- Email: [email protected]
Study of states in 15O by the reactions 14N(τ, d) and 16O(τ, α)
I
2.G
[ I
Nuclear Physics All3 (1968) 97--103; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprmt or microfilm wtthout written permission from the publisher
STUDY OF STATES IN ISO BY T H E R E A C T I O N S 14N(z, d) A N D 160(z, ~) w. BOHNE t, H. HOMEYER, H. MORGENSTERN and J. SCHEER
Hahn-Meitner-lnstitut fiir Kernfbrschung Berlin, Sektor Kernphysik, Berlin-West, Germany Received 22 February 1968
Abstract: Angular distributions of deuterons and ~-particles emitted in the reactions X4N(z,d) and 160(z, ~) going to the first seven states in xsO were measured between 5° and 120° at E~ = 11 MeV. DWBA calculations were performed and spectroscopic factors extracted and discussed. E
NUCLEAR REACTIONS: Z4N(T, d), ~sO(T, ct), E = 11 MeV; measured a(~); 150 deduced levels, spectroscopic factors. Natural targets.
[
I
1. Introduction Various models exist for the states of 150 and 15N. A l t h o u g h nucleon transfer reactions should provide information on these states, only relatively few measurements have been performed, which is p r o b a b l y mainly due to target problems. The aim of the present w o r k was to extract some spectroscopic factors f r o m the reactions 14N(z, d) and 160(% ct) leading to the same states in 150.
2. Experimental procedure D o u b l y charged 3He ions (z-particles) were accelerated in a 5.5 M V Van de G r a a f f generator tt, being selected prior to acceleration in a 30 ° magnet placed in the high voltage terminal. The accelerated beam was deflected and analysed in a 90 ° magnet. Then by means o f two magnetic quadrupole lenses it was focussed into a cylindrical reaction c h a m b e r o f 50 cm diam having a target ladder in its centre and was finally stopped in a F a r a d a y cup that was 3 m long. One blend with a variable diameter placed between the lenses, a pair of blends, 1.5 m m in diam and an antiscattering blend, 4 m m wide, placed respectively, 50 and 15 cm upstream f r o m the target, served to define the beam. On the target it h a d a diameter o f 1-2 mm. As nitrogen targets, we used self-supporting foils ttt of T a N . F o r measurements at angles smaller than 20 ° we used melamine targets evaporated onto a thin c a r b o n backing, as the strong Rutherford scattering f r o m the Ta prohibited use of the T a N target at these angles. The melamine target could stand a current of 20-30 n A for t Work performed in partial fulfillment of the requirements for diploma in physics. tt HVEC, Type CN. ttt They were kindly made for us by Messrs. Mokler and Wlrth, MPI Heidelberg. 97
98
w . BOHNE et aL
several hours without any loss of nitrogen as was observed by comparing the intensity of elastically scattered 3He from carbon and nitrogen. The T a N target could stand a current of several 100 nA practically indefinitely. Oxygen was automatically present as a contamination of the TaN, therefore no special targets were necessary to observe the (z, ,t) reaction. Charged particles emitted from the target were detected by a dE/dx • E solid-state counter telescope t The telescope was mounted 12 cm from the target and could be turned around it. In front of it a collimator (45 mm long, 4 mm wide) was placed to shield it from radiation scattered from the blends. This enabled observation down to 5 ° forward angle, provided the beam was well focussed. The various particle types were identified using a multiplication and addition circuit described in ref. l). Spectra of p, d, z and ~ were registered in four sections of a 4096-channel analyser. A pile-up rejection circuit was employed, in addition to a coincidence between E and dE/dx signals, rejecting pulses from particles stopped in the dE/dx detector. Three further detectors mounted at 45 °, 135 ° and 150 ° served as monitors, either set at prominent lines originating from 14N or registering a whole charged particle spectrum. The over-all energy resolution of the telescope was 50 keV, therefore at most angles it was possible to unfold graphically the lines corresponding to transitions to the doublets at 5.2 and 6.8 MeV. 3. R e s u l t s
The measured angular distributions are displayed in figs. 1 and 2 together with DWBA fits made using the code JULIE 2) with parameters listed in table 1 that were taken from refs. a-5). In most cases the fit is considered satisfactory. For the (z, d) reaction, variation of the cut-off radius from 0 to 4 fm did not alter the quality of the fits appreciably; the spectroscopic factors varied within 15 ~o. In column 5a of table 2, we quote the values obtained from the best fit with cut-off radius R .... = 3 fm. They are given relative to that of the ground state. For the ½+ level, an estimated upper limit is given assuming angular momentum transfer ! = 0. For the (z, ~) reaction, no cut-off ought to be used according to the general considerations of ref. 22), but no good fit could be obtained in this case; however use of Ro.o' = 3 fm, 4 fm or 5 fm gave quite good fits. It may be noted that at an energy close to ours, Alford et al. 3) also obtained quite a good fit to the elastic scattering of aHe with the set of optical potential parameters listed in table 1, which we took from their work for analysis of our data. The relative spectroscopic factors obtained with R .... = 5 fm are listed in column 10 of table 2. Variation of R .... down to 0 fm caused deviations of at most 25 ~o. The transferred angular momenta l are denoted in the figures and listed in columns t ORTEC, 1000/~m+50gm; NUCLETRON, 32/zm.
