Pionic fusion to a halo state, the d(α,6Li∗ )π0 reaction studied close to threshold

25 May 2000

Physics Letters B 481 Ž2000. 165–170

Pionic fusion to a halo state, the dž a ,6 Li ) / p 0 reaction studied close to threshold M. Andersson a , Chr. Bargholtz a , K. Fransson a , L. Holmberg a , K. Lindh a , a L. Martensson , I. Sitnikova a , P.-E. Tegner Engblom b, G. Weiss a , ˚ ´ a, P. Thorngren ¨ a,1 K. Wilhelmsen Rolander a

Department of Physics, Stockholm UniÕersity, Box 6730, S-113 85 Stockholm, Sweden Department of Radiation Sciences, Uppsala UniÕersity, S-751 21 Uppsala, Sweden

b

Received 3 March 2000; received in revised form 11 April 2000; accepted 11 April 2000 Editor: J.P. Schiffer

Abstract The dŽ a ,6 Li )3.56 .p 0 reaction has been studied at Ec.m.s 1.2 and 1.9 MeV above threshold with an alpha-particle beam incident on a deuterium cluster-jet target in CELSIUS. Complete differential cross sections were measured at both energies, integrated to s s 228 " 6 q 70 nb and 141 " 12 q 42 nb respectively. Observed large anisotropies are discussed in relation to the cluster structure of the 6 Li ) halo. q 2000 Elsevier Science B.V. All rights reserved. PACS: 25.10.q s; 25.40.Ve; 25.60.Pj; 21.60.Gx Keywords: Pionic fusion; 6 Li ) ; Differential cross sections; Total cross sections; Cluster structure; Halo

In a nuclear fusion reaction creating a pion, often referred to as pionic fusion, essentially all of the kinetic energy available in the entrance channel has to be transferred to the meson field. It is therefore natural to envisage the process as one to which a large fraction of the nucleons contribute coherently. Any correlations among the nucleons in the initial and final state wave functions may thus be expected to influence the cross section significantly. Leaving the pŽp,pq. d and pŽd,p 0 . 3 He reactions out of the discussion, only a limited number of experiments on pionic fusion reactions have been

1

E-mail: [email protected]

reported. With only one exception they all involve pionic fusion of 3 He with targets ranging from 3 He to 12 C w1–7x, the exception being a measurement of the cross section for the pionic fusion of two 12 C nuclei w8x. Theoretical treatments in the literature w9–15x stress the importance of the detailed structure of the nuclei involved for the cross section of the pionic fusion process. In their treatment of the 4 HeŽ 3 He,pq . 7 Li reaction Kajino, Toki and Kubo w13x obtained an order of magnitude increase in the cross section using a correlated cluster wave function for 7 Li as compared to the result using a shell-model wave function without correlations. The aim of the present investigation was to use the pionic fusion of a deuteron and an alpha particle

0370-2693r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 0 - 2 6 9 3 Ž 0 0 . 0 0 4 9 6 - 2

