Level structure of 49V deduced from 50Cr(t, α) and 48Ti(3He, d) reactions

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<ul><li><p>1 ~ Nuclear Physics A106 (1968) 577--590; (~) North-Holland Publishiny Co., Amsterdam </p><p>Not to be reproduced by photoprint or microfilm without written permission from the publisher </p><p>LEVEL STRUCTURE OF 49V </p><p>DEDUCED FROM SCr(t, ~) AND 4STi(3He, d) REACT IONS </p><p>D. BACHNER *, R. SANTO, H. H. DUHM Tt and R. BOCK Max-Planck-lnstitut fiir Kernphysik, Heidelberg, Germany </p><p>and S. HINDS tit </p><p>A WRE Aldermaston, En#land </p><p>Received 31 August 1967 </p><p>Abstract: The level scheme of 49V has been investigated using the ~Cr(t, c0 and 48Ti(~He, d) reactions. Angular distributions have been measured and spectroscopic factors have been extracted by </p><p>DWBA analysis. The data indicate particle-hole and configuration mixing in the proton states involved. The excitation of states of the (f~_)3 configuration is discussed in connection with pos- sible target excitation processes. </p><p>E [ NUCLEAR REACTIONS sCr(t,~), 48Ti(3He, d), E t = 13 MeV, E3He ~ 18 MeV; measured </p><p>I ~r(E~, 0), </p></li><li><p>f 1"</p><p> 1"</p><p> T </p><p>I" 1"</p><p> T </p><p>T r </p><p>T T </p><p>1 1 </p><p>T r </p><p>F---</p><p> 0 </p><p>20 </p><p>30 </p><p>40 </p><p>50 </p><p>60 </p><p>70 </p><p>posi</p><p>tion</p><p> on</p><p> the</p><p> pl</p><p>ates</p><p> E:</p><p>m] </p><p>E E 2</p><p>00</p><p>- Lo</p><p> O</p><p> if</p><p>) ~ 1</p><p>00</p><p>)" </p><p>! E E 2</p><p>00</p><p>0 U 5 </p><p>loo</p><p>1/2 2 </p><p>3 </p><p>~8T</p><p>i(3H</p><p>e,d)</p><p>49V </p><p>--3He</p><p>= 18</p><p> M e</p><p>V </p><p>eLAB</p><p>= 2</p><p>5 </p><p>I , 4 </p><p>_) </p><p>I I </p><p>I 10</p><p> I </p><p>~0 </p><p>I </p><p>3 4 </p><p>I 0 I I </p><p>2 55</p><p> 5 </p><p>!2Cd</p><p>o </p><p>3 </p><p>I i I </p><p>I I ~</p><p> I,~</p><p> o iI </p><p>I do</p><p> ] il</p><p>eOd~</p><p> 12</p><p>Cd 1 </p><p>I II </p><p>i </p><p>I II I </p><p>~2 </p><p>T </p><p>] </p><p>7 8 </p><p>49</p><p> v e</p><p>xc</p><p>ita</p><p>tio</p><p>n en</p><p>erg</p><p>y o</p><p>f EM</p><p>eV-I </p><p>1 I </p><p>I I </p><p>~0 </p><p>60 </p><p>posi</p><p>tion</p><p> on </p><p>the </p><p>plat</p><p>es ~</p><p>cm~</p><p> I </p><p>I I </p><p>I I </p><p>lt10 </p><p>0 </p><p>,,3 1 </p><p>52C re</p><p>( o 5 </p><p>Ii </p><p>_ I 1 </p><p>5C</p><p>r( t </p><p>,~ )4</p><p>9V</p><p> 4</p><p>E t</p><p> = 13M</p><p>eV, O</p><p>Lab=</p><p>20 </p><p>: 1I 5 </p><p>160(</p><p>~ </p><p>19 </p><p>I 31</p><p> ~</p><p>l </p><p>i 14</p><p> 17 </p><p>I I </p><p>2 </p><p>3 </p><p>4 </p><p>71 </p><p>84 </p><p>101 </p><p>54 </p><p>67 </p><p>l~ </p><p>5861</p><p> 68</p><p> 74</p><p> 79</p><p> go</p><p>e 1 </p><p>91 </p><p>I I </p><p>~Cc~</p><p> o </p><p>d </p><p>2 12</p><p> C 16</p><p>dr </p><p>ii II </p><p>d i I</p><p> II </p><p>ii </p><p>I !3</p><p> iiii</p><p> :1 </p><p>I II </p><p>ii I </p><p>I I </p><p>II 13</p><p> C </p><p>I I </p><p>5 </p><p>6 </p><p>7 </p><p>8 9 </p><p>10</p><p> .