A N N A L E N D E R PHYSIK 7. FOLGE * BAND 21, H E F T 1-2 * 1968 Energy l e v e l s of ''F from "O(d, d)"O By F. MACHALI, Z. A. SALEH,A. T. BARANIK,P. ASFOUR,I. BONDOUK and v . E. STORIZHICO1) With 9 Figures Abstract The differential cross sections for elastic scattering of deuterons from l 6 0 have been measured in the Ed = 1.0. 2.5 MeV region at eight scattering angles. Resonances were observed at Ed = 1.00, 1.80 and 2.45 MeV, corresponding to the excited states in I8F at 8.40, 9.11 and 9.69 MeV. Analysis of the data in terms of the single-level approximation leads to the assignments I" = 1+,3+ and 2+, respectively. Reduced partial widths for elastic scattering were determined. -. 1. Introduction The deuteron binding energy in the l8F nucleus is only 7.514 MeV. Hence, one may expect the analysis of leO + d reactions at low energies to be possible within the framework of the resonance reaction theory. Indeed, earlier measurements [l]of the 1sO(d,d)160elastic scattering cross section in the deuteron energy range 0.65.. .2.00 MeV indicated the presence of two broad resonances at 1.00 and 1.80 MeV with the shape of single resonances. The elastic scattering cross section at Ed > 4 MeV is also of a resonance character [ 2 , 31. The energy range Ed = 2.0.. a4.0 MeV has not been studied previously. Information on 1 S F levels above 7.5 MeV [4--91 comes almost entirely from resonances in various reactions of deuterons with lSO. The available data in the energy range discussed here, are summarized in Table 1. Table 1 Resonances in 650 480 1150 1800 2060 2340 2420 I l60 +d 100 100 240 & 25 99 f 10 260 & 30 1+ 1+ 20- or If 1+ or 1- 1 (2+ or 3+) 7.94 8.09 8.27 8.40 8.54 9.11 9.34 9.42 9.49 9.69 9.65 1) On leave from Physico-Technical Institute, Kharkov, USSR. 1 Ann. Physik. 7. Folge, Bd. 21 2 Annalen der Physik * 7. Folge * Band 21, Heft 1/2 * 1968 No information was available concerning spins and parities for the levels i n an excitation energy above 9 MeV, except some indications [lo] t h a t the 9.66 MeV level has J n = 2+ or 3+. However, this tentative assignment should be verified. The le0 d reactions a t Ed > 1MeV exhibit broad resonances [4, 10-141 in all outgoing channels suggesting compound nucleus formation. However, the reaction mechanism a t these energies has not been clearly established. The question of a relative contribution of direct processes, also, is of interest. I n the present work we measured the excitation functions and angular distributions of the 160(d,d)160reaction a t bombarding energies of 1.0 to 2.5 MeV, corresponding t o 18Flevels between 8.4 and 9.7 MeV. The observed resonances were analysed in terms of the single-level approximation of the dispersion theory t o provide information on energies, widths, spins and parities of the 18Flevels. 18F with + 2. Experimental Procedure The deuterons were accelerated by the electrostatic generator of the U.A.R. Atomic Energy Establishment. The beam passed through a 90" deflecting magnet and a system of collimating diaphragms and entered the scattering chamber . The deuterons scattered from the target were detected by four semiconductor, ORTEC counters. The detectors were mounted radially with respect t o the target at a 20" spacing. Four charge-sensitive preamplifiers in the scattering chamber amplified the signals which were fed t o the amplifiers and then into four memory subgroups of a transistorized RCL 512-channel pulse height analyser. After passing through the thin target the beam was collected in a FARADAY cup and measured with an A-30-9A current integrator. Thin layers of B e 0 or SiO, on silver backings were used as targets. Some measurements were made with targets prepared by evaporation of both materials. A typical l60target was 15 keV thick for 1 MeV deuterons. The energy spread of the beam has been measured previously t o be less than 2.5 keV. The deuteron spectrum taken a t a 130" detector angle and Ed = 2.5 MeV is shown in Fig. 1.All deuteron groups are well resolved a t 60", however, for the forward angles, the resolution was inadequate. 