166

M. Andersson et al.r Physics Letters B 481 (2000) 165–170

as a probe particularly sensitive to the cluster structure of the isobaric analogue state, at 3.56 MeV excitation energy in 6 Li, of the ground state of 6 He. As both particles in the initial state have isospin T s 0 pionic fusion to the ground and first excited states in 6 Li is forbidden. The lowest T s 1 state of the A s 6 system is the lightest nuclear system exhibiting a halo. For the ground state of 6 He experimental information is available from beta-decay experiments w16x, fragmentation reactions w17,18x, elastic scattering, and nucleon transfer reactions w19–22x. Cluster models of 6 He reproduce the main features well w23–25x but detailed questions about correlations between the halo nucleons remain to be resolved. The isobaric analogue state of 6 He Žin 6 Li. has an equally extended halo structure w26x. Forming this state in a pionic fusion reaction thus offers a complementary means to elucidate the structure of a pronounced two-nucleon halo. The experiment was done at the CELSIUS accelerator and storage ring at The Svedberg Laboratory, Uppsala, Sweden. In this internal-target experiment an electron-cooled alpha-particle beam of average current 2.4 mA was used together with a deuterium cluster-jet target of nominal thickness 1.2 = 10 14 cmy2 . The inclusive dŽ a ,6 Li )3.56 .p 0 reaction was studied at two different beam energies, 417.95 and 420.30 MeV, corresponding to Ec.m .s 1.2 and 1.9 MeV above the absolute threshold in the center-ofmass Žc.m.. frame. At the highest beam energy the second T s 1 state in 6 Li at 5.37 MeV is possible to populate. However, the branching ratio for gamma decay of this level to the ground state is negligible w27x. The recoiling 6 Li ions were detected in a window-less position-sensitive detector telescope situated inside the CELSIUS ring. Very close to threshold heavy reaction products carry most of the beam momentum and therefore travel close to the beam. In order to detect such reaction products a small size zero-degree spectrometer has been installed in CELSIUS w28x. The spectrometer uses the focusing and bending magnets of the storage ring in combination with a detector telescope made of high-purity germanium. Its angular acceptance in the laboratory is approximately "0.68 both vertically and horizontally around 08. The detector telescope, consisting of three detector elements, is inserted into the vacuum of the CELSIUS ring

itself, 6.1 m downstream from the target. Its radial position with respect to the beam is continuously adjustable to match the specific conditions for different experiments. In this particular case the first two detectors were transmission Ž D E . detectors of thicknesses 1.7 mm and 1.1 mm and the third was a thicker Ž2.1 mm. stopping Ž E . detector. The first transmission detector was position sensitive with its contacts divided into 18 horizontal strips of 2 mm width on one side and 66 1 mm wide vertical strips on the other side for measurements of angular distributions with a resolution of approximately 1 mrad. The resolution and energy calibration of the D E and E detectors were determined with the aid of alpha-emitting sources Ž 241Am and 232 U. as well as exploiting the energy deposition of 3 He and 4 He ions in the detectors recorded during the experiment. The resolution of the second D E detector was 0.22 MeV ŽFWHM. and for the E detector 0.21 MeV ŽFWHM.. Data were taken with two different sets of pre-amplifiers for the position-sensitive detector. For the first data set the resolution of this detector was 0.6 MeV and for the second part of the data 1.5 MeV. A nominal value for the luminosity could be calculated from the measured beam current and the nominal target thickness corrected by a factor of 1r3. The size of the correction factor, for a cooled beam, has been independently determined in several measurements w29x. However, for an uncooled or incompletely cooled beam somewhat smaller correction factors have been observed w30x. We judge that, in this case, the correction factor of 1r3 represents an upper limit. The corresponding average luminosity during the experiment was 3 = 10 29 cmy2 sy1 . Using the position information, complete angular distributions could be measured at both energies with acceptances ranging from 100% at 08 and 1808 to 63% Ž34%. around 908 in the c.m. frame at the lowest Žhighest. beam energy. A D E–E spectrum from the second and third detectors recorded at 417.95 MeV energy is shown in Fig. 1. The 6 Li events are indeed very well separated from all other charged particles in these essentially raw data, the only additional requirement being a hit in any of the strips of the first detector. The 6 Li events were selected by putting appropriate gates in the D E– D E–E spectrum. Events with

M. Andersson et al.r Physics Letters B 481 (2000) 165–170

Fig. 1. D E – E spectrum from the second and third detectors at 417.95 MeV beam energy. Different ions are identified.

simultaneous hits in two or more non-adjacent horizontal strips were discarded. The loss of efficiency caused by such double hits was 0.8%. An upper limit on the efficiency loss due to nuclear reactions in the D E-detectors, estimated from w31x is 1.4 %. Thus the total efficiency was close to 98%. In an experiment as close to threshold as in the present case knowledge of the exact beam energy is crucial. The difference in energy between 6 Li ions scattered through 08 and 1808 is a sensitive measure of the beam energy. This fact was utilized in the fits described in the following to accurately determine the beam energy. In order to determine the differential cross section simulated events were fitted to experimental data adopting a Maximum-Likelihood method. Each event in the experimental data was characterized by its energy and position coordinates on the position-sensitive detector. The position information was binned in 4 mm wide vertical bins and 3 mm wide horizontal bins. The bin width in energy was 1 MeV, matching the resolution of the telescope. Examples of experimental energy and position spectra are shown in Fig. 2. The simulated data were generated by a Monte Carlo ray-trace code. The following expression for the differential cross section was assumed: 2

ds

ž / dV

s c .m .

