A study of 26Al by the 25Mg(3He, d) reaction

Nuclear Physics A299 (1978) 412-428 ; © North-hfolland PubllsJtlng Co., Amsterdam Not to be roproduced by photoprint or microfilm wdthout wrlttaa permiaion from the publLher

A STUDY OF =~Al BY THE '°Mg(3He, d) REACTION t R . R . BETTS tt and H. T. FORTUNE ftt Physics Department, University of Pemtsyhwnia, Philadelphia, Pennsyhwnia and D . J . PULLEN Department of Physkt and dpplied Physics, University of Lowell, Lowell, Massachusetts Received 7 November 1977 Abstnd : In the "Mg(3He, d)26Á1 reaction, at a bombarding energy of 18 .0 MeV, angular distributions were measured for SS levels below 6 .9 MeV in excitation, and 1-assignments are made for 44 of them . Spectroscopic strengths are compared with theoretical ones from the Nilsson model and from a naive shell model . New J` information is given for many levels.

E

NUCLEAR REACTIONS =6 Mg('He, d), E = 18 .0 MeV ; measured o(Ed , ~. 2 bÁ1 deduced levels l, J, s, (2J+1)S. DWBA analysis .

1 . Introduction

The nucleus 2bÁ1 is currently of some experimental and theoretical interest. 1?revious studies of Z4Mg(3He, py) [ref. t)] and Zs Mg(P, y) [ref. Z)] have assigned several spins below E~ = 4.5 MeV. More vacantly, detailed investigations ofthe 2`Mg(3He, p) [ref. 3)] and 2'Al(3He, a)[ref. 4)] reactions have been reportod-resulting in a number of new spin assignments. The present paper contains the results of the ZsMg(3He, d) reaction. This reaction has previously been studied at a bombarding energy of 12 MeV by Weidinger et al., who extracted angular distributions and spectroscopic strengths for fourteen of the levels up to 4.2 MeV excitation s). The 2'Mg(d, n) proton transfer reaction has been investigated by Fuchs et a1.6) at a bombarding energy of 6 MeV. That work gave results for states up to E_ = 6 MeV; however, their resolution of .. 100 keV prevented the separation of many of the closely spaced multiplets known to exist') in Z 6Á1 . Other recent investigations of Z6Á1 include work on Z'Na(a, ny) [ref. e)], 24Mg(a, d) [ref. 9)],andfurther work on ZsMg(P, y) [ref. to)]. The present report includes results for all observed levels up to E_ = 7 MeV with f work supported by National Science Foundation. tt Present address Yale University, New Haven, Connecticut 06520. ~tf Presently at Oxford University on leave from University of Pennsylvania. 412

uM~sH~ a~zs~

413

an overall resolution of 16 keV. New results are presented for many states resulting in new spin-parity assignments. The results are discussed in terms `of the simple weak-coupling shell model and the strong-coupling Nilsson model. 2. Experimental method and resalb

The reaction was performed using the University of Pennsylvania Tandem Van de Graaff accelerator and multiangle spectrograph. A thin (x 20 pg/cmz) layer of Mg, enriched to 99 .2 ~ in ZsMg and supported by a ~ 100 ~g/~ s gold backing, was bombarded with 18 MeV 3He+ + ions. The reaction deuterons were detected in Ilford IC2 nuclear emulsions after being momentum analyzed in the multiangle spectrograph. A Mylar foi10.25 mm in thickness placed in front ofthe emulsion plates provented scattered beam particles from being detected . Data were taken in 3.75° steps from 3.75° to 33.75° and thence in 7.5° steps to 71.25°. A spectrum measured at 18.75° is shown in fig. 1. Groups identified as belonging to 26A1 are labelled numerically. The numbering scheme is the same as that given in ref. 3,h Contaminant groups due to the (3He, d) reaction on 12C and 160 are shown shaded and are labelled according to the final nucleus and level number. At the high field used in this experiment ( > 13 kG) the magnet calibration deviates from its measured values and therefore excitation energies ofthe levels observed were taken from other work. These are listed in table 1. Angular distributions were extracted for all the observed transitions and are shown in figs . 2-5. The absolute cross section scale was established in the following manner. A thick (~ 60 hgJ~2) 2'Mg target was bombarded with 6 MeV 3He++ ions. The elastically scattered beam particles were detected in nuclear emulsions at four angles from 48.75° to 71.25°. The resulting angular distribution was fitted using the opticalmodel parameters given in sect. 3. Fig. 6 displays the result ofthis procedure, the solid and dashed lines representing the results using different values of the 3He absorption. The effects ofchanging Ware small. Using the predicted optical-model cross sections, a value of60.1 pg/cm2 was obtained for the target thickness. The same target was then usod in a (3He, d) experiment in which angular distributions to the g.s., 0.22 and 0.41 MeV states of 26A1 were measured. Normalizing these distributions to those previously measured with the thin target gave the absolute cross section scale. It is bolieved that this procedure is accurate to within f 10 3. DlSborted-wave aaalyeis

