Chaubey, A K

Sehgal, M L

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SOME CALCULATIONS OF NEUTRON CAPTURE CROSS-SECTIONSA. K. CHAUBEY and M. L. SEHGALD kpabtm ent  of PiiYSicy, x4 u g a r h  MUSLIM U n iv e r sity , Aligarh  U .P., I n d ia{Hecewed M an  196^ )^a b s t r a c t .. Neution cui)ture cross-soc.tions won- calculatcci for ahout 30 casos at 24 keV, using low energy losonanco pnrmiietors. Tliesn cross-sections wc'ro coiuparod with previously measured vaha's of the eross-seetions. In mosi oi tho cases, except neution inagk^  jiumbei' nuclei a pood n«reemcn( wan I'ourul btHwoen the exporimojii«.l and Ihe ihooridical values.J M T R O D U 0 T i O NAVo have measured (Cliauhoy and Soligal lilCf) and capture erofts-scetioiis at 24keV for about r>0 nuclei, using antimony-hcryDinm photomuitron sourc(»s. fVoss-sectious in tho keV cuiergy region are. helpful in tlwi design of the reactors and in th.» study of tho (cosmological fheori((S of clom(mt formation (Biirbidgo c/. (d 1957) as well as in the study c*f nucleitr roactioji tlieorios (Margolis 1952), (Poschbach et al 1954), (Mossion-Kotin d al 1959). Cross-section values at low energios are very useful for testing various nuclear models.In the present work we have calculated the capture crosH-so(di(.ns at 24 keV for about 20 eases. For 10 case results have boon publishod earlier (Cliaubcy and Schgal 1965). Thus in all, for 90 cases, cross-Wictions calculated hy the method of Booth et al (1958) were coiuparod with our previously inoasiired (Chaubey au( Sehgal 1965, 1966) cross-soctiou values (a expt). In this way tho thcorctica formula (Booth et al 1958) of capture cross-sc(dion and hence the theory on which this formula is based was chei^ kiKl at 24 keV.63C A L C U L A T I O N S  OF C A P T U R E  CROS S- SECTI ONSWo havo odoulatod tho oopteo oro...*H,lions at 24 koV. followng tho inrthoa of Booth et of (1968). The following nilation is uswi for the ealeiilatlons o «. (.roes- sections:5678668 A. K. Ohatibey and M. L. Sehgaty 2(1>/+I), / 2 . 6 y l 0 « \ r ,4 ” ( E ~ ) vX [ 1 - ( M = {  1 - ^ ;  j  «x,, ( - ( > ) * } ] .. (iiWhere h r,/(2Forn®),and /  is ilio spin of the target nucleus, J is the total angular momentum of the com­pound nucleus, is the energy of the nutrons expressed in eV and Vq is the peno: tration fa<dor (taken ecjiial to miity for zero angular momentum). The quan­tities Vr^  ^  and are experimentally easured (BNL-32o, Ilnd ed., 1958 and its supplement no. I (1960) and Levin and Hughes 1956), radiation width level spacing and reduced neutron width respectivedy. Tlie value of these parameters were taken as the average over all the ,s-wave reasonances. While calculating tlu*. capture cross-section from this formula it was assumed (Booth el al 1958) that only c9-wavo mmtron contribute to the cross-section and the contribution due to ^-wavo neutron is almost zero. Tt was also assumed that the low energy resonance para­meters can be used at 24 keV.In most of tht‘. cases values of th(i resonance parameters were taken frmn BNL-325, (1958, 1960). While calculating the value of levtd sacing from those references the average level spacing for zero spin targed nuclei was taken to bo equal to the observed level spacing wliereas for nonzero spin target nuclei, the average level spacing is taken to be twice that of the observed level spacing (Cartel’ et al 1954).The values of the (capture cross-sections experimentally moasurcKl (cr^ p^t) theoretically calculaterl (<Ti,,^ „) are shown in table 1. For Mn®^®, Ag^ ®^ , Cd^ ^^ , Te^ ®^, T)y^ ®^ , and Th^ ®^ . Tlio results have been taken fromour previous paj>er (Chaubey and Sehgal, 1965). In Zn®®, Se®®, Br"^ ®, Rh^ ®®, Pd^ ®®, Inii-'i and Dy^ ®^  (Chaubey and Sehgal, 