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The low-energy 3He(d, p)4He and 3H(d, n)4He reactions with polarized deuterons
Volume 238, number 2,3.4
PHYSICS LETTERS B
5 April 1990
THE LOW-ENERGY 3He(d, p)4He AND 3H(d, n)4He REACTIONS WITH P O L A R I Z E D DEUTERONS G. BLUGE, K. LANGANKE, M. PLAGGE lnstitut fiir Theoretische Physik L Universitiit Miinster, D-4400 Miinster, FRG
K.R. NYGA and H. PAETZ gen. SCHIECK lnstitut J~r Kernphysik, Universitdt KOln, D-5000 Cologne, FRG Received 14 November 1989; revised manuscript received 25 January 1990
In a data-independent approach we have studied the 3He(d, p)4He and 3H(d, n)4He reactions at low energies within the multichannel resonating group model. In agreement with the data of Leemann et al. we find that the 3He(d, p)4He cross sections are not purely determined by the 3+ resonance at E ~ b = 4 3 0 keV, but have also contributions from other partial waves. These contributions are noticeably smaller for the 3H (d, n)4He reaction.
At low energies the 3He(d, p)4He and 3H(d, n)4He reactions are dominated by j n = 3 + resonances which are mainly formed by a d + 3 H e ( d + 3 H ) configuration with a relative orbital angular momentum L = 0 and with a total spin S = 3. Thus, in the vicinity of these resonances the unpolarized angular distributions are nearly isotropic. On the other hand, the 3He(d, p)4He and 3H(d, n)4He angular distributions measured with tensor-polarized deuterons show a strong angular dependence while a vector polarization of the deuterons has practically no influence on the angular distributions. These properties make the l o w - e n e r g y 3He ( d , p )4He and 3H (d, n )4He reactions a generally accepted way of measuring the tensor polarization of a deuteron beam. For a precise use of these reactions as analyzers for tensor-polarized deuterons, possible contributions from partial waves other than the resonant one have to be known. Mclntyre and Haeberli [1] observed that the 0 °-90 ° proton anisotropy, measured by using polarized deuterons with an orientation axis parallel to the line of flight, does not remain constant in the energy regime EL,b ~<1.5 MeV. They explained this fact by contributions from the J " = ½+ partial wave suggesting the existence of a resonant state in this channel at about Ecru~ 1.6 MeV. From a high-preci-
sion measurement of the 3He (d, p )4He cross sections with polarized deuterons on top of the j = 3 resonance at Et~b = 430 keV, Leemann et al. [ 2 ] were able to deduce a small, but non-vanishing vector analyzing power which indicates the existence of contributions from d + 3He partial waves with L > 0. To our knowledge a data-independent theoretical explanation and understanding of the low-energy --* p)4He and 3H(d, n)4He cross sections is still 3He(d, missing. Although the individual p+c~ ( n + a ) and d + 3 H e ( d + 3 H ) systems have been successfully investigated within the microscopic resonating group method (RGM) [3,4], a similar study of the lowenergy 3He(d, p)4He and 3H(d, n)4He reactions is strongly complicated by the fact that the j = 3 resonance formed in the d+3He ( d + 3 H ) channels with spin S = 3 can only couple to the outgoing channel ( S = ½) via the tensor part in the nucleon-nucleon (NN) interaction. Very recently the low-energy 3He (d, p ) 4He cross sections have been excellently reproduced within a multichannel RGM calculation based on various p + c~and d + 3He configurations and on a NN interaction containing a central, a spin-orbit and a tensor component [ 5 ]. In the present paper we report about an extension of this RGM calculation to the study of the low-energy 3He (d, p)4He and
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3H(d, n)4He cross sections for tensor-polarized deuterons. In our study, the model space was spanned by p + a ( n + a ) and d+3He (d+3H) configurations as well as by d*+3He (d*+3H) pseudo-states in the sense of ref. [6 ]. Thus, the many-body wave function ~J with total angular momentum J and parity rc has been chosen to be ~j=.~,{(
~=,/: .=+ [0~~ = o ON ]s=l/:YL(r~))ag~L(r~)}
3
+ ~ .~¢{(r,~l=la,,=,/=l~=+ ted,/ "~3 Is=,/2YL(fd))jhijL(rd)} i=1 3
+ EE..~{([OL,..,,,=,,,~,,=+ ,.,- ,~.., ~'3 ss=312 , L ' t , a J ) a f i a L ' ( r a ) } . i=lL'
