Ambiguities in spectorscopic factors deduced from a DWBA analysis of the (16O, 15N) reaction 1172

Volume 43B, number 4

PHYSICS LETTERS

19 February 1973

AMBIGUITIES IN SPECTORSCOPIC FACTORS DEDUCED FROM A DWBA ANALYSIS O F T H E (160, 15N) R E A C T I O N F.D. BECCHETTI * Lawrence Berkeley Laboratory, University of California, Berkeley, California 94 720, USA and The Niels Bohr Institute, Copenhagen, Denmark

P.R. CHRISTENSEN, V.I. MANKO** and R.J. NICKLES*** The Niels Bohr Institue, Copenhagen, Denmark

Received 22 December 1972 The spectroscopic factors deduced from a finite-range DWBAanalysis of the (160, lSN) reaction show systematic discrepancies with those obtained from (z,d), (a,t) and (d,n) reactions depending on whether j = l + 1/2 or ] = l - 1/2. The results depend sensitively on the selection rules used, however. The study of heavy ion induced nucleon transfer reactions promises to provide new information about nuclear structure [ 1-3]. The extraction of spectroscopic information, however, rests on a thorough understanding of the reaction mechanism and the applicability of models such as distorted-wave Born approximation (DWBA). To this end we have made a systematic study of single- and multi-nucleon transfers induced by 12C, 16, 180 ions incident on target nuclei, 40 ~
yond the sum of the projectile and target radii. Data for many targets were consequently obtained only at one or two angles near the grazing angle appropriate to target used. The features of the angular distributions are similar to those reported at other bombarding energies [8]. In fig. 1 we compare the peak cross sections observed for the reactions (d,n), (r,d), and (~,t) on 64Ni populating states in 65Cu with those observed in (160, 15N). The (160, 15N) reaction is observed to selectively populate certain states in the residual nucleus. This is a consequence of stringent orbit matching conditions [9, 10] ,which depend on/-transfer and Q value, and the sensitivity of the transfer cross sections to the asymptotic magnitude of the form factor. The latter depends on the binding energy (hence Q value) and the radial quantum numbers of the transferred nucleon. This selectivity makes it possible to identify states observed in (160, 15N) with certain levels seen in (d,n), 0-,d), and (a,t). Thus, the four prominent peaks seen in 64Ni(160, 15N) 65Cu (fig. 1) are assumed to correspond to the 2P3/2 , 2Pl/2 , lf5/2, and lg9/2 states in 65Cu. According to the theory of Buttle and Goldfarb [9, 10], the single nucleon transfer cross section for the reaction (Cl+t)+c 2

(al)

-+c 1 + ( c 2 + t )

(a2)

(1)

is given by 279

Volume 43B, number 4

PHYSICS LETTERS

6 64Ni(d'n) f 12MeV

~2" I

i

i

64Ni(r, d) 4 / mb l 22 MeV t

g/-

of

E

9_

,

J

~-

~_ .

,

•

I

l

•

64Ni6(160' 065CUMev 15N)

mb

rt

~I~ IIm

w..ll---,, .IL .,, I

~" 64Ni(a,t) "~ or.

b "13

.

i

+

o*

i....

The quantities S 1 and S 2 are the spectroscopic factors o f c 1 +t and c2+t. The quantity TLx(O ) is given by

"~-

I I .

o

I

sr

0

.,I.,.I

.,

5

4

3

z

Ex. (MeV)

i

6

Fig. 1. Cross sections at the first maximum in do/da for various proton stripping reactions populating states in 6SCu. Bombarding energies (lab), and spin and parity assignments are indicated. The (r,d), (a,t) and (d,n) data were taken from refs. [ 19, 20, 21 ] respectively. do da

4 7rbli#f (2nfi2)2

XSIS2

kf ki

2a 2 + 1

(2c 2+1)(2j2+1)

(2)

