Proton scattering on 22Ne

Nuclear Physics A123 (1969) 531--540; (~) North-Holland Publishmy Co., Amsterdam Not to be reproduced by photoprint or m~crofilm without written perrmssmn from the pubhsher

PROTON SCATTERING ON 22Ne H. HULUBEI, I. NEAMU, G. VLA~DUCA, N. SCINTEI, N. MARTALOGU, C. M. TEODORESCU, M. IVA~CU and A. BERINDE Institute for Atomic Physics, Bucharest, Romania Received 14 October 1968 Abstract: Differential cross sections for the P0, Pl and P2 groups from the reaction 22Ne(p, p') have been measured at 12 energies m the range Ep = 4.82-8.20 MeV and at Ep = 14.00 MeV. The Po and Pl angular distr~butlons averaged over the range Ep = 4.82-6.20 MeV have been analysed with the optical model, statistical model and DWBA. The P0 angular distribution at Ep = 14 MeV is m good agreement with the optical-model calculations. Excitation functions in the range Ep = 3.6-6 2 MeV show strong fluctuations A strong resonance m the (p, Pz) excitation function at Eo = 5.73 MeV corresponds to 2aNa(14 27 MeV), 1.e. the mobarlc analogue state of 2aNe(~ 6.50 MeV). The angular distribution at this resonance has been analysed m terms of the single-resonance theory. N U C L E A R R E A C T I O N ruNe(p, p'), E = 3.6-14.0 MeV, measured g(E" Eo,, 0). 2aNa deduced resonance. Enriched target.

1. Introduction Elastic a n d inelastic scattering of p r o t o n s o n 22Ne has been previously investigated [refs. ~-5)]. The a n g u l a r distributions of the p r o t o n s to the first level of 22Ne show a rapid variation with energy in the Ep = 4.95-5.50 MeV range 4). This suggests a comp o u n d nucleus ( C N ) reaction m e c h a n i s m with a limited n u m b e r of interfering resonances. I n a high-resolution experiment, K a t o r i et al. 5) f o u n d a large n u m b e r of resonances in the (p, Po) a n d (p, p~) excitation functions in the Ep --- 0.94-4.20 MeV range. Several of them have been identified as T = ~ states. A c o m p e n s a t i n g v a r i a t i o n with energy of the Z°Ne(p, P0) a n d 2°Ne(p, P l ) cross sections has been previously f o u n d in our l a b o r a t o r y 6). It was suggested that this p h e n o m e n o n was due to the direct interaction ( D I ) m e c h a n i s m c o u p h n g the two reaction channels. The 2°Ne(p, p~y) a n g u l a r correlation m e a s u r e m e n t s established the significance of the D I m e c h a n i s m even at these low energies 7). The i m p o r t a n t D I c o n t r i b u t i o n should be expected from the large value of the d e f o r m a t i o n p a r a m e t e r of the 2°Ne first excited state, which is fl = 0.48 according to R a k a v y ' s 8) estimate. Because R a k a v y estimates fl = 0.47 for 22Ne, one m a y similarly expect a substantial D I c o n t r i b u t i o n in the inelastic scattering of low-energy p r o t o n s on 22Ne. However, it is expected that the difference in (p, n) thresholds of the two n e o n isotopes, namely Q = - 1 6 . 1 MeV for 2°Ne a n d Q = - 3 . 6 3 MeV for Z2Ne should produce some change in the D I m e c h a n i s m a n d c o m p e t i t i o n between D I a n d CN at low energies. 531

532

r~. HULtJaHet al.

In comparison with 2 ONe, the CN contribution for 22Ne is small, and the coupling of a large number of reaction channels affects the DI mechanism. This paper reports the measurement of angular distributions and excitation functions of elastic and inelastic scattering of protons on 22Ne.

