The (3He, α) reactions on even titanium isotopes

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<ul><li><p>2 [ Nuclear Phystcs A100 (1967) 401--415, (~) North-HollandPubhshmg Co Amsterdam B 2 G I </p><p>Not to be reproduced by photoprmt or microf i lm wLthout v, n t ten permlss~on f rom the pubhsher </p><p>THE (3He, ~) REACTIONS ON EVEN TITANIUM ISOTOPES </p><p>J L'ECUYER and C St-PIERRE Physws Department, Umt erstte Laral, Qtwbec, Canada * </p><p>Received 9 May 1967 </p><p>Abstract The angular distnbutmns of the alphas from the reactmns a6Yl(3He, ~)4~T1, 48Tff3He, aWTL and 5Tl(6He, ~)49T1 have been measured at E3H~ -- 10 Me~ A number of In :- 3 transmons corresponding to the pick-up of neutrons from the lf~ shell, has been observed We have also found In ~ 0 and 2 transmons, indicating that the pick-up can also originate from the 2s~ and ld~ shell Finally some In ~ 1 transltmns have been observed, indicating p-wave admixture lO_ the ground state of the e~en t~tamum isotopes SpectroscopLc factors have been deduced for the various transmons by means of a DWBA analys~s The experimental results have been compared with the theoretical pred~cUons of the shell model and of the rotatmnal model with Corlohs couphng </p><p>E NUCLEAR REACTIONS 46,~s,5Tl(3He, ~), E ~ 10 MeV, measured ~(0) 4.,~-49T1 deduced levels, In, spectroscopic factors Enrtched targets </p><p>1. Introduction </p><p>Nuclet in the f: shell have recently been the object of considerable theoretical work </p><p>However, those nuclei are still far from being well known and experimental work ts </p><p>needed to test the different models which are presently proposed Accordingly we decided to study the even t itanium isotopes using the (3He, ~) reaction The results </p><p>of this investigation were analysed using the DWBA Spectroscopic factors were then obtained and compared with the various theoretical predictions </p><p>Previous investigations of the t l tamum tsotopes revealed some rather puzzhng fea- </p><p>tures Since an (3He, ~) reaction amounts to the pick-up of a neutron from the target </p><p>nucleus, one expects that the neutrons will come mainly from the f, shell which is m </p><p>the process of being filled It should also be possible to observe neutrons from the </p><p>s-d shell which is the least bound closed shell One then expects to observe mainly </p><p>1 = 3, 2 and 0 angular momentum transfer and possibly some rather weak l = l </p><p>tt ansmon coming from 2p admixture m the ground state of the even htamum isotopes </p><p>This was observed prewously m the (p, d) work of Kashy and Conlon 1) and of Sherr </p><p>et a/ 2) and also m the (d, t) mveshgahon ofYntema 3) At the same time tt was found that some of the hole states excited by the pick-up of a neut lon m the s-d shell were also clearly seen m the (d, p) work of Rapaport et al 4) This observation would then </p><p>indicate that the ground state of the even t l tamum isotopes Is more comphcated than </p><p>Research supported by the Atomic Energ~ Control Board of Canada </p><p>401 </p></li><li><p>402 J L ECUYER AND C ST-PIERRE </p><p>was first thought because in addition to having 2p admixture, one should also add terms coming from holes m the s-d shell </p><p>In the present lnvestlgaUon we took advantage of the high positive Q of those (JHe, ~) reacUon to look for as many levels as poss%le and we Uied to deduce the occupation number of the various sub-shells In addition m some cases we should then be able to compare our result with the pievmus (p, d) work Since spectroscopic lectors should be identical for (p, d) and (3He, ~) reactions, a comparison between otu result and the one of refs i, 2) prowdes a good test of the rellabflmty of the occupa- tion number which we deduce </p><p>2. Experimental procedure </p><p>The experiment ~as done using the 3He + beam of the Laval 5 5 MV Van de Glaaff The energy was kept fixed at 10 MeV by an analysing magnet A quadrupole lens and a series of slits at the enU ance of the scattering chamber were used to focus and define the beam