. .-.g... .u...‘ ~-.. on G.“ N re) . 7 {mi 2133 'eV In t V... Au askwkn . 5.3% mm, s 4.! a, . «Ham? .. N M 53*er 5ka THE M N ICHIGA F, 0 [Q L a it... 1‘ n3. , ‘3. V, o N .. l . 4.1 wt : ‘ Gil. om. IDJILEr-o .33! r 0: 2.3. . .- This is to certify that the thesis entitled A SURVEY OF THE ( 3He , 7Be) REACTION AT 7 0 MeV presented by William Frederick Steele has been accepted towards fulfillment of the requirements for _Eh‘_D_._degree in _Eh¥sics__ .- l a; v- .. . g . ‘. .l 'v " . - . 4.7 74" 0-7639 4! ‘ E .I in BLUUK B‘NUERV "It; R 1 mND .SLPIFL: mu m IWC "£31 '._:'_ _.a.. ‘ ABSTRACT A SURVEY OF THE (3He,7Be) REACTION AT 70 MeV BY William Frederick Steele Using the 70 MeV 3He beam of the Michigan State Univer- sity cyclotron, a study of the (3He,7Be) reaction has been undertaken. By surveying a wide range of target nuclides, namely 12’13C, 150' zurstg' “°’“°Ca, SBIGOIGZISNNi' 9°Zr, 120”2"Sn, l"“Sm, and 2”Pb, systematics of the a clustering phenomenon are investigated. In addition, masses and energy levels of ““Ar, 6°Fe, and 12°Cd are measured. In order to assure adequate resolution for a large acceptance solid an— gle, an Enge split pole magnetic spectrograph is used to analyze momenta of the reaction products. A single wire gas filled proportional counter measures the relative pos- itions of the ions as they cross the magnet's focal plane. Taking advantage of the well defined time structure of the cyclotron beam, charged particle time of flight, together with the proportional counter energy signal, is used for particle identification. Despite the relatively low yield, excellent particle identification is achieved. Differential cross sections as low as 200 nb/str are successfully measured. The finite range DWBA program LOLA of R. M. DeVries has been used to calculate reaction differential cross sections for comparison to data, assuming the reaction to proceed by a direct a transfer mechanism. a spectroscopic factors are William Frederick Steele extracted. Despite the sharp decline of peak differential cross section with increasing target mass, the corresponding spectroscopic factors remain nearly constant. Since the a spectroscopic factor may be taken as a measure of surface a cluster probability, a clustering appears to remain import- ant for heavy nuclides. A SURVEY OF THE (3He,7Be) REACTION AT 70 MeV BY William Frederick Steele A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Physics 1974 ACKNOWLEDGMENT S I would like to thank the laboratory staff for pro- viding a good environment in which to work. For his guidance and unceasing encouragement, I wish to thank my advisor, Dr. G. M. Crawley. For helping with data collection and analy- sis, I would like to thank Paul Smith. I am particularly indebted to Joseph Finck who, in addition to helping gather and analyze data, has spent many hours preparing the figures and performing the DWBA calculations presented in this work. ii TABLE OF CONTENTS LIST OF TABLES . . . . . . . . . . iv LIST OF FIGURES . . . . . . . . . . V I. INTRODUCTION . . . . . . . . . 1 II. EXPERIMENT . . . . . . . . . 4 III. DATA ANALYSIS . . . . . . . . . 12 IV. DATA A. 12C(3He,7Be)°Be . . . . . . . 17 B. 13C(3He,7Be)9Be . . . . . . . 25 c. 160(3He,’Be)12c . . . . . . . 26 D. 2"Mg(3He,7Be)2°Ne . . . . . . 32 E. 26Mg(3He,7Be)22Ne . . . . . . 34 F. “8Ca(3He,7Be)““Ar . . . . . . 34 G. 58Ni(3He,"Be)5"Fe . . . . . . 53 H. °°Ni(3He,7Be)56Fe . . . . . . 57 I. 62"5"Ni(3He,7Be)59"”Fe . . . . . 69 J. 9°Zr(3He,7Be)BSSr . . . . . . 69 K. 12°'12"Sn(3He,7Be)115’12°Cd . . . . 74 V. DWBA CALCULATIONS . . . . . . . . 80 VI. CONCLUSIONS . . . . . . . . . 92 APPENDIX A . . . . . . . . . . . 103 APPENDIX B . . . . . . . . . . . 105 LIST OF REFERENCES . . . . . . . . . 107 iii L I ST OF TABLES 4.1 Energy levels of 8Be“. . . . . . . 18 4.2 Energy levels of 22Ne. . . . . . . 40 4.3 Measured energy levels of 1"‘Ar. . . . . 52 4.4 Energy levels of 5‘'Fe. . . . . . . 54 4.5 Energy levels of 56Fe. . . . . . . 58 4.6 Energy levels of 58Fe. . . . . . . 70 4.7 Measured energy levels of 6°Fe. . . . . 71 4.8 62Ni(3He,7Be)58Fe do/dQ(ub/str). . . . . 71 4.9 61’Ni(3He,7Be)'5°Fe do/dQ(ub/str). . . . . 71 4.10 Energy levels of 86Sr. . . . . . . 72 4.11 Mass and energy levels of 12°Cd. . . . . 75 4.12 12°'12“Sn(3Re,7Be)“S'INCd do/dQ(nb/str). . 75 5.1 Optical model parameters. . . . . . . 82 6.1 a spectroscopic factors. . . . . . . 101 A.l . . . . . . . . . . . . 106 iv 4.13 4.14 4.15 4.16 4.17 LIST OF FIGURES TIME OF FLIGHT PARTICLE IDENTIFICATION IN THE SPECTROGRAPH . . . . . . . . . Time of flight spectrum for a 12C target. . . Peak analysis for 58Ni spectrum, 10°. . . . Spectra measured with the proportional counter. As for 4.1. Angular distribution together with secondary to primary ratio. convenience. Angular distributions. As for 4.4. AS AS AS AS AS AS A3 A3 AS AS AS Angular distribution. for for for for for for for for for for for The curves are simply for visual 10 13 19 20 21 22 23 24 27 28 29 30 31 33 35 36 37 38 39 AS AS AS AS AS As AS AS As A5 A3 A8 AS AS A3 A5 AS AS As AS AS A8 A8 A3 A8 AS DWBA calculations. for for for for for for for for for for for for for for for for for for for for for for for for for for vi 41 42 43 44 45 46 47 48 50 55 56 59 60 61 62 63 64 65 66 67 68 73 76 77 78 79 84 As for 5.1. . . . . . . . . . 86 As for 5.1. . . . . . . . . 87 As for 5.1. . . . . . . . . . 88 As for 5.1. . . . . . . . . 89 As for 5.1. . . . . . . . . 90 Peak differential cross section for (3He,7Be) reaction at 70 MeV vs. target mass number. . 98 Peak differential cross section for (3He,7Be) reaction at 70 MeV vs. target neutron excess. . 100 vii I . INTRODUCT ION Probably the most obvious and well understood nuclear phenomenon is natural radioactive decay. a, B, and y rad- iations emanating from a variety of nuclides have been stud- ied for decades. y radiation is understood in terms of electromagnetic transitions within the nucleus. 8 decay, before the discovery of the neutron, was thought to be the ejection from the nucleus of a free electron. Now, however, 8 decay is known to be a manifestation of the weak inter- action; a neutron within the nucleus splits into a proton, electron, and an antineutrino. a decay is an example of quan- tum mechanical barrier penetration. In contrast to B and y decay, however, the source of a particles within the nucleus is not clearly established. That is, where do the a parti- cles form, how long do they exist, and to what extent does the nuclear matter condense into a particles? Because of the quantitative uncertainty in the penetrability of the large Coulomb barrier, Wilkinson1 points out that a decay, by itself, is an inadequate tool to answer these questions. He discusses two, nore direct, methods for determining the degree of a clustering: a knockout reactions and K- meson capture studies. Igoz, for example, has investigated the (a,2a) reaction at 915 MeV. The two a particles are detect- ed in coincidence at a relative angle of 87.5°, the angle for a 915 MeV a particle elastically scattered from a free a particle at rest. Because of the strong absorption of a 2 particles in nuclear matter, only the pole caps of the target nucleus where the nuclear density is 5% of the central den— sity may be probed. The number of elastic a-a events obser— ved indicates that all of the nuclear matter in these polar regions is clustered into a particles. More recently, a particle transfer reactions have been used to estimate a clustering. If such a reaction is, in fact, dominated by an a transfer mechanism and is direct, re- action calculations may allow extraction of a spectroscopic factors which may be taken as an indication of a clustering. a spectroscopic factors have been obtained, for example, by Martin3, et. a1. using the (d,5Li) reaction at 28 MeV. The direct character of the (d,‘Li) reaction