COULOMB DISPLACEMENT 'ENERGIES 0F lfm SHELL ’ MIRROR NUCLEI Thesis for the Degree of Ph. D. MICHIGAN STATE UNIVERSITY I DENNIS WARREN MUELLER 1976 ‘ F. v .u- .-.. 33*; w 39¢an? fr " w ". _ V v 9 TV. '7‘ .3. ‘4 v! 1-" ~ ‘-‘- a I.“ o-YL- " t '.‘ , a 'I . . ¢ f- .: ,~ v.9. ' 0 ‘ — .J‘qh} u . 9‘2"“ ' . a! I h i . - ~"r ‘ Fl A 1 Mme-muse“: a» 3293113“ This is to certify that the thesis entitled COULOMB DISPLACEMENT ENERGIES ‘ OF lf7/2 SHELL MIRROR NUCLEI presented by Dennis Warren Mueller has been accepted towards fulfillment of the requirement Ph ° D' degree in_] .332 Date June 21, 1976 0-7 639 ABSTRACT COULOMB DISPLACEMENT ENERGIES OF lf SHELL MIRROR NUCLEI 7/2 by Dennis Warren Mueller 5 The Q-values of the L+6Ti(3He,6He)u3Ti, OCr(3He, 47 5Q 58 6He) Cr, Fe(3He,6He)SlFe and Nit3He,6He)55Ni reactions have been measured and the mass excesses of of the Tz=-l/2 residual nuclei deduced. The exitation energies of several levels below 7 Mev in the final nuclei were measured. Angular distributions of the J”: 7/2-, 3/?+ and 1/2* levels were taken and compared to those from the uzCaC3He,6He)39Ca reaction. The measurements were made using the 70 MeV. 3He beam from the Michigan State University Cyclotron. The 6He particles were detected in the focal plane of an Enge split-pole magnetic spectrograph by'two resistive- wire gas-prOportional counters and a plastic scintillator. The Coulomb displacement energies of the 7/2-, 3/2+and 1/2+ levels of the A=Hn+3, T=l/2 mirror nuclei in the 1f shell were extracted and compared to 7/2 calculations. The new mass values were employed in the Garvey-Kelson Symmetric Mass relation to predict the mass of 32 proton-rich nuclei with T>ll2 from Vanadium through Nickel. COULOMB DISPLACEMENT ENERGIES OF lf SHELL MIRROR NUCLEI 7/2 by DENNIS WARREN MUELLER A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Physics 1976 ACKNOWLEDGMENTS I would like to express my sincere appreciation to the faculty and staff of the Cyclotron laboratory for their support during my graduate study at Michigan State University. In particular, I wish to thank Professor Walter Benenson and Dr. Herman Nann for their help in acquiring some of the data for this thesis as well as Steve Motzny for his help in preparing some of the figures. I am indebted to Dr. Roger Markham for valuable discussions on detector design and to Norbal Mercer and his staff for their help in fabricating the detectors. I am especially grateful to Professor Edwin Kashy for suggesting this tOpic and for his guidance during the work for this thesis. Finally, I wish to thank my wife, Linda, for typing the manuscript and for her patience and support throughout my graduate study. ii TABLE OF CONTENTS Pegs LIST OF TABLES 111 LIST OF FIGURES iv 1. INTRODUCTION 1 2. EXPERIMENTAL PROCEDURE 8 2.1 Particle Identification 10 2.2 Beam Energy 22 2.3 Spectrograph Calibration 2” 2.4 Detector Calibration 26 2.5 Target Thickness 27 3. EXPERIMENTAL RESULTS 3.1 Mass Measurements, Q-Values and Excitation Energies 30 3.2 Angular Distributions ”7 3.3 Displacement Energies 51 H. DISCUSSION 4.1 BFZ Model for Displacement Energies 55 u.2 Mass Predictions ' 63 IAPPENDIX A DETECTOR DEVELOPMENT 66 APPENDIX B 57Ni MASS MEASUREMENT 74 LIST OF REFERENCES 76 (A) H F4 l4 H FJ +4 (A) H H iii LIST OF TABLES Momentum-Matched Reaction Pairs Target Thickness Mass Excesses Q-Values of Reactions Error Analysis . . . 43 . Exc1tation of Levels in T1 Excitation of Levels in ”7Cr Excitation of Levels in Sire Excitation of Levels in SSNi Experimental Displacement Energies Comparison of BFZ to Experiment Inter shell Coulomb Interaction Mass Predictions 57Ni Mass excess Page 23 29 3” 35 36 37 38 39 5a 50 61 6A 75 F4 l4 F‘ +4 I4 F1 +4 14 (II iv LIST OF FIGURES Block Diagram of Electronics Specific Ionization in Propane Time-of—flight Spectra Energy Loss Versus Position Energy Loss Versus Time of flight Light from Plastic Scintillator Light Versus Position 4 . Thick Target Spectra of 6Tl(3He,6He) Thick Target Spectra of 50Cr(3He,6He) Thick Target Spectra of S”Ee(3He,6He) Thick Target Spectra of 58Ni(3He,6He) High Resolution Spectra High Resolution Spectra Comparison of Live and Recovered Spectra 6 Angular Distributions of (3H9, HE) Reactions Reduced Coulomb Displacement Energies of JW = 7/2' levels Coulomb Displacement Energies of JTr = 3/2+ and 1/2+ levels Coil Counter Electronics for Coil Counter Spectra Taken with Coil Counter Page 15 16 17 18 19 20 21 40 41 42 43 44 45 46 50 55 62 71 72 73 I. INTRODUCTION Mirror nuclei are those nuclei which can be made from each other by interchanging all protons and neutrons. Under the assumption that the nuclear part of the nucleon-nucleon force does not depend on whether neutrons or protons are involved, the binding energies of two mirror nuclei differ only by the Coulomb interaction of the protons. This difference in the binding energy is called the Coulomb displacement energy (ABC). The Coulomb displacement energies of mirror nuclei were first measured by determining Emax of the 8+ particles emitted in the decay of the proton rich member of mirror pairs. Then ABC is just Emax+moc2 + (Mn-Mp)c2 where m0 is the electron mass and (Mn-Mp) is the neutron-proton mass difference.EVSS Currently, however, accurate measurement of the masses of nuclei in magnetic spectrographs can be used to determine ABC to the accuracy of a few keV. The experimental value of the Coulomb displacement energy between two isobaric nuclei differing by one unit of charge is given by ABC =M) [M(Z<)] denotes the mass of the nucleus with the greater [fewer] number of protons. l Historically, Coulomb displacement energies have been employed to provide information on the nuclear charge radius. Evans EvSS, for example, discusses nuclear radii extracted from several different types of data including Coulomb displacement energies. He assumes a homogenously charged spherical nucleus and finds QEC ' 6/5 .ELE? for the Coulomb energy ‘difference between twoRmirror nuclei differing by ~ one unit of charge. Here Z p >-70 cm., which corresponds to a distance of 25 cm, along the focal plane, the time- of—flight in the spectrograph varies only by about 2%. Therefore, the time-of—flight of an ion species is about the same at all points along a detector in the focal plane.“ Figure 2.1.3 shows the time-of-flight spectra for several ion species. The time is measured by using the anode signal from the photomultiplier on the plastic scintillator as a start pulse and the 12 r.f. signal from the cyclotron as the stop pulse in a time-to-amplitude converter (T.A.C.). Thus, in the time-of—flight spectrum, the fastest ion species yields the largest signal from the T.A.C. The time resolution is strongly affected by the angular spread accepted by the spectrograph 'entrance aperture. The data in Figure 2.1.3. taken With a 20320 aperature, clearly shows that the slower ion species have a broader time-of-flight peak. The ratio of the widths of the proton to triton peaks is 5:12 instead of 1:3 which is predicted from the ratio of the velocities of the particles, under the assumption of no contribution from the beam or detection system. The small departure from a ratio of 1:3 implies a contribution of less than 1. ms. to the resolution from the beam and detection system. Since the time~oftflight of an ion through the spectrograph is inversly proportional to its charge to mass ratio, there is an ambiguity in the identification of particles having the same charge to mass ratio. This ambiguity is removed by the energy loss in the gas of the proportional counters as Figure 2.1.4 indicates. A 74. Mev. 3He beam incident on a 13 C target produced the reaction products for the plot of time of flight versus energy loss shown in Figure 2.1.5. In this l3 figure, particles having a low specific ionization were eliminated by means of a coincidence requirement that their energy-loss signal be at least as large as that Of 6Li ions having the same magnetic rigidity. It is clear from Figure 2.1.5 that the combination of time-of-flight and energy loss information is a powerful particle identification scheme. There is one further piece of information available for particle discrimination and that is the total light output of the particle in the plastic scintill- ator. Because gamma rays and neutrons arrive at the detector at all times, a gamma ray or neutron could trigger the T.A.C. and produce a time-of-flight signal equal to that of the particle of interest. This time signal in coincidence with an anomalously large energy-loss signal from a lightly ionizing particle or with a large energy-loss signal due to pileup of light ions could cause misidentification