~ ( / l gLOIJ21i )2 ITLx(O)I 2 LX

where Ni,/~f are the reduced masses in the initial and final channels; a 2 and c 2 denote nuclear spins of a 2 and c 2 ; and Jl, J2 are the total angular m o m e n t u m of nucleon t in c 1 +t and c 2 +t, respectively. The sum indicated is over the allowed angular m o m e n t u m transfers L and their projections X where L is restricted by the triangular rules [ll

-121<<'L <~11+12 ,

Ij1

-J2I<~L <~Jl+j 2

(3)

and the parity rule ( _ l ) h +12 = ( _ I ) L . 28O

19 February 1973

(4)

(5)

where ~((.+)and X~-) are the distorted waves describing the incident and outgoing projectiles and FLh h (r) is the form factor as a function of the separation, r , between c 1 and c 2. Most of the calculations cited here used the form factor FLh]:, (r) calculated by a computer code due to Tobocman et al. using the method described in ref. [ 12]. The method decribed by Buttle and Goldfarb [11] was also used and found to give nearly the same asymptotic form factor and peak cross sections (-+3-%). The DWBA integrals TL x (0) were calculated using the program DWUCK [13] which allows up to 140 partial waves to be used for X~+), X}-). The integral was taken out to 40 fm in 0.1 fm steps in r. The "post" re. presentation was used. In evaluating eq. (5) the "norecoil" approximation is used. This introduces approximations in r, r' of the order of mt/mal ("~ 6%). Perhaps most importantly, the no-recoil approximation leads to the parity rule (4). The no-recoil approximation is discussed in refs. [9, 11, 14, 15]. The bound state wave functions were generated in potential wells similiar to those used in ref. [16] for 208pb (160, 15N)at sub-Coulomb energies. Optical parameters determined from fitting the elastic 160 scattering were used for both reaction channels [17]. These were of Woods-Saxon form w i t h R = 1.30 × (AV3 +A21/3) fm, a = 0.5 fm. I41= - 1 5 MeV and V target dependent, with V ~ - 4 0 MeV. We have assumed the 15N (g.s.) to consist of a pure Pl/2 proton hole in the 160 core. The DWBA output was re-normalized to obtain S 2 = 1.0 for the 2t"712 state in 2°9Bi observed in the sub-Coulomb study of 208pb (160, 15N) reported in ref. [ 16]. Calculations were then made for the (160, 15N) reactions of interest here and spectroscopic factors deduced without any parameter adjustments. Some typical fits to the experimental data are shown in fig. 2. With a few notable exceptions the fits are satisfactory. The exceptions appear to be reactions involving mismatched projectile orbits [9, 10] e.g. Q "~ Qopt ~ - 5 MeV. Otherwise, the uncertainties in relative spectroscopic factors due to variations in bound state parameters, etc. are similar to those reported in ref. [16] ( ~ -+ 30%).

Volume 43B, number 4 I

?

PHYSICS LE'FI"ERS I

'

I

~

19 February 1973

I ( '~

EL=60 MeV

4OCa~ 41Sc

0.1

Q=-I1.0MeV L=4

I.C

/

~

48C0~ 49Sc

Q: -2.50MeV L=4

I.C

9ZZr~ 93Nb Q=-6.09 MeV L-5

"c {

v

~

~

'5N)

EL=60 MeV 86Sr_87y Q=-6.19 MeV L-O 88Sr_ 89y Q=-5.05 MeV L-O

54Fe ~ "%Co

",~L

Q= -7.07MeV =4

o.i

b "D

"o I.OiI: /

1.0 ~eNi ~

tf

,~

59Cu

V ~ /

96Zr-- 9ZN b 0=-4.67 MeV

~

-J _:

Q=-8.71MeV

//

0.1

64Ni=T~SC68UMeV L=2

t 20

,

I

40

,

I

60

,

I

80

,

0.I

I

IOO

40

8¢.m.