is questionable how- ever. Comfort“, et. a1. find that complex multistep pro- cesses are significant for the reaction, probably at all en- ergies. On the other hand, the (3He,7Be) reaction seems more likely to proceed via direct a pickup. Détrazs, et. a1. find that at 30 MeV incident 3He energy, the reaction is probably direct. Further work by Détraz‘, et. a1. shows that, for the most part, the a particle is transfered in its ground state rather than an isospin l excited state. Target nuclides as heavy as 93Nb"a have been studied at 3He energies as high as 40 MeV. The peak differential cross section is observed to sharply decline from 12C to l”Ca. However the decrease is arrested past calcium. The 93Nb data suggest the cross section may even rise for targets of greater mass. The present work has sought to extend the 3 previous work to larger masses. A higher beam energy, 70 MeV, is used to assure a direct reaction mechanism, to avoid the Coulomb barrier of heavier nuclides, and to raise the 7Be ejectile energy, thus easing detection difficulties. For 'application to the (3He,7Be) reaction, a detection system should be able to resolve the peak pairs caused by the parti- cle stable 432 keV first excited state of 7Be. The resolu- tion attainable with semiconductor counter telescopes, used for most previous work, is limited by kinematic broadening. Since the cross sections for (3He,7Be) reactions are very small, less than 1 ub/str for heavy targets, as large an ac- ceptance solid angle as possible is desirable. Therefore, for the present work, an Enge9 split pole double focusing magnetic spectrograph is used to analyze the reaction pro- ducts. Its kinematic focusing feature eliminates the kine- matic broadening problem, allowing use of a relatively large entrance slit. In addition to nuclear structure information, the (3He,7Be) reaction presents the Opportunity to study nuclides for which little information is available. In particular, the masses and some energy levels of HAr, 6°Fe, and 12°Cd are measured. II . EXPERIMENT The experimental arrangement used has four primary constituents: the cyclotron and beam transport system, the spectrometer magnet and camera box, the proportional counter photomultiplier detection system, and the electronic analysis equipment. The Michigan State University sector focused cyclotron is used to accelerate E'He‘k+ ions to 70 MeV. 3He++ ions are produced at the center of the cyclotron by a water cooled gas discharge ion source. In order to conserve the expensive isotope, vacuum system exhaust is recovered, cir- culated through a liquid nitrogen cooled carbon trap, and returned to the ion source. Slits located at the eighteenth and twenty-eighth orbit radii stOp errant 3He++ ions in order to precisely define phase and energy of the beam and to re- duce hazardous radiation by stOpping the particles while still at a relatively low energy. Beam energy definition of better than 0.1% is routinely achieved. Because of the small differential cross sections of the reactions herein describ- ed, an effort was made to maximize the beam current reaching the target. Specifically, the ion source was operated at maximum power level and, after initial adjustment of the cyclotron, the twenty-eighth turn slit was removed. Ex- traction efficiency remained greater than 90%. Beam current passing through the target typically ranged from 2 to 3 microamperes, except for those target materials intolerant of such high current levels, for which the current was reduced to a safe value. The beam transport system contains a pair of 45° bending magnets which bend the beam a total of 90° and serve to precisely define the beam energY; which is calcula- ted from a standard calibration1° using a proton nuclear mag- netic resonance measurement of the magnetic field magnitude. As shall be discussed, the major contribution to the experi- mental resolution of peaks in the measured spectra is due to energy loss in the target; the energy distribution of the cyclotron beam being somewhat better than necessary for the experiments here discussed. An Enge split pole magnetic spectrograph9 analyzes the momenta of the reaction products. Two motor driven screws in the camera box allow remote control of the detector pos- ition and orientation. For a given beam energy, target, and scattering angle, the detector is placed to minimize the ef— fect on resolution of the energy spread due to acceptance of particles scattered into a range of angles (kinematic broad- ening). The Enge spectrograph is a double focusing instru- ment which, together with the kinematic focusing, allows use of a relatively large solid angle, typically 2° x 2° (1.218 millisteradians). Use of an angular interval as large as 2° with a typical counter telescope system would be prohibited by the large values, particularly for light target nuclei, of kinematic broadening for the (3He,7Be) reaction. Although the spectrometer has an entrance aperature of 5.6°, a 2° slit was the largest used. Structure of the angular distributions warrant 2° resolution. Furthermore, time resolution of the particle identification system is directly proportional to the angular acceptance of the spectrometer. Therefore the slit width was limited to maintain adequate particle identi- fication. In a typical experiment, the yield for ions such as 3He, a, t, and 6Li is much greater than that for 7Be. Thus the rate at which 7Be ions are detected is a small fraction of the total count rate. Furthermore, the differential energy loss of 7Li+++ ions crossing the focal plane at a given point is very nearly the same as that for 7Be"+ ions at the same point. These facts present a severe challenge to the reliability and efficiency of a particle identification sys- tem. The basic detector11 used is a single wire gas filled proportional counter. Thin windows of Havar, Mylar, or Kapton, 1 cm high by 25 cm long on either side of a slotted 1 cm thick aluminum block contain a gas mixture consisting of He 10%, Ne 85%, and C02 5%12. A nichrome wire 10 or 20 um in diameter runs the length of the counter and is attached to external connectors at either end. Each end of the counter is fitted with a gas connection to allow a flow of gas through the counter, both to maintain the quality of the gas and to satisfy the requirements of a pressure regulation device. Charge from an ion passing through the gas is collected at the two terminals; the ratio of the charges collected at the two terminals being inversely proportional to the ratio of the separations of the event from the respective termin- als. The outputs of the two terminals are amplified, added, 7 digitized, and sent to the comptuer. A second input to the computer is the amplified and digitized signal from one end of the counter. The sum signal represents the total energy deposited in the counter by the passing ion; or equivalently, the differential energy loss of the event. The second sig- nal represents the product of the energy loss by the relative position of the event. The computer program TOOTSIE13 ac- cepts the digitized signals then divides the second input by the first, yielding the position of the event. The results are plotted on an oscilloscope screen. The vertical axis of the display is the energy loss while the horizontal axis is the position of the event. Each event produces a dot at the appropriate point on the screen. The dots distribute them- selves in horizontal bands corresponding to the differential energy loss of the different species detected. Lines may be drawn on the screen to specify to the computer regions to be accepted. Unfortunately, while this method of particle iden- tification performs well for some applications, it is inad- equate for the (3He,7Be) reaction. The energy resolving pow- er of the prOportional counter is inadequate to provide band separation sufficient to assure reliable particle identifi— cation. Measurement of the ion time of flight in the spect- rograph supplies the additional information needed for a sat- isfactory solution. As illustrated in Figure 2.1, a plastic scintillator with attached photomultiplier tube (RCA 8575) is placed behind the prOportional counter. The amplified sig- nals from the phototube start a time to amplitude converter Iadmwomhowam MI... 2. ZO.._.dx32 . J 11 m. 3:01 3 counts in channel j. The parameters are successively rein- , where mj is the number of cremented until x2 ceases to decrease appreciably from one iteration to the next. Let n(p) A x-u 2 k j I (x) = X -—ér—-exp —%[—3—i1 + X a.x , P i=1 PM oi i j=0 3 where 2(p) indicates deletion from the sum of the pth term. From the data value of channel j is subtracted the quantity j+l I Ip(x)dx. The remaining counts are those for peak j 12 13 .ooa .Esnuommm fiz.m How mammamcm xmmm H.m mucosa bfi . _ — < 4 y _ .w .. 