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Isobaric spin dependence in proton transfer reactions
PHYSICS
Volume 29B, number 10
ISOBARIC
SPIN
DEPENDENCE
IN
LETTERS
PROTON
18 August 1969
TRANSFER
REACTIONS
*
R. G. COUCH **, F. G. PEREY and J. A. BIGGERSTAFF Oak Ridge
National
Laboratory.
Oak Ridge,
Tennessee.
USA
and K. K. SETH Northwestern
University.
Evanston.
Illinois,
USA
Received 9 July 1969
Results of an experimental investigation of 54Fe(d, n)5jCo reaction are presented and spectroscopic strengths for both T, and T, states are derived. It is concluded that within the limits of experimental and analytical uncertainties there is no discrepancy between the spectroscopic factors for T, analogue states as derived from the (d, n) and (3He,d) reactions.
Some time ago it was pointed out by Siemssen et al. [l] that apparently the (d,n) spectroscopic factors for T, analogue states in the oddodd nuclei FOB, I4N and 26~1 are a factor 2 to 3 smaller than those derived from (3He, d) experiments. Tamura [2] made some coupled-channel calculations in which the conventional DWBA amplitude was modified to include charge exchange coupling between (d, p) and (d, n) channels. These CC + DWBA calculations gave much reduced theoretical cross sections for the (d, n) reaction and apparently removed the discrepancy in spectroscopic factors. Subsequently it was found [3] that this result was incorrect and arose from a computational error. Actually the CC + DWBA cross sections turn out to be a little bit larger, thereby further increasing the discrepancy. Thus if the experimental effect pointed out by Siemssen et al. is real, no theoretical explanation is presently available. This makes it even more important to see if the experimental effect persists in heavier nuclei for which optical potentials and DWBA analyses are known to be more reliable. In this letter we report on results of a 54Fe(d,n)55Co experiment done at the Oak Ridge National Laboratory time-of -flight facility as a
* Research sponsored by the U.S. Atomic Energy Commission under contract with Union Carbide Corporation. ** Oak Ridge Graduate Fellow from Northwestern University under appointment from Oak Ridge Associated Universities, Inc.
part of a systematic study of the (d, n) reaction on f-p shell nuclei [4,5]. An enriched self-supporting target of 54Fe was bombarded by a pulsed deuteron beam of 10.0 MeV energy from the ORNL tandem. The flight path length was 25 meters and the detected neutron resolution was ( 1.5 ns. The angular distributions were analyzed with the DWBA method using nonlocality and finite-range car rections. The optical potential parameters were taken from global studies of Perey and Perey [6] and Becchetti and Greenlees [7]. Typical fits to the angular distributions are shown in fig. 1, In table 1 we list the spectroscopic strength (2J+ l)C2S obtained for T< states as well as for some of the T, states of the same Jn from our experiment as well as from several (3He,d) experiments reported in the literature [8-lo]. It appears that large differences exist between the (d, n) and (3He, d) results, both of which also dif fer from the corresponding (d,p) results for the T< states in the ‘parent’ nucleus 55Fe. However, it is clear that since the different experiments have been analyzed under different approximations and with different optical potentials, dif ferences are indeed to be expected. It may not be justified, for example to compare the (d,n) results obtained above with the results from the (3He, d) data of Armstrong and Blair [ 10,111 which were analyzed in the local zero-range approximation with the use of a radial cut-off, a simulated spin-orbit effect and a different radius for the proton potential well. To illustrate this point, in column 7 of table 1 we present the re657
Volume 29B. number
Results
10
PHYSICS
of DWBA analyses
LETTERS
18 August 1969
Table 1 of (d,n) and (3He,d) experiments for T< and T> states in the analogue nucleus (d,n) results for the parent nucleus 55Fe.