The distorted-wave analysis of transitions to bound states was performed using the code DWUCK 11, The optical-model parameters usod were taken from other work in this mass region 12' 13) and are listed in table 2. The ip ~ 0,1, 2 and 3 curves were calculated assuming 2sß, 2pß, ld} and lf~ transfer, respectively . All thedistortedwave calculations were done in the zero-range approximation. Angular distributions

414

R . R. BETTS et al. T~tB 1 ResWts of the ='Mg(3 He, d)~ 6 A1 reaction

Level no .

E, ') (kei

Iv

,x b)

0 1 2

0 224 412

3 4

1054 1761

5 6, 7

1849 2071

2 2 0 2 2 0 2 2 0 2

8

2365

9

2545

10

2670

11 12

2740 2915

13

3077

14

3163

15 16 17

3407 3510 3602

18

3680

19 20

3725 3754

21 22 23

3925 3967 ;197 ~)

24 25 26 27 28

4350 4425 4479 4550 4609

29

4708

31 33

4944 5006

ref. °)

ref. e)

5+ 0+, T = 1 3+

1 .85 0 .52 1 .18

1 .60 0 .41 0 .64

1+ 2+

0 .94 0 .33 0 .61 0 .17 0 .07 0 .43

0 .70 0 .22 0 .54 0 .12 0 .04 0 .46

1 .57 0 .21 0 .55 0 .60 0 .72 0 .17 0 .36 0 .22 0 .05 0 .50

0 .05 0 .44 0 .08 0 .33 0 .007 0 .03

0 .03 0 .38 0 .04 0 .37

0 .03 0 .25 0 .06 0 .41 0 .11 0 .12

0 .10 0 .15 0 .01 0 .06 0 .58

0 .08 0 .12

0 .06 0 .27

0 .28 0.54

0 .31 0.28

0.05 0 .15 0.10 0.55

0.05 0 .14 0.08 0.56

0.05 0.16 0.09 0.58

0.26 0.36

0.22 0.40

0.17 0.42

U .09 U.41 0.73

0.30 0.68

0.30 0.60

3+ (2, 3) + 1+ 2+

0 2 0 2 0 2

(2, 3) + 2+, T = 1 5+ 6+ (2, 3) +

0 2 0 2 (2) 0 2

(2, 3)+ `)

2 U 2 (1-3) + (2~ 0 2 2

present

1+ ~ 4+ ~ 2+, T = 1 l+ 3*

0 2 0 2 0 2

1+ (2, 3) + 0+, T = 1 7 + ,5 + ~ (0-S) + h (2, 3) +

h

g) + r)

2J~+ 1 S 2J,+ 1

(2, 3) + 4+, T = 1 2+, T = 1

0.24 0.13 0.20

0.12 0.14

41 S

='Mg('He, d)=sAl Teste 1(continued) Level no

E,') (keV)

