Isobaric analogue resonances in the 80Se(p, n)80Br reaction

Nuclear Physics A315 (1979) 157-162; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

ISOBARIC A N A L O G U E R E S O N A N C E S

IN THE S°Se(p, n)S°Br REACTION S. KA1LAS, S. SAINI and M. K. MEHTA

Nuclear Physics Division, Bhabha Atomic' Research Centre, Bombay 400085, India and N. VEERABAHU, Y. P. VIYOG1 and N. K. GANGULY

VEC Project, Bhabha Atomic Research Centre, Bombay 400085, India

Received 15 August 1978

Abstract:The total (p, n) reactioncross sectionfor S°Sehas been measuredas a function of proton energy in the energy range from ~ 2.7 to 5.375 MeV with fine resolution (~ 5 keV). Several prominent isobaric analogue resonances have been measured. A detailed shape analysis of the isobaric analogue resonanceshas been performed to determine the proton width Fp, the spreading width W and the spectroscopicfactor S for the various resonances. E[

I

NUCLEAR REACTION s°Se(p, n), E ~ 2.7, 5.4 MeV; measured a(E). S°Br deduced isobaric analogue resonances; Fp, spreading width W, and S; enriched target.

1. Introduction Isobaric analogue resonances (IAR) in the compound nucleus have been studied successfully in many nuclei through (p, n) reactions ~- 3). Spectroscopic information comparable to that obtainable from (d, p) reactions has been extracted from a study of the IAR populated through (p, p) and(p, n) reactions. When these IAR are below the Coulomb barrier of the proton-plus-target system, the corresponding anomalies in (p, p) excitation functions are very weak. On the other hand they show up rather prominently in the (p, n) channel 2,3). Hence the spectroscopic information derived from the analysis o f the resonances seen in the (p, n) excitation function may be more reliable and can be compared with the (d, p) predictions with more confidence. In order to test this possibility further, the S°Se(p, n)8°Br reaction has been measured from threshold up to ,~ 5.4 MeV proton energy. All the prominent IAR reported in the earlier S°Se(p, n)a°Br [ref. 1)] and a°Se(p, p)S°Se [ref. 4)] studies up to ~ 5.1 MeV have been measured in the present work. The IAR at Ep ~ 5.2 MeV reported in the present work has not been measured earlier. A preliminary account of the present work is reported elsewhere 5,6). The experimental arrangement, procedure and results are discussed in sect. 2, 157

158

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while the analysis of the measured data is discussed in sect. 3 followed by the conclusions given in sect. 4.

2. Experimental procedure and results The total (p, n) cross section for the reaction 8°Se(p, n)S°Br has been measured utilizing a 4re neutron counter and the thin-target technique. Details of the experimental technique are given elsewhere 7). The 8°Se targets (93 ~o enriched) were prepared by evaporating the Se metal on the ~ 0.15 mm tantalum backings. The target thickness was of the order of 5 keV for 4 MeV protons. Proton beam currents of the order of 20 to 30 nA were used throughout the measurement in order to avoid the deterioration of the target. The excitation function was measured in 5 keV steps from threshold up to ~ 5.4 MeV proton energy. The 90° energy analysing magnet was calibrated by determining the threshold for the reaction 7Li(p, n)VBe at 1.881 MeV. The absolute error in the energy scale is estimated to be of the order of 10 keV. Several prominent IAR were observed in the present work. The measurement was carried out in smaller energy steps (~ 2.5 keV) over the IAR to obtain accurately the shape of these resonances. In fig. 1, the measured excitation function has been shown from ~ 3.8 MeV onwards. The region below this is devoid of IAR and ap, rises smoothly from threshold and merges with the trend above the 3.8 MeV 1AR as shown in the inset in fig. 1. The IAR at Ep = 5.2 MeV has not been reported n

? IARs IN 80Se(p,n) 80Br REACTION A Ec = 10.478 +-.015 MeV

E "~ 320 z

tRELATIVE ERROR *- 5% PROTON OPTICAL PARAMETERS VR = 60.8-.6E RR = 1.17 Q R = 0 . T S

O

280 w

O

V1 =3E

240

R! =1.32

~ .J

~0=7.5

QI =0.45

THEORETICAL FIT USING ROBSON JOHNSON PROCEDURE

200

u 160 c. 120

.•........•.-."1

80

o

40

i

~"

i I,

3.8

I

I

I

I

14'