STATES IN
99
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Fig. l. A n g u l a r distributions o f deuterons f r o m the reaction Z4N(T, d)160 to states w i t h excztation energy Ex; E~ = 11 MeV; solid lines: D W B A fits with parameters hsted in table 1. No fits could be made for the transitions to unbound states. Errors, where not indicated, are smaller than the size of the points. The cross-section scales are arbitrary but consistent for the transitions to different levels of one reaction.
-• l
20 ~-0 S0 so 100 0CM
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Fig. 2. Angular distributions of particles from the reaction 160(T, ~)150, to states with excitation energy Ex; Ez = 11 MeV; solid hnes: DWBA fits wxth parameters hsted in table 1. Errors, where not indicated, are smaller than the size of the points. The cross section scales are arbitrary, but consistent for the transitzons to different levels of one reaction.
TABLE 1 Optical-model parameters for DWBA fit Channel
V W (MeV) (MeV)
14Nq-z 160-t-T 150-t-d 15Oq-oc
71 105 93 100
Vs.o. (MeV)
W' (MeV)
13.1 20.5 6 10
64
ro (fm)
ro' (fm)
a (fro)
1.9 1.5
0.53 0.63 1.05 0.65
1.78 1.6 1 1.5
a' (fm)
re (fm)
Ref.
0.30 0.65
1.3 1.4 1.3 1.4
4) a) 4) a)
The potential had the form -- V f ( x ) - - i ( W - - W ' a ' d / d r ) f ( x ' ) d- (h/m~c) 2//s.o. (I " a ) r - l d / d r • f(x),
f(~) = (1 + e x p ~)-x,
x = ( r - - r o A ~ ) a -1,
x' :
(r--ro'AT)a '-1,
Rcoulom b = reA~.
Cut-off (fro)
3 5
0
6.16
5.18
5.24
6.79
6.87
7.28
1
4
2
3
5
6
7
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~÷
{+
~+
½+
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2
2
0
2
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1
1
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1
(r, d) b)
0.29
0.36
0.39
0.04
=<0.007
0.05
1.00
(5a)
0.42
0.52
0.56
0.06
~0.01
0.07
1.45
(5b)
Srel e) S~el" 1.45
0.014
1.00
(6a)
Srel
0.02
1.45
(6b)
Sabs
Theory a)
Stripping
0.54
0.63
0.47
0.063
0.025
(7)
gabs
Theory e)
0.48
0.50
0.44
0.16
1.00
(8)
Srel
(d, n) t)
1.03
0.60
0.58
0.22
2.11
1.00
(10)
Sre 1g)
0.90
1.00
(11)
SreI
Theory h)
not measurable k)
2
2
2
0
1
1
(9)
l
(T, ct) b)
0
0
0
0
2.00
1.00
(12)
Srel
JJmodelShell
Pick up
0.15
0.018
1.75
1.00
s~x (13)
(dT) 1)
a) Ref. 7). b) This work. e) Errors of Srel:-4-15 ~ , indicated by variation of the cut-off radius from 0 to 4 fm. d) Ref. x3). e) Ref. lg). f) Ref. 9). g) Quoted are the values obtained with a cut-offradius of 5 fm. Variation of the cut off radius from 0 to 5 fm caused deviations up to 25 ~ . u) Ref. 18). l) Ref. 5~). k) or-particles from this transition penetrated the telescope only at the smallest angles. The transition appears to be very weak, however.
(2)
(1)
(MeV)
Ex a)
150 level
TABLE 2 Relative spectroscopic factors from one-particle transfer reactions leading to lbO
oa~
STATES
IN 150
101
4 and 9 of table 2. They are all consistent with the J~ values determined in ref. 7). The level found at 7.28 MeV was identified with the 7.285 MeV state of ref. 7), which has J~ = ~+. No indication of a level 8) at 7.16 MeV was found. Also listed in table 2 are theoretical predictions: Column 6 ab" The results of intermediate coupling calculations of Cohen and Kurath 1a) for stripping to the oddparity states. Column 7: The predictions of Halbert and French for stripping to the even-parity levels in 15N, no calculations being available for 1sO. Column 11" The predictions of Shukla is) for pick up to the odd-parity states. No predictions exist for pick up to the even-parity states. For comparison with the predictions of Halbert and French 19), some absolute normalization was needed. As we find S ( ½ - ) / S ( ½ - ) < < 1 in accordance with the Kurath prediction, for this purpose we adopt the Kurath value Sabs(½-) = 1.45. The values thus renormalized are listed in column 5b. Finally we list some other experimental data for comparison; column 8 contains results 9) from the reaction Z4N(d, n)Z50, and column 13 results 24) from the reaction 1 6 0 ( d , .c)15N.
