The polarization of neutrons from the 2H(d, n)3He reaction for deuteron energies from 35 to 275 keV

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THE POLABIZAI'YON OF NEUTRON3 FBOM THE aH(d, n~He BEACTYON FOB DEUTLRON lavER~itFS FROM 35. TO 275 iteV M".

A.

Deparrnewtr

'

AL30RAYAt and R H. flALLO~VAY

qf Pbyaica,

Uniogrsiry ßl

9l+. Scorlavrd

Iteoeived 23 Npvember 1976

AMract : The dep~deaoe on deuteron energy of the polarization of the neutrons emitted at 45°from the'H(d, n)eHe reaction in the range 35 to 275 koV, was determined from the asymmetry in the scattering of the neutrons by `He. There is no itidicatioa of the mach discussed possible resonance at about 100 keV deuteron energy. TJu results are discussed is relation to the genaral theoretical treatment of the'H-'H interaction put forward bY Boerema. NUCLEAR REACTION3'H(d, n), S ~ 3~275 keV measurpd polarization P(~, B ~ 45°.

1. Ynh+odacdon The stimulus for making the measurements reported here of tho polarization of the neutrons from the 2H(d, n)3He reaction was the theoretical papa by Boersma t ) in which it was shown that for deuteron energies less than 200 keV the energy dependence of the neutron polarization wind be predicted and that the available experimental data on neutron polarisation was inadequate to test the predictions. The data comprised of quite contradictory polarization values (fig. 1) obtained with thick deuterium targets. Relevant new thin target polarization measurements 1 t ), obtained by a different experimental technique from the present ono, only became available while the present measurements were being completed. The possibility of a resonance in the d-d system at about 100 keV deuteron energy was suggested e) on the basis of neutron polarization measurements in which scattering by 1 ~C served as polarization analyser. Although these observations were later attributed to resonance in the n- 1 ~C scattering 1 " i2) . this explanation has recently bt~n disputed l'). Such a resonance in the d-d system has also been suggested from measurements on the ZH(d, p) 3 H reaction induced by polarized deuterons ia), from neutron polarization measurements with ~He as analyser and from measurements of the energy dependence of the ~H(d, a)3He and ~H(d, p)3H differential cross section is). Thus the possibility of such a resonance has remained a live issue [ref. i 6)] . The results presented here extend to lower deuteron energy the neutron polarization data l o. t ~) obtained by a consistent technique of measurement and analysis. A preliminary report of some of the polarization measurements was made to the Zurich Symposium ls). t Oa leave from : Faculty of 3cienoe, Riyadh University, Saudi Arabia. 61

62

A. M: ALSORAYA AND R & GALLOWAY - 24

2N

1 d, n 1 9 He

- 20

Z 0

âN O

o. z 0 F W Z

-b ~'~~

d~~~~

°

~

~~

-4

ß

0

60

t60 AVERAßE DEUTERON ENERßY

2!A

320

( keY1

Fib. 1. The polarlTation of neutrons emitted at about 43°-SO° (lab) from the'He(d, a)'He reaction for deuteron energise up to 300 keV. The symbole corroapond to the followlna (symbol, refer~oe, lab angle, analyser): ": Palma'), 47°, 4He ; A : I{eae'). 46°, "C; ": Boerema et aL `). 33°, 4He ; p: itogere and Hond s), 43°. "C; Y : Haaegen et aL 6), SO°, i'C; " : Hehofet aG'), 47°. `Ne; x Thomas andHofmana s), SO°,'He; D: Prade and Caikai °), 49°-34°, 4He, i't:; p : Davle and Gallo way lo), 46°, `He ; O : 3iklcema and ateendam 11), 47°-SO°, `He.

2. Faperlmonbl tECbOhjOe A magnetically analysed deuteron beam from a S00 keV Van de Graaff accelerator was incident on a water cooled Ti-D target inclined at an angle of 45° to the deuteron beam . This target design i 9) facilitated optical alignment of the neutron polarimeter system . Further it ensured that any small residual energy instability in the accelerator could only cause movement of the beam spot on the target along the direction of neutron collimation so that no false asymmetry could result from the position of the beam spot on the target . The Ti target thicknesses used were 2.2 mg " cm-2, 230 ug " cm-~ and 80 ~g " cm- ~. Neutrons emitted at 45° were collimated and scattered by 4He at a pressure of 70 afro, in the form of a gas scintillation counter, into a pair of liquid scintillation counters symmetrically placed to `right' and to

'H(d, n)'He

63

Fig. 2. The two neutron scattering geometries employed .

