V .._.. ......«..--....,w-w\ RSOBARIC ANALOG 3ng musmons m (pm) ’ REACEONS’ONMCa, 'Zr, Sn, AN Pb AT 25, 35, AND 45 MeV Bissertation for the Degree of Ph. D. MICHEGAH STATE UMVERSETY ROBERT REM) DOERENG‘ 1974 This is to certify that the thesis entitled Isobaric Analog State Transitions in (p,n) Reactions on 48Ca, 90Z r, 1208 n, and 208Pb at 25, 35, and 45 MeV presented by Robert Reid Doering has been accepted towards fulfillment of the requirements for Ph.D. degree in Physics gm #4 Major professor Date 7‘1 5'71; 0-7639 ”9 ABSTRACT ISOBARIC ANALOG STATE TRANSITIONS IN (p,n) REACTIONS ON “Bea, 9°zr, 1208n, AND 208Pb AT 25, 35, AND us MeV By Robert Reid Doering Differential cross sections have been measured for (p,n) reactions to the isobaric analogs of the targets “80a, 90Zr, 1208n, and 208Pb at proton bombarding ener- gies of 25, 35, and 45 MeV. The angular distributions include 0° and generally extend from 100 to 1600 in 5° steps. Neutron spectra at these scattering angles have been obtained with the time-of-flight technique. The isospin-flip strength of a phenomenological nucleon- nucleon force has been determined with microscopic DWBA calculations including the "knockon" exchange amplitude. The strength required to fit the data decreases with increasing bombarding energy. At the higher proton ener- gies a realistic G-matrix effective interaction also provides a reasonable account of the observed angular distributions. ISOBAaIc ANALOG STATE TRANSITIONS IN (p,n) REACTIONS 20 ON “86a, 90Zr, 120Sn, AND 8Pb AT 25, 35, AND 45 MeV By Robert Reid Doering A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Physics 1974 é, ACKNOWLEDGEMENTS I would like to thank the entire staff of the Michigan State University Cyclotron Laboratory for their patient assistance with many essential aspects of this work. I am also grateful to Professor George Bertsch and Professor Hugh McManus for providing answers to numerous theoretical questions. Dr. Don Patterson has actively participated in the experimental phase of this project, and I am indebted to him for his many contributions. Jim Branson also aided with the data collection and reduction, in addition to assembling the neutron detector. Finally, I would especially like to thank Professor Aaron Galonsky for his assistance, encouragement, and guidance. ii TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES I. II. INTRODUCTION A. B. Nuclear Forces (p,n)-IAS Reactions EXPERIMENTAL TECHNIQUE A. B. C. D. E. F. The Proton Beam 1. The Cyclotron 2. The Beam Transport System The Scattering Geometry 1. The 0° System 2. The 10-160° System The Detectors 1. The Proton Monitor 2. The Neutron Detector Electronics 1. The LIGHT Signal 2. The T0? Signal . The Monitor Signal Data Acquisition 1. TOP Spectra 2. Monitor Spectra 3. Charge Collection n. Dead-Time Measurement Data Reduction 1. Spectrum Calibration 2. Peak Fitting 3. Neutron Detection Efficiency iii vi 11 19 19 20 25 27 31 32 36 38 39 39 #0 #0 68 70 71 72 72 75 79 4. Neutron Attenuation 5. Targets 6. Cross Sections III. DATA ANALYSIS A. Calculations B. Results LIST OF REFERENCES iv 89 9O 93 101 101 106 110 1. 2. LIST OF TABLES Neutron Resolution Function Gamma-Ray Sources for Neutron Detector Calibration Neutron Attenuation (En = 11.59 MeV) Target Data Measured Differential Cross Sections (p,n)-IAS Total Cross Sections 76 82 91 92 95 100 1. 3. 4. 5. 7. 8. 9. 10. 11. 12. LIST OF FIGURES Experimental Area of the M.S.U. Cyclotron Laboratory Horizontal Acceptance of the Beam Transport System Following the Target Vertical Acceptance of the Beam Transport System Following the Target Small-Angle Scattering of Protons from a Typical Target Neutron-TOE Beam Line and Detector Cart Neutron-TOP Scattering Chamber and Quadrupole Triplet Neutron-Detector Preassembly Electronics LIGHT-PSD Histogram Neutron and Gamma-Ray Bands in the LIGHT-PSD Plane Neutron and Gamma-Ray TOF Spectra at 0° #8 for 25-MeV Protons on Ca Neutron and Gamma-Ray TOF Spectra at 00 90 'for 25-MeV Protons on Zr vi 22 23 2h 26 28 30 33 37 41 43 45 46 13. i4. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. Neutron and Gamma-Ray TOF Spectra for 25-MeV Protons on 120Sn Neutron and Gamma-Ray TOF Spectra for 25-Mev Protons on 208Pb Neutron and Gamma-Ray TOE Spectra for 35-MeV Protons on 48Ca Neutron and Gamma-Ray TOF Spectra 90 for 35-Mev Protons on Zr Neutron and Gamma-Ray TOP Spectra for 35-MeV Protons on 12oSn Neutron and Gamma-Ray TOF Spectra for 35-MeV Protons on 208Pb Neutron and Gamma-Ray TOP Spectra for 45-MeV Protons on “80a Neutron and Gamma-Ray TOF Spectra 90 for 45-Mev Protons on Zr Neutron and Gamma-Ray TOF Spectra 120 for 45-Mev Protons on Sn Neutron and Gamma-Ray TOP Spectra for 45-MeV Protons on 208Pb IAS-Neutron and Gamma-Ray Arrival for Ep=25 MeV IAS-Neutron and Gamma-Ray Arrival for Ep=35 Mev vii at O at 0 at O at 0 at 0 at 0 at 0 at O at 0 at 0 Times Times 47 48 49 50 51 52 53 54 55 56 59 60 25. 26. 27. 28. 29. 30. 31. 32. 33. 35. 36. IAS-Neutron and Gamma-Ray Arrival Times for Ep=45 MeV Energy vs. BF for the M.S.U. Cyclotron Doubled Neutron-TOP Spectrum Typical Neutron-Energy Resolution Proton-Monitor Spectrum Resolving the 1.87-MeV, 1.17-Mev, and Ground States of 12°Sn at Ep=45 MeV Gaussian-Plus-Quadratic Fit to a Lorentzian Peak IAS of 208 and Gaussian (dashed) Peaks Plus Pb Fit with Lorentzian (solid) Quadratic Background Fit to the Compton Edge for 1.275-MeV Gamma Rays from 22Na Light Resolution of the Neutron Detector Light-Threshold Calibration of the Neutron Detector Efficiency of the Neutron Detector Comparison of EIperimental and Theoretical (p,n)-IAS Angular Distributions viii 61 62 64 67 69 78 80 83 84 86 88 102 I. INTRODUCTION A. Nuclear Forces For almost three hundred years, physicists have attempted to account for natural phenomena in terms of mutual forces between material bodies. Although the venerable Newtonian laws (Ne 87) are presently recognized as approximations most appropriate for macro- scopic physical systems, the term ”force" is still employed to denote the interactions between elementary particles. On the basis of vastly different strengths and symmetry preperties, all known interactions have been classified as manifestations of four fundamental forces: gravitational, ”weak,“ electromagnetic, and ”strong“ (Fe 62). The latter is also referred to as ”the nuclear force," since it is primarily responsible for binding protons and neutrons into stable nuclei. In addition to being the strongest, the nuclear force also appears to be the most complex. The most general expression for the corresponding potential energy between two nucleons, assuming translational, rotational, Galilean, space-reflection, and time- reversal invariance together with charge independence, permutation symmetry, and hermiticity, is v13 z v0 + (9193)? + (31'3”. (I-1) + (sigma-swat + vLs + (;-§)(1_:1-53)va + 81.1er + 813(Eio_3)vT-C 4' L1.1"LL 1* LiJ(Ei’EJ)VLL‘C + (21'2)(23'P.)Vap + (21.2)(gj°2)‘£1°53)vapt + Hermitian conjugate, where 313 = 3(21‘£)(23’£)/r2 - (91-93), L1; = Hell) (23-1) + Raina-y. L.= £32: §.= £1 +.§Jo £=£J'£19 E=23“213 :1, 21, 21, and Ed, are the position, momentum, and Pauli spin and isospin operators, respectively, of the individual nucleons, and each term is a function of r2, p2, and L2 (0k 58). Thus far, it has not been possible to unambiguously derive these functions from a fundamental theory of nuclear forces, although the exchange of pi mesons appears to account for the long- range part of the potential (Re 67). However, several attempts to fit nucleon-nucleon scattering data with phenomenological potentials of the general form given by Equation I-i have been reasonably successful. In particular, the Ramada-Johnston (Ba 62) and Reid (Re 68) potentials reproduce the bulk of the scattering measure- mcnts at nucleon energies up to the threshold for meson production, which is about 300 MeV. The systems of interest in nuclear physics generally contain more than two nucleons. Although, in principle explicitly many-body forces are present in nuclei, calculations indicate that they contribute less than 10% of the binding energy (Be 72A). Thus, the previously discussed two-body potential is considered to dominate nuclear structure and reactions induced by projectiles with energies less than about 300 MeV per nucleon. Therefore, a sufficiently general nuclear Hamiltonian for most purposes is 1.; = 21k1+£v (I—z) 1 + (74-) l (V-U) I34”) . (I-6) where the projectile label has been dropped and (1) 1 (*) XF :‘PFI’E -H¥1607‘F I I I I defines the "distorted waves" which describe elastic scattering by the auxiliary potential (Go 64). The first term of Equation I-6 vanishes if the initial and final states of the target are not identical, since they are orthogonal and unaffected by the one-body potential. Thus, Equation I-6 reduces to D (-> ) TFI = (x? I(V-U)|‘P§:+ > (1-7) for inelastic scattering. In terms of the initial distorted wave, the eigenstate of the total Hamiltonian subject to the appropriate boundary conditions on the incident and outgoing waves is given by (+) (+) (+) ‘1’, =76, +§(v-U>‘PI . (I-8) where the energy denominator is defined by e = EI - H - U + 16L. Thus, the wave operator defined by ‘1’?” = {274” <1-9) satisfies {2: 1 + é‘V’U)n 0 (1-10) Substituting Equation I-9 into Equation I-7 produces -) ) TEI = (x; I(V-U)|fl'X§+ ) . (I-11) Equation I-10 may be used to expand this exact expression for the direct scattering amplitude in "powers" of (V-U). Retaining only the first-order term of such a series yields D (-> (+) TF1” 12:10‘1" IVI'XI > ' ”‘12) which is the usual "distorted-wave Born approximation" (DNBA). The DWBA may be adequate when an auxiliary potential which accurately represents the bulk of the nucleon- nucleus interaction is employed. The common choice for U is an "optical-model" potential obtained from fitting elastic scattering data. The removal of probability flux from the elastic channel by inelastic scattering and other reactions is accounted