. . .. M 1 6 IIV 1 . ebsite D'adi. T. 12 . ' ..1..- . W 1 1 OF ORNL P 2570 . ä : . 1 . 1 . " .. . . d . . S * .in .in 1 ._ . 2. 1 ... is i i 1 : • " . " VUL LE 11:25 11.4 11.6 1:. : . :.. • MICROCOPY RESOLUTION TEST CHART NATIONAL BUREAU OF STANDARDS -1963 • į Kainvited paper to be presented at the International Cc:ference on Nuclear Physics, pr Gatlinburg, Tennessee, September 12-17, 1965) 20570 ON0V. 2 de Conf-660906-43 59 NOV 2 9 1366 Session 1 11.C. $ 2.00, N The Optical: Model and Inelastic Scattering * G. R. Satchler Oak Ridge National Laboratory Celk Ridge, Tennessee RELEASED FOR ANNOUNCEMENT IN NUCLEAR SCIENCE ABSTRACTS 1. The optical model There are many topics of interest which could be discussed under this title, but time and space limitations will enable me only to give the briefest review of a number of features that I personally find especially interesting. First, let me borrow some comments from Dr. Schiffert) on the dis- tribution of data which is available as a function of mass and energy. The point I wish to make is that there has been strong emphasis on measurements with certain target nuclei, like C, Ni, Sn and Pb with large gaps in between. There have usually been good experimental reasons for this, but now thai, for example, better resolution is available it is . important to look into some of these gaps, such as the rare earth nuclei and the very heavy nuclei. The emphasis on Sn and Pb for elastic measure- ments is particularly unfortunate because of the closed-shell charac- teristics of these nuclei. It may turn out that these do not affect the optical model potential, but the possibility should be checked. Ofteri, for example, an estimate of the synmetry term in the nucleon potential ... Research sponsored by the U.S. Atomic Energy Commission under contract with Union Carbide Corporation. LEGAL NOTICE This report was prepared as an account of Government sponsored wor':. Neither the United States, nor the Commission, nor any person acting on behalf of the Commission: A. Makes any warranty or representation, expressed or implied, with respect to the accu- racy, completeness, or usefulness of the information contained in this report, or that the use of any information, apparatus, method, or process disclosed in this report may not infringe privately owned rights; or B. Assumes any liabilities with respeet to the use of, or for damages resulting from the use of any information, apparatus, method, or procese disclosed in As used in the above, "person acting on behalt of the Commission" includes any ea.. ployee or contractor of the Commission, or employee of such contractor, to the extent that guch employee or contractor of the Commission, or employee of such contractor prepares, disseminates, or provides access to, any information pursuant to his employment or contract with the Commission, or his employment with such contractor. .. . depends strongly on the results for these two nuclei. · The discreteness of the spectrum of data with respect to energy is also unfortunate, especially above 40 or 50 MeV where there is a big gap (with small peaks around 150 and 180 MeV for protons). At nigh energies it is much easier to obtain some understanding of elastic and inelastic scattering in terms of the basic nucleon-nucleon interactions. Having data available at intermediate energies would help us to see how this interpretation has to be modified as one goes to progressively lower energies and more complicated many-body erfects come into play. Hopefully the new machines will help fill this energy gap. Turning now to the "experimental" situation, so to speak, on optical model analyses of elastic scattering, there has been steady progress since the last major international conference). The extensive cross section and polarisation data for 30 MeV protons has been re-analysed') and the new 40 MeV data is being studied*), for example. Figure 1 shows best fits to the 30 MeV proton cross sections obtained by adjusting all the parameters, while fig. 2 shows the results for two average potentials with fixed parameters). Extensive measurements of 'He scattering have been analysed”), and triton data is now becoming available for study also°). The analysis of deuteron scattering has been extended to higher energy?), and more work has been done on alpha scattering). Rather than attempting to review all this work, let me point out what I regard as a few highlights. In the nucleon optical potential, clear