4. Discussion
(i) The spectroscopic factors which Mubarakmand and Macefield 9) obtained from the reaction Z4N(d, n)ZSO (column 8) are expected to agree with those from the analogue (z, d) reaction listed in column 5a. In all cases, their relative values are somewhat larger, the discrepancy being worst for the ~- level. Perhaps their deuteron energy of 5 MeV was too low, this conjecture being corroborated by a (d, n) measurement 1z) at 7.7 MeV which yielded Sro~(~-) -- 0.08. A strong energy dependence of S for the 14N(d, p) reaction at low energies was also found by Gallmann et al. 12) who attributed it to compound nucleus interference. The energy used in this experiment is hoped to be sufficiently large to avoid this difficulty. A supporting evidence may be seen in the fact that we find no strong dependence of S on the cut-off radius, contrary to ref. 12). The pick-up spectroscopic factors of Hiebert et al. 24) from the reaction 160(d, z)lSN (column 13) are in reasonable agreement for the ~- state but much smaller for the ½+ and ~+ states. (ii) For the odd-parity levels, the relative spectroscopic factors from the reaction 14N(z, d) are in reasonable agreement with the intermediate coupling results of Cohen and Kurath x3) (column 6). Whether the fact that our value of S,el(½-) came out about four times larger has some significance is difficult to say in view of its smallness. In the 160(~, ~) reaction, Bachner et al. 14) found that Srel(~-) was strongly energy dependent, having the value 1.5 and 2.2 at a aHe energy of 18 and 19.5 MeV, respectively. Therefore they conclude that at these energies the reaction is not suited for extracting spectroscopic information. Our result obtained at 11 MeV is not too different from theirs, therefore we feel that the value of S,,~ ~ 2 might be used with
102
w. nOHNEet al.
some confidence, having in mind the uncertainty caused by the cut-off problem anyway. This value equals the simple jj-coupling shell-model value of 2.00, while the more refined theory of Shukla 18), taking particle-hole correlations in the ground state of 160 into account, yielded a value of 0.9. Conflicting evidence on the nature of this state also arose from pick-up 15,16) and y-transition measurements 17, 25). (iii) The even-parity states are expected to arise from coupling of a 2s or ld particle to the lp -2 state of 14N. Halbert and French 19) have calculated levels belonging to configurations ls*lpl°2s+ l s * l p l ° l d + ls31p 12 and obtained spectroscopic factors for stripping into these levels that are listed in column 7. This refers to lSN but should be comparable for 150. (We have recalculated these values from the reduced widths listed by Halbert and French using the single-particle reduced widths adopted by the same authors.) The agreement with our results (column 5b) is considered satisfactory, with the exception of the ½+ level, which is the only one where the (z, d) angular distribution does not show a distinct stripping pattern anyway. Thus one may say that the Halbert-French model also gives quite a good description for most of the low even-parity states of ~sO. For the formation of these positive-parity states in the 160(z, ~) reactions, no predictions exist. The S-values are all found to be rather large, which in conjunction with the stripping results just described indicates the existence of quite large lp-2(ld, 2s) 2 components in the ground state of 160, possibly also of more complicated components like lp-4(2s, ld) 4 [ref. 23)]. Similar conclusions are drawn by Hiebert e t aL 24) for the reaction 160(d, "~)15N. Of particular interest is the rather strong (z, ~) transition to the ½+ state which has a distinct direct l = 0 angular distribution pattern. From the triton transfer reaction 12C(19F, 160)tSN, Bock e t al. 26) find that the corresponding ½+ state in ~SN (and possibly also the ~ state) has the structure (~2C+3H). Assuming for the 150 level the analogue structure (12C + aHe), one might conclude that the (z, ~) reaction going to this state is associated with a four-particle four-hole component or an ~cluster structure in the 160 ground state. In this context the different spectroscopic factors obtained in the 160(d, z)lSN reaction 2a) may be significant. That the 15N--~+ state has a complicated structure is also concluded by Pelte and Povh 20) from the small f t value observed in the fl-decay of ~5C leading to this state. From inelastic ~-scattering on 15N and 160, Harvey e t aL 21) explained some of the ~SN states of even parity, viz. ~+, ~+, ~+ by a p-hole in the 1- or 3- states in 160. In the (T, ct) reaction to the corresponding tSO states, this mode of formation would require a two-step process, but then the simple DWBA used in this work would not be able to explain the angular distributions so well as is the case. We therefore feel that this way of forming the states can be excluded t. t Note added in proof." The apparently very weak transition to the ~+ state supplies further evidence against the two-step mode.