for in the optical model with an imaginary term in U. However, despite such refinements in the auxiliary potential, the distorted-wave Born series generally fails to converge for the currently popular versions of the free nucleon- nucleon force. For example, the DWBA amplitude given by Equation I-12 would be infinite for the Ramada- Johnston potential, unless the distorted waves contained no overlap of the projectile and target nucleons within the ”hard-core" radius (v13(ré 0.485 F) =00). Fortunately, the multiple-scattering formalism of Watson (Na 5?) allows vi to be replaced with an effective two-body scattering operator which is less pathological. The essential idea is to rearrange the expansion for the scattering amplitude so that the basic interaction includes multiple scattering by a particular target nucleon as the projectile propagates under the average influence of the entire target, as represented by an optical potential for elastic scattering. Such an effective scattering operator may be defined by e 3 t1 8 "1 + wiétig (1'13) where the residual interaction is related to the free two-nucleon potential by W1 2 V1 - ui, “I " <9: '71“. (PI): and A HA (DI " EI (Dr e To first order in t1, the direct scattering amplitude is given by D A (‘> e (+) TF1 “3 142—1051» | 1’1 'XI > ”‘1'" (Ho 67A). This is known as ”the single-inelastic- scattering approximation" (Go 64), since it neglects virtual excitation of the target in intermediate states. Disregarding such processes is an essential feature of the microscopic-direct-interaction” concept of nuclear reactions (Au 70A). However, intermediate excitations are obviously important for a reaction known to proceed through a metastable "compound nucleus" (V0 68). Thus, the single-inelastic-scattering approximation may only be expected to give a reasonable account of reactions induced by projectiles which bring sufficient energy into the compound nucleus so that the probability of its decay to any particular final state is small com- pared to that for the competing direct-reaction process. For nucleon-nucleus elastic scattering, the compound- nucleus reaction.nechanism appears to be relatively unimportant for bombarding energies above about 10 Mev (Be 69). Determinations of the appropriate effective inter- actions and distorted waves are, of course, prerequisite for practical applications of Equation I-14. In general, 10 the first of these problems involves the solution of Equation I-13, which is intractable with the full many-body propagator. However, if the effect of the remaining target nucleons on the scattering by a particular one is neglected, Equation I-13 may be reduced to t (I-15) i - vi I 7is k 1k ti’ 1' O' i+1€ which is just the free nucleon-nucleon scattering operator. Using the free interaction in Equation I-14 results in the ”impulse approximation,“ which has been demonstrated to be useful for nucleon-nucleus scattering at energies greater than about 100 MeV (He 59). At lower energies, the scattering of a pair of nucleons is influenced to a greater extent by the proximity of others. This subject has been studied extensively in relation to nuclear structure (Ba 73), and it has been suggested that the effective interactions used in structure calculations may also be appropriate for ”mediumpenergy' nucleon-nucleus scattering (Fe 70). It seems plausible that a bound target nucleon should not interact much differently with its neighbors than with a free nucleon possessing a kinetic energy only a few tens of MeV’greater. Indeed, Watson's approach to multiple scattering has also been adapted to the 11 derivation of expressions similar to Equation I-13 for bound-state effective interactions. In particular, a 'G-matrix' effective interaction may be obtained from Equation I-13 by replacing the complex Optical-model potential with a purely real Hartree-Fock or ”shell- model" potential, including the Pauli projection Operator in the propagator, and deleting the 16. (Ba 72). The most significant difference is probably the lack of an imaginary term in the bound-state case. Neverthe- less, G-matrix effective interactions have given reasonable descriptions of nucleon inelastic scattering (Lo 70, Fe 70) and the real part of the proton-nucleus optical potential (81 68). B. (P.n)-IAS Reactions The distorted waves in Equation I-14 contain the initial and final states of the target in addition to the wavefunctions for the relative projectile-target coordinate which are more commonly referred to as ”the distorted waves." Thus, the scattering amplitude depends on the bound states of HA as well as the effective nucleon-nucleon interaction. Therefore, if the latter were well established, it would be possible to investigate nuclear structure with nucleon-nucleus scattering. However, as is indicated in Section I.A, 12 the calculation of a realistic effective interaction from a free nucleon-nucleon potential is a formidable undertaking. Furthermore, it is difficult to estimate the effects of the approximations used to calculate interactions on the structure information extracted with them. Thus, it has been suggested that phenomeno- logical effective interactions should be determined from scattering experiments involving nuclei with relatively well-understood structure so that a “cali- brated spectrometer” would be available for exploring more obscure nuclear wavefuncticns (Sa 67). In general, direct nuclear reactions with large cross sections proceed predominantly via the central- force part of the nucleon-nucleon interaction, the standard phenomenolOgical form of which is given by O tij I: V080 + Vogo(r13)gi‘gj (I'lé) ‘wts‘c‘ru )31’2 +VO’I'50'C (r1j).g1'gj.t.1 '23 9 which is a local parameterization of the effective scattering Operator, patterned after the corresponding terms in the general two-body potential of Equation I-i (Au 70A). For simplicity, a common radial function of either Gaussian or Yukawa form is usually selected. Attempts to extract the associated empirical strengths 13 from nucleon-nucleus scattering data have been reviewed by Austin (Au 72). Assuming a Iukawa radial dependence given by eXP(r/,u. )‘ I-1 (r/A.) ( 7) ch) = with a range (As) of 1.0 F, he concludes that V0=-2715 MeV, vets1zizé MeV, and that “5 and Vi are poorly deter- mined. In particular, his compilation includes values of Vt from below 10 to nearly 30 MeV. The present study concentrates on obtaining more precise knowledge of the purely isospin-dependent part of the effective nucleon-nucleon interaction, which refers to the third term of Equation I-16. This term may be isolated by considering transitions from the ground state (GS) of a target with mass number A, com- posed of Z protons and N neutrons, to its ”isobaric analog state” (IAS) in the "residual” nucleus with Z+1 protons and N-i neutrons. The IAS may be defined in terms of the action of the ”isospin-lowering” operator (T‘) on the target ground state by ®m(T=T>eTz=-'T<) = (zerir‘ TGS(T=T>.TZ=T>). (I-18) + + T- = 1:- 2:1 1’ where 14 t x y — + 5.1 a £§19 T) = 2(N‘Z)e and T( = T) - 1e As Equation I-18 indicates, the isospin-lowering Opera- tor creates the IAS by reducing the z-component of the target isospin by one unit while conserving the magni- tude of T. Since the z-component of isospin is defined as half the neutron excess (in the usual nuclear physics convention), the isospin-lowering Operation amounts to converting an excess neutron into a proton. If there is only one excess neutron in the target, the IAS will be the ground state of the ”mirror” nucleus. In the general case, the anaIOg of the target ground state will be the first state with T=T> in the residual nucleus, the lower-energy states having T=Tz=T¢. For transitions between isobaric analog states with zero spin and posi- tive parity (J'=0+), the only nonvanishing matrix elements in Equation I-14 will be for the purely "isospin-flip" term of the effective interaction in Equation I-16 (Au 70A). This term contains a scaler product of projectile and target-nucleon isospin Opera- tors, which may be expanded as + - ' + Z Z IAbe = 2(t1to + tito) + “titO‘ (1'19) 15 The second pair of isospin-raising and lowering Opera- tors in Equation I-i9 is responsible for ”charge- exchange" reactions in which a neutron in the target is converted into a proton while a projectile proton becomes a neutron. Since the isospin-flip term of the effective interaction is the only central-force com- ponent which contributes to the direct amplitude for charge-exchange scattering between J"=0+ analog states, these reactions are quite sensitive to Vt. Except for the smallness Of the cross sections typically observed, (3He,t) charge-exchange reactions are the most experi- mentally convenient means of studying such transitions. Unfortunately, conventional DWBA calculations have often been in relatively poor agreement with the (3He,t) data (Fa 72, Hi 72). Besides the usual optical-model ambi- guities for complex projectiles, complications of the reaction mechanism have been preposed. In particular, a (3He,c¢)(¢x,t) amplitude larger than the direct ampli- tude has been calculated for the 480a(3He,t)uBSc-IAS reaction at 23 MeV (De 72). Generally accepted optical- nodel potentials are available for (p,n) charge-exchange reactions, but it has been suggested that “neutron pickup” followed by ”proton stripping” may also interfere with the direct amplitude in this case (R1 73). The significance of (p,d)(d,n) contributions is currently under investigation, and this problem will 16 not be directly addressed in the present analysis. The major experimental difficulties associated with (p,n) reactions result from the charge neutrality of the neutrons. Conventional charged-particle detectors generally measure the ionization produced by incident radiation. Since neutrons have no Coulomb interaction with atomic electrons, they must be indirectly detected through the charged products of nuclear reactions which they induce. Unless a ”recoil