The beam was stopped in a Faraday cup and the current was continuously monitored Because of the large cross section for elastic scattering at 10 MeV it was necessary to limit the cmrent on the target to values which range from 5 to 500 nA as the angle is increased from 15 ~ to higher values </p><p>The alphas were observed with solid state detectors Most of the small angle meas- uIes x~ere carried out using two AE counters, one of 100/an and the other of 120 Itm m a telescopm ai rangement The first detectm was used to stop the scattered 3He and the second was thick enough to stop all the alphas A fast coincidence module gave the signal required to analyse the pulses coming out of the detectors An antlplle-up- </p><p>TABLE l </p><p>Isotopzc composi t ion of the targets and (aHe, ~) Q-values </p><p>Target ;',, a'T1 "o arT1 o 48Tx ,,o 40Tl o~, oOTl Q(Me\ ) (ref 5) </p><p>48T1 81 2 2 1 145 l 1 1 1 7387 4~T1 0 25 0 26 99 13 0 19 0 17 8 957 Tl 20 I 8 178 20 764 9639 </p><p>system associated with the first detector permitted us to reject pulses separated by more than 100 nsec and less than 3/lsec This system was found to be the most efficient way of rejecting the elastically scattered 3He which otherwise would have produced pile-up in the electromcs This arrangement allowed the observaUon of protons from 3 to 5 MeV, deuterons from 4 to 7 MeV and alphas from 12 to 20 MeV Clearly then the regton above 10 MeV, which is the region of interest here, contained only alphas At hlgher angles, where scattered 3He are less numerous, we used a single 300/~m detectors wath a pile-up lejecuon s~stem The resolution of the system varied between </p></li><li><p>TllaHe, ~) REACTIONS 403 </p><p>75 to 100 keV during the course of the experiment, the resolution being slightly better </p><p>with the second arrangement The targets were m the form of t itanium oxide evaporated onto a carbon backing </p><p>The backing thickness was 50 pm and the evaporated layer thickness was about 75 ~m Ov~lng to the high temperature needed, we found it easier to float the carbon only after the evaporation The composit ion of the isotopic material was as Indicated </p><p>in table 1 The 48T1 was present in all the data and since the 0 16 MeV state of 47T1 has a </p><p>relatively large cross section it was identified and analysed in all the spectra This </p><p>analysis proved to be very useful since all spectroscopic factors could then be nor- mahzed to this unique case Also, the alphas coming from this state were used to cah- brate the energy of the system Other cahbrat lon points were provided by the reac- tions 160(3He, ~)150 and 12C(3He, e)l 1C </p><p>3. Experimental results </p><p>The ~ particle spectra taken at 45 are shown in fig I The peaks have been identi- fied using the energy cal ibration points previously mentioned In many cases the ex- cited levels were observed by Kashy and Conlon 1) and we used their value of exci- tat ion energy since we did not have a better resolution The energies of the other peaks have been determined from the present data and they are accurate to +50 keV Those energies correspond to the 45TI 3 10, 4 79 and 5 78 MeV states, the 4VTl 3 45, 3 80 and 4 20 MeV states and the 49T1 4 20 MeV state The angular distr ibutions cor- responding to the various peaks are shown in figs 2, 3 and 4 The errors indicated are mainly of statistical origin but in some cases background subtraction contributes significantly to the lncertalnty and this has been Included in the error bars The ab- solute cross sections were estimated by comparison with the elastic scattering cross section on 46T1 This procedure is not very accurate since at 45 , the elastic cross sec- tion deviates from the Rutherford formula At smaller angles however, it was not possible to separate the peaks coming from contaminants in the target However, we measured the cross section for elastic scattering of 3He by 46T1 and our final accul acy was +25 % </p><p>A DWBA analysis was performed using the Oak Ridge code T-Sally 6) In this calculation one uses a zero