4" II- 0!- mm: 22. . 8m 14 p alone; that is, the smooth background and counts from near- by overlapping peaks have been eliminated. The size of peak p is then calculated by adding the values of each channel of the processed data. The peak position is taken to be the average channel number weighted by the number of counts per channel. In order to identify peaks in a spectrum, the peak location together with the magnet calibration is used to cal- culate the excitation energy of the level to which it corres- ponds in the product nuclide. Unfortunately, in contrast to the use of photographic plates, the length along the focal plane corresponding to one channel is not directly measurable. Therefore the use of a proportional counter introduces an additional unknown into the calibration procedure. To de- termine the calibration, the excitation energy of a known level for which a peak appears in the spectrum is used to compute the 7Be energy, hence momentum, and, via the spec- trometer calibration and magnetic field value, the peak pos- ition along the focal plane. These data, for several known levels, establish a least squares straight line giving dis- tance along the focal plane in terms of channel number. The excitation energy corresponding to a heretofore unknown peak is computed by using the focal plane position as determined by the peak's channel number and the spectrometer calibration to calculate the effective radius of curvature of the 7Be ions. The magnetic field value from the nuclear magnetic resonance measurement yields the momentum, hence the kinetic energy of the 7Be ion. A correction is made for energy loss 15 in the target according to the formula of Williamson’s, et. al.; then the excitation energy computed by the formula listed in Appendix A. Once the peaks have been identified and processed, the area information of the peaks may be used to calculate the differential cross sections for the reactions to the corres- ponding final states. The differential cross section is com- puted according to the following formula: N_ . cos . A n . 3 A9 pr Q No (1:10: {00 A9 is the solid angle subtended by the spectrometer entrance slit. N is the peak area. o is the target angle. pr is the areal density of the target in gm/cmz. e is the electron charge, 1.6022 x 10'.19 Coulomb. No is Avogadro's number, 6.0222 x 1023. A is the atomic mass of the target. Q is the charge in Coulombs collected in the course of accumulating N counts in the peak. And n is the charge number of the projectile. If A6 and A¢ are the angles subtended by the rectangular ap- erature of the spectrometer entrance slit, the solid angle subtended is A9 = 4 sin-1{sin(8A6) sin(8A¢)}. The cross sec— tions thus obtained are converted to the center of mass 16 coordinate system by multiplying by the center of mass to laboratory cross section ratio. The formulae for computation of the cross section ratio and the center of mass scattering angle are listed in Appendix A. IV . DATA A. 12C(3He,7Be)8Be Energy levels of 8Be are given in Table 4.1. Levels through 17.64 MeV may be observed with this reaction, but the peaks for this level and the ground state may not be si- multaneously placed on the counter system because it is not long enough. Therefore measurement of spectra for the 12C target was split into two series of experiments; one each for two ranges of excitation energies in 8Be. A 100 ug/cm2 commercially obtained target was used for both sets. Con- tamination is not a problem for a carbon target, however energy loss of 7Be in carbon is particularly severe be- cause of the target's small atomic mass. Therefore in order to secure adequate resolution, a thin target is necessary, target thickness being the factor limiting resolution. As a check, a 200 ug/cm2 target was used and resolution was de- graded as expected. Figure 4.1 displays two spectra for the 12C(3He,7Be)°Be reaction at two angles. Noting that the separation of the ground state peaks is about 400 keV, the resolution for the forward angle is about 150 keV, whereas the resolution for the 22° spectrum is somewhat poorer be- cause of the decreased 7Be energy. The broad 2+ and 4+ states at 2.9 and 11.4 MeV respectively, increase relative to the ground state as the scattering angle increases. Fig- ure 4.2 is a spectrum including the 16.63 - 17.6 MeV ex- citation energy region of 8Be. Because the 16.63 MeV and 17 Table 4.1 Energy levels of 8Be“. Ex (MeV) 0.00 2.94 11.4 16.627 16.911 17.642 18.154 18.91 19.06 P (keV) 6.8 ev 1560 7000 107 77 10.7 138 48 270 18 C4 :1 + 4- + 4- + +- + w+NHHNN®NO 19 I l T I I 1 l I 3 o 800- 12C(3HG-7BGJBBe m Emm=70MeV .— eiob=13 deg 900% _ 713 02 C N C O L— g _ I: d L) A T a l 0.) r I V l I l I I Q. (I) C SOO- _ :5 O U _ 9.0.522 deg _ 200~ 1 _ [J I f l r I ' l 50 150 250 350 S50 Chonnel Number Figure 4.1 Spectra measured with the proportional counter. 20 com (.8832 655:0 .flzv How m4 NJ onsmwm om: . 0mm . owm owfi o u ad 1 O n _ w l 3 9 8 .V l J r O m .9 1 omun _® (.9 9 MM GI 91. I. D 1 >22 QT mm ”mm -8. w m m .m c. .e. mmfl mA Imvog We. _ b _ p _ _ _ 21 100_ I I I I I - Z 1 _ o 780(0.00) -« _. . 780L932) 7 7 7 ”C " l (n A :s. 0; : 12C(°He.7Be)°Be (0.00) 0+ 3 '0 I_ : \ __ EaHe—70MeV _ t) _ a ‘0 _ .. 1 l 1 l 1 I l I I I 1.2— _ m m T 52 0.8~ m m T m m .. O _ mm _ a: m m m 0.9— m .. 0.0 1 l 1 l 1 0 20 L10 60 Gem. [degrees] Figure 4.3 Angular distribution together with secondary to primary ratio. The curves are simply for visual convenience. 22 103_ r 1 f l I l - :. 12C[3He.7Be]°Be (2.90) 2* : _. E3Hez70MeV .. E 3 7: “P 3 <0 . I Q 1— d :1. r” 100_ g 1 t 1 S E .. - 1 C2 : : ‘0 __ .- \ t .. b _ . 'CJ 10': -: E 12C[3He.7Be]°Be (11.9] 9* : I .. 1 L 1 l .1 l 0 -20 40 60 9mm [degrees] Figure 4.4 Angular distributions. 100 : l I r r l -< E 12[3[:‘3He.789]°Be E r- : “ 10 :— E3He 70Me V -=-. : m16'87 2+ g 100 E" '2:- E- 16.67[.932l é _ + d - 18.93 2* ‘ 10 5‘ W '3 T _ 7 U) 10 =- '7: \ E 16.93l.‘l32l 5 _Q I: W 2 1 _ -1 1.;— E. 03 1: E U I: .1 \ 10 E. s b :. -‘=‘ ‘O I 17.69 1* ;‘ 1's:- F 10 E. F 17.6%932} C W 15' 1 l L l 1 0 20 40 80 Gem. [degrees] Figure 4.5 As for 4.4. .H.¢ mom ma m.¢ enemas LmnEaz _mccocu 24 P 2mm L omm r 0.2 o Loom _ - 3 as. orufo m 18: w 3 d _ b b r a L J 3 u. 1 D U U z W % 100? now “.0030 1 >mzomu2¢w ommnomuixmaug m loom r . h p p . 