telesOOpe” (Ma 70) is used to define the scattering angle, ionizations created by the reaction products cannot be put into correspon- dence with unique neutron energies. A pOpular alterna- tive for obtaining neutron spectra has been to directly determine their velocities. This method requires the accurate measurement of neutron flight times from the target to the detector, which is facilitated by short- duration beam bursts from the proton accelerator, a long flight path, a rapid-response detector, and precision fast-timing electronics. Of course, longer flight paths give smaller solid angles for a given detector, and, thus, some compromise between resolution and count rate is generally necessary. Anderson and Wong employed the "time-of-flight" technique in the first observations of (p,n)-IAS transi- tions in nuclei heavier than the mirror pairs (An 61). Their measurements revealed the presence of a strongly 17 excited state in each residual nucleus at an energy corresponding to the Coulomb energy required to convert a target neutron into a proton (plus the n-p mass dif- ference). At that time, the discovery of isobaric analog states in such heavy nuclei was unexpected, since it was widely believed that isospin conservation would be significantly broken by the electromagnetic force in all but the lightest nuclei (W1 69). The prominence of heavy-target-ground-state analogs in charge-exchange reactions is presently understood to result mostly from the "dilution” of the isospin impurity of the nuclear core by its coupling to the pure isospin of the neutron excess (So 69, Be 72). During the past decade, additional (p,n)-IAS eXperi- ments have been used to explore the isospin dependence of the nuclear force. However, most of the data has been obtained with proton bombarding energies of less than 30 MeV (An 64, Be 71, No 71, So 73). The few absolute angular distributions previously measured at energies above 30 MeV are essentially confined to forward angles (va 65, Ba 68, La 68, Jo 73), and, except for the 27Al(p,n)27Si-IAS data from the Michigan State University Cyclotron Laboratory (Jo 73), these cross sections generally have relative errors of more than 10%. 18 The present work provides (p,n)-IAS angular distributions from 00 to 1600 at proton energies of 25, 35, and 45 MeV for the targets uaCa, 90Zr, 120Sn, and 208P b. These nuclei span the range of masses for which a "global" optical-model potential has been ob- tained (Be 69). In addition, the ground states (and, hence, the analog states) of these targets have J"=0+ and are considered to be particularly well understood. Thus, this data is well suited to further extend our 'knowledge of the isospin-flip strength of the effective nucleon-nucleon interaction. II. EXPERIMENTAL TECHNIQUE A. The Proton Beam 1. The Cyclotron The Michigan State University Cyclotron produces approximately 25- to 50-MeV proton beams of exceptional quality for time-of-flight (TOF) experiments. Internal slits restrict the phase width of individual beam pulses to about 2°. At a typical repetition rate of one pulse every 60 nsec, this phase width is equivalent to a time spread of 1/3 nsec. In practice, gamma-ray bursts $0.5 nsec (FWHM) in duration are typically observed from thin targets intercepting the external proton beam. Widths in the neighborhood of 0.2 nsec (most of which may represent the inherent resolution of the detector and associated electronics) have been achieved by slightly reducing the magnetic field and/or radio frequency from the normal Operating values. However, the improved resolution is generally more than offset by the loss of beam intensity also incurred from such a detuning of the cyclotron. During these (p,n) experi- ments, the current on target was usually between one and four micrcamps, limited for the tin and lead targets by their relatively low melting points. 19 20 2. The Beam Transport System Figure 1 gives an overview of the ”high bay” at the Michigan State University Cyclotron Laboratory. Neutron TOF measurements are conducted in the shielded experimental area designated Vault #5. The angular divergence of the proton beam transported from the cyclotron to Vault #5 is minimized by leaving off the quadrupole magnets labeled Q3 through Q6, thereby requiring greater than normal focal lengths for the remaining quads. This low-divergence mode of the beam transport system results in fewer background neutrons produced by protons striking the beam pipe. It also tends to increase the size of the beam spot on target. However, the spot diameter has been routinely maintained at ‘<0.5 cm (as observed on a quartz scintillator mounted in the target ladder), which contributes negligible uncertainty in the scattering angle to a detector several meters away. In addition to low divergence, the proton beam is delivered to the neutron TOF line with little momentum dispersion, since the -31.50 bend through the dipole magnet M4 removes most of the dispersion intro- duced by the +450 bend at M3. However, the excellent '3) of the proton beam energy resolution ( AE/Eev'lo completely extracted from the cyclotron on a single turn is seldom a significant fraction of the overall resolution ,Irrlr‘ \ I 21 heapeuonsa nonnoaoho .35.: on» no 393 Heuseaandwm .« enema §§\§§§ is] 3.6 I... all! . i TIES . . .0 I]. \ \\\ \\\\\\ i\\\\\\\\\ x\.\ as O r: a a. \\\\\\\\\\\\\\.\\\\\\\\\\\\ \ \ A ...... .. x max 0 \ \K W x \\\ a mag a .. \\\\\\\\\\\\ eaV\§\\\\\\\ 8 § 22 for neutron TOF experiments. Thus, it is unnecessary to have a dispersed beam available for momentum analysis. Although external slits are not used to select the beam energy spread, remotely positioned, current-sensitive jaws are employed at Box 1 through Box 4 to collimate and monitor the beam. The slits at Box 19 are used only during initial beam alignment. With a vacuum of about 2x10'5 mm Hg in the line, very few protons are scattered into the beam pipe before they reach the target. The quadrupole triplet beyond the scattering chamber is used to refocus target- scattered protons into the heavily shielded beam dump, thus minimizing background from the final sections of beam pipe. The placement of the quads has been optimized with the aid of beam-Optics calculations with the code OPTIK (Do 61). Figures 2 and 3 indicate the acceptance of the triplet for transmission of 45-MeV protons. Each point in one of the phase-space planes represents a possible displacement and scattering angle for a proton at the target. For example, the origin corresponds to an undeflected proton passing through the center of the target. The lines indicate grazing trajectories for various apertures between the target and beam dump. Thus, the area bounded by the innermost lines surrounding the origin represents the domain of horizontal or vertical phase space (at the target) containing protons 23 HORIZONTAL PHASE SPACE AT ms TARGET RADIANS I I I 0.6 1.0 INCHES Figure 2. Horizontal Acceptance of the Beam Transport System Following the Target 24 VERTICAL PHASE SPACE AT THE 1'BABGET RADIANS :::==_____, ‘rr————_______ EEEEE;;;;:::::; 0.02—"' e = t s t : : : : a -0.6 -0.2 0.2 0.6 1.0 INCHES -o.02—— \ _\ Q ‘0.0 "- .1 Figure 3. Vertical Acceptance of the Beam Transport System Following the Target 25 which would be cleanly transported to the dump. These graphs indicate that the limiting horizontal and vertical scattering angles from the center of the target are 0.022 and 0.027 radians, respectively, for 45-MeV protons. Fig- ure 4 displays Rutherford single scattering and multiple scattering at 45 MeV from a typical target used in this experiment. For this case, only about 1% of the protons incident on the target would be deflected into the beam pipe. Multiple scattering has been calculated with the formula of Rossi and Greisen (Se 64). B. The Scattering Geometry o 1. The 0 System A special experimental arrangement is available for observing neutrons at a scattering angle of 0°. The target ladder is mounted on a box just beyond M4, and M6 is used to bend the beam an additional 20° into an auxiliary Faraday cup. Neutrons from the target exit M6 through a 0.8-mm-thick, aluminum port and traverse several meters of air en route to a detector placed along the partially dismantled beam line. A 13.2-cm-thick, brass collimator with a 2.5-cm-diameter aperture adjacent to the port attenuates neutrons produced on the pole faces of M6. At energies of 35 and 45 MeV, the port has been covered with a 5-mm-thick, lucite 26 100 11111 1 Cl SINGLE SCATTERING O MULTIPLE SCATTERING 10 - TOTAL 1’ 1 11 r11 / l SCATTERED BY MORE THAN 0 T % I II III 0_1 1 1 1 1 l 1 1 1 1 l 1 1 1 1 l 1 1 1 1 l 1 1 1 0.00 0.01 0.02 0.03 0.0%t 0.05 0 [RADIANS] Figure 4. Small-Angle Scattering of Protons from a Typical Target 27 absorber to prevent protons which pick up an electron in the target and sneak through M6 as neutral hydrOgen from reaching the detector. Without this absorber, approximately one 35-MeV proton out of every billion in the beam has been observed at the detector, a ratio consistent with previously measured electron-pickup cross sections (Ta 73). Especially high quality spectra may be obtained with the 00 setup. Since the beam is dumped in the main vault and the detector is in vault #5, the background is minimal. In addition, flight paths of up to 15 m are available for the ultimate fractional time resolution. 2. The 10-160° System Figure 5 displays the apparatus used for taking angular distributions from 10° to 160°. The detector rides on a cart which pivots about an axle above the scattering chamber. It is shielded from neutrons and gamma rays not originating in the target by a section of 105-mm gun barrel and stacks of water-filled boxes. The cart floats on an air pad which is pushed by an electric motor to change the observed scattering angle. Both the pad and motor may be remotely operated from the data room. Four closed circuit TV cameras in vault #5 provide feedback on remote adjustments of the beam and targets as well as the cart. The camera mounted next ammo nouoouoa use coda seem mos ..u I icoausoz .m madman v .