 3 - ,4 +

13 .902 ~ 13 .980 q 12 .984 n)

2,3 2+ ,3 2+ , 3 -

14 .358

6 - ;1

Present experiment Es (MeV)

lp

(2J+ 1~5;

11 .656 11 .776

1 +3

0 .22, 1 .62

11 .893 11 .972

2 1+3

4 .68 0 .22, 1 .48

12 .070 12 .919

1 +3 1

0 .36, 0 .65 1 .75

12 .244

2

0 .61

12 .304 12 .485 12 .656 12 .738 12 .796 12 .855 12 .914 12 .990 13 .049 13 .115

1 +3 3 3 1+3 3 1 +3 2 1 1 +3 3

0.76, 0 .36 1 .49 6 .68 2 .83, 0 .22 0 .81 0.11, 0 .36 0.45 0.68 0.63, 0 .22 0.50

13 .195

3

0 .96

13.249

3

5 .87

13 .618 13 .709 13 .801 13 .898

1 3

1 .44 0.47

13 .gg3

3

1 .64

14 .044 14 .096 14 .216 14 .257 14 .360 15 .053 15 .123 15 .494

1 3 1 3 3 3 3 3

1 .91 0 .79 2 .57 0 .47 4 .95 0 .45 0 .81 0 .61

13 .430 13 .489 13 .559

') Ref. ~) . ~ Ref . s ) . The excitation energies of the present experiment have an estimated uncertainty of t 10 keV.

H. Nann / ZBSi

73

Tnsl.s 3

Optical=model parameters used in the DWBA analysis of the Z'Al('He, d)28 8î reaction

3He

d bound state

V (Me~

r (fm)

a (fm)

W~ (Me~

179.12 85 .5

1 .113 1 .05 1 .25

0 .716 0 .84 0 .65

28 .9

WD (MeV)

(fm)

r

a' (fm)

10 .6

1 .312 1 .28

0 .969 0 .808

Vs (MeV)

r~ (fm)

6 .8 A = 25

1 .4 1 .3 1 .25

rs=r,as =a .

ground-state spin of 2'Al is i+, the transitions to the J~ = 0+ states in ZBSi have to . proceed by 1d5î2 transfers. With the spin~rbit strength used here the calculated differential cross sections for a 1d5î2 transfer were about 30% higher than for a 1d3î2 transfer independent of the excitation energy of the final state. Above Ex > 11 .58 MeV, states in ZaSi become proton unbound and a special treatment of the formfactor for these states has to be used to extract spectroscopic factors . The formfactors for the unbound levels were calculated using the method of Youngblood et al. 1°). This method generates the wave function for the unbound particle in a Woods-Saxon well, the depth of which is varied to minimize the ratio of the exterior to interior amplitude of the wave function for a particle of the quantum numbers (nlj) at the appropriate binding energy . Calculated cross sections for 2s1î2, lp3n, 1d3î2, and lf, n transfers to bound and unbound levels are shown in fig. 7. The transition from bound to unbound is smooth and the trend in the cross sections for the unbound levels continues as it is foreshadowed from the bound region . Thus the method used for calculating form factors of unbound states appears to produce meaningful results. The angular distributions leading to the bound level are presented in figs . 2-5 and those leading to the unbound states in fig. 6, together with the DWBA fits . Angular distributions with shapes not characteristic of a direct stripping reaction mechanism are not shown. The differential cross section of these transitions was usually three orders of magnitude smaller than those of the strong transitions. The separation of mixed 1= 0 + 2 transitions (see figs . 2 and 3) into their constituent parts is facilitated by the fact that the first maximum of the l = 2 shape coincides with the first deep minimum of the 1= 0 shape. The analysis of mixed 1= 1 + 3 transitions (see fig. 4) is somewhat more ambiguous, since the l = 1 and I = 3 shapes are rather structureless. Small 1=1 admixtures can be detected in a predominant 1= 3 angular distribution at the forward angles, but large admixtures of l = 3 will remain essentially undetected in a strong 1= 1 transition . The spectroscopic strengths G,i obtained in the above manner are listed in table 1 for the bound states and in table 2 for the unbound states . For the strong transitions to the bound states, an error of about 25% should be assigned to the extracted spectroscopic factors. These errors contain contributions from both the DWBA

74

H. Nann / ZsSi

Fig. 7 . Calculated DWBA differential cross sections for different (nlj) transfers as a function of the excitation energy in the final nucleus . States above Ex = 11 .585 MeV are proton unbound .

