NEUTRON INELASTIC SCATTERING IN Pb 206 AND Pb 207
J. B. GUPTA AND N. NATH
Ka m j a s C o itL E G E , ITn i v e i i s i t y O F D B i i H i , Dt5 Lh i- 7 In d i a
(Received A p r il 29, 1968)
ABSTRACT. Difforontial neutron inelastic s(‘attoring cross sections for individual states in Pb 206 and Pb 207 have been calculated on the basis of the Statistical tlieory of Hauser and Foshbaeh. Calculated excitation functions agrc^o reasonably with experimental data for indivi
dual levels, except for the first excited stated of Pb 200. The agreement in general is closer at higher excitation energies as compared to tlie region nearer threshold. Factors likely to explain the look of agreement observed are discussed.
«
I N T R O D U C T I O N
Tlio study of noutron iuolastic^ sc^attering cross sccjtioris of uu(?lci as a fuuction uf oxcitatiou oixorgy can provide a good test for the Haiiser-Fosliback (1052) theory of inelastic scattering. It maj^ also provide information regarding the spin and parity of individual states of the nuedei. Tlie present work was under
taken to provide suitable interpretation to the available experimental data for the two lead isotopes.
In an earlier report (Gupta and Natli, 1961) avo made similar calculations using the nuclear penetrabilities given by diffiise-odgo potential well with only surfa(}e absorption (Emmerich, 1958). The calculated cross sections were found to be much larger than the experimental valutas for the first ftiw levels of Pb 206. Van Patter and Jackiw (1960) and Jacikiw et al (1961) liave obtaiiuxl much better fit in similar calculations for several even-even nuclei using the penetrabilities given by Bayster et al (1957) for a diffuse-edge potential with volume absorption. Beystor et al (1957) determined the parameters for their potential by fitting the experimental data on noutron total and differential elastic scattering individually for some twentysix elements from Boyrllium to Uranium over a wide energy range. They permitted much greater variation for the absorption parameter with excitation energy than was done by Emmerich (1958). We have therefore repeated the calcu
lations for load nuclei using Boyster’s ixonotrabilities.
R E S U L T S
206P6 : Level scheme of 206Pb was adopted in accordance with the one published in Nuclear Data Sheets (Way 1965) and is indicated figure 1. As
•Physics Department Banaras Hindu University, Varanasi-5.
408
45
Boystor et al (1957) did not specifically fit tlxo data for load isotopes, wo suitably iutorpolated nuclear penotrabilitios given tlusm for tho noiglibouring nucloi of All and Bi to get tho ones for Pb. This resultiid in a general lowering of tho calculated cross section closer in agreomont with experimental data.
N e u tro n I n d a s t i c Sca tte rin g in F b 2 0 6 a n d P b 2 0 7 4 0 9
5* ' 6*^ ■ 5" ■
5* ■Z*
3~6“
4*- • K ‘ 2*3"- O^-
0*- 1
—
MeV 3 40 3 28 3 125 3 017 2 78 2-62 2 53 2 385 220 2 I 6 I 998 1-82I
»*46 1.34 t 19 0 803
68
206 Pb
Figure 1. Level schoino tklopted for 206 Pb.
B .9b
Figure 2. 0.803 and 1.34 MoV level (n, n')croHS Hootioijs— (Closed circles) Lind and Day, 1961;
(open cirtilo) Craiiborg et al, 1956; (Square) Landon et al, 1958, (Triangle) Boring et al, 1961;
(Cross) Nellis et al, 1902.
Figures 2 through 4 show the results of our calculations for tho excitation of 0.803, 1.34, 1.45, 1.72, 2.1G and 2.62 Mov levels as solid curves while the experi
mental results are indicated as explained in the cajition for these figuros. Tho 0.803 and 0.538 Mov gainnia ray production cross sections corresponding to the excitation of 0.803 and 1.34 MeV levels have been corrected for tho known cas- (jades from higher states in order to derive tho level cross-sections. Tlio second 2+ level at 1.46 MeV results in two de-excitation gamma-rays of energies 1.46 and 0.665 MeV. Tlie level cross section is thus obtained by adding tho two gamma ray the ground state transition from 1.82 MoV level and tho decay of 2.62 MeV level to 0.803 MoV level. Therefore, the cross section for the 2.62 MoV level was obtained from the production cross section of 1.82 MeV gamma ray by subtracting the extrapolated contribution for the 1.82 MoV ground-state transition above the threshold for the 2.62 MoV state. It was found (figure 4) that there is a reason- fthly good agreement between the experimental data so obtained and the theoretical calculations for the 2.62 MeV level. However, disagreement was
3
4 10
J. li, Gupta
nbt{iini!(l lor tlu> 1.82 McV'^ lovol iuu^^tion u')< »iu)u'‘ii in figuro 3) Nollis ct al (11)02) ubsorvt) ii guvinm my of 2.02 M(.jV in atKiilion to tho L82 MoV
■ * ■ --- --- -— 2r»u 1 •’
j-
a — — ... i
G 15(> u
b
50
i
/ ■ '0 - -
750 Ir
a j y '
.9 450 b
150 '
j/* *. J 1 . ^ . ___
1.4 1.9 2.4 2.9 3.4 3.9 En in MoV
Figuro 3. 1.4G and 1.72 MeV level (n, n ') c to h b sections. Experimental data points same as in fig. 1.