‘ 29 to the gun barrel is equipped with a 300-mm-focal-length lens on a near-focussing adapter. It gives a close-up view of the target ladder for monitoring the alignment of beam spot, target, and gun barrel. The tight collimation afforded by the gun barrel requires that it be accurately aimed at the target. This is difficult to maintain as the heavily loaded cart traverses imperfec- tions in the concrete floor of the vault. The present system of cantilever pipe and guy wires has been found to provide a satisfactory coupling of the cart and pivot. It has enough vertical flexibility to allow the air pad to support the cart, yet sufficient horizontal rigidity to generally maintain the flight path within 11 cm and the gun barrel orientation within i%°. The camera attached to the cantilever pipe reads the scattering angle from a fixed scale on the pivot support. The remaining pair of cameras view plunging scintillators which intercept the beam immediately before the target ladder and the beam dump. The scattering chamber is shown in Figure 6. It is basically a rectangular section of beam pipe with a neutron-exit window and extra ports for the target ladder and monitor detector. The target ladder holds up to six 5-x2%-cm target frames and provides remotely controlled drives for changing the target angle and height. The neutron window is a sheet of i-mm-thick uoaadha oHoasuumdd and nomadso wnduepudom moaizonpsoz .m ohswam J 31 mylar covering a 2.5-cm-high slot which subtends scattering angles from 60 to 163°. At selected scattering angles, the neutron detector may be positioned from about 1 to 7% m from the target. However, the cart can swing over the full angular range of 10° to 1600 only for flight paths between approximately 3 and 5 m. C. The Detectors 1. The Proton Monitor The monitor detector consists of a 3.2-cm-diameter by 1.3-cm-thick, thallium-activated-Nal scintillator, optically coupled to a 5-cm-diameter RCA #523 photo- multiplier tube. A preamplifier is also included in the detector package. An aluminum window 0.025 mm thick covers the front face of the NaI crystal, and the entire assembly is surrounded by a magnetic shield. The monitor is used to observe protons scattered through 900 by the target. The protons remain in an evacuated pipe extending from the scattering chamber until they reach a 0.025-mm, stainless steel window 98 cm from the target. Between the steel and aluminum windows is placed a 3.2-mm-thick, brass collimator with a 6.h-mm aperture. 32 The pulse-height resolution of this detector has been measured to be 8.6% for 662-Kev gamma rays from a 13708 source. The resolution is principally determined by statistical fluctuations in the number of photons (N) produced in the scintillator by incident particles of a definite energy (E). For large N, the Poisson probability distribution of the number of created photons approaches a Gaussian distribution with a standard deviation of N%. Since the average number of photons produced is prcportional to the available energy, the energy resolution is prOportional to E%. Thus, from the 57-KeV resolution observed for 662-KeV gamma rays, 470-KeV resolution would be expected for 45-Mev protons. This estimate is about 30% below the values achieved in practice. However, the actual monitor resolution pro- vided adequate separation of the elastically and inelas- tically scattered protons in this experiment for the for- mer to be accurately counted. 2. The Neutron Detector Figure 7 gives an exploded view of the neutron detector prior to assembly. The heart of this detector is a 7.0-cm-diameter by 3.8-cm-thick volume of the liquid organic scintillator NE 213, which is encapsulated in a glass cell. The walls of the cell are 2% mm thick hanaommdomm Honoouoalconpsoz .m oasmam 34 both on the flat ends and the curved edge, to which is attached a spherical expansion chamber. The cell is Optically and mechanically coupled to a 5 cm diameter RCA 8575 photomultiplier (PM) tube with a 2.5-cm-long, tapered, lucite light pipe. The glass-lucite interfaces are cemented with Dow-Corning Sylgard resin. The light pipe and cell are coated with Eastman White Reflectance Paint, except for the expansion chamber, which is painted flat black. The high reflectance paint is covered with a layer of aluminum foil to insure Opacity. The PM tube is also protected against light leaks with a wrapping of black vinyl tape. In addition, it is shielded from external magnetic fields with a cylindrical sheet of Netic supported by felt spacers. As a magnetic shield, this high permeability metal complements the lower permeability, but more difficult to saturate, steel of the gun barrel. The PM tube is plugged into an Ortec 27o Constant Fraction Timing Photomultiplier Base, to which is fastened a protective steel cover for the entire detector assembly. The detector is ”breech-loaded” into the gun, with the center of the scintillator 74 cm from the front of the 113-cm length of barrel. Lucite absorbers of sufficient thickness to stop the maximum energy scattered protons are hung from the cantilever pipe about 1 m from the target. For 25-hev protons, the absorber is 10 cm 35 high, 6 cm wide, and 0.3 cm thick. At 35 and 45 MeV, the thickness used is 1.2 cm, and the height and width are increased to 40 and 58 cm, respectively, which eliminates most of the protons rescattered by the air toward the detector. The net detector shielding prevents essentially any radiation except neutrons, gamma rays, and occasional mu.mesons (cosmic rays) from reaching the scintillator. Charged particles, such as the mu mesons, produce ionized tracks as they traverse matter. In scintillators with several states of molecular excitation available, the longer-lived states are preferentially populated along densely ionized tracks (Bo 6h). Thus, the decay rates of light pulses resulting from molecular de-excitation will reflect the specific energy losses of incident charged particles. Neutral radiation may also interact with the scintillator through various mechanisms to yield detectable charged particles. For example, gamma ray energy is converted into electron energy through Compton scattering, pair production, and the photoelectric effect. Similarly, neutrons may be detected via charged products of nuclear reactions which they induce. In particular, if the scintillator contains hydrogen, ionization will result from protons elastically scattered by incident neutrons. Since this process has relatively 36 large and well known cross sections (as a function of neutron energy). it has been extensively exploited for neutron detection. A particularly desirable quality of NE 213 for this experiment is the relatively great sensitivity of its light pulse decay shape to specific ionization (Ni 71). This "pulse-shape-discrimination” (PSD) property, coupled with the abundance of hydrOgen in its solvent (xylene) and its rapid scintillation response, makes NE 213 ideal for detecting fast neutrons in the presence of a large gamma-ray background. D. Electronics 1. The LIGHT Signal Sophisticated electronics are necessary to obtain the maximum amount of information from the fast scintil- lator light pulses. As the block diagram in Figure 8 indicates, the present system derives three linear signals which characterize a light pulse in terms of its amplitude (LIGHT), decay rate (PSD), and time of occurrence relative to the cyclotron HF (TOP). The LIGHT signal is picked off at the ninth dynode in the photomultiplier tube by a preamplifier in the PM base. The tail pulse from the preamp is further amplified and shaped by the single-delay-line stage of a Canberra 1&11 Double Delay Line Amplifier. The llllllill].‘nl’|l( 37 NoI NE 213 SCINT. SCINT. NINTH pm LIGHT DIIL. PREAMP mu PM TUBE TSCA AMP TUBE m START 300 m PREAMP :ig 8"” CABLE QUAD CFPHT DELAY A"P TIME SPECT- SCALER PICK. AMP CONT. START "ON- SEE-Ava SCALER $7 TOF 5"” QUAD TGCA TAC DELAY GEN. DELAY DELAY DUAL AMP AMP FANDUT LINEAR LINEAR LINEAR LINEAR DUAD GATE 8. WE GATE e ‘3‘" ‘3‘" GATE aT WE GATE e m. STR. STR. STR. STR. DISC. z-ADC N-ADC x-ADC Y-ADC MDNITDR LIGHT PSD TOF SIGMA 7 COMPUTER CYCLO. RF Figure 8. Electronics '1. ll'llllll.‘ Il‘."lllllf II (III! 38 resulting unipolar signal is delayed by an Ortec #27A Delay Amplifier until it can be accepted by an Ortec #42 Linear Gate and Stretcher in coincidence with the PSD and TOE signals. Finally, the LIGHT signal is digitized for computer input by a Northern NS-629 Analog to Digital Converter (ADC). 2. The PSD Signal The double-delay-line output of the shaping ampli- fier is fed into a Canberra 1036 Timing Single Channel Analyzer (TSCA). If the amplitude of the input bipolar pulse is above a preselected threshold, the TSCA gener- ates a pair of logic signals delayed by a fixed interval from the zero crossing of the input pulse. The positive logic signal is delayed and fanned-out to open the three linear gates by an Ortec 416A Gate and Delay Generator. Since the linear gates remain simultaneously open for only about a microsecond, the LIGHT, PSD, and TOP signals are required to arrive in coincidence. The fast negative logic signal starts an Ortec 437A Time to Pulse Height Converter (TAG). This PSD TAC is stopped by a signal originating in the PM base, where a constant-fraction- of-pulse-height-trigger (CFPHT) circuit generates a fast logic signal when the PM anode pulse reaches 20% of its peak amplitude. This technique of time derivation has been shown to exhibit minimal variation of triggering 39 time relative to pulses covering a wide dynamic range (Mo 68). Control of the CFPHT threshold and fan-out for the fast logic signal are provided by an Ortec 403A Time Pickoff Control. To prevent the stop signal from reaching the PSD TAC before the start, approximately 300 m of 36-8 cable is employed as a fixed delay. An EG&G AN201/N Quad Amplifier aids in driving the cable delay. The output of the PSD TAC is delivered directly to a linear gate. This system is based on the original ”zero-crossover” PSD technique of Alexander and Goulding (Al 61). 