Inelastic electron scattering from 6Li near the t-τ threshold

Nuclear Physics

A341 (1980) 13 - 20; @

North-Holland

Publishing

Co., Amsterdam

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

INELASTIC ELECTRON SCATTERING FROM 6Li NEAR THE t-r THRESHOLD J. C. BERGSTROM Saskatchewan

Accelerator

Laboratory,

University Received

sf’ Saskatchewan,

24 January

Saskatoon,

Canada S7N 0 WO

1980

Abstract: The form factor for excitation of the t-r continuum in ‘Li has been measured within 4 MeV of threshold for momentum transfers q = 0.48 and 0.58 fm-‘. The results are in good agreement with the Cl form factor calculated in the framework of a t-r cluster model with a spectroscopic factor 0’0 = 0.67.

E

NUCLEAR

REACTIONS

6Li(e, e’), E = 102, 123 MeV; measured deduced form factor. t-3He cluster model.

u(E;

&,

0). 6Li

I

1. Introduction It is well known that the 6Li ground state exhibits both cr-d and t-r clustering degrees of freedom, and a variety of reactions have been used to estimate the corresponding spectroscopic factors. Most studies of the t-r parentage indicate 0; = 0.6-0.8. For example, the reaction 6Li(p, P~)~H [ref. ‘)I when analyzed with Woods-Saxon wave functions, and the radiative reactions 3H(r, y)6Li [refs. ‘3 3)] and 6Li(y, t)3He [ref. “)I when analyzed using resonating-group wave functions, give fairly consistent results. Nevertheless, the deduced 0; are very dependent on the wave functions and can vary by factors of 2 or more, as demonstrated in ref. ‘). In a previous paper ‘) we presented measurements of the form factor for excitation of the cr-d continuum in 6Li near threshold (1.47 MeV). A satisfactory description of the data was given by an g-d cluster model with no renormalization (i.e., B&d) N 1). The transition multipolarities were shown to be a mixture of CO and C2. In this paper, we present the first measurements of the continuum form factor for 6Li(e, e’)tt near threshold (15.8 MeV), and discuss the results in terms of a simple cluster model. This experiment differs in two significant respects from previous studies of the t-r structure of ‘jLi. First, the electron scattering angle was chosen to emphasize the longitudinal, or Coulomb, interaction, while the radiative capture and photonuclear reactions are transverse in nature. Second, the momentum transfer q is far from the “photon point” q = w, so the cross section should be more sensitive to the short-range aspects of the wave functions. The longitudinal electrodisintegration cross section near threshold can, in 13

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principle, contain CO, Cl and perhaps C2 components. Therefore, we have measured the cross section at two momentum transfers, q - 0.5 and 0.6 fm-‘, since our theoretical investigations suggest that the q- and o-dependence of the CA continuum form factors are quite distinct in this region. For example, the monopole and quadrupole form factors are expected to reach their maxima at q - 0.9-l. 1 fm- l, while the maximum of the dipole form factor is expected at q - 0.6-0.7 fm- l. We have calculated the differential form factors within the framework of a t-r cluster model of 6Li, using f?; as given by our fit to radiative capture data. The present (e, e’) results are shown to be in good agreement with the Cl differential form factor predicted by the model. 2. Experimental details and analysis This work was done at the electron scattering facility of the Saskatchewan accelerator laboratory. The target was 99 y0 isotopically enriched 6Li metal, rolled under oil to a thickness of 30 mg/cm’. Electron scattering spectra were obtained for two incident energies, 101.8 MeV and 122.7 MeV, at a scattering angle of 60”. The corresponding momentum transfers are q = 0.48 fm-’ and 0.58 fm-’ at 16 MeV excitation. Data were obtained between 12 and 20 MeV excitation with a statistical accuracy of 0.6-0.8 % per 0.10 MeV. Overall momentum resolution was about 0.2 %.

Fig. 1. Electron scattering spectrum for ‘Li in the excitation energy region w = 12-20 MeV. The data are presented as a total differential form factor, defined by eq. (1). The scale is exaggerated to clearly display the t-r continuum starting at 15.8 MeV, indicated by the arrow. The line represents the estimated total contribution from other processes, as discussed in the text.

J. C. Bergstrom 1 Inelastic

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The spectra were normalized to the elastic peaks, which in turn were calculated in the Born approximation using the Stanford charge density parameters 6). The usual radiative and straggling corrections were applied to the experimental elastic peak areas, and checks were made to ensure that the corrected values were independent of the integration cutoff limits. Finally, the inelastic spectra were converted to differential form factors F’(q, w), which are related to the differential cross section by

(1) where

(2)

6-d4

E, = 122.7 MeV 4

q =0.58

f rn-

’

w(MeV) Fig. 2. Differential form factor for the t-T breakup of 6Li. The excitation energies extend to about 4 MeV above threshold. The curves are the Cl form factors predicted by the t-r cluster model with e:, = 0.61.