Ý a n Pn Ž cos uc .m . . ,

Ž 1.

ns0

where PnŽcos uc.m . . are Legendre polynomials and uc.m . is the c.m. angle of the excited 6 Li ) ion with respect to the beam. The Li ion is created in an

167

excited state J p s 0q, E ) s 3.56 MeV which decays through an M1 transition to the ground state. This decay, which is isotropically modeled in the simulation, affects the final energy and angular distributions significantly. The size and divergence of the beam and the energy resolution of the telescope were also taken into account in the simulation. The Legendre coefficients, a n , were determined from the fit. The beam energy was also treated as a free parameter in the fitting procedure and the results were 417.95 " 0.07 MeV and 420.30 " 0.07 MeV. The same values, albeit with slightly larger uncertainties, were also obtained from the difference in energy between the c.m. forward and backward peaks in the 6 Li energy spectra. The results from the fits are presented in Table 1 and in Fig. 2. It is clearly seen that the forward-backward asymmetry increases rapidly with beam energy as does the width of the 6 Li energy spectra. For the Legendre coefficients only the statistical uncertainty is given in Table 1, any systematic uncertainty in the luminosity having been omitted. However, as previously argued, the number obtained for

Fig. 2. Energy spectrum at the lowest beam energy Ža., horizontal position spectrum for the same beam energy Žb., energy spectrum for the higher beam energy Žc. and horizontal position spectrum for the higher energy Žd.. For the higher energy, events between 266 and 286 MeV were included in the fit. The filled circles represent the experimental data and the histograms the fitted simulation.

M. Andersson et al.r Physics Letters B 481 (2000) 165–170

168

Table 1 Beam energy and Legendre coefficients obtained from the fits of simulated data to experimental. The uncertainties are purely statistical. Beam energy ŽMeV.

a0 Žnbrsr. a1 Žnbrsr.

417.95"0.07 417.95"0.07 420.30"0.07 420.30"0.07

18.2"0.5 18.2"0.8 11.2"1.0 11.4"1.3

a 2 Žnbrsr.

y2.1"0.8 0, fixed y2.1"0.8 0.2"1.2 y4.8"1.0 0, fixed y4.6"1.0 y1.2"1.5

s Žnb. 228"6 228"10 141"12 144"18

the luminosity represents an upper limit and the lower limit of the luminosity is conservatively estimated to be around 30% smaller than this number. The authors wish to stress that the relation between the results at the two energies is independent of the uncertainty in the absolute luminosity and that the values of the Legendre coefficients and cross sections represent strict lower limits. For both energies the first order coefficients, a1 , are vital to fit the data, while higher order coefficients are redundant. The second order coefficients are nevertheless presented to show the validity of the fits. The present result for the total cross section, s s 228 " 6 nb 1.2 MeV above threshold, is approximately a factor of 10 smaller than that measured for the dŽp,p 0 . 3 He reaction at the same energy w32x. In light of the much larger degree of coherence required in the present process this difference is not surprising. Comparing with the cross sections measured for the 3 HeŽ 3 He,6 Li.pq reaction w1,3x involving the same total number of nucleons we see that they are of a comparable magnitude. However, judging by the measured differential cross sections for the latter reaction it appears that the maximum cross section is reached at a pion c.m. energy of more than 10 MeV whereas for the dŽ a ,6 Li ) .p 0 reaction the cross section decreases by 40% as the pion c.m. energy increases from 1.2 to 1.9 MeV. The only reported observation of pionic fusion to the 0q analogue state is the measurement by Le Bornec et al. of 3 HeŽ 3 He,pq . 6 Li ) 11.4 MeV above threshold w1x. At a c.m. angle of 32.28 these authors observed a cross section of 9.2 " 2.7 nbrsr, i.e. approximately the same cross section we measure 1.9 MeV above threshold in the a q d reaction. This surprisingly large cross section for 3 He q3 He fusion

