Evolution of a spallation reaction: experiment and Monte Carlo simulation

NUCLEAR PHYSICS A ELSEVIER

Nuclear Physics A 657 (1999) 317-339 www.elsevier.nl/locate /npe

Evolution of a spallation reaction: experiment and Monte Carlo simulation M. Enke a, C.-M. Herbach a, D. Hilscher a,l, U. Jahnke a, O. Schapiro a, A. Letourneau b, j. Galin b, F. Goldenbaum b,2, B. Lott b, A. P6ghaire b, D. Filges c, R.-D. Neef c, K. Ntinighoff c, N. Paul c, H. Schaal c, G. Sterzenbach c, A. Tietze c, L. Pienkowski d a Hahn-Meimer-lnstitut Berlin, Glienickerstr. 100, D-14109 Berlin, Germany b GANIL (IN2P3-CNRS, DSM-CEA), BP 5027, F-14076 Caen-Cedex 5, France c Forschungszentrum Jiilich, Institutffir Kernphysik, D-52428 Jiilich, Germany d Heavy lon Laboratory, Warsaw University, 02-093 Warszawa, Poland

Received 22 June 1999; revised 9 July 1999; accepted 12 July 1999

Abstract Reaction cross sections and production cross sections for neutrons, hydrogen, and helium have been measured for 1.2, 1.8 GeV p+Fe, Ni, Ag, Ta, W, Au, Pb and U and are compared with different intra-nuclear-cascade- combined with evaporation-models. Agreement for neutrons and considerable differences for light charged particles are observed between experiment and calculation as well as between different models. The discrepancies are associated with specific deficiencies in the models. The exclusive data measured with two 4~r-detectors for neutron and charged particle detection allowed furthermore a systematic comparison of observables characteristic of different stages of the temporal evolution of a spallation reaction: inelastic collision probability, excitation energy distribution, pre-equilibrium emission, and inclusive production cross sections, t~) 1999 Elsevier Science B.V. All fights reserved. PACS: 24.40.Sc; 25.40.-h; 28.20.-v Keywords: Spailation reactions; Total reaction cross section; Production cross section for n, hydrogen, and helium; Excitation energy distributions; Pre-equilibrium emission

I E-mail: [email protected]. 2 Present address: FZ Jtilich, D-52428 Jiilich. 0375-9474/99/$ - see front matter © 1999 Elsevier Science B.V. All rights reserved. PII S 0 3 7 5 - 9 4 7 4 ( 9 9 ) 00345-0

318

M. Enke et aL/Nuclear Physics A 657 (1999) 317-339

,t=

2ooo

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1000 9OO

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o

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Michel 95

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600 O =

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A

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........ L A H E T ....

o~

HERMES

i

200

e A . . . . . . . .

10 -2

i 10 "!

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.

.

. 1

.

.

i tO

proton energy (GeV)

Fig. 1. Helium production cross sections for p-induced reactions in Fe as a function of proton energy. The first authors and year of publications of previous measurements are indicated [4-8]. NESSI 98 refers to the present experiment. The lines show the results of calculations with the INCL, HERMES, and LAHET code, see Section 3. 1. I n t r o d u c t i o n

The need for reliable data for the design and construction of spallation neutron sources such as the European Spallation Source (ESS) [ 1 ] has prompted a renewed interest in corresponding nuclear data for thin as well as thick targets [2]. Thin target data provides insight into the physics of the spallation process, the intra-nuclear cascade (INC) which leads to the formation of excited nuclei subsequently decaying by evaporating predominantly light particles such as n, p, and a-particles. The production of hydrogen and in particular of helium has strong bearings on the structural damages caused to the targetand or window-materials employed in the design of the target station. The amount of produced tritium as a radioactive gas of considerable radio-toxicity may require special radiation safety provisions in particular for a liquid target such as Hg, presently the most favored target material for ESS. Furthermore, spallation reactions allow the study of the decay properties of hot nuclei mostly thermally excited without major distortions due to compression, deformation, and high spin as present in heavy-ion induced reactions [ 3 ]. A considerable amount of data for helium production in a proton energy range up to a few GeV exists in the literature [ 4 - 1 6 ] . These data, however, exhibit a large dispersion as can be seen for instance in Fig. 1 where a compilation of measured helium production cross sections for proton induced spallation reactions on Fe is shown. Previous measurements essentially exploited mass spectrometry methods [ 4 - 9 ] for gas extracted from irradiated samples and only a few measurements employed counting

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319

methods with AE-E telescopes for isotope, mass, and energy identification [10-16]. Very little data exist, however, for hydrogen [ 12] and neutron [2,17-19] production cross sections. Compilations of experimental data as well as calculations can be found in Refs. [20-23] for incident proton energies between 10 MeV and 25 GeV. The above given reasons motivated us to start a campaign [2,24-26] to measure production cross sections for GeV proton induced spallation reactions. We went a step further, however, to obtain exclusive data, and for the first time in proton induced spallation reactions, we employed 4~r-detectors for neutrons and charged particles. With this exclusive data it is possible to reconstruct for each initiated reaction the deposited thermal excitation energy [3] and to investigate pre-equilibrium (PE) emission for peripheral and central collisions. This additional information allows not only the inclusive production cross sections to be measured but also critical model parameters to be tested. Of special interest among the latter are the equilibration criteria after the prompt intranuclear cascade which define the transition from the INC-model to an evaporation model describing the statistical decay of the thermally equilibrated nucleus produced by the INC. The aim of the present contribution is the comparison of measured and calculated observables characteristic of various stages of the temporal evolution of a spallation reaction. Three codes describing spallation reactions in the few GeV region were employed: (i) the Intra-Nuclear Cascade code from Liege, INCL (version 2.0 [27-29] ), coupled with the evaporation code GEMINI (version 5/97 [30]), the combination of both is referred to in the following by INCL, (ii) the JiJlich code system HERMES [31 ], and (iii) the Los Alamos High Energy Transport code LAHET (version 2.7d [32,33] ) including PE-emission [34] by exploiting the exciton model formalism. We used standard parameters of these codes and did not perform an extensive optimization of these parameters. In Section 2 the experimental details and data analysis are described, in Section 3 the results are compared with the above-mentioned three model calculations, and in Section 4 a summary is given.