of the event. However, a low level discriminator is used to analyze the anode signal before it can start the T.A.C. This low level discrimination helps to eliminate random time signals produced by gamma rays and neutrons since the light output from these particles is generally smaller than those for the particles of interest. Figure 2.1.6 shows a plot of light output versus magnetic rigidity 14 for various particle types stopping in the scintill- ator-Be7s The total light output is useful for redundant particle identification, as well as for discrimination against gamma rays and neutrons. The use of very thin (.23 mm.) scintillator aids in the reduction of the neutron and gamma-ray background. Furthermore, lightly ionizing particles pass through the thin scintillator producing only small light signals, thereby facillitating identi- fication of the heavier particles. Resolution of the light output spectrum is limited by the light collection efficiency which varies with position in the detector. A plot of the light output versus position in a typical detector is shown in Figure 2.1.7. Use of a two-dimensional gate for light as a function of position can improve the usefulness of the light output information. Such gates are made possible by the use of the,computer programs III EVE and EVEN.A1176 By employing the particle discrimination system described above, cross-sections as low as 7 nb/sr have been observed, and the use of exotic transfer reactions 8 3 . such as ( He, Li), (3He,8B) and (3He,9C) has been made possible. 15 J\ 1/ -PM BASE (ORTEC 265) .PM TUBE '(RCA 8575) -.LIGHT PIPE IPLEXIGLAS G) '. r-SCINTILLATOR (PILOT BI BACK PROPORTIONAL COUNTER-7 FRONT , PROPORTIONAL COUN’TER; r DEE RF PARTICLES ‘1 <—:.\\ VLT U V AMP AMP AMP AMP AMP DISC 200 l . I____I SUM SUM ' AMP AMP SCA TAC DELAY SCA SCA scq I , . ‘ h 5 r —l [I \ W COINC L ,L J. I I L *1 LIN LIN LIN LIN GATE GATE GATE GATE 2-7 was Y z < I Figure 2.1.1 Block diagram of electronics used in this detection system. Note that only the second proportional counter and the discriminator on the anode signal from the P.M. tube need be used as live gates. All other signals can be event recorded on magnetic tape. .mcow moowsm> mo >pfiowmws aflpmcmme mdmpm> momooso ow .mmw3 one osoz mmocmsmmom 609m coxmu 09o :owpmuficofi oawwooom mo mmoam> one COHPMNHCOfl oamaowam N.H.~ Gasman O _ l6 «Ifi— 4 Id 4 _u_ . r b _L p. 00 mu 7: 30 40 50 60 Particle Energy (ZZIA MeV) 20 IO ae\~eo->e§ 8:822 0%an .90900w0o 05p 00:000& 02 0fi90cwme 0:9 .v0msop w: .mo 0pmwm ocoosm 0gp Eosm mc0H MA may #0:“ £030 003 0H0wm am :0 Emma 0m >0: :.ms 0 >o o0ooooma 0903 muosooso cofiw000s 0:9 .0cmao Hooom commwoepo0om 0:# my p0wsmu 05w Eosm unwfiam mo 0EMB m.a.m 0sowflm 300 H00 200 CHANNEL NUMBER amzz ' tive- Is In a P8818 tic ion 'ty in par it igui the amb 10n versus pOS t ioniza ion removes t The particles were preselected by their time of flight through ioniza Note that the specific from the time of flight. Storage scope display of specific - 0 $4 m 0 -H +4 £4 C m d O > U 0 E‘- H 0 £ 'C U O_-_v-I .H 0': 44.123 Leah OIUC Q9 0 : ODWH -$‘-Io+-* FIQSIM -I P O Nmo-r-I MO)M 0 WCMH F-alUH—I 3 0 C ws40 0 'F‘I'HS'U h 3+MH TIME OF FLIGHT AE 903 1 C foil. 0 he propqrtiona t He beam impinged on an enriched 1n ht versus energy loss ' 1% ted with an external gate. 1 were e imina produced by a 74 MeV 1 6L that Storage scope display of time of fl 10n121ng The particles were Figure 2.1.5 counter. Paricles less \Jbeflul “JILJIJIHI/ L—l\dl H (JJ IO Figure 2.1.6 20 l I 20 plastic scintillator. Except for Be75. energies of 6522/A to 93 22/A MeV. to yield one-half the lig two-thirds the light of He. I 1 30 4-0 ' ' 5C Light versus magnetic rigidity for particles stopped in 6He the curves are from Refere ce 6He data was taken in connection with this thesi at He Also at E=1l Z /A MeV C was found ht of 3He and at E216 22/A MeV, 33 gave about .u. «Km ~ 7... . IDIP.