`left' at a scattering angle of about 120° (fig. 2). The polarization of the neutrons was deduced from the asymmetry in the scattering of the neutrons. Two neutron polarimeters were employed with different orientations of the scintillation counters as shown in fig. 2. In both polarimeters the three scintillation counters wore rigidly mounted to a cradle which could rotate about the collimated neutron beam as axis to permit the interchange of the `right' and `left' hand liquid scintillation counters to cancel out any instrumental asymmetry. The polarimeter of fig. 2a has been described previously, as has the associated olectronic system and procedure for data analysis io. so. u). Pulse-shapo discrimination against y-rays was applied to the liquid scintillation counters . Pulse height spectra dun to 4Ho recoil nuclei detectod in coincidence with neutrons scattered to `right' and to `left' were accumulated along with spectra due to random coincidences in a PDPll/45 computer . The polarimeter cradle was rotated automatically every hour to interchange `right' and `left' hand liquid scintillation counters to cancel any instrumental asymmetry. In addition measurements were made of the scattering asymmetry in the plane normal to the reaction plane, which should be zero, as a test for any instrumental asymmetry. Typical pulse height spectra duo to 4He recoils in coincidence with neutrons scattered to `right' and to `left' along with the associated random coincidence spectra are illustrated in fig. 3, for the case of a mean deuteron onergy of 210 heY in the target. 1a addition to the peal¢ due to the scattering of neutrons by 4He through 120° from

64

A. M. AL30RAYA AND R H. QALLOWAY

*H(d, n)'He

63

which the asymmetry was determined, there was a low energy tail which showed no asymmetry. Allowance for the presence of the low energy tail was necessary is determining the asymmetry associated with the peak, as descr~éb d previously io. ~1). The low energy tail was due to the scattering of neutrons in the stainless steel shell or other material of the gas scintillation counter in addition to scattering by the 4He gas itself 1°). 3. Reealts The results are listed in table 1. The energy calibration of the accelerator was established by observing the well known resonances in the 19F(P, acy) 16 U and ii B(p, y) 1=C reactions ~~). For' thethiclc target measurements, the first six listed in table 1, the mean deuteron energy was calculated as a weighted average with the reaction cross section ss) providing the weighting factor. For the thin target measurements the mean deuteron energy was calculated from stopping power data s4. ss) . The asymmetry associated with the peak in the 4He recoil spectra was evaluated with allowance for the low energy tail extending under the peak 1 °' s~). The mean analysing power was evaluated from the phase shifts of Hoop and Barschall se) with allowance for the finite geometry of the polarimeter systems described in flg. 2. The phase shifts of Stambach and Walter [ref. ~')] would lead to polarization values lower by about 0.002, a difference which is small compared to the statistical uncertainty in the results. The asymmetry observed Incident d-0nergy (key 330 300 300 230 200 130 330 300 230 200 130 12S 100 100 73 30

T~ 1 Polarization of the neutrons emitted at 43° from the °H(d, n)'He reaction Mean Asymmetry Mean Neutron Inatrnmeatal d-energy analysing polarization asymmetry (key power test 240 210 210 180 130 113 273 223 193 180 133 103 83 80 33 33

-0.126f0.008 -0.116f0.006 -0.119f0.007 -0.109f0.006 -0.106f0.003 -0.097f0.003 -0.132f 0.006 -0.123 f0.003 -0.126f0.004 -0.103 f0.003 -0.101 f0.004 -0.081 f0.008 -0.086f0.011 -0.084f0.006 -0.074f0.007 -0.066f0.010

") With the geometry offlg. 2a. b) With the geometry of5g. 26.

0.836 0.833 ~) 0.869 ") 0.864 0.839 0.842

-0.147f0.009 -0.136f0.007 -0.137f0.008 -0.126f0.007 -0.123 f0.006 -0.113f0.006

-0.007f0.012 -0.002f0.007 -0.013 f0.029 -0.002f0.007 -0.003f0.008

0.878 0.834 0.832 0.831 0.847 0.843 0.840 0.839 0.833 0.830

-0.130f0 .007 -0.144f0.003 -0.147f0.003 -0.124f0.006 -0.119f0.003 -0.096f0.009 -0.102f0.014 -0.100f0.007 -0.088f0.008 -0.080f0.011