2. Experimental methods and data analysis We have measured with the NESSI-detector (NEutron Scintillator tank and Silicon ball) at the COSY accelerator in Jiilich the production cross sections of neutrons, hydrogen, and helium for 1.2 and 1.8 GeV proton induced spallation reactions for target nuclei between Fe and U. The experimental setup is schematically shown in Fig. 2. About (1-5) x 105 protons per second passed through a 0.3 mm thick and 20 mm in diameter start scintillator S 1 positioned 11.1 m upstream of the target. The veto detectors $3 and $5-$8, about 1 m in front of the target, were exploited to reject all off-axis particles. The focus at the target position in the center of NESSI was about 2 mm in diameter as measured with a quartz and a TV camera. The scintillators S10-S14 were used for focusing and aligning the beam on axis. The beam normalization for determining absolute cross sections was

320

M. Enke et al./Nuclear Physics A 657 (1999) 317-339

BNB+BSiB ~amdump $1 P------~

--

0

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1110 cm

605 cm

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Fig. 2. Schematic experimental setup of the NESSI experiment at the COSY accelerator. obtained from the counting rate of S1S3S5-$8, corrected for dead time. The targets as well as empty target frames for background measurements could easily be changed with a movable target ladder on which up to 4 targets were mounted. The 2 5 × 2 7 m m 2 target frames were made of 0.2 mm thick A1 with a 20 mm diameter aperture. The targets were mounted on a 14 cm long A1 flag-pole with a 0.5 m m × 5 mm profile and positioned perpendicular to the beam axis. The thicknesses of the self supporting targets ranged between 0.6 and 12.6 m g / c m 2. Thinner targets (less than 1 m g / c m 2) were used to measure proton induced fission in Au and U targets while thicker targets were employed for the measurement of neutron production and total reaction or inelastic cross sections. The target thicknesses were measured by weighing and energy-loss measurements of a-particles from ThC and ThC'. The NESSI-detector consists of two 4~r detectors, the Berlin Neutron Ball (BNB) [ 2 ] for neutron detection and the Berlin Silicon Ball (BSiB) [35] for detection of all charged particles. BNB is a spherical shell of liquid scintillator with an inner and outer diameter of 40 cm and 140 cm, respectively. The scintillator is loaded with Gadolinium (0.3% by weight). The signal induced in BNB by each reaction consists of two components separated in time. The prompt component induced by T-rays, energetic charged particles, and neutrons is exploited to measure the total reaction cross section Crreac for all reactions with an inelasticity of at least 2 MeV. By exploiting the delayed signal of BNB the number of neutrons emitted in each reaction can be obtained by counting the capture "y-rays of neutrons thermalized in the scintillator. The detection efficiency of BNB for evaporative neutrons (a few MeV) is about 85% as measured continuously during the experiment with neutrons from spontaneous fission of 252Cf. For more energetic neutrons the efficiency is considerably smaller, 40 or 15% at 30 or 100 MeV, respectively. Since the energy of each neutron is not measured the response of the detector for a neutron energy spectrum of a given reaction has to be calculated with a model for this reaction. To this purpose a mean efficiency per neutron was calculated with the code INCL by averaging the BNB-efficiency eBNB(En) over the calculated energies E~ and the number M INCE of emitted neutrons of all simulated

M. Enke et al./Nuclear Physics A 657 (1999) 317-339 A

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0.9

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Fig. 3. Upper panel: Calculated efficiency ffBNB(Mdetected ) for the reaction 1.8 GeV p+Au as a function of the detected multiplicity (M d.erects) obtained from the calculated neutron multiplicity folded with the BNB response. Lower panel: calculated (line) and measured (filled circles) mean excitation energy E* as a function of detected neutron multiplicity. Calculations were done with the INCL code.

events resulting in M~CL (~:) = ~

n INCL 6BNB ( Ei ) / M n •

i=1

For the reaction 1.8 GeV p + A u we show in Fig. 3 the differential efficiency eBNB as a function of detected neutron multiplicity (Mdnetected). This simulation demonstrates that for low neutron multiplicities corresponding to peripheral reactions emitting on average higher neutron energies eBNB is smaller than the average value of (e) = 70.1% (73.1% with LAHET), while for central collisions with high neutron multiplicities the average neutron energy is smaller and thus the mean efficiency larger than average. The neutron production cross sections given in this paper have been corrected employing the mean efficiency (e) calculated with INCL. Since in the following we also show some data as a function of measured neutron multiplicity we show in the lower panel of Fig. 3 the mean calculated (line) and experimentally deduced (as described below) excitation energy (E*) for the same reaction 1.8 GeV p+Au. We observe that (E*) is increasing from a few tens of MeV to 600 MeV for peripheral to central collisions, respectively. The silicon ball BSiB is centered around the target in the inner vacuum chamber (40 cm diameter) of BNB. BSiB consists of 162 silicon detectors ( 5 0 0 / z m thick) arranged to a sphere with a diameter of 20 cm. Due to active area (94%) of the BSiB detectors and 11 detectors missing for beam in/out, target in/out, TV-camera, some defect detectors,

322

M. Enke et al./Nuclear Physics A 657 (1999) 317-339

10

p(1.8GeV) + Au

3

.~10 2

- -

INC+EVAP

.........