(1) Here, 0,, 03 and 0o,~ describe the internal degrees of freedom of the a-particle, the 3He (3H) nucleus, the deuteron ground state ( i = 1 ) as well as of the deuteron pseudo-states ( i = 2,3). Note that these pseudostates do not correspond to realistic deuteron states. They might simply be understood a a tractable way of generating additional basis wave functions in the microscopic cluster model space which then allow for a possible distortion of the deuteron in the presence of other nucleons. For the explicit form of the cluster wave functions we closely followed refs. [ 4-6 ]. Thus, the 3He (3H) and the 4He fragments are described by a single gaussian, while the deuteron cluster as well as the deuteron pseudo-states are described by a superposition of three gaussians. The parameters of these wave functions are determined individually for each cluster in order to reasonably reproduce its binding energy and RMS radius. All parameters used presently can be found in refs. [ 5,6 ]. 0N is the spin-isospin function of the proton and neutron, respectively. The internal spins of the fragments I are coupled to the channel spins S, which can take the value S = ½for the p + a ( n + a ) system, while it can be S = 3, ½for the d + 3He ( d + 3 H ) system. The relative orbital angular momentum between the fragments L and the channel spin S are coupled to the total angular momentum J. Considering that all fragment wave functions have positive parity, the total parity of the many-body wave function is determined by the parity of the relative wave function. Our many-body hamiltonian H reads as follows: 138
5 April 1990
~p2 H=-
s
~m + E l= [
V0-Tcm'
(2)
l'~'J = |
where Tom is the kinetic-energy operator of the center-of-mass motion. For our NN interaction Vu we used the Wildermuth-Tang (WT) force [7] as the central component, while we adopted the spin-orbit and the tensor parts from refs. [ 3,8 ], respectively. In applications using the WT interaction the exchange mixture parameter u is customarily adjusted to selected experimental data. In the present case we determined u by reproducing the resonance energy of the 3+ state in the 3He(d, p)4He (3H(d, n)4He) channel. In refs. [ 5,9 ] it is demonstrated that by setting u=0.835 ( u = 0 . 8 3 ) the properties of this resonance as well as the 3He(d, p)aHe (3H(d, n)4He) cross sections at Ecm~< 1 MeV are well reproduced. Simultaneously, these calculations were able to describe the 5Li (SHe) ground states as well as the very broad first excited ½- states in these nuclei. The present value for u is somewhat smaller than the ones used in previous studies of the 5-nucleon system (see e.g. refs. [4,6 ] ). However, none of these calculations has considered the effects of the tensor force which, as discussed above, allows for the coupling of the 3+ resonance to the a-channel and results in a small, but nevertheless important shift of the resonance energy (see the detailed discussion given in ref. [5 ] ). Following the standard procedure [ 10], the unknown relative wave functions g, h and f a r e determined by solving the many-body Schr6dinger equation in the space spanned by the internal d+3He (d + 3H ) and p + a (n + ~ ) basis wave functions. This leads to the well-known RGM set of coupled integrodifferential equations [ 10 ] which we have solved by a discretization method [ 5 ]. Having determined the multichannel reaction matrix, the various tensor moments TQK have been calculated using the computer code Fatson/Tufx [ 11 ]. This code follows the theoretical treatment ofWelton [ 12 ] and its extension to charged-particle reactions by Heiss [13]. The Madison convention has been adopted for the definition of the tensor moments. Partial waves up to J=-~ have been considered. At first we want to discuss our results for the 3 He(d, p)4He reaction on top of the j ~ = 3 + resonance at ELab=430 keV which has been extensively studied by Leemann et al. [2]. In fig. 1 we compare
Volume 238, number 2,3.4 ,
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PHYSICS LETTERS B l 'oo
040
'
,
,
0 40 0 20
010
0
-020 -050
-0 20
-080
-040
-010
-0005
-0 20
-0010
-030
-0015
-0.40
-0020
0
120
160
8'0
I
i
12o 16o