34

S146

36 37

5253 5405

38 39

5442 5469

41 42 43 4S

5525 5552 5597 5687

46 47

5700 5736

48 49

5864 5932

51 52 53 54 55 56 57 S8

5963 6005 6040 6091 6138 6214 6265 6290

59 60 62 63 64 65

6360 6413 6508 6565 6613 6689

66 67 68 69 70

6734 6797 6828 6873 6899

2J~+ 1 S 2J,+1

1,

J, ~

present

0 2 2 1 3 1 0 2 2 2 2 0 2 1 1 3

2*, T = 1

0.10 0.25 0.45 0.12 0.24 0.07 0.01 0.01 0.71 0.52

(0-S)* (l~l)(1-4) (2,3)* (0-5)* (0-5)* (0-5)* (2, 3) * (1-4)(1 ~)_

0.22 0.37 0.17 0.07 0.20

1 3

(1-4)-

0.13 0.20

2

(0-5)*

0.56

(1) 0 2 1

(1 ~)_ (2,3)*

(1 ~)_

2 1 0 2 1 1 1

(0-S)* (1 ~) _

3

(1~ -.

ref.')

0.02 0.05 0.06

(2,3)*

(1 ~) _ (1 ~) _ (1 ~)_

9 Excitation ~a from rd.'). h From ref. ~ and present work, unless otherwise noted . h Doublet. Lower member has J` - (3, 4*), the upper hea J S 4 (~ ~'~)~ Ref. ~. ~ Assigned J - 3 in ref.'s. Hence J' - 3* . ~ Doublet in ref. lq: 4192 keV, J` - (2, 3)* a~ 4205 keV, J ~ 3. ~ Rd.'). h Ref. ~.

ref. ó) 0.06 0.24 0.35 0.10 0.08 0.02 0.20

0.39

0.06

O -O

416

v>

Ó

~~ U

4

W Z W

W H

Z O

~ Q H V X W

O

N

O O N WW yi~

-

-

a3d s~~dal ~o a3ewnN

417

w z w

eo

so o so eo 9e. ,. ( deq rees ) Fig. 2 . The ~°Mg(~He, d)=6Al angular diatributiona that are characteristic of 1 a 0 or I = 0+2.

ssM~sH~ d~36~

419

20

R . R. BETTS et al.

N

E

mti b

Fig.

d. She Z'Mg('Hq d)=6 Al angular distributions characteristic of 1

= 1, / = 3, or ! = 1 +3.

with shapes characteristic ofdirect stripping are shown in fig. 2 (ip = 0 and 1D = 0+2), fig. 3 (lp = 2) and fig. 4 (lp = 1, lP = 3 and lp = 1 + 3). Those angular distributions whose shapes are not characteristic of direct stripping and those that could not be accounted for by a calculated shape are shown in fig. S. The separation of those transitions proceeding by a mixture of lp = 0+2 into their constituent parts is facilitatod by the coincidence ofthe maximum ofthe lp = 2 shape with the first deep minimum ofthe lP = 0 shape. The separation ofmixed Ip = 1 + 3 transitions is somewhat more ambiguous due to the rather structureless shapes ofthe lp = 1 and Ip = 3 curves. The code DWUCK defines the following relation for stripping Qe=p(6) _ ~ NC ~S

2Ir + 1 yawucx(9)

2J,+ 1

2j+ 1

'

aM~sHe, d~ 6A1

421

uwl wu Ea " L7e YN

lwl wC 16 ~ 10 E." 3.61 YN ~

10

L..Y IIa 21 E." 3.ób YW

10

a ..

a

..

á w

m

-

_ t {~t+ + t~ +

t+

I

w

E

T

1+

I I LwY Ns21 E.""Yl YN

1

001

I

I I Lwr wa n E." ~.es rw

L.wl Nol1 E." wf. rw

L..I ~. eo u. eal rw

Lwa w. e: [." a.sl wv

~~ss E. " 5.01 Y.v

a

s-,. _ . _

++t

b

r

I 1 u.r 11n s. fa "6.21 YW

p

a

.