analysis and the experimental data . Since the treatment of transitions to unbound states in the DWBA model is less established and tested, an error of about 40% should be attributed to these spectroscopic factors. For comparison, table 1 contains spectroscopic factors obtained from previous (3He, d) [refs.''Z)] and (d, n) [ref. 3)] studies. In the present experiment more l = 0 strength was detected than previously due to the extension of the angular distributions to very forward angles . Nevertheless, the overall agreement is quite good and the differences lie within the usual errors associated with the DWBA analysis. Recently, Kato and Okada tt) investigated the 2 'Al(3He, d)ZgSi reaction at 25 .8 MeV bombarding energy with an overall resolution of about 110 keV and obtained spectroscopic factors for the 5 - and 6-, T = 0 and 1 states in ZgSi. However, they could not uniquely determine the lP = 3 transfer for the transitions to these states . Their results obtained with the assumption of l, = 3 transfers agree with the present ones within the assigned uncertainties . The transition to the unresolved 3--4+ doublet at 6.88-6 .89 MeV was fitted with both l = 2 + S and ! = 1 + 2 + 3 curves . The inclusion of the l =1 admixture yielded essentially no improvement of the fit (see fig. 5) but reduced the l = 3 strength, whereas the 1= 2 admixture remained the same. The angular distribution leading to the state at 11.08 MeV was decomposed into both a 1=0+2 mixture and a l = 1 + 3 mixture. Inspecting fig. 5, the l = 1 + 3 fit (right half) is slightly better than the 1=0+2 (left half). This ambiguity can be removed, for example, if the parity

H. Nann / ZB Si

75

of this state is known. For later application of the sum rule, the l =1 + 3 decomposition was used. Similarly, the transition to the doublet at 11 .43 MeV was fitted. Here the 1= 0 + 2 mixture gave a somewhat better agreement with the experimental data. For the transitions to the states at 11 .97 and 12 .85 MeV, both a pure l = 2 and a mixed 1=1 + 3 transfer yield similar fits to the experimental data (see fig. 6) . Again the 1= 1 + 3 decomposition was used in the later application of the sum rule . Since Z'Al has a ground-state spin J~ = i+, the observation of an 1= 0 transfer restricts the spin of the final state to 2+ and 3+. This and the information ~r = natural') leads to a J~ = 2+ assignment for the 10 .92 MeV state in ZB Si. Levels populated with 1= 2 can have spins and parity ranging from 0+ to 5+. The observation of an 1= 1 transfer yields J~ _ (1-4)-, and 1= 3 gives J~ _ (1-6)- . From the results of the present work several new T = 1 assignments can be suggested for levels in ZBSi. They are based on the following so-called "weak" arguments: (a) The Coulomb energy difference between the ZBSi level and its ZBAI parent should be approximately constant . (b) The spectroscopic factors for one-proton and one-neutron stripping reaction data on Z'Al should be equal. The T =1 states of ZBSi, selected according to these rules, are listed in table 4. 4. Spectroscopic strengths The spectroscopic strengths extracted from the present experiment are listed in tables 1 and 2. Their distribution among the various levels is displayed in fig. 8. Included in this figure are the spectroscopic factors from ref. 15) for the transitions below 6.27 MeV which were not measured in the present experiment. The sum rule which relates the upper limit of the spectroscopic strength for proton stripping on a target with a spin J; and isospin T; to the number of proton i6) and neutron holes for a particular orbit (lj) in the target is given by CZ _ 1 1 (neutron holes) ;; G~' ~ 2J; + 1 2 T; +

forTf =T;+Z,

CZ _ 1 (proton holes)t; 1 (neutron holes),; 2 T; + ~ 2J; + 1 Gi' -

for Tt = T; - i .

A comparison of the sum rule strengths for the different orbits with the extracted experimental strengths yields information about the number of holes in the target nucleus wave function . The summed strengths, centroids and sum rule limits from the simple singleparticle model for the different orbitals are given in table 5 . From the transitions to the 0+ states, only about 60% of the total ldS;Z single-particle transfer strength

76

H. Nann / ZsSi

TABLE 4

Spectroscopic information on analog states in ZBSi-~Al zsSi

ZsAI

E (MeV)

1~ ;T

lo °)

9.32 9.38 10 .27 10 .38 10 .60 10 .72 10.90

3+ ; T=1 2+ ;T=1 (0, 1)+; T=1 3+ ; T=1 1+ ; T=0+1 1+ ; T=0+1 1+ ; T=1

0+2 0+2 2 0+2 2 2 2

(2J+1)S; °) Ex (MeV) 4.84, 1.28 2.38,2.45 0.18 0.81, 5.38 0.61 0.12 1.17

lA

I

(2J+1)S~ ref .' z )

ref. is)