103
STATES IN 160
Sincere thanks are due to Dr. H. Fuchs, Professor K. H. Lindenberger Sichelschmidt for valuable discussions. For the preparation
a n d F.
of the TaN targets, we
are extremely grateful to Messrs. Mokler and Wirth, MPI Heidelberg. The DWBA calculations were performed at Deutsches Rechenzentrum,
Darmstadt.
References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14)
15) 16)
17) 18) 19) 20) 21) 22) 23) 24) 25) 26)
H. Homeyer, Nucl. Instr. 56 (1967) 355 R. H. Bassel, R. M. Drisko and G. R. Satchler, ORNL 3240 (1962) and addenda W. P. Alford, L. M. Blau and D. Chne, Nucl. Phys. 61 (1965) 368 R. L. Hahn and E. Rlcci, Nucl. Phys. 101 (1967) 353 W. R. Smith and I. V. Ivash, Phys. Rev. 131 (1963) 304 M. H. Macfarlane and J. B. French, Revs. Mod. Phys. 32 (1960) 567 E. K. Warburton, J. W. Olness and E. D. Alburger, Phys. Rev. 140 (1965) B1202 D. F. Hebbard and B. Povh, Nucl. Phys 13 (1959) 642 S. Mubarakmand and B. E. F. Macefield, Nucl. Phys. A98 (1967) 82 H. T. Rlchards and A. Chlba, quoted m ref. e) W. H. Evans, T. S. Green and R. Middleton, Proc. Phys. Soc. A66 (1953) 108 A. Gallman, P. Flntz and P. E. Hodgson, Nucl. Phys. 82 (1966) 161 S. Cohen and D. Kurath, Nucl. Phys. A101 (1967) 1 D. Bachner, M. Betigen, R. Bock, P. David, H. H. Duhm, U. Lynen, S. Martin, W. Melzer, F. Puhlhofer, H. Schimetzek and R. Stock, Max Planck-Instltut Heidelberg, Jahresbemcht (1966) p. 27 E. K. Warburton, P. D. Parker and P. F. Donovan, Phys. Lett. 19 (1965) 397 D. Bachelier, M. Bernas, I. Brissaud, C. Detraz, N. K Ganguly and P. Redvanyi, Phys. Lett. 8 (1964) 56; J. K. P. Lee, S. K. Mark, P M. Portner and R. B. Moore, Nucl. Phys. A106 (1968) 357; C. D. Kavaloski, G. Bassani and N. M. Hmtz, Phys. Rev. 132 (1963) 813 J. S. Lopes, O. Hausser, H. J. Rose, A. R. Polettl and M. F. Thomas, Nucl. Phys. 76 (1966) 223 A. P Shukla, PUC 937-262, thesis Princeton (1967) E. C. Halbert and J. B. French, Phys. Rev. 105 (1957) 1563 D. Pelte, B. Povh and W. Scholz, Compt. Rend. Pans Conf. on nuclear physics, Vol. II, (1964) p. 362 B. G. Harvey, J. R. Merriwether and A. Bussiere de Nercy, p. 379 ibid (1964) R. Stock, R. Bock, P. David, H. H. Duhm and T. Tamura, Nucl. Phys. AI04 (1967) 136 G. E. Brown and A. M. Green, Nucl. Phys. 75 (1966) 401 J. C. Hiebert, E. Newman and R. H. Bassel, Phys. Rev. 154 (1967) 898 R. D. Gill, J. S. Lopes, B. C. Robertson, R. A. T. Bell and H. J. Rose, Nucl. Phys. A108 (1968) 678 R Bock, M. Grol3e-Schulte, H. Gutbrod, W. v. Oertzen and U. Voos, Jahresbericht Max Planck-Institut fur Kernforschung Heidelberg (1966) p. 7
2.G
[ I
Nuclear Physics All3 (1968) 97--103; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprmt or microfilm wtthout written permission from the publisher
STUDY OF STATES IN ISO BY T H E R E A C T I O N S 14N(z, d) A N D 160(z, ~) w. BOHNE t, H. HOMEYER, H. MORGENSTERN and J. SCHEER
Hahn-Meitner-lnstitut fiir Kernfbrschung Berlin, Sektor Kernphysik, Berlin-West, Germany Received 22 February 1968
Abstract: Angular distributions of deuterons and ~-particles emitted in the reactions X4N(z,d) and 160(z, ~) going to the first seven states in xsO were measured between 5° and 120° at E~ = 11 MeV. DWBA calculations were performed and spectroscopic factors extracted and discussed. E
NUCLEAR REACTIONS: Z4N(T, d), ~sO(T, ct), E = 11 MeV; measured a(~); 150 deduced levels, spectroscopic factors. Natural targets.