-0.004f0.007 -0.010 f0 .010

66

A. M. ALSORAYA AND R B. C 3ALLOWAY

in scattering in the plane normal to the ~H(d, n) 3He reaction plane as a test for any instrumental asymmetry is also. listed in table 1. It was oa sash oa~sion consistent with zero. Pttrther confidence in thç neutron polarimeter came from the close agreowent between polarization values obtained with it and those obtained with a polarimeter employing small angle Mott-Schwinger scattering by Pb [ref. ~8)]. 4. Dlscaesbn As may be seen from figs . 4 and S, the present results show no sign of the resonanceliYe behaviour te) near 100 keY deuteron en..°rgy previously suggested from neutron polarization measurements s, t3 . s . g), from the competing . (d, p) reaction ta) and from differential cross-section measurements on both the (d, n) and (d, p) reactions [ref ts )] . The absence of resonance-lilée behaviour is consistent with the recently reported neutron polarization measurements lt), 2H(d, n)3He and ~H(d, p)3H differential cross-sectionmeasurements ~') and ~H(d, d) 2H~elastic scattering measurement3 3~). -

24 2

- 20

H ( d, n 1 3 He

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tC Q 0 o_

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+

- 4 0

0

40

80

120

, 160

AVERAGE DEUTERON ENERGY

200

240

280 .

(k~V)

Fib. 4. The polarization of neutrons emitted at 4S°-SO° from the °H(d, n)'He reaction for deuteron enema ap to 300 keV. Q, Hehof et al. ~) : p, Sikkema and Steeadam I 1); ", present thin target measurements ; ~, present thick tar®et measurements.

'H(d,

67

n)'He

- 20

x

Z O F N M

f6

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O

a

- 4

i

40

i

80

~

120

i

160

i

200

AVERAßE DEUTERON ENERGY

~

2rL0

i

280

i

320

(k~Vl

Fig. S. The Stung of eq. (3) to the present polarization data for E, < 120 keV with ac, ß parameters denotedas follows (the aumbera denote a, Q, c) : " " " " " " " " " " Hoersma 1),1.93, 4,25, -0 .163 ;_ _ _ _ _ Fick and weirs "), 3.2, 4.9, -0 .161 ; 1?ospiechet aL "), 0.4, 3.4, -0.171 ; 3.8, 5.0, -0.166.

In fig. 4 the present measurements are compared with the only other measurements [refs. ~' 11)] which span most of the energy range under discussion. For clarity measurements which provide only a few points in this energy range have been omitted. These points may be identified by reference to fig. 1. Clearly the present measurements are in close agreement with those of Sikl~eema and Steendam 11 ) which were obtained by a quite different experimental technique a t ). The measurements of Behof et aJ. ') from which the present results and those of Sikkema and Steendam 11) differ over most of the energy range were obtained with a thick deuterium target. To establish whether target thickness could account for the discrepancy some of the present measurements were made with a thick target also. However as shown in fig. 4 there is no significant difference in trend of polarization with deuteron energy betwcen the present thick and thin target measurements. The energy dependence of the neutron polarization for low deuteron energies is of interest since it has been the subject of theoretical discussion. Hoth goersma 1) following a DWBA approach and Fick and Weirs 3s) followingan R-matrix approach

68

A. M. AL30RAYA AND R B. ßALLOWAY

ddduced the same expressions elating the energy dependence of the neutron polariz~tion to the energy dependence of the anisotropy of the differential cross section. For energies such that only S- and P-waves are involved, the differential cross section c(B) ~ Ao -~A2ps(cos 9),

(1)

As = .05+Ed 0 ß Ao 1+a(0.05+Ed)'

(2)

tire anisotropy coefficient

aiYd the polarization p.(e)

~

(0 .05+Ed~i(~ 9) 1 +a(o.os+Ed )+ß(o.os+Ed~s(cos e) .