Fig. 1. Comparison of the calculated analyzing powers for the 3He(d, p)4He reaction at EL~b=430 keV with the experimental data of ref. [2]. the calculated analyzing powers TQ~with those deduced from the experimental 3He(d, p)4He cross sections. The agreement for the tensor moments T2K is excellent, except for small deviations in the T21 m o m e n t near the m a x i m u m and minimum. However, this overall agreement should not be overinterpreted, as it is mainly caused by the fact that at this energy the tensor analysing powers are strongly dominated by the contribution from the J n =~3 + resonance. On the other hand, the calculated TzK moments show the same 90 ° asymmetry as the experimental data indicating the presence of contributions from partial waves other than the resonant one. In particular, we calculate T2o(O°)= - 0 . 6 7 9 . This is larger by about 5% than the value one expects for the pure resonant case, T2o(0 ° ) = - 0.707. By inspecting the various contributions to the calculated tensor moments, we find that the observed deviations from the pure resonant case are mainly due to interferences with the d + 3 H e partial waves with quantum numbers (J, L ) = (½, 0), (½, 1) and (5, 1) and spin S-- ½. At ELa b = 430 keV the vector analysing power i T~j is rather small. As can be seen in fig. 1, our calculation reproduces the general trend o f the iT~ angular dependence, however, it misses its magnitude by
5 April 1990
about a factor of 2 at angles around 120 °. The fact that iT~ does not vanish indicates that partial waves with L > 0 contribute. In our calculation, the main contribution comes from the 2p3/2 partial wave, though those arising from the 2p~/2 partial wave and from various d-waves cannot be neglected. To understand the differences in the calculated and experimentally deduced vector analyzing powers, we have compared our calculated d + 3 H e phase shifts with those obtained by an R-matrix analysis of experimental data [14]. We find that most of the phase shifts agree reasonably well at low energies with the exception o f the 2p3/2 partial wave. Here, the R-matrix results show a continuous rise up to a phase shift value of more than 30 ° at ELab----5 MeV, while our calculated phase shifts rise to slightly more than 10 ° in this energy regime. Thus, we believe that the deviations between the theoretical and experimental analyzing powers shown in fig. 1 might be caused by a theoretical underestimation o f the attractiveness in the 2p3/2 partial wave. In agreement with the previous microscopic calculations of the 5Li nucleus, our calculation does not exhibit a J " = ½+ resonance as suggested by Mclntyre and Haeberli and tentatively listed in the compilation of ref. [ 15 ]. To test this statement, we compare in fig. 2 the calculated tensor moments 7"20(0 ° ) with the values experimentally deduced by Grtibler et al. [ 16,17]. the agreement is good up to energies o f ELab= 7 MeV. This justifies some confidence into our calculated S-matrix in the 2S1/2 partial wave as this partial wave contributes noticeably to the 7'2otensor moment. Thus, we conclude that there is most likely no J ~ = ½+ resonance in the d + 3He system at energies below Ecm = 5 MeV. Note that this finding is in agreement with various p + ct and d + 3He phase shift analyses [ 14,18,1 9 ]. The slight deviations between the theoretical and experimental 7"2o(0 ° ) moments at the higher energies might be due to partial waves with J > ~ not considered in our study for numerical reasons. Finally we have calculated the analyzing powers for the 3 H(d, n)4He reaction on top of the j = 3 resonance at Eeab= 107 keV. The results are shown in fig. -~ 3. Compared with the results for the 3 He(d, p)4He reaction, one clearly observes that the vector analyzing power iT~ as well as the 90 ° asymmetry of the calculated T2~ moments are smaller for the 3H(d, 139
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PHYSICS LETTERS B
5 April 1990
-0t, -O6~ -0.8
6"" o w
-1 0
++ -l.g
l 1
I 2
I 3
I /.
I 5
¢,
¢4l 6
l 7
Ea [HEY]
Fig. 2. Comparison of the calculated analyzing powers T2oat 0 ° for the 3He (d, p )4He reaction with the experimental data of refs. [ 16,17 ].
0 ~.0
]-2O
0 40
010
0 20
-020
0
-050
-020
-080
-OA.O
-010
-0001
-020
-0,002
-0.30
-0.003 -0.00~.