~

I

60

,

I/,

80

I

I00

,

I

120

,

I

140

,

160

~c°m.

Fig. 2. DWBAfits to the (160, lSN) data (see text). The angularmomenta transfers,L, allowedby (3) and (4) are indicated. In fig. 3 we compare spectroscopic factors deduced from analysis of the (160, 15N) reaction with those obtained from (z,d). One observes a systematic discrepancy (factor ~ 6) for spectroscopic factors between final states having/=/> = l + 1/2 and t h o s e / = / < - l - 1/2, i.e. spin orbit partners such as lf7/2-1fs/2, 2P3/2-2Pl/2, etc. In addtition to the results shown in fig. 3, we have compared a total of 31 transitions to/> states and find the following ratios (and mean deviations): $2(160' 15N) [ = 1.1 +-0.4 S2(r,d) [/= l + 1/2 whereas for the/< states (16 transitions)

(6)

$2(160' 15N) I S2(r'd)

= 6.2 + 2.2

(7)

[/ = I - I/2

The absolute ratiosgiven in (6) and (7) are rather arbitrary since our DWBA calculations have been normalized to a transition to a/> state (2f7/2) in 209Bi. Normalizing to the lh9/2 state seen in ref. [16] would reduce the ratios given above by about I/3. The results (6) and (7) appear to be consistent with those obtained in the f.p shell at lower bombarding energies [8] and also 208pb(160, 15N) 209Bi at super-Coulomb energies [23]. The apparent failure of DWBA to yield spectroscopic factors in agreement with those obtained by

281

Volume 43B, number 4

PHYSICS LETTERS

(160,15N) o

{T,d) •

• • j=j>= • .,

l+t .

t

o~ 4 t9

2 5 ¢9

~2 Q.

co i I,

(0)

a

19 February 1973

The authors thank A. Winther, R. Broglia, T. Kammuri, P.J. Buttle, L.J.B. Goldfarb, D. Kovar, B.G. Harvey and M.A. Nagarajan for useful and stimulating discussions and N. Baron, F. Videbaek, E.E. Gross, and K. Oldager for their assistance in taking data. We also thank P.D. Kunz and W. Tobocman for making their computer codes available. Three of us (F.D.B., V.I.M., and R.J.N.) acknowledge the hospitality accorded us during our stay at the Niels Bohr Institute by the Institute staff.