55C0, and
(25+ 1)CB.s (d, n)
(3He. d) [‘I
(3He. d) [loI
(3He, d) [II1
(3He, d) [12’ a
E(d) =
10.0 MeV
E(3He) = 11.0 MeV
E(3He) = 16.5 MeV
E(3He) = 22 MeV
E(3He) = 22 MeV
I($-) T<
1.20
1.10
1.68
2.557
I(+-) T< b
0.77
0.64
1.04
1.00
0.63
2.935
I($-) T< b
0.30
0.28
0.46
0.37
0.25
.+I”) T 2.160
3.300
1.40
3(5-) T< 2
2.30
2.2
2.35
3.24
T<
0.35
0.35
0.66
0.44
+H;-)
55Fe
0.94
4.735
I(;-)
T>
0.74
0.92
0.88
0.73
0
0.86
5.170 *
I(;-)
T>
0.26
0.48
0.52
0.32
0.417
0.30
5.743 *
3(5-) T, 2
1.33
1.56
1.62
1.25
0.935
1.49
1 * Unbound state. F Data of ref. [ll] reanalyzed with non-local finite-range DWBA calculations. o Spin assignment is due to ref. [9]. It is also supported by systematics in this region of atomic weight. The value in column 6 has been changed to take account of this assignment. c Average of (d,p) results of refs. 16 and 17 (Ed = 15 MeV, resp. 7.8 MeV) after normalization to sum rule expectations; C2 here refers to (d,n) and (3He,d) reactions.
s4Fe Id, n)”
Co
T< States
1s
States
5 2.160 2
3/2-
-
E
z
v
\
4.732 E
\
z.557 i/2-
3/2-
5.170 1
1/2-
\
en
658
-
40
sults of a non-local finite-range reanalysis of their data. The absolute spectroscopic factors have changed rather drastically, although the strength ratios for transitions of the same Jr are essentially unaltered. Thus a more reliable comparison between the different results can be made for the ratios (2Jt 1)C2S>/2J+ 1)C2S, between T, and T< states of the same Jr. In table2 we present such ratios for states in 55Co. As is clear from table 2, the (3He,d) and (d,n) results agree at least as well as the different (3He, d) results within themselves, and all dif ferences are within the usual 20% errors in spectroscopic factors extracted from DWBA analyses. Thus the possible (d,n), (3He,d) discrepancy is not supported by our data. In table 2 we have also included additional evidence supporting our conclusions. This includes relative spectroscopic factors for sgCu states obtained from (d, n) experiments [4] and (3He,d) experiments [ 12,131, and for %a states obtained from (d, n) experiments [ 141 and (3He,d) experiments [ 151. It appears, quite convincingly, that at least for odd-even and eveneven nuclei in table 2, with A > 40, there is no significant discrepancy between (d, n) and (3He, d) spectroscopic strengths for T> states.
Fig. 1. Angular distributions of three typical T< states and the three T, states observed in this experiment. The curves are predictions of non-local finite-range 60 8c.u. (deg.1 DWBA calculations.
Volume 29B. number 10
PHYSICS
Ratios of spectroscopic
LETTERS
18 August 1969
Table 2 strengths for T< and T, states of same Z(J’).
I Nucleus
55co
59CU
40Ca
* Unbound state. a This experiment.
T< state
T, state
1(Jr)
OLlev)
OLleV)
l$)
2.160
4.135
I(;-)
2.557
5.170 *
3(q-)
3.300
5.743 *
I(;-)
0
C2S>/C2S<
,
(d, n)
(3He, d)
(3HeI 4
0.64 a
0.55b
0.63 ’
0.34a
0.46 b
0.52
0.59 a
0.62 b
0.50 c
0.24 d
0.29 e
0.19 f
I(%_)
0.486
4.355 *
o.26d
0.29 e
0.38 f
3(;-)
0.909
4.301 *
0.55 d
0.44 e
0.43 f
3.895
*
3(3_)
3.738
7.696
3(4_)
5.606
7.655
3(5_)
4.480
8.553 *
b Ref. 9. ’ Refs. 10, 11.
I
d Ref. 4. e Ref. :12.
Perhaps the discrepancy that Siemssen et al. [1] have pointed out only exists for odd-odd nuclei or only for light nuclei.
1.86 g
1.62 h
0.65 g
0.78 h
1.05 g
1.19 h f Ref. 13. g Ref. 14
h Ref. 15.