evidence has been found that the spin-orbit coupling is located somewhat inside the real part of the central potentia13,4,9). That is to say, if we take a Thomas form for the spin-orbit term, the polarisation measurements demand that WA , the radius, or diffuseness, or both are smaller than those for the central potential. This has been interpreteći as being due to the shorter range of the nucleon-nucleon spin-orbit interaction. For example, fig. 2 shows some results of fitting cross-sections and polarisations simultaneously. Fits with the spin-orbit parameters constrained to the same values es these for the real central well show discrepancies at the forward angles; these are only removed by moving the spin-orbit coupling in slightly. There is also evidence that the symmetry term proportioned to t-T/A in the nucleon potential is complex). A comparison of neutron and proton scattering data shows it to be compatible with a surface absorption proportional to (t.T/A) (and so of opposite sign for neutrons and protons). Figure 3, for example, shows the neutron total and non-elastic cross sections predicted by one of the average 30 MeV proton potentials. Too large values are predicted by using the same surface absorption w.* for neutrons and protons, while good agreement is obtained by correlating the W, values with a (t•T/A) dependence so that neutrons experience a weaker surface absorption than protons. The optical model interpretation of (p,n) transitions between analog states had previously suggested that the real part of the symmetry term was also peaked at the nuclear surfaced.). Further, the difference be- tween the mean square radius of the potential and that of the charge distribution appears to increase with increasing neutron excess”). It is possible these various facts are evidence that the neutron distri- bution extends to larger radii than the proton distribution; that 18, nuclei have a neutron-rich surface layer. The symmetry term in the optical potential is associated with another important subject, that of the excitation and de-excitation of analog states in the compound nucleus. These processes have been interpreted successfully within the same model, the t.I term providing & coupling between a proton continuum state and a neutron bound state'). They will be discussed in Session II, however. There is not much that 18 dramatically new to report on the optical potentials for complex particles. There is now evidence that the po- tentials for mass-3 particles also have a complex symmetry term, both from the he,t) transition between analog states) and from direct comparison of "He and t potentials14). Analysis of deuteron scattering at 26 MeV implles that a potential with a real part of about 100 MeV or deeper is required, and shows a definite improvement in fits when a spin- orbit tern 18 Included]). It is also worth commenting on the large radii found for the imagi- · nary potentials for deuterons and Phe or tritons. It has been clained these are unphysical and unnecessary, but in fact they arise from the ease with which these particles undergo stripping. DWBA studies made by Ferey”) in which he sums over all the (d,p) and (a,n) transitions to bound :states agree with activation measurements and show that first, order stripping theory accounts for essentially all the reaction cross section for deuterons of low energies ( 8 MeV, say), while it is still as much as 30% of it at, say, 15 MeV. By studying the stripping ampli- tudes one can get an idea of the spatial localisation of this important part of the absorption; it occurs at quite large radii; between one and two times the nuclear radius. As the available energy increases, strip- ping into the continuum and other processes become more important and simple estimates are more difficult to obtain. However, one would ex- pect the region of absorption to move in closer to the nuclear surface, and this is what is found. There 18 still controversy over the physical eignificance of the optical potentials for complex projectiles. Are they merely devices for generating phase shifts, or do the associated wavefunctions have sig- nificance within the nucleus also? The question has importance when, for example, the wavefunctions are used in LWBA calculations of reactions. Some people maintain that a significant first approximation to the real part of the optical potential is simply the sum of the potentials for each constituent nucleon, averaged