~</p><p>xcit</p><p>atio</p><p>n en</p><p>erg</p><p>y o</p><p>f 49V</p><p> [-M</p><p>eV7 </p></li><li><p>4V LEVEL STRUCTURE 579 </p><p>The level scheme of 49V was investigated theoretically by Bayman, McCullen and Zamick 7) on the basis of a pure f model. By coupling the three protons, states with spin 7- , ~-, ~- , ~-, ~L- and '2 --s-- are expected from this model, the ~- state being the ground state. Only the 2 z - member of this sextuplet can be excited by a first-order stripping or pick-up process. The cross sections of the a2- and ~- states may give an estimate for the amount of mixing of these (f)3 configurations with p~ and f~ single- particle strength. Since the Nilsson-Coriolis coupling model, where orbits 12 and 13 especially are highly mixed, can describe the order of the low-lying levels properly 8), one expects some p~ and f~ strength within these levels. The excitation of the high- spin states, however, would point to a different type of reaction mechanism as target-excitation processes or compound-nucleus reactions. </p><p>2. Experimental procedure </p><p>The (t, ~) experiment was performed with the Aldermaston Tandem using a triton beam of 13 MeV. The ~-groups were analysed by a broad-range multi-angle spectrograph with an energy resolution of about 20 keV. The (3He, d) data were taken at the Heidelberg Tandem using a broad-range single-gap spectrograph. Self- supporting targets of high enrichment were used in the case of 4STi, whereas the 50Cr targets were prepared by evaporation onto a thin carbon backing. </p><p>Energy spectra for the SCr(t, ~)49V and 4STi(3He, d)49V reactions are shown in fig. 1. For the (t, ~) reaction, angular distributions have been measured between 5 and 102.5 in 7.5 steps. Due to the high triton background, however, no use could be made of the 5 and 12.5 spectra. For the 48Ti(aHe, d) reaction, spectra were only taken for seven angles between 5 and 30 , which, in most cases, was sufficient to fix the/-value by means of the DWBA analysis. Absolute cross sections were deter- mined for 48Ti by adjusting the measured elastic 3He cross section at 6 MeV to the Rutherford cross section. </p><p>3. Analysis </p><p>DWBA analyses of the (t, ~) and (3He, d) angular distributions have been perform- ed with the code JUL IEt . The optical parameters used are listed in table 1. The </p><p>TABLE 1 </p><p>Optical-model parameters used in the DWBA calculations leading to the angular distribbtions of figs. 2 and 3 </p><p>V W r r e a r' a' Wd VB.o. Ref. (MeV) (MeV) (fro) (fm) (fm) (fm) (fm) (MeV) (MeV) </p><p>t 144 20 1.36 1.25 0.678 1.45 0.841 5 9) 183.7 26.6 1.4 1.4 0.564 12) </p><p>SHe 165 20.2 1.14 1.3 0.723 1.6 0.81 5 11) d (85.7) 1.15 1.3 0.81 1.44 0.61 66.4 10) </p><p>t We thank Dr. Drisko for making available the JULIE code. </p></li><li><p>580 D. BACHNER et al. </p><p>triton potential was derived from an optical parameter set found by Hafele et al. 9) i an analysis