25 16.91 MeV states are separated by about the same amount as the ground state and first excited state of 7Be, the pri— mary 16.91 peak and the secondary 16.63 peak cannot be re- solved. Therefore the angular distribution in Figure 4.5 is the sum of the 16.91 primary and the 16.63 secondary dis- tributions. The distributions in Figure 4.4 for the 2.9 and 11.4 MeV levels are, of course, sums of the respective pri- mary and secondary distributions as the levels are much too broad to resolve their primary and secondary constituents. The ground state angular distribution is shown in Figure 4.3; both primary and secondary distributions together with the ratio of the secondary to primary cross sections. Note that this ratio distinctly deviates from the expected constant value 8. B. 13C(3He,7Be)9Be Two sharp levels in 9Be are observed with this reaction and, as may be seen from Figure 4.6, several broad levels ap- pear at backward angles. A 200 ug/cm2 enriched 13C target was used so the resolution is not as good as for the 12C experiment but nevertheless is adequate to resolve primary and secondary peaks of the sharp states. The broad 2.78 MeV level under the pair of sharp peaks representing the 2.429 MeV level may be seen in addition to the ground state peaks. No evidence at any angle is discernable for the 210 keV wide 1.68 MeV level. The primary and secondary angular distri- butions together with the secondary to primary cross section 26 ratios are plotted in Figures 4.7 and 4.8 for the 9Be ground state and 2.429 state. The angular distributions are smooth with very little structure and the ratios are more nearly constant than those for 8Be. C. 160(3He,7Be)”c The oxygen target was fabricated by evaporating tungsten oxide (W03) onto a 250 ug/cm2 gold foil. Tungsten and gold were chosen since their 7Be yield from the (3He,7Be) reaction is probably negligible compared to that from 16O. The amount of oxygen on the target was determined by comparing with the 7Be yield from a % mil Mylar target at l7.5°. The oxygen areal density was measured to be 11 ug/cm2 or 53 ug/cm2 W03. Despite the attempt to make a clean target, the presence of a significant amount of 12C is apparent in Figure 4.9 which is a spectrum measured at 20°. The 12C ground state and 4.439 2+ first excited state are strongly excited. The 7.653 0+ and 9.64 3-, on the other hand, are very weak, appearing only at some angles. Higher levels are absent except for a group of weak unresolved levels around 13.35 MeV excitation energy. Angular distributions and ratios are plotted for the 0+ ground state and the 2+ 4.439 level in Figures 4.10 and 4.11. 27 100 I I I T I -« : o 7Bo[0.00) : __ . 7Be(.'+32] T ’Z‘ _ .. (D A 1 w 10:. — CB 2 : U _ _ \ __ 13¢[3He,7391989 [0.00) 3/2" : IE3 — (E3Ik;=77014e\/ — 1 1 1 l l I l ' I I 1.2— 7 .3 0.8—- ‘ O _ a: @m _ CI: m 03 m [n m a] [D m 01 0.9- 7 0.0 n I I ' ‘ o 20 *0 50 8am. [degrees] Figure 4.7 As for 4.3. 28 10C] TE I I I I E 130(3He.7ee)98e (2.429) 5/2‘ E : E3He=70MeV : ,2. h o 789(0.00) A (r) 7 \ - v BO[."+32) " .Q 1 "" 10.. .2 o: G i 'C) : 4 b _ _ ‘O __ .. 1 l 1 l 1 /i I I l l ' 1.2- ‘ :9: 0.8r- I " c L .. 0.4— T- 0.0 1 1 1 l ‘ 0 20 L10 60 Gem. [degrees] Figure 4.8 As for 4.3. 29 .H.¢ How m4 m.v ousmflm Loo£:44_mccoco om} _ 0mm _ DMN om; r om... rlll. II. I .l. 8 8 A m l... o: I a ) . . O O 6 . O o mw mm 1 .0mus_m m >22 on" :3 ,9 - omzmmn mrmvoe w _ C _ I.— o oor 1800003 Jed sIunog dU/dSZ [Rb/er] C) 100 10 1.2 0.8 0.'-+ 0.0 30 90m. [degrees] Figure 4.10 As for 4.3. I T I I I 2 ~ 0 789(0.00) : I— v 7 .... ]- Bo[.'+32] .. [— —4 [-— ——1 I _ :_ 180(3He.7se)120 (0.00] 0* I E3H9=70MeV " P- t I- It » 1 l 1 l , 1“ I r” I I I I— Q I % ‘I . . k i 1 l 1 l 1 0 20 |"1‘0 60 100 dU/dQ [lib/SP] 1.2 .9 0.8 OH 0.0 31 60”. [degrees] Figure 4.11 As for 4.3. I l W I I _ " 4 " o 7Bo(0.00] - __ v 780L932] _ :- —J : 160(3He.7'ee)12(: (11.439) 2+ 3 .. E3H9=70MeV .. 1 l 1 l 1 I l I I T I— m a - 1 1A 1 J 1 0 20 L+0 80 32 D. 2"Mg(3He,"Be)2°Ne The target used for this experiment is a 300 pg/cm2 self supporting enriched 2“Mg foil. The thickness of the target was determined by passing a particles from the decay of 2“Am through the target and noting the energy loss. The areal density of 2“Mg causing the observed energy loss was computed with the aid of the energy loss formula of Williamson‘s, et. a1. Not having been prepared especially for this work, the target had been used previously and stored in the atmosphere. Consequently, carbon and oxygen contamination is particularly severe. The 27.5° spectrum plotted in Figure 4.12 is rela- tively contaminant free as the cross section for carbon and oxygen decrease more rapidly with increasing angle than the cross section for magnesium. The four most strongly excited 2°Ne levels all appear unobscured in this spectrum; the 0+ ground state, 1.63 2+, 4.25 4+, and 5.62 3-. A pure a trans- fer reaction will not excite unnatural parity states. None- theless, the 4.97 2- is present. Although weakly excited, it appears at enough angles to measure the angular distribution plotted in Figure 4.17. States of higher excitation energy appear but are not resolved. Because of a sharp dip noticed in the ground state's secondary to primary cross section ratio at 10°, particular attention was given to the ground state at forward angles. Several spectra were obtained at angles around 10° in 1° steps, using a 1° wide by 2° tall spectrograph entrance slit rather than the usual 2° x 2° slit to improve angular .H.v you m4 NH.v musmflm 18832 Eccoco omm 0mm om“ om 4 _ 33 Invoking 3 0 n U l+. . . s r d m. r 18m w H. 1 8“. Rummage mm __ m 3 .1 .1 1 W >onmn fl 9 m U wzommmmkdrmwmzfi i 8 W b P 1— 1L — 1P h:U+J III 34 resolution. The result, plotted in Figure 4.13, is a deep minimum in the ratio at 13° center of mass angle. Angular distributions and ratios for the other three strong states are plotted in Figures 4.14, 4.15, and 4.16. E. 2°Mg(3He,7Be)22Ne A self supporting 250 ug/cm2 enriched 26Mg target was used for this reaction. This target, as the 2“Mg target, was previously used; however, it had been stored in a vacuum chamber (m10'3torr). Nevertheless, contamination is a ser- ious problem, causing gaps in angular distributions of some states. Numerous states in 22Ne are excited by this reaction, particularly in the range 5 - 9 MeV excitation energy. The observed levels in 22Ne are listed in Table 4.2 together with 22Ne(a,a') spectral measurements of Ollerhead3°, et. al. The 45° spectrum of Figure 4.18 includes all states observed. At this large scattering angle, the contaminant peaks pose no problem, having significantly decreased in magnitude relative to the 22Ne peaks. The largest peak in the spectrum, at 7.53 MeV, is the strongest peak at most angles. Angular distri- butions for the 22Ne states are presented in Figures 4.19 to 4.25. F. “°Ca(3He,7Be)”“Ar This experiment was undertaken primarily to measure the mass of the nuclide HAr. Additionally, excitation energies of some low lying levels were determined. The “80a target 35 I I I I T I _. 2”Mg(3He.7Be)2°Ne (0.00) 0+ 4 EaHe=70MeV ,_. 10— j C. I: o 7BO[0.00] 4 <9 : . 780L932) Z \ __ .4 «Q .- d .3; (3 “o r ‘ b 1 "o :' 1 1: \ 1 1 l 1 l 1 I 1 T I T 1.2- 7 . . é ‘ 2 0.8]— Q Q ‘ 6 I I _. E Q m T “I Q 0 I 0.4- m 7 0 0 .— m «1 0.0 1 l 1 1 4 ‘ 0 20 ‘+0 80 6mm. [degrees] Figure 4.13 As for 4.3. 36 T— I l I I I - 2“Mg[3He,7Be]2°Ne [1.83) 2* . .. E3H8=7OMeV fi 10.. 7 _. (— I; O Be[0.00] : < : V 780(0Q32] d .0 I: J .3,- d 03 .0 _ 4 b "o 1': j _‘_’ 1 _ 4 r- d 1 l 4 J 1 J I I T T I 1 1.2- 7 9 0.8— 9 7 5 II .1 0 m I cc ' 0 m m m 0 ° ° 04— ”Q 0 ‘ I_ -I 0.0 1 1 4 I 1 ' 0 20 LIO 80 Gem. [degrees] Figure 4.14 As for 4.3. 31. I 1 ”T ‘1 ‘ r 1 - 2“Mg[3He.7ee]2°Ne [H.251 4* . E3H9=70Mev ,— 10- 1 c. i o 780(0.00) : ‘9 C . 73.1.9321 -+ \ r -. 4 a - y 4 H _ J (3 . ‘O F' b “ 'o 1: V ‘1 Z 1 _ «J 1 41 11 L 1 J I [ “r | I l 1.2- ‘J 9. 0.8— ¥ - .1— O . § § § Q 1 CE 0 ‘1 Q i 0 "‘ ‘ _ 1 H 4 0‘) 1 1m 1 J 1 l ' o 20 an 80 9mm. [degrees] Figure 4.15 As for 4.3. 38 I I I T I l + - ~ 2“Mg[3He.7Be)2°Ne (5.623] 3' - H _ « EHQ=7OMeV ~ L < 10.: ._ .Q I : 3 ~ 7- O} ' _ ‘0 .. \ o 73o(o.00) ‘ b .. v 784332) . ‘o 1_— .. # % i % % } 1 2— J? - g 0.8% Q i - O r- U i g g (I "m m i J' i 1 0H~ i O Q Q - 0.0 1 1 1 1 1 1 0 20 ‘+0 80 6am [degrees] Figure 4.16 As for 4.3. 39 10 u I I .r, I ' T : 2L’Mg[3He.7Be]20Ne [$87] 2' : P c- L EaHe=70MeV .1 ”C - . 