INC

---

EVAP

10

ii '

J

10 1

10

10 2

10 3 Ep (MeV)

Fig. 4. Calculated protonenergy spectrumfor 1.8 GeV p+Au; INC:protonsfrom prompt intra-nuclear cascade (INCL), EVAP:evaporated protons only. The lowerand upper detection thresholds and their uncertainties are indicated by the vertical shaded bars. The INCL (LAHET) calculated integrated p-yield below 26 MeV is 3.11 (6.73) b of the total p-yield of 7.23 (10.9) b. and in addition 6 detectors replaced by telescopes with 32% active area of the BSiB detectors the geometrical efficiency of BSiB was about 89% of 4rr. Shadowing by the target foil close to 90 ° , which depends on target thickness and specific energy loss of particles, reduces the efficiency further to about 80%. In addition to the above-described geometrical detection efficiencies for charged particles there were additional detection limitations due to upper and lower energy thresholds. The lower cutoff energy was 2.2-{-0.3 MeV. The upper energy cutoff was due to the lower energy detection threshold for particles which were not stopped in the 500/xm thick silicon detectors. These punch through particles deposited only an energy loss AE decreasing with increasing particle energy. This resulted in upper energy cutoffs of 26+4, 494-6, 764-7 MeV for p, d, and tritons, respectively. Consequently very energetic protons or pions produced in the spallation reactions were not detected with BSiB. Calculations to be described below indicate that only 30-60% of all emitted protons have energies below about 26 MeV, depending on the employed model and also on the target. This is illustrated by a calculated proton energy spectrum in Fig. 4 with the upper and lower detector thresholds indicated by the vertical shaded bars. With other words, BSiB measures predominantly evaporative protons which are important for the investigation of radiation damage. Since almost all emitted deuterons and tritons have energies below 49 and 76 MeV, respectively, the upper cutoff energy did not influence the detection of the heavy hydrogen isotopes. For helium the upper cutoff energy was 120 MeV and thus resulting in almost complete detection for helium. Hydrogen production cross sections given below

M. Enke et al./Nuclear Physics A 657 (1999) 317-339

323

E p=I.8GeV 10 3

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rl

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10 2 charged particle mass Acp (amu)

Fig. 5. Inclusive mass distribution of charged particles produced in 1.8 GeV p+U and Au, not corrected for detection efficiency for 4 < Acp • The proton cross sections were measured with the condition 2.2_< Ep < 26 MeV, see text. LCP: light charged particles, IMF: intermediate mass fragments, FF: fission fragments. correspond to the sum o'H = O-p(2.2-26 MeV) + trd(2.2-49 MeV) + trt(2.2-76 MeV) and helium production cross section to the sum O'He = O'3He-'~ O'4He. With BSiB hydrogen, helium, and heavier charged fragments could be separated by measuring time-of-flight and energy while isotope separation was possible only in a limited energy range. The particle mass was deduced from the measured time of flight (TOF) and energy corrected for plasma delay [36] and pulse height defect [37], respectively. The start signal for TOF was provided by the S 1 scintillator while the stop signal was derived from the silicon detectors. The total time resolution was about 0.9 ns resulting in better than unit mass resolution for stopped particles with A < 4 and about 20 mass units for A.~100. In Fig. 5 measured mass distributions of charged particles are shown for 1.8 GeV p on Au and U. The displayed results for A = 2, 3 obtained with telescopes to be described below are also indicated. The nonzero intensity for A = 5 is due to contaminations mainly from A = 4. For heavier masses the distribution is characterized by two further bumps corresponding to intermediate mass fragments (IMF) peaked at a mass of about 10 and fission fragments (FF) at A ,.~ 100 ~ Atarget/2. The considerably larger fission probability for U compared to Au is clearly demonstrated. Heavy evaporation residues are strongly suppressed in the mass yield in Fig. 5 because of the lower probability for

324

M. Enke et al./Nuclear Physics A 657 (1999) 317-339

i

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t

I

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p( 1.8 GeV) 0

20 40 60 80 100 120 140 160 180 0 (deg)

Fig. 6. Angular distribution of p, d, tritons, 3He, and 4He as measured with telescopes for the reaction 1.8 GeV p+Au. The dashed lines correspond to a linear fit of the experimental points. The resulting integrated production cross sections are given in Table 2. their detection. In order to obtain information on the production cross sections for different isotopes six BSiB detectors at angles between 30 ° and 150 ° were replaced by telescopes consisting of two fully depleted AE silicon detectors ( 8 0 / z m and 5 0 0 / z m thick) backed by a 7 cm thick CsI scintillator with photo-diode read out. These telescopes were installed only for the second run at 1.8 GeV and since the summed solid angle of all detectors covered only 1.2% of 47r statistical relevant data could be obtained only for 1.8 GeV p + A u . The above described upper energy cuts for the BSiB detectors were applied also for the telescopes. The lower energy cuts were somewhat higher since the particles had to punch through the first 8 0 / z m AE detector before reaching the 5 0 0 / ~ m trigger detector: 2.8, 3.6, 4.1, 9.7, 10.8 MeV for p, d, tritons, 3He and 4He, respectively. In Fig. 6 the angular distribution of H and He isotopes emitted from the reaction 1.8 GeV p ÷ A u reaction is shown as measured with the telescopes. The distributions show only a slight forward backward anisotropy which is very similar for different isotopes except for protons, where the pre-equilibrium component is cut off by the upper energy threshold. Furthermore, part of the forward backward asymmetry of about 25% for a-particles is due to the momentum transfer to the recoiling Au-nucleus. From this we can conclude already that most of the detected light charged particles are preferentially emitted from an thermally equilibrated nucleus with little pre-equilibrium contribution, as will be discussed further below. The integrated production cross section for tritium is found to be 600-t-140 mb for 1.8 GeV p + A u which is of particular relevance for ESS since

325

M. Enke et al./Nuclear Physics A 657 (1999) 317-339

>" .o_ , m

2O

Q.

