Mass yield distributions for 1 GeV proton-induced nuclear reactions on Ni and Ag

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MASS YIELD DISTRIBUTIONS FOR 1 GeV PROTON-INDUCED NUCLEAR REACTIONS ON Ni AND Ag L N. A N D R O N E N K O , A.A. K O T O V , L.A. V A I S H N E N E , W. N E U B E R T i Leningrad NuHear Phystcs Institute, 188 350 Gatchma, Lenmgrad, USSR

H.W. B A R Z z, j.p. B O N D O R F , R. D O N A N G E L O 2 a n d H. S C H U L Z l The Ntels Bohr InsHtute, Blegdamsvej 17, DK-2100 Copenhagen O, Denmark

Received 19 December 1985, rewsed manuscript received 10 April 1986

For 1 GeV proton-induced reactions on Nl and Ag the inclusive mass spectra covering a wide range of masses are analyzed w~th a two-step statistical multlfragmentatlon model winch considers the secondary decay of the primordial fragments It is found that the yield of hghter clusters can only be reproduced by considering the evaporation processes The experimentally observed U-shaped mass spectra are described by essentially one parameter - the temperature of about 6 MeV The power-law fit gives an exponent about one unit lower than the critical one

1. Introduction. In connection with the possible existence of the fiquld-gas-like phase transition in hot nuclear matter the analysis of the fragment dtsmbutaon from high-energy proton-induced nuclear reactions are drawing considerable attention both experimentally and theoretically. The experimental mass yield dislnbutlons have been Investigated on the basis of various approaches, such as statistical multifragmentatmn models [ 1 - 6 ] or percolation theories [7,8]. Especially m ref. [9] the percolation treatment has been discussed in view of the predictions of the statistical multlfragmentatIon model of refs. [4,5]. In the present paper we will analyze mass spectra of 1 GeV proton-induced nuclear reactions on N1 and Ag, whereby the mass yield data cover a wide range of masses, I.e. larger than half of the considered target mass. In a recent paper [10] a complete mass yield distrlbuUon for the interaction of silver with 300 GeV protons has been given, combining results of radmactlvataon, mass spectrometric and fragment detection experiments It is known that the hghter particle yield (A <~

1 Permanent address Instuuto de Fislca, Unlversldade Federal do Rio de Janelro, 21944 Rio de Janelro RJ, Brazil 2 Permanent address Central Institute for Nuclear Research, DDR-80511 Rossendorf, Dresden, GDR 18

2 0 - 3 0 ) can reasonably well be reproduced by the so-called power4aw fit A - r (see refs. [ 1 1 - 1 3 ] ) , whereby the exponent r has been brought in close connection with the critical one following from Flsher's droplet theory [14]. Since the experimentally observed mass yields seem not to drop further f o r A / > 30 (depending on the initial target mass number) both the experimental and theoretical study of the fragmentation process seems to be rather instructive in gaming valuable information on the reaction mechanism Itself. 2. Experiment The formation cross section of light fragments produced by 1 GeV proton bombardment of medium-weight target nuclei were already obtained in earlier measurements [ 1 5 - 1 8 ] . In these experiments a lens spectrometer was combined with a AE-lonlzatlon, chamber and a silicon detector which allowed to determine the ISOtOpic yields beginning from helium up to carbon in the energy range 5 MeV ~ 13 To go beyond this mass regmn and to cover even the region A >~A r / 2 (where A r is the target mass number) a method [19] was uUllzed which has originally been developed to detect fission frag-

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ments. The fragment masses were determined by a time of flight (TOF) and energy measurements. To obtain the mass spectra of the fragments selfsupporting targets of natural Ag (500 mg cm - 2 ) and natural Ni (200 mg cm - 2 ) were bombarded with 1 GeV protons provided by the Gatchma synchrocyclotron. The emerging fragments were detected at 90 ° with respect to the beam axis. A parallel plate avalanche counter (PPAC) provided the zero-time signal. This counter is still operative at a high background level of hght particles in the vicinity of the target and was housed at a &stance of 38 mm or 70 mm from the target in a small gas Idled chamber with entrance and exit windows made from FORMVAR of about 35/2g cm - 2 . The counter was operated with 7 torr of n-heptane. A properly chosen gas amphficatlon quaranteed full sensmwty to the fragments beginning from A / > 9, but on the other hand hght particles are effectively suppressed. In this way the load of the PPAC did not exceed 104 counts per second even at beam intensities above 1011 protons per second. Preserving this proton Intensity we actueved under beam conditions (beam spot diameter ~<10 ram) a time resolution of about 800 ps FWHM which allowed us to reduce sufficiently the flight path. In order to diminish the energy loss of the fragments we used as electrodes of the PPAC NI mesh-wires of 90% transparency (see ref [20]). The energy losses of the fragments in the windows and the heptane were calculated using the data collection in ref [21]. The fragments entered after a flight path of 32 cm a triplet of SI(Au) surface barrler detectors which provide both the energy and stop signals. The pulse-height defect of the silicon detectors was corrected using the procedure of ref. [22]. The mass resolution of the T O F - E method obtained for fissmn fragments of 252Cf was found to be about 7%. In the TOF measurements a time Intervall of the TDC of 250 ns has been used to extract background distributions from the accompanying bursts (75 ns apart). For the determination of the absolute yields at 01ab = 90 ° the energy spectrum o f a gwen fragment was continued below the registration threshold (typICal between 3 . 5 - 5 MeV) by means of a folded maxwelhan distribution shifted by an effective Coulomb barrier as described in ref. [23]. The parameters of