5K 4K 16 3K 5 2K *1 28 S! 7K 0 720 Channel Number Fig. 1. Deuteron spectrum fobserved at 0 = 130" and Ed = 2.5 MeV F. MACHALIet al. : Energy Levels of l8F from 3 l 6 0 (d, d) l60 To avoid the necessity of accurately stabilizing the geometry and beam current integration, the yield of deuterons from Ag (d,d)Ag was measured a t each bombarding energy. Therefore the scattering from l60could be normalized t o that, from silver, which is a n essentially pure Rutherford scattering below 2.5 MeV. Owing t o this procedure, the errors arising from the finite beam size, target position and detector solid angle were negligible. Statistical errors in the number of counts were also negligible because relatively thick targets were used. The main source of uncertainties is the background subtraction a t backward angles. The systematic errors were checked by measuring the Ag (d, d )Ag cross section a t a number of angles. Fig. 2 shows the results of these measurements at 8 = 150". The combined uncertainties are estimated t o yield a probable error of & 5% in a relative value of the cross section. I Fig. 2. Yield of deuterons from Ag (a,d)Ag divided by the Coulomb scattering cross section I I l,O l,2 I l,rt I I 1,6 t8 2,O Ed(lab),in Mev. I 22 I i Z,+ 3. Experimental Results The yield of elastically scattered deuterons from l60was measured a t eight scattering angles in the incident deuteron energy range 1.0.. a2.5 MeV. Fig. 3 contains the elastic scattering data for all these agnles. The differential cross sections are expressed as fractions of the corresponding differential cross sections for the Rutherford scattering. Cross section measurements were made in 20 keV steps of the bombarding energy. These steps are smaller than widths of resonance observed in previous investigations and are comparable with the experimental energy resolution. The measurements, repeated twice a t several angles t o check the data reproducibility, gave agreement (within errors) with initial values of the cross sections. The anomalies in the cross section (Fig. 3) can be attributed t o two broad resonances at deuteron energies of 1.8 and 2.45 MeV. Our measurements, for the energy region 1.0 -. 2.0 MeV, are in good agreement with previous results of SEILERe t al. [l].Since the peak-to-dip ratio for a 1.OOMeV resonance is small, the precise SEILERdata in the vicinity of this resonance are used in the analysis. The angular distributions of elastically scattered deuterons were measured with one counter in 10" intervals for lab angles between 50" and 150" for Ed = 1.0.. e2.5 MeV in 100 keV steps of bombarding energy. The second counter was placed a t an angle of 150" t o the beam direction and was used as a monitor. The angular distributions are shown in Fig. 4, the ordinates being the ratio of the observed t o the RUTHERFORD cross section. As seen in Fig. 4, the - 1* 4 Annalen der Physik * 7. Folge * Band 21, Heft 1/2 * 1968 angular distributions measured a t 1.1, 1.2, 1.3 and 1.4 MeV energies follow the Rutherford law within the accuracy of the measurements. At higher energies, the shape of the angular distributions changes with energy, and between resonances a t 2.1 MeV it is again close t o the Rutherford distribution. I LA I I I I I I I fl i I Fig. 3. Differential cross section for the elastic scattering of deuterons from la0 as a function of incident deuteron energy for eight scattering angles. The solid lines represent a theoretical fit with parameters taken from Table 2 4. Analysis In the single-level approximation of the dispersion theory, the differential cross section for elastic scattering of charged particles with an arbihary spin i on nuclei with spin I may be written  as: do = [ ( 2 i + 1)( 2 1 + 1 ) I - l ~I f ? (& s,m, 91) l2 dQ (1) 5 F. NACEULI et al.: Energy Levels of l*F from l@O(d,d) l60 where the reaction amplitudes j? are defined as : 1 p ( e ,y ) = - =rj + 1 exp [iq In cosecz cosec2 2 ,[n( 2 I' + 1)]1'2 p ' + 1yl".-"' (13,p) ~ I ~ ' ( l sm rn,pm,! , Is J?ns) m*,l,l x ( l ' s o m , 1 1's Jm,) (eZia2611, - S$ e--2i0n). mVJ2; 0 . Z5MeV - . . /r: ZOMeV 2,IMeV L . ..-.- 20 10 10 Fig. 4. Angular distribution for the 160(d,d)le0. The solid lines are theoretical fits calculated with resonance parameters listed in Table 2 m 9yl 110 130 1% e(C MI, 1 70 110 130 150 DEGREES The matrix elements S$ are related t o single resonance level parameters by the following expression : where the resonance phase shift PJ" = tg-l[- 1 r(E, - J, E) t,he RUTHERFORD phase shift 2 CdL = 2 tg-l(q/s); a0 = 0; s=1 the hard-sphere phase shift: y L= - tgg1(P,/G,). The resonance energy E , is related t o the characteristic energy El by E , = E A A,; A A is the level shift, and rct the total and partial level widths, respectively, P, and G, Coulomb regular and irregular functions, respectively; x? the spin functions; s and s' the channel spins in the incoming mu and outgoing channels ;the deuteron wave vector k = , m the reduced mass, fi + r, r, Annalcn der Physik 6 * 7. Folge * Band PI, Heft 1/2 * 1968 v the relative velocity, PT(8,y ) are the normalized spherical