Charge-exchange p3H → n3He and elastic p3H → p3H differential cross sections at medium energy

2 .B :2 .L

NuclearPhysics A338 (1980) 451-462 Q North-Holland Publishing Co., Amsttrdam

Not to be reproduced by photoprint or microfilm without written permission from the publisher

CHARGE-EXCHANGE p'H -~ n3lie AND ELASTIC pail~ p3H DIFFERENTIAL CROSS SECTIONS AT MEDIUM ENERGY G . BIZARD *, J . L. LAV n-i .F*, C. LE BRUN*, J . F. LECOLLEY, F. LEFEBVRES, A . OSMONT**, R. REGIMBART anä J . C . STECICMEYEiZ

Laborotoirc di Physique Corpraeulairc LA34, associE d 17N2P3, ISMRA, Unitxrsité de Caen, France J. BERGER*, J. DUFLO*, L. GOLDZAHL*, J . OOSTENS*** and F. PLOUIN*

IN2P3, ER S4, Laboratom National Satume, Saclay, France F . L. FABBRI, P. PICOZZA and L. SATTA

Istituto Nazionak di Fisica Nuckarc, Labomtori Nationaai di FYascati, Italy C. SCHAERF

Istituto di Fisiea, Unioasita di Roma, Istituto NazionaltFuica Nuckarc, Sezione di Roma, Italy Received 20 July 1979 (Revised 12 November 1979)

Abstract The Satume I quasi-monokinetic triton beam bas been used to measure the phi-~n~Ie differential eroes section at 415 and 600MeV per nucleon and the p'H-" p3li differential cross section at 415 MeV per nucleon . We covered the four-momentum transfer squared t domain fmm 0 down to -0 .7 (GeV/c)2 . A spin-independent Glauber-model interpretation of the data is discussed . E

NUCLEAR REACTIONS'H(p, p), E =1 .245 GeV ; 3H(p, n) ; E =1 .245 and 1.800 GeV ; measured rr(B) .

1 . IntrodacNon

It h~ been known for a long time that the pion exchange between two nucleons plays a basic role in nuclear interactions. However, the nucleon-nucleon interaction does not proceed entirely via the one-pion-exchange mechanism which can be obscured by other processes such as diffraction in elastic scattering or exchange of heavier mesons t . Moreover, due to the incident beam, it is experimentally difficult to explore the forward elastic scattering to which the one-pion-exchange term is expected to be the main contribution . These difficulties do not exist for the backward elastic neutron-proton scattering (so-called "charge exchange") for which the " CNRS. . ** "Thèse d'État", to appear (LTniventity of Caen). *** Present address : Physics Department, UCLA, Los Angeles 90024 Cal, USA. t For the current statua of the two-nucleon one-boson-ezdtange potential see, for instance, ref . t ).

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one-pion-exchange peak is dominant in a surprisingly large energy range (from less than 100 MeV up to 300 GeV) [refs. z-s)] . Up to now, none of the theories has been able to describe completely this pion-exchange peak: the exchange of apseudoscalar object should induce a dip at 180° in the neutron-proton differential cross section and the absence of this dip has not been understood although phenomenological explanations based upon empirical absorption prescriptions have been proposed 6''). As for nucleon-nucleon interaction, the forward nucleon-nucleus charge-exchange reaction is expected to give information on the pion-exchange mechanism over a large incident energy range. Here again the different electric charges of the incident and scattered beams make a 0° measurement experimentally possible . The simplest among the nucleon-nucleus charge-exchange reactions is p3H -> n3He. Outside the -rr-exchange small-tpeak, the charge-exchange p3H- n3He reaction is still very interesting because, together with already available elastic nucleon-nucleus scattering data, it makesit possible to test, within the Glauber-theory framework, the nuclei wave functions and the nucleon-nucleon amplitude set deduced from pp and pn phase-shift analysis. Microscopic analysis of the elastic reactions based on the spin/isospin dependent Glauber theory has already been proposed ~'~. But we believe that since the charge-exchange reaction amplitude can be expressed as the difference of the elastic reaction amplitudes A(p3H -' n3He) = A(p3He-> p3He) - A(p3H --' p3H),