-0~.0
T22 ~0
BO
i 120
i 160
i Tn L
|
i
~0
80
120
i
160
Fig. 3. The calculated analyzing powers for the 3H(d, n)4He reaction at El~b-=107 keV. n)4He than for the 3He(d, p)4He reaction. At 0 r we find 7"2o= - 0 . 7 0 4 in rather close agreement with the value for a purely resonant reaction. O u r results show that the contributions from partial waves other than the resonant one are small and less i m p o r t a n t for the 3H(d, n)4He than for the 3He(d, p)4He reaction. We therefore conclude that the 3H(d, n)4He reaction in 140
the vicinity o f the j . = 3 + resonance is a good analyzer for tensor-polarized deuterons. We like to m e n t i o n that we have repeated our calculation using the H a s e g a w a - N a g a t a force [20] as central part in our N N interaction rather than the W T force. If some parameters of the N N interaction are slightly m o d i f i e d (these are the strengths o f one o f the c o m p o n e n t s in the tensor force and in the s p i n orbit force as well as the m - p a r a m e t e r o f the gaussian in the H a s e g a w a - N a g a t a force with m e d i u m range [5,9]; the latter is set to m = 0 . 4 1 which is not too different from the value used in order to reproduce the properties o f the 7Li ground state, m = 0 . 3 9 7 [21 ] ), the H a s e g a w a - N a g a t a force is also able to reproduce the 3He(d, p)4He and 3H(d, n)4He cross sections at low energies very well. The calculated 3He(d, p)4He and 3H(d, n)4He analyzing powers are very similar to those obtained with the W T force. In particular: ( i ) there is no resonance in the tial wave, (ii) for the H e ( d , p)4He reaction at Etch= 430 keV the experimental iTI~ values at around 120 ° are u n d e r e s t i m a t e d by about a factor of 2, and ( i i i ) the calculated 2p3/2 phase shifts are too small c o m p a r e d with the experimental data [14]. Thus, these calculations lead us to the same conclusions as given above.
3
2Sl/2par-
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PHYSICS LETTERS B
References [ 1 ] L.C. Mclntyre and W. Haeberli, Nucl. Phys. A 91 (1967) 369. [2] Ch. Leemann, H. Biirgisser, P. Huber, U. Rohrer, H. Paetz gen. Schieck and F. Seiler, Helv. Phys. Acta 44 ( 1971 ) 141. [3] I. Reicbstein and Y.C. Tang, Nucl. Phys. A 158 (1970) 529. [4] F.S. Chwieroth, Y.C. Tang and D.R. Thompson, Phys. Rev. C 9 (1974) 56. [ 5 ] G. Bliige and K. Langanke, submitted to Phys. Rev. C. [6] P.N. Shen, Y.C. Tang, Y. Fujiwara and H. Kanada, Phys. Rev. C 31 (1985) 2001. [7]F.S. Chwieroth, R.E. Brown, Y.C. Tang and D.R. Thompson, Phys. Rev. C 8 (1973) 938. [8] P. Heiss and H.H. Hackenbroich, Phys. Lett. B 30 (1969) 373. [9] G. Blfige and K. Langanke, to be published. [10] K. Wildermuth and Y.C. Tang, A unified theory of the nucleus (Vieweg, Braunschweig, 1977 ). [ 11 ] F. Seiler, Comput. Phys. Commun. 6 ( 1973 ) 229; H. Aulenkamp, Diplomarbeit, Universit~it K61n (1973), unpublished.
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[ 12] T.A. Welton, Fast neutron physics, part lI, eds. J.B. Marion and J.L. Fowler (Interscience, New York, 1963 ) p. 1317. [ 13 ] P. Heiss, Z. Phys. 251 (1972) 159. [ 14 ] B. Jenny, W. Grfibler, P.A. Scbmelzbach, V. K6nig and H.R. Biirgi, Nucl. Phys. A 337 (1980) 77. [ 15 ] F. Ajzenberg-Selove, Nucl. Phys. A 490 (1988) I. [16]W. Griibler, V. K6nig, A. Ruh, R.E. White, P.A. Schmelzbach, R. Risler and P. Marmier, Nucl. Phys. A 165 (1971) 505. [ 17 ] P.A. Schmelzbach, W. Grfibler, V. K6nig, R. Risler, D.O. Boerma and B. Jenny, Nucl. Phys. A 264 (1976) 45. [ 18 ] G.R. Plattner, A.D. Bacher and H.E. Conzett, Phys. Rev. C 5 ( 1972 ) 1158; Nucl. Phys. A 337 (1980) 77. [ 19] A. Houdayer, N.E. Davison, S.A. Elbakr, A.M. Sourkes, W.T.H. van Oers and A.D. Bacher, Phys. Rev. C 18 ( 1978 ) 1985. [20] H. Furutani, H. Kanada, T. Kaneko and S. Nagata, Prog. Theor. Phys. Suppl. 68 (1980) 215. [21 ] T. Kajino, Nucl. Phys. A460 (1986) 559.