2.0 2.4 2.8 3.2 3.6 4.0 En in MeV
Figure 4. 2.16 and 2.62 MoV level (n, n') cross section (circles) Lind and Day, 1961;
(cross) Nollis et al, 1962.
one observed earlier by Lind and Day (1961). We find that if wo combine the experimental cross section for those two gamma rays, it agroos well with the similarly combined theoretical cross sections for inelastic scattering to the l-6^
N eviron Inelastic Scattering in Pb 2 0 6 and Pb 2 0 7 4 1 1 and 2.62 MoV lovols. No corrootions woro appliod to the experimental data on the corresponding yield of gamma-rays to work out oxpoiimontal cross sections for the 1.70 MeV and 2.16 MoV lovols.
9/2*
7/2“
13/2^
a/2”
5 /2 *
1/2“
MeV2-71
2 34 I 90
634
0-894 0-57
207 Pb
Figure 5. Lov(^1 scliomn for 207 Pb.
2.0 2.8 3.6
En in MoV
4.0
Figtiro 6. 0.57 and 0.894 M«'V loved (n, n') orosfi sootions.
(( irclo) Day, 1956; (triangle) Salnikov, 1958.
1.5 2.1 2.7 3.0
En in MoV
figure 7. 1.G3 MoV level (w, w") ftc'etions. (( iroloF) Stellson and riambnll, 1055; (dashed curve) Rothman and Van Patter. (1057), thooreti' al.
207 PI) : The individual le.vol cross se-otiojis for this isotope wovo also cal
culated using ponotra])ilitios giv(‘u hy Boyslcir e,f al, (1057). The level sehomo ado])tod is shown in figure 5. Tin'- (/?, ??/) < ross section thus ca]cmlat<vl are much lower than those obtained oarlifw tming Eimiierieh’s potential with only surface absorption (Gupta and Nath, 1901), espc^idally near the threshold. Tlio now results for the first throe excited states ari^ shown as solid curves in figures 6 and
^ along with the experimental values. For the first two levels at 0.57 and 0-90 MeV, the experimental values of gamma ray production cross section ob
tained by Daj’' (1950) following neutron scattering at incident energy of 2.56 MoV indicate good agreement. Another isolated measurement due to Salnikov (1958) 6»t incident energy o f 2.34 MoV for the 0.57 MeV state is also in reasonable agree- uiont with the present calculations. Unfortunately, data for complete excitation function for 0.57 and 0.90 MoV states does not exist. StoUson and Campbell
4 1 2 J . B . Oupta
(1955) have moasurod the (n, v/ y) cross section with ± 4 0 % error for the 1.63 MeV isomeric state upto incident neutron energy of 3.2 MeV. The agreement o f their data with our calculation is good as shown in figure 7. It is an improvement over OUT oarh'or calculations (Gupta and Nath, 1961). Rothman and Van Patter (1957) also obtained closer agreement with SteUson's data on the assumption of a strong interaction potential model. However, in their calculation the parameters of the potential-well were (*hosen on the basis of Stollson’s data itself. The close agreomont obtained here considering that the ponotral)ilities were obtained through interpolation o f the values for neighbouring nuclei, indicates reliability for Beystor’s parameters oven for load.
D I S C U S S I O N
In the case o f Pb 206 close agreomont is obtained between the caloidated and the experimental values of level cross sections for the 1.72 and 2.02 MoV levtds.
For the 2.16 MoV level the agreement is better with a 2+ spin as compared to either 1+ or 3+, indicating tlw^ro-by that this is most probably a 2+ level. The agreement for the 1.46 and 1.34 MeV levels is not quite satisfactory. Tlao 2+ level at 0.H03 MoV Still shows a marked disagro(^mcnt at lower incident energies.
Lind and Day (1961) had indicated close agreement between their experimental results and the theoretical calculations they made by making an arbitrary choice for the imaginary part W of the Optical ])otential. However, their comparison indicates that the best fit to thii excitation function for the 0.803 MeV level do not provide as good an agreement for the other levels. Towle and Gilboy (1965) used similar arbitrary value for W to fit their results o f inelastic scattering on Pb208.
However, Auerbach and Moore (1964) obtained satisfactory fit to the Pb 208 data without any need for an arbitrarily low value o f W,
We feel that the discreponcuos still left espooially the ones for lowlying states at incident energies closer to their thresholds may be substantially reduced if level-width fluctuations as proposed by Moldauer (1961) are taken into account.
Also, disagreements for levels with low spin values, e.g. 0*+* and 2+ states at 1.19 and 1.46 MoV, may get reduced if corrections duo to anisotropy in the angular distri
bution of gamma-rays from these states are considered. Any uncertainties about the nuclear level schemes can also cause ambiguities in the comparisons between the experimental data and theoretical values.
A C K N O W L E D G M E N T
One o f US (J. B. Gupta) is thankful to Principal P. D. Gupta for providing the the necessary facilities and inspiration for this work.
N eutron In ela stic S cattering in Ph 2 0 0 and P b2 0 7 4 1 3
R E F E R E N C E S
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