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J. C. Bergstrom / Inelastic electron scattering

Here, q is the 3-momentum transfer, o is the excitation energy in the nuclear frame, and M is the mass of the target nucleus. The other symbols have their usual meaning, and ri = c = 1. In applying eq. (l), we are assuming there is negligible transverse contribution to the experimental data. As seen in fig. 1, the spectra from 12-20 MeV are more or less featureless, consisting mainly of the elastic radiation tail plus the various 2- and 3-body continua. The onset of t-r breakup shows as a sudden change in slope near the threshold at 15.8 MeV excitation. It is difficult to make a theoretical estimate of the total “background” underlying the t-r continuum, since the calculated elastic radiation tail accounts for only about 50 % of the observed strength below threshold. Therefore, the following empirical estimate was used. Since the spectra decrease almost linearly from 13 to 16 MeV, a linear tit was made in this region and extrapolated to higher excitation energies. When this empirical function is subtracted from the data, we obtain the differential form factors for the t-z continuum shown in fig. 2. We have neglected any curvature in the background function, and although this is not significant within a few MeV of threshold, it could affect the results at the higher excitation energies. However, above 21.3 MeV excitation, the t-d-p continuum starts contributing, so interpretation of the data more than 5 or 6 MeV from the t-r threshold is questionable in any case. Some of the structure apparent in the 14-16 MeV region of fig. 2 is real, corresponding to excitation of the 15.1 MeV (1’) and 16.1 MeV (2+) levels in ’ 2C from residual oil on the target. The differential recoil between ‘jLi and “C causes the shift in peak positions noticeable in the two figures. A small “peak” occurs in both spectra at u = 15.4 MeV, but the statistical accuracy is not sufficient to ascertain that it is real. There are no known narrow levels in this region in 6Li. 3. Theoretical considerations

and comparison with experiment

A formally correct treatment of the 2-body breakup of 6Li includes antisymmetrization of the wave functions with respect to all nucleons, in which case the ground-state function would contain the various cluster parentages implicitly. This leads to l- and 2-body exchange terms which are usually tedious to evaluate because of the multiple integrals involved. The calculation simplifies considerably if we approximate the effects of antisymmetrization by replacing the ground-state wave function with the cluster model function ‘y = U-(IC/1 0 $2)s 0 u91J> (3) where the parentage is now explicitly introduced by 8,, and I,$~represents the internal wave function of cluster i, in the present case 3H and 3He. The relative motion of the clusters is described by #r(r), where r is the relative position of the respective centers of mass.

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The ground-state cluster configuration is %, (neglecting the small 3D, component), so the Coulomb-excited continuum is necessarily 3L, where L = A is the transition multipolarity. Assuming the final-state interactions are independent of J, the differential Coulomb form factor may be written

1 2

RT(k

r)j,(~vK&9r2dr

,

(4)

where R,(r) is the radial part of 4,,(y), R,(k, r) is the continuum radial wave function, k is the relative t-r momentum and p is the reduced mass. The cluster form factors are f, and f,, taken here to be simple Gaussians : f, = f, = e-4%16.

(5)

We ignore the slight difference in the cluster radii, and adopt r. = 1.87 fm, the rms charge radius of 3He. Our model for R,,(r) is the one-node (i.e., 2s) eigenfunction of a Woods-Saxon potential designed to give the correct t-z binding energy and intercluster separation. The cluster separation R is determined from the 6Li charge radius through the relation rti = ri+aR2,

(6)

and taking rLi = 2.56 fm [ref. 6)], we obtain R = 3.50 fm. In detail, the potential is V,(r) = -v,O[l+exp~-J’+V,OU,, where I$’ = 36.1 MeV, c = 0.50 fm, t = 5.01 fm, and 0.72(3 -ar2) V Coul =

/i 2.88/r MeV

MeV

r 5

2fm

r 2

2fm.

(8)

The continuum wave function R,(k, r) generated by a potential of the form eq. (7) has the usual asymptotic normalization krR,(k,

r) +

e-6”[F,cos6,+G,sin6,],

(9)

where FL and G, are the regular and irregular Coulomb wave functions. We now discuss the CO, Cl and C2 form factors for various final state potentials and compare with the experimental data. For reasons of orthogonality, the CO continuum must be generated by the same potential as the ground state. The resulting form factors Fi(q, w) were found to increase very rapidly in the q-region of the present experiment, for example by more than 50 % from q = 0.48 to 0.58 fm- ‘. As a function of w, Fi(q, o) rises quickly to a maximum within a few MeV of threshold, and then slowly declines, resembling the cc-d CO continuum form factor 5). These properties were found to be quite

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general, as observed by considering alternate Woods-Saxon potentials constrained only by the intercluster radius. The q-dependence of the C2 form factor is nearly as rapid as that of the CO form factor in the region of our measurements. Again, this is relatively independent of the final state potential, even in the limit of no interaction (other than Coulomb). However, F:(q, w) reaches a maximum at somewhat higher excitation energies. Inspection of the data in fig. 2 shows a slight increase in the differential form factor between q = 0.48 and 0.58 fm- ‘, but the increase is much less than the preceding form factors would indicate. Since the o-dependence is also contrary to theory, it appears the CO and C2 contributions are not significant. Finally, we turn to the Cl form factor. Here, we have relied on the reaction 3H(z, y,J6Li to provide some information on the t-t interaction in the 3P wave continuum, since the energy dependence of this reaction is quite sensitive to the effective L = 1 potential and the angular distribution of the radiation is consistent with an El transition. Our procedure was to assume the same c, t parameters as in eq. (7) but vary Vy and the normalization 0: until reasonable agreement was achieved with the capture data of Ventura et al. 3, in the region o = O-10 MeV. This gives Vy = 15.5 MeV,

