Annalen der Physik. 7. Folge, Band 28, Heft 4,1973, S. 315-320 J. A. Barth, Leipzig Anomalies in Elastic Scattering at Isobaric Analogue States By S. A. EL-KAZZAZ, M. ABDELHARITH and L. M. EL-NADI With 4 Figures Abstract Excitation functions for proton elastic scattering on MnSs at proton energies from 1320 KeV to 1480 KeV have been measured at the angles 135' and 160".Anomalies in the differential elastic scattering were observed a t E,, = 1350 f 4 KeV, 1385 f 4 KeV and 1445 & 4 KeV respectively. These resonance states are the isobaric analogues of the ground, first excited and second excited states in MnS6respectively. Analysis of the results showed that these resonance states are best fitted to a J" = 3+, 2+ and 1+which is in excellent agreement with the J" values of the corresponding states in Mns6. The total widths and proton widths of these states were determined. 1. Introduction Proton elastic scattering experiments have proved to be powerful tools for the determination of spin and panty of nuclear energy levels, since it permits the determination of the orbital angular momentum of the captured proton. This is due to the fact that the shape of the excitation function near a resonance level is completely characterized by the orbital angular momentum of the captured proton. I n the present paper, proton elastic scattering on Mn55 was studied in the energy range from 1320 KeV to 1480 KeV. The excitation function of the reaction Mnm (p, y ) Fes* in the same energy range [ l ] showed resonance states which are the isobaric analogues of the low lying states of MnMwhose spins are known from atomic beam experiments , (n, y ) reaction studies [3, 41, study of the t9 decay of C Y 6  and (p, y ) studies on Mnm . 2. Experimental Procedure The 2.5 MeV VAN DE GRAAFFgenerator of the A.R. E. Atomic Energy Establishment provides the beam of protons. The energy resolution in the proton beam was better than 1 KeV. The targets used are of the self supported type prepared by vacuum evaporation of metallic Mnm. The target thickness was about 35 pg/cma. The elastic scattering measurements were carried out in a special scattering chamber [i']. The beam entrance slit was 3 m m in diameter. The scattered protons were detected using three Silicon surface-barrier solid state detectors placed at go", 135" and 150" to the beam direction. I n front of the detectors 316 Annalen der Physik * 7. Folge * Band 28, Heft 4 * 1973 the scattered particles were collimated with a 20 mm long, 5 mm diameter copper collimator with its face 80 mm from the target. A diaphragm of 3 mm diameter was placed just before each detector. The angles used were chosen according to the detector dimensions and the present experimental geometry. Pulses from the detectors were first preamplified, then amplified using an ORTEC type low noise linear amplifiers and the resulting voltage pulses were analysed using two 512 multichannel analysers. The elastic spectra obtained showed proton groups elastically scattered from the target under investigation and weak groups due to carbon and oxygen. These proton groups are well resolved a t angles greater than 90'. For this reason, the experimental results were analysed a t the angles 135' and 150" only. I n measuring the excitation function of the reaction, Mns(p, p) Mn&, the energy of the accelerated protons was varied in steps of 2.5 KeV from 1320 KeV to 1480 KeV. In each step, the data were taken per 6 micro-coulombs of charge at a target current of about 0.15 pA producing small statistical uncertainties in the proton yield. The excitation function was measured two times to test the reproducibility of results. 