= 15 E e ._o 10 Q. 10

5 0

0 0

5

10

15

20

25

30

35

40

Neutron multiplicity Fig. 7. Correlation of measured charged particles versus measuredneutron multiplicityin the reaction 1.8 GeV p+Au.

a 197Au-target is for a spallation reaction very similar to a ~0°°6Hg-target which is the preferred ESS target material. With the described two 4~r-detectors for neutrons and charged particles it is possible to obtain detailed exclusive information on each reaction. In particular we know for each reaction the multiplicity of mainly evaporative neutrons and charged particles from which we can reconstruct the excitation energy for each event. In Fig. 7 we show a correlation of charged particle multiplicity versus measured neutron multiplicity. By exploiting such correlations the thermal excitation energy distribution of the nucleus after the prompt INC can be experimentally deduced from the sum of the multiplicities of neutrons Mn and light charged particles MLCP (LCP with ZLCP _< 2). The sum of light particles (LP) MLp = M~ + MLCP is measured event-wise and correspondingly the excitation energy. The calibration curve E*(MLp) has been obtained from calculations with the statistical model GEMINI [30]. The details of this method have been described in [3] where it was also shown that the uncertainty of the determination of the experimental excitation energy is about 4-10%. An alternative method to determine E* for each event with MLp measured light particles employs the relation E* = ~_,iM=~((Bi + E~n). For n i average binding energies are used, E~ n is measured for light charged particles while for neutrons the not measured kinetic energy can be determined iteratively by means of the relation E~" = 3/2 x v/-E"i'/a with a being the level density parameter. This method agrees with the above described one also within 10%.

M. Enke et aL/Nuclear Physics A 657 (1999) 317-339

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Table l Measured hydrogen (trH) and helium (O'He) production cross sections, total reaction cross section (trreac), and neutron (on) production cross sections at an incident proton energy of 1.2 GeV Target

thickness mg/cm 2

trH (b)

O'He (b)

O'reac (b)

Fe Za W Au Hg Pb U

1.54 1.54 1.54 8.7 6800 12.6 1.54

1.32 2.20 2.21 2.40

0.44 I. l 0 1.15 1.28

0.80

2.27 2.14

1.22 1.17

1.76 1.78 1.73

O'n (b) 5.14

26.7 28.4 30.4

(E}

0.576

0.716 0.716 0.721

O"n1 (b) 3.41

25.3 26.3 28.1

o.L (b) 4.39

27.9 28.7 30.2

O.nH (b) 4.48

28.2 29.5 31.5

The relative errors of the experimental cross sections are +7%. trn has been corrected for a mean efficiency (E}, see Section 2. Results of calculations with INCL (tfln), LAHET (trnL), and HERMES (trnn ) are also given. The calculations have been averaged over natural isotopic abundances.

3. Experimental results and comparison with calculations The measured reaction-, n-, H-, and He-production cross sections at 1.2 GeV are given in Table 1 and for H-, He-production cross sections at 1.8 GeV in Table 2. For the Fe-target we can compare the present result for helium with a recent measurement of Michel et al. [8] who obtained at 1.2 GeV 792-1-55 mb compared to 4404-32 mb in the present experiment. This corresponds to a discrepancy of a factor of 1.8 or about 6 standard deviations (see also Fig. 1). On the other hand, the present results for Fe and Ni agree quite well with the older data of Goebel et al. [6] as is shown in Fig. 1 for Fe and in Fig. 13 for Ni. The deduced total reaction cross sections given in Table 1 agree within 10% with systematics [38]. Before comparing the present measured production cross sections with the results of model calculations for inclusive production cross sections we describe first the basic physical concepts employed in the models INCL [28,30], HERMES [31], and LAHET [32] and, while doing so, we will point out the main differences between the models. These code systems are actually a sequence of 2 or 3 theoretical models: the intra-nuclear cascade, for the LAHET code also pre-equilibrium emission, and sequential evaporation. Employing the exclusive present data we are able for the first time to confront the various stages of the theoretical modeling with experimental data: (i) inelastic collision probability corresponding to the total reaction or inelastic cross section, (ii) excitation energy distribution after INC, (iii) pre-equilibrium emission, and finally (iv) inclusive production cross sections. The starting point of all considered three codes is the intra-nuclear cascade which was initially suggested in 1947 by Serber [39] and extended by Bertini [40]. Intranuclear cascade models employ elastic and inelastic (excitation of the A-resonance) scattering of the incident or secondary hadrons inside the nucleus by exploiting free hadron-nucleon cross sections into unoccupied final states (Pauli blocking) inside the nucleus or into the continuum outside the nucleus. In-medium NN cross sections are

