The soil samples collected from the selected locations were analyzed for 226Ra and 210Po activity. The activity of 226Ra ranges from 2.0 Â± 0.4 Bq kg-1 to 12.9 Â± 1.3 Bq kg-1, whereas that of 210Po ranges from 7.6 Â± 1.2 Bq kg-1 to 37.3 Â± 2.4 Bq kg-1. The activity ratios of 210Po to 226Ra vary by an order of magnitude from place to place. The systematics of these ratios on the distances of the sampling sites from catchment zone water divide towards neighboring river basins, have been observe

Malini, S.

Nagaiah, N.

Paramesh, L.

Venkataramaiah, P.

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PHYSICAL REVIEW C VOLUME 24, NUMBER 3 SEPTEMBER 1981Empirical constraints on the ' 0+ Ca optical potentialS. Krewald, A. Djaloeis, and S. GopalInstitut fiir Kernphysik, Kernforschungsanlage Julich, D 51-70 Julich, West Germany(Received 6 April 1981)The angular distribution between 20' & 0, & 180 of ' 0+ Ca elastic scattering atE, = 35.7 MeV has been analyzed in terms of the optical model. For both the real andimaginary parts, the standard Woods-Saxon and spline-function parametrizations of the op-tical potential have been investigated. In the angular region 0, & 112', Woods-Saxon —Woods-Saxon potential combinations suffice to describe the data; however, no fitcould be obtained either by Woods-Saxon —Woods-Saxon or by Woods-Saxon —Spline-function potentials for the complete angular distribution (0, & 180'). In contrast, theSpline-function —Woods-Saxon combination reproduces the experimental data we11. Nofurther improvement of fit quality is obtained by parametrizing both the real and imaginaryparts in terms of spline functions. The best-fit Spline-function —Woods-Saxon potential isfound to consist of a real part, having significant wiggles in the interior, coupled. to a shal-low imaginary part with a depth 8' —2 MeV and a large radius 8; = 1.60(A~' ' + AT' ')fm.NUCLEAR REACTIONS 0+ Ca elastic scattering,E,~ = 35.7 MeV; optical model analysis including a "model-„ independent" potential parametrization by spline functions.I. INTRODUCTIONIn analogy to the light ion (Ap ( 3) case, thedescription of the elastic scattering of a heavy ionhas been generally attempted in terms of the opticalmodel. Analyses performed so far have given in-consistent pictures regarding how far the elasticscattering data could give information on the poten-tial shape, particularly, in the interior region. Forexample, using the notch perturbation method, Cra-mer and DeVries' have found that neither light- norheavy-ion scattering at any energy probes the interi-or of the nucleus. On the other hand, using a simi-lar method, Delbar et al. have shown that angulardistributions for the a -particle elastic scattering onCa nuclei at E~ = 36.2 MeV are influenced notonly by the tail region of the potential, but also bythe very inner part around R = 2 fm. In fact, thedetails of the potential shape in the interior regionwere found to be responsible for the so-called"anomalous large angle scattering" (ALAS) ob-served in Ca(a,a) elastic scattering. It is worthmentioning that deep penetration ("transparency")of a particles into the Ca nucleus was also sug-gested by Friedman and Batty from their model-independent analysis of o + Ca elastic scatteringat E = 140 MeV. Taking advantage of this tran- 'sparency of Ca to o particles, Michel and Vander-poorten' succeeded at obtaining a consistent descrip-tion of a- Ca elastic scattering over a wide range ofincident energies using a "sphne-parametrization"technique.It is well known that a phenomenon similar tothe ALAS has also been observed in someheavy-ion elastic scatterings. Attempts to explainthis phenomenon in terms of, e.g., quasimolecularresonance, the cluster exchange mechanism, or sim-ple potential scattering have been summarized inRef. 