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this function were obtained from the fits to the measured energy spectra. The isotopic yMds (refs. [ 1 6 - 1 8 ] ) for mass numbers 3 ~
o

Z

r

r

]

l

]

I

/

E

p+Ag,

,~10 2

Ep=IGeV

101

100

a

104 ,

x 1110

/ ~.~-d

~L ~

L,~j-,-~,-J

`

10-2

2O

40

j 60

A

Fig. 1. Expergnental mass spectra for the reaction p + Ag at 1 GeV compared to the histograms calculated with (solid hne) and without (dashed line) taking into account the secondary decay of the fragments An excitation energy of the nucleus ol E*/A = 4.2 MeV is assumed. The curves show theA - r fit to the experunent and the primordial spectra, respectively 19

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Volume 174, number 1 lOa

I

i

i

I

E

~I0 ~

p+ NI

Ep = 1 GeV

100 10-1 •'t:= 1 2 5 +

0 15

10-2 i

0

10

I

I

t

20

30

40

A

50

Fig. 2. The same as f~g 1 for the reaction p + N1. Here an excitation energy ofE*/A = 3.7 MeV was assumed. whereas the yield o f the inclusive mass distribution increases However, the registration threshold and the thickness of the vacuum windows lead to an insensitivity of the spectrometer to masses with A ~> 65 and kinetic energies below 11 MeV, so that we were not able to confirm a further Increase of the formation cross section beyond A = 70

3. Theoretical analysis. In analysing the experimental data we employ the two-step model o f ref. [25], where the further decay of the primordial fragments is considered. At a bombarding energy of 1 GeV the fragmentation cross section amounts to only a few percent of the geometrical one, I.e. only a few o f the incoming protons lose sufficient energy to initiate the multifragmentatIon process. Consequently, except for very heavy fragments, the fragmentation processes are mostly due to central-like collisions Thereby a few nucleons may be ejected and the excited residual nucleus expands somewhat until the disassembly sets in. The formed fragments release their excitation energy mainly by evaporation o f hght particles. The striking fact is that the shape of the mass spectra is nearly independent of the bombarding energy between 1 GeV and 300 GeV, although the cross section differs by a factor o f 30 (cf. ref. [10]). This leads us to the assumption that the fragmentation process is only lmtlated If a certain amount of excitation energy has been deposited into the target nucleus. 20

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The average value of this excitation energy is used in the model calculation as a free parameter which is adjusted by comparing the calculated mass spectrum to the experimental one. Since energy conservation is retained for all possible partitions o f the intermediate system, the temperature becomes a fluctuating quantity, 1.e. the mass spectrum can not be associated with a constant temperature. Figs. 1 and 2 show the model predictions calculated with and without considering the secondary decay of the fragments. The relatively low mass y M d of light fragments (A ~< 4) in the primordial mass spectra is due to the fact that these particles are assumed to have no excited states within our model and, therefore, have a relatively small weight in the thermodynamlcal partition function. By taking into account the evaporation after the initial fragmentaUon process mostly light particles are emitted from the heavier fragments. As seen in figs. 1 and 2 the light particle yield increases significantly implying that the theoretical mass spectra agree now reasonably well with the experimental ones. The fluctuations in the calculated spectra displayed in figs. 1 and 2 are mainly caused by the statistical errors. The only free parameter, which enters the model is the average excitation energy per particle, was chosen to be E*/A = 3.7 MeV and 4.2 MeV corresponding to a temperature of T = 6.1 MeV and 5.1 MeV for NI and Ag, respectively. These excitation energies coincide well with the experimental ones Inferred from measurements of the longitudinal momentum (Pll) of the fragmenting nucleus [26]. The observation o f these large E * / A values supports the assumption of a hmltIng excitation energy above which nuclei undergo fragmentation (see also refs. [ 2 7 - 2 9 ] ) . It is now interesting to compare both the theoretical and the experimental results with the power law fit ~ A - r . In refs. [ 1 1 - 1 3 ] the exponent ~-has been brought in close connection with the critical one following from Flsher's droplet model [14]. Whether the experimentally determined exponents have something to do with the critical behavlour o f nuclear matter near the critical point of the l i q u i d - g a s transition is still disputed among theorists (cf. refs. [3,6,29]). In ref. [29] it was argued that the quantity ~- may give information on the fragmentation onset mainly controlled by the crack temperature T*. The interpretatIon o f the mass spectra as a signal of the critical