.~ . .

so p

eo

so

~ f

0

-

30

t

t I

60

~ 90

0

!0

80

90

0

L-_..60L-~ 90

30

am.( dsgroes 1

9

Fig. S. Angular diáriMrtions not cbaraderirtic of direct stripping.

where Jh J~ andjarc the final, initial and transferred angular moments ; C is an isospin Clebach-Gordan coefficient of the form
422

R. R. Bl?1-IS et al.

9~.m (degrees) Fig. 6. Elastic scattering "Mg+'He angular distribution at 6.0 MeV, and optical-model prodiction . T~at .E 2 Optical model parameters V (Me~

W íMe~

= 'Mg+'He

177.0 177.0

13 .0 7.0

'°Al+d

120.0

Channel

bound state

W' (Me~

100.0 ')

r = r, m a =o,A, (fm) (~)

rc (~)

r' (~)

d (~)

V..,. (MeV) 8.0 8.0

1 .14 1 .14

0.72 0.72

1.40 1.40

1.60 1 .60

0.77 0.77

1.00

0.90

1.30

1 .50

0.50

1.26

0.60

1 .26

~i = 25

~ W' = 4 Wn = (100-2 .0 E~ MeV. ~ Adjusted to give the binding energy given by B = Q('He, d)+5 .52 MeV.

effects of spin-orbit potentials in the entrance and exit channels and in the bound state potential. However, in practice such differences are very difficult to detect, especially when the target hag a non-zero spin since usually then both possible values ofj can occur together for any given l. Thus, for convenience, in the present study we have assumed that j is always given by j = I+ Z. This procedure will, however, lead to too small spectroscopic strengths in some cases. The values of (2Jt +1~S/(2Jt +1) obtained in the above mariner are listed in table 1 in comparison with the values obtained from the previous (3 He, d) and (d, n) studies. Systematically, our strengths for l = 0 are substantially larger than previous values, even though our 1= 0 fits arequite

=eM~aH~ d)se~

423

good . The reason for this difference is not known. Nevertheless, overall agreement is good For the most part, the differences are within the usual errors associated with the distorted-wave method The spin-parity assignments from the present work are listed together with previous assignments in table 1. Since 2'Mg has a i+ ground state, the observation of l = 0 restricts J~ to 2+ or 3 + . We therefore make new J~ _ (2, 3) + assignments to six levels above 4 MeV. Levels populatedwith ! = 2 (fig. 3) can have anyJ~ from 0+ to 5 + . Wemake eight new assignments of this type for levels above 3.9 MeV. Observation of ! = 1 restricts J~ to (1-4)-. This is the case for eleven levels displayed in fig. 4. The sole pure l = 3, to a state at 6.90 MeV, means that level has J~ _ (1-b)- . 4. Tóeoretical spectroscopic fictors

The nucleus 26A1 lies in a transition region between nuclei with large permanent deformations and those believed to be better described by a spherical basis. It is important, therefore, that the character of the level scheme of Z6A1 be established as either rotational or otherwise. Previous investigations of transfer reactions to 26A1 have notod the failure ofthe simple strong~oupling Nilsson model to account for the properties ofthe low-lying levels of 26A1. In this model the lowest states are described by the coupling of an odd neutron and proton in Nilsson orbits no. 5, z + [202] and no. 9, i*[211] . Since the 2 sMg g.s. is described as an odd neutron in the z + [202] Nilsson orbit it is expected that the low-lying positive-parity states populated in proton stripping on this nucleus will belong to one of four bands formed by the coupling of the transferred proton in either of the above orbits to the ~sMg ground state. The lowest negativo-parity bands should be formed by the coupling of the odd proton in the i- [330] Nilsson orbit no. 14 with the odd neutron in the i + [202] Nilsson orbit no. 5, giving two finds with K" = 2- and 3 -, respectively. The configurations ofthe bands formed in this manner arc listed in table 3. The spectroscopic strengths for transitions to the members of these bands were calculated using Satchler's forTeatB 3

i3andheads in ~ 6A1 excited in the =°Mg( 3 He, d) reaction Configuration

K

A

I + [2027 ® ~+C2o27

s u'~

+ +

I+C2o27 ® 4+C2o27 ~+C2o27 ® ~+C2117 i { [2027 ® }+C2117 }+[2027 ® }-C3307

3~ 2~

+ +

2~

~ Eves apin members have T ~ 1, odd spin member have T - 0. h Two bands arise from each configtrtation, one wrath T - 1 and the other with T ~ 0.