(3)

Ed is the incident deuteron energy and a, ß and c are energy-independent parameters which depend on the transition matrix elements. Ia both c8ses l' 3s) the above expressions wen assumed valid for Ed < 200 keV. Thus if a and ß are deter mined from fitting the energy dependence of the anisotropy coefficient A2fA o, only. c remains as a free parameter to fit the polarization data. $oersma 1 ) fitted anisotropy coefficients a4 . ss) over the deuteron energy range 15 to 150 keV by eq. (2) and obtained a = 1 .93 and ß = 4.25. Since the validity of the theory is in least doubt at low deuteron energies, these values of a and ß were used is eq. (3) to fit the present polarization values for Ed < 120 keV (fig. S) giving c = -0.163 . This is in good agreement with c ~ -0.164 found by Sikkema and Steendam 11) and reflects the good agreement between the two sets of polarization values as shown in fig. 4. Fic1E and Weiss 3Z) obtained a = 3.2f0.3, ß = 4.910.2 by fitting anisotropy wefficients s3. sa, ss) over the deuteron energy range 15 to 200 keV and with these values in eq. (3) a best fit for Ed < 120 keV gives c = -0.161 {fig. 5). Most recently Pospiech et al . ~ 9) determined a = 0.4 f0.3, ß = 3.4 f0.2 from their own relative differential cross-section measurements for Ed from 70-144 keV and with these values a best fit to the present polarization measurements for Ed < 120 keV gives c = -0.171 (fig. 5). The parameters of Pospiech et al. z9) are least successful and those of Fick and Weiss 3z) most successful in fitting the low energy polarization data Indeed even larger values of a and ß (3.8 and 5.0 respeotively) in eq. (3) fitted to the polarization values for Ed < 120 keV give c = -0.166 and provide the solid curve (fig . 5) which is slightly closer to the polarization values up to Ed = 300 keV. That such larger values for a and ß may be supported by the energy dependence of the anisotropy coefficient Az fA o is shown in fig. 6, where values up to 300 keV deuteron energy are considered . The fact that the energy dependence of the anisotropy coefficient can be well represented by eq. (2) up to 300 keV deuteron energy makes it of interest to see in fig. 7 how well the energy dependence of the polarization up to 300 keV may be represented by eq. (3) if c is

'H(d, n)'He

69

as

2

I

1

0

RO

1

a0

1

1

120

1s0

1

I

200 ~

AV~RABE DEUFERON ENERbY

~2i0

1

280 ~- .

1

320

(k~Vl

Fig. 6. The e~neroy dependence of the anieotmpp ooel5cieat J1slAa for the ~H(d, n)'He reaixion. The data points are from: ~, Booth er aL sa) ; Q, Bliot et ~.ss)~ ~~~ Preston et a~ "); OI Thenet et d.'s) ; x, Pospiech et ai:'°) . The curves are from e4. (2): -_ ~. _ ___ _ a ~ 3,2f0.3, ß 4.9 f0.2 as found by Fick sad Weiee ") ; a m 3.8, ß ® 5.0.

adjusted to give the best flt over the whole energy range. The best fit is provided by a = 3.8, ß = 5.0 with which the anisotropy coefficients are best fitted in fig. 6 and in this case c = -0.160. A similar curve is obtained with the Ficlt and Weiss sa) values of a and ß (3.2 and 4.9 respectively) and c = -0.153. The Hoersma >, .). values of a and ß (1.93 and 4.25 respectively) are clearly less satisfactory over tho 300 keV deuteron energy raage. Thus within the theoretical framework of l3oersma 1) and of Ficl~ and Weirs' =) a self-consistent description of the energy dependence of the anisotropy coefficient and the polarization is possible . Of the previously proposed parameters those of Fick and Weirs as), a = 3.2f0.3, ß = 4.9 fd:2, are most satisfactory while a better fit up to 300 k~eY deuteron energy can be obtained with the slightly larger values a = 3.8, ß = S.0 with similar uncertainties to the Fick and Weisa vahies .lt remaias to be seen whether a detailed theoretical descriptiôn of the reaction can produce transition matrix elements consistent with these .values of the a, ß, c parameters.

0

~LO

60

120 . .

160

200 . .

AVERAGE DEUTEON ENERGY

2i0

280

320

(k~Vl

FiB. 7 . The 81än8 of eq . (3) to the preemt polarlzatioa data for $ up to 300 keV with ac, ß parameters deoo0ed as follows (the numbers denote ac, ß, c) : . . . . . . . . . Hoanma'), 1 .93, 4.25, -0.130 ; _ _ _ _ _ _ _ _ Fich and Weisa ss), 3 .2 f0.3, 4.910-2. -0.1 53 ; , 3 .8, 5.0, -0.160.