141
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5 April 1990
THE LOW-ENERGY 3He(d, p)4He AND 3H(d, n)4He REACTIONS WITH P O L A R I Z E D DEUTERONS G. BLUGE, K. LANGANKE, M. PLAGGE lnstitut fiir Theoretische Physik L Universitiit Miinster, D-4400 Miinster, FRG
K.R. NYGA and H. PAETZ gen. SCHIECK lnstitut J~r Kernphysik, Universitdt KOln, D-5000 Cologne, FRG Received 14 November 1989; revised manuscript received 25 January 1990
In a data-independent approach we have studied the 3He(d, p)4He and 3H(d, n)4He reactions at low energies within the multichannel resonating group model. In agreement with the data of Leemann et al. we find that the 3He(d, p)4He cross sections are not purely determined by the 3+ resonance at E ~ b = 4 3 0 keV, but have also contributions from other partial waves. These contributions are noticeably smaller for the 3H (d, n)4He reaction.
At low energies the 3He(d, p)4He and 3H(d, n)4He reactions are dominated by j n = 3 + resonances which are mainly formed by a d + 3 H e ( d + 3 H ) configuration with a relative orbital angular momentum L = 0 and with a total spin S = 3. Thus, in the vicinity of these resonances the unpolarized angular distributions are nearly isotropic. On the other hand, the 3He(d, p)4He and 3H(d, n)4He angular distributions measured with tensor-polarized deuterons show a strong angular dependence while a vector polarization of the deuterons has practically no influence on the angular distributions. These properties make the l o w - e n e r g y 3He ( d , p )4He and 3H (d, n )4He reactions a generally accepted way of measuring the tensor polarization of a deuteron beam. For a precise use of these reactions as analyzers for tensor-polarized deuterons, possible contributions from partial waves other than the resonant one have to be known. Mclntyre and Haeberli [1] observed that the 0 °-90 ° proton anisotropy, measured by using polarized deuterons with an orientation axis parallel to the line of flight, does not remain constant in the energy regime EL,b ~<1.5 MeV. They explained this fact by contributions from the J " = ½+ partial wave suggesting the existence of a resonant state in this channel at about Ecru~ 1.6 MeV. From a high-preci-
sion measurement of the 3He (d, p )4He cross sections with polarized deuterons on top of the j = 3 resonance at Et~b = 430 keV, Leemann et al. [ 2 ] were able to deduce a small, but non-vanishing vector analyzing power which indicates the existence of contributions from d + 3He partial waves with L > 0. To our knowledge a data-independent theoretical explanation and understanding of the low-energy --* p)4He and 3H(d, n)4He cross sections is still 3He(d, missing. Although the individual p+c~ ( n + a ) and d + 3 H e ( d + 3 H ) systems have been successfully investigated within the microscopic resonating group method (RGM) [3,4], a similar study of the lowenergy 3He(d, p)4He and 3H(d, n)4He reactions is strongly complicated by the fact that the j = 3 resonance formed in the d+3He ( d + 3 H ) channels with spin S = 3 can only couple to the outgoing channel ( S = ½) via the tensor part in the nucleon-nucleon (NN) interaction. Very recently the low-energy 3He (d, p ) 4He cross sections have been excellently reproduced within a multichannel RGM calculation based on various p + c~and d + 3He configurations and on a NN interaction containing a central, a spin-orbit and a tensor component [ 5 ]. In the present paper we report about an extension of this RGM calculation to the study of the low-energy 3He (d, p)4He and
0370-2693/90/$ 03.50 © Elsevier Science Publishers B.V. ( North-Holland )
137
Volume 238, number 2,3.4
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3H(d, n)4He cross sections for tensor-polarized deuterons. In our study, the model space was spanned by p + a ( n + a ) and d+3He (d+3H) configurations as well as by d*+3He (d*+3H) pseudo-states in the sense of ref. [6 ]. Thus, the many-body wave function ~J with total angular momentum J and parity rc has been chosen to be ~j=.~,{(
~=,/: .=+ [0~~ = o ON ]s=l/:YL(r~))ag~L(r~)}
3
+ ~ .~¢{(r,~l=la,,=,/=l~=+ ted,/ "~3 Is=,/2YL(fd))jhijL(rd)} i=1 3
+ EE..~{([OL,..,,,=,,,~,,=+ ,.,- ,~.., ~'3 ss=312 , L ' t , a J ) a f i a L ' ( r a ) } . i=lL'