424

R . R . BETTS et a/. T~eu 4 Spectroscopic strengths for = 'Mg('He, d)=6 A1 transitions in the extreme singlo-particle model 2J~+ 1 2!, + 1 S

Configuration

1v

.1', T

ld 3  ® ld,

2

0+ , 1 +, 2+, 3*, 4+, 5 +,

1 0 1 0 1 0

0.07 0.43 0.33 1 .00 0.60 1 .57

1d,~2 ® 2s1 

0

2*') 3+

0.83 1 .17

2+ 3+ 4+

0.83 1 .17 1 .50

234S6-

0 .83 1 .17 1 .50 1 .83 2 .17

') The strengths for T = 0, 1 foul states are identical for these configurations . ES " 2071 AIeV J~ "2",7 "1 I ///////// /i%////

e"[e02] JI "o

/////////////%i

E " 2366 NeV Jr " 3~

bie"l:oel ,~ "o E~ " ~.706 YW JT"4",T " 1

~~~~~'_/

.. .

DEFORMATION (a)

Fig . 7 . Expcrim~tal (hatched) and Nílsaon-model (curves) . specUbsoopic strengths for 1 = 2 stripping into the ~ * [202] orbital .

ssM~sHe, d~ a Al

425

t

t

Ea " L761 YW Jr"

2.

i

vz" [:n],a" z

N IN

Ea " 4 .197 WV Jr " 3 " ,T" 1

t

i vz~[zii]x " s

~r

iw:" [zn]x" z

y

40

~

0.1

,

42

43

QO

DEFORMATION (8) Fig. 8. Same as fig . 7, but for l = 0 stripping into the } + [211] orbital .

41

42

43

DEFORMATION (8)

Fig . 9 . Same ad fig. 7, but for I ~ 2 stripping into the }*[202] and }*[211] orbitale.

mina t4) and the expansion coeûtcients of the Nilsson states in terms of shell-model wave functions due to Chi t'). The results of these calculations together with the measured values of the spectroscopic strengths are shown in figs. 7~9. Alternatively, if the Nilsson model is not applicable to 26A1 it is informative to know the degree to which the single-particle strengths are fractionated. The pure single-particle spectroscopic strengths were calculated with the aid of the sum rules for stripping as given by Schiûer' 6), and are given in table 4, 5. Dlecoesion Fig. 7 shows a comparison between the calculated and observed lp = 2 spectra scopic strengths for the bands formed by coupling the transferred proton in Nilsson orbit no. 5, i * [202] to the ~'Mg ground state (~*, k = z) . Since the transferred par_ ticle has k" = i *, the predicted df strength is independent of deformation S, and the 2s} and ld} strengths are predicted to be zero for these bands. The agreement is reasonably good for all states except for the 4.708 MeV 4*, T = l level which has a considerably larger experimental strength than that predicted for a 4* state formed by the coupling of a proton in Nilsson orbit no. 5. Agreement with experiment is

426

R. R . BE11'S et al. .Lp " 1 E_ " a4os wv

wz- taolx" z.+'3 vz- Issolx"e~+" =

Ea " a4~2 wv í

_

Ea " s~oo r .v

"i~~~~. .,,r

E : " a832 Y W

a2

as °áo

ai

a2

as

DEFORMATION (a) Fig. 10. Same as fig. 7, but for l = 3 (~ett) and ! = 1 (right) stripping into the }- [330] orbital .

:~MB(~He, d)zs~

427