3. The TOF Signal Another fast 10gic signal from the time-pickoff control starts the TOP TAC. Its stOp signal originates with the zero crossing of the cyclotron HF, which is detected by an EG&G Tino/N Quad Zero-Crossing Discrimin- ator. The stOp signal may be delayed by up to 25“ nsec in switch-selectable 0.5-nsec increments by an EG&G DBh63 Quad Delay Box. The output of the TOP TAC passes through a delay amplifier to bring it into coincidence with the PSD and LIGHT signals at the linear gates. 4. The Monitor Signal The output of the preamp in the monitor-detector PM base is further amplified and shaped by an Ortec 451 40 Spectroscopy Amplifier. The bipolar output of this unit triggers a logic signal output from an Ortec #20A Timing Single-Channel Analyzer when its amplitude is above a preset threshold. This threshold is selected to cor- respond to a proton energy a few MeV below the elastically scattered protons. Thus, noise and other small pulses resulting from low energy protons, gamma rays, etc. are blocked by the linear gate controlled by the monitor TSCA logic signal. E. Data Acquisition 1. TOP Spectra The w-,X-,Y-, and Z-ADC's, which digitize the LIGHT, PSD, TOF, and monitor signals, respectively, are inter- faced to the Michigan State University Cyclotron Laboratory Xerox Data Systems Sigma 7 computer. The three linear signals from the neutron detector are ana- lyzed on-line with the data-acquisition code TOOTSIE (Ba 71A). In the Setup mode of this program, coincident LIGHT and PSD signals are stored as counts in a 128x128-channel array. An example of the resulting two-dimensional histogram is shown in Figure 9. Light pulses with short decay times produce bipolar signals with early zero crossings when twice differentiated by the DDL amplifier. 1+1 influuu. ::::::::::::' "7:?" l.".. :::':l'."' 'l| I ".' . ::.:lg." O '0 I... II.'I.. . lg. " ' l .l "H” 0 I'::::::‘.' lg... n ‘ “-3.3 ”Wm" 3.7.1.232"... '3 '0»... ll'l‘l:::::'l:.l \\ chill..." \ E::::::'l|,hl I 3.."h “'II‘ I " am ogr SD Hist -P GHT LI igure 9. F 42 Thus, they start the PSD TAC sooner relative to their stop signals than pulses with long decay times and yield larger PSD signals. The largest PSD amplitudes in Figure 9 result almost exclusively from electrons Compton scattered by gamma rays in the scintillator. Since they yield about the same specific ionization as high-energy electrons, "cosmic" mu mesons may also contribute to the "lepton ridge." Protons recoiling from elastic collisions with incident neutrons are responsible for the other prominent cluster of events in Figure 9. Another cluster, due to alpha particles from reactions induced by high- energy neutrons on carbon in the scintillator, has been observed still farther down the PSD axis. The program displays "cross sections" of the histogram, which indicate the channels containing numbers of counts between selected upper and lower bounds. An example of the Setup mode display, as viewed on a Tektronix 611 storage scope, is shown in Figure 10. The user is allowed to define "bands" between pairs of polynomial fits to selected points in the LIGHT-PSD plane. The bands define digital gates used by the program in the Run mode to route TOF signals into separate one-dimensional spectra. For this experiment, "neutron" and ”gamma-ray" bands have been drawn around the proton and lepton clusters, respectively. To avoid losing neutrons, the line between the neutron and gamma-ray bands has generally been constructed slightly closer to the Illlx.I-IsI’III.I. Ill-Ills! II III! I III' lull [III' I ‘IJGYIJ.II'.II||. T‘ 0:63 9”"lean 0:» Eu .3 hlmtdlfldo «a». €93.50! .0.“ gen 44 gammas. Superimposed neutron and gamma-ray TOF spectra obtained in the Hun mode are displayed in Figures 11 through 22. Each figure contains spectra taken at 0°, where the flight paths were generally longer than those employed for scattering angles between 10° and 160°. Since the TOP TAC is started by the neutron detector and stopped by the cyclotron HF, flight time decreases with increasing channel number. Thus, faster neutrons appear to the right as in conventional energy spectra. These TOF spectra have been calibrated at about 0.1 nsec per channel. Thus, the prominent peaks in the gamma-ray spectra, which are due to prompt decays of excited states in the targets, exhibit time resolutions of about i nsec (FWHM). Since the system consisting of the neutron detector and associated electronics has measured gamma-ray burst widths of 0.2 nsec, the typical s-nsec widths are attributed for the most part to the time structure of the incident proton beam pulses. In the spectra taken with 25-MeV protons on the 120Sn and 208Pb targets, leakage of the target gamma-ray burst into the neutron band is visible. Since the relative amount of gamma-ray “feed-through” is not time correlated, the fraction of gamma-ray counts leaking into any channel of a neutron spectrum may be conveniently estimated by comparing the areas of the target gamma-ray peaks in the some so msoooam >ozinm you 00 as oupooom mos admisaamu one soupsoz .HH madman mmmzzz JwZZcz mm n J 1. mzomsz In 82.2.38? a a a a a a a L _ L co... as HNom so msopoam >mzimm you 00 as suuooam mos homisaamo one nonusoz .NH oaawam mmmzzz nmzzcz mm n am «.28sz II szsmEaENsm _ e _ a a a a L a cow“ 4? 'IBNNVHCJ/SLNI'IOC) NOHLHEN :momH so msououm >ozimm no“ 00 no caveman moa nominaaso use convocz .ma oasmam mmmzsz szzozimm you 00 pm sauomqm moa ammimasso and soapsmz .:H madmam mmmzsz szz2 mm n J mzomezmz Tl mesmzésasom a _ _ a e _ _ _ a _ oomfl {Till ll .l'l litllli‘JalIll-Il ‘Illlili‘i‘ Ill 49 some so mcouoem >ozinm Mom 00 on «Moscow moe hsmTeESdo use soapsoz .mH oaswaa mmmzzz T_wzz2; mm n J mzomsz Tl 89.2.38? _ T_ e _. a T_ _ _ a a _ _ _ _ _ a Onzw 50 aNom no msouoam >ozumm you 00 as supooam hoe asmasaasc use coeusoz ‘IBNNVHO/SLNHOC) NOHinEIN .wa oesmaa mmmznz mmzz02 mm H w T mzomsz Tl szsm2.3._N8 e _ _ _ _ _ _ _ Onzw 51 enema no mGOuOHm bozimm no» 00 as shuocnm mos homisaamo use coausoz .mfi seawam mmmzzz nwzz2 mm .T. J T mzomsz Tl £§236§ . a _ . _ a u _ oooN 52 pmmom so msouoam >mzimm you 00 no mauooam mos maximaaso use souusoz .mH oesmam mmmzzz JwZZm2 mm N am T mzomsz TI imsom23§som T a _ a _ a _ Te a a _ _ _ a b .7 a com 53 some so mcouoam bozim: now 00 as «Museum mos hsmidaamc one coausoz .mH oaswam com mfi T o .T. a T 2228.! 2.: m... n J 828sz TI 8?2.38? _ _ _ _ a _ _ _ _ mo mwmznz T_wzzozlm: you 00 no snuooam mos ammioassu use nouusoz .om chewam mwmzzz TEZZ02 8.. u m T mzomezmz IlT nzomficénNom .T. _ a _ _ r, _ _ _ TT_ a r ooofi 55 .Hm shaman 'EINNVHfJ/SINHOIJ NOHJJ'IBN smoma so msopoam >oxim: you oo no «Museum hoe msmisasso use soapsoz mmmzzz 4wzzczim¢ you 00 as mauooam moa msmioasmo one nonusoz .mm shaman mwmzaz szz025“. 92 hmzasa zokaJo>U 3w: H 30’0ka 3' ('0 (AW!) AQUBNB N a 06070ka :r 0‘) CU 63 57.6, and 51.0 nsec, respectively. Thus, most of the TOP spectra in Figures 11 through 22 cut off abruptly at channel numbers between 500 and 700. Figures 15, 18, and 27 display ”doubled" spectra for which this problem has been overcome by eliminating alternate stop signals with a divide-by-two sealer. However, since the proton beam bursts remain separated by THF’ channel numbers still only correspond to flight times modulo THF' For all practical purposes, this ambiguity may be removed by raising the threshold on the TSCA to discriminate against slow neu- trons from a given beam burst which are caught by the fastest neutrons from the following burst. The TSCA threshold for Figure 27 corresponds to a neutron energy of about 6 MeV. With this level, the neutron spectrum is sufficiently suppressed at high excitation in the residual nucleus to avoid overlap with the ground state. If a larger dynamic range is desired, it may only be obtained by eliminating all but one beam burst out of every N in succession. This technique is currently implemented with an external beam deflection system known as the "beam sweeper.“ unfortunately, throwing away beam bursts reduces the current on target. Raising the TSCA threshold also cuts down the counting rate, even for high-energy neutrons, since neutrons of a given energy are potentially detect- able via faint scintillations induced by recoil protons with.much lower energies. Thus, it is generally necessary 64 a com a _ a omk asauooam mOBTSOAusoZ soapson mwmzzz 4wzz02 mm H w nzomflcésNem dT .nm madman om“ oom _ mm: mozuaa.a .>ozTam.H one wsaeeonom son 8 wooasoszoaowm .mm seamed mmmznz szz0: m: n m T HaaaqHCmoNH looom _ _ _ _ a r. F _ a F oooofi 7O 3. Charge Collection Compared to the best charged-particle detectors, the present neutron TOF system affords poor energy resolu- tion and detection efficiency. Thus, relatively thick targets (about 10 mg/cmz) have been used in this experi- ment to compensate for the lack of efficiency with little sacrifice of resolution. Another difference with typical charged-particle experiments is the relatively large distance between the target location and the beam dump, which reduces the neutron background from the dump for most scattering angles. Unfortunately, the thick targets scatter a lot of the beam, making charge collection in the distant Faraday cup incomplete. The quadrupole triplet following the scattering chamber refocusses much of the scattered beam into the dump Faraday cup, but the accep- tance of the magnetic lens is limited (see Section II.A.2). For the worst case in this experiment, 45-MeV protons incident on a 30-mg/cm2 208 Pb target, multiple-scattering calculations indicate that almost 20% of the beam would not be transmitted to the dump. Therefore, a secondary Faraday cup has been created by insulating the beam pipe between the scattering chamber and the dump. From the target, it subtends 0.050 radians out from the beam-pipe axis, which is approximately twice the angular acceptance of the quadrupole triplet. At 50 milliradians, single Rutherford scattering is more than an order of magnitude 71 more probable than multiple scattering of 45-MeV protons from the 30 mg/cm2 208Pb target. Even for this extreme case, less than 2% of the beam is scattered beyond the acceptance of the total charge-collection system. Current from the beam-dump Faraday cup is integrated and sealed with an Ortec 439 Current Digitizer coupled to a Tennelec TC 555P Dual Counter/Timer. The same functions are per- formed for current from the beam-pipe Faraday cup with an Elcor A3103 Current Indicator and Integrator. 