The polarization of protons from the 2H(d, p )3H reaction for deuteron energies below 1 MeV

The polarization of protons from the 2H(d, p )3H reaction for deuteron energies below 1 MeV

Nuclear Physics QNorth-Holland A442 (1985) 17-25 Publishing Company THE POLARIZATION OF PROTONS FROM THE 2H(d,$)3H REACTION FOR DEUTERON ENERGIES BE...

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Nuclear Physics QNorth-Holland

A442 (1985) 17-25 Publishing Company


and P. Bl?M

Institute of Nuclear Physics, 250 68 kei near Prague, Czechoslovakia Received 19 December 1984 (Revised 19 March 1985) Abstract: The angular distribution of proton polarization PJ”(O) from the 2H(d,p)3H reaction has been measured at 975 keV deuteron energy. Moreover, the energy dependence of PY’( Ed) was measured at 45”(lab) for deuteron energies between 250 and 975 keV. The values of ec (0) PY’( 0) were fitted in terms of an associated Legendre polynomial expansion. The measured energy dependence of P.“( Ed) has been analyzed in terms of barrier-penetration parameters.


NUCLEAR REACTION *H(d,p), E = 0.250 - 0.975 MeV; measured P( Ed, 0). Silicon polarimeter, deuterated polyethylene target.



1. Introduction In recent investigation

years a considerable of the 4He nucleus

experimental effort has structure in the excitation

been devoted energy range

to the around

the d f d threshold. In this energy region, a series of accurate cross-section data on the reactions 2H(d,n)3He and *H(~,P)~H with unpolarized and polarized deuterons have been published’). The polarization of outgoing neutrons has also been measured*). Adequately accurate data on the polarization of outgoing protons have been gained only above 1.5 MeV deuteron energy3). This results from methodical difficulties in the proton polarization measurements below 5 MeV. Individual data on proton polarization in the *H(d,lQ3H reaction below 1.5 MeV [ref. 4)] are presented with an insufficient accuracy for the theoretical analysis. In the present work we concentrate on proton polarization measurements in the 2H(d,j3)3H rea ction at energies from 0.25 to 1.0 MeV. In our experiment proton polarization was measured by using a silicon polarimeter. The experimental data were interpreted in terms of barrier-penetration factors in the incoming d + d channel. 2. Experimental procedure and data reduction The experimental set-up is schematically shown in fig. 1. The reaction was induced by a magnetically-analyzed deuteron beam from the Van de Graaff accelerator of 17

P. Kozma, P. Bkm / Polarization ofprotons


Fig. 1. Schematic


of an experimental set-up for the measurement 2H(d,‘j)3H reaction.

of proton


from the

the Nuclear Physics Institute in Rei. The target consisted of a deuterated-polyethylene (CD,),, foil of thickness 0.5 mg/cm-’ sandwiched between two gold layers5). The thickness and homogeneity of targets were determined with an accuracy of 0.01 mg/cm-‘. The mean reaction energy calculated from the energy loss of the deuterons on appropriate foils of a sandwich target was taken to be Ed0- $AE,, Ej being the energy of deuterons which passed the first gold foil of the target block and AE, the energy thickness of the (CD,). foil. For measurements covering the range of mean energies of 1200 to 300 keV the AE, thickness of the target ranged from 30 to 90 keV. The polarization silicon polarimeter

of protons from the *H(d,IQ3H reaction was measured by a described in detail elsewhere 6). Therefore only basic information

will be given here. The polarimeter consisted of two silicon detectors as a target (labelled by AE,,, in fig. 1) and two silicon detectors (labelled by E,,, in the same figure) for the detection of protons scattered to the left and right at 95” lab angle. The large value of polarization analyzability of the p + 28Si elastic scattering near 95” angle was the reason for using two target detectors. Before entering the polarimeter, the protons were slowed down by a thin aluminium foil, the thickness of which was chosen to and then collimated by the stop the particles 3H, 3He and scattered deuterons, double-entrance apperture to a solid angle 24 = 10p3. Detectors, collimators and antiscattering slits were mounted on a support of a turntable. Its azimuthal position may be altered around the proton beam axis so as to permit the interchange of the left and right detectors. The electronics associated with the polarimeter was derived from conventional logic for polarimeter systems employing a detector as a target. Sum-coincidence

P. Kozma, P. Bkm / Polarization ofprotons







Ep(MeV) Fig. 2. Histogram

representing a typical coincidence spectrum A& + E, (true and chance events) measured with the polarimeter at 45” (lab).