(1) Here, 0,, 03 and 0o,~ describe the internal degrees of freedom of the a-particle, the 3He (3H) nucleus, the deuteron ground state ( i = 1 ) as well as of the deuteron pseudo-states ( i = 2,3). Note that these pseudostates do not correspond to realistic deuteron states. They might simply be understood a a tractable way of generating additional basis wave functions in the microscopic cluster model space which then allow for a possible distortion of the deuteron in the presence of other nucleons. For the explicit form of the cluster wave functions we closely followed refs. [ 4-6 ]. Thus, the 3He (3H) and the 4He fragments are described by a single gaussian, while the deuteron cluster as well as the deuteron pseudo-states are described by a superposition of three gaussians. The parameters of these wave functions are determined individually for each cluster in order to reasonably reproduce its binding energy and RMS radius. All parameters used presently can be found in refs. [ 5,6 ]. 0N is the spin-isospin function of the proton and neutron, respectively. The internal spins of the fragments I are coupled to the channel spins S, which can take the value S = ½for the p + a ( n + a ) system, while it can be S = 3, ½for the d + 3He ( d + 3 H ) system. The relative orbital angular momentum between the fragments L and the channel spin S are coupled to the total angular momentum J. Considering that all fragment wave functions have positive parity, the total parity of the many-body wave function is determined by the parity of the relative wave function. Our many-body hamiltonian H reads as follows: 138
5 April 1990
~p2 H=-
s
~m + E l= [
V0-Tcm'
(2)
l'~'J = |
where Tom is the kinetic-energy operator of the center-of-mass motion. For our NN interaction Vu we used the Wildermuth-Tang (WT) force [7] as the central component, while we adopted the spin-orbit and the tensor parts from refs. [ 3,8 ], respectively. In applications using the WT interaction the exchange mixture parameter u is customarily adjusted to selected experimental data. In the present case we determined u by reproducing the resonance energy of the 3+ state in the 3He(d, p)4He (3H(d, n)4He) channel. In refs. [ 5,9 ] it is demonstrated that by setting u=0.835 ( u = 0 . 8 3 ) the properties of this resonance as well as the 3He(d, p)aHe (3H(d, n)4He) cross sections at Ecm~< 1 MeV are well reproduced. Simultaneously, these calculations were able to describe the 5Li (SHe) ground states as well as the very broad first excited ½- states in these nuclei. The present value for u is somewhat smaller than the ones used in previous studies of the 5-nucleon system (see e.g. refs. [4,6 ] ). However, none of these calculations has considered the effects of the tensor force which, as discussed above, allows for the coupling of the 3+ resonance to the a-channel and results in a small, but nevertheless important shift of the resonance energy (see the detailed discussion given in ref. [5 ] ). Following the standard procedure [ 10], the unknown relative wave functions g, h and f a r e determined by solving the many-body Schr6dinger equation in the space spanned by the internal d+3He (d + 3H ) and p + a (n + ~ ) basis wave functions. This leads to the well-known RGM set of coupled integrodifferential equations [ 10 ] which we have solved by a discretization method [ 5 ]. Having determined the multichannel reaction matrix, the various tensor moments TQK have been calculated using the computer code Fatson/Tufx [ 11 ]. This code follows the theoretical treatment ofWelton [ 12 ] and its extension to charged-particle reactions by Heiss [13]. The Madison convention has been adopted for the definition of the tensor moments. Partial waves up to J=-~ have been considered. At first we want to discuss our results for the 3 He(d, p)4He reaction on top of the j ~ = 3 + resonance at ELab=430 keV which has been extensively studied by Leemann et al. [2]. In fig. 1 we compare
Volume 238, number 2,3.4 ,
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PHYSICS LETTERS B l 'oo
040
'
,
,
0 40 0 20
010
0
-020 -050
-0 20
-080
-040
-010
-0005
-0 20
-0010
-030
-0015
-0.40
-0020
0
120
160
8'0
I
i
12o 16o