M. Enke et al./Nuclear Physics A 657 (1999) 317-339

327

of importance below 400 MeV and have been taken into account for INCL [28]. The scattering and decay of all produced hadrons are followed inside the nucleus until they either leave the nucleus or thermal equilibrium is reached. Before discussing the critical criteria for thermal equilibrium we will briefly confront the collision probability Pi,el as measured and calculated by the intra-nuclear cascade resulting in inelastic or reaction cross section O'reac = Pinel " O'geom, w h e r e O'geom is the geometrical cross section. The nuclear density corresponding to the geometrical cross section is sampled with incident hadrons, protons in the present case, employing Monte Carlo methods. In the INCL code the radius of the geometrical cross section is assumed to be 1.12. A 1/3 fm with a constant nuclear density inside this radius and zero density outside. The somewhat small radius parameter of ro = 1.12 fm results in about 20% smaller reaction cross sections than the measured ones given in Table 1 for the reactions 1.2 GeV p + F e to U. Agreement with experiment could be obtained by changing r0 from 1.12 to 1.26 fm. We have instead rescaled all INCL calculated cross sections given in this paper with a parameterization of published inelastic cross sections given in Ref. [ 38 ]. The two Bertini-type codes HERMES and LAHET approximate the radial nuclear density distribution p ( R ) [41 ] by a three step function with ,00.9,/90.2, p0.Ol = 0.9, 0.2, 0.01 times the central nuclear density resulting in considerably larger geometrical cross sections with r0 up to 1.8 fm for p0.ol. The collision probability averaged over geometrical area is considerably smaller, however, resulting in inelastic or reaction cross sections which closely agree (within 5%) with the experimental values given in Table 1. Consequently all cross sections given below for the HERMES and LAHET codes have not been modified. Summarizing the discussion of reaction cross sections we note that INCL has been normalized to systematics [38] of inelastic cross sections while the results of the HERMES and LAHET codes agree within 5% with experiment. A considerable fraction of the initially available energy is carried off by promptly emitted highly energetic nucleons and pions. The calculated yield and spectral shape of those particles cannot be tested directly with the present data as was done for instance recently by Cugnon et al. [28,29] for the INCL-code in order to obtain new constraints on the A-production. After each intra-nuclear cascade a more or less equilibrated excited nucleus is left over. This nucleus decays further via sequential evaporation which is theoretically described by the statistical model. A critical point is, however, the criteria for the decision to switch from the intra-nuclear cascade to the statistical decay. In the Cugnon code INCL, in which the intra-nuclear cascade is followed as a function of time, the criteria is given by the equilibration time reauil which depends on target size, incident energy, and impact parameter. Typical mean values (~'equil) are 18 and 25 f m / c for 1.2 GeV p + F e and U, respectively. These theoretical equilibration times correspond to a slope change in the time dependent emission rates of cascade particles as calculated within the model. This is exploited to fix the equilibration time in a selfconsistent way. In the Bertini type intra-nuclear cascade models HERMES and LAHET the corresponding criteria is given by the condition that the most energetic scattered nucleon in the nucleus has decreased below a given cutoff energy above the Fermienergy.

328

M. Enke et al./Nuclear Physics A 657 (1999) 317-339

p(1.8GeV)+Au

p(1.2GeV)+Fe

10 .0

*

1

10

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-2

10

0

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tk ' :,-t Er]_ ;- , o ~ 1 , : !.~

. . . . . . . .

200

400

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i:. . . . . . . . . . . . . .

0

250

500

;q:"

750 1000 E* (MeV)

Fig. 8. Comparison of experimental (solid circles) and calculated (histogram) excitation energy distributions with the condition of at least one evaporation-like detected charged particle for the reactions 1.2 GeV p + F e (left panel) and 1.8 GeV p + A u (right panel). The solid, dotted, and dashed histograms were calculated with the INCL, HERMES, and L A H E T codes, respectively.

With the present experimental data we can confront the calculated excitation energy distribution do'/dE* of all nuclei produced by the intra-nuclear cascade in order to see whether the energy carried off by cascade particles and/or the above discussed switching criteria are correct. In Fig. 8 the deduced (see Section 2) experimental excitation energy distribution of the residual nuclei (solid circles) under the condition of at least one detected evaporation-like charged particle is compared with the results of calculations with INCL, LAHET, and HERMES as indicated with the solid, dashed, and dotted histograms, respectively. For the reaction 1.2 GeV p+Fe (1.8 GeV p+Au) the mean excitation energies of the four distributions amount to 126 (354), 129 (296), 186 (498), and 150 (462) MeV corresponding to experiment, INCL, HERMES, and LAHET, respectively. We observe that the INCL calculation agrees quite well with the experimental data for both light (Fe) and heavy (Au) targets. The HERMES and LAHET codes, on the other hand, predict considerably higher excitation energies particularly for heavier targets such as Au where the mean excitation energy is overestimated by about 110-140 MeV. This will also result in larger production cross sections for charged particles since charged particles are preferentially emitted from high excitation energies due to the suppression effect of the Coulomb barrier. As will be shown below this expectation agrees with the observation that HERMES and LAHET calculations considerably overestimate the LCP production cross sections. The special importance of the initial excitation energy was early recognized by Green and Korteling [42] who iteratively deduced this distribution by assuming a Maxwellian shape, since their data was insufficient for a reconstruction. They observed, nevertheless,

M. Enke et al./Nuclear Physics A 657 (1999) 317-339

329

10 2 10

1 10 10

g

1

10 M =21-25

10

M.=26-35

1 10

-1 .2

10

~i~ ~W:~'~/~,":l:~i~ ~i~~..~:~i

o

H...........

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.

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ns

En~ (MeV) Fig. 9. Angle integrated He energy spectra (circles) as a function of measured neutron multiplicityfor 1.8 GeV p+Au compared with INCL calculations. that the excitation energy distribution from an intra-nuclear cascade reached to considerably higher excitation energy than the empirically deduced Maxwellian distribution. The dependence of the high energy tails in the excitation energy distribution on the equilibration time was discussed also in [26]. The further de-excitation of the thermally equilibrated nucleus is continued with the evaporation code GEMINI [30] for INCL and similar built-in codes for LAHET and HERMES employing as input the excitation energy, charge and mass of the nucleus left over from the INC. The evaporation of n, p, d, t, 3He and a-particles is considered by the Hauser-Feshbach formalism in competition to symmetric fission described by the transition-state model. The evaporation occurs directly from the excited equilibrated nucleus as well as sequentially from fission fragments. The level density parameter was set for GEMINI to a = A/IO MeV -1 and aF/an = 1.0 while in LAHET2.7 code the Gilbert-Cameron-Cook-Ignatyuk level density formalism [34] was employed. The transition from the fast intra-nuclear cascade is, however, not given by a delta function and one might expect that during a smooth transition from a direct reaction to the statistical decay of a compound nucleus pre-equilibrium emission might occur. The high energy component of the spectra of nucleons or composite particles is usually used as a clear indicator for pre-equilibrium emission. To this purpose we show in Fig. 9