8. B. J. O’Brien, W. E. Dorenbusch, T. A, Belote and J. Rapaport, Nucl. Phys. A104 (1967) 609. 9. B. Rosner and C. H. Holbrow, Phys. Rev. 154 (1967) 1080; ~7.8~rvopou1os et al.. Phys. Rev. 177 (1969)
The authors wish to thank Dr. A. G. Blair for putting their original data at our disposal and Professor T. Tamura for communicating his latest results prior to publication.
References 1. R. H. Siemssen, G. C. Morrison, B. Zeidman and H. Fuchs, Phys. Rev. Letters 16 (1966) 1050. 2. T. Tamura, Phys. Rev. Letters 19 (1967) 321. 3. R. Coker and T. Tamura, to be published. 4. A. Marusak, Ph. D. dissertation, University of Tennessee, 1969, Oak Ridge National Laboratory Report, ORNL-TM-2472, to be published. 5. R. G, Couch, Ph. D. dissertation. Northwestern University, 1969, to be published. 6. C. Perey and F. Perey, Phys. Rev. 132 (1963) 755. 7. F. D. Becchetti and G. W. Greenlees, to be published.
13. 14. 15. 16. 17.
D. D.‘Armstrong and A. G. Blair, Phys. Rev. 140 (1965) B1226. A. G. ‘Blair and D. D. Armstrong, Phys. Letters 16 (1965) 57. G. C. Morrison and J. P. Schiffer. in: Isobaric spin in nuclear physics, eds. J. D. Fox and D. Robson (Academic Press, New York. 1966) p. 748, D. J. Pullen and B. Rosner, Phys. Rev. 170 (1968) 1034. H. Fuchs, K. Grabisch and G. Roschert, Nucl. Phys. Al29 (1969) 545. K. K. Seth, J. A. Biggerstaff, P. D. Miller and G. R. Satchler, Phys. Rev. 164 (1967) 1450. R. H. Fulmer and A. L. McCarthy. Phys. Rev. 131 (1963) 2133. J. R. Maxwell and W. C. Parkinson. Phys. Rev. 135 (1964) B82.
*****
659
Volume 29B, number 10
ISOBARIC
SPIN
DEPENDENCE
IN
LETTERS
PROTON
18 August 1969
TRANSFER
REACTIONS
*
R. G. COUCH **, F. G. PEREY and J. A. BIGGERSTAFF Oak Ridge
National
Laboratory.
Oak Ridge,
Tennessee.
USA
and K. K. SETH Northwestern
University.
Evanston.
Illinois,
USA
Received 9 July 1969
Results of an experimental investigation of 54Fe(d, n)5jCo reaction are presented and spectroscopic strengths for both T, and T, states are derived. It is concluded that within the limits of experimental and analytical uncertainties there is no discrepancy between the spectroscopic factors for T, analogue states as derived from the (d, n) and (3He,d) reactions.
Some time ago it was pointed out by Siemssen et al. [l] that apparently the (d,n) spectroscopic factors for T, analogue states in the oddodd nuclei FOB, I4N and 26~1 are a factor 2 to 3 smaller than those derived from (3He, d) experiments. Tamura [2] made some coupled-channel calculations in which the conventional DWBA amplitude was modified to include charge exchange coupling between (d, p) and (d, n) channels. These CC + DWBA calculations gave much reduced theoretical cross sections for the (d, n) reaction and apparently removed the discrepancy in spectroscopic factors. Subsequently it was found [3] that this result was incorrect and arose from a computational error. Actually the CC + DWBA cross sections turn out to be a little bit larger, thereby further increasing the discrepancy. Thus if the experimental effect pointed out by Siemssen et al. is real, no theoretical explanation is presently available. This makes it even more important to see if the experimental effect persists in heavier nuclei for which optical potentials and DWBA analyses are known to be more reliable. In this letter we report on results of a 54Fe(d,n)55Co experiment done at the Oak Ridge National Laboratory time-of -flight facility as a
* Research sponsored by the U.S. Atomic Energy Commission under contract with Union Carbide Corporation. ** Oak Ridge Graduate Fellow from Northwestern University under appointment from Oak Ridge Associated Universities, Inc.