[
I
1. Introduction Various models exist for the states of 150 and 15N. A l t h o u g h nucleon transfer reactions should provide information on these states, only relatively few measurements have been performed, which is p r o b a b l y mainly due to target problems. The aim of the present w o r k was to extract some spectroscopic factors f r o m the reactions 14N(z, d) and 160(% ct) leading to the same states in 150.
2. Experimental procedure D o u b l y charged 3He ions (z-particles) were accelerated in a 5.5 M V Van de G r a a f f generator tt, being selected prior to acceleration in a 30 ° magnet placed in the high voltage terminal. The accelerated beam was deflected and analysed in a 90 ° magnet. Then by means o f two magnetic quadrupole lenses it was focussed into a cylindrical reaction c h a m b e r o f 50 cm diam having a target ladder in its centre and was finally stopped in a F a r a d a y cup that was 3 m long. One blend with a variable diameter placed between the lenses, a pair of blends, 1.5 m m in diam and an antiscattering blend, 4 m m wide, placed respectively, 50 and 15 cm upstream f r o m the target, served to define the beam. On the target it h a d a diameter o f 1-2 mm. As nitrogen targets, we used self-supporting foils ttt of T a N . F o r measurements at angles smaller than 20 ° we used melamine targets evaporated onto a thin c a r b o n backing, as the strong Rutherford scattering f r o m the Ta prohibited use of the T a N target at these angles. The melamine target could stand a current of 20-30 n A for t Work performed in partial fulfillment of the requirements for diploma in physics. tt HVEC, Type CN. ttt They were kindly made for us by Messrs. Mokler and Wlrth, MPI Heidelberg. 97
98
w . BOHNE et aL
several hours without any loss of nitrogen as was observed by comparing the intensity of elastically scattered 3He from carbon and nitrogen. The T a N target could stand a current of several 100 nA practically indefinitely. Oxygen was automatically present as a contamination of the TaN, therefore no special targets were necessary to observe the (z, ,t) reaction. Charged particles emitted from the target were detected by a dE/dx • E solid-state counter telescope t The telescope was mounted 12 cm from the target and could be turned around it. In front of it a collimator (45 mm long, 4 mm wide) was placed to shield it from radiation scattered from the blends. This enabled observation down to 5 ° forward angle, provided the beam was well focussed. The various particle types were identified using a multiplication and addition circuit described in ref. l). Spectra of p, d, z and ~ were registered in four sections of a 4096-channel analyser. A pile-up rejection circuit was employed, in addition to a coincidence between E and dE/dx signals, rejecting pulses from particles stopped in the dE/dx detector. Three further detectors mounted at 45 °, 135 ° and 150 ° served as monitors, either set at prominent lines originating from 14N or registering a whole charged particle spectrum. The over-all energy resolution of the telescope was 50 keV, therefore at most angles it was possible to unfold graphically the lines corresponding to transitions to the doublets at 5.2 and 6.8 MeV. 3. R e s u l t s
The measured angular distributions are displayed in figs. 1 and 2 together with DWBA fits made using the code JULIE 2) with parameters listed in table 1 that were taken from refs. a-5). In most cases the fit is considered satisfactory. For the (z, d) reaction, variation of the cut-off radius from 0 to 4 fm did not alter the quality of the fits appreciably; the spectroscopic factors varied within 15 ~o. In column 5a of table 2, we quote the values obtained from the best fit with cut-off radius R .... = 3 fm. They are given relative to that of the ground state. For the ½+ level, an estimated upper limit is given assuming angular momentum transfer ! = 0. For the (z, ~) reaction, no cut-off ought to be used according to the general considerations of ref. 22), but no good fit could be obtained in this case; however use of Ro.o' = 3 fm, 4 fm or 5 fm gave quite good fits. It may be noted that at an energy close to ours, Alford et al. 3) also obtained quite a good fit to the elastic scattering of aHe with the set of optical potential parameters listed in table 1, which we took from their work for analysis of our data. The relative spectroscopic factors obtained with R .... = 5 fm are listed in column 10 of table 2. Variation of R .... down to 0 fm caused deviations of at most 25 ~o. The transferred angular momenta l are denoted in the figures and listed in columns t ORTEC, 1000/~m+50gm; NUCLETRON, 32/zm.