‘0: HH acouopm x >0: HH m 5303 x H mesa—ounces.» I m H u coauouwm ovxamv so nosomx. mov\>0x A>0zv om ovxuv u A coda c an naaum :owuooom vacuumxuazucoaox sou H.N.N 0HDMB Q m anacoEO: uoaoopm cowpouox 0:0 magnum anon ucoowocu 7Q 24 2.3 SPECTROGRAPH CALIBRATION The momentum analyzing characteristics of the Enge 90 cm. split pole spectrograph have been cali- brated for the region of the focal plane where both calibration and unknown particle groups are placed. The beam energy was adjusted for momentum matched reactions, thereby determining the magnetic rigidity (B0) of the reaction products. Then a series of other reactions were used to produce reaction products which were placed in turn at the same position on the focal plane. As the field was increased a proton NMR probe measured the magnetic field in a flat region of the spectrograph. In all the measure- ments a cycling procedure was used and the field set on the increasing current side of the cycle. It was found that the magnetic field along the path responsible for the bending, del, was, in Spite of the recycling procedure, sensitive to the rate at which the spectrograph field energizing Sn67 This was ascertained current was increased. by recycling and then increasing the field directly to the value where the momentum matched reactions were observed. The procedure was then repeated allowing the spectrograph to remain at several intermediate field values as the field was increased. In all this, the matched reactions insured that the 25 beam energy and Bo values remained unchanged. The problem was clearly the edge fields. By limiting the rate of increase of the current (15 min. from zero to 16Kg field), reproducibilities at the l/20,000 level can be obtained on successive recyclings.sn67 The magnetic rigidities of the 6 27 He particles from the calibration reactions Al(3He,6He) and 25 M8<3He,6He) are nearly the same as those of the 6He particles from the reactions of interest. Therefore, only small changes in the magnetic field are necessary and these small changes imply an uncertainty in the mass measurements of less than 2 keV. 26 2.4 DETECTOR CALIBRATION A resistive-wire proportional counter was used to detect the position of the reaction particles in the focal plane. The detector was calibrated by performing a least-squares fit of rho versus channel number . . 12 for the alpha particles produced in the C(3He,uHe), 25 5 4 M8(3He, He) and uFe(3He,uHe) reactions. The energy levels in the residual nuclei of these reactions are well known.Aj75’Sh76’ En73, ND73 This procedure resulted in an rms deviation of about 4 keV of the observed from the accepted values for the excitation energies. The gas gain of the detector is adjusted so that the size of the signals is the same for the 6He particles as for the alpha particles. This is done in order to eliminate a shift in the electronically derived position from signals of different sizes. The use of this method of calibra- tion resulted in uncertainties'in the excitation energies of about 2 Rev per MeV of excitation energy due to different calibrations used. This uncertainty is added in quadrature to the uncertainty of 3 keV from the residuals and the uncertainty of 2 to 22_keV in the centroid determination for the low cross-section (3 . 6 . . He, He) reactions. 27 2.5 TARGET THICKNESS MEASUREMENTS The mass measurement of the 4n+3,Tz = -l/2 nuclei has been made on two sets of targets. The first set, with the exception of the 50CP target, consisted of 259 to 324 ug/cm2 carbon backings. The thickness of the self-supported foils was measured by means of the energy loss of 5.48 MeV alpha particles from 21+lAm. The energy of the alpha particles was measured in a surface barrier silicon detector. The thickness of the carbon-backed targets was measured by means of the energy loss of 56 MeV 6Li particles from the 12C(3He,6Li) reaction. A 217: 22 pg/cm2 carbon foil was employed to measure the cross-section for this reaction of 130tl7ug/sr at eLab E 100. The spectrograph was used to measure the energy 0f the 6Li ions. The targets were rotated so that the carbon backing faced either towards or away from the spectrograph aperature. The difference in the observed energy of the 6Li particles for the two target orientations is just thesLi energy loss in the meta1-target. -The size of the 6L1 energy loss was 12. to 27. keV. The specific ionization of 56 MeV 6Li particles is about twice that for 52. N070 MeV 6He particles. Hence, use of the 6Li energy loss should yield an accurate determination for the 6He energy loss in the targets. The thickness of the carbon backings was determined by measuring 28 the relative yields 0f 6Li particles from the backings and from a thick carbon foil, as well as the energy loss of the 6Li ions in the backings and in the thick foil. The thickness of the backings ranged from 25 to 47 U8(em2. Table 2.5.1 shows the thickness, method of measurement and energy-loss corrections of the targets. 