2. Experimental procedure The proton beam with an energy spread of about 1% was produced by the cyclotron of the Institute for Atomic Physics, Bucharest. The incident energy was calibrated either by means of the 2°Ne(p, Pl) excitation function or by total proton absorption in AI. The 2°Ne was contained as an isotopic impurity in the target. The beam energy variations have been obtained by changing the high frequency on the cyclotron dees and by inserting aluminium foils in the beam path. Two tantalum slits defined a 2 x 2 mm 2 beam. The target consisted of a 6 cm diam. gas cell with a lateral opening covered w~th a 5 pm thick AI foil. It allo~ed the measurement of angular distributions in the 20 °- 160 ° range. The 22Ne enriched target contained the following components: 22Ne(80.7 ~o), ~'°Ne(18.0 ~ ) and 2tNe(1.3 ~o)The gas pressure during the experiment was kept between 100-150 Torr. The proton spectra were recorded with a SI(Li) solid-state detector and a 400channel pulse-height analyser. The elastic peak energy resolution was < 2 ~/o- To define the reaction volume, two rectangular apertures were placed in front of the proton detector. The geometrical factor was estimated with the Silversteln 9) formula. A scintillation counter placed at 90 ° and a Faraday cup connected to a current integrator served as beam monitors.

3. Results and analysis 3.1. EXCITATION FUNCTION A typical spectrum of 0 L = 90 ~ scattering at Ep = 5.73 MeV is shown in fig. 1. The elastic peak is labelled P0 and the inelastic peaks with p~(Q = - 1.27 MeV) and p2(Q = - 3 . 3 5 MeV), respectively. The Po and Pl excitation functions in the 3.60-6.23 MeV range are shown in fig. 2. The bumps represent the average of many narrow resonances. The strong resonance at E, = 5.73 MeV in the P2 excitation function (fig. 3) corresponds to a 23Na level at Ex = 14.27 MeV. The large yield suggests an analogue resonance. The Coulomb energy difference given by K a t o n et al. 5) leads to an analogue state in e3Ne at 6.50 MeV. The absence of the 5.73 MeV resonance in the Po and pl excitation functions suggests a high resonance spin. Only the 4 + second excited state of 22Ne then can be populated by protons with low/-values and thus large penetrabilities. The dotted curve in fig. 3 shows the statistical-model predictions. The exotation curves shown on fig. 4 have been obtained by integrating the P0 and Pl differential cross sections over the angular range 0 = 60°-180 ° and 0 = 0~-180 ~,

=2Ne (p,

p')

533

~00

10022Ne+ p Ep=573 MeV

OL=SO"

300

,. 70

zoo

100

0

J

i

0

IO

20

30 40 ~o 6O CHANNEL NUMBER

'°oFV,

70

,

I.,o

,

,

50

,

60

Ep (meV) Fig. 2. ]Excitation functions of protons elastlcally and inelastlcally (Q ~ - 1 . 2 7 MeV) scattered on =~-Neat 0L = 90°. The sohd curves connect the experimental points.

Fig. 1. Spectrum o f 5.73 MeV p r o t o n s scattered on 2~Ne a t 0 L ~ 90 ~.

500

A

/400

,? ~/eLAsnc q

7 #, A~ ~ 90"

~6

/

388 \

-.5

;

"-. 0

t.u

0

200

"-'4 E

~3

/,','ELASTIC ( C Z- - i27 Meg)

I00

---,- . . . . . . . . . 0

~0

55

-

-,"~'SrAr, Sr¢CAI MODEL , 6.0

65

Fig. 3. Excitation function o f p r o t o n s inelastlcally scattered by 22Ne(3.35 MeV) at 0 L = 90 °. The open circles are from angular distribution measurements.

70

0~-

I

50

I

65 Ew (Meg)

I

6B

Fig. 4. Variation wxth energy o f the P0 and p~ cross secnons integrated from 0 ~ to 180 ° and from 60 ° to 180 °, respectively.

I

6#

534

H. HULUBEIet al.

respectively. The compensating variation o f the elastic and inelastic cross sections observed 6) for 2 ONe is practically absent for 22Ne; this is consistent with the suggestion that the compensation is related to a limited n u m b e r of open channels. The low 22Ne(p, n) threshold allows the coupling of a larger n u m b e r o f reactions channels. Stevens, t aL 1o) suggested a similar explanation for the absence o f a compensation effect in the elastic and inelastic scattering of protons on t80. I

J

J

i

I

2,¢Ve C,?g )

tO~

tg 573 MOV

® 620 MeV

3g°

60

90°

tYO"

150"

8,~m

o"

I 33"

[ 6,9"

r 9g"

I /?0"