may perhaps be interpreted as a confirmation of the importance of 3N q 3N clustering in the A s 6, T s 1 system stressed most recently by Arai, Suzuki, and Lovas w33x. They calculate a spectroscopic factor of approximately 0.5 for the t q t configuration in 6 He and in light of the tighter binding of the trinucleon as compared to the di-nucleon it seems reasonable to assume that the relative admixture of t q3 He configurations in the wave function increases with momentum. We measure a strong forward-backward asymmetry for the dŽ a ,6 Li ) .p 0 reaction that grows rapidly with energy. Measured with respect to the momentum of the heavier particle in the initial state the asymmetry has the opposite sign as compared to that observed for the dŽp,3 He.p 0 reaction, i.e. in case of the dŽ a ,6 Li ) .p 0 reaction the pion is emitted preferentially in the direction of the momentum of the heavier particle. At these very low pion energies the mean free path of the pion is long compared to the dimensions of the final state nucleus. The measured differential cross section therefore should not to any significant amount be affected by interactions in the final state. Instead we believe that the specifics of the differential cross section reflect the nuclear structure involved, and in particular the halo structure of the final nucleus. The qualitative features of the measured cross section can be understood in terms of a naive cluster model for the reaction leading to the formation of 6 Li ) . Within such a description the pion is emitted from the deuteron which is transformed into a ‘quasi deuteron’ with T s 1 and J s 0. The pion is then rescattered on the alpha particle which retains its identity. Subsequently the ‘quasideuteron’ and the alpha particle form 6 Li ) . The model is schematically depicted in Fig. 3. Assuming the amplitude of the many-particle pion production and rescattering in the intermediate state to be only

Fig. 3. Model of the pionic fusion reaction.

M. Andersson et al.r Physics Letters B 481 (2000) 165–170

weakly dependent on the final pion momentum the observed pion angular distribution is the result of a projection of the inclusive process onto the final channel. The pion angular distribution would then be dominated by the overlap of the alpha particle and quasi-deuteron wave functions with that of the final state 6 Li ) . In order to show that this description gives results for the angular distribution which are strongly sensitive to the halo wave function and in qualitative agreement with experimental data we calculate the overlap in a simplistic way using harmonic oscillator momentum-space wave functions for the deuteron Ž A s 2. and the alpha particle Ž A s 4., i.e.

F k 1 ,k 2 , . . . ,k A

ž

A

s Ł Ž a'p .

y3 r2

½

exp y

is1

1

ž

2a 2

ki y

p

F Li s F H Ž k 1 ,k 2 . F C k 3 ,k 4 ,k 5 ,k 6

ž

2

ž

'3

k1 y

p Li 6

2

= Ł Ž a H 'p .

/ž

P k2 y

y3 r2

ž

½

p Li

=exp y

6

2

/5 ž

1

2 a C2

½

exp y

is1

= ki y

The form factor is written Fs N Fd Ž k 1 ,k 2 . F H Ž k 1 ,k 2 . Fa k 3 ,k 4 ,k 5 ,k 6

H

ž

A

/5

/

p Li 6

/

1 2 a H2

6

Ł Ž aC'p .

y3 r2

is3

ki y

p Li 6

2

/5

.

Ž 3.