0; = 0.67kO.03,

(10)

Fig. 3. Total El cross sections for the capture reaction 3H(7, yJ6Li leading to the ground state. The solid lines delineate the measurements of Ventura et al., converted here to a total cross section. The dashed line is our tit with the t-r cluster model treating 0; and Vy (the strength of the continuum ‘P potential) as free parameters. The energy dependence of o, determines Vy and 0; is the required normalization. We find 0; = 0.67kO.03.

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where the uncertainty reflects the experimental errors only. The corresponding capture cross section is compared with the data in fig. 3. The Cl form factors, shown in fig. 2, compare favorably with the data as a function of both q and o. Actually, a slight increase in the background function (sect. 2) would give even better agreement. On the basis of this comparison we conclude the Coulomb disintegration cross section is predominantly Cl in character in the momentum transfer region of this work. 4. Discussion The differential form factor for electroexcitation of the t-z continuum in 6Li has been measured up to 4 MeV above threshold, at momentum transfers q = 0.48 and 0.58 fm- ‘. The results are in good agreement with the Cl form factor predicted by a t-z cluster model with a Woods-Saxon interaction. The strength of the finalstate interaction and the spectroscopic factor were determined by fitting to the radiative capture cross section of Ventura et al. 3). Our estimate of the spectroscopic factor, 0: = 0.67, is lower than, but consistent with, the value 15: = 0.8 + 0.2 found by Ventura et al. who employed the resonatinggroup model of Thompson and Tang ‘). The difference may in part originate in the ground-state rms cluster separation R of the two models, since the radiative capture cross section is quite sensitive to this quantity. This can be seen by considering a simple model. For a 2s harmonic oscillator ground state and an undistorted P-wave continuum, the total capture cross section to the ground state may be written 27x2 cxk cc = ~ 2 F;(k,, co), P k,-b

(11)

where

f’:(k,, 4 =

&

pky’R4y3( 1 -$y2)2e-~z,

(12)

is the Cl form factor at the “photon point” q = k,. In the above k, is the photon momentum, b is the t-z separation energy, y ’ = +k2R2, and the other symbols have their previous meaning. Combining eqs. (11) and (12) and using k, = b + k2/2p, one finds that (T, cc R6 in the region of y where the cross section attains its maximum value. Actually, the dependence on R is reduced somewhat when the final-state interaction is included, but does not alter our conclusion that a meaningful estimate of 0; requires model wave functions with realistic radii. As far as we are aware, the radius of the resonating-group model is not given in the literature. We now comment on the photodisintegration reaction 6Li(y, t)3He. Shin et al. “) obtained (3; = 0.68 by comparing their experimental cross section with the resonating-group model of Thompson and Tang. The apparent agreement with the present spectroscopic factor is fortuitous since our model (with 0; = 0.67) yields

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an El cross section about 25-30 % larger than experiment. According to Skopik *), the confidence level of the photonuclear data is about 15 % and the cross sections of ref. “) should probably be considered as the lower limit of the error band, but this is still not sufficient to remove the discrepancy between the photonuclear measurements and the radiative capture and (e, e’) experiments. Note that, in principle, the former cross sections should be related by detailed balance, independent of any model. The smaller spectroscopic factor obtained by normalizing the present model to the data of Shin et al. would imply significant contributions, other than Cl, to the (e, e’) cross sections. Such contributions could come from transverse interactions (assumed negligible in the present analysis). However, preliminary results from a 180” scattering experiment performed at the Bates accelerator laboratory show no evidence for a transverse component large enough to influence our 60” measurements by more than 5 %. To summarize, interpretation of the radiative capture cross section in terms of a simple t-z cluster model leads to good agreement with the electrodisintegration form factor near threshold, but the same model cannot explain the photodisintegration cross section. References 1) P. G. Roos, D. A. Goldberg, N. S. Chant, R. Woody, III and W. Reichart, Nucl. Phys. A257(1976) 317 2) 3) 4) 5) 6) 7) 8)

A. M. Young, S. L. Blatt and R. G. Seyler, Phys. Rev. Lett. 25 (1970) 1764 E. Ventura, J. R. Calarco, W. E. Meyerhof and A. M. Young, Phys. Lett. 46B (1973) 364 Y. M. Shin, D. M. Skopik and J. J. Murphy, Phys. Lett. 55B (1975) 297 J. C. Bergstrom and E. L. Tomusiak, Nucl. Phys. A262 (1976) 196 G. C. Li, I. Sick, R. R. Whitney and M. R. Yearian, Nucl. Phys. Al62 (1971) 583 D. R. Thompson and Y. C. Tang, Nucl. Phys. A106 (1968) 591 D. M. Skopik, private communication