I I /50"

t~,: ,,7

Fig. 5. Angular distributions of elastically scattered protons on 22Ne. The sohd curves are guides

for eye. 3.2. ANGULAR DISTRIBUTION The absolute differential elastic cross sections measured at 12 energies in the Ep = 4.82-8.20 MeV range are shown in fig. 5. The results obtained at Ep = 14 MeV are shown in fig. 8. The uncertainty in the elastic cross sections is a b o u t 5 ~o except at small angles where it a m o u n t s to 10 % due to air impurity. The variation with energy at large angles might be due to a limited number of levels excited in the c o m p o u n d nucleus. The Pt angular distributions obtained in the 4.82-8.20 MeV range are shown in fig. 6. The solid curves have the f o r m tr(0) = ~ A k P g ( c o s 0), where Pg are Legendre polynomials with kma~ = 4. The Ak coefficients obtained by a least-squares fit o f the p t angular distribution are given in table 1. These distributions vary rapidly with energy and are generally asymmetric a b o u t 90 . The interference between the p r o t o n waves scattered on levels of opposite parity results in A t and A 3 coefficients. Some of

~2Ne fp, p ')

535

these asymmetries may also be caused by a D1 contribution, but more precise tests, e.g. (p, Px?) angular correlations, are necessary to substantiate this contribution. The P2 angular distributions measured at six b o m b a r d m e n t energies are shown in fig. 7. In contrast with the p~ angular distributions, they are practically isotropic except for Ep = 5.73 and 8.20 MeV. [A strong resonance has been found at Ep = 5.73 MeV (see above)]. The theoretical angular distribution 1~) at this presumable single I

~0t

I

t

E.=/+82MeV

i i z2Ne (p,p,~

35

30

30t

25

:I

20 i5

tO

I

I

I

I

I

I

I

505MeV

If

70MeV

,q26MeV tJ I z° ©

5, /5"

2O /0 5 I 30"

°ZT.

I 60"

I 90"

I fZG °

I /50 °

I /80 °

OLT°

I 30"

I 60 °

] 90 °

I I20 °

I~ /50 °

f80*

0c m

Ocm

Fig. 6. Inelastic scattering on 22Ne(1). high-spin resonance is W(O) = 0

W(O) =

(l

zo --~rP2)+t(l+½P2) for J= = 7 , 3 4 8 -~¢Pz-~P4)+t(I +~¢Pz+~Px) zo 1

(1) for

jn

=

~5 +

.

(2)

The solid curve in fig. 7 at Ep = 5.73 MeV gives the best fit obtained with t = 0.67 (j* = 7 - ) and the dotted curves the fit obtained with t = 0.28 (J" = ~+). The isotropy of the remaining P2 angular distributions was reproduced by a statistical-model calculation including the (p, n) channels. The proton and neutron transmission coefficients were obtained from the graph of Meldner and Lindner 13). The

I

Z2Ne(p, rz)

I

I

I

Ep = ~ 58 MeV

I

~ ~,

J

670 MeV_~

I

I

60'

I

90" ~c,n

l

frO °

I

i50"

÷+

fSO"

F i g . 7. I n e l a s t i c s c a t t e r i n g o n °-2Ne(2) T h e s o l i d c u r v e a t Ep = 5 73 M e V Is c a l c u l a t e d w i t h the s i n g l e - r e s o n a n c e t h e o r y f o r J~ = ~ a n d t = 0 67 a n d t h e d o t t e d c u r v e f o r Jn = ~ ~ a n d t = 0 28

30"

{ f+ + +

8.ZOMeV

{+,,,,,,,,,::o:.' i

all,

,i';2122

0 O"

~z'

5

f

3

l~

i

qO°

60"

I

I

Ocm

"~

_qo°

J._

t

f?O°

[

ELAGTC i

1

i,~O"

T~

Fig 8. Elastic and meJastlc angular distributions at 14 MeV The sohd curves are optical-model and D W B A predictions for elastic and inelastic scattering

U°

I I

2+0=-/28

\

- - - ~

#

22Ne (p, p')

537

TAnLE 1 Experimental values of the Pl angular distributions parameters Ak (from eq. (1))

Ev

A0

Al

(MeV) 4 82 5.05 5.14 5.26 5.43 5.58 5.73 5.90 6.20 6.70 7.20 8.20

A2

A3

A,

(mb/sr) 23.77 14.61 13.36 15.51 14.02 17.62 16.78 18.3l 15.54 10 42 10 13 10 47

--9.55 0.69 4.29 1 34 5.55 5 12 --0.62 -2.11 - 6.02 -4.82 - 0.72 0 56

-- 5.53 --3.74 --2 24 --4.15 --1.04 --7 79 --3.28 --10.34 --5 20 --3.12 --6 40 --7.74