10. While enhancement of the large-anglecross section can be obtained easily with a conven-tional optical model potential having Woods-Saxonshape in both real and imaginary parts by simplyreducing the strength of the imaginary potential, "the details of the angular distribution cannot bereproduced correctly.In this report, we present results of an opticalmodel analysis of ' 0 + Ca elastic scattering atE,~ = 35.7 MeV, measured' up to 0, ~ = 180'.The objectives are (I) to check whether a betterdescription of the experimental angular distributioncan be obtained by giving more degrees of freedomto the real and/or imaginary part of the optical po-tential, and (2) to see to what extent the Ca nu-cleus can be transparent to an ' 0 projectile whichis considered to consist of a clusters; in particular,to establish whether the elastic scattering cross sec-966 1981 The American Physical Society24 EMPIRICAL CONSTRAINTS ON THE ' 0+ Ca OPTICAL ~ ~ ~ 967tion is also sensitive to the details of the optical po-tential in the interior region.II. METHOD OP ANALYSISThe optical model analysis was performed usingthe computer code "OPTY," which automaticallysearches for the optimum values of the potentialparameters by minimizing the J value defined as21 + p(8') +th(8' a 1 . aM )X (a, ,. . . ,aM) =— (8.)t +exp iAt each angle 8;, the quantities tr,„p(8;), ho,„p(8;),and o;h(8;) represent the experimental value, its es-timated error, and the theoretical value of the elasticscattering differential cross sections, respectively.The potential parameters searched upon are denotedby a ~,. . . ,aM., the quantity I' represents the numberof degrees of freedom.For the spline parametrization, the startingspline parameters S; (i = 1,. . .~;M = 12) at thecorresponding radii r; were computed from the po-tential sets SA, ST1, and ST2 (strong absorption,and surface transparent 1 and 2, respectively) ofRef. 9 (see Table I). Several sets of r; values,among which a set with r; = (i —1) fm,i = 1, ,12, were used to study the dependenceof the resulting best-fit potential (see Sec. III) onthe starting conditions of the search procedure.The error band associated with the extractedbest-fit spline real potential was calculated using thecovariant matrix method as described in Ref. 6. Itshould be emphasized that this error band reflectsonly the statistical uncertainties of the extracted po-tential shape around the 7 -miminum value.III. RESULTSFigure 1 shows the experimental angular distribu-tion relative to the Rutherford cross section. Thedashed curve denotes the optical model predictionusing the Woods-Saxon —Woods-Saxon (WS-WS)potential set'ST1 of Ref. 9. The best-fit curve ob-tained in this work using a spline-function—Woods-Saxon (SPL-WS) potential is given by thesolid line (see Table I).It can be seen from Fig. 1 that the SPL-WS po-tential gives far better fit quality compared to thatobtained using ST1, in particular at angles8, & 112', where the ST1 curve drasticallydisagrees with experiment. It should be recalledthat the sets ST1 and ST2 of Ref. 9 are character-ized by a weak imaginary potential which was re-quired to produce an oscillatory pattern at angles8, & 112' (see Fig. 2). This feature was alsofound by Satchler" in the analysis of the ' 0 + Sielastic scattering data at E, —33 MeV. Wehave also performed further searches using WS-WSpotentials. We confirmed that the use of a strongimaginary part does riot produce an oscillatory pat-tern in the angular distribution at large angles forboth WS and SPL parametrizations of the real partof the potential. For a WS real part, no further im-provement was obtained even after giving more de-grees of freedom to the imaginary potential by usinga spline function. Similarly, the use of a splineparametrization of both the real and imaginary partsdid not bring any significantly better fit quality thanthat represented by the solid line in Fig. 1.Figure 2 shows the radial dependence of the realand imaginary potentials used in the present workand those of Ref. 9. The parameters are listed inTable I. The following features are worth noting:TABLE I. The "0+ ~Ca optical potential parameters for E, = 35.7 MeV. Radii are defined as8 = r(Ap' '+ AT' ') and rc = 1 0Set v (Mev) r, (fm) a„(fm) e' (Mev) r; (fm) a; (fm) Ref.SAST1ST2SPL-WSSPLA10.0124.7650.00spline'spline'1.3641.4031.329spline'spline'0.6160.3990.420spline'spline'23.383.807.602.162.161.2891.2811.0001.6011.6010.5350.2210.3000.1550.155999presentpresent'See Fig. 2.968 S. KRE%ALD, A. DJALOEIS, AND S. GOPAL100.-Real Potential0—10 1.-C'1p 2-OXlC: 10-301P-4PotI I20 40 60 80 100 120 140 160e c.m.FIG. l. The experimental angular distribution of the' 0+ Ca elastic scattering at E, = 35.7 MeV relativeto the Rutherford cross section. The solid line representsthe best-fit obtained in the present work using a SPL-%Sotential (see text); the dashed curve was calculated usingp r.9the potential set ST1 of Kubono et al. (Ref. 9).