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behaviour o f the system becomes questionable for fragment masses exceeding A = 2 0 - 3 0 , because in that range the data do not allow a power-law fit. In fitting the experimental data by means of the A - z power law, one has to keep m mind that the spectra represent the final distributions o f cold fragments, i.e. after secondary decay and evaporation-like processes have been taken place. Figs. 1 and 2 show the results o f such fits to the mass spectra arising from 1 GeV proton-induced reactions on NI and Ag We used the mass range 4 ~
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Our results are also supported by recent studies within the multlfragmentatlon model o f ref. [32]. According to this analysis the experimentally observed power-law behavaour cannot be directly related to the critical behavlour associated with the onset of a phase transition but It has rather to be seen as an effective power depending also on dynamical Ingredients o f the decay, in parUcular, on the branchlng between unstable and stable fragments. In summary, by using a two-step fragmentation model, which Includes the decay of the originally formed hot fragments by evaporation, the average shape of inclusive mass spectra of 1 GeV proton-induced nuclear reactions on N1 and Ag have been well reproduced for a wide range of fragment masses. The mass spectra could be reproduced by assuming an excitation energy corresponding to a temperature of about 5 - 6 MeV. This temperature is very close to the limitmg one that a highly excited compound nucleus could attain. Fitting the theoretical results to a power law A - r , we found that the exponent r is about one unit below the critical one (rcrJt --- 2.3) when considering the primordial mass spectrum. Including the evaporation process r Increases significantly. This makes the interpretation of our results in the frame o f Fasher's droplet model questionable The help by Chr. Schnelderelt for fitting the data is thankfully acknowledged. Two o f the authors (H W.B. and H.S.) are indebted to the Nlels Bohr Institute for the kind hospitality extended to them and the Danish Mlmstry o f Education for financial support.

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[8] W. Bauer, D.R. Dean, U. Mosel and U. Post, Phys. Lett. B 150 (1985) 53. [9] H.W. Barz, J. Bondorf, R. Donangelo and H. Schulz, Phys. Lett. B 169 (1986) 318 [ 10] A. Bujak, J E. Finn, L.J. Gutay, A.S. Htrsch, R.W. Mmich, G. Paderewski, N.T. Pottle, R.P. Scharenberg and B.C. Strmgfellow, Phys. Rev. C32 (1985) 620 [ 11 ] A.S. Hlrsch, A. Bujak, J.E. Finn, L.J. Gutay, R.W. Mlmch, N.T. Pottle, R.P. Scharenberg, B.C. Strmgfellow and F. Turkot, Phys. Rev. C29 (1984) 5O8. [12] R.W. Mmlch, S. Agarwal, A. BuJak, J. Chuang, J.E. Finn, L.J. Gutay, A.S. Hlrsch, N.T. Porfle, R.P. Scharenberg, B.C. Stringfellow and F. Turkot, Phys. Lett. B 118 (1982) 458. [13] A.D. Panaglotou, M.W. Curtm, H. Tokl, D.K. Scott and P. Siemens, Phys. Rev. Lett. 52 (1984) 496. [14] M.E. Fisher, Physics 3 (1967) 255. [15] A.A Vorobyov, E.N. Volnm, D.M. Seleverstov and D.A Alchasow, Proc. All unions Conf. on Hlgh energy nuclear physics (Charkov, 1973), Vol 2(4), p. 81 [In russian]. [16] E.N. Volnm Thesis, Leningrad (1975). [17] E.N. Volnm, A.A. Vorobyov and D.M Seleverstov, Pls'ma Zh. Eksp. Teor Flz. 19 (1974) 691. [18] E.N. Volnm, G.M. Amalsky, D.M. Seleverstov, N.N. Smlrnow, A.A. Vorobyov and Yu.P. Yakovlev, Phys. Lett. B 55 (1975) 409 [ 19] A.A. Kotov, W Neubert, L.N. Andronenko, B.L Gorshkov, G.G. Kovshevny, L.A. Valshnene and M.I. Yazlkov, Nucl. Instrum. Methods 178 (1980) 55.

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