330

M. Enke et al./Nuclear Physics A 657 (1999) 317-339

p(1.8GeV) + Au 8 7

..... ~

/~+

1.9MeV< Ep < 30MeV 2.5MeV< Ep< 22MeV

EVAP

EVAP

1 0.9 0.8

10

15

20

25 30 Mndetected

Fig. 10. Ratio of hydrogen and helium multiplicities as function of measured neutron multiplicities for the reaction 1.8 GeV p+Au. Calculations were performed for evaporated particles only (EVAP) and including low energy protons from the INC (INC+EVAP). Calculations were performed with INCL.

the angle integrated He-energy spectra for 1.8 GeV p + A u gated with different neutron multiplicities and compare them with the expectation of pure evaporation after the INC. Increasing neutron multiplicity corresponds to increasing deposited excitation energy and decreasing average impact parameter. We observe that for low neutron multiplicities corresponding to peripheral reactions the measured helium-spectra are dominated by pre-equilibrium emission while at higher neutron multiplicities the evaporation is dominating the spectrum. The evaporation part is well represented by the INCL-calculation which, however, did not consider PE-emission of composite particles. It should be noted, however, that taking into account pre-equilibrium emission in the LAHET code, as was done in all LAHET calculations presented here, could neither reproduce the high energy tails of the experimental energy spectra shown in Fig. 9. From this figure we deduce a PE-contribution of about 50 and 20% at (Mn) lower or greater than 6, respectively, and overall of 20%. This finding is very similar to the 10 to 30% integral PE-contribution found by Green et al. [ 16] for 4He at considerably lower bombarding energies of 210 to 480 MeV, while the PE-contribution of 3He was found to be 70 to 90% indicating a different emission process for 3He. To obtain a similar information on pre-equilibrium nucleon emission is more complicated since it is conceptually not possible to discriminate between low energetic nonevaporative nucleons from the prompt intra-nuclear cascade and genuine pre-equilibrium nucleons as described in an exciton master equation. Nucleons emitted towards the end of the intra-nuclear cascade can be considered as pre-equilibrium nucleons whereas com-

M. Enke et al./Nuclear Physics A 657 (1999) 317-339

331

Table 2 Measured proton (o'p (2.2-26 MeV), deuteron (o-a(2.2-49 MeV), triton (0-r(2.2-76 MeV), hydrogen (0-H = 0-p + O'd + o-t), 3He (O'3He), 4He (IT4He), and helium (0-He = 0-3He q'- 0-4He) production cross sections at an incident proton energy of 1.8 GeV; the errors are 4-7% if not given otherwise Target

Thickness mg/cm2

Ni Ag Ta Au Pb U

1.4 1.6 7.5 8.7 12.6 0.6, 8.0

0-p (b)

2.10+0.2

0-d (b)

1.00d:0.2

0-t (b)

0.60:1:0.14

0-H (b) 1.70 2.75 3.30 4.00 3.13 3.20

0-3He (b)

0.204-0.08

O'4He (b)

1.784-0.2

(THe (b) 0.63 1.11 1.60 2.00 1.64 1.75

posite particles may imply in addition more complex mechanisms such as coalescence which are not taken into account by the intra-nuclear cascade. From Fig. 4 we can see that protons from the intra-nuclear cascade (dotted histogram in Fig. 4) reach down to proton energies of about 10 MeV and are thus partly included in the measured hydrogen cross section. Consequently it would not be possible to separate such particles from the energy spectra alone, since at low energies the evaporation part dominates the spectrum. That is why we have chosen to investigate the ratio of H- and He-multiplicities (MH/MHe, shown by the filled circles in Fig. 10) as a function of measured neutron multiplicity. From Fig. 9 we know already that for measured neutron multiplicities larger than about 5 the contribution of pre-equilibrium He-emission is only about 20% and consequently up to this level the He multiplicity is essentially due to evaporation. Assuming evaporation as the only source for LCP production we would expect that the MH/MHe ratio increases with neutron multiplicity as indicated by the thin solid and dashed line (EVAP) in Fig. 10 while the experimental data (filled circles) show a decrease from about 5 to 2 for neutron multiplicities of 5 to 15, respectively. This is well described with INCL within the uncertainty of the detection energy-interval for protons as indicated by the thick dashed and solid lines (INC+EVAP). Thus we can conclude that even below 26 MeV a considerable contribution from cascade protons exists for peripheral reactions resulting in thermal excitation energies between 50 and 150 MeV which is well described by the INCL model. After having followed the theoretically modeled evolution of a spallation reaction and simultaneously compared the predictions during the various stages with the experiment we will now compare the calculated inclusive production cross sections with experiment. In Table 1 the experimental neutron production cross sections trn corrected for efficiency (see Section 2) is given and compared with the results of the three models. From the comparison between all three theoretical models and experiment we note that the neutron production cross section is well described. This is also shown in the left top panel of Fig. 11. From the comparison of calculated and measured charged particle cross sections as displayed in Figs. 11 and 12 we note that only the INCL code agrees quite well with

M. Enke et al./Nuclear Physics A 657 (1999) 317-339

332

p(1.2GeV~+X

40 .g t. g~

6

n

'NCL .... LAHEI"

~

-

30

~

L .:

*

D J-

"''" Z , . ~~:[.*,'~.".'~.°,%. .-"

". °

4

20 2

10

0 1.5

0 ..- "'""

d •," . ~ o ¢¢

°° .J.~

....: ....... .tt~

.,..,.."