The differential cross section in the c.m. frame Žwhere pd s ypa and pp s yp Li . is then, in the Hartree approximation neglecting the spurious c.m. motion,

/

6

=F C k 3 ,k 4 ,k 5 ,k 6

ž

½

=

ž

g

1

2

i

18

9

gy1 y

b

1 36 k

2

q

1

b

pa2

/ 5½

q

1

k

3

/ Łd k N is1

=A k 2 exp y

=

,

where k i and p are the nucleon and nucleus momentum respectively and the oscillator constant a 2 s 23 ² k i2 : for the harmonic oscillator ground state. For the excited state of 6 Li a cluster wave function composed of a halo of two p-state nucleons coupled to a total orbital angular momentum zero and an alpha-particle like core is used:

a H2

ž /

2

Ž 2.

s

proportional to a form factor F times the phase space factor ds A Fp Li . Ž 4. d V c .m .

qp 2Li

/

169

ž

g

1 q

2

4

/

1 q 13 pa p Li

cos uc .m .q pa2 p 2Li

Ž g y 1. 18 b

2

2

gy1 y

9bk

cos 2uc .m .

5 Ž 5.

where g s Ž aa2 q 2 k s pa2r4 q p Li r36

to second order in cos uc.m ., a C2 .rŽ a d2 q a H2 ., b s aa2 q a C2 , and uc.m . is the angle between the direction of the excited 6 Li nucleus and the incoming alpha particle in the c.m. frame. We assume the momentum distribution in the core of 6 Li ) to be the same as in the alpha particle, a C2 s aa2 s 0.538 fmy2 Žcorresponding to a root mean square radius of 1.67 fm.. The oscillator constant of the deuteron was determined by the witdh of the momentum distribution ² k i2 :1r2 d s 0.504 fmy1 calculated from a realistic deuteron wave function w34x. The resulting Legendre coefficients and the ratio of the form factors at the two energies are presented in Table 2. The calculations have been done for three different assumptions concerning the halo, namely the limit of a spatially very extended halo Ž a H2 s 0., an oscillator constant equal to that of the deuteron and an oscillator constant equal to that of the core. A negative asymmetry, a1ra0 , the magnitude of which increases with energy, is predicted over the full range of oscillator constants. At the same time the form factor decreases with energy. These results are in qualitative agreement with the experiment and we observe a sensitiv-

M. Andersson et al.r Physics Letters B 481 (2000) 165–170

170

Table 2 Comparison of ratios of Legendre coefficients, a1 ra0 , and form factors calculated from the model and those measured. The values of the oscillator constant pertinent to the halo, a H2 , correspond to the limiting case of infinite spatial extension a H2 s 0, the value for the deuteron and the value for the core.

a H2 s 0 a H2 s a d2 a H2 s a C2 experimental a.

F Ž420.30 .

Legendre coefficient a1ra0 417.95 MeV

420.30 MeV

F Ž417.95 .

y0.40 y0.14 y0.04 y0.11 " 0.04

y0.51 y0.18 y0.05 y0.43 " 0.10

0.87 0.92 0.96 0.48 " 0.04 a

Ratio of measured cross-sections divided by the phase space factor.

ity to the momentum distribution in the halo. A closer comparison between the experimental results and the predictions of the model favors a momentum distribution in the halo which is narrower than that of the deuteron, corresponding to a very large spatial extension of the halo. We must be cautious not to draw any far-reaching conclusions based on this simple calculation. However, we believe it serves as an illustration of the information concerning the cluster structure of the A s 6, T s 1 halo state that may be won by a proper theoretical analysis of the present data. We have completed a measurement of the 4 HeŽd,6 He.pq reaction at the same energies and the analysis is in progress. A measurement of a complete set of differential cross sections of the 3 HeŽ 3 He,6 Li ) .pq reaction would surely be of greatest interest. Acknowledgements The authors wish to thank Davor Protic and the personnel at the detector laboratory in Julich for ¨ manufacturing the germanium detectors. We are greatly indebted to the CELSIUS group for providing excellent experimental conditions. Help from Linda Geren ´ during the analysis is gratefully acknowledged. This work was in part funded by the Swedish Natural Science Research Council ŽNFR.. References w1x Y. Le Bornec et al., Phys. Rev. Lett. 47 Ž1981. 1870. w2x Y. Le Bornec et al., Phys. Lett. B 133 Ž1983. 149. w3x L. Bimbot et al., Phys. Lett. B 114 Ž1982. 311.

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