events between respective pairs of target and asymmetry detectors AE, + E,


AE, + E, were stored. The analyzing power A, of the polarimeter was measured by a double-scattering technique with polarized protons produced by elastic scattering in a carbon target. The analyzing power of the polarimeter was determined to an accuracy of 3%. The average detection efficiency of the polarimeter was 2.5 x 10W6. The proton polarization PY’ was determined from the measured asymmetry r-l

&=Y=PYA... r+l

, Y’


where (2) NL and NR are sum-coincidence counts taken for two alternative azimuthal positions (superscripts + and - , respectively) of the polarimeter. A typical coincidence spectrum, presented in fig. 2, shows the proton peaks from the 2H(d,p)3H and 12C(d, po)13C reactions induced by deuterons on the deuterated-polyethylene target. The correction of measured asymmetry data E for a nonsymmetrical arrangement of the two “left” and “right” scattering planes in the present polarimeter (see fig. 1) was calculated to be less than 1% in the whole range of reaction angles. The

P. Kozma, P. Bt+m / Polarization ofprotons


dominant part of the overall errors quoted for the resulting polarization data corresponds to the statistical uncertainty as well as to errors in the background subtraction.

3. Results and discussion 3.1. NONDYNAMICAL


According to the Simon-Welton formalism’) for describing binary reactions involving polarized particles, the outgoing proton polarization PY’ from the 2H(d,ij)3H rea ction for unpolarized incident deuterons and target nuclei can be expanded in terms of the associated Legendre polynomials PL(cos e), L being even: u~(E,e)P~‘(E,e)=~BL1(E)P;(cOSe).



Here E and t3 are the energy and proton emission angle in the c.m. system, respectively, and a,, is the differential cross section for unpolarized particles. The expansion coefficients B,, are bilinear functions of the reaction matrix elements (1’ S’ J” IRJ 1 S J”) characterized by total angular momentum and parity J”, orbital momentum I and spin channel S, primed quantities referring to the outgoing channel. For deuteron energies below 1 MeV we can restrict ourselves to incoming 1~ 2 waves. In the low-energy limit, quintet states of the incoming channel do not contribute to the differential nucleon polarization q,Pv and expression (3) can be reduced 8, to (4)


(6) Following Boersma9), by (Yand j3 we denote transitions of (I’ S’ J” [RI I S Jr): q)=(o

0 o+ II?/ 0 0 o+),


0 2+ IRI 2 0 2+),


1 2+ IRI 2 0 2’),



1 1- /RI 1 1 1-),

CY*2 = (1 1 2- (RI 1 1 2-),


0 1- JR1 1 1 ll),

PI2 = (3 1 2- IRI 1 1 2-).

1 OP IRJ 1 1 OP),

t tl--l tt f I I0 II: P. Kozma, P. Bt!m / Polarization






I tt



+t+ii tt+tt+t

















E,, (MeV) Fig. 3. (a) Angular distribution of proton polarization P-“’ from the 2H(d,p)3H reaction at Ed = 975 keV. (b) Energy dependence of proton polarization P. “’ from the 2H(d,‘,‘j)3H reaction at/ 8 = 45”(lab). 0 - Dietze and Lorentzen3); 0 - MagliE and VuEovic4); 0 - present measurements.



The angular distribution of the proton polarization from the 2H(d,@)3H reaction was measured at the mean deuteron energy 975 keV (see fig. 3a). The polarization values - as listed in table 1 - were combined with the appropriate cross sections”) TABLE 1


Lab angle

kbl 15 30 45 60 70 80 85


of proton

polarization from the 2H(d,p)3H deuteron energy

cm. angle


17.78 35.38 52.65 69.34 85.42 90.64 95.76

0.020 0.046 0.066 0.051 0.019 0.002 0.022


Weal + 0.008 + 0.008 k 0.006 * 0.007 & 0.009 f 0.009 * 0.012

“) Errors quoted for these data correspond background subtraction.

to the statistical


for 975 keV mean

Mean analyzing power

Proton polarizationa)