part of a systematic study of the (d, n) reaction on f-p shell nuclei [4,5]. An enriched self-supporting target of 54Fe was bombarded by a pulsed deuteron beam of 10.0 MeV energy from the ORNL tandem. The flight path length was 25 meters and the detected neutron resolution was ( 1.5 ns. The angular distributions were analyzed with the DWBA method using nonlocality and finite-range car rections. The optical potential parameters were taken from global studies of Perey and Perey [6] and Becchetti and Greenlees [7]. Typical fits to the angular distributions are shown in fig. 1, In table 1 we list the spectroscopic strength (2J+ l)C2S obtained for T< states as well as for some of the T, states of the same Jn from our experiment as well as from several (3He,d) experiments reported in the literature [8-lo]. It appears that large differences exist between the (d, n) and (3He, d) results, both of which also dif fer from the corresponding (d,p) results for the T< states in the ‘parent’ nucleus 55Fe. However, it is clear that since the different experiments have been analyzed under different approximations and with different optical potentials, dif ferences are indeed to be expected. It may not be justified, for example to compare the (d,n) results obtained above with the results from the (3He, d) data of Armstrong and Blair [ 10,111 which were analyzed in the local zero-range approximation with the use of a radial cut-off, a simulated spin-orbit effect and a different radius for the proton potential well. To illustrate this point, in column 7 of table 1 we present the re657
Volume 29B. number
Results
10
PHYSICS
of DWBA analyses
LETTERS
18 August 1969
Table 1 of (d,n) and (3He,d) experiments for T< and T> states in the analogue nucleus (d,n) results for the parent nucleus 55Fe.
55C0, and
(25+ 1)CB.s (d, n)
(3He. d) [‘I
(3He. d) [loI
(3He, d) [II1
(3He, d) [12’ a
E(d) =
10.0 MeV
E(3He) = 11.0 MeV
E(3He) = 16.5 MeV
E(3He) = 22 MeV
E(3He) = 22 MeV
I($-) T<
1.20
1.10
1.68
2.557
I(+-) T< b
0.77
0.64
1.04
1.00
0.63
2.935
I($-) T< b
0.30
0.28
0.46
0.37
0.25
.+I”) T 2.160
3.300
1.40
3(5-) T< 2
2.30
2.2
2.35
3.24
T<
0.35
0.35
0.66
0.44
+H;-)
55Fe
0.94
4.735
I(;-)
T>
0.74
0.92
0.88
0.73
0
0.86
5.170 *
I(;-)
T>
0.26
0.48
0.52
0.32
0.417
0.30
5.743 *
3(5-) T, 2
1.33
1.56
1.62
1.25
0.935
1.49
1 * Unbound state. F Data of ref. [ll] reanalyzed with non-local finite-range DWBA calculations. o Spin assignment is due to ref. [9]. It is also supported by systematics in this region of atomic weight. The value in column 6 has been changed to take account of this assignment. c Average of (d,p) results of refs. 16 and 17 (Ed = 15 MeV, resp. 7.8 MeV) after normalization to sum rule expectations; C2 here refers to (d,n) and (3He,d) reactions.
s4Fe Id, n)”
Co
T< States
1s
States
5 2.160 2
3/2-
-
E
z
v
\
4.732 E
\
z.557 i/2-
3/2-
5.170 1
1/2-
\
en
658
-
40
sults of a non-local finite-range reanalysis of their data. The absolute spectroscopic factors have changed rather drastically, although the strength ratios for transitions of the same Jr are essentially unaltered. Thus a more reliable comparison between the different results can be made for the ratios (2Jt 1)C2S>/2J+ 1)C2S, between T, and T< states of the same Jr. In table2 we present such ratios for states in 55Co. As is clear from table 2, the (3He,d) and (d,n) results agree at least as well as the different (3He, d) results within themselves, and all dif ferences are within the usual 20% errors in spectroscopic factors extracted from DWBA analyses. Thus the possible (d,n), (3He,d) discrepancy is not supported by our data. In table 2 we have also included additional evidence supporting our conclusions. This includes relative spectroscopic factors for sgCu states obtained from (d, n) experiments [4] and (3He,d) experiments [ 12,131, and for %a states obtained from (d, n) experiments [ 141 and (3He,d) experiments [ 151. It appears, quite convincingly, that at least for odd-even and eveneven nuclei in table 2, with A > 40, there is no significant discrepancy between (d, n) and (3He, d) spectroscopic strengths for T> states.