00 JD .3 ‘1’ '4 : I 03 L - '13 b ‘ b - ' 13 0.11- .1 ": b 1 l 1 l 1 12E ‘ 0 20 90 80 9am. [degrees] Figure 4.17 Angular distribution. 40 Table 4.2 Energy levels of 22Ne. Present Work E (MeV) .x 0.00 1.265 3.350 4.470 9.15 9.82 * The states most strongly excited by (7Li,t). H- H- H- H- H- H- H- H- .03 .04 .05 .16 .17 .17 .20 .27 .35 .40 .75 E x (MeV) 0.00 1.28 3.36 4.46 5.14 5.33 5.36 5.52 5.64 5.93 6.12 6.24 6.35 6.64 6.70 6.82 6.86 6.90 7.05* 7.34* 7.41 7.49* 7.64* 7.66* 7.73* 7.93 8.08 8.14* 8.38 8.50 8.55 8.59 8.74 8.86 8.90 9.04 9.10 Previous Work JW 1 + ++-+ A“ +mOWNwDNO-‘NN15NO +-+ A +-fidt+-+-#v~r + N++UJINHIOHOHN I +14” 4. + + I+IN++ 4. ref. 30,34,35 30,34,35 30,34,35 30,34,35 30,34,35 30,34 30,34,35 30,34,35 30,34,35 30,35 30,34,35 30,35 30,34,35 30,34 30,35 30,34,35 30,34 35 30,34,35 34,35 34,35 34,35 34,35 34 34,35 34,35 34,35 34,35 34,35 34,35 34 34,35 34 34 34 34 34 41 omm LmQEDZ 0mm _ .H.v you me ma.¢ magmas _mccogo am; I 4 I. . . .. a % me 9 L m 8 >szmu£fl _ ozNNHomNJImBZmN _ p .51 00'0 om ooN leuuoqg Jed swnog 10 do/dQ [pb/sr] L2 .9 0.8 0}+ (LO 42 _ I T r' l I q I o 7Be(0.00] I r v 73.31.9321 ‘ F 1 ]. A 1. 28Mg[3He.7Be]22Ne (0.00) 0* .— - fi _ _ a » n [- -1 1 J 1 1 1 I 1 I l I r- *‘ 1 1 Q _ m - g 1 1 1— m -' r _ 1 l 1 l 1 0 20 40 80 Figure 4.19 As for 4.3. 9cm. [degrees] 10 43 I T I W .. C 1‘ [— q ,l C 1 L - < L .. _Q o 7Be(0.00] 3 v 780L932] 1:- :1 O} E I 3 - 28Mgt3He.7Be)22Ne (1.27s) 2+ 3 b .. EaHe=70MeV - “o ,_ - 1 l 1 .1 I l l I 1.2*- ‘ -- 0.8- " '5 CE: F. @ m (D m in g 0»- - 0.0 l 1 l 1 0 20 ‘10 80 9am. [degrees] Figure 4.20 As for 4.3. 10 dU/dQ [uh/SF] 1a2 .9 0.8 0.9 0.0 44 j T T I T .1 E : _ o 7BO[0.00] .4 r . 739L432) q r 4 :' -4 1 ‘ I] " 2614913119789122119 (3.36) 4* ‘ 1. E3H6=70MeV d 1 l 11 l 1 r j I I T r . r 1 11 [— § i i i .1 P d 1 L 1 L 1 0 20 I40 80 Gem. [degrees] Figure 4.21 As for 4.3. 45 1. T r T r T ” o 7Bo[0.00] L . 789L932) ”Z: 1- co 3 1.. _ .3- C : C 1 g .. 1 L . \ 26Mg[3He.7Be]22Ne (“1.96) 2+ b P — 0.1:- b 1 l 1 l 1 I I F T Y 1.2- .9 0.8- ‘5 c: b 1 1 § * 03‘1" Q i Q [- 0.0 L J L 1 1 0 20 “10 em, [degrees] Figure 4.22 As for 4.3. 46 j I T T I I b 2614991111.? Be]22Ne (5,52) E3H9=70MeV 10.. _ : 1 .— —1 .- A F—\ 1— __ L P" —1 a) _ 4 \\~ 3 .0 f 4 5. H 1 l 1 l 1 l I I I I r r C2 3 10 28Mg[3H9.7Be]22Ne [5.92) _ b : 2 U [— .. ’ 1 P 4 F 4 F - 1’ ': b -1 L I L l 1 l 0 20 H0 50 Figure 4.23 9mm. [degrees] As for 4.4. 47 T T T I —T I _ 26Mg[3l-‘le.7Be]22Ne [6.35] .. E3H6=70MeV 10_. _: F: : o 780[O.OO] j < + . 7Bo[.‘+32] - .o '_' . 3 C2 '0 ~ - b “o 1_ i I I 1 1 1 1 1 1 1.2- " g 0 e— 1 1 M1 1 1 - O i . (r r i i i 0.9” Q Q '7 0.0 1 1 L 1 l L l 0 20 L10 80 6mm. [degrees] Figure 4.24 As for 4.3. 48 I l I T, I 26r‘1gl3He.7Be]2;-’I\Je (7.11%) _ F: E3He=7OMeV < 10:. .Q I 3,- - C); P- 'O _ b ”’ ‘ o 78.10.00) . ‘ D . 78.1.4321 ‘ . 1: 2‘ h 1 l 1 l L - l I I l T 1.2*- - O _ _ l; 0.8 III a? ‘ 1 * In 0.11- 111 mm @ g E Q m D .. m - 0.0 1 l 1 1 1 0 20 L10 60 Gem. [degrees] Figure 4.25 As for 4.3. 49 was prepared by reducing with zirconium powder 97.16% iso- topicly enriched “°CaCO3, condensing the liberated calcium metal on a 500 pg/cm2 gold foil. Preparation, storage, and transfer of the target were carried out in high vacuum ap- paratus, the pressure never exceeding 10'“torr, except per- haps momentarily during transfer. The thickness of the tar- get was indirectly estimated to be 200 pg/cm2 by measuring the yield from the I‘°Ca(3He,7Be)3“Ar(l.977) reaction using a commercial “8Ca target of known thickness and isotopic comp- osition, and comparing with the yield from the target in question. Eight spectra were measured at angles ranging from 5° to 10°. A 7° spectrum is plotted in Figure 4.26. Small angles were chosen to maximize the separation from contam- inant peaks of the peaks corresponding to I"’Ar. At angles large enough to shift the contaminants from the critical re- gion of the focal plane, the differential cross section for the reaction becomes so small as to preclude a practical ex- periment. Even at 5°, the peaks corresponding to the lowest observed level of I"‘Ar are very close to the peaks repre- senting the 4.44 MeV level in 12C. This pair, together with the background produced by the broad 2.9 MeV level of °Be, could obscure peaks from potential lower levels of I"’Ar. In order to check this possibility, the reaction was carried out at a lower energy, 37.5 MeV. The experiment becomes more difficult at the lower energy because the 7Be ions lose a large amount of energy in the target, thus degrading resol- ution. Furthermore, since the 7Be ions have insufficient 50 8 _' ' ' l—:§§;;L L K) < j _ 3‘ .1 ’63 > ° F\ a) m '\ Z .0 O — Q; 2 [04.h]Jth [__( ‘_‘ (33— "F C3— u- m i 0.‘+- ' 0.0 I l ' 0 20 HO ec.m. [degrees] Figure 4.33 As for 4.3. dcr/dQ [pb/sr] 0.1 64 6mm ' [degrees] Figure 4.34 As for 4.3. T T I __ o 7BO[0.00] _ .. . v 7391.432) .1 a 3 r - ’ ~\ ]- -1 6°Ni[3He.7Be]56Fe (0.00) 0* :_ E3H8=70MeV .1 - 1 41 1 i T r T _ @ifi § if é - __ é _ ED [— é a 1 l 1 0 220 l+0 65 r T I L 80N5[3H9,7Be)56Fe (0.8%?) 2* “ p Ekflie::;qjh4e\/ ‘ 1 I 1 11 1| 1 o 7Bo[0.00] . 780L432] dcr/dS? [pub/3r] 0‘1’: 1 b ‘1 I J - I I I 1.2- " .3 0.8~ § - C3 _ - a: § § % * 051— §@ § § - 0.0 1 i 1 0 20 '+0 6mm [degrees] Figure 4.35 As for 4.3. I I ' r d 0.1.— _ 6°NI[3He.7Be]56Fe (2.085] . 7: EaHe=70MeV : F .- [- d ,_ 2.658 L d (D .Q 0.14:— - .3 I 1 101:. 1 o; : ' Q - 1 b - ' ‘0 h d ]- -1 1? - F 3.12 . ]. d __ . # d r H P d . I L 0 20 90 0am. [degrees] Figure 4.36 As for 4.4. a... I I I II I] dO/dQ [Vb/3r] 0.1 Figure 4.37 67 l I III] o 78oto.ool v 780L932) 6°Ni[3H9.7Be]56Fe (11.86) E3He =7 OMeV 1 l 1,1 111 l l 1 11 1| .. -I- ‘— AS 0am. [degrees] for 4.3. 40 68 f T I - SONI(3H9.7Be]56Fo (5.90) .. _ E3He=70MeV .. ”Z a) 13' E > : - 1 _ —] " T (:3 _ q “C E ]’ o 780(0.00) -‘ -o v 780L932] 0.l+- " *- 2 ; 2 1r } % 1.2— i % “ .3 0.8- - C3 . r ‘ “C 1 0.4: § § . 0.0 1 l 1 0 20 “[0 90m. [degrees] Figure 4.38 As for 4.3. 69 I. 62'6“N1(3He,738)58’60Fe The self supporting 260 ug/cm 98.83% enriched 62Ni tar- get, as with the other nickel targets, was prepared commer- cially by a rolling procedure. This reaction, as well as the 6“Ni reaction, was executed primarily to obtain a qual- itative comparison of the differential cross section with that of 58Ni and 6°Ni. Therefore spectra for only three an- gles for each were measured. Tables 4.6 and 4.7 list the excitation energies of the levels observed in 58Fe and 6°Fe respectively. Little information on the levels of 6°Fe is available since the nucleus cannot be produced from a stable target with most standard particle transfer reactions. The differential cross sections for the observed levels are com- piled in Tables 4.8 and 4.9. J. 9°Zr(3He,7Be)BGSr A self supporting 500 ug/cm2 enriched 9°Zr target was used for this reaction. Even though the target is somewhat thicker than the targets used for the lighter nuclei, resol- ution does not suffer appreciably because 7Be energy loss is sufficiently less for the larger atomic mass. Figure 4.39 is a spectrum of 86Sr at 21°. The contaminant peaks dominate [simply because the differential cross section for the 9°Zr reaction is so small, for most levels and angles less than 700 nb/str. Fortunately the Q-value for the 9°Zr reaction is sufficiently great so that the contaminants do not interfere with the low lying levels of 86Sr. Table 4.10 lists the 86Sr 70 Table 4.6 Energy levels of 58Fe. Present Work Previous Work 1T Ex(MeV) Ex (MeV) J ref. 0.000 0.000 0: 33,38,39 0.812 1 .003 0.811 2+ 33,38,39 1.659 1 .011 1.676 2+ 33,38,39 2.081 1 .012 2.085 4 + 33 2.132 (3; 38,39 2.254 0 38,39 2.573 1 .012 2.597 4: 33,38,39 2.776 1+ 38,39 2.874 2_ 38,39 2.970 5+ 33 3.030 1 .038 3.080 2 38,39 3.133 + 38 3.151 4 33 3.230 38,39 3.244 + 38 3.389 2 33 3.451 + 38,39 3.522 2+ 33 3.566 1 .022 3.533 1+ 38,39 3.629 2 33,38,39 3.749 38,39 3.785 _ 38,39 3.854 3 33,38,39 3.875 1 + 38,39 3.883 1 .020 3.894 (2,3) 38,39 4.013 2+ 38,39 4.079 4 + 33 4.131 (0.1+2) 38,39 4.158 + 0 + 38,39 4.212 (2 ,3 ,4 ) 38,39 4.230 4+ 33 4.237 (2+) 38,39 4.288 2+ 33,38,39 4.314 2+ 38,39 4.348 2 38,39 4.398 + 38,39 4.438 2_ 39 4.441 3_ 33 4.468 3 38,39 5.315* 39 5.370 38,39 5.393 1 .025 5.370 38,39 5.406 38,39 5.462 38,39 5.506 38,39 * Some levels not near those excited by (3He,7Be) are ex- cluded. 