- 0.308 - 0.378 - 0.452 - 0.478 -0.611 - 0.627 - 0.616

+ +


0.064 0.122 0.147 0.106 0.031 0.004 0.035

+ 0.029 + 0.024 f 0.017 f 0.018 * 0.017 _+0.016 + 0.025

as well as to errors

in the


P. Kozma, P. Bkm / Polarization ofprotons

5: 975 keV






Fig. 4. Angular dependence of differential proton polarization o0P-“’ from the 2H(d,“p)3H reaction at Ed = 975 keV. The curve represents the least-squares fit of expression (4) with parameters B,, = - 0.571 mb*sr-’ and Be1= - 0.068 mb . sr-I.

for which linear interpolation has been used when necessary. The values of the differential polarization uOPY’(fig. 4) were fitted by using the least-squares method. The best fit of eq. (4) yielded B,, (mb/sr) = -0.571 f 0.074, B,u fmb/sr)

= - 0.068 i: 0.080,

at x 2/( N - 2) = 0.99. The values of both parameters are in good agreement with those obtained from the proton polarization analysis at higher energies’). The resulting values B,, and B4r prove the dominant contribution of the incoming p-wave and show that the contribution of the incoming d-wave interference cannot be omitted at deuteron energies of about 1 MeV. As can be deduced from the sign of Bdl, the phase-shift split between singlet-singlet a2 and singlet-triplet & incoming d-wave matrix elements have to reach values of arg(Lu&) > IT.


The energy dependence of P Y’ was measured at 45” lab angle for deuteron energies between 250 and 975 keV. The results of this measurement are displayed in table 2 and in fig. 3b together with data presented earlier by other authors 3”). According to the previous treatmentsl’) we have also tried to interpret the measured energy dependence of P Y’ as a threshold effect. This model is based on the


P. Kozma, P. Bkm / Polarization ofprotons TABLE 2 Polarization Mean d-energy

of protons


emitted at 45” from the 2H(d,‘p)3H Mean analyzing power


PM 250 312 377 455 509 564 620 676 743 798 860 906 962 975

0.029 0.051 0.076 0.075 0.092 0.088 0.078 0.073 0.067 0.061 0.052 0.056 0.047 0.066

k f f * k * + f + + * + f f


0.017 0.016 0.012 0.011 0.010 0.010 0.009 0.008 0.008 0.007 0.007 0.006 0.006 0.006

“) Errors quoted for these data correspond background subtraction.


Proton polarization”)

- 0.065 - 0.096 -0.119 -0.115 -0.144 -0.142 - 0.143 - 0.153 - 0.147 -0.151 -0.141 - 0.146 -0.138 - 0.147

0.449 0.529 0.636 0.654 0.642 0.625 0.550 0.477 0.458 0.409 0.373 0.355 0.341 0.452

to the statistical


k 0.038 i 0.031 * 0.019 k 0.018 k 0.018 & 0.017 * 0.017 f 0.018 f 0.019 + 0.018 f 0.019 k 0.020 + 0.018 * 0.017

as well as to errors

in the

assumption that the energy dependence of the non-resonant matrix elements is governed by the barrier-penetration factors in the incoming d + d channel. In the R-matrix approach ‘*) of this model a matrix element can be parametrized by

(I’ S’ J” IRI I S J”)


&,, - $,(E)} ,



P,(E) S21(E)=[l -cS,(E)]*+[cP/(E)]* ' Here, A, # and c are energy-independent parameters, and PI,S,and $, are the well-known penetrations, shift factors and “hard sphere” phase shifts, respectively, defined on the sphere of interaction radius r. Following this formalism the experimental data of uoP y’(Ed,45 “(lab)) have been fitted using eq. (4) in which expansion coefficients B,,and Bdlwere of the form

B,,=b,Q,(E)/E+ zb2Ln2( E)/E+ sdterm, BN = b&G @)/E


(9) 00)

respectively. E is the c.m. energy in MeV. The numerical value of b, = -0.035 gained from the angular distribution of the PY'analysis was introduced. Again, the interpolated cross-section data”) at 45”(lab) for the a,PJ" calculation were used.


P. Kozma, P. BPm / Polarization ofprotons









I __


I _^




Ed(MeV) Fig. 5. Energy dependence of differential proton polarization crOP” from the 2H(d,ij)3H reaction at 0 = 45’(lab). The solid line represents the least-squares fit including the incoming p-wave (h, = - 0.103) and d-wave interference ( bz = - 0.035) terms, the dashed line shows the contribution of p-wave only.