over the internal motion of the pro- jectile. It correct, this allows us to restrict attention to one of two among the war.y classes of potentiels which can be found to fit the data. dowever, even if this gives a fair account of that part of the wave. function in which the projectile is not excited or disassociated, this · is only a small part inside the nucleus and the contributions to a reaction from the other parts may be just as important. This is a diffi- cult problem, but nonetheless it warrants more theoretical study. Some attempts have been made to find better wavefunctions for reaction calcu- lations19). . . . . . . . .. . : Finally, a comment on the effects of non-locality of the optical : potentials. Any theory assures us they are non-local and that at least part of the energy dependence of the local model potentials is due to this. It has been found that the wavefunction for a non-local potentiel is reduced in amplitude inside the nucleus compared to the wavefunction for an equivalent local potential which gives the same scattering?'). This reduction can be found to a good approximation from a 'simple cor- rection factor?) which may be incorporated into DWBA reaction calcu- lations19). - 1 + 1 . M I 6- Inelastic scattering The most interesting studies in this field are the attenpts to understand the relationship between simple macroscopic models and a more microscopic description of the interaction in terms of the motions of Individual target nucleons. The macroscopic models are based upon the collective model, either through a non-spherical generalisation of the optical potential, or a similar generalisation of diffraction theory. Underlying these mudels is the concept o.? a very simple relationship between elastic and inelastic scattering (at least for the stronger inelastic transitions) 20). let us speak in terms of the non-spherical optical potential. A first order treatment (DWBA) of the non-spherical part 3.s usually adequate; then we have a theory with only one free parameter, the strength or de- formation parameter B for each multipole. The other parameters are de- termined by analysis of elastic scattering. The angular distribution 18 then completely determined, while the cross section magnitude is proportional to 82. This simple model has had remarkable success in reproducing inelastic measurements for a variety of projectiles, even for some of the weaker transitions one would not normally regard as col- lective in any sense). The values of ß obtained are in good agreement with those obtained independently from Coulomb excitation measurements (provided we make both the real and imaginary parts of the potential non-spherical). We might be tempted to conclude from this that the interaction implied by the model really has physical significance. The important thing about this interaction 18. its radial shape; it is proportional to the radial derivative of the central potential and hence is peaked at the nuclear surface. What does the microscopic theory predict? In its present form, this theory assumes a simple static interaction between the projectile and each target nucleon. Even though we know this is a gross simplification, it is similar to the procedure adopted for bound state structure calculations. In addition, exchange terms of the knock- on type are usual.ly neglected. When this interaction is averaged over the motions of the target nucleons we obtain a form factor dependent on the coordinates of the projectile which is directly comparable to the collective model interaction. Firet, however, the basic assumptions should be checked by com- paring with experiment for some nuclei whose wavefunctions we believe we know, and the parameters of the effective interaction determined. For example, in nucleon-inelastic scattering we assume a simpla Gaussian · or Yukawa for the nucleon-nucleon interaction, just as in the shell model. A study of the gozr(p,p') reaction at 18.8 Meval) showed that a Yukawa of range about 1 fm and strength about 200 Mey was required. Other studies in this region and in the 117/2 shell, comparing proton- proton and proton-neutron interactions, showed the iso-spin dependence. was weak; examples are shown in fig. 5. There are indications the ordi- nary spin dependence is also weak. These results are very encouraging; unfortunɛtely there is some evidence that they may be somewhat fortuitous. When applied to proton scatte 'ing from Pb, roughly twice the strength