of elastic triton scattering from 52Cr at 15 MeV. For the deuterons th parameters of Siemssen and Mayer-B6ricke ~ 0) were used with an energy-depender real potential. The resulting DWBA curves are shown in figs. 2 and 3 together wit the experimental data. The stronger (3He, d) distributions allow/-assignments wit </p><p>105 _ </p><p>10 4 </p><p>103 : </p><p>103 i </p><p>102 I </p><p>103-~ </p><p>10 2 </p><p>104 </p><p>103 </p><p>103: _ </p><p>102 </p><p>I I I I I </p><p>\ </p><p>, I , \ </p><p>I I I I </p><p>Ex= 0.000 ~=3 </p><p>0x </p><p>...-,, </p></li><li><p>~gV LEVEL STRUCTURE 581 </p><p>and proton-hole states, respectively. From the comparison of the (aHe, d) and (t, ~) transition strengths for ! = 0, l -- 2, one obtains, of course, an estimate for the s-, d-hole admixtures contained in the +8Ti ground state, and comparing the l -- 1 and l = 3 transition strengths in both reactions one obtains, similarly, the f+ and p+ particle admixtures in the 50Cr ground state. </p><p>103 I i I i I I I I I 103 </p><p>102 !''~ "F ~\+ Ex=2266~ =3 IO2 / </p><p>"-qk\ '~ { + {{ 10 3 101 \ \ </p><p>\ </p><p>10 2 ..e+\ 102 Ex =2.314 </p><p>~,~ ,~\ ~ = 1 103 { \ -~ ~ 101 </p><p>'t \ 10 2; 10 2 '+~ &amp;.2 .~5 </p><p>\\~ ~'\'l' = 2 </p><p>\ </p><p>102; "\ 102 + E x = 2.736 </p><p>lo 3 ~ 4, 4. + 4, ~{ lo 3 </p><p>102 \',,~-4,. ,~ Ex=2.394 q 102 \ , 'L g=2 </p><p>J + t 4. 101 \ /X 101 \ ,.- </p><p>f ? I I ; I I P I I </p><p>0 20 40" 60" 80 100 OCM 0 </p><p>I I I I I I I I I I I </p><p> +, Ex= 3.132 </p><p>, + </p><p>j " Ex = 3.248 ~" // + ' " </p><p>\ - </p><p>Ex =3.345 + +++++ + ,, + + </p><p>\ ,L Ex =3.699 ~'''~, = 2 </p><p>\ L / z \ </p><p>'t +t \ \ </p><p>"~\ \ </p><p>i -~\ \ t + Ex:3"763 ~ ~.\+ g=3 </p><p>\',,~ {+ \ </p><p>I </p><p>] I I f I I t I I I </p><p>20o 400 600 80o 100 @CM </p><p>Fig. 2(b). See caption to fig. 2(a). </p><p>4. D iscuss ion </p><p>The spectroscopic factors l!sted in table 2 were obtained for the (3He, d) data by the DWBA analysis 13) with a normalization constant of N = 4.42. Since absolute cross sections have not been determined for the (t, ~) data and the normalization constant is not well known, the spectroscopic factors for the (t, cQ reaction were normalized to the expected s{ strength: Czss~ = 2.0. This normalization is probably </p></li><li><p>582 D. BACHNER et aL </p><p>only slightly too high for 'Cr, since in a recent 'Cr(aHe, d) experiment t4), th~ 2.23 MeV l = 0 state, which is presumably the ld~ hole state, was only weakl,. excited. We obtain from the ~STi(aHe, d) reaction a value of about 10 % 2s hol, admixture within the proton configuration of the 48Ti ground state. Unfortunately thi value is associated with a large error since it results from unfolding the peak a </p><p>lo 4 </p><p>103 </p><p>103' </p><p>lo ,,1--1 </p><p>Io3 I </p><p>1011 </p><p>0 o </p><p>I I I I I </p><p>,, E x :4.280 \i'~x I~ =2 </p><p>\ </p><p> It \~ /X </p><p>X \ </p><p>\~ "~k Ex = 4.402 \ g:3 </p><p>\4t~ \ </p><p>\ E x = 4.646 </p><p>\ </p><p>E x = 4.680 </p><p>g=2 </p><p>i"i'* + \t \\ ', .