4. Dead-Time Measurement Several components of the TOF system have processing times for electronic signals during which they are unre- sponsive to additional input. The data-acquisition code TOOTSIE and the TOF TAC have minimum processing times of approximately 60 and 5 microseconds, respectively, which introduce the only significant dead times into this exper- iment. The fraction of input signals converted by the TOF TAC is measured directly by counting positive logic sig- nals from the time-pickoff control and the true-start output of the TAC with Ortec 430 Sealers. Similarly, the ratio of events stored with TOOTSIE to the number input is given by the quotient of the charge counts recorded in the Channel-Zero register of TOOTSIE and the beam-dump scaler. During this experiment, the CFPHT-circuit triggering rate was monitored by an Ortec 441 Ratemeter and 72 maintained at less than 10 kHz, which kept the total dead time of the system under 15%. F. Data Reduction 1. Spectrum Calibration To calibrate a TOF spectrum, it is necessary to ascertain the time interval per channel (TC) and the flight time corresponding to channel number 0 (To). TC is conveniently determined by taking a doubled spectrum and dividing the interval between successive gamma-ray bursts from the target by the cyclotron RF period. The result is input to the spectrum-calibration and peak- fitting code ANNIE (Do 73), along with TOF spectra and additional data acquired from a subsequent series of runs. The program first performs a non-linear least- squares fit to the gamma-ray burst from the target with the function F(T) = %A(erf(T+) - erf(T_))/DT + B, (II-2) where -1 + l T+ = 2 g(s/c - T - TDT)/SG, T = TGO - TCI, DT = (n-1)D3/C, 73 B a 30 + 31(1-10) + 82(I-Io)2. C is the speed of light in vacuum, I is channel number in the gamma-ray TOF spectrum, I0 is the center of the fit interval, and n and D3 are the refractive index and thick- ness of the scintillator, respectively. Apart from the quadratic background (B), this function is the convolution of a Gaussian time distribution representing electronic plus beam-pulse time spread with a rectangular distribu- tion resulting from the speed difference between gamma radiation and visible light in the scintillator. The refractive index of NE 213 is 1.508. Thus, light pulses from molecular de-excitation traverse the scintillator only about 2/3 as fast as incident gamma rays. The search parameters are the area (A) and standard deviation (86) of the Gaussian distribution, the gamma-ray flight time corresponding to channel number 0 (T60), and the average magnitude (Bo), slope (Bl), and curvature (82) of the background. In general, the neutron flight time for channel number 0 is given by where N is the number of RF periods between beam bursts responsible for simultaneously observed neutrons and gamma rays from the target. Thus, the neutron flight time 74 corresponding to channel number I is given by TN 2 TNO - TCI. (II-4) The relativistic relationship between flight time (T) and kinetic energy (E) is T = S(1 - (1 + s/soi'2)‘*/c (II-5) for a particle with rest energy E0. This is evaluated for neutrons from the IAS of the target, and the result is compared with flight times calculated with Equations II-3 and II-4 for the minimum and maximum channel numbers of interest and increasing values of N. Thus, for some N, the TNO which calibrates the neutron TOF spectrum for the appropriate range of flight times is determined. Finally, the calibration is converted from flight time to neutron energy with E e Eo((1 - (S/(CT))2)-% - 1). (II-6) which is an inverted form of Equation II-5. The program also calibrates the gamma-ray TOF spectrum in terms of distance along the beam line to potential sources arising from protons striking the pipe. This is often a useful diagnostic for aligning the beam or placing local shielding. 75 2. Peak Fitting In addition to calibration, ANNIE is used for extracting the areas, widths, and centroids of peaks in the neutron TOF spectra. As for the gamma-ray fit, the search routine CURFIT (Be 69A) is employed to vary a parameterized peak-plus-background function until the quantity defined by 2 N 2 x = 1:1(Y1 - F1) /Y1 (II"7) is minimized to the extent of not changing by more than a specified convergence criterion between successive iterations of the search. In this definition, 1 labels the channels within the selected interval where the experimental yield per channel (Y1) is to be fit with the theoretical function (F1). CURFIT is based on a very efficient algorithm (Ma 63) which essentially starts with a gradient search and then smoothly switches to an ana- lytical search (linearizing the fitting function) as the minimum value of 962 in the parameter space is approached. The neutron peaks are fit with a fairly complicated function, which results from attempting to realistically account for all conceivably significant contributions to the observed line shape. The sources and assumed forms of these contributions are listed in Table 1. The total fitting function consists of a quadratic background plus (1) (2) (3) (4) (5) (6) (7) 76 Table 1 Neutron Resolution Function Component Source Assumed Distribution Electronic plus Beam Burst Time Spread Gaussian Scintillator Transit Time Rectangular Target Energy Loss Rectangular Target Energy Straggling Gaussian Beam Energy Spread Gaussian Kinematic Broadening Rectangular Intrinsic State Width Lorentzian 77 a seven-fold integral over these individual distributions, four dimensions of which have been integrated analyti- cally. The remaining three-dimensional integral for the neutron resolution function is evaluated numerically. The primary need for such a program results from the assumed Lorentzian (Breit-Wigner) intrinsic line shape of the isobaric analog resonances (La 69). The normalized Lorentzian distribution is L(x) = __i_ T/2 9 1T (X-Xo)z + (TH/2)?- where x0 is the centroid and T“ is the width (FWHM). The (II-8) tails of this function fall off as X'2 and are generally indistinguishable from a quadratic background. This is demonstrated in Figure 30, which shows a Gaussian peak (upper line) plus a quadratic background (lower line) fit to a Lorentzian distribution on a constant back- ground. A good fit is obtained, but the Gaussian width and area parameters determined by the search are only 80% and 38%, respectively, of their counterparts for the Lorentzian ”data.” {In this example, the fit interval encompasses 1.5T" out from the centroid. As this inter- val is extended, the discrepancy gradually diminishes. By 51‘ , the Gaussian-plus-quadratic fit gives 62% of the Lorentzian area. The increase results from an improved determination of the background. However, a clear fit interval of even :51” is often unavailable in actual 1.5TTTTTTTTTTTTTT T)+-++-++~+-T+-++-+4-+-r+-++-++-+-t+-++-+4-+-P+TT — A (LS— — - GAUSSIAN-PLUS-OUADRATIC FIT + LORENTZIAN + BACKGROUND )— -—4 + BACKGROUND O.OTTTTITTTTITT41 0.0 0.5 1.0 1.5 x [T/2] Figure 30. Gaussian-Plus-Quadratic Fit to a Lorentzian Peak l 11»: T T. :5 .‘ I'll-u. Illa Ill Till! Ililll. 79 spectra. Furthermore, even if the background in the vicinity of the centroid were exactly known, there would remain a large uncertainty in the area contributed by the tails. This is due to the fact that only 80% of the area of a Lorentzian distribution is within 11.57' of the centroid, whereas the comparable figure for a Gaussian distribution is over 99.9% The most significant improvement resulting from the inclusion of a Lorentzian intrinsic line shape in searches on the present data is obtained for the IAS of 208 Pb, since it has the largest natural width. Figure 31 dis- plays a pair of fits determined with ANNIE for this state. The fit incorporating a Lorentzian intrinsic shape gives 50% more area above its background than the one based on a Gaussian line shape. Total cross sections of 7.1 I 0.8 and 9.2 I 1.0 mb have been obtained from IAS peak areas extracted by hand and with ANNIE, respectively, for 208Pb(p,n)208Bi at 25 MeV. Only the latter value is in agreement with the corresponding (p,np) cross section of 10.0 I 1.0 mb (Cr 74). 3. Neutron Detection Efficiency The efficiency of the neutron detector described in Section II.C.2 has been calculated with a modified version of the code TOTEFF (Ku 64). Basically this program evaluates probabilities that an incident neutron 80 moasoawxosm causaomsd mafia mxsom Aeonmouv codename one Audaomv swampsoaoq suds yam pmmow do mma .Hn 99»: >omwzm 205.ij m.m o.m m.m l T 2.: mmusm T T as: 8.823.288 T enswam Doom 0 nu NH MN I. nb 88 W Hm UV MN MW :4 fll Door 1I ll Iii All I'll-Ill I'll I ll." ... l] I: I 81 of a given energy will induce nuclear reactions whose charged products create more than a specified amount of light. The quantity of light produced in a particular scintillator by an electron losing 1 MeV is the ”Light Unit" (L.U.) used in TOTEFF. The light threshold is controlled with the TSCA. Thus, it is necessary to calibrate the TSCA discriminator dial in Light Units. This has been accomplished in two stages. First, light pulse-height spectra have been taken for the gamma-ray sources listed in Table 2. Only Compton edges are prominent in gamma-ray spectra obtained with such a low-Z scintillator. The Compton edges have been fit with electron-recoil spectra derived from the Klein-Nishina formula (Da 65) and folded with a centrally-Gaussian light-resolution function with expo- nential tails. A typical fit is displayed in Figure 32. The search parameters are a normalization factor, the energy per spectrum channel, and the standard deviation of the Gaussian distribution. The latter is used to determine the fractional light-energy resolution at the Compton edge, which should be inversely prcportional to the square root of the energy loss in the scintillator, as previously discussed for the monitor detector (see Section II.C.1). This is plotted in Figure 33 for each Compton edge and each voltage applied to the PM tube. Since the maximum proton recoil energy in the 82 Table 2 Gamma-Ray Sources for Neutron Detector Calibration Source Gamma-Ray Energies (MeV) 22Na 0.511, 1.275 13708 0.662 228Th 2.615 15000 10000 COUNTS/CHANNEL 5000 0 83 TTPTTTTTFFTTTTTTTTTTTTTTTTTTF g 22No T-SOURCE _ )—— iJTTTTTTlTiTTTTTTTlTTTTTTTT 0.9 1.0 1.1 1.2 ELECTRON ENERGY [MeVJ' Figure 32. Fit to thezgompton Edge for 1.275-MeV Gamma Rays from Na .II T l l ' .1 1 III I]! I1 . 