-60—SA---- ST1—-ST2——SPLA~SPL-WSRsa10 R(fmI(i) The real part of the best-fit SPL-WS potentialexhibits significant wiggles in the interior region,10similar to those observed by Barrette and Kahanain the analysis of 0 + Si elastic scattering angu-lar distribution at E, = 21.2 MeV. The effects ofusing different sets of radii r; were investigated andnot found to change the conclusion.(ii) The best-fit imaginary potential is found tohave a depth of only about 2 MeV but having a1/3 g 1/3)large range with a radius 8; = 1.6(A& +AT )fm. This result corroborates those found bySatchler" and Mackintosh et al. ' In the interiorregion, 'this depth is much smaller than that of thesets ST1 and ST2 of Kubono et al. However, inthe surface region near the strong abso+tion radiusRs~ —1.5(Ai ' + AT' ) fm (see Fig. 2), ST1 andST2 give practically no absorption, . whereas in theSPL-WS potential the absorption strength resem-bles that of the strong absorption potential set SA.It is worthwhile to point out (see Figs. 1 and 2)that the experimental data in the angular range8, & 112' do not put strong constraints on thegeometry of the imaginary potential. Good fits ocomparable quality are obtained either with the setSA (strong absorption potential) or with the ex-tremely surface transparent potential ST1 whichreaches its full absorption strength only in the re-gion far inside of the strong absorption radius.The influence of the absorption strength on thetheoretical angular distribution in the present best-fitpo ent tial is illustrated in Fig. 3. It can be seen thata strong oscillatory structure is observed in the ab-sence of absorption. Furthermore, the absorptive0 IImaginary PotentialI I I I I~VIII+SA---- ST1— ST2———SPL-WSRsaT t i i i i i i i Ii iO 5 10 R(~mjFIG. 2. The radial dependence of both the real andimaginary parts of the best-fit SPL-%'S potential corn-pared to those obtained in Ref. 9.potential clearly plays an essential role for theovera11 reduction of the cross sections at large an-gles, as well as for modifying the oscillatory pattern.The fact that an imaginary depth of only about 2MeV is necessary to describe the experimental angu-lar distribution satisfactorily suggests, as in theu+ Ca system, a high degree of transparency of16the Ca nucleus to the incoming 0 projectile.This finding contradicts the claim put by the au-thors of Ref. 1 that neither light- nor heavy-ion24 EMPIRICAL CONSTRAINTS OX THE i60+ ~Ca OPTICAL. . . 96910o,-C' 1p-20Pote ntiaIma gina'60+ 'oca ElasticEc,m. =35.7 MeV (II1P-4 2.———10--- 00I20oI I I I I I I40 60 80 100 120 140 160e c.m.scattering at any energy probes the interior of thenucleus.Figure 4 shows the effects of modifying only theinterior shape of the real potential on the angulardistribution. The dashed curve is obtained using thereal potential SPLA (see Fig. 2) obtained from theSPL set by modifying it to have a smooth shape inthe region R & 8 fm. The angular distribution isstrongly a6ected in the large angle region (8, m& 112'), the resulting curve being in gross disagree-ment with the data. In this analysis the wigglestructure in the interior region of the real potential10010 1.-FIG. 3. Illustration of the sensitivity of the opticalmodel cross section with respect to the variation of thedepth in the imaginary part of the best-fit SPL-WS poten-tial (8' = 0 MeV, dashed line; 8' = 1 MeV, dotted-dashed line; best-fit SPL-WS, solid line).does indeed appear to be necessary to describe theback-angle data correctly. In order to assess thepossible physical significance of the wiggles, oneshould note that the optical potential for the scatter-ing of two composite particles is a highly nonlocalquantity. ' The conventional analysis is heavy ionscatterings in terms of the optical model. has, todate, relied only on local potentials. One should,therefore, ask what the shape of an equivalent localpotential should take. This question has been stu-died recently by Bauhoff et al."for the case of pro-ton scattering from ' C and Ca. They have con-structed an equivalent local potential containing nosingularities from the