3. Results and Discussion The excitation function of the reaction Mn&(p,p ) Mns is shown in Fig. 1. In this excitation function deviations from coulomb scattering were observed a t proton energies 1350 & 4 KeV, 1385 f 4 KeV and 1445 4 KeV. These resonance states are the isobaric analogues of the ground, first excited and second excited states of Mnm. The resonance states observed in the elastic x10 3 50 48 -5 44 - 42 46 n 0 L 2 40 = 38 E a 36 34 32 r - t .. 4 I 1.325 1.375 1.125 P r o t o n Energy (MeV) 1.475 Fig. 1. MnS6 proton elastic scattering data at two angles exhibiting analogue resonances. Arrows indicate resonances that have been analysed 317 EL-KAZZAZ, ABDELHARITH and EL-NADI:Anomalies in Elastic Scattering Table 1 Stgef6in I E ~ (xF e T MeV MeV 0.000 11.471 f 0.074 11.497 f 0.074 11.582 f 0.074 0.02F 0.111 i (P,P) 1 En exp. MeV ( E expMeV 1.350 f 0.004 1.385 f 0.004 1.446 f 0.004 I ~ I 1.303 1.330 1.415 47 55 30 i scattering work are in fair agreement with those observed from the reaction Mn=(p, y ) FeS6in the same energy range [l]. The energy of the isobaric analogue states was calculated on the basis of the universal coulomb displacement energy formula  : d E c = (1.444f 0.005) (z/A1/5)- (1.13 & 0.04) MeV = 8.553 f 0.074 MeV The energy of the first isobaric analogue state in FeS8 corresponding to the ground state of MnS6 is = AEc AB, where AB is the difference in binding energies between Fe6B and MnM . Knowing that the Q-value of the reaction Mn=(p, y ) Fe6B is = 10.1915 f 0.0048 MeV, one can deduce the expected Ep values for the resonance states mentioned before. Table 1, shows the results of such calculations. + 0.66 0.64 0.62 a L m L ” .0 -a L Q 5 0 0.56 0.54 0 0.52 0 .50 Fig.2. &f.nu profon elastic scattering d&t8 8nd the best fit for the resonance state at &d r=-7-KeV. [Sblh line f& 1 =3, daahed line for l ( 2 = 1) 2.4(1 = 3)] + 1 . 1 . 1 . 1 . 1 . 1 Proton Energy ( M r V ) . 1 318 Annalen der Physik 0'50 0.48 1t 1.355 * 7. Folge * Band 28, Heft 4 * 1973 f 1.375 1.415 1.395 P r o t o n Energy (MeV) Fig. 3. MnS6proton elastic scatteringdata and the best fit for the resonance state at Em= 1385 f 4 KeV, Z? = 3, r, = 4 f 0.4 KeVknd line for 1 ( I 1) + 1.6 ( I = 3)] Theoretical differential elastic scattering cross section [lo] for each of the above resonances for different spin assignments was calculated using the formula : do do do do = m ) c o u l o m b + m)resonance + m llnt e f i e r e nc e and applying the R-matrix theory [Ill. I n this case the interference term is given by  : x Re [iT;&C(O)] Pl(cos 0). In the present case, the potential scattering was expected to be very small since the resonance states observed are below the coulomb barrier, also all the nuclear phase shifts were taken to be zero since they are not expected to alter the size of the resonance parameters [lo]. The differential elastic scattering cross-section has been programmed for the 1 ICL - 1905 E Computer for the special case of spin particles scattered from for two angles a t a time and for pure inlet channel spin. Mnu ground state The cross section -for all possible J n values with different and (taking F, and rflfrom Ref. [l],where = I', rfl) was calculated with chosen r r, + + r, r 319 EL-KAZZAZ, ABDELHARITHand EL-NADI:Anomalies in Elastic Scattering Mn55 (p,p, 0.58 0.56 --,, .-c 0.54 0.52 a a L a L .m -; 0 . 4 8 - 0.46 0 0.44 .