Maximum tensor analysing power Ayy = 1 in the 3He(d, p)4He reaction

Z.B :2.G

Nuekar Phyftu A271 (1976) 29-35 ; © North-tlollmrd Pxbliahtny Co., Amsterdam

Not to be reproduced by photoprint or microfilm without written perminion >}om the publLher

MAXIIVIUM TENSOR ANALYSING POWER A = 1 IN THE aHe(~,!)~He REACTION W. GRÛEBLER, P. A. SCHMELZBACH, V. KöNIG, H. JENNY, R. RISLER, H. R. BURGI and J. NURZYNSKI Iaboratorirurt J7ir ICernPhyatk, Eidg . TedFnlaiehe Hodarchuk, 809.7 Z&rJeh, Swttserland

Received 1 July 1976 Aistrttct: An evaluation of polarization measurements on the sHc(~, p)`He reaction süows that the experimental values of .the analysins power A, and A reach nearly tmity between 9 and 10 MeV. A search for A, m 1 and A = 1 values in this eaer8y realon Was performed experlmtntally. The precise eaerebes and an8lta for tho maxima were fotmd by interpolation of the experimental data. The value of the A maximum found is comptittble with 1 within the aacperlmental error. No A, a f1 point could be detected. E

NUCLEAR REACTION

a He(a, p), E = 8.3-10.3 MeV; measured A,(e, E) and A(B. ~"

1. htO~YCdOII Points in energy and angle (E, 8) at which a component of the analysing power for polarized particles reaches its theoretical maximum value are of particular interest and importance. In elastic scattering such maxima have been found for spin~ and spin-1 scattering from spin-0 nuclei . In the former case Planner and Becher t) showed analytically that values A, = f 1 must occur at three energy-angle sets in nucleon 4He elastic scattering. The investigation of conditions for which a componeat of analysing power in d-a scattering reaches a maximum was performed by Crrùebler et al. ~). In the same paper it was analytically proved that three A = 1 points exist in the deuteron energy range between 3 and 12 MeV. These maxima were also found experimentally Z). In all these cases a simple linear relation between two elements of the transition matrix M, which connects the spin states of incoming and outgoing channels, must exist. Here the question arises if such points also appear in nuclear reactions. Rt~ently Seiler s) investigated the relevant conditions imposed on the M-matrix elements for the spin structure 1+}-~ ~}+0 . He found for A = 1 the necessary and sufficient conditions (1) Ml.~:~ _ -M-t .~E:~E~ Mt .-~:~ _ - M-t .-~:~~ where the indices denote the spin projections in the incoming and outgoing channels . This situation is different since two linear relations involving four M-matrix elements 29

so

w. cRUEHLER er et.

have to be fulfilled at the same angle and energy . The existence of such a point cannot be proven analytically in the same way as the maxima found in elastic scattering . Inspecting the analysing powers Ta (in spherical notation) of the 3He(~, p)4He reaction reported in ref. 4), Seder 3) suggests the possibility of an extreme value A = 1 near 9 MeV and a lab angle of 27°. Since in the same region A, also shows a deep minimum 4 ) an extreme value of A, _ -1 could riot be excluded. In this paper we report an experimental search for these maxima by very accurate measurements of the relevant analysing powers with an absolutely calibrated deuteron beam. 2. F.3iperlmeatal procedure The general experimental arrangement was the same as in earlier analysing power measurements carried out in this laboratory s). The spin direction was perpendicular to the scattering plane . The exact spin position was adjusted by the Wien ßlter to a precision better than . 1° before starting the measurements . A polarimetbr which used the 3He(d, p)4He reaction at 0° as a polarization standard measured the beapn polarization continuously 6). This reaction has been recently calibrated in an absolute sense at 0° to a precision better than 1 ~ [ref. ')]. A polarized deuteron beam withp~ x 0.3 and p s;s 0.9 was delivered from the ETHZ tandem âooelerator. The défining diaphragms in front of the detectors were 4 mm wide and 30 mm high at a distance of 256 mm from the middle of the gas target . The procedure of the measurements and the determination of the analysing powers are described extensively in a recent paper 8). This method, which uses detectors at the left and right side of the target and frequent reversal of the sign of the beam polarization cancels instrumentalasymmetries and is independent to second order of small deviations of the spin direction from the required position . 3.1 . EXPERIMENTAL DATA