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The line indicates a shell model prediction of Chung and WildenthalCh7” while the dashed line connects experimental points. 56 ”.1 BFZ MODEL FOR DISPLACEMENT ENERGIES Sherr and Bertsch have employed the Bansal-French- Zamick model (BFZ) to calculate the Coulomb displace- ment energies of excited particle-hole states in light nuclei and report that typically the level shifts are reproduced to within 50 keV.Sh75 The BFZ model can be employed to find displacement energies by finding the difference between the binding energies of the particle-hole state and of its analogue. Under the assumption of charge symmetry and charge independence of the nucleon- nucleon interaction, the difference in the binding energy of the analogues is due to Coulomb effects. Under this assumption in the BFZ model, the binding energies of the nuclei can be replaced by their Coulomb energies, and only the Coulomb part of the particle-hole interaction need be considered. For an m-particle-l-hole state the hole con- figuration is designated by H and the remaining core configuration by C. Then, the particle-hole state can be represented by H 9 C, and the Coulomb energy of a state with isospin (T,Tz) is given by 2 £0 = E (chi) TZ(Ci) TCHi) Tz(Hi)]T Tz) The Ui and “i are the numbers of proton holes and proton particles and c is the Coulomb interaction S7 of a proton hole with a proton particle in a different shell. The index i is used to designate the constituent states necessary for a state of good isospin. In this model it is necessary to distinguish between A = un+l and A = un+3 T = l/2 mirror nuclei. For the latter case, the excited state H 9 C, is given by {(lh) a (A+1)T=O} T=l/2 ”3 . . _ For example in this model the nucleus T1 in its + . . . 3/2 exc1ted state has the configuration: (d )-1 T=l/2 (f )” T=O 3/2 T =1/2 9 7/2 Tzzo z The real nuclei which have the d3/2 neutron 40 hole in a Ca core and 2-f7/2 protons and 2'f7/2 neutrons outside the noCa core are 39Ca and II respectively. The mirror of L‘BTi is 1‘380 Ti + - . . . whose 3/2 configuratlon 1s )-1 T=l/2 9 (f ” T=0 (ds/z Tz=-1/2 7/2) TZ=O in this model. The real nuclei having these (dB/2)-l and (f7/2)I configurations about a ”OCa core are 39K and LW'Ti. Then, the Coulomb displacement energy of the lowest 3/2+ level in these A=u3, T=l/2 mirror nuclei in this model is AB (53,3/2+) = AEC(39,3/2+) + 2c(3/2+,7/2') C where AEC(39,3/2+) is the Coulomb energy difference of the 58 39 39 + - 3/2 ground states of Ca and K, and c(3/2+,7/2 ) is the Coulomb interaction of a <:13/2 proton with an lf7/2 proton. This method can be extended to the lowest 1/2+ states by employing AEC(39,l/2+) and c(1/2+,7/2-). The results of calculations using this method for the A = ”n+3, T = l/2 mirror nuclei with m-particle-l-hole states are given in Table u.l.l Three different methods of determining c were employed. First, the values of c(3/2+,7/2') =289keV. + - and c(l/2 ,7/2 ) =286 keV determined by Sherr and Sh75 Bertsch were used. Those values of c predict ABC to be progressively smaller compared to the experimental values as the shell is filled. That is A: AEccalc - ABC exp. becomes smaller as A increases. Second, a least squares fit of c to the data was performed. The values obtained were C(3/2+97/2-) = 296 keV and c(l/2+,7/2’) : 302 keV. These values improved the overall agreement with experiment, however the systematic trend in A still exists. Finally, the slope of ABC versus A was fit. This leads to the even larger values of c(3/2+,7/2’)= 3162keV and c(l/2+,7/2-) = 321 keV which remove the systematic trend of A. However, this is achieved at the cost of over-predicting ABC by approximately 125 keV throughout the shell. This large difference may be due to the unusually large displacement 39 _39 energy of K Ca, which has been ascribed to the 59 large binding energy of these nuclei.Mu75b Figure u.1.l is a graph of ABC vs A for the 3/2+ and 1/2+ levels in the A = Un+3, f7/2 shell nuclei. The solid line represents the calculated values of ABC using c(3/2+,7/2'),[c(1/2+,7/2‘>] = 295 