84 pOpooumn conusoz 0:» mo coapdaomom pgwaq @6828 29:88 58,2328 no >czfi\: 23:23 m4 o; m6 0.0 a a a a _ a .4 a _ a _ a a _ 1 fl 1 7 T 1. T T \\ 1. I. fl 1 H ommT o H T OWTHI U l I 09.7 o I mo in. T T _ _ e a. _ _ _ _ a _ _ _ _ _ 1 3 ma 0N .mm madman [X] NOIIH'IOSEIH IHGIT 85 scintillator increases with the proton energy on the target, it is necessary to lower the PM voltage to avoid saturation of the detector output as the bombarding energy is raised. In this experiment, the PM tube has been oper- ated at 1550, 1450, and 1400 volts for proton energies of 25, 35, and 45 MeV, respectively, and a separate light- threshold calibration is required for each. Additional pulse-height spectra have been taken with a series of TSCA discriminator settings, which cut off the spectra at a set of corresponding channels. ,Since the channel- energy calibration has been previously determined by the fits to the first group of spectra, this second group completes the calibration of the TSCA discriminator dial in Light Units. The relation between dial setting and "equivalent electron energy" is plotted in Figure 34. Since the neutron TOF spectra are gated by a band in the LIGHT-PSD plane which encompasses predominantly proton light pulses, only the probabilities for neutron- induced reactions producing protons in the scintillator have been summed to yield the total detector efficiency. The relevant nuclear reactions included in TOTEFF are n-p scattering and 12C(n,p)1zB. The probabilities that these reactions will be induced by final-state neutrons 12C(n,n'30<) and n-p scattering are also considered from in the total efficiency. Fortunately, the detection efficiencies calculated for the neutron energies in this 86 nouocpon coausoz on» mo coauonnaamo uaonmeanalunwa . m :0828 205888 58:58 no >sz 39885 agreeing a 3 m m m m m +. m N H o so I. Q I. T 89.. o .u H n owl- D H 1 T QQZT a . e T S I 1 3 I w .T V I UTE/CTR; 2d . 1H 1 I T .T Hm I . 1 H T T 3 T .1 ho T T H II ‘ . I. m T T O IJ I MNTAJ T .. m T T 1 T T 8 l 1 TCC::::.E::: :EE::::_::::_::_ :E::::_:::C::::::::E m 87 experiment result almost exclusively from relatively well determined n-p scattering cross sections. The original n-p angular distributions in TOTEFF have been replaced with values derived from the Yale phase shifts (Ho 71). A few of the carbon reaction cross sections have also been adjusted to agree with recent measure- ments. The remaining significant differences between the original and present versions involve the properties of particular scintillators. The scintillator density, hydrogen-carbon ratio, and light response as a function of proton energy (”light-curve”) have been replaced with appropriate values for NE 213. In particular, the proton light curve presently employed is L(E) = 0.863E (11‘9) _ 3,96(1 - exp(-0.18530.862)) L.U., where E is the proton energy in MeV. This function has been determined by fitting NE 213 data (Ve 68) with a parameterized form previously used for NE 102 (Go 60). Figure 35 displays the efficiency of the detector discussed in Section II.C.Z as a function of incident neutron energy for the lowest and highest light thres- holds used in this experiment. Although the efficiency tends to peak not far above threshold, the present data has been acquired in the region where the efficiency is less sensitive to small variations of energy and threshold. 88 TUTTIITFTIITITIITTIIIIIT 15'— ._T S I UI l NEUTRON DETECTION EFFICIENCY [7.] I _ THRESHOLDS a 011111111J1LU11111L1L11 0 10 20 30 L+0 50 NEUTRON ENERGY [MeV) Figure 35. Efficiency of the Neutron Detector 89 4. Neutron Attenuation The attenuation of a neutron beam traversing a compound medium is given by I/I0 = exp(-O.602(D/W)ZN101) , (II-10) i where IO and I are the initial and final intensities, D and W are the areal density in g/cm? and the molecular weight of the medium, and N1 andTOi are the number of atoms per molecule and removal cross section in barns for the igg'nuclide in the medium. In general, the removal cross section is less than the total neutron cross section since some neutrons may be elastically scattered into the beam. For the present geometry, this corresponds to neutrons from the target being scattered into the detector by, e.g. the air. The absorbers discussed in Sections II.B.1-2 (mylar, aluminum, lucite, and air) are generally several meters from the detector, and neutrons elastically scattered by them at all but very forward angles are attenuated by the shield- ing on the air cart and delayed by longer flight paths en route to the detector. Thus, the removal cross sections have been equated to the total neutron cross sections for these media. In contrast, elastic scatter- ing from the materials immediately surrounding the scintillator (principally reflectance paint and glass; 90 see Section 11.0.2) is not significantly attenuated or delayed with respect to neutrons incident directly from the target. Thus, only the nonelastic neutron cross sections have been used for these absorbers. All cross sections have been obtained from the Brookhaven National Laboratory Sigma Center compilations. Table 3 lists individual neutron attenuation factors and their product for a typical run in the present exper- iment. In this case, the number of neutrons from the IAS of the target which reach the detector has been reduced approximately 10% by nuclear reactions occuring along the flight path. Values ranging from about 5% to 20% have been calculated for the other runs. 5. Targets The “80a, 90Zr, 12OSn, and 208Pb targets used in this experiment are self-supporting, rolled foils with thicknesses of 1-30 mg/cm2 and isotopic enrichments in excess of 96%. Detailed target prcperties are presented in Table 4. The average thicknesses have been deter- mined directly from measured weights and areas. Uniform- ity has been checked by comparing the relative energy losses of 5.5-MeV alpha particles through several regions 2 120Sn and 208Pb targets. of the approximately 10-mg/cm The central densities differ from the average values by less than 5%. The other targets are too thick to be 91 Table 3 Neutron Attenuation (En = 11.59 MeV) Absorber Th_ckness (cm) I110 Air 463.00 0.965 Aluminum 0.00 1.000 Class 0.25 0.982 Lucite 0.32 0.963 Mylar 0.05 0.994 Paint 0.08 0.994 Total -- 0 .900 92 Table 4 Target Data Target Areal Density (mglcmz) Isotopic Enrichment 1%1 “80a 1.08 96.25 9°2r 2.00 97.80 9°Zr 3.00 97.80 9°2r 10.19 98.66 9°2r 10.03 98.66 12°3n 9.90 98.40 12°3n 9.58 98.40 208Pb 5.40 99.14 208Pb 10.22 99.14 208Pb 9.26 99.14 208Pb 30.00 99.14 208Pb 10.05 99.14 208pb 30.20 99.14 1‘!l|.l [Illllll III.I.IIT 93 measured with the alpha gauge, except for the 480a target, which is maintained under vacuum to inhibit oxidation. 6. Cross Sections For a reaction which may be asymptotically repre- sented as two-body scattering, the differential cross section may be defined by 0(6) =fi§§<6h (II-11) where N is the number of particles in a beam incident upon a target with n scattering centers per unit area and I is the number scattered through an angle 9 into a solid angle fl. For the present experiment, Equation II-11 is equivalent to YMcos(O<) = -5 0 ( e) 2.66x10 PQDE(1"T) (1-1“!) mb/sr, (II-12) where I is the number of counts in the IAS peak in the neutron TOF spectrum taken at the scattering angle 9, M is the atomic mass of the target in amu, CK is the angle between the normal to the target and the incident beam, P is the percent isotopic abundance of the target, Q is the time integral of the beam current in microcoulombs, D is the areal density of the target in mg/cmz, E is the fractional efficiency of the detector for neutrons from 94 the IAS of the target, T is the fractional dead-time of the electronics and data-acquisition system, A is the fractional attenuation of neutrons along the flight path, and I) is the solid angle subtended by the neutron detec- tor. Table 5 lists the IAS differential cross sections calculated with Equation II-12. Scattering angles and solid angles as measured in the center-of—mass (c.m.) coordinate system have been used. The dominant source of relative errors in the angular distributions is the neu- tron yield. The errors given in Table 5 result from combining in quadrature statistical and systematic uncer- tainties in the peak fitting. Since the IAS peak area (yield) is a search parameter, its variance is the cor- responding diagonal element of an "error matrix” which is the inverse of the "curvature matrix” defined by N 6F ()1? c = .1- Ti 1 , II-i Jk f; Y1 P1 3?]; ( 3) where PJ is a search parameter and the remaining quantities are defined as in Section II.F.2 (Be 69A). In addition to these statistical errors in the yields, the search program has been used to evaluate the system- atic errors due to uncertainties in the IAS intrinsic widths. 