STATES IN
99
]50
d6 . . . . ~ ' ' ' ' ' ' ' '4 "T~I " ~ + L=2 • \+÷ Ex=5 2&MeV102! ~ +÷÷,÷~5/2" _
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.
103 ~
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I
I
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,
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1
1
1
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i
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I
,
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,
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, j 4 . I Ex=5 2/,MeV "~ 512 +
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103
.
Ex=6 789MeV
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102
/
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7•2+
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$
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~* \**
-
Ex=616MeV 312 :
I I I I I ~ I
I
I
I
I
103~-~ 102~
~
1021 . . . . . . II
20 /.0 60 80 100 OCM
++÷÷+% *'~'1 I I I I ,+l l i l 20 40 60 80 100 OCM l
Ex=6 857MeV
Fx=5 | 8 ~ M . V I
l
1021
V" , , ,
I
a
Fig. l. A n g u l a r distributions o f deuterons f r o m the reaction Z4N(T, d)160 to states w i t h excztation energy Ex; E~ = 11 MeV; solid lines: D W B A fits with parameters hsted in table 1. No fits could be made for the transitions to unbound states. Errors, where not indicated, are smaller than the size of the points. The cross-section scales are arbitrary but consistent for the transitions to different levels of one reaction.
-• l
20 ~-0 S0 so 100 0CM
I
l
I
I
I
I
l
I
I
I
20 ~0 60 a0 100 0CM
Fig. 2. Angular distributions of particles from the reaction 160(T, ~)150, to states with excitation energy Ex; Ez = 11 MeV; solid hnes: DWBA fits wxth parameters hsted in table 1. Errors, where not indicated, are smaller than the size of the points. The cross section scales are arbitrary, but consistent for the transitzons to different levels of one reaction.
TABLE 1 Optical-model parameters for DWBA fit Channel
V W (MeV) (MeV)
14Nq-z 160-t-T 150-t-d 15Oq-oc
71 105 93 100
Vs.o. (MeV)
W' (MeV)
13.1 20.5 6 10
64
ro (fm)
ro' (fm)
a (fro)
1.9 1.5
0.53 0.63 1.05 0.65
1.78 1.6 1 1.5
a' (fm)
re (fm)
Ref.
0.30 0.65
1.3 1.4 1.3 1.4
4) a) 4) a)
The potential had the form -- V f ( x ) - - i ( W - - W ' a ' d / d r ) f ( x ' ) d- (h/m~c) 2//s.o. (I " a ) r - l d / d r • f(x),
f(~) = (1 + e x p ~)-x,
x = ( r - - r o A ~ ) a -1,
x' :
(r--ro'AT)a '-1,
Rcoulom b = reA~.
Cut-off (fro)
3 5
0
6.16
5.18
5.24
6.79
6.87
7.28
1
4
2
3
5
6
7
{-+
~÷
{+
~+
½+
{-
½-
(3)
Jn a)
2
2
0
2
(0)
1
1
(4)
1
(r, d) b)
0.29
0.36
0.39
0.04
=<0.007
0.05
1.00
(5a)
0.42
0.52
0.56
0.06
~0.01
0.07
1.45
(5b)
Srel e) S~el" 1.45
0.014
1.00
(6a)
Srel
0.02
1.45
(6b)
Sabs
Theory a)
Stripping
0.54
0.63
0.47
0.063
0.025
(7)
gabs
Theory e)
0.48
0.50
0.44
0.16
1.00
(8)
Srel
(d, n) t)
1.03
0.60
0.58
0.22
2.11
1.00
(10)
Sre 1g)
0.90
1.00
(11)
SreI
Theory h)
not measurable k)
2
2
2
0
1
1
(9)
l
(T, ct) b)
0
0
0
0
2.00
1.00
(12)
Srel
JJmodelShell
Pick up
0.15
0.018
1.75
1.00
s~x (13)
(dT) 1)
a) Ref. 7). b) This work. e) Errors of Srel:-4-15 ~ , indicated by variation of the cut-off radius from 0 to 4 fm. d) Ref. x3). e) Ref. lg). f) Ref. 9). g) Quoted are the values obtained with a cut-offradius of 5 fm. Variation of the cut off radius from 0 to 5 fm caused deviations up to 25 ~ . u) Ref. 18). l) Ref. 5~). k) or-particles from this transition penetrated the telescope only at the smallest angles. The transition appears to be very weak, however.