I

I

l

2.6

I

I

i

Itl

It

.I- °

• • "ee

3.0 'l'I

,,,

3.4 3.8 E p (MeV) i st I

3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0 5.1 5.2 5.3 E p - PROTON ENERGY ( M e V ) - L A B

Fig. l. Excitation function for the reaction S°Se(p, n)S°Br measured from threshold up to ~ 5.4 MeV proton energy. The arrows indicate the positions of the I A R expected. The continuous curves are RobsonJ o h n s o n fits to the IAR.

ISOBARIC ANALOGUE RESONANCES

159

earlier. An overall error of + 13 % has been assigned to the cross section measurement, consisting mainly of + l0 % error due to target-thickness measurement [measured as described in ref. 7)] and non-uniformity of the target and _ 7 % due to the uncertainty in the efficiency of 4n neutron counter. The error in the cross section estimate due to the presence of the other Se isotopes, viz. 7SSe ( ~ 4 %, Q = ~ - 4 . 4 MeV) and S2Se (.~ 1%, Q = ~ - 0 . 9 MeV), is expected to be small compared to the overall error of _ 13 % in the cross sections. But for these |AR the excitation function is in general structureless and smooth.

3. Analysis 3.1. EXTRACTION OF AEc, FD AND W As the excitation function is structureless in general, excluding the IAR, a smooth excitation function for this reaction was obtained by joining the valleys of the IAR. Starting from the set of optical model parameters determined in this mass region from previous (p, n) work at our laboratory s), the imaginary depth V~and diffuseness parameter a~ were adjusted to fit the excitation function, using the optical model code ABACUS-II 9). The proton optical model parameters determined are listed in fig. 1. Using the standard Robson-Johnson expressions ~o) the analysis of the IAR measured in the present work has been carried out. The 1AR has been shape fitted by the expression %.n = ap, ~(bkg)~L(e_eo)~+¼ro ~(e-e°+~)~

-i I +aptbkg),

(l)

where the parameters Eo, A and F o have the usual meaning ~o) and ap, ~(bkg) = fn~2Tp,,

(2)

where Tp, is the non-resonant transmission factor for the same partial wave that would exist if the resonances were absent. This quantity was calculated with the parameters obtained from the above-mentioned optical model fit. In eq. (l), ap (bkg) is the off-resonance cross section. This can be again obtained through the optical model fit. However, it is very convenient in this type of analysis to use the method of ref. ~). Following this technique we treated O-p(bkg) as a variable quantity with the form A + B ( E - E o ) , with A and B as adjustable constants. A non-linear least squares computer programme has been used to fit the 1AR with expression (1) with E o, F o, A, A and B as free parameters. The values of parameters which gave the best visual fit and minimum ~2 are listed in table I. It should be mentioned that the three 1AR at ED ~ 4.9, 5.0 and 5.1 MeV have been shape fitted simultaneously with a common ap(bkg) = A + B E + C E 2 with A, B and C as free parameters. In fig. l, the continuous lines for the various 1AR represent the best shape fit curves.

S. KAILAS et al.

160

TABLE I a Extraction of Eo, Fo, A, Fo, W and

AE c

from the IAR in the 8°Se(p, n)8°Br reaction

Eo

ro

IAI

rp

w

B.

AE,,

E~

(MeV)

(keV)

(keV)

(keV)

(keV)

(MeV)

(MeV)

(MeV)

3.785_+0.001 4.267_+0.001 4.813+0.001 4.956_+0.007 5.032_+0.001 5.198-+0.003

18_+l 12_+3 11-+1 36_+7 31_+1 27-+8

33 _+2 6 _+1 11 -+1 19 _+2 26 _+2 7.5-+2.9

2.3_+0.1 0.8_+0.1 1.3-+0.1 8.1 +0.9 3.8_+0.3 2.7-+0.1

9.9_+0.6 2.9_+0.5 6.1_+0.6 14.7_+ 1.5 14.2_+1.1 4.6_+ 1.8

6.714 10.499 0 6.245 10.512 0.469 5.661 10.474 1.053 5.480 10.436 1.234 5.410 10.442 1.304 5.307 10.505 1.407 average A E c = 10.478_+0.015 MeV