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Additional searches have also been Sn, and performed with the largest widths consistent with these values. The resulting differences in yields have been used as the appropriate systematic errors. The principal error in the absolute magnitude of the cross sections is the estimated 310% reliability of the neutron detection efficiency calculations (Ku 6# and Th 71). There are also small uncertainties in target thickness, beam current integration,and neutron attenu- ation along the flight path, which may introduce additional systematic errors estimated to be less than 5%. The differential cross sections in Table 5 have been integrated over scattering angle to yield the total cross sections listed in Table 6. The corresponding errors have been obtained by adding the aforementioned relative and absolute errors in quadrature. 100 Table 6 (P.n)-IAS Total Cross Sections Target Ep (MeV) 01' (mb) “80a 25 10.6 t 1.2 35 10.2 t 1.1 45 8.4 i 1.0 9°2r 25 6.7 t 0.8 35 4.8 t 0.5 as 4.4 t 0.5 120521 25 8.5 I 1.0 35 5.6 i 0.6 45 5.8 1 0.7 208Pb 25 9.2 t 1.0 35 6.7 t 0.8 1 45 5.3 0.6 ..... III. DATA ANALYSIS A. Calculations Except for the presence of an effective two-body scattering Operator rather than the free two-body potential, the direct scattering amplitude in the single-inelastic-scattering approximation (Equation 1-14) is equivalent to the corresponding DWBA amplitude (Equation I-12). Thus, if the effective interaction defined by Equation I-13 may be represented by a local pseudOpotential such as in Equation I-16, conventional DUBA programs may be used to compute the cross sections. The theoretical angular distributions in Figure 36 have been calculated with the code DWBA7O (So 70), which incorporates the helicity formalism developed by Baynal (Ba 67). This program is applicable to inelastic scattering and charge-exchange reactions in which the state of the residual nucleus may be expressed as a sum of particle-hole pairs with respect to the target ground state. Thus, the scattering amplitude is decomposed into a series of terms each representing the creation of a particle-hole pair with a spectroscopic amplitude (Ma 66) defined by ZJ(np,nh) a (2J+1)'*(2JI+1)'*<‘I>FIA}'(np,nh)I(1)1) , (111-1) 101 102 woodpsnauumdn amaswcd m3. mm m >21 mm m a I VVVV'V V T I Y .Q 0. (D O (\J C (D C) (\l H L N o 07 O (.3 a) :- >>bebbh>>+>pPP-P‘PbrrphanP*-p Pphh >>Pb>b+PnnPanp >bb>?P>>>b->>b> OOfl 103 where J is the total angular momentum transferred, JI is the spin of the target, and A}(np,nh) is the creation Operator for a particle in a state labeled by np and a hole in state nh, with their angular momenta coupled to J. For charge-exchange transitions between J"=0+ analog states, Equation III-1 may be reduced with the aid of Equation I-18 to 20m = (23n+1)'*(2r,)‘* Zlcm|2-T;n. m (III-2) where I = Teams.) = §°mlll¢n>w ¢n is a ”single-particle orbit” (Bo 69) with quantum numbers labeled by n (e.g., its angular momentum in), m labels the occupation numbers for the orbits and the couplings required to complete the specification of a particular term in the target wavefunction, and TInn is the combined isospin of the nucleons in the nth orbit for the nth term. For the present analysis, the ground of 120 state an has been represented by a BCS wavefunction based on average occupation probabilities derived from 1218n (61 67). phenomenological values for 119Sn and Elementary shellemodel configurations have been assumed for the other targets: (if7/2)8, 0.8(139/2)1° + 0.6(139/2>8(2p1/2>2. and (ing/2)1°<2r7/2)8(1113/2>14 104 2 ) for the excess neutrons in (3p3/z)u(2f5/2)6(3p1/2 90Zr, and 208Pb, respectively. The single- Ca, particle wavefunctions have been calculated in a potential well of the form U(r> = -U0f(r) + USOAZ fig; f(r)_2_L_-g , (III-3) where 1/3 r = (1 + exp>‘1; £"0 1'2 = J(J+1) - 1(l+1) - s(s+1); r0=1.3 F, a0=0.7 F, A =2.0 F, USO=6 MeV, A is the mass number of the target; 1, s, and J are the orbital, spin, and total angular momentum quantum numbers, respec- tively, of the bound nucleon; and U0 has been adjusted to reproduce the observed binding energies (except for the unbound IAS protons in 9°Nb, 1208b, and 20831, which DWBA7O treats as bound by 0.01 MeV). The binding energy of a neutron in a particular target orbit is the separa- tion energy of the least bound neutron (Na 71) plus the excitation energy of the corresponding neutron-hole state in the isotope of the target element with mass number A-i. The binding energy of a proton in the ”analog" orbit is reduced from the neutron value by the amount of kinetic energy converted into mass by the (p,n)-IAS reaction, which is 7.175 MeV for a “BCa target 90 120Sn (Ba 70), 12.03 MeV for Zr (Ca 72), 13.41 MeV for 105 (Ca 72), and 18.82 MeV for 208Pb (Cr 72). The optical- model potentials used for the proton and neutron distorted waves have been taken from the ”Coulomb- corrected” analysis of Becchetti and Greenlees (Be 69). If the optical-model and bound-state potentials were the same, the exchange scattering amplitude in Equation I-# would reduce to the "knockon" amplitude (Au 70A), which is evaluated by DWBA70 without a local approxima- tion (Fe 70). The dashed curves in Figure 36 result from phenomenological nucleon-nucleon forces consistent with Austin's analysis (Au 72). In particular, the effective interaction has been taken to have the form given in Equation I-16, with a 1.0-F-Yukawa radial dependence and V0=-27 MeV, V3=Var=12 MeV, and Vt=12 and 18 MeV. The solid curves have been calculated with a realistic force derived from the Reid soft-core potential (Re 68) by Bertsch (Be 72B), who employed the method of Barrett, Hewitt, and McCarthy (Ba 71) to solve for the corresponding G-matrix in a harmonic- oscillator basis. For compatibility with DWBA70, a superposition of four Yukawa potentials (with ranges of 0.2, 0.4, 0.5, and 0.7 F) has been determined by fitting harmonic-oscillator matrix elements to the original G-matrix (B0 74). Only the central, even-state terms have been retained for the present calculations, a ll .Ii 1 ll. 4 ‘1 w 106 since the central, odd interaction appears to be weak (Ba 74). B. Results Both the phenomenological and realistic forces yield angular distributions which follow the data but are somewhat smoother. The similarity in shape of the dashed and solid curves in Figure 36 results from the 0+-s»0+ IAS transition being dominated by the monopole component of Vtgt(r13). With the 1.0-F-Yukawa form for 819 the average values of Vi required to reproduce the (p,n)-IAS total cross sections (Table 6) measured at proton energies of 25, 35, and #5 MeV are 19.6, 15.3. and 13.3 Mev, respectively. The spread for individual targets combined with the experimental errors (Section II.F.6) indicates that these values are reliable within about 12 Mev, which suggests that Vt is now determined in this energy range at least as well as V0 and “at (An 72). The present phenomenological values of Vi are con- sistent with the microscopic analysis of Batty g§_gl. for (p,n)-IAS reactions on 27Al, 5“Fe, and 56Fe at 30 and 50 MeV (Ba 68). There is also agreement with the isospin-flip strength extracted by Clough g§_§;. from (p,n)-IAS transitions in ip-shell nuclei at 50 MeV (01 70). However, their value of Vt at 30 Mev, even 107 when corrected for the lack of an exchange amplitude in their calculations (Au 72), is about 50% larger than that indicated by the present study. This discrepancy may simply reflect the greater sensitivity which they observe to the selection of optical-model potentials for the calculations at 30 Mev coupled with the rela- tively large uncertainty in this choice for such light nuclei (Gr 68, Ho 71“. The G-matrix interaction produces nearly the same cross sections for the reactions investigated in this work as a 1.0-F-Yukawa potential with Trail-b MeV. Thus, it accounts for the data quite well at 45 Mev and fairly well at 35 MeV. However, the experimental cross sections at 25 MeV’are consistently larger than pre- dicted. Love and Satchler have found the same difficulty for 90Zr(p,n)9oNb(IAS) at 18.5 MeV in a study employing another realistic effective interaction (Lo 70), the long-range part of the Hamada-Johnston potential (Ha 62). The volume integrals of the isospin-flip components of this potential and the long-range part of the Kallio- Kolltveit potential (Ka 6#) are the same as for 1.0-F Yukawas with lift-“'12 and 14 MeV, respectively (Au 72), in close agreement with the monOpole charge-exchange strength of the G-matrix for the Reid soft-core potential. 108 The great similarity of the IAS and ground state wavefunctions generally produces large (p,n)-IAS cross sections which are relatively insensitive to details of the DWBA calculations other than an approximate prcpor- tionality to vfi. In particular, additional calculations have been performed for 90Zr(p,n)90Nb(IAS) at 35 MeV with ‘I’GS=(1g9/2)10, ro=i.25 and a0=0.65, the Becchetti- Greenlees "best-fit” Optical-model potential (Be 69), and noncentral (spin-orbit and tensor) components of the G-matrix interaction (B0 7“), all with very little effect on the resulting angular distributions. Unfor- tunately, the M.S.U. version of DWBA70 has no provision for including an imaginary term in the effective inter- action, the influence of which would also be interesting to investigate. For (p,p') reactions, it has been noted that a complex force generally yields a relative increase of the forward-angle cross sections and enhances the overall oscillatory structure of the angular distribu- tions (Sa 72), both of which would improve the agreement of the theoretical curves in Figure 36 with the data. The phenomenological values for Vt(Ep) obtained in the present study give slopes of -0.# and -0.2 for the ranges 25-35 and 35-45 MeV, respectively, in contrast to a corresponding number of about -0.83 for 30-50 MeV (-0.75 with exchange corrections (Au 72)) derived from the previous work of Clough et al. (Cl 70). 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