4.42 3 94 0.39 --1.64 --0 91 --3.54 --4.04 0 07 0 57 3 18 0 68 1.36

--2.34 0.08 --0.52 --2.69 - 2 70 --1.01 --2.65 --2 82 --2.33 --1 81 -0.16 - 0 88

calculated &fferential cross sections were practically isotropic, b u t the absolute values were smaller t h a n the experimental ones. T h e disagreement for the absolute values o f the cross section is p r o b a b l y due to the impossibility to satisfy the statistical model requirements. The elastic differential cross sections at Ep = 14 MeV given in fig. 8 were calculated with the optical m o d e l a n d the inelastic ones with D W B A . The optical potential used has the following form:

V(r) = Uc(r, r c ) - U f ( r , r ~ , a ) - i W o ( r , r ~ , a ' ) - U s h ( r ,

rs, as) , ol,

(3)

Uc(r, re) is the C o u l o m b p o t e n t i a l of a u n i f o r m l y charged sphere of radius Rc = r¢A ~, U a n d W the real a n d i m a g i n a r y potentials, U~ the spin-orbit potential

where

depth a n d a a n d l the Pauli spin operator a n d a n g u l a r m o m e n t u m operator, respectively. The -eal potential has the W o o d s - S a x o n form

f(r, ro, a) =

l+exp

(4)

The i m a g i n a r y potential is peaked at the surface of the nucleus

o(r, r~, a') = - 4 a ' d f(r, r~, a').

(5)

The s p i n - o r b i t potential is of the T h o m a s type

h(r, rs, a~) = _~2 r1 d f(r, rs, a~), where ~. =

(6)

h/m~c is the C o m p t o n wavelength of the pion. The code JIB 3 was used x4).

H. H U L U B E I et

538

al

It allowed the variation of a number of preselected parameters to find the minimum of the quantity

,=, L

Aa,x(O,)

_] '

(7)

where a,h(0,) is the computed cross section at the scattering angle 0,, ae,(O,) the experimental cross section and AO'ex(0,) the standard deviation of the differential cross section. To obtain a good fit, six parameters have been varied namely U, I4,', Us, a, a' and r~. The resulting differential cross section is plotted in fig. 8. This corresponds to the following parameters: U = 41.7MeV,

W=

12.2 MeV,

a~ ~ 0 . 6 5 f m ,

U~ = 12.6 MeV,

a = 0.67 fro, a' = 0.39 fro, t

ro = r ~ = r c = 1.25fm, r 0 = 1.11 fm.

The relatively large value of the spin-orbit potential should be noticed. The inelastic differential cross sections at Ep = 14 MeV were compared with DWBA predictions obtained with the J U L I E 15) code including a spin-orbit potential. The optical-model parameters which fit the elastic data were used in the entrance channel for D W B A calculation. In the exit channel, the same parameters were used except the real potential depth, which was allowed to vary with energy according to U = 4 8 . 7 - 0 . 5 E (MeV).

(8)

A simple collective form factor with complex coupling was used for the transition between the internal states of the nucleus. The obtained results are plotted in fig. 8 as solid curves. The theoretical inelastic differential cross section corresponds to the deformation parameter of the first excited state of 22Ne g = 0.52. This may be compared with the Rakavy s) estimate fl = 0.47. The poor fit with the angular distribution seems to be determined by the simple collective form factor used in the D W B A calculation. More realistic wave functions are needed for this transition. The Po and pt angular distributions measured at lower energies were averaged over the range Ep = 4.82-6 20 MeV. It should be expected that some of the interference terms will be cancelled. The averaged elastic and inelastic differential cross sections corresponding to the Ep = 5.45 MeV mean energy are shown in fig. 9. The shape elastic angular distribution was calculated with the optical model and the compound elastic angular distribution with the statistical model. The Perey 16) average opticalmodel parameters without spin-orbit term were used. The calculation was performed with the S A N D A 17) code. The same parameters were used in the D W B A calculation of the p~ inelastic differential cross section. In the latter case the ELISA code 17) was used.