Fig. 1. Comparison of the calculated analyzing powers for the 3He(d, p)4He reaction at EL~b=430 keV with the experimental data of ref. [2]. the calculated analyzing powers TQ~with those deduced from the experimental 3He(d, p)4He cross sections. The agreement for the tensor moments T2K is excellent, except for small deviations in the T21 m o m e n t near the m a x i m u m and minimum. However, this overall agreement should not be overinterpreted, as it is mainly caused by the fact that at this energy the tensor analysing powers are strongly dominated by the contribution from the J n =~3 + resonance. On the other hand, the calculated TzK moments show the same 90 ° asymmetry as the experimental data indicating the presence of contributions from partial waves other than the resonant one. In particular, we calculate T2o(O°)= - 0 . 6 7 9 . This is larger by about 5% than the value one expects for the pure resonant case, T2o(0 ° ) = - 0.707. By inspecting the various contributions to the calculated tensor moments, we find that the observed deviations from the pure resonant case are mainly due to interferences with the d + 3 H e partial waves with quantum numbers (J, L ) = (½, 0), (½, 1) and (5, 1) and spin S-- ½. At ELa b = 430 keV the vector analysing power i T~j is rather small. As can be seen in fig. 1, our calculation reproduces the general trend o f the iT~ angular dependence, however, it misses its magnitude by
5 April 1990
about a factor of 2 at angles around 120 °. The fact that iT~ does not vanish indicates that partial waves with L > 0 contribute. In our calculation, the main contribution comes from the 2p3/2 partial wave, though those arising from the 2p~/2 partial wave and from various d-waves cannot be neglected. To understand the differences in the calculated and experimentally deduced vector analyzing powers, we have compared our calculated d + 3 H e phase shifts with those obtained by an R-matrix analysis of experimental data [14]. We find that most of the phase shifts agree reasonably well at low energies with the exception o f the 2p3/2 partial wave. Here, the R-matrix results show a continuous rise up to a phase shift value of more than 30 ° at ELab----5 MeV, while our calculated phase shifts rise to slightly more than 10 ° in this energy regime. Thus, we believe that the deviations between the theoretical and experimental analyzing powers shown in fig. 1 might be caused by a theoretical underestimation o f the attractiveness in the 2p3/2 partial wave. In agreement with the previous microscopic calculations of the 5Li nucleus, our calculation does not exhibit a J " = ½+ resonance as suggested by Mclntyre and Haeberli and tentatively listed in the compilation of ref. [ 15 ]. To test this statement, we compare in fig. 2 the calculated tensor moments 7"20(0 ° ) with the values experimentally deduced by Grtibler et al. [ 16,17]. the agreement is good up to energies o f ELab= 7 MeV. This justifies some confidence into our calculated S-matrix in the 2S1/2 partial wave as this partial wave contributes noticeably to the 7'2otensor moment. Thus, we conclude that there is most likely no J ~ = ½+ resonance in the d + 3He system at energies below Ecm = 5 MeV. Note that this finding is in agreement with various p + ct and d + 3He phase shift analyses [ 14,18,1 9 ]. The slight deviations between the theoretical and experimental 7"2o(0 ° ) moments at the higher energies might be due to partial waves with J > ~ not considered in our study for numerical reasons. Finally we have calculated the analyzing powers for the 3 H(d, n)4He reaction on top of the j = 3 resonance at Eeab= 107 keV. The results are shown in fig. -~ 3. Compared with the results for the 3 He(d, p)4He reaction, one clearly observes that the vector analyzing power iT~ as well as the 90 ° asymmetry of the calculated T2~ moments are smaller for the 3H(d, 139
Volume 238, number 2,3.4
PHYSICS LETTERS B
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-0t, -O6~ -0.8
6"" o w
-1 0
++ -l.g
l 1
I 2
I 3
I /.
I 5
¢,
¢4l 6
l 7
Ea [HEY]
Fig. 2. Comparison of the calculated analyzing powers T2oat 0 ° for the 3He (d, p )4He reaction with the experimental data of refs. [ 16,17 ].
0 ~.0
]-2O
0 40
010
0 20
-020
0
-050
-020
-080
-OA.O
-010
-0001
-020
-0,002
-0.30
-0.003 -0.00~.