~ Ex = 4 .743 </p><p>\ \ </p><p>I I I I I 20 ,40 60 80 IO0"@CM </p><p>I0" </p><p>103 </p><p>l o 2' </p><p>103' </p><p>lo2E </p><p>lo3i </p><p>102 t </p><p>103i </p><p>lo2t </p><p>101 [ </p><p>0 o </p><p>I I I I 1 </p><p>\ E x = 4 .959 </p><p>',I ,1~; 1~=0 '&lt; ,,., ,. </p><p>\41 \ \ </p><p>Ix E x = 5.018 \~, ~--3 </p><p>\ \ </p><p>~, E x :5.072 </p><p>\ E x : 5.285 ~* ~\ ~ :0 </p><p>\ {i/-\\ </p><p>~1 ~ Ex = 5.522 / ~ ~ :0 </p><p>v \4 i~\ k/ \ </p><p>I I I I I 20 40 60 80 IO0@CM </p><p>Fig. 2(c). See caption to fig. 2(a). </p><p>1.65 MeV by a superposition of DWBA curves with 1 = 0 and l = i. We attribu the l = 1 distribution to a level at 1.67 MeV. </p><p>The main d~ hole strength in 49V is found to be concentrated in the level at 0.7~ MeV. This is in fair agreement with an excitation energy of about 1 MeV predict~ for the d~ hole state by the formula of Bansal and French ts). In addition to t~ strong transition, a number of l = 2 transitions are observed with appreciable cro </p></li><li><p>49V LEVEL STRUCTURE 583 </p><p>section up to an excitation energy of 6.56 MeV, indicating a large fragmentation of the ld hole strength. The sum of l = 2 spectroscopic factors (cf. table 3), however, exceeds the expected d~ strength, so that some higher l = 2 transitions very likely proceed to ld~ states. The l= 2, 0.752 MeV level is also excited in the 48Ti(3He, d) </p><p>10 </p><p>10-1 </p><p>10 </p><p>1 </p><p>10 -1 </p><p>1 </p><p>10 -1 </p><p>I I I I I i I </p><p>E=O.OO </p><p>, t&amp; /* / ' / ,k. </p><p>Ex=0.155 /I ~,,g=l *-. </p><p>Ex:OZ50 </p><p>N/ </p><p>Ex:I.672 </p><p>,\ / x~/\ =0\, / \, </p><p>\ / </p><p>"Ex=2.193 =3 </p><p>Ex=2.204 =3 </p><p>I I I I I I </p><p>0 o 10 o 20 30OCM </p><p>I I I I I I </p><p>E=2.279_ _-- ,~ /~,-.\ =1 </p><p>- / / +\X ~ #. "--. ~ </p><p>Ex=2.317 </p><p>\ </p><p>- Ex=2821 " </p><p>Ex = 3.137 </p><p>Ex=3.152 - + </p><p>++ ++ +, </p><p>"t \ </p><p>', l/lf ',t v </p><p>Ex=3.248 g=O ' </p><p>0 o 10 20 30OcM </p><p>Fig. 3(a). Angular distributions of deuterons from the 48Ti(3He, d) reaction at 18 MeV. The dashed curves represent DWBA calculations. The levels at 1.672 MeV and 3.748 MeV seem to be doublets since their angular distributions can only be fitted by a superposition of two different /-values. </p><p>reaction. Its strength of excitation corresponds to about 15 % proton d~ hole ad- mixtures in '~8Ti, which is comparable with the amount of neutron d~ hole strength observed in the Ca region 16). </p><p>A number of I = 3 transitions are observed in (3He, d) as well as in the (t, ~) reaction in addition to the ground state. The strongest of these transitions seen in </p></li><li><p>584 D. BACHNER et al. </p><p>(3He, d) goes to the level at 4.65 MeV which, according to its excitation energ3 should be the main f{ state. In (t, c 0, this level is also excited, and we obtain an est mate of about 20 % f{ strength contained in the 50Cr ground state. Among the oth{ </p><p>low-lying 1 = 3 transit ions the 2.19 MeV and 2.82 MeV states are rather strongl </p><p> 1 L_ I i I I t I _ _ 1 </p><p>F Ex--3"401 _11.