22Ne (p, p')

539

The transmission coefficients calculated by Perey's 16) average optical-model p a r a m eters were used for protons. The obtained Pl inelastic differential cross section was larger than the experimental value by a factor o f two. A considerable decrease of the theoretical cross section was obtained by including the open (p, n) channels in the calculation. F o r neutrons, the transmission coefficients 13) calculated with the Percy

k

22N@+~ 6 =5 5 u,v

qo2 "X~.

~

, CD+ D[

%%,,,% •

•

•

•

•

\

)

",,,','I

8on Fig. 9. Averaged elastic and inelastic differential cross sections in the 4.82-6.20 MeV energy range. The DI curves were calculated with the optical model for Po and wRh DWBA for Pr The CN curves for elastic and inelastic scattering were calculated by the statistical model.

a n d Buck 18) non-local optical potential were used. The statistical-model prediction o f the elastic and inelastic angular distributions at Ep = 5.45 MeV are shown by d o t t e d curves in fig. 9. F o r comparison with the experimental data, the statisticalmodel cross sections have been added to the optical-model and D W B A cross sections, respectively. The deformation parameter/? = 0.52 obtained at 14 MeV was used for the D W B A calculation at Ep = 5.45 MeV. The fits are reasonable. The elastic angular distribution fit m a y be improved by adjusting the optical-model parameters and by including a spin-orbit potential.

540

H. HULUBEIet aL

4. Conclusions The results obtained in this work, especially in the low-energy range, show a rather complicated behaviour due to the mixing of different reaction mechamsms. It was possible to obtain some useful information about the competition of CN and DI reaction mechanisms by averaging the experimental data over a wide energy range. Compensating variations in the Po and p~ cross sections have not been observed. A strong resonance at Ep = 5.73 MeV was found in the yield to the 4 + second excited state. We suggest that it is a 2 - or a ~2--~ analogue resonance. The elastic experimental data at 14 MeV could not be fitted with Perey's optical parameters. The inelastic data at the same energy are also unsatisfactorily explained by D W B A calculation using a simple collective form factor. These facts suggest that for the light nuclei more data are needed to establish an average set of optical-model parameters. Some form factors reflecting more accurate the structure of the excited states would also be of great use. The authors wish to express their thanks to the Niels Bohr Institute for making available the computer codes JIB 3 and JULIE and the IBM computer.

References 1) A. Galonsky, W. Haeberh, E. Goldberg and R. Douglas, Phys. Rev. 91 (1953) 439(A) 2) P. V. Sorokm, A. I. Popov, V. E. Stonshko and A. Yu. Taranov, ZhETF (USSR) 43 (1962) 749 3) M. A. Abuzeld, Y. P. Antoufiev, A. T. Baranlk, M. I. E1-Zalki, T. M. Nower and P. V. Sorokm, Nucl. Phys. 50 (1964) 106 4) Y. Oda, M. Takeda, C. Hu and S. Kato, J. Phys. Soc. Japan 14 (1959) 396 5) K. Katon, R. Ch~ba, K. Etoh, T. Matura, M. Morl and lq. Kawal, J. Phys. Soc. Japan 22 (1967) 35 6) H. Hulubei, A. Berlnde, I Nearnu, J. Franz, N Martalogu and M. lva~cu, Nucl Phys. 39 (1962) 686 7) H. Hulubei, N. Martalogu, M. Iva~cu, N. Scmtel, A. Bermde and J. Franz, Phys Rev. 132 (1963) 796 8) G. Rakavy, Nucl. Phys. 4 (1957) 375 9) E. A Sdverstem, Nucl Instr. 4 (1959) 53 10) J. Stevens, H. F. Lutz and S. F. Eccles, Nucl. Phys. 76 (1966) 129 11) J. M Blatt and L. C. Biedenharn, Revs. Mod. Phys. 24 (1952) 258 12) W. T. Sharpe, J. M. Kennedy, B. J. Sears and M. G. Hoyle, AECL-97 (1954) 13) H. Meldner and A. Lmdner, Z. Phys. 180 (1964) 362 14) F. G. Perey, unpubhshed 15) R. H. Bassel, R M. Dnsko and G R. Satchler, unpubhshed 16) F. G. Perey, Phys. Rev. 131 (1963) 745 17) G. Vl~.duc/i, unpubhshed 18) F. G. Perey and B. Buck, Nucl. Phys. 32 (1962) 353