71 Table 4.7 Measured energy levels of 6°Fe. Excitation energy (MeV) 0.000 0.835 .010 2.109 1 .020 3.077 1 .014 H- Table 4.8 62Ni(3He,7Be)5°Fe do/dQ(ub/str). center of mass scattering angle Ex (MeV) 5.4O 9.2° 14.0° 0.000 2.24 2.59 0.86 0 000+ 1.21 1.04 0.59 0.812 1.59 1.69 0.74 0.812+ 0.90 0.94 0.38 1.659 0.41 0.34 -- 2.081 0.43 0.69 0.32 2.573 0.69 1.07 0.79 3.03 0.56 1.03 0.45 3.56 -- 1.32 1.04 3.88 -- 1.25 0.70 5.39 -- 0.58 0.89 1 7Be first excited state peak. Table 4.9 6|’Ni(3lie,7Be)"°Fe do/dQ(ub/str). center of mass scattering angle Ex (MeV) 10.80 14.00 17.30 0.00 1.06 0.74 1.21 0.00Jr 0.37 0.56 0.66 0.84 0.97 0.55 0.62 0.841 0.58 0.41 0.38 2.11 0.64 0.63 0.34 3.08 0.56 0.44 0.44 .1- 7Be first excited state peak. Table 4.10 Energy levels of 86Sr. Present Work Ex (MeV) 0.000 1.085 1.841 2.227 2.705 3.031 3.440 3.958 H-H' H- H- H- l+ H- .018 .020 .052 .069 .072 .082 .068 72 86y(8+)3u* (MeV) 0.000 1.077 1.854 '2.230 2.482 2.642 2.673 2.788 2.878 2.997 3.056 3.185 3.362 3.500 3.926 3.942 3.968 4.146 C4 :1 + -+ +- + WDNNO * Some levels not near those excited by (3He,7Be) have been Information similar to that in the guoted ref- erence is contained in the Nuclear Data Sheets °. excluded. 73 .H.q now we mm.v «names 18832 .91ch 0mm 0mm 0.9 om 3 O n U r 1 .. t I .+ comm nu Any a w d .. I? m 6,. .1 m m 3 I; as. amass 1 W. # 1 >62?” 1mm w 1 twatomNJIthom W L P h L . Om 74 levels observed, and the angular distributions for these lev— els are plotted in Figures 4.40 to 4.42. K. 120I1248n(3He'7Be)116I120cd 12°’12“Sn02 were reduced in vacuum by passing an elec- tric current through a tantalum tube containing the oxide. The metallic tin evaporated onto a glass substrate coated with a thin film of C31. The resulting layers of tin were floated off the substrate onto a water surface and picked up onto an aluminum target frame. The results were respectively a 525 pg/cm2 and a 290 pg/cm2 self supporting tin target. The tin oxide from which the targets were made was isotopicly enriched as follows: 98.39% 12°Sn and 96.0% 12"Sn respective— ly for the two oxide samples. The thicknesses were deduced by comparing 3He elastic scattering data at forward angles with the corresponding calculations performed by the optical model program GIBELUMP“. The 12"Sn(3He,7Be)”"Cd reaction was done to determine the mass of the heretofore unknown nuc- lide 12°Cd. The 12°Sn reaction served to check the accuracy of the energy calibration. Measurements were made at three angles. Although the differential cross sections for both reactions are less than 900 nb/str, distinct ground state peaks are observed for both 116Cd and 12"Cd (Figure 4.43). The mass values presented in Table 4.11 are averages of the results for the three measurements, the spread of which de- termines the listed uncertainties. In addition to new mass information, the reactions provide information useful for 75 determining the qualitative variation of peak differential cross section with atomic mass. tions tions Table Level 1 2 3 Garvey-Kelson ground state mass excess: Table 116cd 116cd lzocd 120cd .1. The differential cross sec- measured for the 116Cd and 120Cd ground state transi- are compiled in Table 4.12. 4.11 Mass and energy levels of Mass Excess -83.98 1 -83.48 2 -82.68 1 (MeV) .03 .05 .04 120cd. E (MeV) 0.00 0.50 1.30 X -83.92 MeV. 4.12 120'12“Sn(3He,7Be)“5'12°Cd do/dQ(nb/str). (9.8.) (9.5.)Jr (g.s.) (g.s.)1L center of mass scattering angle 7.30 530 560 510 425 10.40 850 530 630 550 13.5° 420 570 365 410 7Be 432 keV first excited state peak. 16.6° 64 64 145 85 76 :1: I I I‘ - i '1 ”C " " (D _ - '3. o :Be[0.00] ‘—’ 0.1 __ v BOI.‘+32) -: G : I -o __ 1 b b - '0 _ . 9°Zr[3He.788]868r (0.00) 0+ E3H3=70Mev 1 l 1 I l I 1.2- “ g 0 8- 1 1 - o - .. cr 1 1 1 0.”... i i ‘ 0.0 n l 1 0 20 90 ec.m. [degrees] Figure 4.40 As for 4.3. 77 “I r T 1 :— .. ”C : " w «.1 E b . 3 o 7Be(0.00) '- v 780L932) 4 G ‘O 0.1 _. ‘ .. E : 9°ZrI3He.7Be]86$r : .. ' V - . E3He =7 OMeV - L- . L l 1 l [ T 1.2 - '- ’ '1 2 0.85 § - 25 a: i § § ' 0.“! '- é ¥ i i 4 0.0 l l 1 0 20 90 Gem. [degrees] Figure 4.41 As for 4.3. 78 _«4<fi_ « _»__.PF < b ##414 u did 5,-3.039 mv 4 —q‘.4_ « q 33.85% HOV _.««q~ q 4 L+0 20 ~q_.ququ _ 14d.—q m “u . 3 I I E :ppb_b _ _ ______ b 1 l . 0 ?.qdqq . .qeaqqq 9°ZrI3Ho.7 801°85'- —dddd— - BHO=7OMeV q 4fi4q4d4 * fi ddd#44 Tl rm}: au\bu v m m m 7 m n w e a. 1n 2 an n! I! I E E E —~_»#7L L b.._bb» . » ~p»..~. » » _..~._» _ —_b__r+» :brppr _ 0 0 0 H0 GaNL [degrees] 20 Figure 4.42 As for 4.4. 79 50 I l I 12°SnI3He.7Be]“st EgHe=70MeV elob-"10 dog 25- '5 c C r— O .C C.) 5 so . , I Q. (0 12"Sn[3He.7Be)12°Cd E L EgHe=70MeV g Olaf-'13 deg L) 25*- . .L. I r Channel jNumber Figure 4.43 As for 4.1. V . DWBA CALCULATIONS If the (3He,7Be) reaction is assumed to pick up an a particle from the surface of the target nucleus, the a spect— roscopic factor, Sa = do/dfl(measured)/do/dQ(reaction theory), provides an indication of the extent to which surface a clus- ters occur. In order to compute the differential cross sec- tion, it is necessary to assume that a monolithic a particle is transfered from the nuclear surface to the 3He projectile, thus forming the 7Be ejectile. Most DWBA computer programs employ the zero range approximation which, in this case, as- sumes the 3He and a particles to interact only when occupying the same point in space. If the 7Be nucleus is viewed as a two particle system, an a particle bound to a 3He nucleus, the a particle has one unit of angular momentum relative to the 3He. Since for such a p state the a - 3He separation is never zero, the zero range approximation is inappropriate. Programs exist which use a finite range approximation, how- ever the program LOLA2° makes no simplification beyond the usual distorted wave Born approximation. Therefore the pro- gram LOLA has been applied to the problem of computing a single particle transfer reaction differential cross section, the transfered particle being an a particle. In order to use any DWBA program, it is necessary to supply optical model parameters for both the entrance and exit channels. Optical model parameters for elastic scat- tering of 3He from the various target nuclides are available, 80 81 however only for energies somewhat lower than the 70 MeV bombarding energy of the present work. In most cases the 1 who used a folding parameters used are taken from Doering2 model. Since 7Be has a half life of only 53 days, 7Be beams are unavailable. Therefore 7Be elastic scattering data, from which optical model parameters are deduced, do not exist. In the absence of 7Be parameters, 7Li optical parameters are used instead. Although the 7Li complex optical potential should probably be increased when applied to 7Be to allow for the greater absorption of the more weakly bound 7Be, no ad- justment is made. Any such change would be negligible com- pared to the inherent uncertainty in the parameters. For many cases, several sets of parameters have been tried. The parameters used for the final calculations, along with their sources, are listed in Table 5.1. The program LOLA computes, for a given transition and orbital angular momentum transfer £, a corresponding diff- erential cross section, 02(6). The final reaction differ- ential cross section is given by the formula: do _ 2s +1 55(9) — §§::I $152 §(2£+1) W2(2131£2j238x£) 02(9): where 3x = O = a spin, sa = 3/2 = 7Be spin, sb = 1/2 = 3He spin, £1 = l = orbital angular momentum internal to 7Be, £2 = orbital angular momentum of a in target nuclide, jl = 11+ Sx = 11, and 82 ¢N hm mm mm mm mm Hm .wou own. mm. va. No. omw. Ho.H mam. “sebum 5H.N mm.N 0N.H MH.N mH.H mH.N mN.H laucflu m.