-0~.0
T22 ~0
BO
i 120
i 160
i Tn L
|
i
~0
80
120
i
160
Fig. 3. The calculated analyzing powers for the 3H(d, n)4He reaction at El~b-=107 keV. n)4He than for the 3He(d, p)4He reaction. At 0 r we find 7"2o= - 0 . 7 0 4 in rather close agreement with the value for a purely resonant reaction. O u r results show that the contributions from partial waves other than the resonant one are small and less i m p o r t a n t for the 3H(d, n)4He than for the 3He(d, p)4He reaction. We therefore conclude that the 3H(d, n)4He reaction in 140
the vicinity o f the j . = 3 + resonance is a good analyzer for tensor-polarized deuterons. We like to m e n t i o n that we have repeated our calculation using the H a s e g a w a - N a g a t a force [20] as central part in our N N interaction rather than the W T force. If some parameters of the N N interaction are slightly m o d i f i e d (these are the strengths o f one o f the c o m p o n e n t s in the tensor force and in the s p i n orbit force as well as the m - p a r a m e t e r o f the gaussian in the H a s e g a w a - N a g a t a force with m e d i u m range [5,9]; the latter is set to m = 0 . 4 1 which is not too different from the value used in order to reproduce the properties o f the 7Li ground state, m = 0 . 3 9 7 [21 ] ), the H a s e g a w a - N a g a t a force is also able to reproduce the 3He(d, p)4He and 3H(d, n)4He cross sections at low energies very well. The calculated 3He(d, p)4He and 3H(d, n)4He analyzing powers are very similar to those obtained with the W T force. In particular: ( i ) there is no resonance in the tial wave, (ii) for the H e ( d , p)4He reaction at Etch= 430 keV the experimental iTI~ values at around 120 ° are u n d e r e s t i m a t e d by about a factor of 2, and ( i i i ) the calculated 2p3/2 phase shifts are too small c o m p a r e d with the experimental data [14]. Thus, these calculations lead us to the same conclusions as given above.
3
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References [ 1 ] L.C. Mclntyre and W. Haeberli, Nucl. Phys. A 91 (1967) 369. [2] Ch. Leemann, H. Biirgisser, P. Huber, U. Rohrer, H. Paetz gen. Schieck and F. Seiler, Helv. Phys. Acta 44 ( 1971 ) 141. [3] I. Reicbstein and Y.C. Tang, Nucl. Phys. A 158 (1970) 529. [4] F.S. Chwieroth, Y.C. Tang and D.R. Thompson, Phys. Rev. C 9 (1974) 56. [ 5 ] G. Bliige and K. Langanke, submitted to Phys. Rev. C. [6] P.N. Shen, Y.C. Tang, Y. Fujiwara and H. Kanada, Phys. Rev. C 31 (1985) 2001. [7]F.S. Chwieroth, R.E. Brown, Y.C. Tang and D.R. Thompson, Phys. Rev. C 8 (1973) 938. [8] P. Heiss and H.H. Hackenbroich, Phys. Lett. B 30 (1969) 373. [9] G. Blfige and K. Langanke, to be published. [10] K. Wildermuth and Y.C. Tang, A unified theory of the nucleus (Vieweg, Braunschweig, 1977 ). [ 11 ] F. Seiler, Comput. Phys. Commun. 6 ( 1973 ) 229; H. Aulenkamp, Diplomarbeit, Universit~it K61n (1973), unpublished.
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[ 12] T.A. Welton, Fast neutron physics, part lI, eds. J.B. Marion and J.L. Fowler (Interscience, New York, 1963 ) p. 1317. [ 13 ] P. Heiss, Z. Phys. 251 (1972) 159. [ 14 ] B. Jenny, W. Grfibler, P.A. Scbmelzbach, V. K6nig and H.R. Biirgi, Nucl. Phys. A 337 (1980) 77. [ 15 ] F. Ajzenberg-Selove, Nucl. Phys. A 490 (1988) I. [16]W. Griibler, V. K6nig, A. Ruh, R.E. White, P.A. Schmelzbach, R. Risler and P. Marmier, Nucl. Phys. A 165 (1971) 505. [ 17 ] P.A. Schmelzbach, W. Grfibler, V. K6nig, R. Risler, D.O. Boerma and B. Jenny, Nucl. Phys. A 264 (1976) 45. [ 18 ] G.R. Plattner, A.D. Bacher and H.E. Conzett, Phys. Rev. C 5 ( 1972 ) 1158; Nucl. Phys. A 337 (1980) 77. [ 19] A. Houdayer, N.E. Davison, S.A. Elbakr, A.M. Sourkes, W.T.H. van Oers and A.D. Bacher, Phys. Rev. C 18 ( 1978 ) 1985. [20] H. Furutani, H. Kanada, T. Kaneko and S. Nagata, Prog. Theor. Phys. Suppl. 68 (1980) 215. [21 ] T. Kajino, Nucl. Phys. A460 (1986) 559.
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