6

49Sc ~Co ~Cu 65Cu

agy

9~Nb 9"tNb

References

[ 1 ] Nuclear reactions induced by heavy ions, eds. R. Bock and W. Hering (North-Holland, Amsterdam, 1970). [2] Proc. Int. Conf. on Heavy ion physics (Dubna, 1971). [3] J. Phys. Suppl. No. 11-12, Tome 32 (1971). [4] P.R. Christensen, F.D. Becchetti, V.I. Manko and R.J. Nickles, Proc. Int. Conf. on Heavy ion physics (Dubna, 1971) pp. 235,361. [5] R.J. Nickles, V.I. Manko, P.R. Christensen and F.D. other means depends sensitively on the selection rules Becchetti, Phys. Rev. Lett. 26 (1971) 1267. assumed. Owing to the critical orbit matching condi[6] V.I. Manko, F.D. Becchetti, P.R. Christensen and R.J. tions [9, 10] the DWBA cross section OL(-F~xlTLx(O)I 2) Nickles, J. Phys. Suppl. No. 11-12, Tome 32 (1971) C6-225. are found to depend strongly on L(and Q). For most o f [7] P.R. Christensen, V.I. Manko, F.D. Bechetti and R.J the cases of interest here o1.+1 ~ 10oL -1. Using the selecNickles, to be published in Nucl. Phys. tion rule (3) for (160,15N) with Jl = 1/2 and l1 = 1 one has [8] G.C. Morrison, H.J. KiSrner, L.R. Greenwood and R.H. L = l 2,12+1 f o r j 2 = l 2 + 1 / 2 a n d L = l 2 , l 2 - 1 f o r j 2 = l 2 - 1 / 2 . Siemssen, Phys. Rev. Lett. 28 (1972) 1662, and to be The parity rule (4) excludes L = l 2 for either j2 = l 2 + 1/2. published. [9] P.J.A. Buttle and L.J.B. Goldfarb, Nucl. Phys. A176 Thus, DWBA predicts o/>/o/< ~ Olz+l/Ol2-1 "~ 10 (1971) 299. whereas one typically has o/>/o/< ~ 3 which results in [10] D.M. Brink, Phys. Lett. 40B (1972) 37. the discrepencies noted in (6) and (7). Such discrepen[11] P.J.A. Buttle and L.J.B. Goldfarb, Nucl. Phys. 78 (1966) cies, however, can be substantially reduced by abandon409. ing the parity rule (4) and allowing terms L = l 2 in (2). [12] F. Schmittroth, W. Tobocman and A.A. Golestaneh, Phys. Rev. C1 (1970) 377. Such terms result in an enhancement o f / < states re[ 13 ] P.D. Kunz, private communication. lative to j > states owing to an increase in the L value [14] K.R. Greider, Nuclear reactions induced by heavy ions, allowed for transition t o / < states. Violation of the eds, R. Bock and W. Hering (North-Holland, Amsterdam, parity rule (4) can be shown to be a consequence o f 1970) p. 217. recoil effects [ 14, 15, 24] which introduce angular mo[15] N. Austern, Direct nuclear reaction theories (John Wiley and Sons, N.Y., 1970) Chap. 5. mentum transfers in addition to those allowed by the [16] A.R. Barnett, W.R. Phillips, P.J.A. Buttle and L.J.B. no-recoil selection rules (3,4). Goldfarb, Nucl. Phys. A176 (1971) 321. It is also possible that the results (6) and (7) may [17] F.D. Becchetti, P.R. Christensen, V.I. Manko and R.J. be a consequence of higher-order processes in Nickles, to be published in Nucl. Phys. (160, 15N) or configuration mixing in the projectile [18] D.D. Armstrong and A.G. Blair, Phys. Rev. 140 (1965) B1226; wave functions, however, this is not obvious. In any B. Cujec and I.M. Sz6ghy, Phys. Rev. 179 (1969) 1060; event it appears that a better understanding o f DWBA D.J. Pullen and B. Rosner, Phys. Rev. 170 (1968) 1034; theory as applied to heavy-ion induced nucleon transfer J.V. Maher, J.R. Comfort and G.C. Morrison, Phys. Rev. reactions is required before reliable spectroscopic inforC3 (1971) 1162; mation can be ontained from the study of such reactions. J. Picard and G. Bassani, Nucl. Phys. A131 (1969) 636; Fig. 3. A comparison of spectroscopic factors C2S (=S 2 ) deduced from DWBA analyses of the (z,d) reaction [18, 19] and (160, 15N)(see text) where C2S ~< 1 for pure shell model states. The bracketed results are based upon spins assigned from systematics.

282

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M.R. Cates, J.B. Ball and E. Newman, Phys. Rev. 187 (1969) 1682; R.L. Kozub and D.H. Younblood, Phys. Rev. C4 (1971) 535. [191 A.G. Blair, Phys. Rev. 140 (1965) B648. [20] P. Roussel, G. Brugge, A. Bussiere, H. Faraggi and J.E.

19 February 1972

Testoni, Nud. Phys. A155 (1970) 306. [21] V.V. Okorokov et al., Yad Fiz. 8 (1968) 668; Soy. J. Nucl, Phys. 8 (1969) 387. [22] D. Kovar et al., Phys. Rev. Lett. 29 (1972) 1023. [23] M.A. Nagarajan, B.A.P.S. 17 (1972) 902 and UCLBL Report LBL-697 (submitted for publication).

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