~H ma.m e.o~ m.HH m.ma mm.oa s.oa A>mzv>z emm. omh. hmm. mo.H mmm. omm. mmm. raglan mom.H mm.H NH.H vh.H mH.H mb.H wH.H lamb“ m.sma o.mmH m.mma ¢.mm o.vHH H.em o.o~H A>mzv> ow“ wzom.om Hzc¢.om ozo~.:~ mzm~.:~ UN“ ou~.0- How coma mm N.NH on H.HN ow vm >mz on wmumcm U-.1 Has flzom + Has Hzom.¢ wmm has + was H2; 3.2km . J22 J P! r f L » HmomtmopH.caoo or d oN 1’ [IT *Nuhvfil >mz om.mu.m .mgoeumasoamo emza H.m musmwm cm or am < a _ q 4 1 Avoutq) >3; 8qu I r171 >ozoku§u ommflmeJImUmfi ‘7‘ o [.18/qu gp/Dp 85 measured data. The assumption is probably a poor one in view of the measured ratios for other states. Most ratios are not constant and assume values significantly different from 8. Unfortunately, however, no other alternative is available. The spectrosc0pic factor values obtained are .042, .120, and .022 respectively for the 0+, 2+, and 4+ levels. The calcu- lations presented in Figure 5.2 for the 12C ground state and 4.44 MeV 2+ reproduce the foward angle data reasonably well, considering the crudeness of the optical parameters. At an- gles larger than 30°, however, the data falls much faster than the calculated cross section. The 0+ and 2+ spectro— sc0pic factors .75 and 2.27 are inexplicably large because the DWBA calculations are anomalously small for this reaction. Figures 5.3 and 5.4 present calculations for 2°Ne and 22Ne respectively. The calculations for the corresponding states in the two isotopes are quite similar, however the data ex- hibit significant differences. For both 2°Ne levels the cross section rises with decreasing angle, as do the calcu- lations, at forward angles. The 22Ne states, however, de- cline, in sharp contrast to the data, as the scattering an- gle is reduced from 20°. All four levels have nearly equal spectroscopic factors. For the 0+ and 2+ 2"Ne levels the values are .022 and .023 while for 22Ne 0+and 2+ they are .038 and .028. As in the case of the neon isotopes, the cal- culations for 5"Fe and 56Fe are almost identical. As can be seen from Figure 5.5, the calculation matches the 5"Fe data very well, at least below 20°. On the other hand, Figure 86 .H.m you we m.m musmfim 385mg .846 cm or em 0 _ q a 4 j l T 1 T 1 1 l I +Nn=o 1.0%: >8: rtruxm 1 L L hid T 1 p . — _ em or oN 7 jITW +OHFHJ m >2 8.0km W o fio [Js/quff 6p/Dp 87 or om o I ITI +NH¥7 i: mmguxm .1: we .H.m “on ma m.m museum ~38me .Edo ow or am +Ofltj m >21 8qu m a m. >ozomussw a mzoNEmmérmBZTN » b L h r b l 1 TS we LJS’//QLLH (SDI/’IJP 88 DJ “J , F‘ I I I I r’ I « P I I I I I +- - b- -. *- 4 v- 4 r- ~ ~ 4 . 1 . .1 » 2E3Mg[3He.7Be]22Ne . EzH.=70MeV mq— - 1V2 - u 3 ‘3 . . U) " -I E . f I . E f G 'O b U ml 1 _ Ex=0.00 MeV . » _ J"=o* f . _ .J“=2* . _l 1 1 l 1 l 1 l 1 l _L l 0 20 HO 60 O 20 HO 60 Gem. [degrees] Figure 5.4 As for 5.1. dCT/dQ [mb/sr] 10‘2 t—fi c’. (A) 89 58Ni[3He.7Be]57Fe E3H9370Mev E,=0.00 MeV J"=0* l L 1 20 HO 10'? T171 f Ex=1.'-}11 MeV .J"=2+ 1 l 0 20 ean.[degrees] Figure 5.5 As for 5.1. “+0 9O -2 10 , , dcr/dQ [mb/sr] Ex=0.00 MeV J“=0+ 1 1 L BONi[3He,7Be]SSFe _ E3H0=70Mev , 10'2 1111 Trlj L Ex=0.8'-[2 MeV .J"=2+ 1 1 [ Figure 5.6 As for 5.1. H0 0 9mm. [degrees] 90 91 5.6 displays very little resemblance between the 56Fe calcu- lations and the corresponding data. The extracted spectro— scopic factors for 5"Fe 0+, 2+, and 56Fe 0+ and 2+ are respec- tively .045, .026, .071, and .025. The actual size of the spectroscopic factors may not be significant because of the assumptions made in obtaining them. Their relative sizes however, indicate the trend of a cluster probability with increasing mass number. The approximate constancy of the a spectroscopic factors agrees with deter- minations by Martin3, et. a1. with the (d,6Li) reaction. VI. CONCLUSIONS The (3He,7Be) reaction has been studied at a bombarding energy of 70 MeV, somewhat higher than previous work on this reaction. Target nuclides used for the present work include 12C, 13C, 160’ zuMg’ stg, 5°Ni, 5°Ni, 52Ni, 5“Ni, 9°Zr, 12°Sn, and 12"Sn,. A limited amount of additional data has been gathered for the targets “°Ca, ll"*Sm, and 2”Pb. An- alysis of the data has proceeded in three directions. An attempt has been made to investigate the extent to which the reaction proceeds by a direct a pickup mechanism. Assuming the reaction to be a direct a pickup, finite range DWBA cal- culations are used to determine a spectroscopic factors, which are taken as an indication of the extent to which a clusters occur on the nuclear surface. As a third use of the (3He,7Be) reaction, the masses of '"'Ar and 120Cd were measured. In addition, some energy levels of ““Ar and 6°Fe were determined. Some stable nuclides, in particular “°Ca, 6"Ni, and 12“Sn, have such an unusually large neutron excess that the nuclides obtained from them by removal of two proton neutron pairs cannot be produced from a stable target by most stand- ard particle transfer reactions. Since the (3He,7Be) reac- tion transfers the correct particles, the opportunity was seized to measure new masses and spectra. Although target contamination presented serious problems, the ““Ar mass ex- cess was measured to be -32.27 1 .04 MeV or about 500 keV 92 93 greater than the Garvey—Kelson mass formula prediction. The Garvey-Kelson mass excess for 12°Cd is closer, only 60 keV above the measured value of —83.98 i .03 MeV. The first ex- cited state of HAr has the anomalously low excitation energy of 700 keV. The lowest first excited state energies of all other even argon isotopes are greater than 1 MeV. Indeed, no even even nuclide of smaller mass has such a low level, most excited states being well above 1.5 MeV. Lawsonz8 has re— ported a calculation indicating a low lying level in ““Ar resulting from core excitation. On the other hand, the first excited state of 6°Fe at 835 i 20 keV continues the pattern of the other iron isotopes: 5"Fe 1409 keV, 56Fe 847 keV, and 58Fe 811 keV. Another problem to which the data have been applied is the question of the reaction mechanism. In contrast to the (d,6Li) reaction, the (3He,7Be) reaction appears to be a dir- ect process. Comfort“, et. al. have concluded that the (d,°Li) reaction mechanism is largely a complex multistep process, probably at all energies. They find that unnatural parity states, which should not be excited by a purely a transfer mechanism, are as strongly excited as many natural parity states. On the other hand, Détraz, et. al. have found that even at 30 MeV, because of primary and secondary an— gular distribution similarity and forward peaking, the (3He,7Be) reaction is predominantly a direct a pickup re- action. Further work by Détraz has confirmed the direct nature of the reaction and has established that four nucleons 94 are transfered predominantly as an a particle fragment. Transfer as an isospin l excited a particle was found to be only a negligible component of the reaction mechanism. If the (3He,7Be) reaction at 30 MeV is direct, then it certainly will be at 70 MeV. Indeed, aside from the 8Be (17.64) 1+ and 2°Ne (4.97) 2- levels, unnatural parity states are not observed; the two exceptions being only weakly excited. The 2°Ne (4.97) 2- peak differential cross section, for example, is 5 pb/str whereas the 2°Ne (1.63) 2+ has a maximum cross section of 20 ub/str. Furthermore, most angular distri- butions show sharply decreasing differential cross section with increasing scattering angle. Since the reaction cal- culations, which are based on the assumption that the double proton neutron pair is transfered as an a particle, are able to produce a reasonable description of the experimental angu- lar distributions, the reaction may be regarded to some ex- tent as a direct a transfer