keV [302 keV]. The dashed line represents the calculated ABC with c(3/2+,7/2‘) [cl/2+7/2-)] = 316 keV [321 keV] with 126 keV [117 keV] subtracted from all the calculated 3/2+ [1/2+] levels. The dashed curves exhibit remarkable agreement with the data. The values 126 and 117 keV subtracted from the calculated values of ABC agree with the increase of ABC in mass 39 expected due to the large 39 Mu75b neutron separation of K Finally, the f7/2-d3/2 and f7/2-281/2 Coulomb 1nteract1on was calculated using both harmonic oscillator and Woods-Saxon wave functions. Table u.l.2 summarizes these calculations which exhibit approximate agree- ment with the experimentally derived Coulomb inter- actions. 60 .>mx Hmmuxlm\h.+w\floo new .>mx mamuxlm\s.+w\mvo ocflm Op omEnomwwm mma mmfimwmcm pcmsmomammfio may mo macaw esp 0p paw mmnmsdm ummma < Amv .>mx Nomuxlm\s.+m\aso cam .>wx mmmux-m\s.+m\mvo ocwm ow omenomnma mos mmwwnmcm pcmEmomammflo Hopcmeflpmaxm may ow uwm mmbmsdm pmmma < Amy .cowpomnmpcfl «\smum\amm may pom .>mx mmmufinm\n.+m\avo new coyonm «\um m sea: couoaa «\mo m mo coapomnmpcw nsoasoo may pom .>mx mmNuA-~\s.+m\moo mo nomppmm can ppmgm no monoco may muomawmn meowpmflsoflmo mo pmm whee AHV Amavmm + Amvmmm.m Amavmuu Amvmom.m Amavmomu Amvasm.m Amva:u.m +N\H mm AmvamH+ Amvoma.m Amavmm+ Amvmmo.m “mavanu .Amvmmm.m Amavojo.m +N\H Hm Amavo:a+ Amvhmm.m Amavzm+ Amvamz.m “wave + Amvumm.m Amavumm.m +N\H a: Awavoaa+ Amvmmm.m Amavmu+ Amvnmm.> Amavoa+ Amvmmm.n Amavmm>.n +N\H m: Amavmma Amvmmm.m Amavmma Amvmso.m Amavumn Amvmam.m Amavmou.m +m\m mm Azavwma+ Amvoom.m Azavam: Amvomo.m Aravmmn Amvmmo.m Amavmno.m +m\m Hm Azfivmma+ Amvmmm.m Azavm3+ Amvmm:.m A3vaa+ Amvom:.m. AmHVm::.m +N\m u: “mavema+ Amvmmm.m Amavum+ Amvmmm.h Amavmu+ Amvmmm.u Aaavmom.w +N\m m: a A$28 oma a A$33 oma a 2v28 oma axm oma :5 < .>mx an “muons Hamnm «\sea .m+c:u< .~\Hua no mmpmum maonuanmaowppmmns mo mofimnmcm “cosmomammwa H.H.: manme Table H.l.2 61 Coulomb Interaction Between Shells Exp. (keV) H.O. a) w.s. (keV) (keV) Direct Exchange f7/2'd3/2 316 f7/2‘281/2 321 308 338 -16 29M 328 - 6 a) Calculationomade using the oscillator parameter v =.258 fm'“. 62 l l l l 3/2+ LEVELS \lVleV) u . — I/2+ LEVELS 8.4- 8.0 - 7.6- 72 ~ ‘ “ ' ' ‘Figure u.l.1 Plot of the Coulomb displacement energies of the lowest 3/2+ and 1/2+ levels of the A=un+3, T=l/2 mirror pairs the f7/2 shell. The lines are the results of the calculations discussed in the text. 55 in 63 ”.2 MASS PREDICTIONS The current mass-excesses of the nuclei in the f7/2 shell can be used to update the mass predictions based on the Garvey-Kelson symmetric mass relationKe66 of the proton-rich f.”2 shell nuclei. This method, based upon an independent particle model, takes into account size, shell and pairing effects. In the cases where prediction and experiment can be compared, agreement at the 150 keV level is found with the largest deviations observed when nuclei from more than one sub shell are used in the relation. Table‘4.2.l lists the calculated mass excesses of 23 T2 3 -1 isotopes from V through Ni which ‘are predicted to be stable against alpha particle emission and against one or two-proton emission. Also listed are the first two isotopes predicted to be unbound to one or two-proton emission. U8 . In view of the predicted particle stability of N1 and que, it appears that the experimental observation of nuclei all the way out to the proton drip line will require some rather exotic heavy ion reactions and pose quite a challange to the experimentalists. 6I Table Ll~2-1- Predicted mass excess using Garvey-Kelson symmetric mass relation.a Mass excess Separation energyb (MeV) Nucleus (MeV) One proton Two protons -1 L”‘v -23.93 1.91 6.31 ”5CrC -29.56 5.02 6.6I 48mm —29.31 2.03 6.81 50Fe -3I.50 I.13 5.22 5200 -3I.39 1.I9 6.3I 5”Ni -39.27 3.92 5.53 13 2 ”3v -17.92 0.10 3.97 ”SCr -19.SI 3.1I I.95 1”Mn -22.65 0.32 5.3I ”9Fe -2I.76 2.76 I.79 5100 -27.I0 0.19 I.32 53Ni -29.66 2.59 I.07 T =-2 ”2v - 9.02 -0.37 2.09 ””Cr -13.5I 2.96 3.06 “Sun -12.62 0.22 3.36 ”8Fe -19.17 2.92 3.1I 5006 -17.73 0.26 3.02 52Ni -22.68 2.59 2.77 -2 2 ”iv 0.09 -1.91 0.I3 ”3Cr - 2.19 1.I5 1.09 l+5191 — 5.17 -1.1I 1.92 I”Fe - 7.15 1.9I 2.06 “900 - 9.95 -0.93 1.99 51N1 -12.02 1.59 1.95 —3 ”zap 6.17 1.25 -0.56 ””Mn 6.35 -1.26 0.19 1+5Fe 0.53 1.60 0.I5 I800 0.97 -0.9I 1.00 50Ni - I.13 1.I9 0.56 ”5 ”9N1 H8 _ 7 Tz--7 13.58 0.08 -l.18 7.61 0.67 ‘ -0.17 T =-I 2 15.43 0.50 -l.3l b) c) Masses used in the relation are the present experimental results, Mass 71 mass values of A.H. Wapstra and N.B. Gove, Nucl. Data A9, 267(1971), for the 55Co mass excess is -5I.027510;0022 MeV from P.L. Jolivette et al. Phys. Rev. 910, 2u$9(197u) and for the mass excess of ”9Cr is -u5.327-0.0029 MeV from P.L. Jolivette et a1. private communication and Phys. Rev. 913, u39 (1976). Negative binding energy indicates nucleus unbound to particle emission. Experimental mass excess is -29.I6:0.03 J. Zioni et al. Nucl. Phys. A181, ”65(1972). 