regular and the irregular solu-tions of the nonlocal scattering problem. In thecase of 30 MeV protons, the equivalent local poten-tial resembles a WS shape only in the surface re-gion; the interior part, however, exhibits rapid oscil-lations. In view of this, we suggest that the wigglesin the real part of the present best-fit potential maybe due to the nonlocality of the heavy-ion potential.Indeed, nonlocality effects for the ' 0 + Ca sys-tem due to the Pauli principle have been taken intoaccount by Friedrich et al. ' using a one-channelapproximation to the resonating group method. Astrong backward rise in the angular distribution waspredicted for E, = 30 MeV, which qualitativelyagrees with the currently analyzed data atE, = 35.7 MeV.Finally, to test the sensitivity of the predictedcross section to the deep interior region of the realpotential, we modified the SPL potential by settingthe potential value for zero for R & 1 fm. Theresulting angular distribution is shown in Fig. 4(dotted-dashed curve). The large angle cross sec-tions are strongly affected, a feature similar to thatfound by Delbar et al. 21p-2D10 3,—XI1P-4PotI I I I I IQ 40 6Po 80 1QQ 120 140 160ec.m.FIG. 4. Illustration of the sensitivity of the opticalmodel cross section with respect to changes in the radialdependence of the real part of the ' 0+ Ca optical po-tential (see text). Dashed line: potential set SPLA of Fig.2; dotted-dashed line: best-fit SPL-WS potential cutoff at8 = 1 fm; solid line: best-fit SPK,-WS potential.IV. CONCLUSIONSFrom the present model-independent analysis ofthe ' 0 + Ca elastic scattering angular distributionat E, = 35.7 MeV the following conclusions canbe drawn:(i) Fixing the analytic form of the real potential toa WS shape cannot lead to a good description of theexperimental data.(ii) On the other hand, the data are successfullydescribed by, a spline real potential in combinationwith either a WS or a spl'ine imaginary part. How-ever, no significant improvement is obtained by giv-ing more freedom (through a spline parametrization)970 S. KRE%ALD, A. DJALOEIS, AND S. GOPALto the imaginary part.(iii) The best-fit SPL-WS potential is characterizedby a real part having an oscillatory pattern in theinterior region and by a shallow (W —2 MeV) ima-ginary potential with a large radius R; = 1.6(Az'~ + AT'~ ) fm. The theoretical cross sectionsare found to be sensitive to the depth of the ima-ginary potential as well as to the shape of the interi-or part of the real potential.In order to assess the significance of the presentresults, the following steps are necessary:(i) Consistency checks should be performed byanalyzing experimental data which cover a large an-gular range at.other incident energies. However, nosuch data ' 0+ Ca are available at present.(ii) It is extremely important to check theoretical-ly whether the oscillatory structure in the interiorregion of the real potential is indeed due to the non-locality of the ' 0+ Ca optical potential.One of the authors (S.G.) would like to sincerelythank Professor C. Mayer-Boricke for providing anopportunity to stay in Julich. -'J. G. Cramer and R. M. DeVries, Phys, Rev. C 22, 91(1980).T. Delbar et al. , Phys. Rev. C 18, 1237 (1987).3D. M. Brink and N. Takigawa, Nucl. Phys. A279, 159(1977).4H. P. Gubler et al. , Phys. Lett. 74B, 202 (1978).5F. Michel and R. Vanderpoorten, Phys. Lett. 82B, 183(1979).6E. Friedman and C. J. Batty, Phys. Rev. C 17, 34(1978).7C. K. Gelbke et a/. , Phys. Rev. Lett; 41, 1778 (1978).SP. B. Munzinger et al. , Phys. Rev. Lett. 38, 944 (1977).S. Kubono, P. D. Bond, and C. E. Thorn, Phys. Lett.81B, 140 (1979).' J. Barrette and S. Kahana, Comments Nucl. Part.Phys. 9, 67 (1980).G. R. Satchler, Nucl. Phys. A329, 233 (1979).' H. Dabromski, R. Planeta, and A. Djaloeis, IKP-KFAJiilich, Report 1637, 1980.i3R. S. Mackintosh and A. M. Kobos, Phys. Lett. 92B,59 (1980).H. Feshbach, Ann. Phys. (N.Y.) 5, 287 (1962).'5W. Bauhoff, H. V. v. Geramb, and G. Palla (unpub-lished).6H. Friedrich, K. Langanke, and A. Weiguny, Phys.Lett. 63B, 125 (1976).

226Ra and 210Po in the soils of Mysore, Karnataka, India

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226Ra and 210Po in the soils of Mysore, Karnataka, India

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