process. The secondary to pri- mary cross section ratios, however, show that this view of the reaction mechanism cannot be completely correct. Assum- ing direct transfer of a monolithic a particle, the secondary to primary ratio should equal 2j1+l/2jo+l = 8, jo and j; de- noting respectively the ground and first excited state spins of 7Be. The two 7Be levels differ only in the orientation of the 3He spin relative to the 3He - a orbital angular momen- tum. Therefore any deviation of the secondary to primary ratio from 8 indicates that either a process more complicated than a transfer occurs, or the differential cross section for 95 the reaction somehow depends on the internal spin orientation of the 7Be nucleus. In fact the data does exhibit such de- partures from 8. Although many individual ratio values are near 8, for most angular distributions the ratio behavior with angle is not constant. For many distributions, the ratio varies smoothly with angle and in one case, the 2°Ne ground state, the ratio reaches a distinct minimum of 0.2 at a center of mass angle of 13°. The ratios range, for the most part, between 0.2 and 0.8. Only in isolated cases does the ratio exceed 1, i.e. the primary peak is almost always larger than the secondary peak. Although ratio values sig- nificantly different from 8 occur, the sensitivity of the transfer hypothesis to these departures is not clear. There— fore, for the purposes of the present work, the a transfer mechanism is assumed to be substantially correct. In fact, ratios for some levels actually have a reasonably constant value near 8; for example 9Be (0.00) 3/2-, 2°Ne (1.63) 2+, and 22Ne (1.28) 2*. To the extent the direct a particle transfer mechanism is correct, the data, together with the reaction calculations, may be used to obtain an estimate of the probability for oc- curance of a particle clusters on the nuclear surface. Be- cause 3He particles are strongly absorbed, a 3He penetrating the nuclear surface loses its identity. Thus an a particle picked up by a passing 3He may be assumed to have come from the nuclear surface. As a numerical measure of clustering, a particle spectroscopic factors have been calculated. Peak 96 differential cross section for the ground state transitions are plotted in Figure 6.1 against target mass number. The cross section drops dramatically from 70 ub/str for 12C to 8 ub/str for 2"Mg. The cross section continues to decline, though less rapidly, to less than 0.2 pb/str for 2”Pb. From 5“Ni to 1HSm the cross section has the nearly constant value of 1.0 ub/str. The cross section decreases smoothly with atomic mass number except for the low 13C point; anomalous perhaps because, in contrast to the other targets, its mass number is odd. In addition to declining with increasing tar- get mass, the peak differential cross section decreases as additional neutrons are added to the target. Figure 6.2 plots peak differential cross section of the ground state transitions against neutron excess. Data for several ele- ments are included on the same plot by normalizing the data for a given atomic number so as to make the normalized value 1 for the nuclide with the smallest neutron number. The ab- scissa is taken to be the number of neutrons exceeding the number for the lightest isotope of the given element. In all cases measured, the peak cross section declines with neutron excess. The decrease is about the same for all ele- ments so the effect is independent of target mass. It would appear that excess neutrons tend to dilute a particle clus- ters on the nuclear surface. The decline of peak cross section with increasing mass number and neutron number would tend to indicate a decrease of surface a cluster probability. That is, a clustering is 97 Figure 6.1 Peak differential cross section for (3He,7Be) at 70 MeV vs. target mass number. 98 100 I I III 9 1 1 11 T 1 10 ° 1,1 1 1111 do/dQ [ub/Sfr‘] . (3 p..- l Ifi’IT] #94 14H h—ihd l 11 111 I I 1 1 1 _ . f 1 1 l. 1 1 l 1 1 l 1 1 1 l 1 1 1 1. l 1 1 l 0 30 80 90 120 150 180 210 Torge+ Moss Number Figure 6.1 99 Figure 6.2 Peak differential cross section for (3He,7Be) at 70 MeV vs. target neutron excess. 100 mmooxm c0L+Joz m .m 6.33m m m m m r m o _ _ _ _ _ _ m 1 1N5 m 1:4.Mw p 1m.om0 - m1 cm .v 1mgrmw _z p - DU 0 . a: . 1oH 0 x 1 b _ — _ _ _ NA 101 Table 6.1 a spectroscopic factors. Reaction Ex (MeV) 12C(3He,7Be)eBe 0.00 2.94 11.4 160(3He,73e)”c 0.00 4.44 2‘*Mg(3He,713e)"-°Ne 0.00 1.63 26Mg(3He,7Be)22Ne 0.00 1.27 58Ni(3He,7Be)5"Fe 0.00 1.41 6°Ni(3He,7Be)56Fe 0.00 0.85 O NO 102 most likely to occur for light a particle nuclei, those for which neutron and proton number are equal and even. However a more valid conclusion is to be drawn from a spectroscopic factor values. By comparing the data to the DWBA calcula- tions, as the spectroscopic factors do, decreases in cross section not related to a clustering are removed. Table 6.1 lists the a spectroscopic factors determined with the DWBA calculations. In contrast to the peak cross section values, the spectroscopic factors do not decline. Except for the anomalous 16O values, they are nearly constant. Therefore the a clustering phenomenon does not lose importance for heavy nuclides. APPENDICES APPENDIX A KINEMATICAL FORMULAE The following formulae have been used for the kine- matical calculations discussed in Chapter III. They apply to a nuclear reaction of the form A1(A2,A3)Au , where nuclide A1 is initially at rest. Nuclide Au may be left in an ex— cited state, the excitation energy of which is denoted by Xu. The formulae also can be applied to the case where nuclide A3 is excited, e.g. 7Be (.432), by subtracting the excitation energy X3 from the Q-value and adding it to the ground state mass. Ti shall denote the kinetic energy of nuclide Ai' pi its momentum, and mi its mass. 6 is the laboratory scatter- ing angle while ¢ is the scattering angle in the center of mass reference frame. 0 denotes the center of mass to labor— atory differential cross section ratio. Let Q(m1+m2'm3-5Q) + T2(m1-m3) B = m1+m2+T2 Y = m1+m2+T2 [111311111 (2 (m2+T2)+m1) B = /(2m2+T2)T2 m1+m2+T2 6 = JBZ+m3(213+m382co?‘e) . Then the kinetic energy of the particle to be detected is given by _ B+m382cosze+68cose . T3 — l—BzcosYG and Its momentum by P3 = /(2m3+T§)T3 . 103 104 The kinematic broadening is (in energy units per degree) 1:3 _ _ Bsine mchose d6 — .0175 1_B:COS¢§»{ZBCOSBT3+m38cosa(2+———E———]+6}. Given the detected particle's kinetic energy, the excitation energy of the residual nuclide may be computed as follows: Let 00 be the Q-value to the ground state of the residual nuclide and let a = 2T2(m1-m3)-2(T3-Bcosep3)(m1+m2+T2), then _ Q§+ZQomu+a Xu- 4 . Finally, the center of mass m.+/(m1+m2-m3)z+a angle and cross section ratio are given by = -1 P3Sin6 ¢ tan [7(p3cose-B(T3+m3))] and p = [Yiipacose-8(T3+m3))Zipgsin2633/z YP§(P3‘BCOSBIT3+m377 ° APPENDIX B Y DECAY KINEMATICS The decay of the 432 keV first excited state of 7Be in- troduces an additional energy spread into secondary peaks of (3He,7Be) spectra. The mean lifetime of the state is 0.27 ps so most excited 7Be nuclei travel no more than 1 um before decaying. None enter the spectrometer magnet. In the center of mass reference frame of the excited 7Be nucleus, the re- coiling 7Be ground state nucleus has velocity C = —;7——7- where m* is the excited 7Be mass and m is the ground state mass. The velocity of the center of mass system relative to the laboratory is 72m*T+Tz B = T+m* where T is the kinetic energy of the excited 7Be nucleus. Let E - 1 = 91::2: and «T? 21m“ y: 1 =1+I%*o /1-82 If the photon is emitted at a center of mass angle 8 relative to the direction of travel, the recoil energy of the ground state 7Be nucleus relative to laboratory coordinates is T' = m[€y(l-Bccos6)-l] . 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