65 66 APPENDIX A DETECTOR DEVELOPMENT Previously resistive-wire-proportional counters have been used successfully at the Michigan State University Cyclotron Laboratory and elsewhere.F1173 However, position resolution has been limited for particles incident at ”5° to the counter to full widths at half maxima of 1.8 mm. for 35. MeV protons, 0.8 mm. for 25 MeV deuterons and 0.6 mm. for 25 MeV alphas. There are three difficulties to be overcome in improving these counters. The first is the lack of isolation between the preamps at each end of the coil, which limits the signal-to-noise ratio. Second is straggling which causes an uncertainty in the position of particles with non-normal incidence. Straggling_affects the position since a particle with non-normal incidence that loses more energy on one side of the wire than on the other would have its position signal shifted. Third is small angle scattering by the entrance window of the counter and by the gas in the counter. The effect on observed resolution caused by both straggling and by small angle scattering is calculable and can be reduced by employing a thinner detector; however, the signal-to-noise ratio is made worse by using 67 a thinner detector. The effect due to straggling can be reduced by using higher gas pressure in the detector, but this increases the small angle scattering in the gas and necessitates using a higher voltage on the central wire. Finally, the size of all three effects is dependent on both the particle type and its energy. The design and per- formance of two variations of the resistive- wire-proportional counter will be discussed. The first detector to be discussed was designed to give best results for 50 MeV. 6He particles. This detector has an active region that is 1.0 cm. thick by 1.8 cm. high by 18 cm. long. The entrance window is .013 mm. thick aluminized Kapton which defines the front surface of the active region of the counter. The exit window is 250 ug/cm2 A1 leaf which defines the back surface of the counter and separates it from a second proportional counter. The central wire is .0076 mm. diameter nichrome wire that has a resistance of 3800 ohms (19 ohm/mm). This wire is thinner than the .012” mm. diameter wire previously used, and has approximately 1.6 times the resistance per unit length of that previously used, thereby improving the signal-to- noise ratio. Also, therwire is of better quality, and it gives uniform charge multiplication along 68 its entire length. The block diagram of the elec- tronics for this detector, shown in Figure 2.1.1 also illustrates the electronics for the particle identification system used in conjunction with this detector. The contribution to the FWHM of the observed peak from straggling is proportional to the square root of the counter thickness and inversely proportional to the square root of the pressure of the gas used in the counter. A calculation of the contribution from straggling for this counter and a pressure of .67 atm. of propane gives .25 mm. for 50 MeV 6He particles at #50 incidence.Ma7S The contribution to the resolution from small angle Ja62, Ma75, M1711.to be less scattering is calculated than .1 mm. for scattering from the Kapton window and less than .03 mm. for the propane. In the gas, the rms. deviation in position due to scattering in the first 5 mm. of gas was calculated. Scattering in the second 5mm. of gas was neglected. For 77 MeV alpha particles, and therefore, for the more 50MeV 6He particles, the signal-to-noise ionizing ratio is not a limiting factor in this detector. This was checked experimentally.by measuring the resolution as a function of amplifier gain. 69 The amplifier gain was varied by a factor of 5 while adjusting the