harmonics and rj e2Z,Z,/tiv. At bombarding energies below 2.5 MeV, the elastic scattering competes with the following reactions : = Since many particle channels are open and their widths are not negligible, the resonant amplitude of elastic scattering decreases by a factor TJT.Previous investigations of these reactions above Ed = 1.0 MeV show a broad anomalous region, where the individual states are not completely resolved. When the present work was undertaken, there was no conclusive assignment of either the number of states in this region, or widths, spin and parity of these states. Therefore, the values of T,/r were not known and need to be determined. I n deuteron elastic scattering on l60, the spins of incoming and outgoing channels are s = s' = 1, and there are two values of the orbital momentum 1 corresponding t o a given value of the total momentum and parity J". However, it is usually enough to consider only the least possbile value of the orbital momentum. The known WIGNERsum rule  was used to restrict the number of possible orbital momenta for each resonance. Tentative values of the total widt,hs 'I and resonance energies E , were used in these calculations. It was found that 1 5 2 for all three analysed resonances, therefore, only spin values of the compound nucleus levels J = 0, 1, 2 and 3 were considered. I n the elastic scattering, the shape of the resonance curves for single resonances differs essentially for different 1 and changes little with the incident particle energy. Therefore, in most cases even a qualitative comparison of the calculated and experimental curves is sufficient t o determine the effective orbital moment u m value. From this point of view it seems preferable t o begin the experimental data analysis with a consideration of the excitation functions. The calculated resonance shapes in the l6O (d,d)I60reaction are shown in Fig. 5 for the three c.m. angles 87", 131" and 153.3' at E , = 1.80MeV and T = = 200 keV for the states with different values of the orbital momentum 1 and spin J . Calculations were performed making the following assumptions : 1.the resonance is isolated, 2. only the least value of the orbital moment u m 1 gives a contribution, 3. only the elastic scattering channel is open, i.e. rd Fig. 5. Theoretical isolated resonance curves for the elastic scattering of deuterons bv l60. The resonance enerav is taken to"be 1.8 MeV and the widTh 200 keV F. XACHALI et al. : Energy Levels of l8F from 7 l60(d,d) l60 r, = I'. Since the resonance shape depends only slightly on r,/rit was also assumed that r and rdare independent of energy. I n these and subsequent calculations, we use the interaction radius a = 4.54 fm. The potential phases y z were calculated using the tables of BLOCH et al. [IS]. A remarkable feature of the resonance shapes of Fig. 6 is the dip in the cross section a t 87" for the even 1 resonances, and the peak superimposed on a smooth background for the odd 1 resonances. The deuteron brbital momentum 1 and, consequently, the parity of the l*P states, responsible for the three observed resonances, can be directly inferred from a comparison of the resonance shapes (Fig. 3) with the single level shapes (Fig. 5). Since the experimental curves have the dip for all three resonances, then only even values contribute. The shape of each anomaly for 125" and 150" is consistent with formation of a 1.00MeV resonance (Fig. 6) by I = 0 deuterons, and 1.80 and 2.45 MeV resonance by 1 = 2 deuterons. While a check on the 1 values and parity of the states can reasonably be made from the shape of the resonances, the data must be further examined t o obtain values for the resonance energies, total and partial widths and spins. R e s o n a n c e a t Ed = 1.00 MeV: The analysis of this resonance is particularly simple, as in this case the non-resonance cross section is practically equal t o the Coulomb cross section and only one spin value J" = 1+is possible since the resonance is due t o the s-wave. The detailed calculations for this resonance were performed for the c.m. angles go", 125.26" and 140.8'. As a first approximation t o the fit, a resonance energy and total width were taken from previous investigations, (Table 1). The calculations then proceeded in two steps. The value of was varied t o obtain experimental values of the dip-to-peak ratio for every angle. The next step consisted of fitting the c/oRvalues t o the experimental ones. The resonance energy and total width were varied until the best agreement with experimental data was reached. Fig. 6 shows the results