3He

~"

0.5

ee,.,"

~

.........

..... ..... .-.......

0.2

1

,~.~"

.°.°.,'"

...........

0

- '"

t

.

4He

,,"-..:

.,g... :

0 3 2

0.1 0 8

1 ,

~

:

,

~

.

-

~ -

"

6

.

4

•

H

-

_

.

_

,

-

.

_

,

_

.

.

,

.

.

.

,

-

_

_

,

-

.

He

.-'" ¢ ;.....,

:

,

,

r

.

.,*

."

. ..:?<;~y .~f,..

"

$t~o.

~.~go,

'

c.

i,

0 3 2

.'*'

""

1

2 0

0 20

40

60

80

20

40

60

80 Ztarget

Fig. 11. Experimental (filled circles) and calculated (solid line INCL, dotted line LAHET, dashed line HERMES) n, p, d, triton (t), 3He, 4He production cross sections for 1.2 GeV proton induced reactions as a function of target atomic number Ztarget. LCP cross sections were calculated for the experimental energy windows as described in Section 2. Experimental neutron production cross sections have been corrected for detection efficiency, see Section 2. Note different scales of left and fight panels.

experiment for light and heavy targets. The HERMES- and LAHET-code agree with experiment only for light targets while for heavy targets the measured cross sections are overestimated by a factor of 2 to 3. For the INCL the He production cross sections agree mostly within 10 and 20% at both incident energies. At 1.8 GeV where we can confront the calculations also with the p, d, and triton production cross sections separately for a Au-target we observe in Fig. 12 excellent agreement for INCL while LAHET and HERMES overestimate all three cross sections. The 3He emission, however, is strongly underestimated by INCL and overestimated by LAHET. As already mentioned above, the emission process for 3He seems to be mainly nonevaporative at incident proton energies lower [ 16] and higher [ 12] than the present 1.8 GeV. If we assume a similar evaporative contribution of only 20% as found for 480 MeV p + A g [43] then the INCL calculation

333

M. Enke et al./Nuclear Physics A 657 (1999) 317-339

p(1.8GeV)+X -

n

40 g~

....

LAHET

--

HERMES

-

-

-

i

-

8

Z;

-,~c~

"

|

.t#~/4,~.

#,~ t

° ~ss~

t

.

#

'

" p

S

!"

.~.,,,.,~:f '*-.-. :" . . . . . . . . . . . .

6 4

20

2 0 4

-

• o°

3

-

-

0

n

t

...¢.

2

°,.o,,,

o.,,~o°

2

"

.d¢.~,-:':- °

1 0 0.6 0.4

|

-

•

0

•

-

,

-

-

-

i

-

i 3He

-

-

i

-

P

,

i

4

-

-

-

i

-

-

-

u

-

-

-

,

•

.

He

4

0

4

•-"°

:"Y"

•

"

.,,.,,,•,

," - ,'° ........ -.-....

'7, ,'77

....

~

.

H

~

~

~°

3 2

°..~#o

= .---" : t o . . =

10

-

..,.-',.....

i

•

0.2

-

•

o =

,

,,~,~,,,~.:....,...,. .... ......

,,,I °

J " .... .,r':':'...

He ~ "

34 2 1

" ""

0

20

40

60

80

20

40

60

80 Ztarget

Fig. 12. Experimental and calculated production cross sections for 1.8 GeV proton induced reactions, same as Fig. 11.

reproduces quite well the evaporative part of the measured cross section. It should be added that the uncertainty of the upper energy cutoff for protons of 26 4- 4 MeV translates into an uncertainty of the corresponding production cross section of about + 6 ( 7 ) % and -t-18(14)% for 1,2 (1.8) GeV p+Fe and U, respectively. In Figs. 11 and 12 these additional errors are included in the shown error bars. Finally in Fig. 1 and 13 the helium production cross sections are compared with previous measurements and with the results of all three models as a function of incident proton energy corroborating once more the above finding of relative good agreement with the INCL model and large differences with the LAHET and HERMES codes. Recent results of measured mass distributions in the reverse kinematic reaction of 800 MeV/nucleon A u + p are also very well described [44] by the INCL code coupled, however, to a different evaporation and fission code [45,46]. As pointed out above we associate part of the discrepancies between the data and the

334

M. Enke et al./Nuclear Physics A 657 (1999) 317-339

Ni 10

• Bieri 62 O Goebel 64 1~" Dubost 67 Hyde 71 ~IE P o s k a n z e r 71 "k Volnin 74 A Gneen 8ll

3

ola~

10

2

Ag 0

eCll

~

!

10 3

10

2

INCL LAHET HERMES

,I"S "'":';"':'"

Au

°rr ~'''''"

W

I-'1 G r e e n 88 ~ Michel95 • N E S S I 98

-.'."..........

10 3 s. t

~10 2 Pb

-/~

:

U

- :" " ~ "

10 3 10 2

10

i

-1

i i itBll

i

1

10 Ep

(GeV)

Fig. 13. Comparison of experimental helium production cross sections (symbols) and calculations (lines) ax a function of proton energy for Ni, Ag, Ta, Au, Pb and U. The filled circles are the result of the present experiment (NESSI 98). The first authors and year of publications of previous measurements are indicated [5-8,10-12,15].