3. Besalts

The analysing powers A,, and A have been measured between 8.5 and 10.5 MeV deuteron energy in an angular range Bi,b = 12° to 32°. The results are shown in fig. 1 . They are not corfected for finite solid angle. The statistical errors are smaller than the dot size. The curves are fits from a interpolation in order to .find the angular position and value of the A maxima for each energy . Since the measurements show clearly that for these energies no maximum of A, occurs at the same angle as A, the vector analysing power A~ was not fitted . These results, however, are very accurate A, data and can be used to calibrate the vector polarization of polarized deuteron beams. 3.2. INTERPOLATION OF THE EXPERIMENTAL DATA

The experimental mapping of the interesting region was followed by an interpolation calculation. For this procedure each single angular distribution was locally

-0.2 A y -0.a -0.6 -0.8 10

ß

20

25

30

35

BLob

Fly. 1. Measurement of tho analysing powers A, and A as a function of enyle and' energy between 8.5 and 10.5 MeV. The statistical ermrs aro smaller than the dot size. The eurves aro polynomial fits.

fitted by a polynomial the order of which was determined by the largest probability of the fit to the data. In all cases a cubical interpolation was required . In this way the maximum value and the angle where the maximum occurs as well as the uncertainty of the maximum were determined . For this calculation the rough data without correction in respect to the solid angle was used. Finally the same interpolation method was used for all local maxima for the determination of the value of the ab3olute maximum and its energy and angle. The fit for this final interpolation calculation is

32

W. ORÛEHL~R et al.

Fig. 2. holynomiai flt of the mamma found by interpolation of the e~cperimeatal data at the corre:ponding energy " The maxima (dots with error bars) are corrected for 8aite solid angle. The shaded band indicate's the uncertainty of the St, which only inclndea statistical error of the measuremeata. The uncertainty is the absolute calibration is shown by the dashed line .

ÎIA d

Fia. 3. Contour plot of the tensor analysing power A calculated by an interpolation method.

shown in fig. 2. The dots and the error bars are the results fromthe different energies, corrected for the ßnite solid angle (see subsect. 3.3). The thick solid line is the ßt as a function of energy, and the shaded band indicates the uncertainty of this ßt due to statistical errors of the measurements . These errors do not include the uncertainties due to the absolute determination of the beam polarization by the polarimeter. This uncertainty is shown by a dashed line. A survey of the whole region measured is shown as a contour plot in ßg. 3. 3.3 . Gb1tREC1TONS AND 1;JNCERTAINTIE3

The result of the uncorrected interpolation gives a maximum value dy, _ 0.98110.003. This A valve obtained from the interpolation procedure must be

'He(d, p)

33

TiuüB 1 Corrections and uncertainties for A Corrections Correction due to the extended azimuthal an81e ~ Con;oction due to the ßaito scatterInB an81e B Total conroction for A

-H0.007 -I-0.002 ~-0.009

Unoertaintiea Statistical uncertainty of A Statistical uncertainty in the determinatIoa of the beam polarization Uncertainty in the absolute value of the aaalysine power of the polarimeter') Total uncertainty of A

0.3 0.5 0.9

f 1.1

') Ref. 6). T~ 2 Maximum A, its energy and aa=lo found A $,,°, B, ° B°,e,

0.990 f0 .011 .030 MeV 9 .28 f0 23 .6° f0.2° 28.1° f0.2°

corrected for the finite solid eagle used in the experiment. The error given in the above result does not include the uncertainties due to the determination of the beam polarization by the polarimeter. The corrections and uncertainties calculated for the final result are shown in table 1 . 3.4. FINAL RESULT