of the cross section fit in the vicinity of the 1.00 MeV resonance. The calculated curve was obtained by using the resonance level parameters listed in TabJe 2. The experimental data are seen t o agree well with the assumption that 1 = 0 and J" = l+.The penetrability calculations whow that the contribution from the state with 1 = 2 may be neglected a t these energies. rd/r Table 2 Resonance level p a r a m e t e r s r E;, (MeV) 1.00 & 0.03 1.80 0.03 2.45* 0.03 1 90 & 20 200 30 120 & 30 -+. I 12 & 3 88 & 1 2 75 15 11 1 0.13 1.10 0.23 1 ::?: I2I 0.07 0 '1 1 1:6 8.40 R e s o n a n c e a t Ed = 1.80 MeV. As mentioned above, the preliminary analysis shows t h a t this resonance is due t o d-wave, i.e. the spin of the corresponding l*F level may be 1, 2 or 3. The shape of single resonance for these three cases is practically the same (Fig. 5) if one takes into account t h a t in a general case, I',/I' 1. Therefore, it is impossible t o determine unambiguously the spin value without detailed calculations for each individual case. + 8 Annalen der Physik * 7. Folge * Band 21, Heft l j 2 * 1968 I n the analysis, the contribution from the 2.45 MeV resonance was neglected, since its resonance phase is negligible a t Ed = 1.8 MeV (Fig. 7). It can be seen in Fig. 3 that the elastic scattering cross section displays some weak anomalies which probably can be associated with earlier observed resonances in (d, p ) and ( d , a ) reactions . However, in the elastic scattering, these resonances are weak and do not much distort the shape of the resonances under consideration. 300 0 - - 725,26O 49 1,o 1,l Ed (Lab) Mev Fig. 6. Differential cross sections for the elastic scattering in the 1 MeV region plotted as afunction of incident deuteron energy for the centre-of-mass scattering angles of go", 125.26' and 140.8". The dots represent the experimental points [l] and the solid curves the cross sections obtained for the 1+assignment. The parameters used in the calculations are listed in Table 2 Fig.. 7. Resonance phase shifts for the Ed"= 1.80 and 2.4dMeV resonances in the reaction IfiO(d,d)l60 The analysis then proceeded in a manner similar t o that described for the resonance at 1.OOMeV. Initially the data a t &., = 135.5" were fitted by varying the value. After having determined the resonance energy and width were varied until the best f i t was obtained for the excitation functions a t &,. = 116.5', 135.5' and 153.5'. I n these calculations it was necessary t o assume values for the non-resonant phase shifts. Initially we used the s-kave phase shift value based on the hard sphere model. Other non-resonant phase r,/r rdjr F. MACHALIe t al.: Energy Levels of ?E' from '60(d,d)lsO 0 shifts are negligible at these energies. It was found t h a t with these non-resonant phases, the data could be reasonably fitted only a t &,,. = 153.5", but for other angles a large disagreement was found for all possible assignments. Fig. 8 8 shows results of these calculations. The disagreement observed suggests that the chosen s-wave phase shift is not correct. Accordingly, the s-wave phase was ' Fip.. 8. Differential cross section for elastic scattering of deuteronsfromIsO i n the vicinity of the 1.80 MeV resonance a t fIc.m. = 116.5', 135.5" and 153.5'. The solid lines represent theoretical fits for J" = If. 2+ and 3+: curves A are calculated with t h e hard sphere phase shift; curves B with t h e reduced potential phase shift , I -& b c J 1,o Ed (fdb) / f l MeV adjusted t o provide a better fit. It was found that a reduction of the magnitude of the s-wave shift by 7" makes a considerable improvement (Fig. 8B). The reduction of the potential phase is not difficult t o explain, since many reaction channels with large cross sections are open. The assignment J n = 3+ is seen t o fit reasonably well a t the three angles considered. We failed t o get satisfactory agreement with the experimental data for other spin values. The final theoretical fit obtained with J n = 3+, ' I = 200 keV, = 0.44 and E , = 1.80 MeV is shown together with the experimental results in Fig. 3. R e s o n a n c e a t Ed = 2.45MeV: The cross section in the picinity of this resonance was measured only u p t o 2.5 MeV and resonances in leO(d,d)160a t higher energies are not known. Therefore it was assumed that the data of the 2.5 MeV region could be explained in terms of a single resonance. There was, of course, no way of knowing that only one state is involved, but it was natural t o consider a simplier possibility first. The interference dip observed a t &,,,. = 87" suggests that the resonance involves I = 0 or 2 formation. The possibility of s-wave formation can be ruled out on the basis of the peak observed a t backward angles. All possible values of J were tried for 8c.m.