is required, and the interaction is not very successful in describing data at other energies or in explaining inelastic polarisation measure- ments. It is very likely that the interaction should be complex (as it is at high energies when the impulse approximation may be used), and it 13 possible that it is enhanced when the interacting pair are close to 1. . * -8. the nuclear surface. It is also possible that the neglected exchange effects are not so negligible. Attempts are being made to investigate these possibilities. If we ignore these difficulties, we can now compare the microscopic form factors obtained with a simple interaction to those given by the collective model. For so-called collective states we may use modern wavefunctions such as hole-particle mixtures with RPA, Figure 6 shows a form factor for the lowest 27 state in 6°Ni; the left side illustrates 60 the phase coherence which gives the collective enhancement, while the right side compares it to the real part of the collective model inter- action). At first sight there is considerable agreement between the two form factors. However, the microscopic form is broader and generally peaks at a somewhat smaller radius. These differences are significant, especially for strongly absorbed particles like alphas. Indeed, to dete the only successful alpha-nucleon effective interaction has a repulsive core; fig. 7 shows two examples of fits to data using it"?). Even then there remain some discrepancies in the angular distributions. : . At high enough energies we may use the impulse approximation; that.. is, the effective interaction operator becomes the scattering amplitude for free projectile-nucleon scattering, which can be determined inde- pendently. For nucleons this is applicable above about 100 MeV. An example is shown in fig. 8 which 11lustrates the use of inelastic scat- tering to check model wavefunctions for the nucleus; in principle there are no free parameters in these calculations-4). Unfortunately at present data are very sparse in this energy region compared to lower energies, and often they are reduced in value because of poor resolution. In summary, microscopic analysis of inelastic scattering promises + 7 -9- · to be a powerful spectroscopic tool for checking nuclear wavefunctions. Already we have a qualitative understanding of the origin of collective enhancements. However, it is also clear that more work is needed in crder to understand the reaction mechanism in detail, especially the effective interaction between projectile and target nucleons. Witam! R1- . References 1. J. P. Schirfer, Proc. of Summer Study Group, Brookhaven National Laboratory Report BNL.948 (1965). 2. P. E. Hodgson, Proc. Paris Congress on Nuclear Physics (Paris, 1964). 3. G. W. Greeniees and G. J. Pyle, to be published; G. R. Satchler, to be published in Nuclear Physics. 4. L. N. Blumberg et al., Phys. Rev. 147, 812 (1966); R. H. Bassel, i private communication. 5. R. H. Bassel et al., to be published. 6. R. N. Glover and A. D. W. Jones, Nuclear Phys. 81, 268 (1966); R. H. Bassel and R. M. Drisko, to be published. 7. C. M. Perey and F. G. Perey, to be published. 8. For example, B. T. Lucas et al., Phys. Rev. 144, 972 (1966); L. McFadden and G. R. Satchler, to be published in Nuclear Physics. 9. Other references are given in refs. 3 and 4. 10. G. R. Satchler, to be published. 11. G. R. Satchler et al., Phys. Rev. 136, B637 (1964); see also contri- bution to this conference by C. J. Batty et al. . .. See, for example, T. Tamura, Proc. of Conf. on Isobaric Spin in Nuclear Structure (Tallahassee, 1966). P. G. Roos, private communication. . R. M. Duisko and R. H, Bassel, private communication. 15. F. G. Perey, private communication. 16. G. Rakany, Nuclear Physics 7, 553 (1958); N. Austern, Proc. Summer Study Group, Brookhaven National laboratory Report BNL-948 (1965); M. Tanifuji, Nuclear Physics 58, 81 (1964); S. T. Butler, Aust. J. R2- be published; R. C. Johnson, contribution to this conference. F. G. Perey, Proc. Conf. on Direct Interactions (Padua, 1962). F. G. Perey and D. S. Saxon, Physics Lett. 10, 107 (1964); . Austern, Phys. Rev. 137, B752 (1965); A. M. Saruis and F. G. Perey, Nuclear Phys. 70, 225 (1965). 19. See, for example, S. A. Hjorth et al., Phys. Rev. 138, B1425 (1965) and J. K. Dickens et al., contribution to this conference, 20. See, for example, N. Austern and J. S. Blair, Ann. Phys. 33, 15 (1965). 21. See, for example, W. S. Gray et al., Phys. Rev. 142, 735 (1966). 