the differential cross section p3H-> n3He should be very sensitive to the difference between the np and pp amplitudes and also between the 3H and 3He wave functions, bringing new constraints into the analysis. Except for a large angle 156 MeV measurement 11), the charge-exchange differential cross sections reported here are, to our knowledge, the first to appear in medium-energy physics. Previous measurements of the elastic differential cross sections have been made at 415 MeV and around 600 MeV for p3He -> p3He [refs. lz-la)] and around 600 MeV for p3H->p3H [ref. 13)]. We report in this paper measurement at Saclay with the Saturne I synchrotron of the charge-exchange 3 p H-s n3He reaction at 415 and 600 MeV and of the elastic p3H reaction at 415 MeV. So, two complete sets of differential cross sections for the proton mass-3-nuclei reactions (i.e. p3H-> p3 H, p3He-> p3He and p3H -~ n3He) are now available, the former at 415 MeV and the latter at 600 MeV. 2. Ezperlment The measurement of the p3H-r nzHe cross section could be designed in different ways : either using a neutron beam and a 3 He target, or a proton beam and a tritium target, or lastly a triton beam and a hydrogen target . The first solution was dropped because of the technological difficulty of matching the size of a 3He target with that of a high intensity neutron beam, and we discarded the second solution to avoid the

p3 ii-~rt3 He, p3Ii-rp3 Ii

453

problem associated with a highly radioactive tritium target . So we chose to measure the differential p3 H~ n3He and p3 H ~ p3H cross sections using a quasi-monokinetic triton beam obtained by stripping an a-particle beam extracted from Saturtte I. The intensity of the triton beam was a few times 10' nuclei per burst, its relative momentum spread was t1.5% and the size of the beam spot at the hydrogen target was 5 cm x 1.5 cm. The angular divergence was t0.4°. A detailed description of the beam can be found in a previous publication ts) . The final nucleus 3 He or 3 H emitted in the reaction was detected in an achromatic magnetic spectrometer fully described elsewhere t6) . The identification of the detected nucleus was achieved by a measurement of its time of flight and a selection on its differential energy loss . At a fixed laboratory angle, the final nucleus momentum spectrum allows a clear separation of the two-body reaction to be studied. A momentum spectrum of the 3He nuclei emitted at 0.2° in the charge exchange reaction p3H~n3He at 3 GeV/c is shown in fig. 1. The width of this distribution is essentially due to the momentum

9, .nz'-

.G

in

GeV~c

3He momentum spectrum in the reaction p 3 H-. n3 He at 415 MeV per nucleon and near 0°. This spectrum is very similar to that of the incident triton beam . The continuous line is an empirical gau~ian-like fit of the data. F& 1 .

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spread of the incident triton beam . The shape of the distribution and in particular its slight asymmetry has been satisfactorily explained by a Monte Carlo reconstruction of the beam trajectories ls). An empty target effect has been measured and subtracted from the raw spectra. This correction was always less than 15% . In order to measure very forward cross sections, a careful check of the 0° direction was made, observing in wire chambers the direct beam trajectory entering the spectrometer . For larger angles, two-body reactions previously measured with the same apparatus l''1g) bring kinematic constraints which determine the laboratory angles, in the 3°-15° range, with an accuracy of t0.2°. The spectrometer transmission factor, in the angle-momentum plane, has been calculated by a simulation program taking into account multiple scattering as well as detected nuclei energy losses . The uncertainty on this acceptance is about t4% . Incident beam monitoring was done carefully by cross checking information from two independent devices: (i) a plastic scintillation counter was placed in the triton beam. The flux was determined by integration of the output. (ü) a two counter telescope counted the secondary particles emerging at a fixed angle from the hydrogen target . The absolute calibration of these monitors has been achieved by comparing their results with those of a graphite irradiation method. An experiment was specially designed to measure the 11 C production cross section in 3H-1ZC interactions'. We estimate the precision of the incident triton beam intensity to be better than 10% . 3. Rewlts Our results are displayed in tables 1 to 3 respectively for the elastic p3H differential cross section at 415 MeV per nucleon and the charge-exchange differential cross section at 415 MeV and 600 MeV per nucleon. The 600 MeV results are not absolute measurements . Because the impulse approximation appears to be a very good tool to link together the small transfer p 3li -> n3He and np -> pn chargeexchange reactions (see next section) we decided to normalize our 600 MeV p 3H charge-exchange data, at 0°, on the np-> pn data of ref. 2). The errors shown on the four-momentum transfer squared t come mainly from the momentum and angular spreads of the incident beam and from the scattering angle uncertainty. Besides the statistical errors of dv/dt displayed in the tables, the 415 MeV data are affected by a t 11% systematic error resultingfrom the uncertainties in the beam intensity and the spectrometer acceptance . The charge-exchange differential cross sections at 415 and 600 MeV per nucleon exhibit identical shapes (fig. 2): a steep slope in the very small transfer region [~t~ < 0.02 (GeV/c)Z] becoming progressively gentler as ~t~ increases. The width of the forward peak is a signature of the ~r-exchange just as in the np->pn process.