= 116.5", 135.5' and 153.5". From the observed maximum and minimum cross section the possibility of the assignments 1+or 3+ can be excluded. The values of E , and I' were then adjusted t o yield the best fit t o the measured cross section. The curves presented in Fig. 9 show the fit obtained. I'Jr 10 Annalen der Physilr * 7. Folge * Band 21, Heft l j 2 * 1968 The final fit of the 160(d,d ) l60elastic scattering data for eight scattering angles is shown in Fig. 3. The parameters used in these calculations are summarized in Table 2. To calculate the cross section in the Ed = 2.0... 2.3 MeV region, the effect of two resonances was considered. The overall agreement with experimental data is quite satisfactory. 22 Z4 2,6 2,d Ed (lab), in MeV Fig. 9. Differential cross section for the elastic scattering of deuterons from l60i n the vicinity of the 2.45 MeV resonance a t 9c.m. = 116.5', 135.5" and 153.5'. The solid lines correspond to theoretical fits obtained for J n = 1+,2f and 3" A n g u l a r d i s t r i b u t i o n a n a l y s i s : The analysis of the angular distribution of elastically scattered deuterons may provide a good test of the correctness of the level assignments made above. Calculations were performed ma,king the same assumptions as in the excitation function analysis and with the parameters listed in Table 2. The f i t obtained is shown in Fig. 4. The observed agreement, of the theoretical and experimental distributions confirms the correctness of the excitation function analysis and the spin assignments for the 18Flevels. Conclusions The information obtained from the analysis of the l6O(d, d ) l 6 0 elastic scattering data is summarized in Table 2. The assignments of the orbital angular momentum and parity for the resonance levels of lSF are quite unambiguous. The spin assignment for the 8.40 MeV level (1.00 MeV resonance) is unique, since the resonance is due t o the s-wave. It confirms the previous assignments  J" = 1+and 1- for the levels a t 8.40 and 8.54 MeV respectively, and rules out the assignments J n = 0- and I+. The present elastic scattering data are consistent with J n = 3+ and J7 = 2+ assignments for the 9.11 and 9.69MeV levels, respectively. However, it was felt that the evidence is insufficient t o exclude completely other possible assignments. The main reasons are: 1. partial widths are assentially energy dependent, 2. the cross section a6 a higher energy is not known. More data on the reaction cross section are neces- I?. MACHALIet al.: Energy Levels of I*Ffrom 160(d,d)160 11 sary t o draw a final conclusion about spin assignment for these two levels. Since the isotopic spin T = 0 for both the deuterons and l60ground state it is probable that the three observed levels in 18F are T = 0 states. The reduced widths 6%for elastic scattering are given in units of the WIGNER single-particle limit 3fi2 --. The reduced elastic width for the 9.11 MeV level 2 ma represents a n appreciable fraction of the single particle limit and therefore this level may be interpreted by the cluster model as two particle excitation of a system consisting of l60in the ground state plus deuteron. One should note that this configuration is realized with an appreciable probability a t rather high excitation energies. Levels with large deuteron widths were also abserved by KASHYet al. , who studied 14Nlevels in the elastic scattering of deuteron by 12C nuclei. The authors wish t o thank Professor M. EL-NADI for his encouragement and interest in this investigation. The authors are greatly indebted t o Dr. A. A KRESNIN for valuable discussions. References [l] SEJLER, R. F., C. H. JONES,W. J. ANZIGK,D. F. KERRINGand K. W. $OX%. Nuclear Physics 45 (1965) 647.  BAUMGARTNER, E., and K. W. FULBRIGHT, Physic. 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Physique Radium 16 (1955) 241. 1141 ROCLAWSKI-COAJBAND, N., and R. COTTON,Nuclear Physics 1 (1956) 603. M. A., A. T. BARANIK,M. I. EL-ZEIKI,V. Y. GONTCHAR, S. M. MORSY and  ABUZEID, I. I. ZALOUBOVSRY,Nucl. Instr. 30 (1964) 151.  KASHY,E., R. R. PERRYand J. R. RISSER,Physic. Rev. 117 (1960) 1289. 1171 TEICRMANN, T., and E. P. WIUNER,Physic. Rev. 87 (1952) 123. El81 BLOCH, J., M. H. HULL, A. A. BROPLES, W. 0. BOURICIUS,B. E. FREEMATand G. BREIT,Rev. mod. Physics 23 (1951) 347. C a i r o / Egypt (UAR), Atomic Energy Establishment. Bei der Redaktion eingegangen am 6. Juni 1967.