The errors given for all values are fitting errors. In addition the values of E 0 have an absolute energy calibration error of about 10 keV. Here, E X are the excitation energies of levels in 8~Se. The IAR in 8~Br corresponding to the other levels in 8~Se are not prominently seen in the excitation function as they involve large lp values iof the order of 3 to 4) and hence have reduced probability of formation at these low proton energies. TABLE I b Background parameters involved in fitting the IAR in the d°Se(p, n)8°Br reaction E0 (MeV)

ap..(bkg) (mb)

3.785 4.267 4.813 4.956 5.032 5.198

3.5 19 26 44 32 53

A (mb)

B (mb/MeV)

39 88

193 256

- 8464

3285

238

855

C (mb/MeV 2)

- 310

With values of E 0 determined from this analysis, the Coulomb displacement energy A E c (for the 8 ~Se_8 ~Br pair) has been extracted for the various levels in 81Br and 81Se, utilising the expression A E c = Bn+E~, "m (with Ep m' = Eo). The neutron separation energies B, are taken from the literature. The A E c values are listed in table 1. Thus an average value of A E c = 10.478+0.015 MeV has been obtained from a measurement of the six 1AR observed in the present work. Having extracted the A-values for the various resonances through shape analysis, the proton partial widths Fp and the spreading widths W of the IAR have been determined in the manner as described in refs. ~o. 2). However, in the present work, the matching radius a c is taken as 1.05A ~ + 1.5F [ref. 12)] which is the same as that used in the (p, p) analysis of Balamuth et al. 4). The Fp and W values determined corresponding to this radius are also listed in table 1. The errors quoted for the various quantities are those determined from the fitting procedure. In all these cases the spreading width has come out to be larger than the proton partial width. This is true in general for the 1AR at proton energies above neutron threshold 13).

ISOBARIC A N A L O G U E RESONANCES

161

3.2. D E T E R M I N A T I O N OF S

It is well known that the neutron spectroscopic factor (S) determined from IAR analysis is expected to be the same as the one extracted from (d, p) data on the same target for the parent levels in question 14). In cases when (d, p) spectroscopic factors are not measured, this is the only way to extract S. Utilising the familiar relationship between £p and S [ref. 2)], the neutron spectroscopic factors (S) for all the IAR measured in the present work have been extracted. The computer code SEARCH 15) and the proton and neutron optical model parameters listed in table 2 have been TABLE 2 Optical model parameters used in the calculation of S

proton neutron

VR (MeV)

RR (fm)

aR (fro)

VI (MeV)

RI (fm)

al (fm)

V~.o. (MeV)

R .... (fm)

a .... (fro)

58.0

1.25 1.25

0.65 0.65

5.0

1.25

0.47

7.5 7.5

1.25 1.25

0.65 0.65

Derivative Woods-Saxon form factor for Vu.

used in the determination of S. As S varies with the channel radius a¢, the S-values in all the cases have been determined for ac ~ 6 fro. The spectroscopic factors obtained in the present work along with the ones determined in (d, p) [ref. 16)] and (p, p) [ref. 4)] works are listed in table 3. TABLE 3 Comparison of the spectroscopic factors obtained from (p, n), (p, p) and (d, p) works on 8°Se

E,I (MeV)

J~

3.785 4.267 4.813 4.956 5.032 5.198

zt ~z~+ ½+ ~+ ~-

a) Present work. ") Ref. 16).

/ I I 2 0 2 1

S(p.n) a)

S(d,p) h)

0.22 0.026 0.15 0.32 0.32 0.022

0.30 0.045 0.26 0.64 0.40 0.075

Sip. p) c) 0.09 0.18 0.85 0.41

¢) Ref. 4).