The .final result obtained for point geometry and taking into account all possible errors of the measurement is given in table 2. Also indicated are the energy and angle the maximum was found. This result is compatible with a maximum value A equal to unity within the experimental error. 4. DiscAeslon The result of the investigation shows that within experimental errors a maximum tensor analysing power A = 1 in the 3He(d, p)4He reaction is found. This result can be tested by measurements of other observables which must fulfil at the critical angle and energy certain conditions s) due to eqs . (1). Resides the vanishing of several polarization transfer ~cienta and polarization cornlation coefficients also the proton polarization P~ for unpolarized beam and target must be equal to minus the analysing power A e ,, of a polarized 3 He target . Although such experimental

34

W. GRßEBLER ct al.

data at the exact angle and energy found are not available, results nearby agree fairly well 9'11). An R-matrix fit performed by Dodder and Hale 12) for the data. of the polarization transfer coefficients K= and 1~`' measured by Hardekopf et a1. 11 ) at 8 MeV shows vanishing values near the critical angle, as required by eq . (1). All these data apparently support the result found in the present work. However, the significance is not very high since if eq . (1) is only nearly fulfilled the conditions for the observables approach the required values . This view also is supported by the relatively flat behaviour of A around the critical point as seen in fig. 3. A further experimental although not easy test of the maximum found would be an investigation of the inverse reaction ~He(p, d)3He, where the emitted deuterons should have a maximum tensor . polarization p = 1 for the corresponding incident proton energy . After the empirical establishment of an A,,, = 1 point, one wonders about the physical significance of the fulfillment of eqs. (1). The probability that the sum of two pairs of complex amplitudes vanish simultaneously in an accidental way is very low. A possible reason for the fulfillment ofeq . (1) may lie in the particular symmetric structure of these relations. This feature suggest that a resonance occurs near this energy. Such a connection also has been found in d-a scattering . In this case, it has been shown that for a resonance with J ~ 2 two maximum points A = 1 appear pairwise symmetric around 90° [refs. s' 13)]. Physically eq. (1) mean that the spin non-flip amplitudes for deuterons in the magnetic substete with ms = + 1 are equal to the negative value ofthe spin flip amplitude with m~ _ -1 independent of the 3He spin direction. This condition is very similar to that in spin-1 spin-0 scattering (e.g. d-a scattering) suggesting that the equality relations of the amplitudes in question is a more general condition for an A~~ maximum, independent of target spin. In the 6Li(d, a)~He reaction an A maximum has recently been found in measurements done at this laboratory la) . Since in this reaction both particles in the exit channel have spin zero, the necessary condition is slightly changed as can be seen in table 3. In this case the sum of the amplitudes with parallel and antiparallel spins in the entrance channel should vanish. For comparison the conditions for an A maximum in reaction induced by polarized deuterons for target spin 0, ~} and 1 are listed in table 3 . This comparison shows clearly the similarity of the necessary and sufllcient conditions in all cases. In the light of this comparison it seems that the two relations of the'He(d, p)4He reaction are not independent at an A = 1 point. The reason for this correlation may br found in the reaction mechanism. It tends to point towards a compound nucleus resonance, which reestablishes or prefers statistical distribution of the spins. This view is supported by an .analysis of the ~He(~, p)4He reaction over the energy range between 2.8 to 11 .5 MeV in terms of Legendre polynomials 4). Here the tensor analysing powers T2o, T21 and T22 show for the L = 6 term corresponding to an orbital angular momentum 1. = 2 ~ resonancelike behaviour around 9 MeV deuteron energy. Seder ls) has proposed, based on a

Tssis 3 Necessary and sutü«eat conditions for the M-matrix okmenta M+, a, in order to obtain A = 1 Spin structuro

Example

1-I- 0-" 1-~-0 1 -I-} -' }-}-0

'He(d,d) 4He 'He(d, P) 4He

1-F1 --" 0-i-0

6Li(d, a)~He

Conditions for Mme ,~,

Mio,io .