22. N. K. Glendenning and M. Veneroni, Phys. Rev. 144, 839 (1966). 23. V. A. Madsen and W. Tobocman, Phys. Rev. 139, B864 (1965); N. Baron et al., Phys. Rev. 146, 861 (1966). 24. R. M. Haybron and H. McManus, Phys. Rev. 140, B638 (1965). .. Figure Captions Figure 1 - Comparison with experiment of cross sections for 30.3 MeV protons predicted by optimum fits with constrained (solid curves) and independent (dashed curves) spin-orbit coupling)). Figure 2 - Comparison with experiment of cross sections for 39.3 MeV protons predicted by average potentials”). Figure 3. - Comparison with experiment of polarisations for 30 MeV protons obtained by simultaneous fits to cross section and polarisation data. Figure 4 - Comparison of measured values of total and non-elastic cross sections for 24 MeV neutrons with predictions from average proton potential in which the surface absorption has not (dahsed curves) or has (full curves) a term proportional to t.T/A. Figure 5 - Measured cross sections for excitation of 2* states in "cr and Zr; and the" (p,n) transitions between analog states, coñ- pared with predictions using Yukawa effective interaction of range 1 fm and strength Vor + VOR TOTz. Vos ~ 210 MeV for Zr, a 170 MeV for Cr, while Vos 20 MeV. 06 Figure 6 - Form factors for excitation of lowest 2* state in 6°Ni, using RPA wavefunctions22). Left side shows the total and the various components; right side compares this microscopic form factor with the real part of the derivative of the optical potential given by the collective model. Figure 7 - Comparison with measured (ca') excitation of lowest 2* states in Sn and Ni of the predictions using a microscopic form factor and a sum of two Yukawas for the alpha-nucleon inter- action23). Figure 8 - Impulse approximation for the excitation of the 4.43 Mev 2* state in 12c by high energy protons 24). I (TDA) and II (RPA) refer to the wavefunctions of Gillet and Vinh Mau. ORNL-DWG 66- 2052 ORNI - AEC - OFFICIAL 0.5 IKIT ,IKITIL KILIKIL KILTT, toplop. 2 NARU VL-AEC - OFFICIAL 10 20 30 40 50 60 70 110 120 130 140 150 160 80 90 100 c.m. (deg) ORNL-OWG-86-2053 . ORNI - AEC - OFFICIAL - O . man - - Toplon _ 0.05 . . 1 0.02 0.01 10 20 30 40 50 60 70 110 120 130 140 150 160 80 90 100 8c.m. (deg) ORN! - AEC - OFFICIAL ORNL-DWG 66-4721 ORNL.-'AEC - OFFICIAL SSN POLARIZATION 6ONI 10 20 30 40 50 60 90 100 110 120 130 70 80 Oc.m.(deg) ORNI - AEC - OFFICIAL . . 3日 ​5 we HIGH AS ード ​- ー大 ​. One 9 HOH -------- 。\ ORNL-DWG 66-6683 ORNL - AEC-OFFICIAL ORNI - AEC-OFFICIAL ORNL-DWG 66-8558 E=14 (o,p') E =14.65. (20) E = 18.85 OO.Omit I (pp') E = 17.45 doldw (mb/steradian) - - 92zr(2,p) E ={9.4 (n,n) E = 149 (pen) E = 18.5 -Zr (pon) E = 18.5- 50 . 150 120 100 OC.M. (deg) 80 Bc.m. (deg) DRNL - AEC - OFFICIAL ORNL - AEC - OFFICIAL Titipan 1000- TTTTTT ultuuh! 100 Ni 60 72F. (F) Form factor xp? (MeV dx2 Krfsy2-185/27 ? 298 2P3p! 12P3/žlf spel 1223/2-2P3/2!! Miligra-2P312) X(1992-1992) 1 2 3 4 5 r 6 (F) 7 8 9 10 0 1 2 3 7 8 9 10 4 r 5 6 (F) ORNI - AEC - OFFICIAL ORNI - AEC - OFFICIAL 10= snl20 Q -- 1212 - Cz!culated cross Se' 3.03 . Differential cross section 2 ms. பாடப்பட்ட காட்டபட்ட 10 5/ar) பட * 0° 10° 200 30° 40 50 GO 70° ec.m. Scattering angic, lcm ORNI - AEC - OFFICIAL ORNL - AEC - OFFICIAL - ' பட - - -- L க ' - ' . K ORNL-DWG 65-3687 I chot 2012,pll2c*: Ep = 156 MeV 24, 7 = O AT 4.43 MeV - ze== II (4.8 MeV) . ------- I (3.23 MCV) ------ (183/2)- 10/2 o 155 MeV. o 185 MeV Dasma CROSS-SECTION (mb/sieradian) on about any . . . comme دسته مه به مع معه 10 20 30 40 50 60 CENTER-OF-MASS SCATTERING ANGLE (deg) 70 ORAL-AEC - OFFICIAL ORNL - AEC - OFFICIAL 1 .23 - -.. ... ... ... ... ... ... .. . .. . ... ORNL-OWG 66-2052 LINHLINHLKIL KILL KILIMLJIMAT Hop/op Pb 1. 10 20 30 40 50 60 70 110 120 130 140 150 160 80 90 100 Oc.m. (deg) ORNL-OWG 66-2053 none, 44. Boolen M . - 10 20 30 40 50 60 70 110 120 130 140 150 160 80 90 100 c. m. (deg) . . ... 4 Skrut ORNL-DWG 66-4721 POLARIZATION 60Ni 10 20 30 40 50 90 100 110 120 130 60 - 70 80 c.m. (deg) " ! ... EC" 16 : !!! 1. . 4 .. . .", . . ORNL-DWG 66-6683 og ---7--- F olje oto trbat 3 o(b) . .. ORNL-DWG 66-8558 . . . . . 52crl WILH:... (p.p') E:14.65 o Ozr (pap) E = 48.83 .. # o o i n L# w o doldu (mb/steradian) (esp) E = 17.45 N 92zr Tep') E = 19.4 - P2 ti N ? (n,no) E = 14 - . ū (pin) E = 18.5 -Zr (pin) E = 18.5 io 50 100 150 120 (bəp) W38 4080 OC.M. (deg) oooلللللللل 4001 ا او و Form factor xp? (MeV F? (R) .25 ملاع : ار azz**