It is clear that in general the S-values extracted from the various works are comparable. However, for the IAR much below the Coulomb barrier, the S-values determined from the present (p, n) work agree better with (d, p) work, whereas the (p, p) work gives values widely different from the (d, p) measurements. As the large Coulomb cross section at these energies makes the IAR a weak anomaly in the (p, p) excitation function, the determination of Fp may have larger errors. This point is well illustrated by the weaker 1AR around 4.2 MeV which is not observed at all in

162

S. KAILAS

et al.

(p, p) w o r k , b u t which a p p e a r s as a m e a s u r a b l e r e s o n a n c e in fig. 1 a n d which c o u l d be subjected to d e t a i l e d s h a p e analysis.

4. Conclusion T h e p r e s e n t investigation involving the s t u d y o f the (p, n) r e a c t i o n on 8°Se has resulted in p r o v i d i n g s p e c t r o s c o p i c factors for a n a l o g states in 8~Br which are in g o o d a g r e e m e n t with those m e a s u r e d for the c o r r e s p o n d i n g p a r e n t states in SlSe t h r o u g h (d, p) reactions. In the case o f the a n a l o g states w h i c h are c o n s i d e r a b l y b e l o w the C o u l o m b b a r r i e r , the c o r r e s p o n d i n g r e s o n a n c e s in the (p, p) e x c i t a t i o n f u n c t i o n m a y be t o o week to analyse, a n d for such cases the (p, n) s t u d y m a y be the o n l y m e t h o d to d e t e r m i n e the relevant I A R p a r a m e t e r s as illustrated b y the first two r e s o n a n c e s in table la. T h e help o f Messrs. C. V. F e r n a n d e s , V. V. T a m b w e k a r , M. B a l a k r i s h n a n , A. C h a t t e r j e e a n d G u l z a r Singh at v a r i o u s stages o f the e x p e r i m e n t is gratefully acknowledged.

References 1) G. P. Couchell, D. P. Balamuth, R. N. Horoshko and G. E. Mitchell, Phys. Rev. 161 (1967) 1147 2) M. K. Mehta, S. Kailas and K. K. Sekharan, Pram~na 9 (1977) 419 3) Y. P. Viyogi, P. Satyamurthy, N. K. Ganguly, S. Kailas, S. Saini and M. K. Mehta, Phys. Rev. C18 (1978) 1178 4) D. P. Balamuth, G. P. Couchell and G. E. Mitchell, Phys. Rev. 170 (1968) 995 5) Y. P. Viyogi, S. Kailas, S. Saini, M. K. Mehta, N. K. Ganguly, N. Veerabahu and T. K. Bhattacharjee, Nucl. Phys. and Solid State Phys. (India) 19B (1976) 36 6) S. Kailas, N. K. Ganguly, M. K. Mehta, S. Saini, N. Veerabahu and Y. P. Viyogi, lnt. Conf. on nuclear structure, Tokyo, contributed paper, 1977, p. 297 7) S. Kailas, S. K. Gupta, M. K. Mehta, S. S. Kerekatte, L. V. Namjoshi, N. K. Ganguly and S. Chintalapudi, Phys. Rev. CI2 (1975) 1789 8) S. Kailas, M. K. Mehta, Y. P. Viyogi and N. K. Ganguly, Nucl. Phys. and Solid State Phys. (lndia) 18B (1975) 12 9) E. H. Auerbach, BNL-6562 (1962) 10) C. H. Johnson, R. L. Kernell and S. Ramavataram, Nucl. Phys. AI07 (1968) 21 11) B. Ya. Guzhovskii, A. G. Zvenigorodskii, S. V. Trusillo and S. N. Abramovich, Soy. J. Nucl. Phys. 20 (1975) 242 12) D. Robson, Isobaric spin in nuclear physics, ed. J. D. Fox and D. Robson (Academic Press, New York, 1966) p. 411 13) W. Mittig, Phys. Rev. C15 (1977) 1228 14) W. J. Thompson and J. L. Ellis, Nuclear isospin, ed. J. D. Anderson, S. D. Bloom, J. Cerny and W. W. True (Academic Press, New York, 1969) p. 689 15) R. Van Bree, private communication (1975) 16) E. K. Lin, Phys. Rev. 139 (1965) B340