p3H-~n 3He, p3Fi-"p'H

4SS

The elastic p3 H data at 415 MeV per nucleon clearly exhibit the single-scattering and double-scattering regions (fig. 3a). For comparison, the available elastic p3 He data in the same energy region are displayed in fig. 3b . The destructive interference which is responsible for the t -~ -0.30 (GeV/c)Z dip in the 600 MeV p3He and p3 H elastic scattering appears to be less important at 415 MeV in p3 He as well as in p3H, although the existence of a minimum near t = -0 .4 (Gev/c) 2 in this last differential cross section cannot be ruled out. Figs. 3a and 3b show that the shape of the 415 MeV elastic data is intermediate between those of the 600 MeV and 156 MeV data tt): as the energy increases the minimum deepens and its position shifts toward lower transfers. Twst.E 1 p3H-+p3H at 415 MeV per nucleon

-t [(GeV/c)Z]

dt [(GeV/c) Z]

0.045 0.096 0.168 0.261 0.287 0.345 0.376 0.442 0.535 0.596 0.686

0.01 0.015 0.019 0.024 0.026 0.028 0.029 0.033 0.034 0.038 0.038

dt

[mb~ (GeV/c)-= ] 140.9 36 .07 8.56 1.21 0.781 0.431 0.243 0.212 0.128 0.108 0 .050

Error on

d

5.5 1 .44 0.37 0.06 0.037 0.023 0.014 0.013 0.007 0.008 0.006

TwHire 2 p3I3in 3Fie at 415 MeV per nucleon

-t [(GeV/c)Z] 0.0002 0.0014 0.004 0.013 0.026 0 .045 0.069 0.098 0.131 0.170 0.215 0.264 0.381

dt [(GeV/c) Z] ~

0.0006 0.002 0.003 0.005 0.008 0.010 0.012 0.015 0.017 0.020 0.023 0.025 0.031

dt [mb~ (GeV/c) -Z] 138.3 130.8 99.8 47.2 35 .18 18 .61 9.57 3.77 1.48 0.821 0.461 0.333 0.165

Error on 5.5 5.3 4.0 2.0 1.62 0.82 0.42 0.17 0.07 0.038 0.023 0.019 0.010

d

456

G. BIZARR et nl. TASr.t? 3 p~I ~ n3üe at 600 MeV per nucleon

-t [(GeV/c)2 1

dt [(GeV/c)~)

dQ [mb " (GeV/c)-~] dt

0.0003 0.002 0.012 0.030 0.055 0.088 0.129 0.178 0.234 0.298 0.370 0.493

0.0006 0.002 0.004 0.007 0.009 0.012 0.015 0.018 0.020 0.024 0.028 0.030

92.9 73.4 37.8 18.73 7.29 2.83 0.686 0.436 0.193 0.125 0.095 0.060

Error on

Q dt

3.7 2.94 1.55 0.75 0.29 0.12 0.029 0.021 0.011 0.008 0.005 0.006

4. Interpretation 4.1 CHARGE-EXCHANGE DATA

In the impulse approximation frame, the p3H-> n3He differential cross section is proportional to the product of the np-> pn differential cross section and the nuclear form factor. Taking as a first approximation the same radius R (expressed in terms of the mean squared nuclear radius (rN) by Rz =~( rzrr)) for the tritium and 3He nuclei and assuming that due to the Pauli exclusion principle only one of the tritium neutrons can participate in a 0° charge exchange, we get: ~(p3H ~ n3He)

dt

= dQ(np ~pn) e`a ~ /z dt '