0.00 0.03 0.97 1.01

3+ 2+ 0+ 3+

0+2 0+2 2 0+2

4.3, 1.2 2.0,1 .1 (0 .20) 0.44, 7.5

3 .1, 0.42 1.7,0 .54 0.30 0.30, 4.7

1.37

1+

2

0.85

0.78

2+(3+)} 0+2 0+2 2+

0.16, 1 .4

0:12, 1.9

11 .43 q (2, 3)+; T=1

0+2

3.65, 7.94

1.623 2.14

11 .90

(4+); T=1

2

4.68

2.66

4+

2

4.9

3.1

12 .66 12 .74

4- ; T =1 3- ;(T=1)

3 1+3

6.68 2.83,0.22

3.47 3.59

4-(2 -) 3-

1 +3 1+3

1.0, 5.E 1.3,4 .2

0.78, 5.2 0.90,4.1

12 .918

(2, 3)+; T=1

2

0.45

3.67

3+

0+2

0.04, 0.13

0.03, 0.42

13 .05

2- ; T=1

1+3

0.63, 0.22

3.88

2-

1+3

0.37, 1 .4

0.30, 0.90

13 .25

5- ; T =1

3

5.87

4.03

5-(3 -)

1 +3

9.3

14 .04

1

1.91

4.69

(2, 3) -

1 +3

2.2, 0.55

1.2, 2.1

14 .22

1

2.57

4.91

2-

1+3

1.2, 0.30

0.72, 1 .6

3

4.95

5.17

(6)-

3

8.5 ~

14 .36

6- ; T=1

0.75, 2.7

0.66, 1.8

0.12, 4.7

°) Present experiment. Doublet, fitted only with 1p = 0+2. ~ Ref . la).

isseen. The remaining strength could not be extracted, since the present experiment did not allow us to distinguish between a ldsiz and ld3iz transfer for transitions to non-zero spin states. Some lds iz strength is seen for the transition to the (0 +) ; T =1 state at 10.27 MeV indicating that the ld siz neutron orbital is not completely filled in the ground state of the target nucleus z 'Al . Indeed, from the studies of the z 'Al(3He, ~) z6A1 [ref. ")] and the z 'Al(p, d)z6 A1(refs . 18 '' 9 )] it is known that the 1d 5~z neutron orbital is only about 75 to 80% filled in the ground-state wave function of z'Al . The extracted 2sl~z spectroscopic strengths for both T = 0 and T = 1 states (see table 5) is in good agreement with the sum rule limit. However, it should be noted

H. Nann / 28Si

77

~o

a b N

O% T O~

m

v N =

m O N_ "~

iG

m

a N 0

W

M u

NQ N W

w

~O

v ô e

o -

F_

N

F_

.°

~ N

N ~ .

a

0 . 0 p

a

~5 O v

A "w"

ry

I.

d

78

H. Nann / ZaSi TABLE S

Summed spectroscopic strengths and centroid energies from the Z~AI( 3He, d) ZSSi reaction

Configuration nlj

T~

1d,~ 2 °)

0

2s 1 ~2 `) ` 1d3~2 .b) 1f~~ 2

lps~a

1 0 1

0

1

0

1 1 1

E G observed

limit

Centroid (MeV) =E (EG,~)/E G,j

7 .07 0.18 11 .91 11 .68 25 .25 18 .83 26 .69 17 .94 7 .02 7 .94

12 0 12 12 24 24 48 48 24 24

0 .47 10 .27 7 .03 10 .06 7 .48 10 .66 11 .63 13 .33 11 .89 13 .56

°) Includes the spectroscopic strengths for the states below Es =6 .27 MeV from ref. ") . b) Includes also ld s ~ Z transfer strengths for states where it could not be separated from the ld 3 ~Z transfer .

that there exist inaccuracies in the DWBA analysis ; for instance the inclusion of finite range and nonlocality would reduce the spectroscopic strengths by approximately 20% . The energy splitting of the T = 0 and T = 1 centroids of the 2s,~2 configuration is about 3 .0 MeV. This number can be compared to the T-dependent term in the modified surface delta interaction (MSDI) used in several shell-model calculations around A = 28 . In this interaction 2°) the spacing between the T = 0 and T = 1 centroids of levels is given by d = 4B. Values for B of 0.7 MeV [ref. 2')] and 0.8 MeV [ref. 22)] have been used in the past which yield a spacing in good agreement with the present value . On the other hand the spacing between the T = 0 and T = 1 centroids can be~used to calculate the nuclear symmetry potential. Using the formulas given by Bohr and Mottelson Zs) one obtains a value of Vt ~110 MeV. The experimental, summed l = 2 transfer strength to the T = 0 states exceeds the 1da~2 sum rule limit, since some of the 1d5î2 transfer admixtures could not be separated out in the present experiment. On the other hand, nearly no 1d5î2 admixture should be present in the summed l = 2 transfer strength to the T = 1 states . Only small fractions of the l = 1 and ! = 3 experimental spectroscopic strengths (see table 4) are seen. The missing ! = 1 strength is probably spread over many unobserved unbound levels which have considerable widths due to the small centrifugal barrier. In contrast, the l = 3 centrifugal barrier is much higher, but quite some 1= 3 transfer strength could have escaped observation because of the difficulties described above.