range approximat ion and does not include spin-orbit coupling The optical potential we used is of the following form </p><p>U(r) = - V(e~+ l ) - J - tW(e x +1) -1+ Uc, </p><p>where </p><p>x = ( r - roA+) /a , ~c' = ( r - roA '~) /a ' </p><p>and U c is the Coulomb potential due to a uniform sphere of radius roc A~ Different sets of optical model parameters were used for the calculation, but only two sets were </p></li><li><p>404 J L ' LCUYER AND C ST-PIERRE </p><p>400_ </p><p>300 </p><p>200 </p><p>I00 </p><p>016 T j46(He3,~) T 45 </p><p>0 EHe 3 = I0 MeV ,1. :45 o </p><p>elGb </p><p>5 78 0 </p><p> I l , , t tml* ,~| ~, , - </p><p>o -c o </p><p>g u~ </p><p>g o </p><p>4ooJ 300 i </p><p>2001 </p><p>I O01 . . . . . . . .... ":. </p><p>48 3 47 Ti (He,o</p></li><li><p>TJ(SHe, ~) REACTIONS 405 </p><p>found to gwe satisfactory fits to the data They are hsted in table 2 The first set is nearly identical to the one used by Chne et al 7) for their analysis of the 4Ca(3He, c 0 agca reaction at 10 MeV In the second set we took the entrance channel parameters from an analysis done by Yntema et al 8) of the 12 MeV 3He elasnc scattering on various T1 isotopes Various exit channel parameters, adapted from an analysis done </p><p>0 </p><p>5 ~,,t~"~l 02 </p><p>0 2 ~ '14- f f t~ E: 0 OMen/ in = 3 OI </p><p>OI </p><p>005 </p><p>002 </p><p>001 </p><p>OO5 \ </p><p>I I I I </p><p>o,I- t, mb/~rO 05 </p><p>002 </p><p>001 </p><p>-% </p><p>1 I 1 I </p><p>OI </p><p>00 I </p><p>O5 1 </p><p>02 Ex=O 55MeV </p><p>In=2 OI </p><p>0O5 </p><p>\\ </p><p>0 I ' ', </p><p>005 </p><p>002 </p><p>00 I 0 o- </p><p>! l 20 40 </p><p>Ex ;3 IOMeV </p><p>' t t tit tt )i t </p><p>I A L ! I </p><p>t t f~i t </p><p>i 1 </p><p>Ex= 4 79MeV </p><p>E ~ 5 78 MeV </p><p>0 2[ ~ Lr 0 </p><p>'\ 0 05 \ _ </p><p>t i IO 80 lu~ 60 1 80 1 IO0 0 2~0 40 ~ ~L~__~- </p><p>Ocm ecm </p><p>Fig 2 Angular distributions of the alphas from the reaction 46Tl('~He, a)45Tl The sohd curve represents the result of a DWBA fit No such fit was attempted for the alphas leading to unresolved </p><p>levels at an excitation energy of 3 10 and 4 79 MeV </p><p>by McFadden and Satchler 9) of scattering of 25 MeV alphas by various nuclei were reed The set hsted m table 2 is the only one to have gwen an acceptable fit It ~s interesting to note that tMs set has V, ~ V3H~+ 30 MeV which appears to confirm an observanon of Duhm et al lO) on 54Cr(3He, ~)53Cr We did not vary the exit channel V and I41 w~th the energy of the outgoing ~ since th~s does not affect slgmficantly the result (refs 11,12)) </p></li><li><p>\ , \ \ \ Ex-O 16MeV OI </p><p>t [ In .5 0 \ </p><p>\ ' k ' , 00~ 0 05 </p><p>0 OI </p><p>\ , \ </p><p>0005 / , , - d~ 0 005 </p><p>m~ 0 05 l i d~. </p></li><li><p>Tl(3He, ~) REACTIONS 407 </p><p>O2 </p><p>OI i </p><p>005 </p><p>002 </p><p>001 </p><p>d__~ d.~- </p><p>mb 002 7~r </p><p>001 </p><p>0005 </p><p>0002 </p><p>&gt;X~', </p><p>-u_ L </p><p>Ex=O OMeV in=5 </p><p>\ ---~ </p><p>t ] "~f </p><p>I 1 t </p><p>tt t </p><p>I t t I </p><p>0 021, Ex= 155MeV | </p><p>t t+ o o, I~, t t t ooo5) [I 1 </p><p>. I I i ! 0 o 20 40 60 80 ICO o 120 </p><p>@cm </p><p>Fig 4 </p><p>0 05~ ' '~- </p><p>| - -h </p><p>[ i I I i t </p><p>I 19,&lt; ' I ~. Into </p><p>oo2J~ / ~) d~ I I I I I mb/s ~ </p><p>O05F ~ t ~H,~ , Ex=2 62MeV </p><p>0o2{ \ \ ) t t "~J. . </p><p>iL" I I t </p><p>005 - -~- 54 I Ex=420MeV j t ~4 , in :3 </p><p>002 i Q~ </p><p>00 l </p><p>1 L I ! I 0 20 40 60 80 100 </p><p>6cm </p><p>Angular dmtnbut lons of the alphas from the reaction 5Tl(aHe, :z)49T1 The sol,d curve represents the result of a DWBA fit </p><p>TABLE 2 </p><p>Ophcal model parameters used m DWBA calculat ions </p><p>V W ro a r" o a" roe (MeV) (MeV) (F) (F) (F) (F) (F) </p><p>3He l 175 15 1 07 0 854 1 81 0 592 1 4 c~ I 40 10 1 75 0 520 1 75 0 520 1 4 3He I I 97 10 1 07 0 754 1 81 0 592 1 4 </p><p>II 130 24 1 47 0 51 1 47 0 5l 1 4 </p><p>Both sets of parameters predicted similar angular distributions but their magnitude was found to differ uniformly by about 20 ~o It was finally found that set I, with a radial cut-off at 4 5 