HERMES and LAHET calculations with the finding that these codes overestimate the excitation energy after the prompt INC. To demonstrate the sensitivity of the equilibration time 7"equiI in the INCL code we have artificially modified this time between 14.5 and 37 fm/c resulting in mean excitation energies of 440 and 130 MeV residing in the residual nucleus after a 1.8 GeV p+Au reaction and prior to evaporation. The production cross sections for Hydrogen (Hdet) and protons (Pdet) displayed in Fig. 14 have been calculated for the same experimental energy windows (see Section 2) as employed for the calculations shown in Figs. 11 and 12. For very long equilibration times the production cross sections of nucleons become, however, insensitive to time since there is a compensation between nucleons emitted during the INC and those evaporated afterwards, which are increasing and decreasing, respectively, with the chosen

335

M. Enke et al./Nuclear Physics A 657 (1999) 317-339

37.5 33

Xequi I ( f m / c )

<

I

I

28

23.5

19

14.5

I

I

I

I

p(1.8GeV)+Au

10 2

10 ndet

Pdet He d

-1 10

t

-2

3He

10

0

INCL with standard parameter i

i

i

i

100

200

300

400

500

(MeV) Fig. 14. Dependence of the production cross sections of n, He, d, t, and 3He on the mean equilibration time
equilibration time. This compensation, however, does not apply for composite particles since their emission is not considered in the INC-stage. As shown in Figs. 11 and 12 the discrepancy between LAHET/HERMES and INCL is increasing with the charge of the target nucleus and is present only for evaporated charged particles. This observation hints to different handling of the Coulomb barriers in the employed evaporation codes. To this purpose we compared the energy spectra of emitted cascade as well as evaporated particles. The results obtained with the three codes are compared in Fig. 15 for the reaction 1.8 GeV p+Au. Though the cascade particles show only small differences the evaporation spectra for charged particles are very different close to the Coulomb barriers. Compared to INCL the maxima of the emission spectra for p, d, tritons, 3He, and 4He are at considerably smaller energies for the LAHET- and HERMES-code by about 3, 5, 4, 10, and 4 MeV, respectively. In Fig. 16 we compare the measured angle integrated helium-energy spectrum from the reaction 1.8 GeV p+Au with those obtained with the INCL- and LAHET-code. The comparison demonstrates that the INCL code reproduces the distribution near the Coulomb barrier considerably better than the LAHET-code. The small bump at the low

336

M. Enke et al./Nuclear Physics A 657 (1999) 317-339

p(1.8GeV) + Au:

cascade

neutrons

lO 3

........

1

LAHET 10

%'~'~ 102

rotons

I

"'-.'~.

,I

I-_~. ~ / ; 103

l0

102

103

evaporation 10 3

~

.: neutrons

l

f*~.

protons

r

....

deuterons

10 3

tritons

1

I0 3

3He

20

40

4He

20

40

60

Eki n

(MeV)

Fig. 15. Comparison of calculated particle energy spectra with the INCL- (solid histogram), LAHET-(dotted histogram), and HERMES-code (dashed line). The top two panels represent the nucleons emitted during the INC while the lower panels display the energy spectra of evaporated particles.

energy side of the measured helium spectrum can be shown to be due to the emission from fission fragments. The HERMES calculation is not shown since the spectra are very similar to LAHET as shown in Fig. 15. Summarizing these findings we conclude that a large fraction of the observed discrepancy between INCL and LAHET as well as HERMES displayed in Figs. 11-13 is due to different employed Coulomb barriers. On the other hand for lighter targets such as Fe we did not observe such a strong discrepancy in the Coulomb barriers between the two types of codes. The above-discussed difference of the excitation energies after the INC is also corroborated by the calculated spectral shapes of the evaporated particles displayed in Fig. 15. The inverse logarithmic slopes of the spectra, representative for the inverse temperature l/T, are smaller for the LAHET- and HERMES-code compared to the INCL-code indicating a smaller mean temperature and thus smaller mean excitation energy for the latter one.

M. Enke et al./Nuclear Physics A 657 (1999) 317-339

[

/.,-~

p(1.8GeV) + Au

,4

-1

l0

337

"..

l a ;II .

0

l0

.

20

.

.

.

.

30

.

40

50

60

EH~(MeV)

Fig. 16. Comparison of measured (solid circles) and calculated helium energy spectra with the INCL (solid histogram) and LAHET-code (dashed histogram). The experimental helium spectrum was integrated over

0 < 0 < 66° and 114 < 0 < 180°, the Au target thickness was 8.7 mg/cm2.

4. Conclusions Exploiting the detailed exclusive data measured with two 4~" detectors for neutrons and charged particles allowed for the first time a systematic comparison with theoretical models during different stages of the temporal evolution of the spallation process: inelastic collision probability, excitation energy distribution, pre-equilibrium emission, and inclusive production cross sections. The comparison with three different intra-nuclear cascade models has shown that the excitation energy distribution represents a critical test for the transition from the prompt nuclear cascade to the statistical decay of the produced compound nuclei. The calculated charged particle production cross sections are particularly sensitive to the high energy tails of the excitation energy distribution while neutron production cross sections are less sensitive. Best agreement between calculated production cross sections for H (below 26 MeV) and He has been obtained with the INCL-code, while the LAHET- and HERMES-code show large deviations in particular for heavy nuclei. We associate this discrepancy with (i) the mean excitation energy residing in the nuclei after the INC and (ii) different employed Coulomb barriers in the evaporation codes. Due to low statistics it was not possible in the present work to perform a detailed study of the various isotope ratios - frequently exploited as thermometers - as a function of dissipated excitation energies which, however, will be a challenge for future exclusive experiments.

338

M. Enke et al./Nuclear Physics A 657 (1999) 317-339

Acknowledgements We are indebted to the COSY staff for the good beam quality, M. Morjean and W.-U. Schr6der for taking part in some of the measurements, J. Cugnon for providing us with the latest version of his INC code. This work was supported by the EU TMR-project ERB-FMRX-CT98-0244.

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