With R =1 .5 fm and using the np-> pn cross sections of ref. z), we obtain the fits drawn in fig. 2b. The agreement with our data at small-t is fairly good. We may also extract from our small-t 415 MeV data the ~3He3He coupling constant fz(~3He3He). Keeping in the p3H->n3He and np->pn cross section calculations the only ~r-exchange contribution, we find that the ratio of these two cross sections, at the same incident energy, is simply equal to fz(~3He3He)/fz (~rfN~ [ref. z~]. Fig. 4 shows the experimental values of [dQ(p3H-> n3He)/dt]/[dQ(np->pn)/dt] at 415 MeV and as a function of t, the np-~pn data being those of ref. z). The extrapolation of this ratio to the ~r-pole t = m ~ is expected to give fz(~3He3He)/fz(~NN). With a linear extrapolation we find 0.92 t 0.11 . This value is far from that of ~0.5 derived recently zt .zz) : it is clear in fig. 4 that so low a value is probably not compatible with a smooth extrapolation of [d~(p3H-> n3He)/dt]/[dQ(np -ipn)/dt] outside the physical regiop . On the other hand, the

p3H-" n 3He, p3H-" p3Fi

457

(GeV~c ~~ Fg. 2 . Charge-exchange p 3 H-" n3 He diäerential cross sections : triangles denote 415 MeV per nucleon and circles denote 600 MeV per nucleon (this experiment) ; and squares denote 156 MeV per nucleon [ref . ir )J " (2a) The dashed line denotes the Glauber model, and the solid line the same model without interference effects. (2b). Small-t impulse approximation fits . The values of the parameters used in the calculation are : Q = 28 mb, a = 2.0 (GeV/c)-~, p s 0.6, R =1 .5 fm at 415 MeV ; v = 38 mb, a = 2 .5 (GeV/c)-Z, p =-0.1, R =1 .5 fm at 600 MeV .

value of 1.30 derived in recent literature by a different method 23) cannot be completely ruled out by our data . To describe the behaviour of ourcharge exchange data at larger ~t~, we have to take into account the double and triple scattering terms which arise when the np ~ pn charge exchange is accompanied by one or two elastic nucleon-nucleon scatterings . A rigourous analysis should of course use the spin-dependent nucleon-nucleon amplitudes to describe simultaneously the three differential cross sections p 3H ->

1

.2

.3 in

.4

.5

.6

.7

(GeV~c)~

Fg . 3a : Elastic p 3H- p3 H differential cross sections. The symbols are as follows : triangles, 415 MeV per nudeon (this experiment); plus signs, 600 MeV per nucleon [ref . ~] ; squares, 156 MeV per nucleon [ref. ")] . The oontinuoue line is the result of a Glauber-model calculation at 415 MeV with the following values of the parameters: v = 28 mb, a = 2.0 (GeV/c) -Z , p = 0 .6.

n3He, p3H- " p3H and p 3He-~p3He . Such an analysis is underway and will be published later ti`) . VVe shall limit ourselves here to a crude spin/isospin independent Zs) Glauber analysis of the nucleon-nucleus charge-exchange process : This formalism, which in its first-order term reduces to the impulse approximation, makesuse of

p3 H-~n3He, p3 Hip3H

1000

459

b

100

10 c tr

b

t, ~ o +

1.

0

++++ i

v

o

+ ++ ++~

+,~+. + 0

.1

.2

.3 -t

.4 in

.5

.ß

.7

(GeV/c) 2

Fig. 36. Elastic p3 He-" p3He ditierential cross sections at 156 MeV per nucleon [ref. ll )] (s9uares), 415 MeV per nudeon [ref. 14)] (triangles), 600 MeV per nucleon [ref. ~] (plus signs).

the np~pn amplitudes fa =(t). To extract these amplitudes from the np ~ pn cross sections, we have assumed that f~(t) which is purely real when the only exchange term is considered, remains real in the whole t-range of our experiment . We have parametrized f~(t) as a sum of exponential forms f~(t)=E,_t .a a, e~~2 and the a, and ß, real ooefftcients have been adjusted on the np data of ref. Z). For the elastic