1965, 1966) values of cTe^ pt the sum of the cross-sections for the isomeric and the ground states and thus are total capture cross-section. The calculated cross-section in all the above cases is also the total capture cross-section. We find that except in the case of Zn®® and Pd^ ®* there is a reasonable agreement between cr,,xpt and <Ttheo* Pd^ ®^ and In^ ®^ values of o-expt are only for the ground state as the cross-section for the isomeric state is not knoMm, therefore it is not desirable to make any comparison between (T^ xpt ®*nd cTtheo-In figure 1 the ratio o'<.xpt/<^ theo been plotted versus the number of neutrons in the target mudous. It is clear from this figure that in most of the cases the points lie around th(^  line corresponding to the ratio 1. In general the agreement in the experimental and theoretical values of the cross-sections is good. It interesting to note that in the above calculations of the cross-sections only theNeutron Capture Cross-Sections 569lablo 1. Table siioAvs a eojiipaiison in tlw oxperiiueutally moasnred and theoretically ealcu]at(i(l <'a|>tnro eToss-soi-tioiisTurj^otnucleuse^xpt{mb) t^heo{mb)Keferynce Cor Fr and D401 35 aZn0» 2 7 1  3 1.0 a60 i r> 120.4 a7.6 _ 10 122 a.So«» J3-J: l .S 14.7 a0 2 4 1  46 072 aBr8i 500:! 100 360 c.610:f 61 610 aPJ108 1S6 i 16 624 aFMiio 120 : 16 2031 aAgio- 8 1 0 1  90 962 a.Agio*-- 009 J 00 047 1)(V p u 240.i 26 103 alnii3 200.1 loo 1040 1)soo  ; 00 S13 (•0 0 1  11 06 .6 a7 1 .4 0 .6 a60 : 10 173 b1^141 100 ‘ 16 49 aDyl«> 1901 20 203.6 aH oICb 990 i 70 936 aLu»’^ ' 1070 i 120 1700 a166.;. 20 64 aH(.185 1706 i 206 1970 b87 6 -i SO 037 aIriOT 030 i 60 6230 bJJpOB 2 0 5 .L 30 200 a600 !' 35 007 apb2O0 0 .5 ^  1 .6 0 .07 aTh232 4 8 0 1  60 340 aa -S u p p le m e n t. n o . 1 o f  BN L-;t25, I9fi0 b -B N h -325  l l - i id o d ., 195S c— Cartor et al (1964).contribution due to .<j-wave neutrons has b(K)n taken into account. It is a well known fact that at this energy there will be appreciable contribution due to j9- wavo and rf-wave neutrons, which, when taken into account will change the valueii5 7 0 A . K .  G havbey an d  M . L .  Sehgalof the theoretically calculated croas-sectious giving poor agreement with the ex­perimental values. It may be worthwhile for some theorist to look into this ox- pressioii of tho croaR-section for thin auamolv.0 15050 100Neutron number of the target nucleus Figure 1. The ratio of experimontally measured and thooretioaUy calculated cross-sootions 18 plotted against the neutron number of the target nucleus. In general the points mo scattered about tho line having ratio 1.A C K N O W L E D G E M E N TAuthors wish to thank Professor Rais Ahmed for liis kind interest in this work.One of the authors (A.K.C.) is thankful to O.S.I.R. for providing him a Seninor Research Fellowship.R E F E R E N C E SBooth, R. Well, W. P. and MacGregor, M. H. 1968, Phys. Rev., 112, 226.Brookhaven National Laboratory report-325, Il-nd edition, 1968 and supplement No. 1. I960. D. J. Hugheo and R. SwartzBurbid^ E. M. Burbidge, O. R.. Fowler and Hoyle F„ 1957, Rev. M od. Phys., 29, 647. Carter, Harvey, Hughes and Pilcher 1964, Phya. Rev., 96, 11.3.Chaubey, A. K. and Sehgal, M. L., 1965, Nuclear Phyeica, W , 267.” ” 19«6, Phya. Rev., 152, 1065.Feshbaoh. F. H. Foshbaoh, Porter C. and Weisskopf V. F. 1954, Phya. Rev., 96. 448. Levm, J. S, and Hughes, D. J., 1956, Phya. Rev., 101, 1228.Margolis, B.. 1962, Phya. Rev., 88, 327.Mossm-Kotin, C., B. Margolis and E. S. Troulsetzkoy 1959, Phya. Rev., 116, 937.

Some Calculations of Neutron Capture Cross-Sections

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Some Calculations of Neutron Capture Cross-Sections

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