$ b Fig. 4. Mns5proton elastic scattering data and the best fit for the resonance state a t E, = 1445% 4KeV,Z, = 1,1'n=3f0.2KeV;nd r = 15 KeV l . l , I 1.415 . l , 1.435 I , I 1.455 . I 1.475 P r o t o n Energy (MeV) 1 values. The experimental results were compared with the calculated cross sections and the best fitted data are then adopted. Analysis of experimental results showed t h a t the above mentioned resonance states in the reaction Mne(p, p ) MnS6a t proton energies of 1350 f 4 KeV, 1385 f 4 KeV and 1445 f 4 KeV are best fitted t o 3+, 2f and I+ states with lp values 1, 3 and 1respectively. Figures 2, 3 and 4 show the result of the fitting of the experimental data t o the theoretical calculations. Table 2 summarizes the nuclear parameters, obtained from such fitting, for each of the resonance states mentioned. From Table 1 the observed coulomb energy shifts differ about 20-50 KeV from the calculated ones, indicating that the coulomb displacement equation Table 2 Elastic scattering parameters for Fe68 levels and comparison t o MnS6levels E,, lab KeV 1I MuS6 P) (a9 Eex.(FeS6) MeV ~ 2 V IGV 1 f 0.2 1385 f 4 11.497 & 0.074 4 f 0.4 9 " 1445 f 4 11592 f 0.074 3 & 0.2 15 I 3 2 1 0.026 + 1+ I (Mns6) MeV Eex. 0.000 11.471 f 0.074 1350 f 4 1 I Mus5 (4P) [I31 Jn ~ 0.111 I In l ( 1 = 1) + 2.4 (1 = 3) + 1 ( I = 1) 1.6 ( I = 3) 1 320 Annalen der Physik * 7. Folge * Band 28, Heft 4 * 1973 could be adopted successfully for nuclei in the f;/z shell. As clear from Table 2 and Figures 2, 3 and 4, the proposed spin and parity assignments are in good agreement with the corresponding M n s states. The experimental data for the three states are fitted through pure 1 values, although in Mn=(d, p) reactions  mixing of I was observed for the first two states. From the present results, one may conclude that elastic scattering of protons through nuclear isobaric analogue regions can be a powerful means of measuring the properties of the nuclear levels, and the “R-matrix Theory” fits the elastic scattering data successfully. The authors would like to thank Prof. M.EL-NADI, for his interest and encouragement during this work. The help of Dr. M.SIMBELin Computer programming is greatly acknowledged. The authors are also greatful t o the A. R. E. Atomic Energy Authorities for allowing them t o carry out the present work in their laboratories, and would like t o thank the VAN DE GRAAFF group for the efficient operation of the machine. References [l] OTTO,G., R.MEHNERT and G.TOMASELLI, Nuclear Phys. A 109 (1968) 118.  CHILDS,W.J., L.S.GOODMAN and L.J.KIEFFER, Phys. Rev. 122 (1961) 891.  D’ANQELO,N., Phys. Rev. 117 (1960) 510.  ESTULIN,I.V., A.S.MELIORANSEY. and L.F.KALINEIN, Nuclear Phys. 24 (1961) 118. B.J., A. W.SCHARDT and T.T.SHULL,Nuclear Phys. 16 (1960) 357.  DROPESEY, [S] SAKAI,M., R.BERTINIand C.GEHRINQER, JAERI-1184 (1969).  SALEH,Z.A., Thesis, Atomic Energy Establishment, A.R.E. (1970). [a] ANDERSON, J.D., C.Woaa and J.W.MCCLURE,Phys. Rev. 188 (1965) B 615.  MATTAUCH,J.H.E., W.THIELE and A.H.WAPSTRA,Nuclear Phys. 67 (1965) 1. [lo] MOORE,C.F., P.RICHARD,C.E.WATSON,D.ROBSONand J.D.Fox, Phys. Rev. 141 (1966) 1166. [ll] LANE,A.M., and R.G.THoMAs,Rev. mod. Phys. 80 (1958) 257.  Fox, J.D., Private Communications (1971).  COMFORT,J.R., Phys. Rev. 177, no. 4 (1969) 1673. G i z a , Cairo University, Department of Physics, Facult,y of Science Atab Republic of Egypt. Bei der Redaktion eingegangen am 24.November 1971. Anschr. d. Verf.: Dr. S.A.EL-KAZZAZ, Dr. M . ~ D E L HABITH und Dr. L.M.EL-NADI Department of Physics, Faculty of Science, Cairo University Giza/Arab Republic of Egypt.