G. BIZARR et aL R R . ~ [P ~FI ~ n ~Hs] / ~ [p n _ np]

et 416 MeV

L

Ob

0

_J02 ror~n

0

,02

_t

,04

in (GeV/c)

Fg . 4 . R~

doip3H-~ n3Fie)/dt at 415 MeV dv(np i pn)/dt

The solid circle denotes the linear extrapolation at the ~r pole which gives : Ro =~(~~~ ) = 0.9210.11 . The cross, diamond and triangle give the value of Ro found in refs . si .~ .~) respectively.

nucleon-nucleon amplitudes, we used the standard forms frlx(t)=K

o(1+tp) ~N2, 4~r

where o~, a and p are respectively the total cross section, the forward elastic peak slope and the forward real amplitude to imaginary amplitude ratio . Using these simplified expressions for the amplitudes and gaussian wave functions for the 3He and 3H nuclei, the single, double and triple scattering terms which contribute to the phi ->n3He process can be analytically worked out zs) . The results of the calculation are shown in fig. 2a. Sizable destructive interference effects are predicted by this model, in complete contradiction to the data. This result may be interpreted as a proof of the importance of the spin and isotopic spin effects: a spin and isotopic spin~ependent analysis should introduce a large number of orthogonal amplitudes,

p3Ii-" n3 He, p 3ii-p3 H

461

leading to a reduction of the interference effects. Ignoring completely the interference effects strikingly enablesoursimple model to describe satisfactorily the data, as is shown in the full line in fig. 2a. 4.2 . ELASTIC DATA

An attempt to describe the elastic differential cross section p3H in the spin/isospin independent Glauber-model framework with gaussian parametrizations of the nucleon-nucleon amplitudes and of the tritium wave function faces a difficulty already met in similar intermediate-energy nucleon nucleus or nucleus-nucleus data ~): the destructive interference between the single and double scatterings is much larger than in experimental data, even when the Coulomb interaction is taken into account. The only way to reduce the size of this interference is assigning parameter p-values definitely larger than those deduced from nucleon-nucleon phase-shift analysis : for instance, the fig. 3a curve is obtained assuming p~ = 0.67 instead of 0, which is the current 415 MeV value of this parameter z') . Here again neglecting the spin effects probably overestimates the interference term .

5. Cond~sion In order to measure for the first time intermediate energy proton-triton charge exchange differential cross sections, we developed a quasi-monokinetic triton beam at Saclay . In the small transfer region, these cross sections are in good agreement with the impulse approximation hypothesis using the Saclay np charge-exchange data and a gaussian nuclear form factor . A naive derivation ofthe ANN to ~3He3He coupling constants ratio leads to a value compatible with 1. The elastic proton-triton differential cross section was also measured at one energy . Putting together our data and previous results on p3He and p3H elastic scattering two complete sets of differential cross sections, p3H- P3H~

p3He -~ p3He, P3H-i n3He, are now available at 415 and 600 MeV. Acrude spin/isospin independent Glaubermodel analysis shows that the charge-exchange data are not well described unless interference effects are discarded. We conclude that the spin effects are too important to be neglected. Adetailed spin/isospin dependent analysis intending to describe simultaneously the two sets of data is now underway . As a last remark let us point out that, due to the importance of the spin effects, polarization measurements in the elastic and charge-exchange channels should certainly be of great interest .

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G. BIZARR et al.