- , . . *~ "~., ~ =1 </p><p>10-~ ",.. ~ ~ 1; </p><p>1 ~ 10 ~ </p><p>10 10 Ex=3.922 </p><p>1 - ~-.~ ~* 10 </p><p>1 1" *~ Ex=4,012 ~ ~\~=I </p><p>10 -'1- , 10 -1 Ex=4135 - </p><p>10_1: g=3 - </p><p>F__.X=4224 - </p><p>I .~,r-.~ ~=1 -; 10 -1 ".. ,t,- </p><p>\ </p><p>! I I I '1' / I </p><p>0 o 10 20 30@CM 0 </p><p>I I I I I t [ </p><p>- ,/*--*-- Ex=425"3--- = / "~\~=I - </p><p>..,,_, ~=4.379~ </p><p> ~ Ex:4-502- </p><p>" ",..gx=l - </p><p>Ex=4645 - g=3 </p><p>..,~_, .. Ex=4.852:- *~=1 . </p><p>"Ii "# "~ ~\ ,I, </p><p>Ex=4.945_- </p><p>~-,~.,i =1 ! </p><p>E~=5.057- g=l </p><p>I I I I I I </p><p>10 20 30@CM </p><p>Fig. 3(b). See caption to fig. 3(a). </p><p>excited in the (3He, d) reaction t. The observed excitation energies of these states a close to values predicted by McCullen, Bayman and Zamick 7) for higher - state For a 5 - assignment, however, we would expect to excite these states in the (t, reaction, too, but this was not observed experimentally. This suggests a { - assig </p><p>t A similar situation seems to occur in the 4~Ti(aHe, d) reaction studied by Rosner and Pullen z Here two l = 3 transitions are observed to states at 2.548 MeV and 2.724 MeV with apprecia[ strengths and are assigned ~-. </p></li><li><p>49V LEVEL STRUCTURE 585 </p><p>ment to these states 4). Adopting this assignment, we obtain for the collected fl strength of the lower-lying T~ . . . . levels </p><p>(3He, d) Z(2J--I.-1)C2Sf~_ = 4.5, (t, ~) ~ C2Sf~ = 3.45. </p><p>The (3He, d) strength is smaller than the value of 5.6 to be expected for the lower </p><p>t0 </p><p>10-1 </p><p>1 </p><p>1 </p><p>10-1 </p><p>1 </p><p>10-1 </p><p>I I1{11 </p><p>Ex=5.216 L___,~ *-*~ \ =1 </p><p>Ex=5257 </p><p>- * \=1 </p><p>1 </p><p>i </p><p>104 </p><p>I l l l l l </p><p>. Ex= 5.718 </p><p>Ex=5.826 t .~=3 </p><p>Ex=~37o- 1 ~b E~:~sse =1 </p><p>~-~ g=l -7 . - , </p><p> 1 Ex=5.947 : </p><p>lo --,.&lt; </p><p>Ex=5.987 1 ~ , =1 </p><p>10-1 L-- " # - - </p><p>0 o 10 20 30@CM 0 10 </p><p>I I I I I I </p><p>10 </p><p>Ex=614E 1 ~ t'4-~, = 1 </p><p>1~- , . Ex= 6 220-: </p><p>{'---+ </p><p>F Ex= 633-3 </p><p>1 I- ! f i - \ f .=l . </p><p>10 l + Ex=6.474 </p><p>1L- 4, + - l Ex =6.555 : </p><p>l t : - t - ,~=l - "-(-'! t , Ex=6 603-~ </p><p>I o </p><p>20 30ecM 0 10 20 30cM </p><p>Fig. 3(c). See caption to fig. 3(a). </p><p>isospin states * from pure f~ configurations but can easily be explained by assuming the number of effective proton holes Neff = 4.8 and neutron holes Vef f = 1.6 which is consistent with about 20 % core excitation derived from the (3He, d) transitions to the d~ and s~ states discussed above. </p><p>t The expected strength is given by the expression 2](2J -L 1)C 2 S~k =/~ref r - ~tf/5. </p></li><li><p>586 D. BACHNER et al. </p><p>TABLE 2 </p><p>Excitation energies, /-values from DWBA analyses and assumed