(2)
(1)
(MeV)
Ex a)
150 level
TABLE 2 Relative spectroscopic factors from one-particle transfer reactions leading to lbO
oa~
STATES
IN 150
101
4 and 9 of table 2. They are all consistent with the J~ values determined in ref. 7). The level found at 7.28 MeV was identified with the 7.285 MeV state of ref. 7), which has J~ = ~+. No indication of a level 8) at 7.16 MeV was found. Also listed in table 2 are theoretical predictions: Column 6 ab" The results of intermediate coupling calculations of Cohen and Kurath 1a) for stripping to the oddparity states. Column 7: The predictions of Halbert and French for stripping to the even-parity levels in 15N, no calculations being available for 1sO. Column 11" The predictions of Shukla is) for pick up to the odd-parity states. No predictions exist for pick up to the even-parity states. For comparison with the predictions of Halbert and French 19), some absolute normalization was needed. As we find S ( ½ - ) / S ( ½ - ) < < 1 in accordance with the Kurath prediction, for this purpose we adopt the Kurath value Sabs(½-) = 1.45. The values thus renormalized are listed in column 5b. Finally we list some other experimental data for comparison; column 8 contains results 9) from the reaction Z4N(d, n)Z50, and column 13 results 24) from the reaction 1 6 0 ( d , .c)15N.
4. Discussion
(i) The spectroscopic factors which Mubarakmand and Macefield 9) obtained from the reaction Z4N(d, n)ZSO (column 8) are expected to agree with those from the analogue (z, d) reaction listed in column 5a. In all cases, their relative values are somewhat larger, the discrepancy being worst for the ~- level. Perhaps their deuteron energy of 5 MeV was too low, this conjecture being corroborated by a (d, n) measurement 1z) at 7.7 MeV which yielded Sro~(~-) -- 0.08. A strong energy dependence of S for the 14N(d, p) reaction at low energies was also found by Gallmann et al. 12) who attributed it to compound nucleus interference. The energy used in this experiment is hoped to be sufficiently large to avoid this difficulty. A supporting evidence may be seen in the fact that we find no strong dependence of S on the cut-off radius, contrary to ref. 12). The pick-up spectroscopic factors of Hiebert et al. 24) from the reaction 160(d, z)lSN (column 13) are in reasonable agreement for the ~- state but much smaller for the ½+ and ~+ states. (ii) For the odd-parity levels, the relative spectroscopic factors from the reaction 14N(z, d) are in reasonable agreement with the intermediate coupling results of Cohen and Kurath x3) (column 6). Whether the fact that our value of S,el(½-) came out about four times larger has some significance is difficult to say in view of its smallness. In the 160(~, ~) reaction, Bachner et al. 14) found that Srel(~-) was strongly energy dependent, having the value 1.5 and 2.2 at a aHe energy of 18 and 19.5 MeV, respectively. Therefore they conclude that at these energies the reaction is not suited for extracting spectroscopic information. Our result obtained at 11 MeV is not too different from theirs, therefore we feel that the value of S,,~ ~ 2 might be used with
102
w. nOHNEet al.
some confidence, having in mind the uncertainty caused by the cut-off problem anyway. This value equals the simple jj-coupling shell-model value of 2.00, while the more refined theory of Shukla 18), taking particle-hole correlations in the ground state of 160 into account, yielded a value of 0.9. Conflicting evidence on the nature of this state also arose from pick-up 15,16) and y-transition measurements 17, 25). (iii) The even-parity states are expected to arise from coupling of a 2s or ld particle to the lp -2 state of 14N. Halbert and French 19) have calculated levels belonging to configurations ls*lpl°2s+ l s * l p l ° l d + ls31p 12 and obtained spectroscopic factors for stripping into these levels that are listed in column 7. This refers to lSN but should be comparable for 150. (We have recalculated these values from the reduced widths listed by Halbert and French using the single-particle reduced widths adopted by the same authors.) The agreement with our results (column 5b) is considered satisfactory, with the exception of the ½+ level, which is the only one where the (z, d) angular distribution does not show a distinct stripping pattern anyway. Thus one may say that the Halbert-French model also gives quite a good description for most of the low even-parity states of ~sO. For the formation of these positive-parity states in the 160(z, ~) reactions, no predictions exist. The S-values are all found to be rather large, which in conjunction with the stripping results just described indicates the existence of quite large lp-2(ld, 2s) 2 components in the ground state of 160, possibly also of more complicated components like lp-4(2s, ld) 4 [ref. 23)]. Similar conclusions are drawn by Hiebert e t aL 24) for the reaction 160(d, "~)15N. Of particular interest is the rather strong (z, ~) transition to the ½+ state which has a distinct direct l = 0 angular distribution pattern. From the triton transfer reaction 12C(19F, 160)tSN, Bock e t al. 26) find that the corresponding ½+ state in ~SN (and possibly also the ~ state) has the structure (~2C+3H). Assuming for the 150 level the analogue structure (12C + aHe), one might conclude that the (z, ~) reaction going to this state is associated with a four-particle four-hole component or an ~cluster structure in the 160 ground state. In this context the different spectroscopic factors obtained in the 160(d, z)lSN reaction 2a) may be significant. That the 15N--~+ state has a complicated structure is also concluded by Pelte and Povh 20) from the small f t value observed in the fl-decay of ~5C leading to this state. From inelastic ~-scattering on 15N and 160, Harvey e t aL 21) explained some of the ~SN states of even parity, viz. ~+, ~+, ~+ by a p-hole in the 1- or 3- states in 160. In the (T, ct) reaction to the corresponding tSO states, this mode of formation would require a two-step process, but then the simple DWBA used in this work would not be able to explain the angular distributions so well as is the case. We therefore feel that this way of forming the states can be excluded t. t Note added in proof." The apparently very weak transition to the ~+ state supplies further evidence against the two-step mode.