We are indebted to Mr R. Schcen and to the crew of Saturne I for their contribution in the setting up of the triton beam . We are grateful to Professor B. Diu for fruitful discussions. We also acknowledge Dr J. Duchon, Mr P. Guillouet and Mr G. Simonneau for their technical support during the whole experiment. References 1) K. Erkelenz, Phys. Reports 13 (1974)191 2) G. Bizard, F. Bonthonnesu, J. L. Laville, F. Lefebvrea, J. C. Malherbe, R. Regimbaitt, J. Duflo and F. Plouin, Nucl. Phys . BSS (1975) 14 3) P. F. Shepard, T. J. Devlin, R E. Mischlee and J. Salomon, Phys . Rev. D10 (1974) 2735 4) B. E. Bonner, J. E. Simmons, C. L. Holles, C. R. Newsom, P. J. Riley, G. Glass and M. Jain, Phys. Rev. Lett. 41(1978) 1200 S) H. R. Barton, N. W. Reay, K. Reibel, M. Shaevitz, N. R Stanton, M. A. Abolins, P. Brindza, J. A. J. Mattheros, R Sidwell, K. W. Edwards, G. Luxton and P. Kitching, Phys. Rev. Lett 37 (1976) 1656, and references therein 6) P. K. Williams, Phys . Rev. 181 (1969) 1963 7) G. Bizard and B. Diu, Nuovo Cim. 23A (1975) 467. 8) R. Frascaria, D. Legrand, V. Comparat, M. Monet, N. Marty and A. Willie, Nucl. Phys. A264 (1976) 44S 9) L. Meritet, Thesis, Clermont-Ferrand (1977) 10) N. P. Goldstein, A. Held and D. G. Stairs, Can. J. Phys . 48 (1970) 2629 11) H. Langevin-Joliot, Ph . Narboni, J. P. Didelez, G. Duhamel, L. Marcus and M. Roy-Stephan, Nucl. Phys . A158 (1970) 309 12) E. T. Boschitz, W. R. Roberts, J. S. Vincent, M. Blecherf, K. Gotow, P. C. Gugelot, C. F. Perdrisat, L. W. Sroenson and J. R. Priest, Phys. Rev. C6 (19'72) 457 13) J. Fein, J. Garden, A. Lefoit, L. Meritet, J. F. Panty, G. Peynet, M. Querrou, F. Veuille and B. Ille, Nud. Phys. A262 (1976) 413 14) R. Frascaria, L. Bimbot, Y. le Bornec, M. Monet, B. Tatischeff, N. Willllis, D. Logrand, R Beurtey, G. Bruge, P. Couvert, D. Garrets, G. A. Moss and Y. Tonion, Proc . 7th Int. Conf . on high-energy physics and nuclearétructure, Zürich 1977, p. 218 1S) G. Bizard, J. L. Laville, C. le Brun, J. F. Lecolley, F. Lefebvres, A. Osmont, R. Regimbart, J. C. Stecl®eyer, J. Berger, J. Dutio, L. Goldzahl, J. Oostens, F. Plouin, F. L. Fabbri, P. Pioorca, L. Satte and C. Scbaerf, Nud. Instr. 166 (1979) 323 16) G. Bizard, C. le Brun, J. Berger, J. Duflo, L. Goldzahl, F. Plouin, J. Oostens, M. van den Bossche, L. Vu Hai, F. L. Fabbri, P. Picozza and L. Satte, Nucl. Phys. A285 (1977) 461 17) J. Berger,J. Dufio, L. Goldzahl, F. Plouin, J. Oostena, M. van den Bossche, L. Vu Hai, G. Bizard, C.le Brun, F. L. Fabbri, P. Picoda and L. Satte, Phys . Lett . 63B (1976) 111 18) J. Berger,J.Duflo, L. Goldzahl, F. Plouin,J.Oostens, M. van den Bossche, L. Vu Hai, G. Bizard, C.le Brun, F. L. Fabbri, P. Picoz7a and L. Satte, Phys. Rev. Lett . 37 (1976) 1195 19) J. Berger, J. F. Leoolley and H. Quechon, to be published 20) C. W. Kim and H. Primaleoff, Phys. Rev. 139 (1965) 1447 21) O. Dumbrajs, Phys . Left. 78B (1978) 24 22) C. Leroy and J. Pestisu, Phys. Left . 82B (1979) 31 23) H. Primaleoff, Nucl. Phys. A317 (1979) 279 24) G. Bizard and A. Osmont, to be published 2S) Li Yang Kuo, Liu Haien Hui and Ma Wei Hsing, Scientia Sinica, Vol. XVIII N° 1, 38 (1975) 26) J. Berger, J. Duft, L. Goldzahl, J. Oostens, F. Plouin, F. L. Fabbri, P. PiooTra, L. Satte, G. Bizard, F. Letebvres, J. C. Steckmeyer and D. Logrand, to be published 27) W. Grein, Nucl . Phys. B131 (1977) 2SS