spins </p><p>Level Ex 1 j C2S C2(2j+1)S ~) b) ~) ~,b) ~,b) ~) b) </p><p>0 0.000 0.000 1 0.090 (0.092) 2 0.153 0.155 3 0.752 0.750 4 1.025 1.025 5 1.148 6 (1.183) 7 1.531 8 1.610 9 1.652 </p><p>10 1.672 11 1.999 12 2.189 2.193 13 2.204 14 2.241 15 2.266 16 2.279 17 2.314 2.317 18 2.358 19 2.394 20 (2.425) 21 2.681 22 2.736 23 2.812 24 2.821 25 3.132 3.137 26 3.152 27 3.248 3.248 28 3.345 29 3.388 30 3.401 31 3.465 32 3.699 33 3.748 34 3.763 35 3.929 3.922 36 3.976 37 4.005 4.012 38 4.042 39 4.090 40 4.135 41 4.152 42 4.224 43 4.253 44 4.280 45 4.379 46 4.402 47 4.448 48 4.511 4.502 </p><p>0.000 3 - 2.96 4.3 0.091 3 ~- 0.21 0.152 1 ] - 0.12 0.17 0.749 2 ~+ 2.7 0.36 1.025 (7) a) 1.140 (3 ~- 0.1 ) 1.157 1.521 1.607 (5) d) 1.647 0 ~+ 1.54 0.21 1.664 1 ~- 0.50 1.999 0 e) + 0.12 2.184 3 (~-) t) 0.79 </p><p>3 (~-) t) 0.63 2.240 2.266 </p><p>2.312 2.357 2.395 2.413 2.679 2.796 2.820 </p><p>3 (~-) 0.07 1 -~- 0.55 1 ~- 0.02 1.31 </p><p>2 0.41 </p><p>2 0.12 3 ( t - ) t) 0.79 4 ~+ 0.25 </p><p>0 + 0.13 0.01 </p><p>1 0.02 </p><p>2 0.46 1 0.08 3 ({-) 0.09 0.18 1 0.29 </p><p>1 0.04 </p><p>3 (~-) 0.10 </p><p>1 0.08 1 0.05 2 0.55 1 0.04 3 (~-) 0.12 </p><p>1 0.22 </p></li><li><p>49V LEVEL STRUCTURE </p><p>TABLE 2 (continued) </p><p>Level Ex 1 j C2S C2(2j + I )S ~) b) ) ~,b) ~,b) .) b) </p><p>49 4.538 50 4.587 51 4.599 52 4.646 4.645 3 (~--) 0.42 2.11 53 4.680 2 0.13 54 4.743 2 0.19 55 4.838 4.852 1 0.27 56 4.871 57 4.945 1 0.02 58 4.959 0 + 0.05 59 5.018 5.017 3 (~-) 0.11 60 5.057 1 0.05 61 5.072 2 0.15 62 5.130 63 5.146 64 5.216 1 0.15 65 5.239 66 5.257 1 0.03 67 5.285 0 + 0.07 68 5.355 (2 0.21) g) 69 5.375 5.370 1 0.02 70 5.403 3 (~--) 0.35 71 5.522 0 + 0.09 72 5.554 73 5.590 5.597 1 0.03 74 5.631 (2 0.16) g) 75 5.676 1 0.04 76 5.718 1 0.03 77 5.826 3 (,'] - ) O. 13 78 5.890 5.889 1 0.02 79 5.931 (2 0.14) g) 80 5.947 3 (~-) O. 10 81 5.979 82 5.987 1 0.06 83 6.045 1 0.04 84 6.058 (2 0.27) g) 85 6.146 1 0.10 86 6.170 87 6.184 88 6.218 6.220 1 0.05 89 6.258 90 6.286 91 6.309 92 6.333 1 0.05 93 6.353 94 6.368 95 6.392 96 6.430 97 6.467 </p><p>587 </p></li><li><p>588 D. BACHNER et al. </p><p>TABLE 2 (continued) </p><p>Level E x l j C2S C2(2jq-1)S </p><p>98 6.474 99 6.521 6.521 </p><p>100 6.555 1 0.22 101 6.563 2 (0.22) g) 102 6.603 1 0.17 103 6.661 </p><p>a) 50Cr(t ' a)49V. b) 4aTi(3He ' d)49V. e) Ref. a), s2Cr(p ' a)49V. All spectroscopic factors are extracted by DWBA calculations assuming the spins of column 6. d) The angular distributions to levels 4 and 8 are discussed in the text. e) In the 5Cr(aHe, ~) reaction to the analogue state, a clear l = 0 angular distribution has been observed. f) The 6- assignment for these states is discussed in the text. Levels 12 and 13 could not be resolved at all angles. Although levels 23 and 24 coincide within the accuracy of the energy calibration, wc label these levels as different states, since they correspond to different/-values. g) The/-assignment of these states is based only on four o...</p></li></ul>