gas gain by changing the high voltage and no change in resolution was observed. The resolution deteriorated at gains above and below these limits. Figure 3.1.7 shows a spectrum of 6He particles in which 30 keV resolution was obtained. This corresponds to .6 mm. full width at half .maximum. The energy loss in the 82 pg/cm2 50 Cr target contributes only 6 keV. (”.1 mm.) to the peak width while small angle scattering in the target contributes only 2 keV to the width. The sum of the contributions to the resolution from the target and from the detector is only half that obtained experimentally. This indicates a significant contribution to the peak width from the incident beam and that a better dispersion matching situation could improve the resolution substantially. The second detector is a novel design which employs a thin coil of 7000 ohms resistance, which defines the active region of the counter, and a central wire. The coil has a rectangular cross- section, dimensions of 1.27 cm. high by 0.” cm. wide by 6.2 cm. long and turn spacing of 1.3 mm. Nichrome wire of .178 mm. diameter was used for both the coil and central wire. Photographs of the detector are shown in Figure A.l, and Figure A.2 70 shows a block diagram of the electronics. Windows of aluminized Kapton were used. The detector is filled with a gas mixture of 5% C02, 9.5% He and 85.5% Ne at two atmospheres absolute pressure. A bias of +900 volts is used on the central wire and —900 volts on the coil. In operation the center wire acts as a proportional counter producing charge multiplication, and the coil picks up the complimentary positive signal. The position is then determined by division of the signal from one end of the coil by the sum of the signals from both ends of the coil. The results of testing this counter indicate that the observed peak width varies with position periodically as the turn spacing. The bottom half of Figure A.3 shows a proton peak that is 3 times as broad as that in the upper half. The only difference in the experimental setup between the two was that the spectrograph field was changed in order to move the peak position .6 mm. (one half the turn spacingl). Moving the peak an additional .6 mm. causes the peak to become broad again. This experimental evidence suggests that the use of such a coil-type counter is of questionable value if the turn spacing is the same size or larger than the peak width being observed. ‘\ >- u r l ’1 4;) ,— .r I". \‘I‘ an .,;._.. , "5530:; {fro 1:? 7“- E "Term!- 5 2.. 4§% .. I ‘L-i‘r: M .. Figure A.l Photograph of coil detector 72 POSITION SENSITIVE DETECTOR COIL AND CENTER WIRE J. L J. l. ‘m‘T r _ AMP AMP f I. 9 SUM SCOPE AMP .3 03‘ ~ - g |- l +-» z 9 “J h E LIN E. .-°-.--.... LIN g. GATE E|/(E' + E2) GATE 3 I I __L_ S w ., x 3 ADC "‘ 2'7 “""' ADC .. 73 .Hfioo 03w mo wcwomam away mnu mamzumco >n pmmwflo macawflmom saucy page ma mxmma 03p mgu cmmzumn mocmLmMMflo 0:9 ..pxmp mew Cw omnwpommo prczoo afloo one Ca ompowpmp mm: :Ofizs UNH 509M Umbmppmom >HHMOHpmmHm mcowopa >mme mo xmmm m.< wpswwm AU 4 . d _ nu fl 4 q , _ Rq . A Ir l 0 IO .4 IL 0 ) Pm p: I.\ .0: 4| C MD. _. w... DUE _ L L L m nu . _ nU2u 900 ‘- 300 - m 0 OJ amzzqzo mma mezsou _ O O 7 .2 CHANNEL NUMBER 79 APPENDIX B MASS 03 57Ni In order to check an inconsistency found during the 58 analysis of the (3He,6He) data, the Ni(3He,uHe)57Ni Q-value was measured. The experimental technique used was that which is described in the main body of this thesis. The magnetic rigidities of the alpha particles from the 58 (3 Ni He,“He)55Ni 5 reaction were compared to those from the 2Cr(3He,uHe)SlCr reaction. The targets employed were isotopically-enriched evaporated targets on Carbon backings. The target thicknesses were measured by means of the energy—loss of zulAm alpha 68 52 particles. Several runs were made on both the Ni and Cr targets. Table 8.1 lists the targEt thickness, the Q-value of 57Ni determined from the 57 the reactions and the mass excess Of Ni mass excess is 24 keV more positive than the Mass-71 valuewa7l, and the error average of all the runs. The result for the has been reduced from 7 to 4.6 keV. 75 Table 8.1 Reaction Target Thickness Q-Value Mass Excess of (ug/cmz) (MeV) Residual Nucleus (MeV) 52Cr<3He,”He)SlCr 50(10) +8.5378(22)a) -51.uu60(10)a) 58Ni(3He,”He)57Ni 90(10) +8.3503(u0) -56.oaou