In the first step of the fitting procedure the sd term in eq. (9) was neglected. In this case, the best least-squares fit at x2/( N - 1) = 0.386 gives b, = - 0.103 for the interaction radius r = 7.5 fm whose value corresponds to the minimum of x2 when r is varied from 1 to 15 fm. The influence of the shift factor S,(E) was found to be statistically insignificant and therefore this factor was neglected in further analysis. The result of this fit is shown in fig. 5. Here the small contribution of the dd interference term to the differential proton polarization from the 2H(d,@)3H reaction at 45”(lab) is also shown. As can be seen from this figure, the energy dependence of u,PY ’ is surprisingly well fitted mainly by the p-wave barrier-penetration factor in a wide energy region. The wide (r - 2 MeV) resonance with spin and parity J” = 1 - near the d + d threshold in the 4He nucleus proposed by Griiebler et al. 13) should occur at deuteron energies about 500 keV. Although some deviations of experimental data from the b,P,( E) curve can be observed, the dominant contribution of the incoming non-resonant p-waves is evident. Therefore, a wide p-wave resonance with only a weak proton reduced width - if it exists - ought to be seen. An attempt has been made to interpret deviations of experimental data from the b,P,(E) fit in terms of sd admixture. While the amplitude of the Im(cu,&) transition was found to be about 0.05 in various fits, the relative phase could not be established unambigously according to the experimental values.

P. Kozma, P. B6m / Polarization ofprotons


4. Conclusions

Our experimental data provide new information on the outgoing polarization of protons from the 2H(d, p)3H reaction below 1 MeV deuteron energies. Analysis of the angular distribution of proton polarization proved that the contribution of non-resonant I = 2 wave singlet-singlet and singlet-triplet matrix elements cannot be neglected at about 1 MeV. The excitation curve of proton polarization was shown to be a slowly-varying function of deuteron energy. The barrier-penetration factor corresponding to the I = 1 wave in the incoming channel of the reaction studied was found to be sufficient to describe the energy dependence of the product u,PY’ in this energy region. Thus, it is quite unbelievable that some of incoming p-wave matrix elements could show a strong resonance behaviour. However, it is evident that the unambiguous identification of the supposed 13) J” = 1- triplet-singlet p-wave resonance requires an analysis of a more complete set of polarization observables. The authors are grateful to Drs. B.P. Ad’yasevich and V.G. Antonenko for many helpful discussions on the subject of this work. We are also indebted to Dr. V. Presperm for his interest in this work and a critical reading of the manuscript. References 1) H.W. Franz and D. Fick, Nucl. Phys. Al22 (1968) 591; B.P. Ad’yasevich, V.G. Antonenko and D.E. Fomenko, Sov. J. Nucl. Phys. 33 (1981) 601 2) C.P. Sikkema and S.P. Steendam, Nucl. Phys. A245 (1975) 1; A.M. Alsoraya and R.B. Galloway, Nucl. Phys. A280 (1977) 61 3) G. Dietze and K. Lorentzen, Nucl. Phys. AIS8 (1970) 577 4) B. MagliE and J. VuPoviE, Nucl. Phys. 6 (1958) 443 5) P. Kozma et al., Nucl. Instr. Meth. 228 (1985) 579 6) P. Bern et al., Nucl. Instr. Meth., to be published 7) A. Simon and T.A. Welton, Phys. Rev. 90 (1953) 1036 8) B.P. Ad’yasevich, V.G. Antonenko, P. Bern, P. Kozma and J. Mares, Czech. J. Phys. B32 (1982) 1349; and to be published 9) H.J. Boersma, Nucl. Phys. A135 (1969) 609 10) A.S. Ganeev et al., Sov. J. Atom. En., Suppl. 5 (1958) 21; R.B. Theuss, W.I. McGarry and L.A. Beach, Nucl. Phys. 80 (1966) 273; N. Ying, B.B. Cox, B.K. Barnes and A.W. Barrows, Nucl. Phys. A206 (1973) 481 11) F.M. Beiduk, J.R. Pruett and E.J. Konopinski, Phys. Rev. 77 (1950) 622, 628; J.R. Rook and L.J. Goldfarb, Nucl. Phys. 27 (1961) 79; D. Fick and U. Weiss, 2. Phys. 265 (1973) 87 12) J.E. Monahan, A.J. Elwyn and F.J.D. Serduke, Nucl. Phys. A269 (1976) 71 13) W. Grliebler, V. Konig, P.A. Schmelzbach, B. Jenny and J. Vybiral, Nucl. Phys. A369 (1981) 381