We wish to thank Dr. G. $radford, Dr. A. S. Hall, Mr. H. d. Napier, Mr. G. Turnball and Mr. F. McN. Watson for their willing assistance. One of us (A.M.A.) acytnowled8es with thanl~ the financial support of the iIniveraity of Riyadh. Refa~eaces 1) 2) 3) 4) S) 6) 7) 8) 9) 10) 11) 12) 13) 14)

H. J. Hoenma, Nucl. Phys. A136 (1969) 609 P. J. Pa:ma, Nucl. Phys. 6 (1958) 141 P. P. Kane, Nucl. Phys. 10 (1959) 429 H. J. Hoersma, G G Jonker, J. Q. N(jenhuis and P. J. van Hall, Nucl. Phys. 46 (1%3) 660 J. T. Roeecs aad G D . Hoad, Nncl. Pl~ys. S3 (3964) 297 I-~. Haas®em, H. Pose, C~. Schirmer aad D. SeeliBer, Nacl . Phys . .76 (1%5) 417 A . F. Hehof, T. H. May ead W. L McCiarry, N~1. Phys. A108 (1968) 250 K. Thomas and A. Hofmaàn, 2. Pl~ys. 217 (1968) 128 H. Pralle aad J. ßihai, NncL Phys. A123 (1969) 365 ' H. Davie and R. H . ßalloway, Nucl. Instr. 108 (1973) 581 G P. Sikkema and S. P. Steendam, Nuct . Pl~ys. A246 (1975) 1 Ii . HansBen aad M. Nitzeche, Nacl. Pl~ys. A166 (1971) ~Ol H. D . Knox, J. M. Cox, R. W. Fialay and R . O. Laae, Nucl . Phys . A317 (1973) 61 t H. W. Fraaz aad D. FIck, Nucl. Phys. A122 (1968) 591

sH(d, n)rHo' 1 S) 16) 17) 18) 19) 20) 21) 22) 23) 24) 23) 26) 27) 28) 29) 30) 31) 32) 33) 34) 33) 36)

71

Y. Ying, B . B. Cox, B. K. Barnes and A. W. Barmws, Nncl. Phyr . A206 (1973) 481 F. A. Gockel and D . Fick, Z . Puys. 271 (1974) 39 R B . Galloway, A . S . Hall, R M. A. Msayouf and D. G. Vacs, NucL Phys. A242 (1973) 122 A. Akoraya, R B . Galloway and A. S. Hall, Proc . 4th Int . 3ymp. on polarization phenomena in nuclear reactions, ed. W. Gruebler and V . Kosig (Birkhaurer Verlag, Basel, 1976) p. 520 K . Masood Ali, R B. Galloway and D. G. Vara, NucL Insu. 92 (1971) 553 H . Davie and R B . Galloway, Nucl. Inrtr . 92 (1971) 547 R M. A. Maayouf and R B . Galloway, NuçL Insu . 118 (1974) 343 F. .~jsenberg-Selove and T. Lauritren, NucL P)~ys. 11 (1939) 1 H. Liskeia and A . Pauken, NucL Data Tables 11 (1973) 387 J. H. Coon, Faat neutron physics, vol. 1, ed. J. B. Marion and J.1.. Fowbr (Intaactemoe, New York, 1960) ch. IVD J. H. Ormrod, Nucl. Insu. 9S (1971) 49 B . Hoop and H. H. Herschall, NucL P)~ys. 83 (1966) 65 Th. Stambach and R L. Walter, NucL Phys. A180 (1972) 223 R . B . Galloway and R M. Lugo, Proc. 4th Int. Symp. on polarization phenomena is nuclear reactions, ed. W. Gruebler and V. Kosig (Hirkhauser Verlag, Basel, 1976) p. 881 G. Pospiech, H . Genz, & H. MarHngheua, A . Richter and G. Schrieder, NucL P>~ys. A239 (1973) 125 E. H. Marlinghaus, H. Genz, G. Poapiech, A . Richter and G. Schrieder, Nucl. P)~ys. A2SS (1975) 13 C . P . Sikkema, Nucl. Insu. 122 (1974) 415 D. Fick and U . Weirs, Z. Phys. 265 (1973) 87 D. L. Booth, G. Proaton and P. F. D . Shaw, Pros . ~ . Soc. A69 (1956) 265 E. A . F.liot, D. Roaf and P. F. D. Shaw, Pros. Roy. Soc. A216 (1933) 57 G . Preston, P. F. D. Shaw end S. A . Young, Pros. Roy. Soc. A226 (1954) 206 R B . Thus, W . L McGarry and L. A. Heach, NucL Phys . "0 (1966) 273