103
STATES IN 160
Sincere thanks are due to Dr. H. Fuchs, Professor K. H. Lindenberger Sichelschmidt for valuable discussions. For the preparation
a n d F.
of the TaN targets, we
are extremely grateful to Messrs. Mokler and Wirth, MPI Heidelberg. The DWBA calculations were performed at Deutsches Rechenzentrum,
Darmstadt.
References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14)
15) 16)
17) 18) 19) 20) 21) 22) 23) 24) 25) 26)
H. Homeyer, Nucl. Instr. 56 (1967) 355 R. H. Bassel, R. M. Drisko and G. R. Satchler, ORNL 3240 (1962) and addenda W. P. Alford, L. M. Blau and D. Chne, Nucl. Phys. 61 (1965) 368 R. L. Hahn and E. Rlcci, Nucl. Phys. 101 (1967) 353 W. R. Smith and I. V. Ivash, Phys. Rev. 131 (1963) 304 M. H. Macfarlane and J. B. French, Revs. Mod. Phys. 32 (1960) 567 E. K. Warburton, J. W. Olness and E. D. Alburger, Phys. Rev. 140 (1965) B1202 D. F. Hebbard and B. Povh, Nucl. Phys 13 (1959) 642 S. Mubarakmand and B. E. F. Macefield, Nucl. Phys. A98 (1967) 82 H. T. Rlchards and A. Chlba, quoted m ref. e) W. H. Evans, T. S. Green and R. Middleton, Proc. Phys. Soc. A66 (1953) 108 A. Gallman, P. Flntz and P. E. Hodgson, Nucl. Phys. 82 (1966) 161 S. Cohen and D. Kurath, Nucl. Phys. A101 (1967) 1 D. Bachner, M. Betigen, R. Bock, P. David, H. H. Duhm, U. Lynen, S. Martin, W. Melzer, F. Puhlhofer, H. Schimetzek and R. Stock, Max Planck-Instltut Heidelberg, Jahresbemcht (1966) p. 27 E. K. Warburton, P. D. Parker and P. F. Donovan, Phys. Lett. 19 (1965) 397 D. Bachelier, M. Bernas, I. Brissaud, C. Detraz, N. K Ganguly and P. Redvanyi, Phys. Lett. 8 (1964) 56; J. K. P. Lee, S. K. Mark, P M. Portner and R. B. Moore, Nucl. Phys. A106 (1968) 357; C. D. Kavaloski, G. Bassani and N. M. Hmtz, Phys. Rev. 132 (1963) 813 J. S. Lopes, O. Hausser, H. J. Rose, A. R. Polettl and M. F. Thomas, Nucl. Phys. 76 (1966) 223 A. P Shukla, PUC 937-262, thesis Princeton (1967) E. C. Halbert and J. B. French, Phys. Rev. 105 (1957) 1563 D. Pelte, B. Povh and W. Scholz, Compt. Rend. Pans Conf. on nuclear physics, Vol. II, (1964) p. 362 B. G. Harvey, J. R. Merriwether and A. Bussiere de Nercy, p. 379 ibid (1964) R. Stock, R. Bock, P. David, H. H. Duhm and T. Tamura, Nucl. Phys. AI04 (1967) 136 G. E. Brown and A. M. Green, Nucl. Phys. 75 (1966) 401 J. C. Hiebert, E. Newman and R. H. Bassel, Phys. Rev. 154 (1967) 898 R. D. Gill, J. S. Lopes, B. C. Robertson, R. A. T. Bell and H. J. Rose, Nucl. Phys. A108 (1968) 678 R Bock, M. Grol3e-Schulte, H. Gutbrod, W. v. Oertzen and U. Voos, Jahresbericht Max Planck-Institut fur Kernforschung Heidelberg (1966) p. 7