fro, was slightly better The presence of a cut-off did not change qualitatively the angular distribution but could alter its magnitude by as much as </p></li><li><p>408 J L'ECUYER AND C ST-PIERRE </p><p>20 ~/o This deviation is again systematic and depends only on the value of the cut-off radms To obtain the fo im factor, the code calculates the wave functmn for the trans- ferred neutron in a Saxon well of radms 1 2 A ~ fm and diffuseness 0 65 fm The depth of the potentml was adjusted so as to reproduce the binding energy of the transfe~ red neutron </p><p>In terms of the previous calculations, the experimental cross section can be written m the fol lowing way </p><p>(~)exp = NSO'DWBA(O)" </p><p>where S is the spectroscopic factor for the level under study and 0"DWBA(0) the cal- culated cross section, N is a normahzmg factor which depends on the part icular type of reaction which is employed For the (3He, ~) reaction, N has been found to be of the order of 30 but large variations have been noticed 7 ,~) In our case, we used sum rules on the spectroscopic factors and comparison with spectroscopic factors extracted from (p, d) experiments to set the value of N equal to 20 </p><p>3 1 THE REACTION 46TI(3He, :~)4~Tl </p><p>The spectrum of this reaction contains only six peaks The first three peaks cor- respond to L = 3, 2 and 1 neutron transfer The peak at 3 1 MeV is weakly excited </p><p>and appears to be composite Its angular distr ibution seems to be fitted by an l = 3 transfer but this might be fortuitous The peak at 4 79 MeV has been shown 13) to be </p><p>made up of two states at 4 73 and 4 79 MeV showing I = 3 and 2 angular momentum transfer These states as well as the l = 0 state at 5 78 MeV are the analogues of the 45Sc low-lying states at 0, 0 013 and 0 94 MeV The shell model predicts that 46T1 has fore neutrons in the lfff shell Accordingly the 1 = 3 transit ion should correspond to a state having J~ = 5 - Higher subshells should be admixed an the ground state wave function due to pair ing correlat ion and accordingly the state obtained via the l = 1 tlansltxon should correspond to the 2p~ subshell and have 3 - as J~ One does not expect to observe the effect of 2p~ and l f_: subshells since they he at a much h~gher energy The 1 = 2 and 1 = 0 angular distr ibutions should correspond to the p~ck-up of a l d~ and 2s~ neutron and consequently lead to z a + and + state Those assumptions fo lm the basis for the plesent spin assignments </p><p>Table 3 gives the spectroscopic factors for the various levels of 45T1, as well as their </p><p>spin, pal l ty and lsospln The spectroscopic factors obtained m other experiments are also shown for comparison The 1 = 1 level at 1 58 MeV excitation energy was not cleally seen by Kashy and Conlon J) but it stands out vely well hele and its angular distr ibution is unambiguous and shows an l = 1 pattern A notable point here is the absence of any l = 0, T&lt; level corresponding to a hole m the 2s, subshell Cor- iespondmg states were seen m 47T1 and 9T1 but we were unsuccessful m our effort to locate it In 45T1, unless it is pal t of the composlte 3 1 MeV peak </p></li><li><p>TJ(aHe, ~) REACTIONS </p><p>TABLE 3 </p><p>Summary of the data deduced from the present experiment </p><p>409 </p><p>E. (MeV) </p><p>I n Jn S(aHe, 7) S(p, d) (ref 1)) </p><p>33 58 10 79 ~) </p><p>78 </p><p>016 1 55 181 2 34 2 56 28 l </p><p>318 3 45 3 80 4 20 </p><p>46Tl(aHe, ~)4~Tt </p><p>3 ~- 27 25 2 ]~ 1 5 07 1 I - 0 52 </p><p>3 2,- 2 ? 0 }~ 0 82 </p><p>4STl(aHe, ~)47T1 </p><p>3 -;- 35 38 l }- 033 11 2 ~+ 16 07 o - ]o </p><p>(0, 1) (~+, 3-) 0 26-0 43 1 ~- 017 05 3 ~- 020 04 3 j - 075 </p><p>(3) (7~-) 0 23 (3) (-,_) 0 40 </p><p>~OTl(aHe, ~)49T1 </p><p>0 3 ~- 40 44 1 36 1 ~- 048 04 1 55 2 23 3 {- 0 62 0 6 245 0 ~ 1 5 2 62 2 ~+ 0 98 0 7 4 20 3 (~-) 0 51 </p><p>S(p, d) (ref ~)) </p><p>25 </p><p>~0 14 </p><p>39 </p><p>0 26 </p><p>a) Results from ref la) </p><p>3 2 THE REACTION 4STI(aHe, g)l:Tl </p><p>Several levels were seen m this reacnon Owing to the condmons of the experiment...</p></li></ul>