Fig. 1. Angular distributions of three typical T< states and the three T, states observed in this experiment. The curves are predictions of non-local finite-range 60 8c.u. (deg.1 DWBA calculations.
Volume 29B. number 10
PHYSICS
Ratios of spectroscopic
LETTERS
18 August 1969
Table 2 strengths for T< and T, states of same Z(J’).
I Nucleus
55co
59CU
40Ca
* Unbound state. a This experiment.
T< state
T, state
1(Jr)
OLlev)
OLleV)
l$)
2.160
4.135
I(;-)
2.557
5.170 *
3(q-)
3.300
5.743 *
I(;-)
0
C2S>/C2S<
,
(d, n)
(3He, d)
(3HeI 4
0.64 a
0.55b
0.63 ’
0.34a
0.46 b
0.52
0.59 a
0.62 b
0.50 c
0.24 d
0.29 e
0.19 f
I(%_)
0.486
4.355 *
o.26d
0.29 e
0.38 f
3(;-)
0.909
4.301 *
0.55 d
0.44 e
0.43 f
3.895
*
3(3_)
3.738
7.696
3(4_)
5.606
7.655
3(5_)
4.480
8.553 *
b Ref. 9. ’ Refs. 10, 11.
I
d Ref. 4. e Ref. :12.
Perhaps the discrepancy that Siemssen et al. [1] have pointed out only exists for odd-odd nuclei or only for light nuclei.
1.86 g
1.62 h
0.65 g
0.78 h
1.05 g
1.19 h f Ref. 13. g Ref. 14
h Ref. 15.
8. B. J. O’Brien, W. E. Dorenbusch, T. A, Belote and J. Rapaport, Nucl. Phys. A104 (1967) 609. 9. B. Rosner and C. H. Holbrow, Phys. Rev. 154 (1967) 1080; ~7.8~rvopou1os et al.. Phys. Rev. 177 (1969)
The authors wish to thank Dr. A. G. Blair for putting their original data at our disposal and Professor T. Tamura for communicating his latest results prior to publication.
References 1. R. H. Siemssen, G. C. Morrison, B. Zeidman and H. Fuchs, Phys. Rev. Letters 16 (1966) 1050. 2. T. Tamura, Phys. Rev. Letters 19 (1967) 321. 3. R. Coker and T. Tamura, to be published. 4. A. Marusak, Ph. D. dissertation, University of Tennessee, 1969, Oak Ridge National Laboratory Report, ORNL-TM-2472, to be published. 5. R. G, Couch, Ph. D. dissertation. Northwestern University, 1969, to be published. 6. C. Perey and F. Perey, Phys. Rev. 132 (1963) 755. 7. F. D. Becchetti and G. W. Greenlees, to be published.
13. 14. 15. 16. 17.
D. D.‘Armstrong and A. G. Blair, Phys. Rev. 140 (1965) B1226. A. G. ‘Blair and D. D. Armstrong, Phys. Letters 16 (1965) 57. G. C. Morrison and J. P. Schiffer. in: Isobaric spin in nuclear physics, eds. J. D. Fox and D. Robson (Academic Press, New York. 1966) p. 748, D. J. Pullen and B. Rosner, Phys. Rev. 170 (1968) 1034. H. Fuchs, K. Grabisch and G. Roschert, Nucl. Phys. Al29 (1969) 545. K. K. Seth, J. A. Biggerstaff, P. D. Miller and G. R. Satchler, Phys. Rev. 164 (1967) 1450. R. H. Fulmer and A. L. McCarthy. Phys. Rev. 131 (1963) 2133. J. R. Maxwell and W. C. Parkinson. Phys. Rev. 135 (1964) B82.
*****
659