possible, however, ifthis state is the 4+ member of either the K = 2 or K = 3 bands formed by the coupling ofa proton in Nilsson orbit no . 9, i + [211]. Fig. 8 shows lp = 0 spectroscopic strengths for the 0.412(3 +), 1 .761(2*) and 3.163(2 + , T = 1) MeV states in comparison with those calculated for the confiig~ ,rations shown. The 0.412 MeV state is too strong by halfan order ofmagnitude if the Nilsson configuration is as shown. In fact the observed strength is more consistent with this state being a pure single-particle state (see table 4). The strengths of the 1.761 and 3.163 MeV states are not inconsistent with their proposed configurations. The lp = 2 spectroscopic strengths shown in fig. 9 for the 1 .761 and 4.197 MeV states are in poor agreement with the theoretical predictions although the 4.197 MeV state is known to be a doublet and the excitation of the other member may account for some of the observed strength . In summary, the observed strengths for the low-lying positive-parity states, whilst not excluding the validity of a Nilsson model interpretation of 26A1, show relatively poor agreement with the calculated strengths. Inclusion of Curious coupling may well rectify the discrepancies. The results for the lowest negative-parity states are shown in fig.10. While plausible results for the lp = 1 strengths are obtained, only one configuration has enough Ip = 3 strength to account for the data. It must be eoncludod therefore, that the Nilsson interpretation fails for these states. Again, however, the inclusion of Curious coupling with the attendant redistribution of the single-particle strengths may improve the agreement somewhat . á Coodaeloos

The strong coupling Nilsson model without Curious coupling has been shown to fail to account for the observed strengths in the 2'Mg('He, d) reaction. Inclusion of the Curious coupling term would appear to be necessary to account for the experimental results although qualitative results of such a calculation make this unlikely . A more fruitful approach would be a detailed shell-model calculation of the type which has recently been successful in accounting for the results ofthe 2'Al(3He, a)~6A1 reaction Referaoee 1) G. A. siwn"er, P. A. Qain and P . R . cha~on, Nucl . P~. . Alls (1969) 33 ; Al3a (1969) s29 z) o. Hamer and N. A~aa-weir, can . J. Phyn. 46 (1968> 2809 ; O . Hauser, fi. K. Alexander and C. i3rouae, Can. J, Phya. If (1968) 1035 3) R . R . Hetta, H . T. Fortune and D. J . Pullen, Phya. Rev. C6 (1972) 937 4) R . R. Heth, H . T. Fortune and D. J . Pullen, Phy~. Rev . A (1973) 670 S) A . Weidiner, R . H. Siemseo, G . C. Morrison and H. Z,eidman, Nnd . Plrya. Al"" (1968) 547 6) H . Fncbs, R. Grabi~ch, P. Kraaz and G. Raadtert, Nnd . Phys. All" (1968) 65 7) P. M . F~dt and C . van der Lean, Nuc1 . .Phys. A214 (1973) 1 8) H. G . Price, P . A. Butler, ~A . N . James, P . J . Nolan and J . F . Sharpey-Schafer, Phyr: Rev. CI" (1974) 41s

428 9) 10) 11) 12) 13) 14) 15) 16)

R. R. BETTS et a1. D. W. Oliver, K. W. Kamper and J. D. Fox, Phys. Rev. A (1973) 2144 E. O. DeNeijs, M. A. Meyer, J. P. L. Reinecke and D. Reitmann, Nucl . Phys . A230 (1974) 490 P. D. Kunz, private communication H. T. Fortune, N. G. Puttaswamy and J. L. Yntema, Phya. Rev. 1~ (1969) 1546 H. T. Forhme, T. J. Gray, W. Trost and N. R. Fletcher, Phys. Rev . 179 (1969) 1033 G. R. Satchler, Ann. of Phys. 3 (1958) 275 B. E. Chi, Nucl . Phys. ái (19(~ 97 J. P. Schiffer, Isospin in nuclear physip, ed. D. H. Wilkinson (North-Holland, Amsterdam, 1969) p. 667