H. Nann /, ZS Si

5.

79

$U111~18irf

The structure of levels in 28Si has been studied with the 2'Al( 3He, d)ZSSi reaction at a bombarding energy of 35 MeV. Angular distributions for a total of about 60 transitions were analyzed with DWBA calculations to extract the transferred l-values and spectroscopic strengths. In the present experiment, nearly all l = 0 strength was detected, since the measurements of the angular distributions were extended to very forward angles. For the [(ldsn)-t (2st~2)t ] configuration, it was found that the T=0 strength is spread over many states between 1 .78 and 10.92 MeV, whereas the T =1 strength is concentrated in only four states . From the energy spacing between the two centroids a value of Vt -110 MeV for the nuclear symmetry potential was obtained . Some ldsiZ transfer strength was observed for the transition to the (0+) ; T =1 state at 10.27 MeV indicating that the neutron ld siZ orbital is not completely filled in the ground-state wave function of 2'Al. This is in agreement with the results of the Z'Al( 3 He, a) and Z'Al(p, d) reactions. The observed, summed spectroscopic strengths for l =1 and l = 3 transfer is considerably below the simple, single-particle shell-model limit for the 1f,~2 and 2psiz orbitals . The remaining, unobserved strengths probably are spread over many weak states and, therefore, escaped detection. The author is grateful to D. Youngblood and R.L. Kozub for performing the DWBA calculations for the transitions to the unbound levels . The assistance of J.A. Nolen, Jr., in data taking and many useful discussions with G,T, Emery are gratefully acknowledged . This work was supported in part by the US National Science Foundation and the US Department of Energy . References 1) R.W . Barnard and G.D . Jones, Nucl. Phys. A108 (1968) 641 2) J. Kalifa, G. Rotband, M. Vergnes and G. Ronsin, J. de Phys . 34 (1973) 139 3) W. Bohne et al., Nucl . Phys . A131 (1969) 273 4) G.S. Adams et al., Phys . Rev. Lett. 24 (1977) 1387 5) M.A . Meyer, I. Venter and D. Reitmann, Nucl . Phys . A250 (1975) 235 6) J. W. Maas et al., Nucl . Phys . A301 (1978) 213 7) P.M . Endt and C. van der Leun, Nucl. Phys. A310 (1978) 1 8) P.D . Kunz, University of Colorado, private communication 9) R.H . Basel, Phys . Rev. 149 (1966) 791 10) D.H . Youngblood, R.L . Kozub, R.A . Kenefick and J.C . Hiebart, Phys . Rev. C2 (1979) 477 11) S. Kato and K. Okada, J. Phys . Soc. Japan 50 (1981) 1440 12) T.P.G. Carola and J.G . van der Baan, Nucl . Phys . A173 (1971) 414 13) S. Chen, J. Rapaport, H. Enge and W.W. Buechner, Nucl . Phys . A197 (1972) 97 14) R.M . Freeman, F. Haas, A.R. Achari and R. Modjtahed-Zadeh, Phys . Rev. Cll (1975) 1948 15) P.M . Endt, Atomic Data and Nucl . Data Tables 19 (1977) 23 16) J.B . French and M.H . Macfarlane, Nucl . Phys . 26 (1961) 168 17) R.R . Betts, H.T . Fortune and D.J . Pullen, Phys . Rev. CS (1973) 670

80

H. Nann / ZsSi

18) J. Ktoon, B. Hird and G.C . Ball, Nucl . Phys . A204 (1973) 609 19) D.L. Show, B.H . Wildenthal, J.A . Nolen, Jr. and E. Kashy, Nucl . Phys . A263 (1976)293 20) P.J . Brassard and P.W.M . Glaudemans, Shell-model applications in nuclear spectroscopy (NorthHolland, Amsterdam, 1977) p. 113 21) P.W.M . Glaudemans, P.J . Brassard and B.H . Wildenthal, Nucl . Phys . A102 (1967) 593 22) F. Meuders, P.W .M. Glaudemans, J.F .A . van Hienen and G.A. Timmer, Z. Phys . A276 (1976) 113 23) A. Bohr and B.R . Mottelson, Nuclear structure I (Benjamin, New York, 1969) p. 329