° - Mio,-io = MiiF.iFo _M_i}.~o Mi - } .iFo = -~- i - } .~o ~ii,oo

= -~i-i,oo

The indices a and b denote the spin projections in the incoming and c, d is outgoing channel.

more detailed analysis and a stretched spin configurâtion, a ~+ resonance in sLi at an excitation energy of about 22 MeV. A matrix element (l', s', J~~R~I, s, J+) _ (4, ~, ~+ ~R~2, ~, ~+) should be resonant. Further evidence of such a resonance also comes from the p-x scattering, the côrresponding exit channél of the âbove reaction. In the phase shift analysis 16) an indication of a resonance-life behaviour was found in the 2G~ phase shift near 27 .5 MeV' proton energy, corresponding to a sLi level -at an excitation energy at .about 22 MeV. The 4He+p channel must have channel spin s = ~}, whereas the 3 He+d can have channel spin s. m ~. Thus the coupling can only bè achieved by forces which change the orbital angular momentum by two units, i .e. by tensor forces . This change in . ôrbital angular mômentum is confirmed by the analyses mentioned above a ' is): Tensor forces can cause strong spin flip and therefore support the idea of the origin of the A = 1 point suggested. For a final decision further theoretical and experimental work:is needed in order to clear up these interesting phenomena of A maxima. i n reactions of light nuclei . References 1) G. R. Plattaar and A. D. Becher, Phys . Loft. 36B (1971) 211 2) W. Grüebler, P. A. Schmelzbach, V. König, R. Riskr, B. Jenny and D. O. Boerma, Nucl. Phys. A242 (1973) 283 3) F. Seiler, Phys. Lott. 61tB (1976) 144 4) W. Grüebler, V. König, A. Ruh, P. A. Schmelzbach, R W. White and P. Marinier, Nucl . Phya. A176 (1971) 631 3) W. Grùebkr, V. König, P. A. Schmalzbach sad P. Marinier, Nucl. Phys. A134 (1969) 686 6) W. Grüebler, V. König, A. Rah, R E. White, P. A. Schmelzbach, R Rider and P. Marinier, Nucl . Phys . A165 (1971) 303 7) P. A. Schmelzbach, W. ßrüebkr, V. König, R. Rider, D. O. Boerma and B. Jenny, Nucl . Phys ., in pros 8) V. König, W. Grüobkr and P. A. Schmelzbach, Proc. 4th Int. Symp. on polarization phenomena in sucker reactions, ed. W. Grüebler and V. König (Birkhâuser Verlag, 1976) p. 893 9) R I. Brows and W. Haeberli, Phys. Rev. 130 (1963) 1163 10) W. Grüebkr, V. König andP. A. Schmelzbach, Results of measurements and analyses of nuclear reactionsinduced by polarizedanduapolarized deuterons, Internal report ETH Zùrich, May 1973 11) R A. Hardekopf, D. D. Armstrong, W. Grüebkr, P. W. Keaton and U. Meyer-Berkhout, Phys . Rev. C8 (1973) 1629 12) D. C. Dodder and A. Hale, privato communication; and rof. li) 13) M. 5Imoaius and W. Grùobkr, Annual report 1974, Laboratorium für Kernphysik ETHZ p. 247 14) R Rider, W. Grüebler, V. König, B. Jenny, H. R Bürgt and J. Nnrcynski, Nucl. Phys., to be published IS) F. Seiler, Nucl . Phys. A187 (1972) 379 16) G. R. Plattaar, A. D. Becher and H. E. Conzett, Phys . Rev. CS (1972) 1138